PraiseforThinkingStrategically

“Machiavelliisbroughtup-to-dateinthisbookbyDixitandNalebuff.Theymakestrategictoolshumorous,human,andeffective.”

—ElizabethBailey,formerdean,GraduateSchoolofIndustrialAdministration,CarnegieMellonUniversity

“IconfessthatIhaveneverthoughtofmonetarypolicyorgovernmentasagame,butProfessorsDixitandNalebuffsucceedbrilliantlyinclarifyingquestionsweallfaceindecision-making,elevatedormundane.”

—PaulA.Volcker

“ThinkingStrategicallygivesyouthevitalcomponentsforgoodandeffectivenegotiating.”

—BobWoolf,authorofFriendlyPersuasion

“Tobeliterateinthemodernage,youneedtohaveageneralunderstandingofgametheory.DixitandNalebuffprovidetheskeletonkey.You’llbenefitfromThinkingStrategicallyandenjoythebook.”

—PaulSamuelson

Abouttheauthors

AVINASHK.DIXITisJohnJ.F.SherrerdUniversityProfessorofEconomicsatPrincetonUniversity.Hehastaughtcoursesongamesofstrategyandhasdoneresearchintostrategicbehaviorininternationaltradepolicy.HeearnedhisPh.D.at the Massachusetts Institute of Technology and has taught previously atWarwickUniversity(U.K.),Berkeley,andOxford.

BARRYJ.NALEBUFFisProfessorofEconomicsandManagementattheYaleSchool of Organization and Management. He teaches courses on strategy,politics, and decision-making.A frequent contributor on questions of strategy,hisworkhasappearedintheNewYorkTimesandtheWashingtonPost,amongother widely read publications. He has also applied the tools of thinkingstrategically for Chemical Bank, McKinsey & Co., and the Sawyer-MillerGroup.ARhodesScholar,heearnedhisdoctorateatOxfordUniversity.

ThinkingStrategically

TheCompetitiveEdgeinBusiness,Politics,andEverydayLife

AvinashK.DixitandBarryJ.Nalebuff

W.W.Norton&CompanyNewYorkLondon

Copyright©1991byAvinashK.DixitandBarryJ.NalebuffAllrightsreserved.

Illustrationcredit:Chapter2:CartoonbyCharlesSchulz.ReprintedwithpermissionofUnitedFeatureSyndicate,Inc.

LibraryofCongressCataloginginPublicationDataDixit,AvinashK.Thinkingstrategically:thecompetitiveedgeinbusiness,politics,andeverydaylife/byAvinashK.DixitandBarryJ.Nalebuff.p.cm.1.GameTheory2.Management3.CompetitionI.Nalebuff,Barry,1958–.II.Title.HD30.28.D591991658.4'012–dc2090-33760

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Contents

Preface

Introduction:WhatIsStrategicBehavior?

PARTI1TenTalesofStrategy

2AnticipatingYourRival’sResponse

3SeeingthroughYourRival’sStrategy

EpiloguetoPartI

PARTII

4ResolvingthePrisoners’Dilemma

5StrategicMoves

6CredibleCommitments

7Unpredictability

EpiloguetoPartII

PARTIII8Brinkmanship

9CooperationandCoordination

10TheStrategyofVoting

11Bargaining

12Incentives

13CaseStudies

Notes

Preface

Strategic thinking is the art of outdoing an adversary, knowing that theadversary is trying to do the same to you. All of us must practice strategicthinking atwork aswell as at home. Businessmen and corporationsmust usegood competitive strategies to survive. Politicians have to devise campaignstrategies to get elected, and legislative strategies to implement their visions.Footballcoachesplanstrategiesfor theplayers toexecuteon thefield.Parentstryingtoelicitgoodbehaviorfromchildrenmustbecomeamateurstrategists(thechildren are the pros). For forty years, superpowers’ nuclear strategies havegovernedthesurvivalofthehumanrace.

Good strategic thinking in suchnumerousdiverse contexts remains an art.But its foundations consist of some simple basic principles—an emergingscience of strategy. Our premise in writing this book is that readers from avariety of backgrounds and occupations can become better strategists if theyknowtheseprinciples.

Thescienceofstrategic thinking iscalledgametheory.This isarelativelyyoung science—less than fifty years old. It has already providedmany usefulinsightsforpracticalstrategists.But,likeallsciences,ithasbecomeshroudedinjargonandmathematics.Theseareessentialresearchtools,buttheypreventallbut the specialists from understanding the basic ideas. We have attempted atranslationofmanyimportantinsightsfortheintelligentgeneralreader.Wehavereplaced theoretical argumentswith illustrative examples and case studies.Wehaveremovedall themathematicsandmostof the jargon.Thebookshouldbeaccessibletoallreaderswhoarewillingtofollowalittlebitofarithmetic,charts,andtables.

Manybooks have already attempted to develop ideas of strategic thinkingfor particular applications. Tom Schelling’s writings on nuclear strategies,particularlyTheStrategyofConflictandArmsandInfluence,arejustlyfamous.Infact,Schellingpioneeredalotofgametheoryintheprocessofapplyingitto

nuclearconflict.MichaelPorter’sCompetitiveStrategy,drawingonthelessonsof game theory for business strategy, is equally famous. Steven Brams haswrittenseveralbooks,themostnotablebeingGameTheoryandPolitics.

In thisbookwedonotconfine theideas toanyparticularcontext. Instead,weofferaverywiderangeofillustrationsforeachbasicprinciple.Thusreadersfrommany different backgrounds will all find something familiar here. Theywill also see how the same principles bear on strategies in less familiarcircumstances;we hope this gives them a new perspective onmany events innews as well as history. We also draw on the shared experience of mostAmerican readers,with illustrations from, for example, literature,movies, andsports.Seriousscientistsmay think this trivializesstrategy,butwebelieve thatfamiliar examples from movies and sports are a very effective vehicle forconveyingtheimportantideas.

LikeTolkien’sLordof theRings, thisbookgrew in the telling. Its ancientorigins are a course on “games of strategy” thatAvinashDixit developed andtaught at Princeton’s Woodrow Wilson School of Public and InternationalAffairs. Barry Nalebuff later taught this course, and a similar one at YaleUniversity’s Political Science Department and then at Yale’s School ofOrganization and Management (SOM). We thank many students from thesecourses for their enthusiasm and ideas. Particularmention should bemade ofAnne Case, Jonathan Flemming, Heather Hazard, Dani Rodrik, and JonathanShimshoni.TakashiKannoandYuichiShimazuundertookthetaskoftranslatingourwords and ideas into Japanese; in the process, they improved the Englishversion.

Theideaofwritingabookatamorepopularlevelthanthatofacoursetextcame fromHal Varian of the University ofMichigan. He also gave usmanyuseful ideas and comments on earlier drafts.DrakeMcFeely atW.W.Nortonwasanexcellentifexactingeditor.Hemadeextraordinaryeffortstofashionouracademicwriting into a lively text. If the book still retains some traces of itsteachingorigins,thatisbecausewedidnotlistentoallofhisadvice.

Many colleagues and friends read earlier drafts with care and gave usnumerous detailed and excellent suggestions for improvement. At the risk ofomitting some, we should make particular mention of David Austen-Smith(Rochester),AlanBlinder(Princeton),SethMasters(S.Bernstein),CarlShapiro(Princeton), Louis Taylor (MITRE Corporation), Thomas Tren-dell (ATT-Paradyne), Terry Vaughn (MIT Press), and Robert Willig (Princeton). Asmanuscripteditors,StaceyMandel-baumandLauraKangWardweregeneroustoourfaults—eachtimeyoudon’tfindamistake,youshouldthankthem.

Wealsowanttogivecredittothosewhohavehelpedusfindatitleforthis

book.HalVarianstartedusoffwithThinkingStrategically.YaleSOMstudentsgave usmanymore choices.Our favoritewasDeborahHalpern’sBeyond thePlaygroundandanadvertisingcampaignwrittenbyWilliamBarnes:“ThinkingStrategically—Don’tCompeteWithoutIt.”*

AvinashDixitBarryNalebuffOctober1990

ThinkingStrategically

Introduction

WhatIsStrategicBehavior?

Howshouldpeoplebehaveinsociety?Ouranswerdoesnotdealwithethicsoretiquette.Nordoweaimtocompete

withphilosophers,preachers,orevenEmilyPost.Ourtheme,althoughlesslofty,affectsthelivesofallofusjustasmuchasdomoralityandmanners.Thisbookisaboutstrategicbehavior.Allofusarestrategists,whetherwelikeitornot.Itisbettertobeagoodstrategist thanabadone,andthisbookaimstohelpyouimproveyourskillsatdiscoveringandusingeffectivestrategies.

Work, even social life, is a constant stream of decisions. What career tofollow, how tomanage a business,whom tomarry, how to bring up children,whethertorunforpresident,arejustsomeexamplesofsuchfatefulchoices.Thecommonelementinthesesituationsisthatyoudonotactinavacuum.Instead,youaresurroundedbyactivedecision-makerswhosechoicesinteractwithyours.Thisinteractionhasanimportanteffectonyourthinkingandactions.

To illustrate the point, think of the difference between the decisions of alumberjackand thoseof ageneral.When the lumberjackdecideshow tochopwood,hedoesnotexpectthewoodtofightback;hisenvironmentisneutral.Butwhen the general tries to cut down the enemy’s army, hemust anticipate andovercomeresistancetohisplans.Likethegeneral,youmustrecognizethatyourbusiness rivals, prospective spouse, and even your child are intelligent andpurposive people.Their aimsoften conflictwith yours, but they include somepotential allies. Your own choice must allow for the conflict, and utilize thecooperation. Such interactive decisions are called strategic, and the plan ofactionappropriatetothemiscalledastrategy.Thisbookaimstohelpyouthinkstrategically,andthentranslatethesethoughtsintoaction.

Thebranchofsocialsciencethatstudiesstrategicdecision-makingiscalledgametheory.Thegames in this theoryrangefromchess tochild-rearing, fromtennis to takeovers, and from advertising to arms control. As the HungarianhumoristGeorgeMikesexpressedit,“Manycontinentalsthinklifeisagame;theEnglishthinkcricketisagame.”Wethinkbothareright.

Playing these games requires many different kinds of skills. Basic skills,suchasshootingabilityinbasketball,knowledgeofprecedentsinlaw,orablankfaceinpoker,areonekind;strategicthinkingisanother.Strategicthinkingstartswith your basic skills, and considers howbest to use them.Knowing the law,youmustdecidethestrategyfordefendingyourclient.Knowinghowwellyourfootball teamcanpassor run,andhowwell theother teamcandefendagainsteachchoice,yourdecisionasthecoachiswhethertopassortorun.Sometimes,asinthecaseofsuperpowerscontemplatinganadventurethatrisksnuclearwar,strategicthinkingalsomeansknowingwhennottoplay.

OuraimistoimproveyourstrategyI.Q.Butwehavenottriedtoprovideabookof recipes forstrategies.Wedevelop the ideasandprinciplesofstrategicthinking; to apply them to a specific situation you face and to find the rightchoicethere,youwillhavetodosomemorework.Thisisbecausethespecificsofeachsituationarelikelytodifferinsomesignificantaspects,andanygeneralprescriptions for actionwemight give could bemisleading. In each situation,youwillhavetopulltogetherprinciplesofgoodstrategywehavediscussed,andalso other principles from other considerations. Youmust combine them and,where they conflict with each other, evaluate the relative strengths of thedifferentarguments.Wedonotpromisetosolveeveryquestionyoumighthave.The science of game theory is far from being complete, and in some waysstrategicthinkingremainsanart.

Wedoprovideguidancefortranslatingtheideasintoaction.Chapter1offersseveralexamplesshowinghowstrategicissuesariseinavarietyofdecisions.Wepoint out some effective strategies, some less effective ones, and even somedownrightbadones.The subsequent chaptersproceed tobuild these examplesintoasystemoraframeworkofthought.Inthelaterchapters,wetakeupseveralbroad classes of strategic situations—brinkmanship, voting, incentives, andbargaining—whereyoucanseetheprinciplesinaction.

The examples range from the familiar, trivial, or amusing—usually drawnfrom literature, sports, or movies—to the frightening—nuclear confrontation.Theformeraremerelyaniceandpalatablevehicleforthegame-theoreticideas.As to the latter, at one pointmany readerswould have thought the subject ofnuclearwar toohorrible topermit rationalanalysis.Butas thecoldwarwindsdownandtheworldisgenerallyperceivedtobeasaferplace,wehopethatthe

game-theoretic aspects of the arms race and the Cuban missile crisis can beexamined for their strategic logic in some detachment from their emotionalcontent.

The chapters are full of examples, but these serve primarily to develop orillustrate the particular principle being discussed, and many other details ofrealitythatpertaintotheexamplearesetaside.Attheendofeachchapter,wepresent a “case study,” similar to one you might come across in a business-schoolclass.Eachcasesetsoutaparticularsetofcircumstancesandinvitesyoutoapplytheprinciplesdiscussedinthatchaptertofindtherightstrategyforthatsituation.Somecasesareopen-ended;butthatisalsoafeatureoflife.Attimesthere is no clearly correct solution, only imperfect ways to cope with theproblem. A serious effort to think each case through before reading ourdiscussionisabetterwaytounderstandtheideasthananyamountofreadingofthetextalone.Formorepractice,thefinalchapterisacollectionoftwentythreemorecases,inroughlyincreasingorderofdifficulty.

By the end of the book, we hope that you will emerge a more effectivemanager,negotiator,athlete,politician,orparent.Wewarnyouthatsomeofthestrategiesthataregoodforachievingthesegoalsmaynotearnyoutheloveofyourdefeatedrivals.Ifyouwanttobefair,tellthemaboutourbook.

PartI

TenTalesofStrategy

Webeginwith ten talesof strategy fromdifferentaspectsof lifeandofferpreliminarythoughtsonhowbesttoplay.Manyofyouwillhavefacedsimilarproblemsineverydaylife,andwillhavereachedthecorrectsolutionaftersomethoughtortrialanderror.Forothers,someoftheanswersmaybesurprising,butsurpriseisnottheprimarypurposeoftheexamples.Ouraimistoshowthatsuchsituationsarepervasive,thattheyamounttoacoherentsetofquestions,andthatmethodical thinking about them is likely to be fruitful. In later chapters, wedevelopthesesystemsofthoughtintoprescriptionsforeffectivestrategy.Thinkofthesetalesasatasteofdessertbeforethemaincourse.Theyaredesignedtowhetyourappetite,notfillyouup.

1.THEHOTHANDDoathleteseverhavea“hothand”?SometimesitseemsthatLarryBirdcannotmiss a basket, orWayne Gretzky or DiegoMaradona a shot on goal. Sportsannouncersseetheselongstreaksofconsecutivesuccessesandproclaimthattheathlete has a “hot hand.” Yet according to psychology professors ThomasGilovich,RobertVallone,andAmosTversky,thisisamisperceptionofreality.1Theypointoutthatifyouflipacoinlongenough,youwillfindsomeverylongseriesofconsecutiveheads.Thepsychologistssuspectthatsportscommentators,shorton insightful things tosay,are just findingpatterns inwhatamounts toalong series of coin tosses over a long playing season. They propose a morerigorous test. Inbasketball, they lookatall the instancesofaplayer’sbaskets,andobserve thepercentageof times thatplayer’snext shot isalsoabasket.Asimilar calculation is made for the shots immediately following misses. If abasketismorelikelytofollowabasketthantofollowamiss,thentherereallyissomethingtothetheoryofthehothand.

They conducted this test on the Philadelphia 76ers basketball team. The

resultscontradicted the“hothand”view.Whenaplayermadehis lastshot,hewasless likely tomakehisnext;whenhemissedhispreviousattempt,hewasmore likely tomakehis next.Thiswas true even forAndrewToney, a playerwith the reputation for being a streak shooter. Does this mean we should betalkingof the“stroboscopichand,” like thestrobe light thatalternatesbetweenonandoff?

Game theory suggests a different interpretation. While the statisticalevidencedeniesthepresenceofstreakshooting,itdoesnotrefutethepossibilitythata“hot”playermightwarmupthegameinsomeotherway.Thedifferencebetweenstreakshootingandahothandarisesbecauseoftheinteractionbetweentheoffensiveandthedefensivestrategies.SupposeAndrewToneydoeshaveatrulyhothand.Surelytheothersidewouldstarttocrowdhim.Thiscouldeasilylowerhisshootingpercentage.

Thatisnotall.WhenthedefensefocusesonToney,oneofhisteammatesisleftunguardedandismorelikelytoshootsuccessfully.Inotherwords,Toney’shothandleadstoanimprovementinthe76ers’teamperformance,althoughtheremaybeadeterioration inToney’s individual performance.Thuswemight testforhothandsbylookingforstreaksinteamsuccess.

Similar phenomena are observed in many other team sports. A brilliantrunning-back on a football team improves its passing game and a great pass-receiverhelpstherunninggame,astheoppositionisforcedtoallocatemoreofitsdefensiveresourcestoguardthestars.Inthe1986soccerWorldCupfinal,theArgentine starDiegoMaradona did not score a goal, but his passes through aringofWestGermandefendersledtotwoArgentinegoals.Thevalueofastarcannotbeassessedbylookingonlyathisscoringperformance;hiscontributiontohis teammates’performanceiscrucial,andassiststatisticshelpmeasurethiscontribution.Inicehockey,assistsandgoalsaregivenequalweightforrankingindividualperformance.

Aplayermay even assist himselfwhenonehot handwarmsup the other.TheBostonCelticsstar,LarryBird,prefersshootingwithhisrighthand(thoughhis left hand is still better than most). The defense knows that Bird is right-handed, so theyconcentrateondefendingagainst right-handed shots.But theydonotdo soexclusively, sinceBird’s left-handed shots are tooeffective tobeleftunguarded.

WhathappenswhenBirdspendshisoffseasonworkingtoimprovehisleft-handedshooting?Thedefenserespondsbyspendingmoretimecoveringhisleft-handedshots.Theresultisthatthisfreeshisrighthandmoreoften.Abetterleft-handedshotresults inamoreeffectiveright-handedshot. In thiscasenotonlydoesthelefthandknowwhattherighthandisdoing,it’shelpingitout.

Going one step further, in Chapter 7 we show that when the left hand isstrongeritmayevenbeusedlessoften.Manyofyouwillhaveexperiencedthisseeminglystrangephenomenonwhenplayingtennis.Ifyourbackhandismuchweakerthanyourforehand,youropponentswilllearntoplaytoyourbackhand.Eventually,asaresultofallthisbackhandpractice,yourbackhandwillimprove.Asyourtwostrokesbecomemoreequal,opponentscannolongerexploityourweakbackhand.Theywillplaymoreevenlybetweenforehandsandbackhands.Yougettouseyourbetterforehandmoreoften;thiscouldbetherealadvantageofimprovingyourbackhand.

2.TOLEADORNOTTOLEADAfter the first four races in the 1983 America’s Cup finals, Dennis Conner’sLibertyled3–1inabest-of-sevenseries.Onthemorningofthefifthrace,“casesofchampagnehadbeendeliveredtoLiberty’sdock.Andontheirspectatoryacht,the wives of the crew were wearing red-white-and-blue tops and shorts, inanticipationofhavingtheirpicturetakenaftertheirhusbandshadprolongedtheUnitedStates’winningstreakto132years.”2Itwasnottobe.

Atthestart,Libertygotofftoa37-secondleadwhenAustraliaIIjumpedthegunandhadtorecrossthestartingline.TheAustralianskipper,JohnBertrand,tried to catch up by sailingway over to the left of the course in the hopes ofcatching awind shift.DennisConner chose to keepLiberty on the right-handsideofthecourse.Bertrand’sgamblepaidoff.ThewindshiftedfivedegreesinAustraliaII’sfavorandshewontheracebyoneminuteandforty-sevenseconds.ConnerwascriticizedforhisstrategicfailuretofollowAustraliaII’spath.Tworaceslater,AustraliaIIwontheseries.

Sailboat racing offers the chance to observe an interesting reversal of a“followtheleader”strategy.Theleadingsailboatusuallycopiesthestrategyofthetrailingboat.Whenthefollowertacks,sodoestheleader.Theleaderimitatesthe followerevenwhen the follower isclearlypursuingapoor strategy.Why?Because insailboat racing (unlikeballroomdancing)closedoesn’tcount:onlywinningmatters. If you have the lead, the surestway to stay ahead is to playmonkeysee,monkeydo.*

Stock-market analysts and economic forecasters are not immune to thiscopycat strategy.The leading forecasters have an incentive to follow the packandproducepredictionssimilartoeveryoneelse’s.Thiswaypeopleareunlikelyto change their perception of these forecasters’ abilities. On the other hand,newcomerstaketheriskystrategies:theytendtopredictboomordoom.Usually

theyarewrongandareneverheardofagain,butnowandagaintheyareprovencorrectandmovetotheranksofthefamous.

Industrial and technological competitions offer further evidence. In thepersonal-computer market, IBM is less known for its innovation than for itsability to bring standardized technology to the mass market.More new ideashave come fromApple, Sun, and other start-up companies.Risky innovationsaretheirbestandperhapsonlychanceofgainingmarketshare.Thisistruenotjust of high-technology goods. Proctor and Gamble, the IBM of diapers,followedKimberlyClark’sinnovationofresealablediapertape,andrecaptureditscommandingmarketposition.

Therearetwowaystomovesecond.Youcanimitateassoonastheotherhasrevealedhisapproach(asinsailboatracing)orwait longeruntil thesuccessorfailure of the approach is known (as in computers). The longer wait is moreadvantageous inbusinessbecause,unlikesports, thecompetition isusuallynotwinner-take-all.As a result,market leaderswill not follow the upstarts unlesstheyalsobelieveinthemeritsoftheircourse.

3.GODIRECTLYTOJAILThe conductor of anorchestra in theSovietUnion (during theStalin era)wastravelingbytraintohisnextengagementandwaslookingoverthescoreofthemusichewastoconductthatnight.TwoKGBofficerssawwhathewasreadingand,thinkingthatthemusicalnotationwassomesecretcode,arrestedhimasaspy.HeprotestedthatitwasonlyTchaikovsky’sViolinConcerto,buttonoavail.Ontheseconddayofhisimprisonment,theinterrogatorwalkedinsmuglyandsaid,“Youhadbettertellusall.WehavecaughtyourfriendTchaikovsky,andheisalreadytalking.”

So begins one telling of the prisoners’ dilemma, perhaps the best-knownstrategicgame.Letusdevelop the story to its logical conclusion.Suppose theKGB has actually arrested someone whose only offense is that he is calledTchaikovsky,andareseparatelysubjectinghimtothesamekindofinterrogation.Ifthetwoinnocentswithstandthistreatment,eachwillbesentencedto3years’imprisonment.* If the conductor makes a false confession that implicates theunknown“collaborator,”whileTchaikovskyholdsout, then theconductorwillget away with 1 year (and the KGB’s gratitude), while Tchaikovsky gets theharsh sentence of 25 years for his recalcitrance. Of course, the tables will beturned if the conductor stands firmwhileTchaikovskygives in and implicateshim.Ifbothconfess,thenbothwillreceivethestandardsentenceof10years.†

Nowconsidertheconductor’sthinking.HeknowsthatTchaikovskyiseitherconfessingorholdingout.IfTchaikovskyconfesses,theconductorgets25yearsbyholdingoutand10yearsbyconfessing,soitisbetterforhimtoconfess.IfTchaikovskyholdsout,theconductorgets3yearsifheholdsout,andonly1ifheconfesses;againitisbetterforhimtoconfess.Thusconfessionisclearlytheconductor’sbestaction.

In a separate cell in Dzerzhinsky Square, Tchaikovsky is doing a similarmental calculation and reaching the same conclusion.The result, of course, isthatbothofthemconfess.Later,whentheymeetintheGulagArchipelago,theycomparestoriesandrealizethattheyhavebeenhad.Iftheybothhadstoodfirm,theybothwouldhavegottenawaywithmuchshortersentences.

Ifonlytheyhadhadanopportunitytomeetandtalkthingsoverbeforetheywere interrogated, theycouldhaveagreed thatneitherwouldgive in.But theyare quick to realize that in all probability such an agreement would not havedonemuchgood.Once theywereseparatedand the interrogationsbegan,eachperson’sprivateincentivetogetabetterdealbydouble-crossingtheotherwouldhavebeenquitepowerful.OnceagaintheywouldhavemetintheGulag,thereperhaps to settle the score of the betrayals (not of the concerto).Can the twoachieveenoughmutualcredibilitytoreachtheirjointlypreferredsolution?

Manypeople,firms,andevennationshavebeengoredonthehornsof theprisoners’dilemma.Lookatthelife-or-deathissueofnucleararmscontrol.Eachsuperpowerlikedbesttheoutcomeinwhichtheotherdisarmed,whileitkeptitsown arsenal “just in case.”Disarming yourselfwhile the other remains armedwas the worst prospect. Therefore no matter what the other side did, eachpreferredtostayarmed.However,theycouldjoininagreeingthattheoutcomein which both disarm is better than the one in which both are armed. Theproblemistheinterdependenceofdecisions:thejointlypreferredoutcomeariseswhen each chooses its individuallyworse strategy.Could the jointly preferredoutcomebe achieved given each side’s clear incentive to break the agreementandtoarmitselfsecretly?InthiscaseitneededafundamentalchangeinSovietthinkingtogettheworldstartedontheroadtonucleardisarmament.

Forone’scomfort,safety,orevenlifeitself,oneneedstoknowthewaystogetoutoftheprisoners’dilemma.InChapter4welookatsomesuchavenues,andseewhenandhowwelltheyarelikelytowork.

Thestoryoftheprisoners’dilemmaalsocarriesausefulgeneralpoint:mosteconomic,political,orsocialgamesaredifferentfromgamessuchasfootballorpoker. Football and poker are zero-sum games: one person’s gain is anotherperson’s loss.But in the prisoners’ dilemma, there are possibilities formutualadvantageaswellasconflictofinterest;bothprisonersprefertheno-confession

result to its opposite. Similarly, in employer-union bargaining, there is anopposition of interests in that one side prefers low wages and the other highones,butthereisagreementthatabreakdownofnegotiationsleadingtoastrikewouldbemoredamagingforbothsides.Infactsuchsituationsaretheruleratherthan the exception. Any useful analysis of games should be able to handle amixtureofconflictandconcurrenceofinterests.Weusuallyrefertotheplayersinagameas“opponents,”butyoushouldremember thatonoccasion,strategymakesstrangebedfellows.

4.HEREISTANDWhentheCatholicChurchdemandedthatMartinLutherrepudiatehisattackonthe authority of popes and councils, he refused to recant: “I will not recantanything, for togoagainstconscience isneither rightnorsafe.”Norwouldhecompromise:“HereIstand,Icannotdootherwise.”3Luther’sintransigencewasbasedonthedivinityofhispositions.Whendefiningwhatwasright,therewasno room for compromise.His firmnesshadprofound long-termconsequences;his attacks led to the Protestant Reformation and substantially altered themedievalCatholicChurch.*

Similarly,Charles deGaulle used the power of intransigence to become apowerful player in the arena of international relations.As his biographerDonCookexpressedit,“[DeGaulle]couldcreatepowerforhimselfwithnothingbuthisownrectitude,intelligence,personalityandsenseofdestiny.”4Butaboveall,hiswas“thepowerofintransigence.”DuringtheSecondWorldWar,astheself-proclaimedleaderinexileofadefeatedandoccupiednation,heheldhisowninnegotiationswithRooseveltandChurchill.Inthe1960s,hispresidential“Non!”swungseveraldecisionsFrance’swayintheEuropeanEconomicCommunity.

Inwhatwaydidhisintransigencegivehimpowerinbargaining?WhendeGaulletookatrulyirrevocableposition,theotherpartiesinthenegotiationwereleft with just two options—to take it or to leave it. For example, he single-handedlykeptEnglandoutoftheEuropeanEconomicCommunity,oncein1963andagain in1968; theothercountrieswereforcedeither toacceptdeGaulle’svetoortobreakuptheEEC.DeGaullejudgedhispositioncarefullytoensurethat itwouldbeaccepted.But thatoftenleft the larger(andunfair)divisionofthe spoils to France. De Gaulle’s intransigence denied the other party anopportunitytocomebackwithacounterofferthatwasacceptable.

Inpractice,thisiseasiersaidthandone,fortwokindsofreasons.Thefirstkindstemsfromthefact thatbargainingusuallyinvolvesconsiderationsbeside

thepieontoday’s table.Theperceptionthatyouhavebeenexcessivelygreedymaymakeotherslesswillingtonegotiatewithyouinthefuture.Or,nexttimethey may be more firm bargainers as they try to recapture some of theirperceivedlosses.Onapersonallevel,anunfairwinmayspoilbusinessrelations,or even personal relations. Indeed, biographer David Schoenbrun faulted deGaulle’s chauvinism: “In human relations, those who do not love are rarelyloved: those who will not be friends end up by having none. De Gaulle’srejectionoffriendshipthushurtFrance.”5Acompromiseintheshorttermmayproveabetterstrategyoverthelonghaul.

The second kind of problem lies in achieving the necessary degree ofintransigence.LutheranddeGaulleachievedthisthroughtheirpersonalities.Butthisentailsacost.Aninflexiblepersonalityisnotsomethingyoucanjustturnonandoff.Althoughbeing inflexiblecansometimesweardownanopponentandforcehim tomakeconcessions, it canequallywell allowsmall losses togrowintomajordisasters.

FerdinanddeLessepswasamildlycompetent engineerwith extraordinaryvision and determination. He is famous for building the Suez Canal in whatseemedalmost impossibleconditions.Hedidnotrecognize the impossibleandthereby accomplished it. Later, he tried using the same technique to build thePanamaCanal.Itendedindisaster.*WhereasthesandsoftheNileyieldedtohiswill,tropicalmalariadidnot.TheproblemfordeLessepswasthathisinflexiblepersonalitycouldnotadmitdefeatevenwhenthebattlewaslost.

How can one achieve selective inflexibility? Although there is no idealsolution, there are variousmeans bywhich commitment can be achieved andsustained;thisisthetopicforChapter6.

5.BELLINGTHECATIn thechildren’sstoryaboutbellingthecat, themicedecidethat lifewouldbemuchsaferifthecatwerestuckwithabellarounditsneck.Theproblemis,whowillriskhislifetobellthecat?

Thisisaproblemforbothmiceandmen.Howcanrelativelysmallarmiesofoccupying powers or tyrants control very large populations for long periods?Whyisaplaneloadofpeoplepowerlessbeforeasinglehijackerwithagun?Inboth cases, a simultaneousmove by themasses stands a very good chance ofsuccess. But the communication and coordination required for such action isdifficult,andtheoppressors,knowingthepowerofthemasses,takespecialstepsto keep it difficult.When the people must act individually and hope that the

momentumwill build up, the question arises, “Who is going to be the first?”Sucha leaderwillpayaveryhighcost—possiblyhis life.His rewardmaybeposthumous glory or gratitude. There are people who are moved byconsiderationsofdutyorhonor,butmostfindthecostsexceedthebenefits.

KhrushchevfirstdenouncedStalin’spurgesattheSovietCommunistParty’s20thCongress.Afterhisdramaticspeech,someoneintheaudienceshoutedout,askingwhatKhrushchevhadbeendoingatthetime.Khrushchevrespondedbyasking the questioner to please stand up and identify himself. The audienceremainedsilent.Khrushchevreplied:“ThatiswhatIdid,too.”

Inasense,wehaveseen theseexamplesbefore.Theyare justaprisoners’dilemmawithmorethantwopeople;onemightcallthisthehostages’dilemma.Here we want to use this dilemma to make a different point—namely, thefrequent superiority of punishment over reward. The dictator might keep thepopulacepeacefulbyprovidingitmaterialandevenspiritualcomforts,butthiscanbeaverycostlyproposition.OppressionandterrorrelyingontheHostages’Dilemmacanbeamuchcheaperalternative.

Therearemanyexamplesofthisprinciple.Inalargetaxifleet,carsareoftenassigned to drivers by a dispatcher. The fleet has some good cars and someclunkers.Thedispatchercanusehisassignmentpower toextractasmallbribefromeachofthedrivers.Anydriverwhorefusestopayissuretogetaclunker,whilethosewhocooperatearegiventheluckofthedrawfromtheremainder.*

Thedispatchergetsrich,andthedriversasagroupendupwiththesamesetofcabs that they would have if no one used bribery. If the drivers acted incollusion,theyprobablycouldstopthispractice.Theproblemliesingettingthemovementorganized.Thepoint is not somuch that thedispatcher can rewardthosewhobribehim,butthathecanpunishseverelythosewhodon’t.

A similar story can be told about evicting tenants from rent-controlledapartments. If someonebuys suchabuilding inNewYork,hehas the right toevictonetenantsoastobeabletoliveinhisownbuilding.Butthistranslatesintoapowertoclearthewhole.Anewlandlordcantrythefollowingargumentwith the tenant in Apartment 1A: “I have the right to live in my building.Therefore, Iplan toevictyouandmove intoyourapartment.However, ifyoucooperateand leavevoluntarily, thenIwill rewardyouwith$5,000.”This isatokenamountinrelationtothevalueoftherent-controlledapartment(althoughit still buys a few subway tokens in New York). Faced with the choice ofevictionwith$5,000orevictionwithout$5,000,thetenanttakesthemoneyandruns.Thelandlordthenoffersthesamedealtothetenantin1B,andsoon.

TheUnitedAutoWorkershaveasimilaradvantagewhentheynegotiatewith

the auto manufacturers sequentially. A strike against Ford alone puts it atparticulardisadvantagewhenGeneralMotorsandChryslercontinuetooperate;thereforeFordismorelikelytosettlequicklyontermsfavorabletotheUnion.SuchastrikeisalsolesscostlytotheUnionasonlyonethirdoftheirmembersareout.AfterwinningagainstFord,theUniontakesonGMandthenChrysler,using each previous success as precedent and fuel for their fire. In contrast,Japanese union incentives work the other way, since they are organized bycompany and have more profit sharing. If the Toyota unions strike, theirmembers’incomessufferalongwithToyota’sprofitsandtheygainnothingfromtheprecedenteffect.

Weare not saying that anyor all of these are goodoutcomesor desirablepolicies.Insomecasestheremaybecompellingargumentsfortryingtopreventthe kinds of results we have described. But to do so effectively, one has tounderstand the mechanism by which the problem arose in the first place—namely, an “accordion effect,”where each fold pushes or pulls the next. Thisphenomenonarisesagainandagain;butitcanbecountered,andwewillshowyouhowinChapter9.

6.THETHINENDOFTHEWEDGEMost countries use tariffs, quotas, and other measures to restrict importcompetitionandprotectdomesticindustries.Suchpoliciesraiseprices,andhurtall domestic users of the protected product. Economists have estimated thatwhenimportquotasareusedtoprotectindustriessuchassteel,textiles,orsugar,the rest of us pay higher prices amounting to roughly $100,000 for each jobsaved.6Howisitthatthegainstoafewalwaysgetpriorityoverthemuchlargeraggregatelossestothemany?

Thetrickistobringupthecasesoneatatime.First,10,000jobsintheshoeindustryareatrisk.Tosavethemwouldcostabilliondollarstotherestofus,orjustover$4each.Whowouldn’tagree topay$4 tosave10,000 jobsevenfortotalstrangers,especiallywhennastyforeignerscanbeblamedfortheirplight?Thenalongcomesthegarmentindustry,thesteelindustry,theautoindustry,andsoon.Beforeweknowit,wehaveagreedtopayover$50billion,whichismorethan $200 each, or nearly $1,000 per family. If we had foreseen the wholeprocess,wemighthave thought thecost toohigh,and insisted thatworkers ineachoftheseindustriesbeartherisksofforeigntradejustastheywouldhavetobear any other economic risk. Decisions made case by case can lead toundesirableresultsoverall. Infact,asequenceofmajorityvotescanleadtoan

outcomethateveryoneregardsasworsethanthestatusquo.The income tax reform of 1985–86 almost collapsed because the Senate

initially took a case-by-case approach. In the first round of the FinanceCommittee’s markup sessions, the amended Treasury proposal became soweighteddownwithspecialinterestprovisionsthatitsanktoamercifuldeath.Thesenators realized that theywere“powerless” topreventanyoneorganizedlobby from getting special treatment. Yet the combination of these lobbyistscoulddestroythebill,andthiswouldbeworsethanproducingnolegislationatall. So Senator Packwood, the committee chairman, made his own lobby: hepersuadedamajorityofthecommitteememberstovoteagainstanyamendmentto the tax bill, even those amendments that especially favored their ownconstituents.Thereformwasenacted.Butspecialprovisionsarealreadystagingacomeback,oneortwoatatime.

Along similar lines, the line-item veto would allow the president to vetolegislationselectively.Ifabillauthorizedmoneyforschool lunchesandanewspace shuttle, the president would have the option of neither, either, or both,insteadofthecurrentneitherorboth.Althoughafirstreactionisthatthisallowsthe president greater control over legislation, the opposite might end uphappening as Congress would be more selective about which bills it passes.*

Whiletheline-itemvetoisgenerallythoughttobeunconstitutional,thisquestionmayhavetoberesolvedbytheSupremeCourt.

Theseproblemsarisebecausemyopicdecision-makersfailtolookaheadandseethewholepicture.Inthecaseoftaxreform,theSenaterecovereditsvisionjustintime;theissueofprotectionismstillsuffers.Chapter2developsasystemforbetterlong-rangestrategicvision.

7.LOOKBEFOREYOULEAPItisalltoocommonforpeopletogetthemselvesintosituationsthataredifficulttogetoutof.Onceyouhaveajobinaparticularcity,itisexpensivetoresettle.Onceyoubuyacomputer and learn itsoperating system, itbecomescostly tolearnanotheroneandrewriteallyourprograms.Travelerswhojointhefrequent-flyer programof one airline thereby raise their cost of using another.And, ofcourse,marriageisexpensivetoescape.

The problem is that once youmake such a commitment, your bargainingposition is weakened. Companies may take advantage of their workers’anticipatedmovingcostsandgivethemfewerorsmallersalaryraises.Computercompanies can charge higher prices for new, compatible peripheral equipment

knowing that their customers cannot easily switch to a new, incompatibletechnology.Airlines,havingestablisheda largebaseof frequent flyers,willbelessinclinedtoengageinfarewars.Acouple’sagreementthattheywillsplitthehousework50:50maybecomesubjecttorenegotiationonceachildisborn.

Strategistswho foresee suchconsequenceswilluse theirbargainingpowerwhileitexists,namely,beforetheygetintothecommitment.Typically,thiswilltaketheformofapaymentupfront.Competitionamongthewould-beexploiterscanleadtothesameresult.Companieswillhavetooffermoreattractiveinitialsalaries,computermanufacturerswillhavetochargesufficientlylowpricesfortheir central processing units (CPUs), and airline frequent-flyer programswillhave to offer larger signing-on mileage bonuses. As for married couples,exploitationmaybeagamethattwocanplay.

Thesameforesightiswhatpreventsmanycuriousbutrationalpeoplefromtrying addictive drugs such as heroin. A Tom Lehrer song describes the drugdealer’sploy:

“Hegivesthekidsfreesamples

BecauseheknowsfullwellThattoday’syounginnocentfacesWillbetomorrow’sclientele.”

Smartkidsknowittoo,andturndownthefreesamples.

8.MIXYOURPLAYSLetusreturnforamomenttotheworldofsports.Infootball,beforeeachsnapof theball theoffensechoosesbetweenpassingand runningwhile thedefenseorganizesitselftocounteroneoftheseplays.Intennis,theservermightgototheforehandorthebackhandofthereceiver,whilethereceiver, in turn,cantrytoreturncrosscourtordowntheline.Intheseexamples,eachsidehasanideaofitsownstrongpointsandofitsopponent’sweaknesses.Itwillhaveapreferenceforthe choice that exploits these weaknesses, but not exclusively. It is wellunderstood, by players and sports fans alike, that one shouldmix one’s plays,randomlythrowingintheunexpectedmove.Thepointisthatifyoudothesamethingallthetime,theoppositionwillbeabletocounteryoumoreeffectivelybyconcentratingitsresourcesonthebestresponsetoyouronestrategy.

Mixing your plays does notmean rotating your strategies in a predictablemanner.Youropponentcanobserveandexploitanysystematicpatternalmostaseasily as he can the unchanging repetition of a single strategy. It isunpredictabilitythatisimportantwhenmixing.

Imagine what would happen if there were some known formula thatdeterminedwhowouldbeauditedbytheIRS.Beforeyousubmittedataxreturn,you could apply the formula to see if you would be audited. If an audit waspredicted,butyoucouldseeawayto“amend”yourreturnuntiltheformulanolonger predicted an audit, you probably would do so. If an audit wasunavoidable, you would choose to tell the truth. The result of the IRS beingcompletelypredictableisthatitwouldauditexactlythewrongpeople.Allthoseauditedwouldhaveanticipatedtheirfateandchosentoacthonestly,whilethosesparedanauditwouldhaveonlytheirconsciencestowatchoverthem.WhentheIRSauditformulaissomewhatfuzzy,everyonestandssomeriskofanaudit;thisgivesanaddedincentiveforhonesty.

Therearesimilarphenomenainthebusinessworld.Thinkofcompetitioninthemarketforrazors.ImaginethatGilletterunsacouponpromotiononaregularschedule—say,thefirstSundayofeveryothermonth.BiccanpreemptGilletteby running a competing coupon promotion the week before. Of course, Bic’s

moveisthenpredictableandGillettecanpreempttheweekbefore.Thisprocessleads to cutthroat competition and bothmake less profit. But if each uses anunpredictableormixedstrategy,togethertheymightreducethefiercenessofthecompetition.

The importance of randomized strategieswas one of the early insights ofgametheory.Theideaissimpleandintuitivebutneedsrefinementifitistobeusefulinpractice.Itisnotenoughforatennisplayertoknowthatheshouldmixhisshotsbetweentheopponent’sforehandandbackhand.Heneedssomeideaofwhetherheshouldgototheforehand30percentor64percentof thetimeandhowtheanswerdependsontherelativestrengthsofthetwosides.InChapter7wedevelopmethodstoanswersuchquestions.

9.NEVERGIVEASUCKERANEVENBETInGuysandDolls,gamblerSkyMastersonrelatesthisvaluableadvicefromhisfather:

“Son,oneof thesedays inyour travelsaguy isgoing tocometoyouandshowyouanicebrand-newdeckofcardsonwhich theseal isnotyetbroken,andthisguyisgoingtooffertobetyouthathecanmakethejackofspadesjumpoutofthedeckandsquirtciderinyourear.Butson,donotbetthisman,forassureasyoustandthereyouaregoingtowindupwithciderinyourear.”

ThecontextofthestoryisthatNathanDetroithadofferedSkyMastersonabetabout whether Mindy’s sold more strudel or cheesecake. Nathan had justdiscovered the answer (strudel) and was willing to bet if Sky would bet oncheesecake.

Thisexamplemaysoundsomewhatextreme.Ofcoursenoonewouldtakesucha suckerbet.But lookat themarket for futurescontractson theChicagoBoardofExchange.Ifanotherspeculatorofferstosellyouafuturescontract,hewillmakemoneyonlyifyoulosemoney.Thisdealisazero-sumgame,justlikesports competitions, in which one team’s victory is the other’s loss. Hence ifsomeoneiswillingtosellafuturescontract,youshouldnotbewillingtobuyit.Andviceversa.

The strategic insight is that other people’s actions tell us something aboutwhat theyknow,andweshouldusesuch information toguideourownaction.Of course, we should use this in conjunction with our own information

concerningthematteranduseallstrategicdevicestoelicitmorefromothers.In theGuysandDolls example, there is a simpledeviceof this kind.Sky

shouldaskNathanatwhatoddshewouldbewillingtotakethecheesecakesideofthebet.Iftheansweris“notatanyodds,”thenSkycaninferthattheanswermustbestrudel.IfNathanoffersthesameoddsforbothstrudelandcheesecake,heishidinghisinformationatthecostofgivingSkytheopportunitytotakeanadvantageousgamble.

In stock markets, foreign exchange markets, and other financial markets,people are free to take either side of the bet in just thisway. Indeed, in someorganized exchanges, including theLondon stockmarket,when you ask for aquote on a stock the market-maker is required to state both the buying andsellingpricesbeforeheknowswhichsideofthetransactionyouwant.Withoutsuchasafeguard,market-makerscouldstandtoprofitfromprivateinformation,andtheoutsideinvestors’fearofbeingsuckeredmightcausetheentiremarkettofold.Thebuyandsellpricesarenotquitethesame;thedifferenceiscalledthebid-askspread.In liquidmarkets thespreadisquitesmall, indicatingthat littleinformation is contained in any buy or sell order. On the other hand, NathanDetroitiswillingtobetonstrudelatanypriceandoncheesecakeatnoprice;hisbid-askspreadisinfinity.Bewareofsuchmarket-makers.

We should add that Sky had not really learned his father’s teaching verywell.AminutelaterhebetNathanthatNathandidnotknowthecolorofhisownbowtie.Skycannotwin:ifNathanknowsthecolor,hetakesthebetandwins;ifhedoesnot,hedeclinesthebetanddoesnotlose.

10.GAMETHEORYCANBEDANGEROUSTOYOURHEALTHLateonenight,afteraconferenceinJerusalem,twoAmericaneconomistsfounda licensed taxicab and gave the driver directions to their hotel. Immediatelyrecognizing themasAmerican tourists, thedriverrefused to turnonhismeter;instead,heproclaimedhis loveforAmericansandpromisedthema lowerfarethan themeter.Naturally, theywere somewhat skeptical of this promise.Whyshouldthisstrangeroffertochargelessthanthemeterwhentheywerewillingtopay themetered fare? Howwould they even knowwhether or not they werebeingovercharged?*

Ontheotherhand, theyhadnotpromised topay thedriveranythingmorethan what would be on the meter. If they were to start bargaining and thenegotiationsbrokedown,theywouldhavetofindanothertaxi.Theirtheorywasthat once they arrived at the hotel, their bargaining position would be much

stronger.Andtaxiswerehardtofind.Theyarrived.Thedriverdemanded2,500Israelishekels($2.75).Whoknew

what farewas fair?Because people generally bargain in Israel, they protestedand counteroffered2,200 shekels.Thedriverwasoutraged.He claimed that itwould be impossible to get from there to here for that amount. Beforenegotiationscouldcontinue,he lockedall thedoorsautomaticallyand retracedtherouteatbreakneckspeed, ignoring traffic lightsandpedestrians.Were theybeing kidnapped to Beirut? No. He returned to the original position andungraciously kicked the two economists out of his cab, yelling, “See how faryour2,200shekelswillgetyounow.”

Theyfoundanothercab.Thisdriverturnedonhismeter,and2,200shekelslatertheywerehome.

Certainlytheextratimewasnotworththe300shekelstotheeconomists.Onthe other hand, the story was well worth it. It illustrates the dangers ofbargainingwiththosewhohavenotyetreadourbook.Moregenerally,prideandirrationalitycannotbeignored.Sometimes,itmaybebettertobetakenforaridewhenitcostsonlytwodimes.†

There is a second lesson to the story. Think of how much stronger theirbargainingpositionwouldhavebeeniftheyhadbeguntodiscussthepriceaftergettingoutofthetaxi.(Ofcourse,forhiringataxi,thislogicshouldbereversed.Ifyoutellthedriverwhereyouwanttogobeforegettingin,youmayfindyourtaxichasingaftersomeothercustomer.Getinfirst,thensaywhereyouwanttogo.)11.THESHAPEOFTHINGSTOCOMETheexampleshavegivenusglimpsesofprinciplesthatguidestrategicdecisions.Wecansummarizetheseprincipleswithafew“morals”fromourtales.

The story of the hot hand told us that in strategy, no less than in physics,“For every action we take, there is a reaction.”We do not live and act in avacuum. Therefore, we cannot assume that when we change our behavioreverythingelsewillremainunchanged.

DeGaulle’ssuccess innegotiationssuggests that“thestuckwheelgets thegrease.”*Butbeingstubbornisnotalwayseasy,especiallywhenonehastobemorestubbornthananobstinateadversary.

The tale from the Gulag and the story of belling the cat demonstrate thedifficulty of obtaining outcomes that require coordination and individualsacrifice.Theexampleoftradepolicyhighlightsthedangerofsolvingproblemspiecebypiece.Intechnologyracesnolessthaninsailboatraces,thosewhotrailtend to employ more innovative strategies; the leaders tend to imitate the

followers.Tennis and tax audits point out the strategic advantage of being

unpredictable.Suchbehaviormayalsohave theaddedadvantage that itmakeslifejustalittlemoreinteresting.

Wecouldgoonofferingmoreexamplesanddrawingmoralsfromthem,butthis is not the best way to think methodically about strategic games. That isbetterdonebyapproaching the subject fromadifferent angle.Wepickup theprinciples—forexample,commitment,cooperation,andmixing—oneatatime.Ineach instance,weselectexamples thatbearcentrallyon that issue,until theprincipleisclear.Thenyouwillhaveachancetoapplytheprincipleinthecasestudiesthatendeachchapter.

12.CASESTUDY#1:REDIWIN,BLACKYOULOSEWhilewemightnevergetthechancetoskipperinanAmerica’sCuprace,oneof us found himself with a very similar problem.At the end of his academicstudies, Barry celebrated at one of Cambridge University’s May Balls (theEnglishequivalentofacollegeprom).Partof thefestivities includedacasino.Everyonewasgiven$20worthof chips, and thepersonwhohadamassed thegreatest fortune by evening’s endwouldwin a free ticket to next year’s ball.When it came time for the last spin of the roulette wheel, by a happycoincidence, Barry led with $700 worth of chips, and the next closest was ayoung Englishwoman, with $300. The rest of the group had been effectivelycleanedout. Just before the last betswere to beplaced, thewomanoffered tosplit next year’s ball ticket, butBarry refused.With his substantial lead, therewaslittlereasontosettleforhalf.

Tobetterunderstand thenextstrategicmove,we takeabriefdetour to therulesofroulette.Thebettinginrouletteisbasedonwhereaballwilllandwhenthe spinning wheel stops. There are typically numbers 0 through 36 on thewheel.Whentheballlandsonzero,thehousewins.Thesafestbetinrouletteistobetonevenorodd(denotedbyBlackorRed).Thesebetspayevenmoney—aone-dollarbet returns twodollars—while thechanceofwinning isonly18/37.Evenbettingherentirestakewouldnotleadtovictoryattheseodds;therefore,thewomanwasforcedtotakeoneofthemoreriskygambles.Shebetherentirestakeonthechancethattheballwouldlandonamultipleofthree.Thisbetpaystwotoone(soher$300betwouldreturn$900ifshewon)buthasonlya12/37chanceofwinning.Sheplacedherbetonthetable.Atthatpointitcouldnotbewithdrawn.WhatshouldBarryhavedone?

CaseDiscussionBarryshouldhavecopiedthewoman’sbetandplaced$300ontheeventthattheballlandedonamultipleofthree.Thisguaranteesthathestaysaheadofherby$400andwins the ticket:either theyboth lose thebetandBarrywins$400to$0, or they both win the bet and Barry ends up ahead $1,300 to $900. Thewoman had no other choice. If she did not bet, shewould have lost anyway;whatevershebeton,Barrycouldfollowherandstayahead.*

HeronlyhopewasthatBarrywouldbetfirst.IfBarryhadbeenfirsttoplace$200onBlack,what should shehavedone?She shouldhavebether$300onRed.BettingherstakeonBlackwoulddohernogood,sinceshewouldwinonlywhenBarrywins(andshewouldplacesecondwith$600comparedwithBarry’s$900).WinningwhenBarrylostwouldbeheronlychancetotakethelead,andthatdictatesabetonRed.

ThestrategicmoralistheoppositefromthatofourtaleofMartinLutherandCharlesdeGaulle.Inthistaleofroulette, thepersonwhomovedfirstwasatadisadvantage.Thewoman,bybetting first, allowedBarry tochoosea strategythat would guarantee victory. If Barry had bet first, the woman could havechosenaresponsethatofferedanevenchanceofwinning.Thegeneralpointisthatingamesitisnotalwaysanadvantagetoseizetheinitiativeandmovefirst.Thisrevealsyourhand,andtheotherplayerscanusethistotheiradvantageandyourcost.Secondmoversmaybeinthestrongerstrategicposition.

AnticipatingYourRival’sResponse

1.IT’SYOURMOVE,CHARLIEBROWNInarecurringthemeinthecartoonstrip“Peanuts,”Lucyholdsafootballontheground and invites Charlie Brown to run up and kick it. At the lastmoment,Lucypullstheballaway.CharlieBrown,kickingair,landsonhisback,andthisgivesLucygreatperversepleasure.

AnyonecouldhavetoldCharliethatheshouldrefusetoplayLucy’sgame.EvenifLucyhadnotplayedthisparticulartrickonhimlastyear(andtheyearbeforeandtheyearbeforethat),heknowshercharacterfromothercontextsandshouldbeabletopredictheraction.

At the time when Charlie is deciding whether or not to accept Lucy’sinvitation,heractionliesinthefuture.However,justbecauseitliesinthefuturedoesnotmeanCharlieshouldregarditasuncertain.Heshouldknowthatofthetwo possible outcomes—letting him kick and seeing him fall—Lucy’spreference is for the latter. Therefore he should forecast that when the timecomes,sheisgoingtopulltheballaway.ThelogicalpossibilitythatLucywilllethimkicktheballisrealisticallyirrelevant.Relianceonitwouldbe,toborrowDr.Johnson’scharacterizationofremarriage,atriumphofhopeoverexperience.Charlieshoulddisregardit,andforecastthatacceptancewillinevitablylandhimonhisback.HeshoulddeclineLucy’sinvitation.

2.TWOKINDSOFSTRATEGICINTERACTIONThe essence of a game of strategy is the interdependence of the players’decisions.Theseinteractionsariseintwoways.Thefirstissequential,asintheCharlieBrownstory.Theplayersmakealternatingmoves.Eachplayer,whenitis his turn, must look ahead to how his current actions will affect the futureactionsofothers,andhisownfutureactionsinturn.

Thesecondkindofinteractionissimultaneous,asintheprisoners’dilemmataleofChapter1.Theplayersactat thesametime, inignoranceof theothers’currentactions.However,eachmustbeawarethatthereareotheractiveplayers,whointurnaresimilarlyaware,andsoon.Thereforeeachmustfigurativelyputhimselfintheshoesofall,andtrytocalculatetheoutcome.Hisownbestactionisanintegralpartofthisoverallcalculation.

When you find yourself playing a strategic game, you must determinewhether the interaction is simultaneous or sequential. Some games such asfootballhaveelementsofboth.Thenyoumustfityourstrategytothecontext.Inthischapter,wedevelopinapreliminarywayideasandrulesthatwillhelpyouplaysequentialgames;simultaneous-movegamesare thesubjectofChapter3.

Webeginwithreallysimple,sometimescontrived,examples,suchastheCharlieBrown story. This is deliberate; the stories are not of great importance inthemselves,andtherightstrategiesareusuallyeasytoseebysimpleintuition,sothe underlying ideas stand out that much more clearly. The examples getincreasingly realistic and more complex in the case studies and in the laterchapters.

3.THEFIRSTRULEOFSTRATEGYThe general principle for sequential-move games is that each player shouldfigure out the other players’ future responses, and use them in calculating hisownbestcurrentmove.Soimportantisthisideathatitisworthcodifyingintoabasic ruleof strategicbehavior:Rule1:Lookaheadandreasonback.Anticipate where your initial decisions will ultimately lead, and use thisinformationtocalculateyourbestchoice.

In theCharlieBrownstory, thiswaseasytodoforanyone(exceptCharlieBrown).He had just two alternatives, and one of them led toLucy’s decisionbetween two possible actions. Most strategic situations involve a longersequence of decisions with several alternatives at each, and mere verbalreasoning cannot keep track of them. Successful application of the rule oflookingaheadandreasoningbackneedsabettervisualaid.A“treediagram”ofthechoicesinthegameisonesuchaid.Letusshowyouhowtousethesetrees.

4.DECISIONTREESANDGAMETREESAsequenceofdecisions,withtheneedtolookaheadandreasonback,canariseeven for a solitary decision-maker not involved in a game of strategy withothers.ForRobertFrostintheyellowwood:

Tworoadsdivergedinawood,andIItooktheroadlesstravelledby,Andthathasmadeallthedifference.1

Wecanshowthisschematically.

Thisneednotbetheendofthechoice.Eachroadmightinturnhavefurther

branches.Theroadmapbecomescorrespondinglycomplex.Hereisanexamplefromourownexperience.

Travelers from Princeton to New York have several choices. The firstdecision point involves selecting themode of travel: bus, train, or car. Thosewho drive then have to choose among the Verrazano Narrows Bridge, theHollandTunnel, theLincolnTunnel, and theGeorgeWashingtonBridge.Railcommuters must decide whether to switch to the PATH train at Newark orcontinue to Penn Station. Once in New York, rail and bus commuters mustchoose amonggoing by foot, subway (local or express), bus, or taxi to get totheirfinaldestination.Thebestchoicedependsonmanyfactors,includingprice,speed, expected congestion, the final destination in New York, and one’saversiontobreathingtheairontheJerseyTurnpike.

Thisroadmap,whichdescribesone’soptionsateachjunction,lookslikea

treewith its successively emerging branches—hence the term “decision tree.”The right way to use such a map or tree is not to take the route whose firstbranch looks best and then “cross the Verrazano Bridge when you get to it.”Instead, you anticipate the future decisions anduse them tomakeyour earlierchoices. For example, if you are commuting to the World Trade Center, thePATH trainwould be superior to driving because it offers a direct connectionfromNewark.

Wecanusejustsuchatreetodepictthechoicesinagameofstrategy,butonenewelemententersthepicture.Agamehastwoormoreplayers.Atvarious

branchingpointsalongthetree, itmaybetheturnofdifferentplayerstomakethedecision.Apersonmakingachoiceatanearlierpointmustlookahead,notjusttohisownfuturechoices,buttothoseofothers.Hemustforecastwhattheotherswilldo,byputtinghimselffigurativelyintheirshoes,andthinkingastheywould think.To remindyouof thedifference,wewill call a tree showing thedecisionsequenceinagameofstrategyagametree,reservingthetermdecisiontreeforsituationsinwhichjustonepersonisinvolved.

ThestoryofCharlieBrownisabsurdlysimple,butyoucanbecomefamiliarwithgametreesbycastingthatstoryinsuchapicture.StartthegamewhenLucyhasissuedherinvitation,andCharliefacesthedecisionofwhethertoaccept.IfCharlierefuses, that is theendof thegame.Ifheaccepts,Lucyhas thechoicebetween letting Charlie kick and pulling the ball away.We can show this byaddinganotherforkalongthisroad.

Aswesaidearlier,Charlieshouldforecast thatLucywillchoosetheupper

branch.Thereforehe should figurativelyprune the lowerbranchof her choicefrom the tree.Now if he chooses his own upper branch, it leads straight to anastyfall.Thereforehisbetterchoiceistofollowhisownlowerbranch.

Tofixtheidea,considerabusinessexamplethathasthesamegametree.Toavoid impugning any actual firms, and with apologies to Graham Greene,suppose themarket forvacuumcleaners inpre-CastroCuba isdominatedbyabrandcalledFastcleaners,andanewfirm,Newcleaners,isdecidingwhethertoenter this market. If Newcleaners enters, Fastcleaners has two choices:accommodateNewcleanersbyacceptinga lowermarket share,or fightapricewar.* Suppose that if Fastcleaners accommodates the entry, Newcleaners willmakeaprofitof$100,000,butthatifFastcleanersstartsapricewar,thiscausesNewcleanerstolose$200,000.IfNewcleanersstaysawayfromthismarket,itsprofitis,ofcourse,zero.Weshowthegametreeandtheprofitamountsforeach

outcome:

WhatshouldNewcleanersdo?Thisisthekindofproblemdecisionanalystssolve,andbusinessschoolsteach.Theydrawaverysimilarpicture,butcallitadecision tree. The reason is that they often think of the outcomes“accommodation” and “price war” as alternatives that could arise by chance.Therefore,theyassignprobabilitiestothetwo.Forexample,ifaccommodationandwararethoughtequallylikely,eachgetsaprobabilityof1/2.ThentheycancalculatetheaverageprofitthatNewcleanerscanexpectfromentry,multiplyingeachprofitorlossfigurebythecorrespondingprobabilityandadding.Theyget(½)$100,000 - (½)$200,000 = -$50,000. Since this is a loss, with theseprobabilities the business analysts’ verdict would be that Newcleaners shouldkeepawayfromCuba.

Wheredo theprobability estimates come from?Game theoryprovides theanswer: the probabilities come from Newcleaners’ beliefs about Fastcleaners’profits in each of these cases. In order to estimatewhat Fastcleaners will do,NewcleanersshouldfirstestimateFastcleaners’profitsinthedifferentscenarios.Thentheplayerscanlookforwardandreasonbackwardtopredictwhattheothersidewilldo.Tocontinuethisexample,supposethatasamonopolistFastcleanersis able to make profits of $300,000. Sharing the market with Newcleanersreducesitsprofitsto$100,000.FightingapricewarcostsFastcleaners$100,000.Thenwecanfilloutthetree,addinginthesepayoffs.

Weusetheinformationinthetreetopredictallfuturemoves.Sinceactions

canbedeterminedfromthestructureofthegame,thetreeisproperlyseenasagametree,notadecisiontree.Forexample,topredictFastcleaners’responsetoentry, we recognize that it makes $100,000 under accommodation and loses$100,000 in the event of a price war; Newcleaners should forecast thatFastcleaners will choose accommodation. Looking ahead in this way, andreasoningback,Newcleanersshouldmentallycutofftheprice-warbranch.Theyshouldenter,reckoningtomake$100,000.

Thedecisionmightbedifferentinothercircumstances.Forexample,ifthereis a possibility that Newcleaners would go on to enter other islands whereFastcleaners has established markets, Fastcleaners may have an incentive toacquireareputationfortoughness,andmaybewillingtosufferlossesinCubatothisend.Newcleanersshould reckononasure lossof$200,000,and thereforeshouldkeepout.

Newcleanerscanseehowanygivenpayoffstranslateintoactions.ButtheymaybeunsureofFastcleaners’rewardsattheendofthetree.Itistheuncertaintyabout profits that translates into an uncertainty about actions. For example,Newcleanersmightbelievethatthereisa33.3percentchancethatFastcleanerswilllose$100,000inapricewar,a33.3percentchancethattheywillbreakeven($0profits)inapricewar,andafinal33.3percentchancethatFastcleanerswillmake$120,000inspiteofapricewar.Inthatevent,“lookforwardandreasonbackward” says that in two of the three cases Fastcleaners will want toaccommodate—$100,000isbetterthanlosing$100,000orbreakingevenbutnotasgoodasmaking$120,000.Thechanceofapricewaristhen33.3percent.Theonly way to find out what will actually happen is to enter. Given the odds,Newcleaners expects to make $100,000 in two out of three cases and lose$200,000theotherthirdofthetime:itsexpectedprofitsareexactlyzeroandsothereisnopointinentering.

InthisexampleitwasstraightforwardtotranslateNewcleaners’uncertaintyabout Fastcleaners’ payoffs into a probability estimate of Fastcleaners’responses. But onemust be careful aboutwhere to place the uncertainty. Therightplaceisattheendofthetree.Lookatwhatgoeswrongifwelookifwetrytojumpaheadinourestimation.Onaverage,Fastcleanerscanmakemoneyinapricewar [(1/3)$120,000+ (1/3)$0–(1/3)$100,000= $6,667].But that doesn’tmean theywill alwayswant to fight. The probability is not 100 percent. Nordoesthepresenceofuncertaintymeanthatoneshouldguessaprobabilityof50percent.Thecorrectway toanalyze theproblem is forNewcleaners to start attheendofthegameandfigureoutwhatFastcleanersshoulddoineachcase.

5.MORECOMPLEXTREESInreality,thegamesyouplayaremorecomplexthantheonesweusedaboveforillustrative purposes. But the same principles apply as these saplings developinto trees. Perhaps the best example is chess. While the rules of chess arerelatively simple, they produce a game that lends itself to strategic reasoning.White opens with a move, Black responds with one, and so on in turns.Therefore the “purest” kind of strategic reasoning in chess involves lookingaheadtotheconsequencesofyourmoveinjustthewaywesaw.Anexampleofsuchreasoningmightbe:“IfImovethatpawnnow,myopponentwillbringuphisknightandthreatenmyrook.Ishouldprotectthesquaretowhichtheknightwantstomovewithmybishop,beforeImovethepawn.”

Sincechessisagamewithalternatingmoves,wecanrepresentthegamebyatree.Whitecanopenwithanyoneof20moves.2Inthepicturebelow,weshowWhite’sfirstopportunitytomovebythefirstdecisionpoint(ornode)ofthetree,labeledW1.The20moveshecanmakebecome20branchesthatemanatefromthisnode.Eachbranchislabeledbythemoveitrepresents:pawntoking-4(P-K4,ore4 inalgebraicnotation),pawntoqueen-4,andsoon.Wewantonly toconvey the general idea, and so to avoid cluttering the picture, we have notshown or labeled all branches. Each branch will lead to a node representingBlack’sfirstmove,labeledB1.Blackcanalsomakeanyof20moves,sotherewillbe20branchesemanating fromeachsuchB1node.Afteronemovefrombothsides,wearealreadylookingatatotalof400possibilities.Fromhereon,thenumberofbrancheswilldependonthemovepreviouslymade.Forexample,ifWhite’sfirstmoveisP-K4,hehasnumerouspossiblesecondmovesbecausehisqueenandhisking-sidebishopcannowventureout.Youseehowsimplythetreeisconstructedinprinciple,andhowcomplicateditquicklygetsinpractice.

Wecanselectabranchateachdecisionpoint(node)of thegametree,andfollowapathdownit.Thiswillrepresentoneparticularwayinwhichthegamecouldevolve.Chessexpertshaveexaminedmanysuchpathsintheearlyphases(openings)andspeculatedwheretheymightlead.Forexample,thepathwehavelabeled,wherethefirstmovesareP-K4forWhiteandP-QB4forBlack,istheominous-soundingSicilianDefense.*

Inmanygames,eachsuchpathendsafterafinitenumberofsteps.Inasportoraboardgame, thismightbewhenoneof theplayerswinsor thegame isadraw.Moregenerally,theendresultofthegamecanbeintheformofmonetaryor nonmonetary rewards or penalties for the players. For example, a game ofbusinessrivalrymightendwithasizableprofittoonefirmandbankruptcyoftheother.The“game”ofthenucleararmsracemightendinasuccessfultreatyorinmutualdestruction.

Ifthegameisgoingtoendinafinitenumberofmovesnomatterwhichpathis followed, then we can in principle solve the game completely. Solving thegamemeansfindingoutwhowinsandhow.Thisisdonebyreasoningbackwardalong the tree.Oncewehaveworked through theentire tree,wewilldiscoverwhetherornotwecanwin,andifsowhatstrategytouse.Foranygamewithafinitenumberofsequentialmovesthereexistssomebeststrategy.Ofcourse,justbecauseabeststrategyexistsdoesn’tmean thatwecaneasilyfind it.Chess istheprimeexample.

Chessexpertshavebeenverysuccessfulatcharacterizingoptimalstrategiesneartheendofthegame.Oncethechessboardhasbeenreducedtothreeorfourpieces,expertplayersareabletoseeaheadtotheendofthegameanddetermine(byworkingbackward)whetheronesidehasaguaranteedwinningstrategyorwhether theother side can force a draw.They can thenuse thedesirability ofdifferent endgamepositions toevaluate the strategies in themiddlegame.Theproblemisthatnobodyhaseverbeenabletoworkthroughthetreeallthewaybacktotheopeningmove.

Some simple games can be solved completely. For example, in three-by-threetic-tac-toe,adrawcanalwaysbeobtained.*Thatiswhyitisagameplayedbychildrenratherthangrownups.Eventhegameofcheckersisindanger.Itisbelieved,althoughnotyetconfirmed,thatthesecondplayercanalwaysachieveatie. Inorder tomaintain interest,checkers tournamentsstart theplayersatanintermediateposition,whereawinningortyingstrategyisnotknown.Thedayitbecomespossibletosolvechesscompletelyinthisway,therulesmayhavetobechanged.

Inthemeantime,whathavechessplayersdone?Theydowhatweallshould

do when putting sequential strategies into practice: combine forward-lookinganalysiswithvaluejudgments.Theyask,“Willthispathafterfourorfivemovesleadtoagenerallygoodpositionorabadone?”Theyassignavaluetoeachofthepossibleoutcomes,pretendingthatitistheendofthegame.Thentheylookforwardand reasonbackward towarda strategy that leads to thehighestvaluefivemoves hence. Backward reasoning is the easy part. The hard problem isassigningavalue toan intermediateposition.Thevalueofeachpiecemustbequantifiedandtrade-offsbetweenmaterialandpositionaladvantageconsidered.

PaulHoffman, in his bookArchimedes’ Revenge, describes the success ofHans Berliner’s computer chess program. A postal chess world champion,Berlinerhasbuiltacomputerdedicatedtochessthatcanexaminethirtymillionoptions in the three minutes allocated to each move and has a good rule forvaluing intermediatepositions.Fewer than threehundredhumanchessplayerscanbeat this computer program. In backgammon,Berliner has a program thathasbeatentheworldchampion.

The combination of explicit logic from backward reasoning and rules ofthumbforvaluingintermediatepositionsbasedonexperienceisausefulwaytotacklecomplicatedgamesotherthanchess.

6.BARGAININGIn business and in international politics, the parties often bargain or negotiateoverthedivisionofatotalgain—thepie.WewillexaminethisinmoredetailinChapter11.Hereweuseitasanillustrationofhowbackwardreasoningenablesustopredicttheoutcomeofgameswithalternatingmoves.

Mostpeoplefollowsocialconventionandpredictthatsplittingthedifferencewillbetheoutcomeofanegotiation.Thishastheadvantageofbeing“fair.”Wecandemonstratethatformanycommontypesofnegotiations,a50:50splitisthebackward-reasoningsolution,too.

There are two general features of bargaining that we must first take intoaccount.Wehavetoknowwhogetstomakeanoffertowhom,i.e.,therulesofthegame.Andthenwehavetoknowwhathappensifthepartiesfailtoreachanagreement.

Differentnegotiationstakeplaceunderdifferingrules.Inmostretailstoresthe sellerspost apriceand thebuyers’onlychoice is toaccept thepriceor totaketheirbusinesselsewhere.*Thisisasimple“take-it-or-leave-it”rule.Inthecase ofwage bargaining, a labor unionmakes a claim and then the companydecideswhethertoaccede.Ifitdoesnot,itmaymakeacounteroffer,orwaitfor

theuniontoadjustitsdemand.Insomecasesthesequencingisimposedbylawor custom; in others it may have a strategic role of its own. Below, we willexamineabargainingprobleminwhichthetwopartiestaketurnsmakingoffers.

Anessentialfeatureofnegotiationsisthattimeismoney.Whennegotiationsbecomeprotracted, thepiebegins toshrink.Still, thepartiesmayfail toagree,eachhopingthatthecostsofnegotiatingwillbeoutweighedbyamorefavorablesettlement. Charles Dickens’s Bleak House illustrates the extreme case; thedispute over the Jarndyce estate was so prolonged that the entire estate wasswallowed up by lawyers’ fees. In the same vein, if failure to reach a wageagreement leads to a labor strike, the firm losesprofits andworkers lose theirwages.Ifnationsenterintoaprolongedroundofnegotiationstoliberalizetrade,they forgo the benefits of the enlarged tradewhile they are arguing about thedivisionof thegains.Thecommon thread is thatallparties to thenegotiationsprefertoreachanygivenagreementsoonerratherthanlater.

In reality the shrinkage occurs in complex ways and at different rates indifferent situations.Butwe can adequately illustrate the idea in a very simpleway:supposethatthepieshrinkstozeroinequalamountsateachstepofofferorcounteroffer.Thinkof it asan ice-creampie,whichmeltsaschildrenargueoveritsdivision.

Firstsupposethere isonlyonestepinvolved.There isanice-creampieonthetable;onechild(Ali)proposestotheother(Baba)howtodivideit.IfBabaagrees, the division occurs as agreed; if not, the pie melts and neither getsanything.

NowAli is in a powerful position: she is able to pose to Baba the starkchoice between something and nothing. Even if she proposes to keep 100percentofthepieforherselfandjustletBabalicktheknifeattheend,theonlythingBabacandoistotakethatlickorgetnothing.

OfcourseBabamayturndowntheofferfromsheerangerattheunfairnessof it. Or he may want to build or maintain a reputation for being a toughbargainer, tohelphim in futurebargains,whetherwithAliorwithotherswhocome toknowofBaba’s actionshere. InpracticeAliwill have to think aboutsuchmatters,andofferBabajustenough(perhapsasmallslice?)toinducehimtoaccept.Tokeeptheexpositionsimple,wewillleavethesecomplicationsasideandsuppose thatAlicangetawaywithclaiming100percent. In fact,wewillforgetabout the lick forBabaandsay thatAlicanget thewholepiebybeingabletomakea“take-it-or-leave-it”offer.*

Oncethere isasecondroundofnegotiations, thingscomeoutmuchbetterfor Baba. Again there is an ice-cream pie on the table but now it takes two

roundsofbargainingbeforetheentirepiemelts.IfBabaturnsdownAli’soffer,he can come back with a counteroffer, but at that point only half of the pieremains. If Ali turns down Baba’s counteroffer, that half alsomelts and bothsidesareleftwithnothing.

NowAlimustlookaheadtotheconsequencesofherinitialoffer.SheknowsthatBaba can turn downher offer and comeback in the powerful position ofmakingatake-it-or-leave-itofferinsplittingtheremaininghalfofthepie.Thiswill giveBaba essentially all of that half.Therefore he is not going to acceptanythinglessfromAli’sfirst-roundoffer.IfAliweretoallowthissecondstagetocome topass, shewouldgetnothingat all.Knowing this, shewillopenbyofferingBabahalf, that is, justenough to induceacceptancewhilegettinghalfforherself.Theyagreeimmediatelytosplitthepie50:50.

Theprincipleisnowclear,andwecaneasilyaddonemorestep.Againletthe negotiations speed up or the pie melt more slowly. With each offer andcounteroffer, thepiegoes fromwhole to two-thirds toone-third tozero. IfAlimakesthelastoffer,whenthepiehasshrunktoathird,shegetsitall.Knowingthis, Baba will offer her a third when it is his turn and two-thirds of the pieremains.ThusthebestBabacanexpect isone-third, i.e.,halfof theremainingtwo-thirds.Knowingthis,Aliwillopenthebargainingbyofferinghimtheone-third(justenoughtoinduceacceptance)andgettwo-thirdsforherself.

What happened to the 50:50 split? It reappears every time the number ofstepsiseven.Moreimportantly,evenwhenthenumberofstepsisodd,thetwosidesgetcloserandcloserto50:50asthenumberofstepsincreases.

Withfoursteps,Babawillmakethelastofferandgetthequarterthatisonthetableatthatpoint.ThereforeAlihastoofferhimaquarteratthelast-but-oneturnwhenthereishalf.Thenattheturnbeforethat,BabacangetAlitoacceptonly a quarter out of three-quarters. Therefore, looking ahead to all this, AliopensthebargainingbyofferingBabahalfandgettinghalfherself.

With five steps, Ali will open by offering Baba two-fifths of the pie andkeeping three-fifths toherself.With six thedivision isonceagain50:50.Withseven,Aligets4/7andBaba3/7.Moregenerally,whenthenumberofstepsiseveneachsidegetshalf.Whenthenumberofsteps,n,isodd,Aligets(n+1)/(2n)andBaba gets (n–1)/(2n).By the time the number of steps reaches 101,Ali’sadvantagefromgoingfirstisthatshegets51/101whileBabagets50/101.

Inthetypicalnegotiationprocess,thepieshrinksslowlysothattherewillbetime for many offers and counteroffers before the pie disappears. What thissuggestsisthatitusuallydoesn’tmatterwhogetstomakethefirstoffergivenalongbargaininghorizon.The split-the-difference solution seemspretty hard toescapeunlessthenegotiationshavebeendeadlockedforalongtimeandthereis

hardly anything left to win. It is true that the person who goes last can geteverything that remains. But by the end of the negotiations process there ishardly anything left to win. Getting all of nothing is winning the battle andlosingthewar.

It is important to observe that even though we have considered manypossible offers and counteroffers, the predicted outcome is forAli’s very firstoffer tobeaccepted.The laterstagesof theprocessarenevercalled intoplay.However, the fact that those steps would be invoked if agreement were notreached on the first round is crucial inAli’s calculation of the just-acceptablefirstoffer.

This observation in turn suggests another dimension of strategy inbargaining.Theprincipleof lookingaheadand reasoningbackmaydeterminethe outcome of the process even before it starts. The time for strategicmaneuveringmaybeearlier,whentherulesofnegotiationarebeingdecided.

The same observation also leads to a puzzle. If the process of bargainingwereexactlylikethatdepictedhere,therewouldbenolaborstrikes.Ofcoursetheprospectofastrikewouldaffecttheagreementreached,butthecompany—or theunion, as the casemaybe—at itsvery first opportunitywouldmakeanofferthatwasminimallyacceptabletotheotherparty.Therealityofstrikesor,more generally, breakdowns of negotiations must arise from more subtle orcomplexfeaturesofrealitythatwereexcludedfromthesimplestoryabove.WewilltouchuponsomeoftheseissuesinChapter11.

7.WARANDPEACEAsecondillustrationofbackwardreasoningcomesfromconsideringhowpeacecanbemaintainedthroughaseriesofbilateralantagonisms.

Letustakeanexamplethatisonlypartlyhypothetical.Sudanisarelativelyweak country in danger of being attacked by its neighbor Libya. If these twocountriesweresomehowinisolationtherewouldbelittletopreventLibyafromattackinganddefeatingSudan.

Whiletwoantagonisticneighborsmaynotmaintainpeace,thepresenceofathirdmayprovidethenecessarydeterrence.InthecaseofLibyaandSudan,thisprinciplemightbereferredtoas“Myenemy’senemyismyfriend.”ThedangerforLibyaifitentersabattlewithSudanisthatthiswilldrawtroopsawayfromitseasternborderwithEgypt.AlthoughEgyptwouldnotwant toattackafull-strength Libya, if Libya were weakened through war with Sudan, this couldprovide awelcome opportunity for the Egyptians to dispose of a troublesome

neighbor.Libyacan(oratleastshould)reasonbackwardandpredictanattackbyEgyptweretheytogoafterSudan.ItappearsthatSudanissafe.Butstoppingthechainofthoughtafterthreecountriesleadstoafalsesenseofsecurity.

If threeenemiescreatestability,whataboutfour?EnterIsrael.WereEgypttogoafterLibyathiscouldopenituptoanattackbyIsrael.BeforeSadatandBeginnormalized relations, thiswasa real threat forEgypt. In thosepre-1978years,LibyahadlessreasontofearanattackbyEgyptbecauseoftheinsecurityofEgyptwithrespecttoIsrael.Asaresult,SudancouldnotcountonEgypttocontrol Libya’s expansionary interests.* With improved Israeli-EgyptianrelationsthebackwardchainstopsatEgypt,andSudanissafe,forthemoment.

Thisexampleofdeterrenceiscertainlystylized.Takenatfacevalueitwouldsuggestthatwhetherornotacountrywillbeattackeddependsonwhetherthereareanevenoranoddnumberoflinksinthechainofpotentialpredators.Amorerealistic scenariowould take account of the complicated relationshipsbetweenthe countries and provide more detail about their willingness to attack eachother.Yet,thereisanimportantobservationthatcarriesforward:theoutcomeofgamesdependscriticallyonhowmanypeopleareplaying.Moremaybebetterand thenworse,even in thesamegame.Theobservation that twoantagonisticcountriesmake unstable neighbors but three antagonists restores stability doesnotimplythatfourisevenbetter;fourinthiscaseisthesameastwo.*

To develop this idea of deterrence further, we invite you to look at the“Three-WayDuel”inthecollectionofcasestudiesattheendofthebook.Threeantagonists, each with a different level of ability, have to decide whom theyshouldattack.Youmayfindtheanswersurprising.

8.GAMESTHEBRITISHPLAYThroughout this chapter we have talked of games in which actions or movesfollowed one another in an orderly sequence. In fact, few games in life havewell-specified rules that the players must obey. The players make their ownrules.Howcantheylookaheadandreasonback,andindeedhowcantheyknowifthereisanysequencetothegameatall?

Toillustratethispoint,weusethesettingoftheBritishelectioncampaignof1987. The incumbent Conservative Party underMargaret Thatcher was beingchallenged by the Labor Party under the leadership of Neil Kinnock. In thecampaign, each had to choose between the high road—a campaign based onissues—andthelowroad—abattleofpersonalities.AsufficientlylargecoreofvotersweresatisfiedwithMrs.Thatcher’sperformancetoensurethat,ifthetwo

fought similarly oriented campaigns, the effects of the two would cancel andMrs.Thatcherwouldwin.

Mr. Kinnock’s only hope was that he would make a sufficiently betterimpression incampaignsofcontrastingstyles; letussupposehischanceswerethe samewhenMrs.Thatcher took thehigh road andhe took the low road astheywould bewith the opposite choices. Suppose each of them preferred thehighroad,butthisconsiderationwassubordinatetovictory.

Whichwouldbe“theroadlesstraveled”?Theanswerhangscriticallyontheorder in which the two parties make their decisions. Let us look at somealternativepossibilities.

SupposeMrs.Thatcherchoosesthecampaignstylefirst—because,say,itistraditional for the incumbent party to publicly launch itsmanifesto before theopposition.Shecanwritedownthefollowinggametree.

Bylookingforwardandreasoningbackward,Mrs.Thatchercanpredictthat

ifshetakesthehighroad,thenMr.Kinnockwilltakethelow,andviceversa.*

Sincethetwoalternativesgiveherthesamechanceofvictory,shepreferstakingthehighroad.

Thefact thatMrs.Thatchermovesfirst is toherdisadvantage,as itallowsMr.Kinnocktotaketheoppositetack.Butthefactthatshemovesfirstdoesnotinitselfcausethisproblem.Letusringaslightchangeonthescenario.SupposeMrs.ThatcherhasmetwithherConservativePartyadvisorsandtheadvertisingcampaignmanagers,anddecidedherstrategy.Butthechoiceisnotmadepublic.Mr.Kinnock is holding a similarmeeting.What should he decide?Should heassumethat,inmakingthefirstmove,Mrs.Thatcherwillreasoninthewaywejust described? That would mean that she had chosen the high road, andthereforethatMr.Kinnockshouldchoosethelow.ButifMrs.ThatcherthoughtthatMr.Kinnockwouldthinkinthisway,sheshouldchoosealow-roadstrategyofherown.Mr.Kinnockdoesnotknowherchoice for sure,andhewouldbefoolishtodisregardthepossibilityofsucha“second-level”thinking.Shouldhe

thenchoosethehighroad?Notnecessarily,forMrs.Thatchercanthinkatathirdlevel,andsoon.Thegeneralpointisthatfortheprincipleoflookingaheadandreasoningbacktoapply,itisessentialthatearliermovesbeobservabletothosewhochooselater.

EvenifMrs.Thatchermovesfirstandherchoiceisobservable,whatifshecouldchangeherstrategyduringthecourseofthecampaign?Supposeit isthefinalimpressiononthevotersthatmattersmost,andwhatMrs.Thatchersaidinherfirstannouncementis irrelevant.Mr.Kinnockcannottakeitasgivenwhendecidinghisstrategy.Inturn,Mrs.ThatchercannotrelyonafixedresponsebyMr. Kinnock when she thinks about her first move. So we have anotherconditionforthevalidityoftheprincipleoflookingaheadandreasoningback:strategiesmustbeirreversible.

Whathappensifoneofthesetwoconditionsisnotmet?Evenifthechoicesof the two parties are made at different times, so far as strategic thinking isconcerned they might as well be simultaneous. This shift from sequential tosimultaneousmaybeadvantageoustoeitherorbothoftheparties.Infact,inthe1987Britishcampaigntherewasat leastonereversalofstrategybyeachside.Chapter3providestherulesforactioninsimultaneousgames.

Athleticcontestsprovideanotherviewofthedifferencebetweensequential-and simultaneous-move games. A hundred-yard dash is simultaneous becausethere is no time for sequencing. In a butterfly-stroke swim race, theremaybetimetorespond,butcompetitorsfinditdifficulttoseetheiropponent’sposition;henceitshouldbeviewedassimultaneous.Amarathonhastheingredientsforasequential structure: the runners can observe each other’s positions (up to apoint),andstrategiesareirreversibleinthatthereisnogoingbackandrerunningtheearlierpartoftherace.

Toendthischapter,wereturntoCharlieBrown’sproblemofwhetherornottokick the football.Thisquestionbecamea real issue for football coachTomOsborneinthefinalminutesofhischampionshipgame.Wethinkhetoogotitwrong.Backwardreasoningwillrevealthemistake.

9.CASESTUDY#2:THETALEOFTOMOSBORNEANDTHE

1984ORANGEBOWLIn the1984OrangeBowl theundefeatedNebraskaCornhuskersand theonce-beatenMiamiHurricanesfacedoff.BecauseNebraskacameintotheBowlwiththe better record, it needed only a tie in order to finish the season with thenumber-oneranking.

But Nebraska fell behind by 31–17 in the fourth quarter. Then theCornhuskers began a comeback. They scored a touchdown tomake the score31–23. Nebraska coach Tom Osborne had an important strategic decision tomake.

Incollegefootball,ateamthatscoresatouchdownthenrunsoneplayfromahashmark2½yardsfromthegoalline.Theteamhasachoicebetweentryingtorun or pass the ball into the end zone,which scores two additional points, ortrying the less risky strategy of kicking the ball through the goalposts, whichscoresoneextrapoint.

CoachOsbornechosetoplayitsafe,andNebraskasuccessfullykickedfortheoneextrapoint.Nowthescorewas31–24.TheCornhuskerscontinuedtheircomeback. In thewaningminutes of thegame they scored a final touchdown,bringingthescoreto31–30.Apointconversionwouldhavetiedthegameandlandedthemthetitle.Butthatwouldhavebeenanunsatisfyingvictory.Towinthechampionshipwithstyle,Osbornerecognizedthathehadtogoforthewin.

The Cornhuskers went for the win with a two-point conversion attempt.IrvingFryergottheball,butfailedtoscore.MiamiandNebraskaendedtheyearwithequalrecords.SinceMiamibeatNebraska,itwasMiamithatwasawardedthetopplaceinthestandings.

PutyourselfinthecleatsofCoachOsborne.Couldyouhavedonebetter?

CaseDiscussionManyMondaymorningquarterbacksfaultOsborneforgoingforthewinratherthanthetie.Butthatisnottheboneofourcontention.GiventhatOsbornewaswilling to take the additional risk for the win, he did it the wrongway. TomOsbornewouldhavedonebettertofirsttrythetwo-pointattempt,andthenifitsucceededgofortheone-point,whileifitfailedattemptasecondtwo-pointer.

Letuslookatthismorecarefully.Whendownby14points,heknewthatheneededtwotouchdownsplusthreeextrapoints.Hechosetogofortheoneandthen the two. If both attemptsweremade, theorder inwhich theyweremadebecomes irrelevant. If the one-point conversionwasmissed but the two-pointwassuccessful,heretootheorderisirrelevantandthegameendsuptied,withNebraska getting the championship. The only difference occurs if Nebraskamisses the two-point attempt.UnderOsborne’splan, that results in the lossofthe game and the championship. If, instead, they had tried the two-pointconversionfirst,thenifitfailedtheywouldnotnecessarilyhavelostthegame.Theywouldhavebeenbehind31–23.When theyscored theirnext touchdown

thiswouldhavebrought themto31–29.Asuccessful two-pointattemptwouldtiethegameandwinthenumber-oneranking!*

Wehaveheard thecounterargument that ifOsbornefirstwentfor the two-pointer andmissed, his teamwouldhavebeenplaying for the tie.Thiswouldhave provided less inspiration and perhaps they might not have scored thesecond touchdown. Moreover, by waiting until the end and going for thedesperationwin-lose two-pointerhis teamwould rise to theoccasionknowingeverything was on the line. This argument is wrong for several reasons.Remember that ifNebraskawaitsuntil the second touchdownand thenmissesthetwo-pointattempt,theylose.Iftheymissthetwo-pointattemptontheirfirsttry,thereisstillachanceforatie.Eventhoughthechancemaybediminished,somethingisbetterthannothing.Themomentumargumentisalsoflawed.WhileNebraska’s offense may rise to the occasion in a single play for thechampionship, we expect the Hurricanes’ defense to rise as well. The play isequallyimportantforbothsides.Totheextentthatthereisamomentumeffect,ifOsborne makes the two-point attempt on the first touchdown, this shouldincreasethechanceofscoringanothertouchdown.Italsoallowshimtotiethegamewithtwofieldgoals.

Oneof thegeneralmorals from this story is that ifyouhave to takesomerisks,itisoftenbettertodothisasquicklyaspossible.Thisisobvioustothosewho play tennis: everyone knows to take risks on the first serve and hit thesecond servemore cautiously. Thatway, if you fail on your first attempt, thegamewon’tbeover.Youmaystillhavetimetotakesomeotheroptionsthatcanbringyoubacktoorevenaheadofwhereyouwere.

SeeingthroughYourRival’sStrategy

Everyweek,Time andNewsweek compete to have themore eye-catchingcoverstory.Adramaticorinterestingcoverwillattracttheattentionofpotentialbuyersatnewsstands.ThuseveryweektheeditorsofTimemeetbehindcloseddoorstoselecttheircoverstory.TheydosowiththeknowledgethattheeditorsofNewsweek aremeeting elsewhere, also behind closed doors, to select theircover.TheeditorsofNewsweekinturnknowthattheeditorsofTimearemakingasimilardecision,thoseofTimeknowthatthoseofNewsweekknow,andsoon.

The twonewsmagazinesareengaged ina strategicgame,but thisgame isquite different in nature from thosewe have already examined. The games inChapter2hadasequenceofalternatingmoves.CharlieBrowndecidedwhetherornottokickknowingthatLucy’sdecisionwhetherornottopulltheballawaylayin thefuture.Inchess,White’smovesalternatedwithBlack’s.Bycontrast,theactionsofTimeandNewsweekaresimultaneous.Eachmustactinignoranceoftheother’schoice.Bythetimeeachdiscoverswhattheotherhasdone,it istoo late to change anything. Of course the loser for one week might try torespondthenextweek,butinthisfast-movingworldawholenewsetofstoriesandawholenewgamewillprobablyhaveemergedbythen.

Thenatureof thestrategic thinkingandactionneededfor the twotypesofgamesdiffersmarkedly.Forthesequential-movegamesdiscussedinChapter2,eachplayerhadtolookaheadandanticipatehisrival’sfutureresponsesinorderto reasonbackanddecidehisowncurrent action.Therewasa linear chainofreasoning: “If I do this, the other player will do that—in which case, I willrespondthus,”andsoon.

Forthesimultaneous-movegamesweconsiderinthischapter,neitherplayerhasthebenefitofobservingtheother’scompletedmovebeforemakinghisown.Here, the interactionreasoningworksnotbyseeing theother’sstrategybutbyseeing through it. For this, it is not enough simply to put yourself in youropponent’s shoes.What would you find if you did?You’d only discover thatyouropponentisdoingthesamething,thatis,thinkingwhatitmustbeliketobe

wearingyourshoes.Eachpersonhastoplacehimselfsimultaneouslyinbothhisownandtheotherguy’sshoesandthenfigureoutthebestmovesforbothsides.Insteadofalinearchainofreasoning,thereisacirclethatgoes“IfIthinkthathethinksthatIthink…”Thetrickistosquarethiscircle.

Notsurprisingly,SherlockHolmesandhisarch-rivalProfessorMoriarty,theNapoleon of crime, were masters of this type of reasoning. As Holmes toldWatsoninTheFinalProblem:

“AllthatIhavetosayhasalreadycrossedyourmind,”saidhe.“Thenpossiblymyanswerhascrossedyours,”Ireplied.

LikeDr.Watson,youmaybewonderinghowHolmesdoesit.Afterhearingourexplanation,wehopeyouwillagreethatitisratherelementary.

Howdoyousee throughall the interlockingbut invisible strategies?First,youmustnotregardtheunknownactionsoftheotherplayersasbeinguncertaininanimpersonalwayliketheweather.Beforegoingtowork,theeditorofTimemightlistentotheweatherforecastthatpredictsa40percentchanceofrain,andhemight use this information to decidewhether or not to take anumbrella towork.TheprobabilitythatNewsweekisusingaparticularcoverthemeisquiteadifferentmatter.

The difference is that the editor of Time has a very pertinent piece ofinformation aboutNewsweek: unlike nature, the other magazine’s editors arestrategicgame-players just asTime’s owneditors are.*Even thoughoneeditorcannot actuallyobserve theothermagazine’sdecision,he can think thematterthroughfromitsperspective,andtrytofigureoutwhatitmustbedoing.

InChapter2,wecouldofferasingle,unifyingprinciple todevise thebeststrategiesforgameswithsequentialmoves.ThiswasourRule1:lookaheadandreason back. It won’t be so simple in this chapter. But the thinking aboutthinking required for simultaneousmoves can be summarized in three simplerules for action. These rules in turn rest on two simple ideas—dominantstrategies and equilibrium. As in Chapter 2, we develop such ideas and rulesthroughsimpleexamples.

1.DOMINANTSTRATEGIES

Inbaseball,whentherearetwooutsandthecountstandsatthreeballsandtwostrikes, any forced base runners should run on the pitch. This can be seen bythinking through all possible cases. Inmost cases it does notmatterwhat therunnersdo.Ifthepitchisnottouchedbythebatter,eitherthepitchisthefourthballandtherunnersadvance,oritisthethirdstrikeandtheinningends.Ifthepitchisfouledoff,therunnerssimplyreturntotheiroriginalbases.Ifitisfoul-tipped and caught, the inning ends. But in one case running has a clearadvantage:ifthebatterhitsthepitchintofairterritory,therunnershaveabetterchanceofadvancingorscoring.

Wesaythatrunningonthepitchisthedominantstrategyinthissituation;itisbetter insomeeventualities,andnotworseinany.Ingeneral,aplayerhasadominantstrategywhenhehasonecourseofactionthatoutperformsallothersnomatterwhattheotherplayersdo.Ifaplayerhassuchastrategy,hisdecisionbecomes very simple; he can choose the dominant strategy without worryingabouttherival’smoves.Thereforeitisthefirstthingoneshouldseek.

There are interesting examples of dominant strategies everywhere,detectable once you know what to look for. Consider the position of IndianaJonesin theclimaxof themovieIndianaJonesand theLastCrusade. IndianaJones,hisfather,andtheNazishaveallconvergedatthesiteoftheHolyGrail.ThetwoJonesesrefusetohelptheNazisreachthelaststep.SotheNazisshootIndiana’sdad.OnlythehealingpoweroftheHolyGrailcansavetheseniorDr.Jonesfromhismortalwound.Suitablymotivated,IndianaleadsthewaytotheHolyGrail.But there isone final challenge.Hemust choosebetween literallyscoresofchalices,onlyoneofwhich is thecupofChrist.While the rightcupbringseternallife,thewrongchoiceisfatal.TheNazileaderimpatientlychoosesabeautifulgoldenchalice,drinkstheholywater,anddiesthesuddendeaththatfollows from a wrong choice. Indiana picks a wooden chalice, the cup of acarpenter.Exclaiming“There’sonlyonewaytofindout”hedipsthechaliceintothefontanddrinkswhathehopesisthecupoflife.Upondiscoveringthathehaschosenwisely,Indianabringsthecuptohisfatherandthewaterhealsthemortalwound.

Although this scene adds excitement, it is somewhat embarrassing (to us)that such a distinguished professor as Dr. Indiana Jones would overlook hisdominantstrategy.Heshouldhavegiventhewatertohisfatherwithouttestingitfirst.IfIndianahaschosentherightcup,hisfatherisstillsaved.IfIndianahaschosenthewrongcup,thenhisfatherdiesbutIndianaisspared.Testingthecupbeforegivingit tohisfatherdoesn’thelp,sinceifIndianahasmadethewrongchoice, there is no secondchance—Indianadies from thewater andhis father

diesfromthewound.*

Finding dominant strategies is considerably easier than the search for theHolyGrail.ConsiderAlfred,LordTennyson’sfamiliarline:“Tisbettertohaveloved and lost than never to have loved at all.”1 In other words, love is adominantstrategy.

2.OVER-COVERWARFAREIn the competitionbetweenTime andNewsweek, think of a hypotheticalweekthat produces twomajor news stories: there is an impasse between theHouseandtheSenateonthebudget,andanewdrugisclaimedtobeeffectiveagainstAIDS.Theeditors’choiceofcoverstoryisprimarilybasedonwhatwillattractthemost newsstand buyers (subscribers buy themagazine nomatterwhat thecover). Of these newsstand buyers, suppose 30 percent are interested in thebudget story and 70 percent in the AIDS story. These people will buy themagazine only if the story that interests them appears on the cover; if bothmagazineshavethesamestory,thegroupinterestedinitsplitsequallybetweenthem.

NowTime’seditorcanreasonasfollows.“IfNewsweekusestheAIDSstory,thenifIusethebudgetstoryIgetthewholeofthe‘budgetmarket’(30percentofallreaders),whereasifIusetheAIDSstorywesharethe‘AIDSmarket’(soIget35percentofallreaders);so,theAIDSstoryyieldsmemoresalesthanthebudgetstory.IfNewsweekusesthebudgetstory,thenIget15percentusingthebudgetstory,and70percentwiththeAIDSstory;onceagainIdobetterusingthelatter.ThereforeIhaveadominantstrategy,namelyusingtheAIDSstory.Itworks better for me than the other strategy regardless of which of the twocoursesmyrivalchooses.”

Wecanseethelogicofthisreasoningmuchmorequicklyandclearlyfromasimpletable.WeshowtwocolumnscorrespondingtoNewsweek’schoices,andtwo rows corresponding to Time’s choices. This produces four boxes; eachcorresponds to one combination of strategies. The entry in each box showsTime’ssales,measured inpercentageof the totalpotential readership.Thefirstrow shows Time’s sales from choosing the AIDS story, as we range overNewsweek’s alternative choices. The second row shows Time’s sales fromchoosing the budget story, again as we range over Newsweek’s choices. Forexample,inthebottomleftorsouth-westcornerbox,TimehasthebudgetstoryandNewsweekhastheAIDSstory,andTimegets30percentofthemarket.

Time’sSales

Thedominantstrategyiseasytosee.Thefirstrowisuniformlybetterthan

thesecondrow:eachentryinthefirstrowisbiggerthantheentryimmediatelybelowit inthesecondrow.This is thecriterionfordominance.Withthetable,youcanmakeaquickvisualcheckofwhetheror,notthecriterionismet.Youcanfigurativelyliftthefirstrowandlayitoverthesecond,andeachnumberinthe second row will be covered by a bigger number in the first. The visualadvantageofthetableovertheverbalreasoningofthepreviousparagraphgrowsinmorecomplicatedgames,inwhicheachsidehasseveralstrategies.

Itsohappensthatinthisgame,bothplayershaveadominantstrategy.Toseethis, drawup a table forNewsweek’s sales, shown below.The first column ofnumbers showsNewsweek’s sales if it uses theAIDS story, aswe range overTime’s choices.This column isuniformlybetter than the secondcolumn;onceagain you can perform the overlaying test in your mind’s eye. Therefore theAIDSstoryisthedominantstrategyforNewsweek,too.

Newsweek’sSales

Games inwhicheach sidehasadominant strategyare the simplestgames

fromthestrategicperspective.Thereisstrategicinteraction,butwithaforegoneconclusion.Eachplayer’s choice ishisdominant strategy, irrespectiveofwhattheotherdoes.Thatdoesnotmakesuchgamesuninteresting,eithertoplayortothinkabout.Forexample,inthehundred-yarddash,thedominantstrategyistorunasfastasyoucan.Butmanypeopleenjoyparticipatinginandviewingsuchraces.InChapter1’sPrisoners’Dilemma,asplayedinDzerzhinskySquare,bothplayers have dominant strategies. Yet this compelling force takes them to amutuallydisastrousoutcome.This raisesavery interestingquestion—howcantheplayers cooperate toget a better result?Wewill havemore confessions tomakeaboutthisinournextchapter.

Sometimesoneplayer has a dominant strategybut theother doesnot.Weillustrate thiswith just a slight change in the cover story competitionbetweenTime andNewsweek. Suppose that the readership has a slight bias in favor ofTime.When the twomagazines have the same cover story, 60 percent of thepotential buyers who like that story will pick Time and 40 percent will pickNewsweek.NowthetableofTime’ssalesisasfollows:Time’sSales

ForTime,theAIDSstoryisstillthedominantstrategy.ButNewsweek’stable

becomesNewsweek’sSales

Ifyouliftthefirstcolumnandlayitoverthesecond,30getscoveredbya

smaller number (28), and 12 by a larger (70). Neither strategy dominates theother.Inotherwords,Newsweek’sbestchoiceisnolongerindependentofTime’sstrategy.IfTimechoosestheAIDSstory,Newsweekdoesbetterbychoosingthebudgetstory,andviceversa.ForNewsweek, thewholeofthebudgetmarketisnowbetterthanthesmallershareofthelargerAIDSmarket.

TheeditorsofNewsweekdonotobservewhatthoseofTimechoose,buttheycanfigureitout.SinceTimehasadominantstrategy,thatmustbetheirchoice.SoNewsweek’seditorscanconfidentlyassume that thoseofTime have chosentheAIDSstory,andpicktheirownbestresponse,namelythebudgetstory.

Thusgames inwhichonly one side has a dominant strategy are also verysimple. This side plays its dominant strategy, and the other chooses its best

responsetothatstrategy.Now thatwe have introduced the idea of a dominant strategy, it isworth

emphasizingtwopointsaboutwhatadominantstrategyisnot.It iseasytogetconfusedaboutjustwhatitisthatadominantstrategyactuallydominates.

In 1981, Leonard Silk, writing about the Congressional debate on theEconomic Recovery Tax Act, concluded: “Mr. Reagan has sensed that theRepublicans have what game theorists call a ‘dominant strategy’—one thatmakes a player better off than his opponent, no matter what strategy hisopponentuses.”2WewilllookatthisgamemorecarefullyinChapter5,butherewe only want to point out that Silk’s definition of a dominant strategy isincorrect.Thedominancein“dominantstrategy”isadominanceofoneofyourstrategiesoveryourotherstrategies,notofyouoveryouropponent.Adominantstrategy is one thatmakes aplayerbetteroff thanhewouldbe if heusedanyother strategy, no matter what strategy his opponent uses. Recall that in thecoverpictureexample,bothTimeandNewsweekhaveadominantstrategy;yetbothcannothavehighersalesthantheother.

Asecondcommonmisperceptionisthatadominantstrategyrequiresthattheworst possible outcome playing the dominant strategy be better than the bestoutcomeofsomeotherstrategy.Thishappenstobetrueintheexamplesabove.With the numbers in the original setup, the worst that could happen to TimewhenusingtheAIDSstorywasa35percentshare;thebesttheycouldhopeforwiththebudgetstorywas30percent.However, this isnotageneralfeatureofdominantstrategies.

ImagineapricewarbetweenTimeandNewsweek.Supposeeachissuecosts$1 toproduce, and there are just twopossiblepricing choices: $3 (implying aprofitmarginof$2percopy)and$2(implyingaprofitmarginof$1percopy).Suppose that customerswill alwaysbuy the lower-pricedmagazine, and if thepricesareequal,theywillsplitequallybetweenthetwo.Thetotalreadershipis5millionifthepriceis$3,andrisesto8millionifthepriceisonly$2.Youcaneasily calculate Time’s profits in the four possible pricing combinations, andproducethefollowingtable.

Time’sProfits

Time’sdominantstrategyistocharge$2(andsoisNewsweek’s).Theworst

that can happen to Time from following the dominant strategy is to net $4million.Butthebestthatcanhappenfromfollowingtheotherstrategyisbetter,namely $5million. The point is that the comparison of those two numbers ismeaningless. The $5 million arises if both magazines charge $3; then Timewoulddoevenbetter($8million)byswitchingto$2.

We can sum up the lessons of these examples into a rule for behavior ingameswithsimultaneousmoves:Rule2:Ifyouhaveadominantstrategy,useit.Donotbeconcernedaboutyour rival’schoice. Ifyoudonothaveadominantstrategy,butyourrivaldoes,thenanticipatethathewilluseit,andchooseyourbestresponseaccordingly.

Aword of caution.We developed the concept of a dominant strategy forgameswith simultaneousmoves. Caremust be taken in using it ifmoves aresequential.Becausethenatureofthestrategicinteractionisdifferent,theideaofa dominant strategy is no longer the same. Suppose we say that you have adominantstrategy if foreachgiven choiceof the rival,youdobetterwith thisstrategythanwithanyother.Whenmovesaresequentialandyourrivalmovesfirst, youwould always choose your dominant strategy. Aswe just said, it isyourbestresponsetoeachofyourrival’smoves,andthereforetotheparticularonehehaschosen.Butifyoumovefirst,yourrival’smoveisnotgiven.Hewillobserve your choice when he makes his, and you have the opportunity toinfluencehisbehavior.Insomecircumstancesthismaybestbedonebychoosingsomethingotherthanyourdominantstrategy.WeexplainthisfullyinChapter6,whenwediscusscommitment.

3.DOMINATEDSTRATEGIESNotallgameshavedominantstrategies,evenforoneplayer.Infact,dominanceis the exception rather than the rule. Although the presence of a dominantstrategy leads to very simple rules for action, these rules are inapplicable tomanyactualgames.Otherprinciplesmustthenbebroughtintoaction.

Just asadominant strategy isuniformlybetter thaneveryother strategy, adominated strategy is uniformly worse than some other strategy. Just as youchooseyourdominantstrategyifyouhaveone,andcanbesurethatyourrivalwillchoosehisifhehasone,youshouldavoidyourdominatedstrategiesifyouhaveany,andcanbesurethatyourrivalwillavoidhis,ifhehasany.

If you have just two alternative strategies, and one of them is dominated,then the other must be dominant. Therefore examples of avoiding dominatedstrategiesthataregenuinelydifferentfromthoseofchoosingdominantstrategiesmustbebasedongamesinwhichatleastonesidehasatleastthreestrategies.Letusconsiderasimpleexampleofthiskind.

Thinkofaplayinfootballinwhichtheoffense’ssoleconcernistogainasmanyyardsaspossible,andthedefense’ssoleconcernistoholdthemtoasfewyardsaspossible.Forexample,withverylittletimeleft,theoffensemaywanttoimproveitschancesofkickingawinningfieldgoal.

Supposetheoffensehasjusttwostrategies,runandpass,whilethedefensehasthreestrategies:countertherun,counterthepass,andblitzthequarterback.Wecancalculatetheyardslikelytobegainedbytheoffensiveteamforeachofthesixstrategycombinations.Forexample, take thecase inwhich thedefenseblitzesandtheoffensetriesapass.Supposethereisa10percentchancethatthequarterbackwillbesackedforalossof10yards,a70percentchanceofaquick10-yard pass, and a 20 percent chance of a longer 20-yard pass. The averageworksoutat

0.1×(-10)+0.7×10+0.2×20=-1+7+4=10.

Thenumbersobviouslydependonthespecialskills(orlackthereof)ofthetwoteams;wehavechosenparticularonesjustforillustration.*

Weshowtheoutcomesofsuchcalculationsforallsixpossiblecombinationsinthefollowingtable.

Offense’sExpectedYardageGain

The offense tries to achieve the largest possible number in this table. The

defense tries to secure the smallest possible number, so we do not need aseparatetablefromwhichtodeterminetheiractions.*

Neither side has a dominant strategy: there is no row with numbersuniformly higher than those in the other row, and no column with numbersuniformlysmallerthanthoseineachoftheothercolumns.Butthedefensedoeshaveadominatedstrategy,namelytheblitz.Theresultofablitzisayardagelossthatisuniformlylarger,andthusworseforthedefense,thanthosepossiblewitheither of the other strategies. Therefore this defense should not blitz, and theoffensecanbeconfidentthattheywillnot.

The argument doesn’t stop there. The blitz strategy might as well beremovedfromthedefensivecoach’splaybook,andthegamecanbetreatedasifeachsidehad twostrategies. In this reducedgame, theoffensehasadominantstrategy,namelypass.Itsnumbers,9and8,areuniformlyhigherthanthoseoftherunstrategy—3and7,respectively.Thereasonpasswasnotdominantintheoriginalgamewasthatrunhadabetteryieldagainstthedefense’sblitz(astheball-carriermightbreakintoopenfieldwiththeblitzingdefensivesafetiesoutofposition),butthathasnowbeenremovedfromconsideration.Sotheoffensewillchoose thepass.Thedefense in turn should think this through, andchoose itsbestresponse,namelythepassdefense.

The general idea can be summed up into one more rule of behavior forgames with simultaneous moves: Rule 3: Eliminate anydominated strategies from consideration, and go ondoingsosuccessively.

If,duringtheprocess,anydominantstrategiesemergeinthesmallergames,theyshouldbechosensuccessively.Ifthisprocedureendsinauniqueoutcome,youhave found the prescriptions of action for the players and the outcome of thegame.Eveniftheproceduredoesnotendinauniqueoutcome,itwillreducethesizeandthecomplexityofthegame.

We illustrate the idea of successively eliminating dominated strategies bymakingupastoryofanimpendingnavalengagementinthePersianGulf.*Thegridbelowshowsthepositionsandthechoicesofthecombatants.AnIraqishipatthepointI isabout tofireamissile, intending tohitanAmericanshipatA.Themissile’spathisprogrammedatthelaunch;itcantravelinastraightline,ormake sharp right-angled turns every 20 seconds. If the Iraqimissile flew in astraight line from I to A, American missile defenses could counter such atrajectoryveryeasily.ThereforetheIraqiswilltryapathwithsomezigzags.AllsuchpathsthatcanreachAfromIliealongthegridshown.EachlengthlikeIFequalsthedistancethemissilecantravelin20seconds.

The American ship’s radar will detect the launch of the incoming Iraqi

missile, and the computerwill instantly launch an antimissile. The antimissiletravels at the samespeedas the Iraqimissile, andcanmake similar90-degreeturns.Sotheantimissile’spathcanalsobesetalongthesamegridstartingatA.However, to allow for enoughexplosives to ensure adamagingopen-airblast,theantimissilehasonlyenoughfueltolastoneminute,soitcantraveljustthreesegments(e.g.,AtoB,BtoC,andCtoF,whichwewriteasABCF).

If, before or at the end of theminute, our antimissilemeets the incomingmissile,itwillexplodeandneutralizethethreat.Otherwisetheirmissilewillgoon to hit our ship. The question is, How should the trajectories of the two

missilesbechosen?Only the firstminute of travel is relevant for this game. Each side has to

think ahead for three 20-second segments. Counting up all the alternatives ateach segment, both sides have eight possible paths. We then examine all 64combinations,andcalculatewhichonesarehitsandwhicharemisses.

Forexample,consider the Iraqi strategy IFCBofgoing in thestraight linefromItoFtoCforthefirsttwosegments,andthenmakingtheright-angledturntoB for the last.Confront thiswith theAmerican strategyofABCF. The twomissiles meet at C at the end of two segments (40 seconds); therefore thiscombination counts as a hit. If the same Iraqi strategywere countered by theAmericanABEF,thiswouldbeamiss.ThetrajectoriesseemtohavethepointsBandF incommon,but the twomissilesreach thesepointsatdifferent times;forexampletheAmericanmissileisatBafter20secondsandtheIraqionegetstoBafter60seconds.

Thetableshowsallsuchcombinations.TheeightIraqistrategiesarelabeledI1toI8,andthepathforeachisalsoshown—forexample,I1standsforIFCB.Similarly theAmericanstrategiesare labeledA1toA8.ThehitsarewrittenH;themisses,O.

TableofHitsandMisses

This looks complicated, but the rule of eliminating dominated strategies

simplifiesitveryquickly.TheAmericanantimissileistryingtoscoreahit,soHisbetterfortheAmericansthanO.ThenitiseasytoseethatfortheAmericans,

thestrategyA2isdominatedbyA4:ifyoulifttherowA4andlayitoverA2,youwill see thatA4 has anH everywhere thatA2 does, and in onemore place—namely, inresponseto theIraqistrategyI5.Doingsuchcalculationsforall thepossibilitiesshowsthatthestrategiesA2,A3,A6,andA7aredominatedbybothA4andA8,A1isdominatedbyA8,andA5byA4.SotheIraqiswillbesurethattheAmericanswillnotuseanythingotherthanA4orA8.Confiningattentiontothese two rows, the Iraqis are trying to achievemisses rather than hits, so forthemI2,I3,I4,I6,I7,andI8aredominatedbyI1orI5.Afterwecrossouttherowsandcolumnsofdominatedstrategies,thegameisreducedtothefollowing.

TableofHitsandMisses

ReducedTableofMissileHitsandMisses

Our two rules cannot simplify it any further; there are no longer any

dominantordominatedstrategies.Butwehaveachievedquitealot.Lookingatthe remainingstrategies in themap,wesee that the Iraqimissile should travelalongtheouteredgesofthegrid,whereastheAmericanantimissileshouldprowlinsmall loops.Weshallsoonseehowtochoosefromthetwoalternativesthatremainforeachside.

4.EQUILIBRIUMSTRATEGIESWhenallsimplificationsbasedondominantanddominatedstrategieshavebeenused, the game is at its irreducible minimum level of complexity and theproblemofthecircularreasoningmustbeconfrontedhead-on.Whatisbestforyou depends on what is best for your opponent and vice versa. Here, weintroduce the technique for squaring the circle, the way out of the circularreasoning.

For this, letusgoback to thepricewarbetweenTime andNewsweek,butinsteadofjusttwoalternativepricesof$2and$3,allowawholerangeofprices.NowthemanagementofTimemustthinkofitsbestresponseforeverypossibleprice thatNewsweekmightcharge.Supposeeachmagazinehasacoreof loyalreaders, but there is also a floating readership that can be attracted by pricecompetition.IfforsomereasonthemanagementofNewsweeksetapriceof$1,thecostofproduction,thenthemanagementofTimewouldnotfollowthemintothisno-profitstrategy,butwouldsetahigherprice,say$2,andmakesomeprofitfrom the sales to its loyal readers.AsNewsweek charged a higher price,Timewould raise its price, but by less, thus getting some competitive advantage.Supposethatforeach$1increaseintheNewsweekprice,Timedoesbesttoraiseits price by 50 cents. This relationship ofTime’s best response to all possiblepricesofNewsweekisshowninthechartbelow.

Supposethetwomagazinesarealikeinhavingsimilarcosts,equalpoolsof

loyal readers, and similar drawing power over floating readers. Then therelationshipofNewsweek’s best response to all possible prices ofTime has anidenticalchart.

Nowwe can imagine the twomanagers separately engaged in a round ofthinking.ThusTime’smanagersays:“Ifhecharges$1,1shouldcharge$2.Buthe,knowingIamthinkinginthisway,willchargenot$1,buthisbestresponsetomy$2,namely$2.50.ThenIshouldchargenot$2,butmybestresponsetohis$2.50,namely$2.75.Butthenhe…”Wheredoesthisend?

Itendsat$3.IfthemanagerofTimethinksthattheNewsweekpricewillbe$3,thenhisbestresponseistocharge$3forTime.Andviceversa.Thecircularreasoninghasconverged.

Wecanshowthisinanotherchart,wherethetworesponsesarejuxtaposedinthesamepicture.Thetwolinesmeetatthepointwhereeachpriceis$3.

Wehavefoundacombinationofstrategiesinwhicheachplayer’sactionis

the best response to that of the other. Given what the other is doing, neitherwants to change his own move. Game theorists call such an outcome anequilibrium.Thisconceptwasdevelopedby thePrincetonmathematicianJohnNashandinhishonorisoftencalledaNashequilibrium.Nash’sideaunderliesourfinalruleofbehaviorforsimultaneous-movegames:

Rule4:Havingexhaustedthesimpleavenuesoflookingfordominantstrategiesorrulingoutdominatedones,thenextthingtodoistolookforanequilibriumofthegame.

ThismustbethetrickthatSherlockHolmesandProfessorMoriartywereusinginseeingthrougheachother’smind.

Thisruleneedsalittlemoreexplanation.Whyshouldtheplayersinagamebedrawntosuchanoutcome?Severalreasonscanbegiven.Nooneofthemisabsolutelycompellingonitsown,buttogethertheymakeastrongcase.

First,thereistheneedtoavoidcircularreasoning,whichgetsnowhere.Theequilibriumstaysstableundersuccessiveroundsof“Ithinkthathethinks…”Itmakes theplayers’ expectations about eachother’s action consistent.Eachhascorrectlypredictedtheother’saction,andhaschosenhisownbestresponse.

A second virtue of the equilibrium strategy arises in zero-sum games, inwhichtheplayers’interestsarestrictlyopposed.Insuchagame,youropponentscannot gain by deceiving you into playing an equilibrium strategy. You havealreadytakenintoaccounttheirbestresponsetowhatyouaredoing.

The third reason is pragmatic. The proof of the pudding is in the eating.Throughoutthisbook,wediscussseveralgamesusingtheequilibriumapproach.We ask you to examine the predictions of outcomes and the prescriptions forbehaviorthatemergefromthiswayofthinking.Webelievethiswillmakeourcasebetterthananyabstractdiscussionofitsmerits.3

Finally,thereisapossiblemisinterpretationofthenotionofequilibriumweurgeyoutoavoid.Whenwesaythatanoutcomeisanequilibrium,thereisnoautomaticpresumptionthatitisbestforalltheplayersinthegame,letaloneforsociety as awhole. Such an evaluation is always a separate question, and theanswer varies from one context to another. InChapters 4 and 9wewillmeetexamplesofbothkinds.

5.FEASTORFAMINE

FeastIs the notion of equilibrium a complete solution to the problem of circularreasoninginsimultaneous-movegames?Alas,no.Somegameshavemanysuchequilibria, others have none. In still others, the notion of equilibriummust bemademore subtlebyadmittingnewkindsof strategies.Wenow illustrate andexplainthesepoints.

Which side of the road should you drive on? This question cannot beanswered through the use of dominant or dominated strategies. Even so, theanswerseemseasy.Ifeveryoneelsedrivesontheright-handside,youtoowillwanttodriveontheright-handside.Toputit inthe“IfI thinkthathethinks”framework, if everybody thinks that everybody else thinks that everybody isgoingtodriveontheright-handside,theneverybodywillwanttodriveontheright-handsideandtheirexpectationswillallbeconfirmed.Drivingontherightwillbeanequilibrium.

Butsoisdrivingontheleft,asinEngland,Australia,andJapan.Thegamehastwoequilibria.Nothinginthenotionofequilibriumtellsuswhich(ifeither)doesorshouldprevail.Whenagamehasmanyequilibria,theplayersmusthavea common understanding of which one to pick. Otherwise there can beconfusion.

Inthedrivingexample,anestablishedrulegaveyoutheanswer.ButwhatdoyoudowhenaphonecallbetweenPeterandPaulaaccidentallygetscutoff?IfPetertriestocallPaula,thenPaulashouldstayoffthephone(andnottrytocall

Peter)soastopreventherphonefrombeingbusy.Ontheotherhand,ifPaulaiswaitingforPetertocall,andPeterwaitstoo,thentheirphoneconversationwillneverbecompleted.Whatisbestforonedependsonwhattheotherdoes.Againtherearetwoequilibria,oneinwhichPetercallsandPaulawaits,andtheothertheotherwayaround.

Thetwoneedasocialconventiontohelpthemchooseconsistentstrategies,thatis,acommonunderstandingofwhichequilibriumtoattain.Onesolutionisfor the person who originally made the call to also make the callback. Thepersonwhoansweredthephonewaitsforthephonetoringagain.Theadvantageof this is that the originator knows the other party’s phone number,while thereversemaynotalwaysbetrue.Anotherpossibilityisthatifonepersoncancallfor free and the other cannot (say Peter is in his office and Paula is at a payphone),thenthepersonwiththefreeaccessshouldcallagain.

Totestyourabilitytocoordinateonanequilibrium,considerthefollowingquestion:YouaretomeetsomeoneinNewYorkCitysometimetomorrow.Theyare told to meet you. Neither you nor the other person is given any moreinstructionsaboutwheretomeetorwhen.Whenandwheredoyougo?

Thomas Schelling made this question famous in his Strategy of Conflict.There is no predetermined right answer other than the one most commonlygiven.Amongour students,GrandCentralStationatnooncontinues tobe themost common answer. This is true even for Princeton students whose trainarrivesinNewYorkatPennStation.*

FamineTheothercomplication is thatnotallgameshaveevenasingleequilibriumofthekindwedescribedabove.Inthemissilestory,notoneofthefourremainingoutcomesisanequilibrium.Forexample,lookatthecombinationofIraqiI1andAmericanA4.Thisproducesamiss,andtheAmericansdobetterbyswitchingtoA8.ButthentheIraqisshouldswitchtoI5,inturntheAmericansshouldswitchtoA4, theIraqisbacktoI1,andsoon.Thepoint is that ifonesideengagesinanydeterminatebehavior, theothercantakeadvantageofit.Theonlysensiblethingforeachtodoistomixitsmovesrandomly.Thisproblemissosymmetricthat therightmix isobvious: theAmericansshouldchooseeachofA4andA8with equal likelihood, and the Iraqis should likewise place a 50 percentprobabilityonchoosingeachofI1andI5.

Thismixingstrategycanariseevenwhenpartiesaretryingtocooperate.Inthe phone-call example, imagine that both parties flip a coin to determine

whether or not they should be the one to return the call. This pair of randomactions is a third equilibrium to the phone problem based on the criteriadescribed above. If I try to call you, I have a 50 percent chance of gettingthrough(whenyouarewaitingformycall)anda50percentchanceoffindingyourlinebusy.IfIwaitinstead,thenIalsohavea50percentchanceofgettingbackin touch; the50percentcomesfromtheone-halfchance thatyouwillbetryingtocallme.Eachround,bothpartiesarecompletelyindifferentaboutwhataction to take: their responses are in fact optimal to each other. Since there isonly a 50percent chanceof resumingour conversation,we expect that itwilltaketwotries(onaverage)beforewesucceed.

Inother games, the right proportions inwhich eachplayer shouldmixhisstrategiesisnotsoobvious.InChapter7wedevelopasetofrulestodeterminewhenmixedstrategiesareneededandamethodtofindtherightmixture.

Let us recapitulate briefly. We have three rules for action in games withsimultaneousmoves: first, look for andusedominant strategies;next, look forandavoiddominatedstrategies, ineachcaseassumingsimilarbehavioron thepartofyourrivals;andfinally,lookforanduseanequilibrium.Toconcludethischapter,weconsideracasethatshowshowyoucantranslatethesethoughtsintoaction.

6.CASESTUDY#3:TOUGHGUY,TENDEROFFERWhenRobertCampeaumade his first bid forFederatedStores (and its crownjewel, Bloomingdales), he used the strategy of a two-tiered tender offer. Thiscase study looksat theeffectivenessof the two-tieredbidasa strategicmove:doesitgivetheraideranunfairadvantage?

Atwo-tieredbidtypicallyoffersahighpricetothefirstsharestenderedandalowerpricetothelatersharestendered.Tokeepnumberssimple,welookatacase inwhichthepre-takeoverprice is$100pershare.Thefirst tierof thebidoffers a higher price, $105 per share to the first shareholders until half of thetotalsharesare tendered.Thenextfiftypercentof theshares tenderedfall intothesecondtier;thepricepaidforthesesharesisonly$90pershare.Forfairness,sharesarenotplacedinthedifferenttiersbasedontheorderinwhichtheyaretendered. Rather, everyone gets a blended price: all the shares tendered areplacedonaproratedbasisintothetwo-tiers.(Thosewhodon’ttenderfindalloftheirsharesendupinthesecondtierif thebidsucceeds.)*Wecanexpresstheaveragepayment for sharesbya simplealgebraicexpression: if fewer than50percent tender, everyone gets $105 per share; if an amountX% ≥ 50%of the

company’s total stock gets tendered, then the average price paid per share is

One thing tonoticeabout theway the two-tieredoffer ismade is that it is

unconditional;eveniftheraiderdoesnotgetcontrol,thetenderedsharesarestillpurchasedat the first-tierprice.The second feature tonote about theway thistwo-tiered offer works is that if everyone tenders, then the average price pershareisonly$97.50.Thisislessthanthepricebeforetheoffer.It’salsoworsethan what they expect should the takeover fail; if the raider is defeated,shareholdersexpect theprice toreturn to the$100level.Hence theyhope thattheofferisdefeatedorthatanotherraidercomesalong.

Infactanotherraiderdidcomealong,namelyMacy’s.ImaginethatMacy’smakesaconditionaltenderoffer:itoffers$102pershareprovidedthatitgetsamajorityoftheshares.Towhomdoyoutenderandwhich(ifeither)offerdoyouexpecttosucceed?

CaseDiscussionTendering to the two-tiered offer is a dominant strategy. To verify this, weconsiderallthepossiblecases.Therearethreepossibilitiestocheck.

The two-tiered offer attracts less than 50 percent of the total shares andfails.Thetwo-tieredofferattractssomeamountabove50percentandsucceeds.Thetwo-tieredofferattractsexactly50percent.Ifyoutender,theofferwillsucceed,andwithoutyouitfails.

In the first case, the two-tiered offer fails, so that the post-tender price is

either$100ifbothoffersfailor$102ifthecompetingoffersucceeds.Butifyoutender you get $105 per share, which is bigger than either alternative. In thesecondcase,ifyoudon’ttenderyougetonly$90pershare.Tenderinggivesyouat worst $97.50. So again it is better to tender. In the third case, while otherpeople are worse off if the offer succeeds, you are privately better off. Thereason is that since there are exactly 50 percent tendered, youwill be getting$105pershare.Thisisworthwhile.Thusyouarewillingtopushtheofferover.

Because tendering is a dominant strategy, we expect everyone to tender.Wheneveryonetenders, theaverageblendedpricepersharemaybebelowthepre-bid price and even below the expected future price should the offer fail.

Hencethetwo-tieredbidenablesaraidertopaylessthanthecompanyisworth.Thefactthatshareholdershaveadominantstrategydoesnotmeanthattheyendup ahead. The raider uses the low price of the second tier to gain an unfairadvantage.Usuallythemanipulativenatureofthesecondtierislessstarkthaninourexamplebecausethecoercionispartiallyhiddenbythetakeoverpremium.Ifthecompanyistrulyworth$110afterthetakeover,thentheraidercanstillgainanunfairadvantagebyusingasecondtierbelow$110butabove$100.Lawyersview the two-tiered bid as coercive and have successfully used this as anargument to fight the raider in court. In the battle for Bloomingdales, RobertCampeau eventually won, but with a modified offer that did not include anytieredstructure.

Wealsoseethataconditionalbidisnotaneffectivecounterstrategyagainstan unconditional two-tiered bid. In our example, the bid byMacy’swould bemuchmoreeffectiveifitsofferof$102pershareweremadeunconditionally.Anunconditional bid byMacy’s destroys the equilibrium inwhich the two-tieredbid succeeds.The reason is that ifpeople thought that the two-tieredbidwerecertain to succeed, theywouldexpectablendedpriceof$97.50,which is lessthan they would receive by tendering to Macy’s. Hence it cannot be thatshareholdersexpectthetwo-tieredbidtosucceedandstilltendertoit.*

In late 1989, Campeau’s operations unraveled because of excessive debt.Federated Stores filed for reorganization under Chapter 11 of the bankruptcylaw.WhenwesayCampeau’s strategywassuccessful,wemerelymean that itachievedtheaimofwinningthetakeoverbattle.Successinrunningthecompanywasadifferentgame.

EpiloguetoPartI

In the first three chapters, we introduced several concepts and methods,usingexamplesfrombusiness,sports,politics,etc.,asvehicles.Inthechapterstofollow,wewillputtheideasandtechniquestowork.Herewerecapitulateandsummarizethemforreadyreference.

A game is a situation of strategic interdependence: the outcome of yourchoices (strategies) depends upon the choices of another person or personsactingpurposively.Thedecision-makersinvolvedinagamearecalledplayers,andtheirchoicesarecalledmoves.Theinterestsoftheplayersinagamemaybein strict conflict; one person’s gain is always another’s loss. Such games arecalledzero-sum.Butmoretypically,therearezonesofcommonalityofinterestsaswellasofconflict;therecanbecombinationsofmutuallygainfulormutuallyharmfulstrategies.Nevertheless,weusuallyrefertotheotherplayersinagameasone’srivals.

The moves in a game may be sequential or simultaneous. In a game ofsequentialmoves,thereisalinearchainofthinking:IfIdothis,myrivalcandothat,andinturnIcanrespondinthefollowingway….Suchagameisstudiedbydrawing thegame tree. The best choices ofmoves can be found by applyingRule1:Lookforward,andreasonbackward.

Inagamewithsimultaneousmoves,thereisalogicalcircleofreasoning:IthinkthathethinksthatIthinkthat….Thiscirclemustbesquared;onemustseethroughtherival’sactioneventhoughonecannotseeitwhenmakingone’sownmove. To tackle such a game, construct a table that shows the outcomescorresponding toallconceivablecombinationsofchoices.Thenproceed in thefollowingsteps.

Beginbyseeingifeithersidehasadominantstrategy—onethatoutperformsallofthatside’sotherstrategies,irrespectiveoftherival’schoice.ThisleadstoRule 2: If youhavea dominant strategy, use it. If you don’t have a dominantstrategy, but your rival does, then count on his using it, and choose your bestresponseaccordingly.

Next, ifneithersidehasadominantstrategy,see ifeitherhasadominated

strategy—onethatisuniformlyworseforthesideplayingitthananotherofitsstrategies. If so, apply Rule 3: Eliminate dominated strategies fromconsideration.Goondoingsosuccessively.Ifduringtheprocessanydominantstrategies emerge in the smaller games, they shouldbe chosen successively. Ifthis procedure ends in a unique outcome, you have found the prescriptions ofactionfortheplayersandtheoutcomeofthegame.Eveniftheproceduredoesnot lead to a unique outcome, it can reduce the size of the game to a moremanageablelevel.Finally,ifthereareneitherdominantnordominatedstrategies,or after thegamehasbeen simplifiedas far aspossibleusing the second step,apply Rule 4: Look for an equilibrium, a pair of strategies in which eachplayer’sactionisthebestresponsetotheother’s.Ifthereisauniqueequilibriumofthiskind,therearegoodargumentswhyallplayersshouldchooseit.Iftherearemanysuchequilibria,oneneedsacommonlyunderstoodruleorconventionfor choosing one over the others. If there is no such equilibrium, that usuallymeans that any systematic behavior can be exploited by one’s rivals, andthereforeindicatestheneedformixingone’splays.

Inpractice,gamescanhavesomesequentialmovesandsomesimultaneousmoves;thenacombinationofthesetechniquesmustbeemployedtothinkaboutanddetermineone’sbestchoiceofactions.

PartII

ResolvingthePrisoners’Dilemma

Throughout the1970s, theOrganizationofPetroleumExportingCountries(OPEC)colludedtoraisethepriceofcrudeoilfromunder$3perbarrelin1973toover$30perbarrel in1980.Theworld awaited themeetingof eachOPECprice-settingmeetingwithanxiety.Bytheendofthe1970s,someenergyexpertswerepredictingthatthepriceofoilwouldrisetoover$100perbarrelbytheendofthecentury.Thensuddenlythecartelseemedtocollapse.Pricesmoveddown,brieflytouching$10perbarrelinearly1986beforerecoveringto$18perbarrelin1987.*Aswewritethis,theIraqiinvasionofKuwaithasshotthepriceofoilupto$35perbarrelandexpertsaredividedaboutthefutureofOPEC.

Whatgoverns the successor failureof such cartels?Moregenerally,whatgoverns thebalancebetweencooperationandcompetitionnot just inbusiness,butalsoinpoliticsandsocialsettings?Thisquestioncanbeanswered,atleastinpart, using theprisoners’ dilemma thatweplayedout inKGBheadquarters inChapter1.

ThestoryofOPECisjustsuchagame.Ofcoursewetellitinastylizedway,highlightingthedilemmaandleavingoutmanyhistoricaldetails.Tostartwith,look at the production decisions of just twomembers, say Iran and Iraq. Forfurther simplicity, allow each just two production levels, either 2 or 4millionbarrelsofcrudeoiladay.Dependingontheirdecisions,thetotaloutputontheworldmarketwillbe4,6,or8millionbarrels.Suppose thepricewillbe$25,$15,and$10perbarrel, respectively.Extractioncostsare$2perbarrel in Iranand$4perbarrelinIraq.Thenwecanshowtheprofits(measuredinmillionsofdollarsaday)ofthetwocompetitorsintheusualtable.Ineachbox,thetoprightentryisIraq’sdailyprofit,thebottomleftisIran’s.*

TableofProfits(Iran,Iraq)

Each country has a dominant strategy: produce at the higher of the two

availablelevels.Iran,forexample,seesthat itsprofitrowcorrespondingtotheproduction levelof4,namely [$52and$32], isuniformlyhigher than theonecorresponding to theproduction level of 2, namely [$46 and$26].When theybothchoosetheirdominantstrategies,theirprofitsare$32and$24millionaday,respectively. Nothing to sneeze at, but cooperation would have gotten themmore,$46and$42.

Thispredicamentiscalledtheprisoners’dilemma.Itsremarkablefeatureisthatbothsidesplaytheirdominantstrategy,thusmaximizetheirpayoff,andyetthe outcome is jointlyworse than if both followed the strategy ofminimizingtheirpayoff.Sowhydon’ttheyfollowtheminimizingstrategy?LookbackattheproblemforIranandIraq.EvenifIranweretofollowtheminimizingstrategyofproducing2millionbarrels,Iraqstillhasanincentivetoproduce4million.ThentheoutcomewouldbeIraq’sidealandIran’sworst.IfIrandoesn’tcooperateandproduces 4million, then Iraqwould be foolish to sacrifice its own profits byproducing2million.The cartel’s problem is to find away to sustain the low-output, high-price strategy that yields the highest joint profit, given thetemptationforeachtocheatandgainattheexpenseoftheother.

IranandIraq’ssituationisanalogoustothatoftheKGB’sprisoners.Eachofthemfounditdominanttoconfess:iftheoneheldout,theothergotabetterdealby confessing; if one confessed, the other would be foolish not to. Hencewhatever one does, the other wants to confess. But that’s true for both. Andwhenbothconfess,eachgetsaharshsentence.Againtheselfishpursuitofone’sinterests leads to an inferior outcome.Whenneither confesses, theoutcome isbetter for both. The problem is how to attain such cooperation given thecompetitiontoobtainanespeciallygooddealforoneself.

The same problem arises when there are several competing firms in theindustry.Theproblemplaguesnotjustbusinesses,butalsostudentsofbusiness.

AprofessoratTexasA&MUniversityhadhisclassof27studentsplayagamethattrappedthemintheprisoners’dilemma.1Eachstudentownedahypotheticalfirm and had to decidewhether to produce 1 and help keep the price high orproduce2andgainattheexpenseofothers.Dependingonthetotalnumberofstudents producing 1, money would be paid to students according to thefollowingtable:NumberofStudentsWriting“1”

PayofftoEachStudentWhoWrites“1”

PayofftoEachStudentWhoWrites“2”

0

$0.50

1

$0.04

$0.54

2

$0.08

$0.58

3

$0.12

$0.62

…

…

…

25

$1.00

$1.50

26

$1.04

$1.54

27

$1.08

Thisiseasiertoseeandmorestrikinginachart:

Thegameis“rigged”sothatstudentswhowrite2alwaysget50centsmore

thanthosewhowrite1,butthemoreofthemthatwrite2,thelesstheircollectivegain.Supposeall27startplanningtowrite1,soeachwouldget$1.08.Nowonethinks of sneaking a switch to 2. Therewould be 26 l’s, and eachwould get$1.04(4centslessthantheoriginal),buttheswitcherwouldget$1.54(46centsmore).Thesameistrueirrespectiveoftheinitialnumberofstudentsthinkingofwriting1versus2.Writing2isadominantstrategy.Eachstudentwhoswitchesfromwriting1towriting2increaseshisownpayoutby46cents,butdecreasesthat of each of his 26 colleagues by 4 cents—the group as a whole loses 58cents.Bythetimeeveryoneactsselfishly,eachmaximizinghisownpayoff,theyeachget50cents. If, instead, theyconspiredandactedsoas tominimize theirindividualpayoff,theywouldeachreceive$1.08.Howwouldyouplay?

Insomepracticeplaysofthisgame,firstwithoutclassroomdiscussionandthenwithsomediscussiontoachievea“conspiracy,”thenumberofcooperativestudentswriting1rangedfrom3toamaximumof14.Inafinalbindingplay,thenumberwas4.Thetotalpayoutwas$15.82,whichis$13.34lessthanthatfromtotally successful collusion. “I’ll never trust anyone again as long as I live,”muttered the conspiracy leader. And how did he vote? “Oh, I voted 2,” hereplied.

This situation reminds us ofYossarian’s position in JosephHeller’s novelCatch-22.TheSecondWorldWarwasnearlywon,andYossariandidnotwanttobeamongthelasttodie.Hiscommandingofficerasks,“Butsupposeeveryoneon our side felt that way?” and Yossarian replies, “Then I’d certainly be adamnedfooltofeelanyotherway.Wouldn’tI?”

Politicians,too,areprisonersofthesamedilemma.In1984,itwascleartomostpeoplethattheU.S.federalbudgetdeficitwastoolarge.Expenditurecutsoftherequiredmagnitudewerepoliticallyinfeasible,andthereforeasignificanttax increase was inevitable. But who was going to exercise the politicalleadershipnecessarytobringthisabout?TheDemocraticpresidentialcandidate,WalterMondale,triedtosetthestageforsuchapolicychangeinhiscampaign,andwassoundlydefeatedbyRonaldReagan,whopromisednotaxincrease.In1985,theissuegotstalled.Nomatterhowyouformedthepoliticaldivisions—Democratsvs.Republicans,theHouseofRepresentativesvs.theSenate,ortheAdministration vs. theCongress—each side preferred to leave the initiative totheother.

For each, the best outcome was one in which the other proposed the taxincreasesandexpenditurecuts,payingthepoliticalprice.Conversely,proposingsuchpoliciesoneselfwhile theotherremainedpassivewas theworstoutcome.Bothsidesagreedthattheexerciseofjointleadership,sharingthecreditandtheblame,wouldbebetterforthecountry,andevenforthemselvesinthelongrun,thanthecombinationinwhichbothwerepassiveandthelargedeficitcontinued.

Wecanrepresentthisasagamebydrawinguptheusualtableofstrategiesandoutcomes.Thetwosidesare theRepublicansandtheDemocrats.Toshowwhopreferswhat,letusranktheoutcomesfrom1to4fromeachside’spointofview.Lownumbersmeanbetter ranking. Ineachbox the lower leftnumber istheRepublicans’ranking;theupperright,theDemocrats’.

RankingsforRepublicansandDemocrats

Youcaneasilyseethatforeachside,passivityisthedominantstrategy.This

is just what happened; there was no move toward tax increase in the 99thCongress.The99thCongressdidpasstheGramm-Rudman-Hollingsact,which

mandated thedeficit-reductionpolicies tobe followed in futureyears.But thatwasmerelyapretenseofactivity,infactpostponingthehardchoices.Itstargetsarebeingmetmorebyaccountingtricksthanbygenuinefiscalrestraint.

1.HOWTOACHIEVECOOPERATIONThosewhofindthemselvesinaprisoners’dilemmawilllookforwaystoescapeandachievethecooperativeoutcometheyjointlyprefer.Othersmayliketoseethe players remain trapped in the dilemma. For example, buyers benefit fromlower prices when the prisoners’ dilemma prevents firms in an industry fromcolluding.Inthiscasesocietywantstothwarttheindustry’sattemptstoresolvethedilemma,andantitrustlawsarepartofthiseffort.Ineithercase,whetherweseekcollusionor its opposite,wemust first understand theways inwhich theprisoners’dilemmamightbeaverted.Thenwecantrytofacilitatetheseways,ortoblockthem,asisappropriateinthecasebeingconsidered.

Theunderlyingproblemistheplayers’incentivetocheatonanyagreement.Therefore thecentralquestionsare,Howcansuchcheatingbedetected?Whatprospectofpunishmentwilldeterit?Letusexaminetheseinturn.

2.DETECTIONOFCHEATINGAcartelhastofindwaystodiscoverifcheatinghasinfactoccurred,andifso,thendeterminewhohascheated.Recognizingthatsomeonehascheatedisofteneasyintheexampleswehaveused.InthecaseofIranandIraq’soilproduction,the price will be $25 only if both countries cooperate and produce 2 millionbarrelsdaily;anypricebelow$25perbarrel isasure indicatorofcheating. Inreality,mattersaremorecomplicated.Thepricecanbeloweitherbecauseofafall indemandorbecauseofcheatingbyaproducer.Unlessthecartelcansortouttheseseparateinfluencesanddeterminethetruth,itmightinfercheatingandsetinmotionitspunishmentmeasureswhennocheatinghasinfactoccurred,orerr the other way around.* This will reduce the accuracy and therefore theefficacyofthemeasures.Acompromisesolutionisacriticalor“trigger”price;iftheprice fallsbelow thisvalue, thecartelpresumes thatcheatinghasoccurredandthepunishmentensues.

Thereisyetanothercomplicationinreality.Gamesof thiskindoftenhavemany dimensions of choice, and the possibility of observing cheating differsamong them. For example, firms compete with one another in price, product

quality,after-salesservice,andmanyotheraspects.Thepriceisrelativelyeasytoobserve,althoughsecretdiscountsorflexibilityinpricingtrade-inscancausecomplications.There aremanydimensionsofquality that arehard tomonitor.Therefore a cartel that tries to enforce collusive high prices finds competitioncontinually breaking out in new dimensions. This happened in the airlineindustry. During the years of regulation, fares were fixed and entry of newcompetitorswas effectively barred. Thiswas as if the airlines formed a cartelwith enforcement provided by theCivilAeronautics Board.Airlines began tocompete, or cheat on the cartel.While they couldn’t lower prices, they couldprovide more valuable services through elaborate meals and beautifulstewardesses.Whenlaborlawsforcedairlinestohiremalestewardsandnotfirestewardessesoverthirty,competitionswitchedtononstopschedules,seatwidth,andlegroom.

Another instanceof thisprocessoccurred in theareaof international tradepolicy. Tariffs are the most visible tools for restricting trade, and successiveroundsofnegotiationsof theGeneralAgreementonTariffsandTrade(GATT)achieved largemutual reductions of tariff rates of all industrial countries. Buteach country still had its domestic political pressures from powerful specialintereststorestrictimports.Thereforecountriesgraduallyswitchedtoother,lessvisible means, such as voluntary restraint agreements, customs valuationprocedures,standards,administrativepractices,andcomplicatedquotas.*

Thecommonthemeoftheseexamplesisthatcollusionfocusesonthemoretransparentdimensionsofchoice,andcompetitionshifts to the lessobservableones:wecallthistheLawofIncreasingOpaqueness.Thoughyoumightnotseeit clearly, the collusion still hurts you.Whenquotas on Japanese auto importswent into effect in 1981, not only did the prices of all cars, Japanese andAmerican,goup,butthelow-endJapanesemodelsdisappearedfromthemarket.Opaquecompetitionwasdoublybad:priceswerehigher,andthebalanceoftheproductmixwasdistorted.

Identifyingthecheatermaybeevenmoredifficult thandetectingcheating.With just twoplayers,anhonestpartyknowsthat theotherhascheated.Theremaystillbeaproblemwithgettinghimtoadmithisfault.Withmorethantwoplayers, we may know that someone has cheated, but no one (other than thecheater)knowswho.Inthiscase,thepunishmenttodetercheatingmustbebluntandaffecttheinnocentandtheguiltyalike.

Finally, cheating may consist of remaining passive and may thereby bedifficult to isolate.Thiswasso inourexampleof theexerciseof leadership inproposinghighertaxes.Insuchacase,itisfarhardertoinferorallegecheating.

While positive action is there for all to see, there are numerous excuses forinaction:greaterurgencyofotherissues,timeneededtoconsolidateforces,andsoon.

3.PUNISHMENTOFCHEATERSBehindeverygoodschemetoencouragecooperationisusuallysomemechanismto punish cheaters. A prisoner who confesses and implicates his collaboratorsmaybecomethetargetofrevengebytheothers’friends.Theprospectofgettingoutofprisonmorequicklymaylooklessalluringgiventheknowledgeofwhatwaitsoutside.Policehavebeenknowntoscaredrugdealersintoconfessingbythreateningtoreleasethem.Thethreatisthatiftheyarereleased,theirsupplierswillassumetheyhavesquealed.

In the example of the Texas A&M classroom experiment, if the studentscoulddetectwhohadrenegedontheconspiracyforallofthemtowrite1,theycouldostracizethecheatersfortherestofthesemester.Fewstudentswouldriskthat for the sake of fifty cents. In OPEC, because of the social and politicalcohesion of theArab states in the 1970s, a country thinking of cheatingmayhavebeendeterredbya fearofostracism.Theseareexamplesofpunishmentsthatareaddedontotheoriginalgame,inordertoreducetheincentivetocheat.

Otherkindsofpunishmentsarisewithinthestructureof thegame.Usuallythis happens because the game is repeated, and the gain from cheating in oneplay will lead to a loss in other plays. We illustrate this using the crude oilexamplewithIranandIraq.

Thepossibilityofpunishmentarisesbecausethetwocountriesareinvolvedinthisgamedayafterday.Supposetheystartonabasisoftrust,eachproducing2millionbarrelsadayandhelpingkeepthepricehigh.Eachwillconstantlybetempted to sneak in a defection. Look again at the table of daily profits. Asuccessfuldayof cheatingwhile Iraq stayshonestwill raise Iran’sprofit from$46millionto$52million,againof$6million.

TableofProfits(Iran,Iraq)

The question iswhat happenswhen Iraq recognizeswhat has gone on.A

plausible scenario is that themutual trustwill collapse, and the twowill settledowntoaregimeofhighoutputsandlowpricesfromthatdayonward.Relativetothecontinuationoftrust, thisgetsIran$14millionaday(4632)lessprofit.The short-term gain from cheating seems small in comparison with thesubsequentcost: if it takes Iraqamonth todetect Iran’scheatingand respond,themonth’sextraprofittoIran($180million)wouldbewipedoutiftheperiodofcollapsedtrustlastsjust13days.Ofcoursetimeismoney,andhigherprofitstodayareworthmorethananequalreductionofprofitinthefuture;butstillthiscalculation looks distinctly unfavorable. For Iraq, breaking the cartel is evenworse; thedailygainwhile its cheatinggoesundetected andunpunished is $2million,whereasthedailycostoncetrustcollapsesis$18million.Itappearsthatinthisinstance,evenaslightfearofthecollapseoftheirmutualtrustshouldbeenoughtokeepthetwocompetitorsabidingbytheagreement.

Trustcanbreakdownforallsortsofreasons.Forexample,thewarbetweenIranandIraqmadeitdifficultforOPECtoimposeproductionquotasoneithercountry.Trustinmaintainingcartelquotasisbasedonthesubsequentabilitytopunishthosewhoviolatetheagreement.Butwhatadditionalpunishmentscouldbeimposedontwocountriesalreadypunishingeachotherwithexplosivesand“humanwave”assaults?Withthewarended,thereisonceagainapotentialforcooperationbecausethereisapotentialforpunishment.

Tosumup,thereisnosolutionthatachievesreciprocalcooperationinaone-timegame.Onlyinanongoingrelationshipisthereanabilitytopunish,andthusastick tomotivatecooperation.Acollapseofcooperationcarriesanautomaticcostintheformofalossoffutureprofits.Ifthiscostislargeenough,cheatingwillbedeterredandcooperationsustained.

There are somecaveats to this general principle.The first ariseswhen therelationshiphassomenaturalend,suchastheendofaterminanelectedoffice.

Inthesesituations,thegameisrepeatedonlyafixednumberoftimes.Usingtheprincipleoflookingaheadandreasoningback,weseethatcooperationmustendwhen there is no longer any time left to punish. Yet neither wants to be leftcooperatingwhile theother cheats. If ever someone cooperates, then someonemustgetstuckintheend.Sinceneitheriswillingtoplaythefool,cooperationnevergetsstarted.Thisistruenomatterhowlongthegameis,providedtheendisknown.

Letuslookatthisargumentalittlemorecarefully.Rightfromthestart,bothplayersshouldlookaheadtopredictthelastplay.Onthislastplay,therewillbenofuturetoconsider,andthedominantstrategyistocheat.Theoutcomeofthelastplayisaforegoneconclusion.Sincethereisnowaytoaffectthelastplayofthegame,thepenultimateplayeffectivelybecomesthelastonetoconsider.

Onceagain,cheating isadominant strategy.The reason is that theplay inthenext-to-lastperiodhasnoeffectonthestrategieschoseninthefinalperiod.Thus the penultimate period can be considered in isolation. For any period inisolation,cheatingisadominantstrategy.

Now theplayof the final twoperiods canbe taken as given.Cooperatingearly on won’t help, as both players are resigned to cheat in the final twoperiods.Hence,thethird-to-lastperiodiseffectivelythelastonetoconsider.Thesame argument applies and cheating is a dominant strategy. This argumentunwindsallthewayback,sothatthereisnocooperationeveninthefirstplay.

Thelogicofthisargumentisimpeccable,andyetintherealworldwefindepisodesofsuccessfulcooperation.Therearevariouswaystoexplainthis.Oneis thatallactualgamesof thiskindarerepeatedonlyafinitenumberof times,butthatnumberisunknown.Sincethereisnofixedlasttime,thereisalwaysthepossibilitythattherelationshipwillgoon.Thentheplayershavesomeincentiveto sustain the cooperation for the sake of such future contingencies; if thisincentiveislargeenough,thecooperationwillpersist.

Anotherexplanationisthattheworldcontainssome“nice”peoplewhowillcooperate no matter what the material advantages of cheating may be. Nowsuppose you are not so nice. If you behaved true to your type in a finitelyrepeatedgameofprisoners’dilemma,youwouldstartcheatingrightaway.Thatwould reveal your nature to the other player. To hide the truth (at least for awhile)youhavetobehavenicely.Whywouldyouwanttodothat?Supposeyoustartedbyactingnicely.Then theotherplayerwould think itpossible thatyouare one of the few nice people around. There are real gains to be had bycooperating for a while, and the other player would plan to reciprocate yournicenesstoachievethesegains.Thathelpsyou,too.Ofcourseyouareplanningtosneakinadefectionneartheendofthegame,justastheotherplayeris.But

youtwocanstillhaveaninitialphaseofmutuallybeneficialcooperation.Thuswhile each side is waiting to take advantage of the other, both are benefitingfromthismutualdeception.

A third qualification to the emergence of trust in a repeated prisoners’dilemma is that the gains from cheating take place before the costs of thebreakdownof cooperation occur. Therefore the relative importance of the twodependsontherelativeimportanceofthepresentversusthefuture.Inbusinesscontexts, current and future profits are compared using an appropriate interestrate todiscount the future. Inpolitics, the judgmentofpresentversus future ismoresubjective,butitseemsthattimebeyondthenextelectioncountsforverylittle.Thismakescooperationhardtoachieve.Eveninbusiness,whentimesarebad, thewhole industry ison thevergeof collapse, and themanagement feelsthatthereisnotomorrow,competitionmaybecomemorefiercethaninnormaltimes.Similarly, theneedsofwarmadecurrentprofitsmore important to IranandIraq,andcontributedtothedifficultiesofOPEC.

4.THEPUNISHMENTISGUARANTEEDTheneatesttrickisenforcingpricecollusionthroughapunishmentguarantee,allinthenameofcompetition.HereweturntoNewYorkCityanditsstereowars.CrazyEddiehasmadehis trademark“Wecannotbeundersold.Wewillnotbeundersold.Our prices are the lowest—guaranteed.Our prices are insane.”Hismaincompetitor,Newmark&Lewis, isno lessambitious.Withanypurchase,yougetthestore’s“Lifetimelow-priceguarantee.”Itpromisestorebatedoublethedifferenceifyoucanfindalowerpriceelsewhere.

“If,afteryourpurchase,youfindthesamemodeladvertisedoravailableforsale for less (confirmed printed proof required) by any other local stockingmerchant, in this marketing area, during the lifetime of your purchase, we,Newmark&Lewis,willgladlyrefund(bycheck)100%ofthedifference,plusan additional 25% of the difference, or if you prefer,Newmark&Lewiswillgive you a 200% gift certificate refund (100% of the difference plus anadditional100%ofthedifference,ingiftcertificates).”

—fromNewmark&Lewis’sLifetimeLow-PriceGuaranteeYet,althoughtheysoundcompetitive,thesepromisestobeattherival’spricecan

enforcedisciplineinaprice-settingcartel.Howcanthishappen?SupposeeachVCRcosts$150wholesale, and for themomentbothCrazy

Eddie and Newmark & Lewis are selling it for $300. Crazy Eddie iscontemplatinga sneakycut to$275.Without thebeat-the-rivalpromise,CrazyEddiewouldhopethathislowerpricewouldattractsomeofthecustomerswhowould otherwise have gone to his rival—say, because they lived nearer to aNewmark&Lewis outlet, or had bought from thembefore.Unfortunately forCrazyEddie, his price cut has the reverse effect.With theNewmark&Lewispriceguarantee,thesepeoplearenowtemptedjusttowalkovertoNewmark&LewisandbuytheVCRfor$300andthenclaima$50rebate.ThisisjustasifNewmark & Lewis had reduced its price to $250, automatically undercuttingCrazyEddie.ButofcourseNewmark&Lewiswouldprefernot togiveawaythe fiftydollars. Its responsewill be to lower theprice to$275. In any event,CrazyEddieisworseoffthanwherehestarted.Sowhybother?Thepricestaysat$300.

AlthoughcartelsareillegalintheUnitedStates,CrazyEddieandNewmark&Lewishavethemakingsofone.Youcanseehowtheirimplicitcartelworksinterms of the requirements of enforcement we mentioned before: detection ofcheating,andpunishmentofcheaters.Newmark&LewiscanmoreeasilydetectCrazy Eddie’s cheating. The customers who bring them the news of CrazyEddie’s lower price, and ask them to beat that, are acting as unwittingenforcement agents for the cartel. The punishment comes in the form of thecollapseofthepricingagreementandconsequentlylowerprofits.The“beat-the-competition”adsalsosetthepunishmentinmotion,automaticallyandquickly.

AcelebratedantitrustcasebeforetheFederalTradeCommissionconcernedtheuseofasimilardevicethatappearstomakecompetitionmorefierce,butcaninfactserveasacartelenforcementmechanism.E.I.DuPont,Ethyl,andothermanufacturersofantiknockgasolineadditiveswerechargedwithusinga“most-favored-customer” clause. This clause says that the seller will offer to thesefavored customers the best price they offer to anyone. Taken at face value, itseems that themanufacturers are looking out for their favored customers.Butlet’s look deeper. The clausemeans that themanufacturer cannot compete byofferingselectivediscountstoattractnewcustomersawayfromhisrival,whilecharging the old higher price to his established clientele. They must makegeneralpricecuts,whicharemorecostly,becausetheyreducetheprofitmarginonallsales.Youcanseetheadvantageofthisclausetoacartel: thegainfromcheatingisless,andthecartelismorelikelytohold.

Inevaluatingmost-favored-customerclauses,theFederalTradeCommissionruledthat therewasananticompetitiveeffect,andforbadethecompaniesfrom

using such clauses in their contractswith customers.* Howwould you rule ifsuch a case were brought against Crazy Eddie and Newmark & Lewis? Oneyardstick by which to judge the fierceness of competition is the level ofmarkups. Many “discount” stereo stores charge almost a hundred-percentmarkupoverthewholesalecostoftheircomponents.Itishardtosaywhatpartofthemarkupisduetothecostsofcarryinginventoryandadvertising,butthereisatleastaprimafaciecasethatthereismethodtoCrazyEddie’smadness.

5.ACHOICEOFPUNISHMENTWhen several alternative punishments could deter cheating and sustaincooperation,howshouldonechooseamongthem?Severalcriteriahavearole.

Perhapsmost importantaresimplicityandclarity,sothataplayer thinkingofcheatingcaneasilyandaccuratelycalculateitsconsequences.Acriterionthatinfers someone has cheated if your discounted mean of profits from the lastseventeen months is 10 percent less than the average real rate of return toindustrialcapitaloverthesameperiod,forexample,istoocomplicatedformostfirmstofigureout,andthereforenotagooddeterrent.

Nextcomescertainty.Playersshouldhaveconfidencethatdefectionwillbepunishedandcooperation rewarded.This isamajorproblemfor theEuropeancountrieslookingtoenforcetheGeneralAgreementonTariffsandTrade.Whenonecountrycomplains thatanotherhascheatedon the tradeagreement,GATTinitiatesanadministrativeprocessthatdragsonformonthsoryears.Thefactsofthe case have little bearing on the judgment, which usually dependsmore ondictates of international politics and diplomacy. Such enforcement proceduresareunlikelytobeeffective.

Nextweaskhowsevereapunishmentshouldbe.Mostpeople’sinstinctivefeelingisthatitshould“fitthecrime.”Butthatmaynotbebigenoughtodetercheating.Thesurestwaytodetercheatingistomakethepunishmentasbigaspossible. Since the punishment threat succeeds in sustaining cooperation, itshouldnotmatterhowdireitis.Thefearkeepseveryonefromdefecting,hencethebreakdownneveractuallyoccursanditscostisirrelevant.

Theproblemwith thisapproach is that it ignores theriskofmistakes.Thedetectionprocessmaygowrong,indicatingcheatingbyamemberofthecartelwhen the real cause of low prices is an innocent one such as low demand. Ifpunishmentsareasbigaspossible,thenmistakeswillbeverycostly.Toreducethecostofmistakes,thepunishmentshouldbethesmallestsizethatsufficestodeter cheating.Minimaldeterrence accomplishes itspurposewithout imposing

anyextracostswhentheinevitablemistakesoccur.

6.TIT-FOR-TATThis list of the desirable properties of a punishment mechanism looks quitedemanding.ButUniversityofMichiganpoliticalscientistRobertAxelrodclaimsthattheruleoftit-for-tatdoesverywellinmeetingthesedemands.2Tit-for-tatisavariationofthe“eyeforaneye”ruleofbehavior:dountoothersastheyhavedoneontoyou.*Moreprecisely, the strategycooperates in the first periodandfromthenonmimicstherival’sactionfromthepreviousperiod.

Axelrod argues that tit-for-tat embodies four principles that should beevident in any effective strategy: clarity, niceness, provocability, andforgivingness.Tit-for-tatisasclearandsimpleasyoucanget.Itisniceinthatitnever initiates cheating. It is provocable, that is, it never lets cheating gounpunished.Andit is forgiving,becauseitdoesnotholdagrudgefor toolongandiswillingtorestorecooperation.

Axelrod confirmed the power of tit-for-tat through experiment, not justtheory.Hestagedatournamentoftwo-personprisoners’-dilemmagames.Gametheorists from around the world submitted their strategies in the form ofcomputerprograms.Theprogramswerematchedagainsteachother inpairs toplay a prisoners’-dilemma game repeated 150 times. Contestants were thenrankedbythesumoftheirscores.

ThewinnerwasAnatolRapoport,amathematicsprofessorattheUniversityofToronto.Hiswinningstrategywas tit-for-tat.Axelrodwassurprisedby this.He repeated the tournament with an enlarged set of contestants. Once againAnatolRapoportsubmittedtit-for-tatandbeatthecompetition.

Oneoftheimpressivefeaturesabouttit-for-tat isthatitdidsowelloveralleven though it did not (nor could it) beat any one of its rivals in a head-oncompetition.At best, tit-for-tat ties its rival. Hence ifAxelrod had scored thecompetitionasawinner-take-allcontest,tit-for-tatwouldhavescoredbelow500andsocouldnothavewon.

But Axelrod did not score the pairwise plays as winner-take-all: closecounted.Thebigadvantageoftit-for-tatisthatitalwayscomesclose.Atworst,tit-for-tatendsupgettingbeatenbyonedefection;i.e.,itgetstakenadvantageofonceandthentiesfromthenon.Thereasontit-for-tatwonthetournamentisthatitusuallymanagedtoencouragecooperationwheneverpossiblewhileavoidingexploitation.Theotherentrieswereeithertootrustingandopentoexploitationortooaggressiveandknockedoneanotherout.

In spite of all this, we believe that tit-for-tat is a flawed strategy. Theslightest possibility of misperceptions results in a complete breakdown in thesuccess of tit-for-tat. This flaw was not apparent in the artificial setting of acomputertournament,becausemisperceptionsdidnotarise.Butwhentit-for-tatis applied to real-world problems, misperceptions cannot be avoided and theresultcanbedisastrous.

Forinstance, in1987theUnitedStatesrespondedtotheSovietspyingandwiretappingoftheU.S.embassyinMoscowbyreducingthenumberofSovietdiplomats permitted to work in the United States. The Soviets responded bywithdrawingthenativesupportstaffemployedattheU.S.Moscowembassyandplaced tighter limits on the size of theAmerican delegation.As a result, bothsides found it more difficult to carry out their diplomatic functions. Anotherseriesoftit-for-tatretaliationsoccurredin1988,whentheCanadiansdiscoveredspyingonthepartofthevisitingSovietdiplomats.TheyreducedthesizeoftheSoviet delegation and the Soviets reduced the Canadian representation in theSoviet Union. In the end, both countries were bitter, and future diplomaticcooperationwasmoredifficult.

Theproblemwithtit-for-tatisthatanymistake“echoes”backandforth.Oneside punishes the other for a defection, and this sets off a chain reaction.Therival responds to the punishment by hitting back. This response calls for asecondpunishment.Atnopointdoes thestrategyacceptapunishmentwithouthittingback.TheIsraelispunishthePalestiniansforanattack.ThePalestiniansrefuse to accept the punishment and retaliate. The circle is complete and thepunishmentsandreprisalsbecomeself-perpetuating.

The long-standing feuds between the Hatfields and the McCoys or MarkTwain’sGrangerfordsandShepherdsonsoffermoreexamplesofhowtit-for-tatbehaviorleadstomutualloss.Feudistsoneithersidearenotwillingtoendthefeud until they consider themselves even. But in a continuing attempt to geteven, they end up knocking each other further and further down. Eventuallythey’llendupdeadeven.Rarelyisthereanyhopeofgoingbackandsolvingthedisputeat itsorigin, foroncebegun, it takesona lifeof itsown.WhenHuckFinn tries tounderstand theoriginsof theGrangerfords-Shepherdsonsfeud,herunsintothechicken-or-eggproblem:

“Whatwasthetroubleabout,Buck?—Land?”“Ireckonmaybe—Idon’tknow.”“Well,whodonetheshooting?WasitaGrangerfordoraShepherdson?”“Laws,howdoIknow?Itwassolongago.”“Don’tanyoneknow?”

“Oh yes, pa knows, I reckon, and some of the other old people, but theydon’tknownowwhattherowwasaboutinthefirstplace.” Whattit-for-tatlacksisawayofsaying“Enoughisenough.”Itisdangeroustoapplythissimpleruleinsituationsinwhichmisperceptionsareendemic.Tit-for-tat is too easily provoked.You shouldbemore forgivingwhen a defectionseemstobeamistakeratherthantherule.Evenifthedefectionwasintentional,afteralong-enoughcycleofpunishmentsitmaystillbetimetocallitquitsandtry reestablishing cooperation. At the same time, you don’t want to be tooforgivingandriskexploitation.Howdoyoumakethistrade-off?

A useful way to evaluate a strategy is to measure how well it performsagainst itself. If one thinks in terms of evolution, the “fittest strategies” willbecomedominantinthepopulation.Asaresult,theywillencountereachotheroften. Unless a strategy performs well against itself, any initial success willeventuallybecomeself-defeating.

Atfirstglance,tit-for-tatdoesverywellagainstitself.Twotit-for-tatterswillstart off cooperating, and since each is responding in kind, this cooperationseems destined to go on forever. The pair of strategies appears to completelyavoidtheproblemoftheprisoners’dilemma.

Butwhathappensifthereisachancethatonesidemisperceivestheother’smove?To findout,we follow two families, theHatfields and theMcCoys, astheyusetit-for-tatintheirneighborlyrelations.Theybeginpeacefully(P).

Suppose that in round 4 a Hatfield misinterprets a McCoy. Although the

McCoysweretrulypeaceful,theHatfieldsmistakenlysawanactofaggression(A).

The single misunderstanding “echoes” back and forth. In round 5, the

imaginedMcCoyaggressionbecomesrealintheHatfieldresponse.Nowthetwotit-for-tat clans are trapped in a situation in which they alternate retaliatingagainsttheotherforthepreviousretaliation.Inround6,theMcCoyspunishtheHatfields for theiraggression in round5,which leads theHatfields to retaliateoncemoreinround7.Andsoitgoes.Tryingtogetevenforbeingdownonejustdoesn’twork.

Thesituationcontinueslikethisuntilasecondmisinterpretationarises.Twodevelopments are possible. The Hatfields could misinterpret peace foraggression or they could misinterpret aggression as peace.* If aggression ismisinterpretedaspeace,thefeudisended(atleastuntilthenextmisperception).

Ifthesecondmisperceptionispeaceasaggression,bothsideswillresorttocontinual retaliation. This is illustrated below in round 9. Here the singlehelixliketwistingstrandofpeaceismisinterpretedasaggression.Consequently,the Hatfields respond by retaliating in round 11. Until another misperceptionoccurs, both sides continue to punish the other for the other’s previouspunishments.Althoughtit-for-tatterscangiveit,theycan’ttakeit.

What can we conclude about the performance of tit-for-tat? When

misperceptionsarepossible, in the long run tit-for-tatwill spendhalf the timecooperating and half of it defecting. The reason is that once misperceptionsarise, they are just as likely to get compounded as they are to get cleared up.Hence, tit-for-tat will do no better than a strategy based on a coin toss thatcooperatesanddefectswithequalprobability.

In this discussion, we seem to have left out an important ingredient: theprobabilitythatamisperceptionoccurs.Infact,ourconclusiondoesnotdependonthisprobability!Nomatterhowunlikelyamisperceptionis(evenifitisoneinatrillion),inthelongruntit-for-tatwillspendhalfofitstimecooperatingandhalf defecting, just as a random strategy does. When the probability of amisperceptionissmall,itwilltakealotlongerforthetroubletoarise.Butthenonceamistakehappens,itwillalsotakealotlongertoclearitup.

Thepossibilityofmisperceptionsmeansthatyouhavetobemoreforgiving,but not forgetting, than simple tit-for-tat. This is true when there is apresumption that the chanceof amisperception is small, say fivepercent.Butwhatstrategywouldyouadoptinaprisoners’dilemmainwhichthereisafiftypercentchancethattheothersidewillmisinterpret(reverse)youractions?Howforgivingshouldyoube?

Once the probability ofmisunderstanding reaches fifty percent there isnohope for achieving any cooperation in the prisoners’ dilemma. You shouldalways defect. Why? Consider two extremes. Imagine that you alwayscooperate.Youropponentwillmisinterpretyourmoveshalfthetime.Asaresult,hewillbelievethatyouhavedefectedhalfthetimeandcooperatedhalfthetime.Whatifyoualwaysdefect?Again,youwillbemisinterpretedhalfthetime.Nowthis is toyourbenefit, as theopponentbelieves that you spendhalf your timecooperating.

Nomatter what strategy you choose, you cannot have any effect onwhatyourpartnersees.Itisasifyourpartnerflipsacointodeterminewhathethinksyou did. There is simply no connectionwith reality once the probability of amistake reaches fifty percent. Since you have no hope of influencing yourpartner’s subsequent choices, youmight as well defect. Each period you willgatherahigherpayoffanditwon’thurtyouinthefuture.

The moral is that it pays to be more forgiving up to a point. Once theprobabilityofmistakesgetstoohigh,thepossibilityofmaintainingcooperationinaprisoners’dilemmabreaksdown.Itisjusttooeasytobetakenadvantageof.The large chance of misunderstandings makes it impossible to send clearmessages through your actions. Without an ability to communicate throughdeeds,anyhopeforcooperationdisappears.

A 50 percent chance of a misperception is the worst possible case. If

misperceptionswerecertain tooccur,youwould interpreteverymessageas itsopposite, and therewould be nomisunderstandings.A stock forecasterwhoseadviceisalwaysdeadwrongisasgoodapredictorasonewhoisalwaysright.Youjusthavetoknowhowtodecodetheforecasts.

With this inmind,we look for awayout of thedilemmawhen there is achanceofmisperception,butnottoobigofachance.

7.ANALTERNATIVETOTIT-FOR-TATThebasicpropertiesofclarity,niceness,provocability, and forgivingness seemlikely to be true of any good rule of behavior for extricating oneself from aprisoners’ dilemma. But tit-for-tat is too quick to punish someone who has ahistoryofcooperating.Weneedtofindastrategythatismorediscriminating:itshould bemore forgivingwhen a defection appears to be an exception, and itshouldpunishwhendefectionappearstobetherule.

You can consider the following guidelines as a step in that direction. (1)Begincooperating.(2)Continuecooperating.(3)Keepcountofhowmanytimesthe other side appears to have defectedwhile you have cooperated. (4) If thispercentage becomes unacceptable, revert to tit-for-tat.Note that unlike before,tit-for-tat is not used as a reward for good behavior; instead, tit-for-tat is thepunishmentifitappearsthattheothersideistryingtotakeadvantageofyou.

Todeterminewhatisanunacceptablepercentageofdefections,youneedtoknowbothashort-,medium-,andlong-termhistoryoftheotherside’sactions.The long run is not enough. Just because someonehasbeen cooperating for alongtimedoesnotmeanthathenowwon’ttakeadvantageofyouwhileherunsdown his reputation. You also need to know “What have you done for melately?”

Hereisanexampleofonesuchstrategy.Itisnicer,moreforgiving,notquiteas provocable, and a littlemore complicated than tit-for-tat. Start cooperatingandcontinuetodosountiloneofthefourtestsbelowfails.

Firstimpression:Adefectiononthefirstmoveisunacceptable.Reverttotit-for-tat.Shortterm:Twodefectionsinanythreeturnsisunacceptable.Reverttotit-for-tat.Medium term: Three defections out of the last twenty periods is

unacceptable.Reverttotit-for-tat.Long term: Five defections out of the last one hundred periods isunacceptable.Reverttotit-for-tat.

Thepunishmentoftit-for-tatneednotlastforever.Keeptrackofhowoften

theothersidehasviolatedanyofthesefourtests.Onthefirstviolation,returntocooperation after twenty periods of the tit-for-tat “echo” of alternatingdefections.Butputtheothersideonprobation.Reducethenumberofdefectionsallowed in themedium-and long-term tests by one. If the other side does notviolatetheprobationforfiftyperiods,thenstriketherecordcleanandreturntotheoriginalstandards.Iftheothersideviolatestheprobation,resorttotit-for-tatforever.

The exact rules for first, short-term, medium-term, and long-termimpressions will depend on the probabilities of error or misperception, theimportanceyouplaceonfuturegainsandcurrentlosses,andsoon.Butthistypeofstrategyislikelytooutperformtit-for-tatintheimperfectrealworld.

The important principle to remember is that when misperceptions arepossible, you shouldn’t punish every defection you see. You have to make aguess as to whether a misperception has occurred, either by you or by yourpartner.Thisextraforgivenessallowsotherstocheatalittleonyou.Butiftheycheat, theyuseup theirgoodwill.When theeventualmisperceptionsariseyouwillno longerbe inclined to let the incidentpass.Opportunismon thepartofyouropponentwillbeself-defeating.

8.CASESTUDY#4:CONGRESSV.FEDERALRESERVETheUnitedStatesCongressandtheFederalReserveoftenclashovereconomicpolicy. To explain why the conflict arises and where it leads, we presentPrinceton economist Alan Blinder’s game-theoretical analysis of the conflict.3The two institutions have separate and largely independent powers inmakingeconomicpolicy.Fiscalpolicy (taxationandexpenditures) is the responsibilityof theCongress,andmonetarypolicy(moneysupplyandinterestrates) thatoftheFederalReserve.Eachcandeployitspoliciesinanexpansionarymodeoracontractionarymode. Expansionary fiscal policymeans high expenditures andlow taxes; this reduces unemployment but carries a risk of inflation.Expansionary monetary policy means low interest rates and therefore easierborrowingconditions,butagainattheriskofinflation.

Thetwobrancheshavealsodevelopedseparatepreferencesabouteconomicoutcomes. Voters like the benefits they get from government spending, as incheaper mortgages, and dislike paying taxes. Congress responds to this byfavoring expansionary policies, unless inflation is imminent and serious. Incontrast, the Fed takes a longer viewpoint and thinks inflation the greaterproblem;thereforeitfavorscontractionarypolicies.

In 1981–82, Congress no longer regarded inflation as a sufficiently greatrisk. It felt that the economy could afford an expansionary fiscal policy andwantedtheFedtoaccommodatebypursuinganexpansionarymonetarypolicy.ButtheFedunderPaulVolckerwasafraidthatthiswouldjustrekindlethefiresofinflation.TheFed’sfirstpreferencewasforbothfiscalandmonetarypoliciestobecontractionary.WhatseemedbestfortheCongresswasworstfortheFedandviceversa.

The interests of the Congress and the Fed were not entirely opposed. Insearchofacompromise,thetwosidesdebatedtherelativemeritsofcombiningone expansionary and one contractionary policy. Eitherway the policiesweremixed would have similar effects on general employment and inflation, butdifferedinotherimportantrespects.Fiscalexpansionandmonetarycontractionwouldleadtoalargebudgetdeficitandhighinterestratesastheneedtofinancethis deficit ran up against the tightmoney. The high interest rateswould hurtsuchimportantsectorsasautosandconstructionespeciallyhard.Foreigncapitalwouldflowin,attractedbythehighU.S.interestrates.Thedollarwouldriseandourinternationalcompetitivenesswouldsuffer.

Fiscal contraction and monetary expansion would have just the oppositeeffects—lowinterestratesandalowdollar—favoringourautoandconstructionindustries,andmakingour tradedgoodsmorecompetitive.BothCongressandtheFedpreferredthissecondcombinationofpoliciestothefirst.

What would you predict in this situation? How would you judge theoutcome?Whatreformsinthepolicy-makingprocesswouldyouprescribe?

CaseDiscussionThis is a prisoners’ dilemma. (Otherwise the casewouldn’t be in this chapter,would it?) Let the Congress and the Fed rank the four possible policycombinations,1beingthebestand4theworstineachcase.Thenwehavethistable.

RankingsofOutcomesfor(Fed,Congress)

HighexpendituresisadominantstrategyfortheCongress;tightmoney,for

theFed.Whenthetwothinkinthiswayandeachselectsitspreferredstrategy,theresultisabudgetdeficitandtightmoney.Thisisexactlywhathappenedintheearly1980s.Butthereisabetteroutcomeforboth,namelyabudgetsurplusandloosermoney.

Whatpreventsthemfromreachinganoutcomebothprefer?Theanswerlies,onceagain, in the interdependenceofdecisions.The jointlypreferredoutcomeariseswheneachchoosesitsindividuallyworsestrategy.Congressmustrestrictspendingtoachieveabalancedbudget.Havingdoneso,howcanitbesurethattheFedwillnotrespondwithatightmoneysupply?ItknowsthattheFedhasatemptation to sneak a switch to a tight money supply to achieve its idealoutcome,whichwould result in theworst possible outcome for theCongress.Congress does not trust the Fed to refrain from this temptation. It is theirinabilitytomakecrediblepromisestoeachotherthatlockstheadversariesintoanoutcometheycouldjointlyimproveupon.

Can we suggest a way out of this dilemma? The two have an ongoingrelationship,andcooperationmightemergeintherepeatedgame.However,thatonly happens if the players put sufficient weight on future benefits;Congressmenwhomust run for reelection every two years find it hard to actwithsuchforethought.

Let us try a different avenue. The Federal Reserve is itself a creation ofCongress. Inmost other countries, the government (the TreasuryDepartment)exercisesmuchmorecontroloverthecentralbank.IfthesameweretrueintheUnitedStates, theCongresscould imposeanexpansionarymonetarypolicyontheFedandachieveitsmostpreferredoutcome.OfcoursethosewhosharetheFed’sconcernforinflationwouldfindthisregrettable.

Thisseemsano-winsituation:coordinationoffiscalandmonetarypoliciesis tantamount to a triumph of the shortsighted political objectives of theCongress, but the checks and balances supplied by an independent FederalReserveleadtoaprisoners’dilemma.PerhapsasolutionistolettheFedchooseexpendituresandtaxes,andlettheCongresssetthemoneysupply?

StrategicMoves

“Wemust organize amerciless fight.The enemymust not lay hands on asingleloafofbread,onasingleliteroffuel.Collectivefarmersmustdrivetheirlivestock away and remove their grain. What cannot be removed must bedestroyed. Bridges and roadsmust be dynamited. Forests and depotsmust beburned down. Intolerable conditionsmust be created for the enemy.”—JosephStalin,proclaimingtheSoviets’“scorchedearth”defenseagainsttheNazis,July3,1941.

Today Stalin’s campaign lives on in the battlefields of corporate control.WhenWesternPacificattemptedto“annex”thepublishingcompanyHoughtonMifflin, the publishing house responded by threatening to empty its stable ofauthors. JohnKennethGalbraith, ArchibaldMacLeish, Arthur Schlesinger Jr.,and many profitable textbook authors threatened to find new publishers ifHoughton Mifflin were acquired. “When Western Pacific Chairman Howard(Mickey)Newmangotthefirstfewlettersfromauthors,hethoughtitwasabiglaugh,andcalledita‘put-upjob.’Whenhebegangettingmoreletters,hebegantorealize,‘I’mgoingtobuythiscompanyandIain’tgoingtohavenothing.’”1WesternPacificwithdrewitsbid,andHoughtonMifflinremainedindependent.

Thisstrategydoesn’talwayswork.WhenRupertMurdochwasinterestedinacquiringNew York magazine, the incumbent management attempted to fighthim off. Many of the magazine’s best-known writers threatened to quit ifMurdoch attained control. Murdoch was not deterred. He acquiredNew Yorkmagazine. The writers quit. But the advertisers stayed on. AndMurdoch gotwhathewaslookingfor.Thewritersburnedthewrongfields.Forthescorchedearthstrategy tobeeffective,youmustdestroywhat the invaderwants,whichmaynotcoincidewithwhatthepresentoccupantsvalue.

We do not mean to imply any moral approval of such tactics or theiroutcomes—successful or not. We can easily imagine circumstances where

societywouldwishtopreventthewastefuldestruction.Ourpurposeistoexplainthenatureofthesestrategiessothatyoumaybetterusethemorpreventthem.

Thescorchedearthdefenseisbutoneexampleofdevicesgametheoristscallstrategicmoves.2Astrategicmoveisdesignedtoalterthebeliefsandactionsofothersinadirectionfavorabletoyourself.Thedistinguishingfeatureisthatthemove purposefully limits your freedom of action. This can be done in anunconditional way; a presidential candidate pledges he will not raise taxes,period.Or,freedomcanbelimitedbecausethestrategicmovespecifiesaruleforhow to respond under different circumstances. For example,many states havemandatorysentencinglawsforcrimeswithhandguns;thesestatutespurposefullylimitjudicialdiscretion.

Youmighthavethoughtthatleavingoptionsopenisalwayspreferable.Butin the realm of game theory that is no longer true.Your lack of freedom hasstrategic value. It changes other players’ expectations about your futureresponses,andyoucanturnthistoyouradvantage.Othersknowthatwhenyouhavethefreedomtoact,youalsohavethefreedomtocapitulate.ToquoteOscarWilde,“Icanresistanythingexcepttemptation.”3

1.UNCONDITIONALMOVESPicturearivalrybetweentheUnitedStatesandJapantodevelophigh-definitionTV.AlthoughtheUnitedStateshasatechnologicaledge,italsohasmorelimitedresources owing to accumulated budget deficits.The Japanese play off of thishandicapandonceagainbeattheUnitedStates.ButastrategicmovethatatfirstglanceappearstohandicaptheUnitedStatesfurthercanchangeallthat.

In the absence of any unconditional moves, Washington and Tokyosimultaneouslychoose their strategies.Eachcountrydecidesbetweena loworhigh level of research and development effort; a high-effort level shortensdevelopmenttime,incurringmuchgreatercosts.Wedepict thisasagame,andsetup thepayoff table.Eachsidehas twostrategies,so therearefourpossibleoutcomes.

Wesupposebothsidesregardahigh-effortraceastheworstscenario—theJapanesebecausetheUnitedStatesismorelikelytowinanall-outrace,andtheUnitedStatesbecauseofthegreatercost.Callthispayoff1foreachside.Eachside’s secondworst outcome (payoff 2) is pursuing low effortwhile the othergoesallout:thisisspendingmoneywithlittlechanceofsuccess.

PayoffsforHigh-DefinitionTVRace(U.S.,Japan)

The Japanese like best (labeled as payoff 4) the situation in which they

pursue high effort and the United States follows low effort; their chances ofwinningarehigh,andresourcecostsmatterlessforthem.FortheUnitedStates,thebestsituation iswhenbothsidesmake loweffort; theyare likely towinatlowcost.

Loweffort is thedominantstrategyfor theUnitedStates.Theproblemforthe United States is that the Japanese can anticipate this. The Japanese bestresponse is to followhigh effort.The equilibriumof thegame is the top rightcell, where the United States gets its second worst payoff. To improve itspositioncallsforastrategicmove.

Suppose the United States preempts. It announces its unconditional effortlevelbeforetheJapanesereachtheirdecision.Thisturnsthesimultaneous-movegame into a sequential-move game, one inwhich theUnitedStates goes first.Thetableturnsintoatree.*

TreeandPayoffsinSequential-MoveGame

Payoffsto(U.S.,Japan)

Thisgame is solvedby looking forwardand reasoningback. If theUnitedStatespursuesloweffort,theJapaneserespondwithhigh,andtheU.S.payoffis2. If theUnitedStatespursueshigheffort, theJapanese respondwith low,andthe U.S. payoff is 3. Therefore the United States should announce high, andexpect the Japanese to respond low. This is the equilibrium of the sequential-movegame.ItgivestheUnitedStatesapayoffof3,morethanthe2itgotinthesimultaneous-movegame.

ThestrategicmovethatbringstheUnitedStatesthisadvantageisaunilateralandunconditional declarationof its choice.The choice isnotwhat theUnitedStates would have made in simultaneous play. This is where the strategicthinkingenters.TheUnitedStateshasnothingtogainbydeclaringthechoiceofloweffort;theJapaneseexpectthatanywayintheabsenceofanydeclaration.

To behave strategically, you must commit not to follow your equilibriumstrategyof thesimultaneous-movegame.ThestrategicmovechangesJapaneseexpectations, and therefore their response. Once they believe that the UnitedStates is committed to high effort, the Japanese will choose low effort. Ofcourse,aftertheJapanesechoosetheirpath,theUnitedStateswoulddobettertochangeitsmindandswitchtoloweffort,too.

This raises several questions: Why should the Japanese believe the U.S.declaration?Wouldtheynotanticipateachangeofmind?Andiftheyanticipatesuchareversal,wouldtheynotchoosehigheffort?

In other words, the credibility of the U.S. unconditional first move issuspect.Withoutcredibility,themovehasnoeffect.Moststrategicmovesmustconfront thisproblemof credibility.Recall theexamples at theopeningof the

chapter.Althoughthepolitician’spledgenottoraisetaxesisunconditional,itisnotirreversible.Onceelected,excusesareoftenfoundtoraisetaxes.Conditionalrules are also subject to exceptions when the time comes; the mandatorysentence iswaivedwhen a neurologist uses an illegal handgun in self-defenseagainstaderangedpatient.

Togiveastrategicmovecredibility,youhavetotakesomeothersupportingactionthatmakesreversingthemovetoocostlyorevenimpossible.Credibilityrequires a commitment to the strategic move. In the case of Stalin’s threat tostarvetheenemy,burningthefieldsmadehisthreatcredible.Inothersituations,credibilityisamatterofdegree.Precedentinthelegalsystemgivescredibilitytothe mandatory sentencing rule (in most cases); for politicians’ promises,exceptionsaremoretherule.Intheraceforhigh-definitionTV,theUnitedStatesmight commit funds to which interested companies can lay claim in order tomakeahighR&Deffortcredible.

Strategicmovesthuscontaintwoelements:theplannedcourseofactionandthe commitment that makes this course credible. In this chapter we focusattention on the actions. We classify and explain different types of strategicbehavior, leaving aside for the moment the problem of how to make themcredible.Tomakeananalogywithcooking, thenextchapteroffers recipes forcommitment.Wecontinueherewithamenuofmoves.

2.THREATSANDPROMISESAnunconditionalmovegivesastrategicadvantagetoaplayerabletoseizetheinitiative and move first. Even when you don’t actually move first, you canachieveasimilarstrategicadvantagethroughacommitmenttoaresponserule.The response rule prescribes your action as a response to the others’ moves.Althoughyouactasafollower,thecommitmenttotheresponserulemustbeinplacebeforeothersmaketheirmoves.Aparenttellingachild“Nodessertunlessyoueatyour spinach” is establishing sucha response rule.Of course this rulemustbeinplaceandclearlycommunicatedbeforethechildfeedsitsspinachtothedog.

Response rules fall under two broad categories: threats and promises. Athreat is a response rule that punishes others who fail to cooperate with you.Therearecompellentthreats,aswhenaterroristhijacksaplaneandestablishesaresponserulethatthepassengerswillbekilledifhisdemandsarerejected,andthere are deterrent threats, as when the United States threatens that it willrespondwithnuclearweaponsiftheSovietUnionattacksanyNATOcountry.A

compellent threat is designed to induce someone to action, while a deterrentthreat is designed to prevent someone from taking an action. The two threatsshareacommonfeature:bothsideswillsufferifthethreathastobecarriedout.

Thesecondcategoryofresponserulesispromises.Thisisanoffertorewardsomeonewhocooperateswithyou.Insearchofawitness,aprosecutorpromisesone defendant amore lenient sentence if he turns state’s evidence against hiscodefendants. Again there can be compellent and deterrent promises. Acompellent promise is designed to induce someone to take a favorable action,such as turning state’s evidence. A deterrent promise is designed to preventsomeonefromtakinganunfavorableaction,suchaswhenthemobsterspromisethe witness they will take care of him if he keeps his mouth shut. The twopromisesalsoshareacommonfeature:once theaction is taken (ornot taken),thereisanincentivetogobackonone’sword.

Sometimes the distinctions between threats and promises are blurred. AfriendwasmuggedinNewYorkCitywiththefollowingpromise:Ifyou“lend”metwentydollars,IpromiseIwon’thurtyou.Morerelevantwasthemugger’simplicitthreatthatifourfrienddidn’tlendhimthemoney,hewouldbehurt.

As this story suggests, the distinction between a threat and a promisedependsonlyonwhatyoucallthestatusquo.Thetraditionalmuggerthreatensto hurt you if youdon’t give him somemoney. If youdon’t, he starts hurtingyou,making that thenewstatusquo, andpromises to stoponceyougivehimmoney. A compellent threat is just like a deterrent promise with a change ofstatusquo; likewise,adeterrent threatandacompellentpromisedifferonly intheirstatusquo.

3.WARNINGSANDASSURANCESThe common feature to all threats and promises is this: the response rulecommitsyoutoactionsthatyouwouldnottakeinitsabsence.Iftherulemerelysaysyouwilldowhatisbestatthetime,thisisasifthereisnorule.Thereisnochangeinothers’expectationsaboutyourfutureactionsandhencenoinfluenceof the rule. Still, there is an informational role for stating what will happenwithoutarule;thesestatementsarecalledwarningsandassurances.

Whenitisinyourinteresttocarryouta“threat,”wecallthisawarning.Forexample,ifthepresidentwarnshewillvetoabillnottohisliking,thisissimplyanindicationofhisintentions.Itwouldbeathreatifhewerewillingtosignthebill,but strategicallycommitted toveto it inorder to induceCongress tooffersomethingevenbetter.

Awarning is used to informothersof the effect of their actions.Aparentwhowarnsachildthatastove-topishot,makesastatementoffact,notstrategy.

When it is in your interest to carry out a “promise,” we call this anassurance.A childwho ignores thewarning that the stove-top is hot andgetsburnedassurestheparentthathewon’tdothisagain.

Weemphasize thisdistinction for a reason.Threatsandpromisesare trulystrategicmoves,whereaswarningsandassurancesplaymoreofaninformationalrole. Warnings or assurances do not change your response rule in order toinfluenceanotherparty.Instead,youaresimplyinformingthemofhowyouwillwant to respondbasedon theiractions. Instarkcontrast, thesolepurposeofathreatorpromise is tochangeyour responseruleawayfromwhatwillbebestwhen the time comes. This is done not to inform but tomanipulate. Becausethreatsandpromisesindicatethatyouwillactagainstyourowninterest,thereisanissueofcredibility.Afterothershavemoved,youhaveanincentivetobreakyourthreatorpromise.Acommitmentisneededtoensurecredibility.

We summarize the options for strategic moves in a chart below. Anunconditionalmoveisaresponseruleinwhichyoumovefirstandyouractionisfixed.Threatsandpromisesarisewhenyoumovesecond.Theyareconditionalmovesbecausetheresponsedictatedbytheruledependsonwhattheothersidedoes.

Astrategicmoveisalwaysapreemptiveaction.Theresponserulemustbein

placebefore theothersidemoves.Thatmeans thatwhateverstrategicmove ismade,thegameshouldbeanalyzedasonewithsequentialmoves.Whenyouareintransigent, others respond to your unconditional action. With threats andpromises,youfirstlaydownaresponserule,thenothersmoveandyourespondaccordingtoyourresponserule.

As a result, commitment to an action or response rule transforms anotherwisesimultaneous-movegameintoasequential-movegame.Althoughthe

payoffsremainunchanged,agameplayedwithsimultaneousmovesinonecaseandsequentialmovesinanothercanhavedramaticallydifferentoutcomes.Thedifferentoutcomesareduetothedifferentrulesofplay.Weillustratedthiseffectwith an unconditional move in the story of U.S.-Japanese rivalry; let us nowlookatthreatsandpromisesarisinginaconfrontationbetweentheUnitedStatesandtheSovietsandthentheDemocratsandtheRepublicans.

4.NUCLEARDETERRENCEForover fortyyears, theNorthAtlanticTreatyOrganization (NATO) sought acredible deterrence to any Soviet attempt to invade Western Europe. Aconventional defense by NATO forces was not likely to succeed. A primarycomponentoftheNATOdeterrencewasbasedontheU.S.nuclearforces.Yet,anuclear response would be devastating for the whole world. How could thiswork?

Letusshowthegameinatree.TheSovietshavethefirstmove.Iftheydonotattack,wehavethestatusquo;scorethis0foreachside.IftheyattackandNATOattemptsaconventionaldefense, suppose theSovietshave thepayoff1andtheUnitedStateshas-1.Anuclearresponsegives-100toeachside.

TreeandPayoffsinSequential-MoveGame

In thisgame, theSoviets lookaheadandforecast that theiraggressionwill

notbring forth anuclear response. It is not in theU.S. interests after the fact.Thusattackingwillgivethemthepayoff1;notattacking,0.Thereforetheywill

attack.If you think this an unlikely scenario, the European members of NATO

thoughtitalltoolikelythattheUnitedStateswoulddesertthemintheirtimeofneed in just thisway. Theywanted theUnited States to commit credibly to anuclearresponse.

Let us leave aside the issue of credibility for now, and examine themechanicsofhowsuchathreatcouldwork.NowtheUnitedStateshasthefirstmove,namelytheresponseruleitputsinplace.Thepertinentruleisthethreat:“If the Soviets attack Western Europe, our response will be nuclear.” If theUnitedStatesdoesnotmake the threat, therestof thegameunfoldsasbefore.With the threat inplace, thechoiceofaconventionaldefenseno longerexists.Thefullgametreeisasfollows.

PayoffsinSequential-MoveGamewithThreatinPlace

Once theU.S. threat is inplace, theSoviets lookaheadandrecognize that

aggressionwillmeet a nuclear response and result in aSoviet payoff of -100.Theyprefer thestatusquo,andsodonot invade.NowtheUnitedStates in itsfirstmovelooksaheadtoallthisandseesthatitspayoffis0withthethreatand1without.ThereforeU.S.interestsdictatemakingthethreat.

Once again, observe that theU.S. response rule requires doing somethingthatisnotthebestresponseafterthefact.Thereinliesthestrategicpurpose:bycrediblyaltering theSoviets’perceptionof theU.S. responseafter thefact, theUnitedStatescanchange“thefact”—namely,theSovietdecisionwhetherornottoinvadeWesternEurope.

Therulemustbeinplacebeforetheotherpartyhasalreadytakentheactionyouwanttoinfluence.Afterthefact,neitheranunconditionalmovenorthreatsandpromiseshaveanyrelevance.

Thisfirstmovemustbeeitherobservedorinferredbytherival,orelseyoucannotuseitforstrategiceffect.InthefilmDr.Strangelove, theSovietsinstalltheir sure deterrent, the doomsday device, on a Friday, but delay telling theAmericans untilMonday. Over the weekend, U.S. Air ForceGeneral JackD.Ripperordershis squadronofplanes to launchanuclear attack.Thedeterrentfailsbybeingunobservable.

Observability is not as straightforward as it seems.One need not actuallyobserve the other person’s actions if the action can be inferred from theconsequence.IfIamallergictoshellfish,IcantellthatyoucookedwithshrimpevenifIdidnotactuallyobserveyouinthekitchen.*

Justasyourunconditionalmovemustbeobservableifitistoinfluenceyourrival,hisactionsmustbeobservable ifyouare to influence thembythreatsorpromises.Otherwiseyoucannotcheckhiscompliance,andheknowsthis.

Nowthatyouhaveseenhowcredibleunconditionalmovesandthreatshavetheir effects, you will be able to analyze most simple situations of this kindwithout drawing a game tree in all its detail. A verbal argument will usuallysuffice.Ifeveritdoesnot,andyoudoubtiftheprosehascoveredallthecasescorrectly,youcanalwayscheckthereasoningbydrawingthetree.

5.STRATEGIESOFTHETIMESIn1981,RonaldReaganwasanewlyelectedpresidentwithtremendouspopularappeal. But, could he carry his vision for tax reform through Congress? Thebattle lines were drawn in the fight over his first budget proposal. TheDemocratswantedReagantocompromise,sacrificingpartofthetaxcutforthesakeof a smallerdeficit.TheRepublicanswanted the fulldoseof supply-sideeconomics.Theoutcomewoulddependonhowthetwopartiesplayedthegame.

In theSenate, theDemocratswent alongwithReagan’s budget, hoping toinducesomeRepublicancompromiseinreturnforthebipartisansupport.ButtheRepublicansheldfirmtotheoriginalplan.ThusthesceneturnedtotheHouseofRepresentatives.WastheresomebetterstrategyfortheDemocrats?

A pair of New York Times columns by Leonard Silk neatly laid out thestrategic possibilities.4 As he described the negotiations, each party had twochoicesandtherewerefourpossibleoutcomes.WereproduceSilk’stableofthegame.

RankingofOutcomesfor[Democrats,Republicans]

TheDemocratsregardasbesttheoutcomewheretheyattackReaganandthe

Republicanscompromise,becausetheDemocratscanclaimthecreditforfiscalresponsibilitywhileimplementingtheirfavoredbudget.FortheRepublicans,thebest outcome occurs in the top left, where Reagan’s budget gets bipartisansupport.WhentheDemocratsattackwhiletheRepublicansholdfirm,theresultis a stalemate and both parties lose. The Democrats would be willing tomoderatetheirattackiftheRepublicanswouldcompromise;bothpartieswouldgettheirsecond-bestoutcome.

The Democrats’ main problem is that the Republicans have a dominantstrategy:supportReagancompletely. If theDemocratsmainlysupportReagan,theRepublicansshouldsupportReagancompletelytoattaintheirtopoutcome.IftheDemocratsattackReagan, theRepublicansshouldsupportReagantoavoidtheir worst outcome. Whatever the Democrats do, it is always better for theRepublicanstosupportReagancompletely.*

ThustheRepublicanstrategyseemseasytopredict.TheDemocratsshouldexpect theRepublicans to supportReagancompletely,and then theDemocratsdobest by following suit andmainly supportingReagan.This is exactlywhathappenedintheSenate.

So far, the outcome greatly favors the Republicans. To improve theirposition, theDemocratsneedtomakesometypeofstrategicmove.Theymustturnthesituationintoasequential-movegame,movingfirstandthenlettingthe

Republicans respond to their strategy.†Thusweconsiderwhat typeof threats,promises,orothermovesshifttheoutcomeinfavoroftheDemocrats.

NoneofthebasicstrategiesseemtoworkfortheDemocrats.Unconditionalmoves, promises, even threats all fail.Only the combined use of a threat andpromisecaninduceRepublicancompromise.

Theproblemwithunconditionalityisthatitdoesn’tinfluencetheRepublicanposition.TheDemocratsarecurrentlyexpectedtosupportReagan.Committingthemselves to this action does not alter the Republicans’ perception and thusleadstothesameoutcome.TheonlystrategicpossibilityisfortheDemocratstoattackReagan unconditionally. In this case, they can look forward and reasonthat theRepublicanswill still respondby supportingReagan completely. (TheRepublicans alwaysprefer to supportReagan completely—it is their dominantstrategy.) But the combination of Democrats attacking with the RepublicansgivingcompletesupportisworsefortheDemocratsthanthealternativeofbothpartiessupportingReagan.

TheDemocratswant to induce theRepublicans tomove from completelysupporting Reagan to compromise. Therefore, they might promise to supportReaganiftheRepublicansagreetocompromise.*Butthispromisewillnothelpthem. The Republicans know that if they ignore the promise and choose tosupportReagancompletely,theDemocrats’bestresponseistosupportReagan.The effect of the Democrats’ promise is that they end up unconditionallysupporting Reagan. The Republicans appreciate this gesture and proceed tosupport Reagan completely, maintaining their best outcome. The promise ispointless.TheRepublicanscansafelyignoreit.

TheDemocratshaveonlyonethreatthattheycanusetostoptheRepublicansupport of Reagan. They can threaten to attack Reagan if the Republicanssupporthimcompletely.Butthethreatisnotenough.Theeffectofthethreatisthat the Democrats have unconditionally committed to attack Reagan. If theRepublicans support Reagan, the Democrats carry out their threat and attackReagan; if theRepublicanscompromise, it is in theDemocrats’best interest toattackReagan.SincetheDemocratsattackReaganwhatevertheRepublicansdo,the Republicans support Reagan completely, making the best of the twopossibilities.

ApromiseendsupbeingequivalenttounconditionalDemocratsupportforReagan, while a threat is equivalent to an unconditional Democrat attack onReagan.NeitheriseffectiveinchangingtheRepublicans’actions.

IftheDemocratscombineapromisewithathreat,theycanachieveabetterresultforthemselves.TheyshouldpromisetosupportReaganiftheRepublicans

compromise and threaten to attackReagan if theRepublicans support Reagancompletely. This strategy achieves the Democrats’ goals.With this threat andpromise in place, the Republicans must choose between compromising andgetting the Democrats to mainly support Reagan, or supporting Reagancompletely and thereby provoking the Democrats to attack Reagan. Betweenthesetwoalternatives,theypreferthecompromise.

WhatactuallyhappenedwasthatRepublicanssupportedReagancompletelyinboththeSenateandintheHouse.TheSenateDemocratswentalongwiththeRepublicans.IntheHouse, theDemocrats’s initialresistancequicklygavewaytoathirdstrategy:theyout-ReaganedReaganinthetax-cuttinggame.Theresultwas a bipartisan “Christmas-tree” tax cut.The economic bills for that are justcomingdue,andthenegotiationstogetoutofthedifficultyaredevelopingintonewstrategicgames.

6.MORESTRATEGICMOVESIn addition to the three basic strategic moves, there are more complicatedoptions. Instead of establishing a response rule directly, you can purposefullyallowsomeoneelse to takeadvantageofoneof thesestrategies.Threeoptionsare

Youmayallow someone tomakeanunconditionalmovebeforeyourespond.Youmaywaitforathreatbeforetakinganyaction.Youmaywaitforapromisebeforetakinganyaction.

We have already seen examples in which someone who couldmove first

doesevenbetterbyrelinquishingthisoption,allowingtheothersidetomakeanunconditionalmove.Thisistruewheneveritisbettertofollowthantolead,asinthetalesoftheAmerica’sCupraceandgamblingattheCambridgeMayBall.Whileitcanbeadvantageoustogiveuptheinitiative,thisisnotageneralrule.Sometimes your goal will be to prevent your opponent from making anunconditional commitment. Chinesemilitary strategist Sun Tzuwrote: “Whenyousurroundanenemy,leaveanoutletfree.”5Oneleavesanoutletfreesothattheenemymaybelieve there is a road to safety. If theenemydoesnot seeanescapeoutlet,hewill fightwith thecourageofdesperation.SunTzuaimed to

deny theenemyanopportunity tomakehisownverycrediblecommitmentoffightingtothedeath.

It isneveradvantageoustoallowothers to threatenyou.Youcouldalwaysdowhattheywantedyoutodowithoutthethreat.Thefactthattheycanmakeyou worse off if you do not cooperate cannot help, because it limits youravailableoptions.But thismaximappliesonly toallowingthreatsalone. If theothersidecanmakebothpromisesandthreats,thenyoucanbothbebetteroff.

7.ASLEDGEHAMMERTOCRACKANUT?

It isclear thatwhenmakingapromise,youshouldnotpromisemorethanyouhave to. If the promise is successful in influencing the other party’s behavior,youexpecttocarryoutyourword.Thisshouldbedoneascheaplyaspossible,andthatmeanspromisingtheminimumamountnecessary.

It is less apparent that moderation applies equally well to threats. Youshouldn’tthreatensomeoneanymorethannecessary.Thereasonismoresubtle.

Whydoesn’ttheUnitedStatesthreatenamilitaryattackagainsttheJapaneseiftheydon’tagreetoimportmoreAmericanrice,beef,andoranges?*TheideamayhavesomeappealtosomeAmericanfarmersandpoliticians.Butthereareseveralgoodreasonsagainstit.

1. Nobodywouldbelievethethreat,andthusitwouldn’twork.2. Even if the threat did work, the Japanese might wisely want toreconsiderwhethertheAmericansarereallytheirallies.3. If the Japanese didn’t import more oranges and the U.S. actuallycarriedoutitsthreat,therestoftheworldandespeciallytheJapanesewould sanction the U.S. for selecting an inappropriate method ofpunishment. But if theU.S. didn’t carry out its threat, that hurts itsreputationinthefuture.EitherwaytheUnitedStatesloses.4. Thethreatdilutestheclarityoftheoriginalproblembyintroducingtheotherwiseextraneousissueofmilitaryforce.

Theessenceofallthesepointsisthatthethreatisexcessivelylarge—toobig

tobecredible,toobigtocarryout,andtooserioustostakeareputationover.Thefirstconcernofaplayermakingathreatwouldbejusttheopposite—a

threatmust be large enough to achieve the desired deterrence or compellence.Thenextthingthatmattersiscredibility—theotherside’sbeliefthatifitdefiesthe threat, it will suffer the stated consequences. Under ideal circumstances,nothing else should matter. If the threatened player knows and fears theconsequencesofdefiance,hewillcomply.Thethreatenedactionwillneverhavetobecarriedout.Thenwhydoesitmatterhowterribleitwouldhavebeenifitwerecarriedout?

Thepointisthatcircumstancesareneveridealinthissense.Ifweexaminethe reasons for our not threatening to usemilitary power in this case,we seemoreclearlyhowrealitydiffersfromtheideal.

First,theveryactofmakingathreatmaybecostly.Nations,businesses,andevenpeopleareengagedinmanygames,andwhattheydidinonegamehasanimpactonalltheothergames.InourdealingswithJapaninthefuture,andwithother countries now and in the future, our use of an excessive threat will beremembered.Theywillbereluctanttodealwithusatall,andwewillforgothebenefitsofmanyothertradesandalliances.

Second,anexcessive threatmaybecounterproductiveevenin thegameinwhich it is used. The Japanesewill throw up their hands in horror, appeal toworld opinion and the decency of the American people, and more generallydelay the negotiation to the pointwhere our timetable for compelling them toopentheirmarketsisslowedratherthanspeeded.

Third,thetheorythatasuccessfulthreatneedneverbecarriedoutisfinesolongasweareabsolutelysurenounforeseenerrorswilloccur.Supposewehavemisjudged theJapanesefarmers’power,and theyarewilling to let theirnationgo towar rather thansee theirprotectedmarketdisappear.Orsuppose that theJapaneseagree toour terms,butsomeU.S.militarycommanderdownthe linewhoremembershisexperienceasaP.O.W.andisitchingforrevengetakestheopportunity to launch an attack all the same. The possibility of such errorsshouldgiveuspausebeforewecommitourselvestoaverylargethreat.

Finally, inviewof this, a threat starts to lose credibility just forbeing toolarge.IftheJapanesedonotbelievewearetrulycommittedtocarryingoutthethreat,itwillnotdeterthemeither.

The conclusion is that one should strive for the smallest and the mostappropriatethreatthatwilldothejob—makethepunishmentfitthecrime.WhentheUnitedStateswantstostimulatetheJapanesetoimportmoreoranges,itusesamorereciprocalthreat,onethatmorecloselyfitsthecrime.TheUnitedStatesmight retaliate in kind by limiting the quotas on imports of Japanese cars or

electronicgoods.Sometimesfittingthreatsarereadilyavailable.Atothertimes,thereareonly

excessivethreats,whichmustsomehowbescaleddownbeforetheycanbeused.Brinkmanship is perhaps the best scaling device of this kind, and we shallexplainitinChapter9.

8.CASESTUDY#5:BOEING,BOEING,GONE?

Developing a new commercial airplane is a gigantic gamble. The cost ofdesigninganewenginealonecanreachtwobilliondollars.Itisnoexaggerationtosaythatbuildinganewandbetterplanerequires“bettingthecompany”.6Nowonder governments get involved, each trying tomake a largermarket for itsdomesticfirm.

Here we look at the market for 150-passenger medium-range jets: theBoeing 727 and theAirbus 320.Boeing developed the 727 first.Did itmakesenseforAirbustoenterthemarket?

The primarymarket for these aircraftwas in theUnited States and in theEuropean Economic Community (E.E.C.) countries.We assume each of thesemarkets is worth $900 million to a monopoly firm. Were the two firms tocompete head-on, total profits fall from $900 to $600million, divided evenlybetween the two firms. Although profits fall, competition results in cheaperplanesandlowerairfares,soconsumersbenefit.Thesebenefitstoconsumersareworth$700millionineachmarket.

AirbusIndustriesestimatesthatitwillcost$1billiontodeveloptheAirbus320. If they go ahead without any government assistance, they can expect tomakeaprofitof$300millionineachofthemarkets,AmericanandE.E.C.Thetotalof$600millionisnotenoughtocoverthedevelopmentcosts.

The E.E.C. governments cannot offer direct assistance in the form ofsubsidies because their budget is already committed to subsidizing farmers. Inthetraditionaltrade-offbetweengunsandbutter,theE.E.C.hasgoneforbutterandhaslittleleftforeithergunsorAirbuses.

You are called to Brussels and asked for advice on whether the E.E.C.shouldassistAirbusbygivingitaprotectedmarket,thatis,requiringEuropeanairlinestobuytheAirbus320overtheBoeing727.Whatdoyousuggest?HowdoyouexpecttheUnitedStatesgovernmenttorespond?

CaseDiscussionIf the E.E.C. protects its home market and the American market stays open,Airbuswillearn$900millionasamonopolistinEuropeand$300millionasaduopolistintheUnitedStates.Thisisenoughtocoverthedevelopmentcostsof$1billion.

IsthispolicyintheinterestsoftheE.E.C.asawhole?Wehavetoconsiderthegain toAirbusversus the loss toEuropeanconsumers.Withoutaprotectedmarket, Airbus would not enter. Boeing would have a monopoly in Europe.Consumerswouldbenobetteroff.Thereforethereisnolosstoconsumers.TheeconomicgainstotheE.E.C.asawholecoincidewiththeprofitsofAirbus.Itseems that the E.E.C. should support the venture by promising a protectedmarket.

ItisimportantthattheE.E.C.commititselftoprotectionistpolicy.Supposeitkeeps itsoptionsopen, andAirbus enters themarket.At thispoint it doesnothave an incentive to protect Airbus. Keeping the markets open will reduceAirbus’s expectedprofit by$600million (from$200million tonegative$400million), but the competition from Boeing will raise the E.E.C. consumers’benefits by$700million.Knowing this,Airbuswill not enter, because it doesnot have a credible commitment that the E.E.C. governments will maintain aprotectedmarket.

Whatabout theAmericanresponse?If theAmericansactquickly, theytoocancommittoprotectingtheirdomesticmarketbeforeAirbusbeginsproduction.Letuslookaheadandreasonbackward.IftheAmericanmarketiskeptopen,thepictureunfoldsasbefore.BoeingisshutoutofEuropeandmakes$300millionin competitionwith Airbus in the Americanmarket. TheAmerican consumergetsanextra$700millionofbenefitsfromthecompetition.ThetotalgaintotheU.S.economyifitmaintainsanopenmarketis$1,000million.

Say the United States reciprocates and requires American airlines topurchasetheBoeing727overtheAirbus320.Theneventhemonopolyprofitof$900 million in Europe falls short of the Airbus development costs. So theAirbus320willneverbebuilt.Boeingwillenjoyamonopolyinbothmarkets,makingprofitsof$1,800million.ThistotaleconomicgaintotheUnitedStatesisconsiderablyhigherthanwhenitsmarketisopen.7

TheUnitedStatescandefeattheE.E.C.supportforAirbusbyreciprocatingprotectionism.Itisinitsinteresttodoso.

CredibleCommitments

In most situations, mere verbal promises should not be trusted. As SamGoldwynput it, “Averbal contract isn’tworth the paper it’swritten on.”1Anincident in The Maltese Falcon by Dashiell Hammett (filmed by Goldwyn’scompetitorWarnerBrothers,withHumphreyBogartasSamSpadeandSydneyGreenstreet as Gutman) illustrates this point. Gutman gives Sam Spade anenvelopecontainingtenthousanddollars.

Spade looked up smiling. He said mildly: “We were talking about moremoney than this.” “Yes sir, we were,” Gutman agreed, “but, we were talkingthen.Thisisactualmoney,genuinecoinoftherealm.Withadollarofthis,youcanbuymorethanwithtendollarsoftalk.”2

This lessoncanbe tracedall thewayback toThomasHobbes: “Thebondsofwords are too weak to bridle men’s avarice.”3 Women’s too, as King Leardiscovered.

Credibility is a problem with all strategic moves. If your unconditionalmove,orthreatorpromise,ispurelyoral,whyshouldyoucarryitoutifitturnsout not to be in your interest to do so?But thenotherswill look forward andreason backward to predict that you have no incentive to follow through, andyourstrategicmovewillnothavethedesiredeffect.

The whole point behind the strategies of Chapter 5 is to change anopponent’sexpectationsaboutyourresponsestohisactions.Thiswillfailifhebelieves thatyouwillnotcarryout the threatsorpromisesyoumake.Withoutanyeffectonhisexpectations,therewillbenoeffectonhisactions.

An action that can be changed loses strategic effect against a rival whothinksstrategically.Heknowsthatyourutterancesmaynotmatchyouractions

andsoisonthelookoutfortacticalbluffing.A famousexampleof the reversalwasmadeby theRothschilds following

the Battle of Waterloo. The Rothschilds supposedly used carrier pigeons andhencewerethefirsttoknowthebattle’soutcome.WhentheydiscoveredthattheEnglishhadwon,theysoldBritishbondspubliclyandthusledotherstobelievethatEnglandhadlost.ThepriceofBritishgovernmentbondsplummeted.Beforethetruthwasdiscovered,theRothschildssecretlyboughtanevengreaternumberofbondsattherock-bottomprice.*

Had the others in the London stock exchange recognized that theRothschildsmight reverse theirmove in thisway, theywouldhaveanticipatedthe tactical bluffing and it would not have worked. A strategically awareopponentwillexpectyoutomisleadhimandthereforewillnotbeinfluencedbyactionsthatheperceivesasbeingputondisplayforhisbenefit.

Establishingcredibilityinthestrategicsensemeansthatyouareexpectedtocarry out your unconditional moves, keep your promises, and make good onyour threats. Unlike the Rothschilds, you cannot count on an ability to foolpeople.Commitmentsareunlikelytobetakenatfacevalue.Yourcommitmentmaybetested.Credibilitymustbeearned.

Credibility requires finding a way to prevent going back. If there is notomorrow, today’s commitment cannot be reversed. The fact that deathbedtestimony can never be altered leads the courts to give it tremendousweight.Morecommonly,thereisatomorrow(andadayafter)sothatwemustexploretheproblemofhow tomaintaincommitmentover the longhaul. “Feast today,fortomorrowwefast”istheexcuseforputtingontodaywhatcanbetakenofftomorrow.

1.THEEIGHTFOLDPATHTOCREDIBILITYMakingyourstrategicmovescredibleisnoteasy.Butitisnotimpossible,either.Whenwe first raised this issue inChapter 5,we said that tomake a strategicmovecredible,youmusttakeasupportingorcollateralaction.Wecalledsuchanactioncommitment.

We nowoffer eight devices for achieving credible commitments. Like theBuddhistprescriptionforNirvana,wecallthisthe“eightfoldpath”tocredibility.Depending on the circumstances, one or more of these tactics may proveeffectiveforyou.Behindthissystemarethreeunderlyingprinciples.

Thefirstprincipleistochangethepayoffsofthegame.Theideaistomakeit in your interest to follow through on your commitment: turn a threat into a

warning, a promise into an assurance. This can be done through a variety ofways.

1. Establishanduseareputation.2. Writecontracts.

Boththesetacticsmakeitmorecostlytobreakthecommitmentthantokeepit.

Asecondavenueistochangethegametolimityourabilitytobackoutofacommitment.Inthiscategory,weconsiderthreepossibilities.Themostradicalissimplytodenyyourselfanyopportunitytobackdown,eitherbycuttingyourselfofffromthesituationorbydestroyinganyavenuesofretreat.Thereiseventhepossibilityofremovingyourselffromthedecision-makingpositionandleavingtheoutcometochance.

3.Cutoffcommunication.4.Burnbridgesbehindyou.5.Leavetheoutcometochance.

These twoprinciples canbecombined:both thepossible actions and their

outcomes can be changed. If a large commitment is broken down into manysmallerones,thenthegainfrombreakingalittleonemaybemorethanoffsetbythelossoftheremainingcontract.Thuswehave

6.Moveinsmallsteps.

Athirdrouteistouseotherstohelpyoumaintaincommitment.Ateammay

achieve credibility more easily than an individual. Or you may simply hireotherstoactinyourbehalf.

7.Developcredibilitythroughteamwork.8.Employmandatednegotiatingagents.

ReputationIf you try a strategicmove in a game and then back off, youmay lose yourreputation for credibility. In a once-in-a-lifetime situation, reputation may beunimportant and therefore of little commitment value. But, you typically playseveral games with different rivals at the same time, or the same rivals atdifferent times. Then you have an incentive to establish a reputation, and thisservesasacommitmentthatmakesyourstrategicmovescredible.

DuringtheBerlincrisisin1961,JohnF.KennedyexplainedtheimportanceoftheU.S.reputation:

IfwedonotmeetourcommitmentstoBerlin,wherewillwelaterstand?Ifwearenottruetoourwordthere,allthatwehaveachievedincollectivesecurity,whichreliesonthesewords,willmeannothing.4

Anotherexample isIsrael’sstandingpolicynot tonegotiatewith terrorists.This is a threat intended to deter terrorists from taking hostages to barter forransomorreleaseofprisoners.Iftheno-negotiationthreatiscredible,terroristswill come to recognize the futility of their actions. In the meantime, Israel’sresolvewillbetested.Eachtimethethreatmustbecarriedout,Israelsuffers;arefusal tocompromisemaysacrifice Israelihostages’ lives.EachconfrontationwithterroristsputsIsrael’sreputationandcredibiltyontheline.Givinginmeansmore than just meeting the current demands; it makes future terrorism moreattractive.*

Reputation effect is a two-edged sword for commitment. Sometimesdestroying your reputation can create the possibility for a commitment.Destroyingyourreputationcommitsyounottotakeactionsinthefuturethatyoucanpredictwillnotbeinyourbestinterests.

Thequestionofwhethertonegotiatewithhijackershelpsillustratethepoint.Before any particular hijacking has occurred, the governmentmight decide todeterhijackingsbythreateningnevertonegotiate.However,thehijackerspredictthat after they commandeer the jet, the government will find it impossible toenforceano-negotiationposture.Howcanagovernmentdenyitself theabilitytonegotiatewithhijackers?

Oneanswer is todestroy thecredibilityof itspromises. Imagine that afterreaching a negotiated settlement, the government breaks its commitment andattacks the hijackers. This destroys any reputation the government has fortrustworthy treatment of hijackers. It loses the ability to make a credible

promise,andirreversiblydenies itself the temptation torespondtoahijacker’sthreat.Thisdestructionofthecredibilityofapromisemakescrediblethethreatnevertonegotiate.

Congresshasasimilarproblemofmaintainingconsistencyovertimewhenit comes to tax amnesty programs. Such programs allow thosewho owe backtaxes to pay upwithout penalty. This appears to be a costless way of raisingmore revenue. All those who have second thoughts about having cheated ontheir taxes give the government money owed. In fact, if it could be crediblyestablishedthattherewouldneverbeanotheramnesty,thenCongresscouldraiseadditional tax revenuesatnocost.But if amnestywas suchagood ideaonce,whynottryitagaininafewyears?NothingpreventsCongressfromofferinganamnesty on a regular basis. Then a problem arises. Cheating becomes moreattractive,sincethereisthepossibilityofgettingamnestyinthefuture.

Congressmustfindawaytopreventitselffromeverrepeatingtheamnestyprogram. In aWall Street Journal article, Robert Barro and Alan Stockmanproposethatthegovernmentofferataxamnesty,thenrenegeonitspromiseandprosecute thosewho turn themselves in.5Thiswould raise evenmore revenuethan a simple amnesty. And once the government cheats on its amnesty, whowouldbelievethegovernmentwereittotryagain?Bydestroyingitscredibility,thegovernmentcanmakeacrediblecommitmentnottoofferanamnestyagain.

Youwillprobablythinkthisisanabsurdidea,andwithgoodreason.First,itwill not work against strategically aware taxpayers. They will expect thegovernmenttorenegeonitspromise,sotheywillnotparticipateintheamnestyatall.Secondly,andmoreimportantly,catchingtaxcheatersisnottheonlygameintown.Anybenefitsfromdouble-crossingtaxcheaterswillbemorethanoffsetbytheharmtothegovernment’sreputationinotherareas.

Oneofthemostimpressiveexamplesofhowtobuildareputationbelongstothe Mayflower Furniture Company. On a large billboard located along theMassachusettsTurnpike, theyproudly advertise that theyhavegone127yearswithout a sale. (Are they still waiting for their first customer?) Thisunconditionalcommitment toeveryday lowpricesbrings inasteadystreamofcustomers.A salemight temporarily raiseprofits, but itwouldbe another127yearsbeforetheycouldrepeatsuchacleveradvertisement.Nextyear,weexpectthe sign will read 128 years. The reputation becomes self-perpetuating as itbecomesmorevaluable.*

Inall these instances, theplayercultivatesa reputationwith thedirectandconsciousaimofcreatingcredibilityforhisfutureunconditionalcommitments,threats, and promises. However, reputation can also arise for nonstrategic

reasons,andyetbejustaspowerfulinachievingcredibility.Thefeelingofprideinnotbreakingone’swordisanexample.ThomasHobbeswrotethattheweakbondsofwordscanbestrengthenedintwoways:afearof theconsequenceofbreakingone’sword;oraglory,orpride,innotbreakingit.Suchprideisofteninstilled in people’s value system through education or general socialconditioning. It may even have the implicit social aim of improving thecredibilityofourmanifolddailyrelationships.Yetwearenottoldtotakeprideinbeinghonorablebecause itwill bringus strategic advantagebymakingourthreatsandpromisescredible;wearetoldthathonorisagoodthinginitself.

Someonewhohasareputationforbeingcrazycanmakesuccessfulthreatsthatwould be incredible coming from a saner and cooler person. In thisway,apparent irrationality can become good strategic rationality. One can evencultivate such a reputation. A seemingmadman, therefore,may be a superiorstrategist,becausehisthreatsaremorereadilybelieved.CouldColonelGhadafiand Ayatollah Khomeini have understood this principle better than the cool,rational leadersofWesternnations trying todealwith them?Wedonotknow,butwearewillingtobetthatyourchildwhoistooirrationaltobedeterredbyyourthreatsofpunishmentisabetterinstinctivegame-playerthanyouare.

ContractsA straightforward way to make your commitment credible is to agree to apunishmentifyoufailtofollowthrough.Ifyourkitchenremodelergetsalargepayment up front, he is tempted to slow down the work. But a contract thatspecifies payment linked to the progress of the work and penalty clauses fordelay canmake it in his interest to stick to the schedule. The contract is thecommitmentdevice.

Actually,it’snotquitethatsimple.Imaginethatadietingmanofferstopay$500 to anyone who catches him eating fattening food. Every time the manthinks of a dessert he knows that it just isn’t worth $500. Don’t dismiss thisexampleasincredible;justsuchacontractwasofferedbyaMr.NickRusso—excepttheamountwas$25,000.AccordingtotheWallStreetJournal:

So,fedupwithvariousweight-lossprograms,Mr.Russodecidedtotakehisproblemto thepublic. Inaddition togoingona1,000-calorie-a-daydiet,he isoffering a bounty—$25,000 to the charity of one’s choosing—to anyonewhospotshimeatinginarestaurant.Hehaspepperedlocaleateries…with“wanted”

picturesofhimself.6

But this contract has a fatal flaw: there is no mechanism to preventrenegotiation. With visions of eclairs dancing in his head, Mr. Russo shouldargue that under the present contractual agreement, no one will ever get the$25,000penaltysincehewillneverviolate thecontract.Hence, thecontract isworthless. Renegotiation would be in their mutual interest. For example, Mr.Russomightoffertobuyaroundofdrinksinexchangeforbeingreleasedfromthecontract.Therestaurantdinerspreferadrinktonothingandlethimoutofthecontract.7

For the contracting approach to be successful, the party that enforces theactionorcollectsthepenaltymusthavesomeindependentincentivetodoso.Inthedietingproblem,Mr.Russo’sfamilymightalsowanthimtobeskinnierandthusnotbetemptedbyamerefreedrink.

The contracting approach is better suited to business dealings. A brokencontract typicallyproducesdamages, so that the injuredparty isnotwilling togive up on the contract for naught. For example, a producermight demand apenaltyfromasupplierwhofailstodeliver.Theproducerisnotindifferentaboutwhetherthesupplierdeliversornot.Hewouldrathergethissupplythanreceivethe penalty sum.Renegotiating the contract is no longer amutually attractiveoption.

What happens if the supplier tries the dieter’s argument? Suppose heattempts to renegotiate on the grounds that the penalty is so large that thecontractwillalwaysbehonoredandtheproducerwillneverreceivethepenalty.This is just what the producer wants, and hence he is not interested inrenegotiation.Thecontractworksbecausetheproducerisnotsolelyinterestedinthepenalty;hecaresabouttheactionspromisedinthecontract.

It ispossible towrite contractswithneutralparties as enforcers.Aneutralpartyissomeonewhodoesnothaveanypersonalinterestinwhetherthecontractisupheld.Tomakeenforcementcredible,theneutralpartymustbemadetocareaboutwhetherornotthecommitmentiskeptbycreatingareputationeffect.Insomeinstances,thecontractholdermightlosehisjobifheallowsthecontracttobe rewritten. Thomas Schelling provides a remarkable example of how theseideas have been implemented.8 In Denver, one rehabilitation center treatswealthycocaineaddictsbyhaving themwriteaself-incriminating letterwhichwillbemadepubliciftheyfailrandomurineanalysis.Afterplacingthemselvesvoluntarilyinthisposition,manypeoplewilltrytobuytheirwaybackoutofthe

contract.Butthepersonwhoholdsthecontractwilllosehisjobifthecontractisrewritten;thecenterwillloseitsreputationifitfailstofireemployeeswhoallowcontractstoberewritten.

Themoralisthatcontractsalonecannotovercomethecredibilityproblem.Successrequiressomeadditionalcredibilitytool,suchasemployingpartieswithindependent interests in enforcement or a reputation at stake. In fact, if thereputationeffectisstrongenough,itmaybeunnecessarytoformalizeacontract.Thisisthesenseofaperson’swordbeinghisbond.*

CuttingOffCommunicationCuttingoffcommunicationsucceedsasacrediblecommitmentdevicebecauseitcanmakeanactiontrulyirreversible.Anextremeformofthistacticarisesintheterms of a last will and testament. Once the party has died, renegotiation isvirtually impossible. (For example, it took an act of the British parliament tochange Cecil Rhodes’s will in order to allow female Rhodes Scholars.) Ingeneral,wherethereisawill,thereisawaytomakeyourstrategycredible.

Forexample,mostuniversitiessetapriceforendowingachair.Thegoingrateisabout$1.5million.Thesepricesarenotcarvedinstone(norcoveredwithivy). Universities have been known to bend their rules in order to accept thetermsandthemoneyofdeceaseddonorswhofailtomeetthecurrentprices.

Oneneednotdietryingtomakecommitmentscredible.Irreversibilitystandswatchateverymailbox.Whohasnotmailedaletterandthenwishedtoretrieveit? And it works the other way. Who has not received a letter he wishes hehadn’t?Butyoucan’tsenditbackandpretendyou’veneverreaditonceyou’veopenedtheletter.

Before the practice became widespread, a successful commitment devicewas to mail one’s bill payments in unstamped letters with no return address.Mailingaletterwithnoreturnaddressisanirreversiblecommitment.Thepostoffice used to deliver such letters, and the receiver could accept delivery bypayingthepostagedue.Autilityorphonecompanyknewthatsuchaletterwaslikelytocontainacheck.Itwouldratherpaythepostageduethanwaitanotherbilling cycle before receiving payment (or another unstamped letter with noreturnaddress).

Thesolutiontothecompanies’problemcamewhenthepostofficechangeditspolicy.Letterswithoutpostagearenolongerdeliveredtotheaddressee;theyarereturnedtothesenderifthereisareturnaddressandnotdeliveredifthereisno return address.Now the company can commit itself not to receive a letter

withpostagedue.Butwhatifyouputthecompany’saddressasboththemailingaddressand

the return address? Now the post office has someone to return the letter to.Remember,youdidn’thear this ideahere first.And if itbegins to spread, restassuredthatthepostofficeruleswillbechangedsothatletterswithoutastamparenotevenreturnedtothesender.

Thereisaseriousdifficultywiththeuseofcuttingoffcommunicationasadevicetomaintaincommitment.Ifyouareincommunicado,itmaybedifficultifnot impossible tomakesure that therivalhasaccordedwithyourwishes.Youmusthireotherstoensurethatthecontractisbeinghonored.Forexample,willsare carried out by trustees, not the deceased. A parental rule against smokingmaybeexemptfromdebatewhiletheparentsareaway,butunenforceabletoo.

BurningBridgesbehindYouArmies often achieve commitment by denying themselves an opportunity toretreat.Thisstrategygoesbackatleastto1066,whenWilliamtheConqueror’sinvadingarmyburneditsownships,thusmakinganunconditionalcommitmenttofightratherthanretreat.CortésfollowedthesamestrategyinhisconquestofMexico.Uponhisarrival inCempoalla,Mexico,hegaveorders that led toallbutoneofhisshipsbeingburntordisabled.Althoughhissoldierswerevastlyoutnumbered, they had no other choice but to fight and win. “Had [Cortés]failed,itmightwellseemanactofmadness….Yetitwasthefruitofdeliberatecalculation….Therewasnoalternativeinhismindbuttosucceedorperish.”9

Destroying the ships gave Cortés two advantages. First, his own soldierswereunited,eachknowingthattheywouldallfightuntiltheendsincedesertion(orevenretreat)wasanimpossibility.Second,andmoreimportant,istheeffectthis commitment had on the opposition. They knew that Cortés must eithersucceedorperish,whiletheyhadtheoptiontoretreatintothehinterland.Theychose to retreat rather than fight suchadeterminedopponent.For this typeofcommitmenttohavetheproposedeffects,itmustbeunderstoodbythesoldiers(yoursandtheenemy’s),notjustbythearmchairstrategists.Thusitisespeciallyinterestingthat“thedestructionofthefleet[was]accomplishednotonlywiththeknowledge, but the approbation of the army, though at the suggestion ofCortés.”10

Thisideaofburningone’sownshipsdemonstratestheevolutionofstrategicthinkingovertime.TheTrojansseemedtogetitallbackwardwhentheGreekssailedtoTroytorescueHelen.*TheGreekstriedtoconquerthecity,whilethe

Trojans tried to burn the Greek ships. But if the Trojans had succeeded inburningtheGreekfleet, theywouldsimplyhavemadetheGreeksall themoredeterminedopponents.Infact,theTrojansfailedtoburntheGreekfleetandsawtheGreeks sail home in retreat.Of course theGreeks left behind agift horse,whichinretrospecttheTrojanswereabittooquicktoaccept.11

Inmodern times, thisstrategyapplies toattackson landaswellasbysea.For many years, Edwin Land’s Polaroid corporation purposefully refused todiversify out of the instant photography business.With all its chips in instantphotography,itwascommittedtofightagainstanyintruderinthemarket.

OnApril20,1976,after twenty-eightyearsofaPolaroidmonopolyontheinstant photography market, Eastman Kodak entered the fray: it announced anewinstantfilmandcamera.Polaroidrespondedaggressively,suingKodakforpatentinfringement.EdwinLand,founderandchairman,waspreparedtodefendhisturf:

Thisisourverysoulweareinvolvedwith.Thisisourwholelife.Forthemit’sjustanotherfield. Wewillstayinourlotandprotectthatlot.12

MarkTwainexplainedthisphilosophyinPudd’nheadWilson:

Behold,thefoolsaith,“Putnotallthineeggsinonebasket” butthewisemansaith,“PutallyoureggsinonebasketandWATCHTHATBASKET.”13

ThebattleendedonOctober12,1990.ThecourtsawardedPolaroida$909.4millionjudgmentagainstKodak.*Kodakwasforcedtowithdrawitsinstantfilmandcamerafromthemarket.AlthoughPolaroidrestoreditsdominanceovertheinstant photography market, it lost ground to competition from portablevideocassette recorders and minilabs that developed and printed conventionalfilm inonehour.Lackingbridges,Polaroidbegan to feel trappedona sinkingisland.Withachangeinphilosophy,thecompanyhasbeguntobranchoutintovideofilmandevenconventionalfilm.

Oneneednot literallyburnbridges,nor ships thatbridgeoceans.Onecanburn bridges figuratively by taking a political position that will antagonizecertain voters. WhenWalter Mondale said in accepting the 1984 Democratic

presidentialnominationthathewouldraisetaxesifelected,hewasmakingsuchacommitment.Voterswhobelievedinsupply-sideeconomicswereirretrievablylost,andthismadeMondale’spositionmorecredibletothosewhofavoredataxincreaseinordertoreducethedeficit.Unfortunately(forMondale)thegroupofvotersantagonizedbythismoveturnedouttobefartoolarge.

Finally, building rather than burning bridges can also serve as a crediblesource of commitment. In the December 1989 reforms in Eastern Europe,building bridgesmeant knocking downwalls. Responding tomassive protestsandemigration,EastGermany’sPrimeMinisterEgonKrenzwantedtopromisereformbutdidn’thavea specificpackage.Thepopulationwas skeptical.Whyshouldtheybelievethatthevaguepromiseofreformwouldbegenuineandfar-reaching?EvenifKrenzwastrulyinfavorofreform,hemightfalloutofpower.DismantlingpartsoftheBerlinWallhelpedtheEastGermangovernmentmakeacrediblecommitment to reformwithouthaving todetail all the specifics.By(re)openingabridgetotheWest,thegovernmentforceditselftoreformorriskan exodus. Since it would be possible to leave in the future, the promise ofreformwas both credible andworthwaiting for. Reunificationwas to be lessthanayearaway.

LeavingtheOutcomebeyondYourControlThe doomsday device in themovieDr. Strangelove consisted of large buriednuclearbombswhoseexplosionwouldemitenoughradioactivitytoexterminatealllifeonearth.ThedevicewouldbedetonatedautomaticallyintheeventofanattackontheSovietUnion.WhenPresidentMiltonMuffleyoftheUnitedStatesaskedifsuchanautomatictriggerwaspossible,Dr.Strangeloveanswered:“Itisnotmerelypossible;itisessential.”

Thedeviceissuchagooddeterrentbecauseitmakesaggressiontantamounttosuicide.*FacedwithanAmericanattack,SovietpremierDimitriKissovmightrefrainfromretaliatingandriskingmutuallyassureddestruction.AslongastheSoviet premier has the freedom not to respond, the Americans might risk anattack.Butwiththedoomsdaydeviceinplace,theSovietresponseisautomaticandthedeterrentthreatiscredible.

However,thisstrategicadvantagedoesnotcomewithoutacost.Theremightbe a small accident or unauthorized attack, afterwhich the Sovietswould notwanttocarryouttheirdirethreat,buthavenochoiceasexecutionisoutoftheircontrol.ThisisexactlywhathappenedinDr.Strangelove.

Toreducetheconsequencesoferrors,youwantathreat that isnostronger

thanisnecessarytodetertherival.Whatdoyoudoiftheactionisindivisible,asanuclearexplosionsurelyis?Youcanmakethethreatmilderbycreatingarisk,butnotacertainty,thatthedreadfuleventwilloccur.ThisisThomasSchelling’sideaofbrinkmanship.HeexplaineditinhisbookTheStrategyofConflict:

Brinkmanship is…thedeliberatecreationofa recognizable risk,a risk thatone does not completely control. It is the tactic of deliberately letting thesituationget somewhatoutofhand, justbecause itsbeingoutofhandmaybeintolerable to theotherpartyandforcehisaccommodation. Itmeansharassingandintimidatinganadversarybyexposinghimtoasharedrisk,ordeterringhimbyshowingthatifhemakesacontrarymovehemaydisturbussothatweslipoverthebrinkwhetherwewanttoornot,carryinghimwithus.14

The use of brinkmanship formed the basis of the U.S. nuclear deterrentpolicy.Duringthecoldwar,theUnitedStatesdidnotneedtoguaranteeanuclearretaliation if theSoviets invadedEurope.Evena small chanceofnuclearwar,say 10 percent,was enough to deter the Soviets.A 10 percent chance is one-tenth the threat and consequently requiredmuch less commitment in order toestablishcredibility.While theSovietsmightnothavebelievedthat theUnitedStates would surely retaliate, they couldn’t be sure that Americans wouldn’teither. There was always the possibility that a Soviet attack would start anescalatorycyclethatgotoutofcontrol.

Thisbriefdescriptiondoesnotdobrinkmanshipjustice.Tobetterunderstandthe probabilistic threats behind brinkmanship, Chapter 7 develops the role ofmixed strategies.Then inChapter8wegivebrinkmanship the full attention itdeserves.

MovinginStepsAlthoughtwopartiesmaynot trusteachotherwhenthestakesarelarge, if theproblemofcommitmentcanbereducedtoasmall-enoughscale,thentheissueofcredibilitywill resolve itself.The threatorpromise isbrokenup intomanypieces,andeachoneissolvedseparately.

Honoramongthievesisrestorediftheyhavetotrusteachotheronlyalittlebit at a time. Consider the difference between making a single $1 millionpayment to another person for a kilogram of cocaine and engaging in 1,000sequential transactions with this other party, with each transaction limited to$1,000 worth of cocaine.While it might be worthwhile to double-cross your“partner” for $1 million, the gain of $1,000 is too small, since it brings aprematureendtoaprofitableongoingrelationship.

Wheneveralargedegreeofcommitmentisinfeasible,oneshouldmakedowith a small amount and reuse it frequently.Homeowners and contractors aremutually suspicious. The homeowner is afraid of paying up front and findingincomplete or shoddy work. The contractors are afraid that after they havecompletedthejob,thehomeownermayrefusetopay.Soattheendofeachday(oreachweek),contractorsarepaidonthebasisoftheirprogress.Atmosteachsideriskslosingoneday’s(oroneweek’s)work.

Aswithbrinkmanship,movinginsmallstepsreducesthesizeofthethreatorpromiseandcorrespondinglythescaleofcommitment.Thereisjustonefeaturetowatchout for.Thosewhounderstand strategic thinkingwill reason forwardandlookbackward,andtheywillworryaboutthelaststep.Ifyouexpecttobecheatedonthelastround,youshouldbreakofftherelationshiponeroundearlier.Butthenthepenultimateroundwillbecomethefinalround,andsoyouwillnothaveescapedtheproblem.Toavoidtheunravelingof trust, thereshouldbenoclearfinalstep.Aslongasthereremainsachanceofcontinuedbusiness,itwillneverbeworthwhile tocheat.Sowhenashadycharacter tellsyou thiswillbehislastdealbeforeretiring,beespeciallycautious.

TeamworkOftenotherscanhelpusachievecrediblecommitment.Althoughpeoplemaybeweakon theirown, theycanbuild resolveby formingagroup.Thesuccessfuluse of peer pressure to achieve commitment has been made famous byAlcoholics Anonymous (and diet centers too). The AA approach changes thepayoffs frombreakingyourword. It setsupa social institution inwhichprideandself-respectarelostwhencommitmentsarebroken.

Sometimes teamworkgoes farbeyondsocialpressureandemploysstrong-armtacticstoforceustokeeptruetoourpromises.Considertheproblemforthefront lineof anadvancingarmy. If everyoneelse charges forward,one soldierwho hangs back ever so slightly will increase his chance of survival withoutsignificantlyloweringtheprobabilitythattheattackwillbesuccessful.Ifeverysoldierthoughtthesameway,however,theattackwouldbecomearetreat.

Ofcourseitdoesn’thappenthatway.Asoldierisconditionedthroughhonortohiscountry,loyaltytofellowsoldiers,andbeliefinthemillion-dollarwound—an injury that is seriousenough tosendhimhome,outofaction,butnotsoserious thathewon’t fully recover.15Those soldierswho lack thewill and thecourage to follow orders can be motivated by penalties for desertion. If thepunishment for desertion is certain and ignominious death, the alternative of

advancingforwardbecomesmuchmoreattractive.Butsoldiersarenotinterestedinkilling their fellowcountrymen,evendeserters.Howcansoldierswhohavedifficultycommittingtoattacktheenemymakeacrediblecommitmenttokillingtheircountrymenfordesertion?

TheancientRomanarmymadefallingbehindinanattackacapitaloffense.Asthearmyadvancedinaline,anysoldierwhosawtheonenexttohimfallingbehindwasorderedtokillthedeserterimmediately.Tomakethisordercredible,failing tokilladeserterwasalsoacapitaloffense.Thuseven thoughasoldierwouldrathergetonwiththebattlethangobackafteradeserter,failingtodosocouldcosthimhisownlife.*

ThetacticsoftheRomanarmyliveontodayinthehonorcoderequiredofstudentsatWestPoint.Examsarenotmonitored,andcheatingisanoffensethatleads to expulsion. But, because students are not inclined to “rat” on theirclassmates, failure to report observed cheating is also a violationof thehonorcode.Thisviolation also leads to expulsion.When thehonor code is violated,students reportcrimesbecause theydonotwant tobecomeguiltyaccomplicesbytheirsilence.Similarly,criminallawprovidespenaltiesforthosewhofailtoreportacrimeasanaccessoryafterthefact.

MandatedNegotiatingAgentsIf aworker sayshe cannot accept anywage increase less than5percent,whyshouldtheemployerbelievethathewillnotsubsequentlybackdownandaccept4percent?Moneyonthetableinducespeopletotrynegotiatingonemoretime.

Theworker’ssituationcanbeimprovedifhehassomeoneelsenegotiateforhim.Whentheunionleaderisthenegotiator,hispositionmaybelessflexible.Hemaybeforcedtokeephispromiseor losesupportfromhiselectorate.Theunion leader may secure a restrictive mandate from his members, or put hisprestigeon the linebydeclaringhis inflexibleposition inpublic. Ineffect, thelabor leader becomes a mandated negotiating agent. His authority to act as anegotiator isbasedonhisposition. Insomecaseshesimplydoesnothave theauthoritytocompromise;theworkers,nottheleader,mustratifythecontract.Inothercases,compromisebytheleaderwouldresultinhisremoval.

Inpracticeweareconcernedwiththemeansaswellastheendsofachievingcommitment. If the labor leader voluntarily commits his prestige to a certainposition, should you (do you) treat his loss of face as you would if it wereexternally imposed?Someonewho tries to stopa trainby tyinghimself to therailroadtracksmaygetlesssympathythansomeoneelsewhohasbeentiedthere

againsthiswill.Asecondtypeofmandatednegotiatingagentisamachine.Veryfewpeople

hagglewithvendingmachinesovertheprice;evenfewerdososuccessfully.*

Thiscompletesouraccountoftheeightfoldwaytosuccessfulcommitment.In practice, any particular situationmay requiremore than one. Here are twoexamples.

2.BUTONELIFETOLAYDOWNFORYOURCOUNTRYHowcananarmygettheenemytobelievethatitssoldierswillinfactlaydowntheir lives for theircountrywhencalledupon todoso?Mostarmieswouldbefinishedifeachsoldieronthebattlefieldstartedtomakearationalcalculationofthecostsandthebenefitsofriskinghislife.Otherdeviceshavetobefound,andthey includemanyof theonesabove.Wehavealreadymentionedthe tacticofburning bridges, and the role of punishments and teamwork in deterringdesertion.Nowweconcentrateonthedevicestomotivateindividualsoldiers.

The process begins in the boot camp. Basic training in the armed forceseverywhereisatraumaticexperience.Thenewrecruitismaltreated,humiliated,andputundersuchimmensephysicalandmentalstrainthatthefewweeksquitealterhispersonality.Animportanthabitacquiredinthisprocessisanautomatic,unquestioning obedience. There is no reason why socks should be folded, orbedsmade,inaparticularway,exceptthattheofficerhassoordered.Theideaisthat the same obedience will occur when the order is of greater importance.Trained not to question orders, the army becomes a fighting machine;commitmentisautomatic.

Theseemingirrationalityofeachsoldierthusturnsintostrategicrationality.Shakespeareknewthisperfectlywell;inthenightbeforethebattleofAgincourt,KingHenryVprays:

OGodofbattles!steelmysoldiers’hearts;Possessthemnotwithfear;takefromthemnow

Thesenseofreckoning, if th’opposednumbersPlucktheirheartsfromthem…(italicsadded)

Nextcomesthepridethatisinstilledineachsoldier:prideinone’scountry,

pride in being a soldier, and, perhaps above all, pride in the tradition of thefightingunit.TheU.S.MarineCorps,famousregimentsoftheBritishArmy,andthe French Foreign Legion exemplify this approach. Great deeds from pastbattlesfoughtbytheunitareconstantlyremembered,heroicdeathsareglorified.

Constant repetitionof thishistory ismeant togivenewrecruitsapride in thistradition,andaresolvenottoflinchfromsimilardeedswhenthetimecomes.

Commandersoftroopsalsoappealtoafarmorepersonalsenseofprideoftheir men. According to Shakespeare, King Henry V inspired his troops atHarfleur thus: “Dishonour not your mothers; now attest that those you call’dfathersdidbegetyou.”Pride isoftenanelitistemotion; itconsists indoingorhavingsomethingthatmostotherslack.Thus,again,wehaveHenryVspeakingtohistroopsbeforethebattleofAgincourt:

Wefew,wehappyfew,webandofbrothers;Forhe to-day thatshedshisbloodwithmeShallbemybrother;…

AndgentlemeninEnglandnowa-bedShall thinkthemselvesaccurs’dtheywerenothereAndholdtheirmanhoodscheapwhilesanyspeaksThatfoughtwithusuponSaintCrispin’sday.

There is also the use of commitment through a combinationof teamwork,

contracting, and burning one’s bridges. Once again we turn to Shakespeare’sHenryVspeakingtohistroopsbeforethebattleofAgincourt.

That he which hath no stomach to this fight, Let him depart; hispassport shall be made, And crowns for convoy put into his purse: Wewouldnotdieinthatman’scompanyThatfearshisfellowshiptodiewithus.

Ofcourseeveryoneistooashamedtotakethisofferuppublicly.Butevenso,bytheir act of rejecting the offer, the soldiers have psychologically burned theirships home.They have established an implicit contractwith each other not toflinchfromdeathifthetimecomes.HenryV’sbrilliantunderstandingofhowtomotivateandcommithisarmytobattleisreflectedinsuccessonthebattlefield,evenwhenvastlyoutnumbered.

3.ANOFFERYOUCAN’TREFUSEIt’snotonlyinthefilmTheGodfatherthatonehearsan“offeryoucan’trefuse.”Withminorvariations,thissituationarisessurprisinglyoften.

At the end of what appeared to be a successful job interview, our friendLarrywasaskedwherethefirmrankedinhislistofpotentialemployers.Beforeanswering,hewas told that the firmhiredonly thoseapplicantswho ranked itfirst. If thefirmwas infacthis firstchoice, then theywantedhimtoaccept in

advance a job offer should one bemade.*With this prospect of an “offer youcan’trefuse”(becauseotherwiseyoudon’tgetit),whatshouldLarryhavedone?

WiththeX-rayvisionofgametheory,wecanseethroughthisploy.Thefirmclaims that itwants to hire only peoplewho rank it first.However, the effectthesepressure tacticshave is theoppositeofwhat theyclaim. If thefirmtrulywantedtohaveemployeeswhorankeditfirst,thenitshouldnotmakejoboffersconditional on the applicant’s ranking of the firm. If, after completing theinterview process, the firmwas in fact Larry’s first choice, then the firm canexpecthimtoacceptitsoffer.Nofirmneedworryabouthavingitsofferturneddownbysomeonewhomostwantstoworkthere.Ontheotherhand,ifthefirmwasinfactLarry’ssecondchoice,butLarry’sfirst-choicefirmhadyettomakeanoffer, thenhemightbewilling toaccepthissecond-choice job toavoid theriskofgettingnone.The firm’spressure tacticof saying that itwilloffer jobsonlytothosewhoacceptfirsthastheeffectofhiringcandidateswhodonotinfactrankthefirmfirst.

Moretruthfulandwhattheyreallymeanis,“Wewantyoutoworkforus.Ifyourankusfirst,thenweknowwe’llgetyou.However,ifyourankussecond,wemightloseyou.Togetyouevenifwearenotyourfirstchoice,wewantyoutoagreeinadvancetoacceptourofferoryouwillgetnoneatall.”Seeninthislight,thisdoesnotseemtobeacrediblethreat.ThefirmwantstohireLarrysomuchthatitiswillingtotakehimevenifitisnothisfirstchoice.Atthesametime,itclaimsthatifLarryrefusestoacceptinadvance,butinsteadcomesbacklatertoaccept,itwillnolongerofferhimajob.Itispossiblebutunlikely.

Our friendLarry explained that hewas only beginning his interviews andthushad too little information tomakea ranking.The firm remindedhim thatunless he accepted in advance, he would not be offered a job. He left theWednesdayinterviewwithoutanoffer.ThatFriday,hereceivedanofferonhisansweringmachine.Mondaytherewasanothermessagereiteratingtheoffer.OnWednesday, a telegram arrived offering a sign-on bonus. It is hard tomake acrediblecommitmentnottoofferajobtosomeoneyouwanttohire.

Whatcouldthefirmhavedonetomakeitsthreatcredible?Here,teamworkcanhelp,butnot in theusual sense.Once thereare severalpeoplewithhiringpower, it ispossible that shouldyounot accept immediately, thecoalition thatsupportedyourcandidacymaybreakdowninfavorofsomelaterapplicant.Aswe will see in Chapter 10 on voting, the order in which candidates areconsideredmaydeterminetheultimatedecision.Inthiswayadecisionmadebyacommitteeissufficientlydependentonchancethatitcannotpromisethatgiventhesameinputsitwillreachthesameverdict.Acommittee’sinabilitytocommit

itselfto“rational”decision-makingmakesthetake-it-or-leave-itthreatcredible.An offer valid now but not necessarily later prevents people from

comparisonshopping.Stereostoresandcardealersusethistactictogreateffect.Buthowdothesesalesmenmakecredibletheirthreattoturndowntomorrowanoffer that theywould accept today?The answer is that businessmay turn up,cash-flowproblemsmaybelessened.Astheyarefondofsaying,thisisaonce-in-a-lifetimeopportunity.

4.CASESTUDY#6:WOULDYOURATHERRENTA

COMPUTERFROMIBM?

Afterabattlethatlastedlongerthantwelveyears,UnitedStatesv.IBMstandsasamonumental eyesore of antitrust litigation.One of themany issues revolvedaroundIBM’spolicyofleasingratherthansellingitsmainframecomputers.

The government argued that IBM’s emphasis on short-term leasesconstituted an entry barrier resulting in monopoly profits. IBM defended thepractice as being in consumers’ interest. It argued that a short-term leaseinsulates customers from the risk of obsolescence, provides flexibility whenneeds change, commits IBM to maintain its leased equipment (since it isresponsible for the operation of the leased computers), and provides financingfromthecompanywiththedeepestpockets.16

Many find these arguments a convincing defense. Yet there is a strategicadvantage to leasing that seems to have been overlooked by both sides. Howwould you expect prices to differ if IBM primarily sold its large mainframemachinesratherthanleasedthem?

CaseDiscussionEven a company without an outside competitor must worry about competingwithitsfutureself.Whenanewcomputerisintroduced,IBMcansell thefirstmodelsatveryhighprices tocustomers impatientlyawaiting the technologicaladvance. Once the computers are available in large numbers, there is thetemptation to lower the price and attract more customers. The main cost ofproducing the computer has already been incurred in the development stage.Eachadditionalsaleisgravy.

Hereinliestheproblem.IfcustomersexpectthatIBMisabouttolowerits

price,theywillwaittomaketheirpurchase.Whenthemajorityofcustomersarewaiting, IBMhasan incentive to speedup itsprice reductionsandcapture thecustomers sooner. This idea, first expressed by University of Chicago lawprofessor Ronald Coase, is that for durable goods, in effect, a monopolistcompeteswithitsfutureselfinawaythatmakesthemarketcompetitive.17

Leasing serves as a commitment device that enables IBM to keep priceshigh.TheleasingcontractsmakeitmuchmorecostlyforIBMtoloweritsprice.Whenitsmachinesareonshort-termleases,anypricereductionmustbepassedalong toall customers, not just the oneswho haven’t yet bought. The loss inrevenue from the existing customer base may outweigh the increase in newleases. In contrast, when the existing customer base owns its computers, thistrade-off does not arise; the customerswho already bought the computer at ahighpricearenoteligibleforrefunds.

Thus leasing is an example of moving in small steps. The steps are thelengthofthelease.Theshorterthelease,thesmallerthestep.Customersdon’texpectIBMtokeepitspricehighwhenthestepsaretoobig;theywillwaitforaprice reduction andget the samemachine a little later at a lowerprice.But ifIBMleasesitscomputersonlyonshort,renewablecontracts,thenitcancrediblymaintainhighprices,customershaveno reason towait,and IBMearnshigherprofits.

Ascollegeprofessorsandauthors,weencounterthesameproblemclosertohome in the market for academic textbooks. If commitment were possible,publishers could raise profits by bringing out new editions of a textbookon afive-yearcycle,ratherthanthemorecommonthree-yearcycle.Greaterlongevitywould increase the text’svalueon theused-bookmarket andconsequently thestudent’sinitialwillingnesstopaywhenaneweditionappears.Theproblemisthat once theusedbooks are out there, thepublisher has a strong incentive toundercut this competition by bringing out a new edition. Because everyoneexpectsthistohappen,studentsgetalowerpricefortheirusedbooksandthusarelesswillingtopayfortheneweditions.ThesolutionforthepublisheristhesameasforIBM:rentbooksratherthansellthem.

Unpredictability

In the 1986 baseballNational League championship series, theNewYorkMetswonacrucialgameagainsttheHoustonAstroswhenLenDykstrahitDaveSmith’ssecondpitchforatwo-runhomerunintheninthinning.Thetwoplayerslatertalkedaboutwhathappened.1Dykstrasaid,“Hethrewmeafastballonthefirst pitch and I fouled it off. I had a gut feeling then that he’d throw me aforkball next, and he did. I got a pitch I saw real well, and hit it real well.”AccordingtoSmith,“Whatitboilsdownto,isthatitwasbadpitchselection.”By that he meant Dykstra was guessing that, because the first pitch was afastball,Smithwouldalterthevelocity.“IfIhadittodooveragain?Itwouldbe[another]fastball.”

ShouldSmithadopt thestrategyof throwinganother fastball thenext timesuchasituationarises?Ofcoursenot.Thebattercansee through this levelofSmith’sthinking,andexpectafastball.ButthenSmithshouldmovegearstothenext level of thinking, and throw a forkball, after all.And so on. There is nodefinite stopping point to this process. The batter can see through and exploitany systematic thinking and action by the pitcher, and vice versa. The onlysensiblecourseofactionforbothistobeunpredictable.*

In thesesituations,aclassicmistake in strategic thinking is tobelieve thatyou can predict your rival’smoves simply bywearing his shoes.We see thismistake in David Halberstam’s book The Summer of ’49 as he describes thestrategicawakeningoftheseventeen-year-oldTedWilliams.2

Like so many other young players, Williams had trouble with breakingpitches.Hewasnever ready for them.Onceapitchergothimoutonacurve.Williams,furiouswithhimself,trottedbacktohispositionintheoutfield.OneoftheSanDiegopitchers, a formermajor-leaguer, yelledover to him, “Heykid,what’dhegetyououton?”“Agoddamnslowcurve,”Williamsanswered.“Can

you hit his fastball?” the pitcher continued. “You bet,” Williams answered.“What do you think he’ll be looking to put past you next time?” the pitcherasked.Therewasabriefpause.TedWilliamshadneverthoughtaboutpitchingto Ted Williams—that was something pitchers did. “A curve,” he answered.“Heykid,”thepitchersaid,“whydon’tyougoupthereandwaitonitthenexttime.”Williamsdid,andhit theballoutforahomerun.Thusbeganatwenty-five-yearstudyofthemindofthepitcher.

Apparently the pitcher hadn’t learned the need to be unpredictable, but thenneither had Williams, for if Williams were thinking about how to pitch toWilliams, he wouldn’t throw a curve when he recognized that Williams wasexpecting it!This chapter showswhat to expectwhenboth sides are trying tooutsmart theother.Even thoughyou can’t guess right all the time, you can atleastrecognizetheodds.

Correctly anticipating and responding to unpredictability is useful wellbeyond thebaseball diamond.Unpredictability is a critical elementof strategywheneveronesidelikesacoincidenceofactions,whiletheotherwishestoavoidit.TheIRSwantstoauditthosewhohaveevadedtaxes,whilethosewhohavecheatedhopetoavoidanaudit.Amongchildren,theoldersiblingusuallywantstoavoidhavingtheyoungeronetagalong;theyoungeroftenlookstofollowtheolder’sfootsteps,literally.Aninvadingarmywantstoachievetacticalsurpriseinits choice of the place to attack; the defending armywants to concentrate itsforceonthespotwheretheattackcomes.

The setters of fashion in nightclubs, restaurants, clothing, and art wantexclusivity;thegeneralpublicwantstominglewiththetrendsetters.Eventually,the“in”placesarediscovered.Butbythenthebeautifulpeoplehavemovedontosomewhereelse.Thishelpsexplaintheshortlifespanofnightclubs.Onceanightclubgets tobesuccessful, toomanypeoplewant togo there.Thisdrivesthe trendsettersawayand theystart anew fadsomewhereelse.AsYogiBerrasaid,“Theplaceissocrowded,noonegoesthereanymore.”

Whilethebaseballplayer’schoiceofpitchortheIRS’sdecisionofwhomtoauditonanyoneoccasionmaybeunpredictable,therearerulesthatgoverntheselection.Therightamountofunpredictability shouldnotbe left tochance. Infact, the odds of choosing one pitch over another or ofwhom to audit can bepreciselydeterminedfromtheparticularsofthegame.“Thoughthisbemadness,yetthereismethodin’t.”Hereweexplainthemethod.

1.HOWTOEVENTHEODDSManyof youwill remember a game fromelementary school called “one-two-three shoot” or “matching fingers.” In this contest, oneof theplayers chooses“evens”andtheotherplayergets“odds.”Onthecountofthree,eachofthetwoplayerssimultaneouslycastsouteitheroneortwofingers.Ifthetotalnumberoffingers is even, the “evens” player wins, while if the sum is odd, the “odds”playerwins. Suppose the loser pays thewinner a dollar.We can compute theusualtableofwinsandlossesinrelationtothechoicesofstrategies.

Payoffsto[“Evens,”“Odds”]

Thereisnoequilibriumtothisgameifthetwoplayersdonotactrandomly.

Imaginethat“Odds”weretoplay1fingerwithcertainty.“Evens”wouldalwayschoose toplay1fingeraswell.Nowthe logic turnson itself.Since“Odds” iscertainthathisopponentwilldisplay1finger,hewillchoosetoshow2fingers.Thisleads“Evens”torespondwith2fingers.Inwhichcase,“Odds”willplay1finger.Wearebackwherewestarted,andthereisnoendinsighttothiscircularreasoning.

Aneasywaytocheckifrandomnessisneededistoconsiderwhetherthereisanyharm in letting theother player seeyourmovebefore he responds.Whenunpredictability is needed, it would be disadvantageous to move first. Thinkwhat would happen in “one-two-three shoot” if you moved first: you wouldalwayslose.

Notjustanyrandomnesswilldo.SupposeOddschooses1finger75percentofthetimeand2fingers25percentofthetime.ThenEvens,bychoosing1,canwin75percentofthetime,andonaverageget.75×1+.25×(-1)=.5dollarsper play. Similarly, the choice of 2 would lose Evens fifty cents per play on

average.SoEvenswouldchoose1.ButthenOddsshouldbechoosing2,notthe75:25mixture.Themixturewouldnotsurvivethesuccessiveroundsofthinkingabouteachother’sstrategy.

Inotherwords,thereisanequilibriumpatternofrandomness,andithastobe calculated. In this example, the whole situation is so symmetric that theequilibriummix has to be 50:50 for each player. Let us try that out. If Oddschooses1and2equallyoften,thenEvenswins.5×1+.5×(-1)=0perplayonaverage,whetherheplays1or2.Thereforehealsowins0onaveragewhenheplayshis50:50mix.Theargumentalsoworkstheotherwayaround.Sothetwo50:50mixesarebestresponsestoeachother,thatis,anequilibrium.Thenamefor this solution is a “mixed-strategy” equilibrium, reflecting the necessity fortheindividualstorandomlymixtheirmoves.

The equilibrium mix in more general situations is not so evident fromsymmetry, but there are some simple rules for calculating it.We develop therulesusingthegameoftennis.

2.ANYONEFORTENNIS?

Oneofthefirststrategiclessonsintennisisnottocommittoadirectionuntilthelast possible fraction of a second. Otherwise, the opponent can exploit yourguess and hit the ball the other way. But even when one can’t observe theopponent’smove,thereisagreatadvantagetopredictingit.Iftheserveralwaysaims to the receiver’s backhand, the receiverwill prepare his grip and start tomovetowardthatsideinanticipation,andconsequentlywillbemoreeffectiveinthereturnofserve.Theserver,therefore,attemptstobeunpredictableinordertopreventthereceiverfromsuccessfullysecond-guessinghisaim.Conversely,thereceivermust not exclusively favor one side or the other inmaking his initialmove.Unlikematchingfingers,playersshouldnotequateunpredictabilitywitheven odds. Players can improve their performance by systematically favoringoneside,althoughinanunpredictableway.

Forconcreteness,letusthinkofapairofplayerswithparticularskills.Thereceiver’s forehand is somewhat stronger. If he anticipates correctly, hisforehand returnwillbe successful90percentof the time,whileananticipatedbackhand returnwillbe successfulonly60percentof the time.Ofcourse, thereturnerfaresworseifhestartstomovetoonesideandtheservicegoestotheother.Ifhegoestothebackhandsidewhiletheserviceistohisforehand,hecan

shiftandreturnsuccessfullyonly30percentofthetime.Theotherwayaround,hischancesare20percent.Wecanshowallthisusingthetablebelow.

ProbabilityThatReceiverSuccessfullyReturnsServe

Theserverwantstokeepthesuccessfulreturnpercentageaslowaspossible;

thereturnerhasexactlytheoppositeinterest.Beforethematch,thetwoplayerschoosetheirgameplans.Whatisthebeststrategyforeachside?

If the server alwaysaimshis serves toward the forehand, the receiverwillanticipatethemovetohisforehandandsuccessfullyreturntheserves90percentof the time. If the server always aimshis serves to thebackhand, the receiverwillanticipate themovetowardhisbackhandandwill return60percentof theservessuccessfully.

Onlybymixinghis aimcan the server reduce the receiver’s effectiveness.He keeps the receiver guessing and therefore unable to take full advantage ofanticipatingthecorrectposition.

Supposetheservertossesanimaginarycoinjustbeforeeachserve,andaimstotheforehandorbackhandaccordingtowhetherthecoinshowsheadsortails.Nowlookwhathappenswhenthereceivermovestotheforehandposition.Thisguesswill be correct only half the time.When correct, the forehand return issuccessful 90 percent of the time, and when the move to the forehand is anincorrect guess, the receiver’s successful return rate falls to 20 percent. Hisoverall success rate is (1/2)90%+ (1/2)20%=55%.By a similar argument, amove toward thebackhand leads to successful returns (1/2)60%+ (1/2)30%=45%ofthetime.

Giventhe50:50mixingruleoftheserver,thereceiverchoosestheoptionsbest from his perspective. He should move toward his forehand, and thepercentageofsuccessful returnswillbe55%.For theserver, this isalreadyan

improvement over the outcomewhen he aims his serve the sameway all thetime.Forcomparison, thereceiver’ssuccessrate is90percentor60percent iftheserveraimsexclusivelytowardforehandorbackhandserves,respectively.

Thenextobviousquestionis,whatistheserver’sbestmix?Toanswerthis,we show the consequences of the variousmixes in a chart.Thepercentageoftimestheserveraimstowardforehandgoeshorizontallyfrom0percent to100percent.Foreachofthesemixtures,oneofthetwolinesinthechartshowsthereceiver’s success rate when he anticipates a move toward the forehand; theother, his success rate when he expects a move toward the backhand. Forexample, if the receiver anticipates amove to the forehand, the zero-percent-forehand(i.e.,backhand)servepolicyholdsthereceivertoa20percentsuccessrate, while the hundred-percent-forehand serve policy allows a 90 percentsuccessrate.Thereceiver’ssuccesspercentagerisesalongthestraightlinefromoneendtotheother.

The two linesmeet at the pointwhere the server aims at the forehand 40

percentofthetime.Totheleftofthis,thereceiverdoesbetterbyanticipatingaservicetothebackhand;totheright,hedoesbetterbyanticipatingaservicetotheforehand.*

The40:60mixtureofforehandstobackhandsistheonlyonethatcannotbeexploitedbythereceivertohisownadvantageinthisway.Onlyatthismixtureisitthecasethatthereceiverdoesequallywellwitheitherofhischoices.Bothensurethereceivera48percentsuccessrate.Anyothermixbytheserver,whenproperlyexploited,willgivethereceiverasuccesspercentagealongtheupperofthetwolinesinthechart,andthereforemorethan48percent.Thusthemixofaimingtohisforehand40percentofthetimeistheserver’sbestchoice.

Theexactproportionsofthemixaregovernedbythefouroutcomesofthecombinationsofthebasicpairsofactions.Forplayersofdifferentabsoluteandrelativestrengths,thenumbersthathereare90,60,30,and20willbedifferent,

andthensowillthebestmixestouse.Wewillsoonfindsomesurprisingresultsofmakingsuchchanges.Herethepointissimplythatyouwillhavetoworkoutyour ownbestmixby estimating the four basic outcomes for the actual gameyouareplaying.

There is a shortcut; one can calculate the equilibrium strategies withoutdrawingachartliketheoneabove.ThesimplearithmeticmethodisduetoJ.D.Williams.3Goback to the tableof thebasicoutcomes.For theserver, takehisaimtotheforehandstrategyandfindthedifferenceofitsyieldsagainstthetwochoicesof the receiver;wehave90 -30=60.Do thesameforhisaim to thebackhandstrategy:60-20=40.Thenumbers inreverseorderare theoddsofusing the two strategies in the best mix.* So the server should aim to theforehandorthebackhandinproportionsof40:60.

Now let us look at the same game from the receiver’s point of view.Thenext figure shows the chart of the consequencesofhis choices. If the serve isaimed at his backhand, then a move toward the backhand means 60 percentsuccessfulreturns,whereasamovetotheforehandmeans20percentsuccessfulreturns.Changingtheproportionofmovestotheforehandfrom0percentto100percenttracesoutalinejoiningthesetwopoints.Similarlywehavealinerisingfrom 30 to 90when the server aims at his forehand side. The two linesmeetwhere the receivermoves towardhis forehand30percent of the time, andhispercentageofsuccessfulreturnsis48percentnomatterwheretheserveraims.Any other mix would be exploited by the server, choosing the better of hisstrategiesandreducingthereceivertoasuccessratebelow48percent.

Alternatively, we can use Williams’s method. The table gives us the

differencesofoutcomes for the twochoicesof the receiver.Foramove to theforehandwehave90-20=70;foramovetothebackhand,60-30=30.Thebestmixhastheseproportionsinreverseorder:30percentofthetime,anticipateaforehand;theother70percent,anticipateabackhand.

You may have noticed an interesting common feature of the best mixescalculatedfromthetwoplayers’separatepointsofview.Thetwogivethesamesuccessfulreturnpercentage,namely48percent.Usinghisbestmix,thereceiveris able to hold the server down to exactly the same success percentage as theserverisabletoachieveusinghisownbestmix.Thisisnotacoincidencebutageneral property of all games with two players whose interests are strictlyopposedtoeachother.

This result, called the min-max theorem, is due to the former PrincetonmathematiciansJohnvonNeumannandOscarMorgenstern.Thetheoremstatesthatinzero-sumgamesinwhichtheplayers’interestsarestrictlyopposed(one’sgain is theother’s loss),oneplayershouldattempt tominimizehisopponent’smaximumpayoffwhile his opponent attempts tomaximize his ownminimumpayoff.Whentheydoso, thesurprisingconclusion is that theminimumof themaximum(mini-max)payoffsequalsthemaximumoftheminimum(maxi-min)payoffs.Neitherplayercanimprovehisposition,andsothesestrategiesformanequilibriumofthegame.

We illustrate theargumentwheneachplayerhasonly twostrategiesusingthetennisexample.Iftheservertriestominimizethereceiver’smaximalsuccessrate,heshouldactasifthereceiverhascorrectlyanticipatedhismixingstrategyandhas respondedoptimally.That is, the receiver’s success ratewouldbe themaximum of the two lines as drawn below. The minimum of the maximumoccurswherethelinescross,whichisata48percentsuccessrate.

Nextwelookattheproblemfromthereceiver’sperspective;heistryingto

maximize his minimal payoff. If the receiver moves to the forehand andbackhandequallyoften,hisnewpayoffcurvewillbetheaverageoftheoriginaltwo lines, shown as a dotted line. Because this line is sloped upward, itsminimumoccursallthewayattheleft,ata40percentsuccessrate.Nomatterwhatmixturethereceiveruses,thelinemustgothroughthe48percentsuccessratebecause theserverhas theoptionofusinga40:60mixture. If the linehasany slope at all, one endmust fall below 48 percent.Onlywhen the receivermixesintheratioof30:70isthelineperfectlyflat,andtheminimumisthen48percent. Thus the minimum of the maximum equals the maximum of theminimum—48percent.

The general proof of the min-max theorem is quite complicated, but the

result isusefulandworthremembering. Ifallyouwant toknowis thegainofone player or the loss of the otherwhenboth play their bestmixes, you needonlycomputethebestmixforoneofthemanddetermineitsresult.

Ourothertools,Williams’smethodandthesecharts,workwellforanyzero-sumgamewithtwoplayerseachwithtwostrategies.Unfortunately,theydonotapplywhengames are not zero-sum, or havemore than twoplayers, or allowmore than two strategies for any player. Economists andmathematicians have

developedmore general techniques, such as linear programming, to solve forequilibriumstrategiesineventhemostcomplicatedzero-sumgames.Althoughthesetechniquesarebeyondthescopeofthisbook,wecanstillmakeuseoftheresults.

A general feature of all mixed-strategy equilibria is that each person isindifferent between any strategy he uses in the equilibrium.When mixing isnecessary,thewaytofindyourownequilibriummixtureistoactsoastomakeothersindifferentabouttheiractions.Althoughthismaysoundbackward,itfitsexactlywiththemotivationforrandomizationinzero-sumgames:youwant topreventothers fromexploitinganysystematicbehaviorofyours. If theyhadapreferenceforaparticularaction,thatwouldmeanonlythattheyhadchosentheworstcoursefromyourperspective.

Atthispointwehaveexplainedtheadvantages,eventhestrategicnecessity,ofusingmixedorrandomstrategies.Thebasicideaisthatoneresortstochanceas the means of keeping the other player from exploiting any systematicbehavioronyourpart.Turning this idea intopractice ismore subtle.Thenextfivesectionsactasaminiuser’sguidetomixedstrategies.

3.WHYYOUSHOULDCHOOSETHERIGHTMIXIfitiseverdiscoveredthatoneplayerispursuingacourseofactionotherthanthe equilibrium random mix, the other player can exploit this to his ownadvantage.Inthetennisexample,thereceivercouldachievea48percentsuccessrate when the server followed his equilibrium strategy of mixing 40 percentforehandsto60percentbackhands.Thereceivercandobetteriftheserverusesany other mix of strategy. For example, if the server foolishly aimed all hisservesat the receiver’sweakbackhand, the receivercouldanticipatehismoveandimprovehissuccessrateto60percent.Ingeneral,ifthereceiverknowstheserver and is sure of his foibles, he can react accordingly. But then there isalwaysthedangerthat,likethepoolshark,theserverisasuperiorstrategistwhousedpoorstrategiesinunimportantmatchestodeceivethereceiverintoreactingthus, and will exploit him on a really important occasion. Once the receiverdeviatesfromhisequilibriummixtureinordertotakeadvantageoftheserver’s“perceived”deviation,thereceiverbecomessubjecttoexploitationbytheserver.The server’s apparently poormixing could be a setup.Only by playing one’sequilibriummixtureisthisdangeravoided.

Justasimportantastheproperproportionsofthemixtureisthenatureoftherandomness.Ifaserveradoptsthesystemofservingfourtimestotheforehand,

thensixtimestothebackhand,thenfourtimestotheforehandagain,andsoon,thiswillachievetherightproportions.Butitissystematicbehaviorthatwillbenoticedby the receiver.Hewill respondbymovingappropriately,andachieve(4/10)90%+(6/10)60%=72%success.Inordertobemaximallyeffective,theserverneedsgenuineunpredictabilityofeachserve.Messrs.SmithandDykstrainourbaseballstoryseemednottorealizethisprinciple.

4.WHYNOTRELYONTHEOTHERPLAYER’SRANDOMIZATION?

Ifoneplayer isusinghisbestmix, thenhissuccesspercentage is thesamenomatterwhattheotherdoes.Supposeyouarethereceiverinthetennisexample,andtheserverisusinghisbestmixof40:60.Thenyouwillreturnsuccessfully48percentof the timewhetheryoumove to the forehand,or thebackhand,oranymixtureofthetwo.Observingthis,youmightbetemptedtospareyourselfthecalculationofyourownbestmix,juststicktoanyoneaction,andrelyontheother player using his bestmix.The problem is that unless you use your bestmix, the other does not have the incentive to go on using his. If you pick aforehandmove, for example, hewill switch to serving to your backhand.Thereasonwhyyoushoulduseyourbestmixistokeeptheotherplayerusinghis.

5.HOWYOURBESTMIXCHANGESASYOURSKILLSCHANGE

Suppose the receiver practices to improve his backhand return, until hispercentage of successful returns on that side goes up from 60 to 65.We canmodifythechartfromwhichwecomputedhisbestmix.Thisisdoneinthenextfigure.Wesee that theproportionof thereceiver’smoves to theforehandsidegoesupfrom30percentto33.3percent,andtheoverallpercentageofsuccessfulreturnsgoesupfrom48to50.

It is natural that the receiver’s success rate should increase as his skill

improves. But it is rather surprising that the success is achieved by using theimprovedbackhandlessoften.In thehothandstoryofChapter1,wesaid thiscouldhappen;nowweexplainhow.

The reason lies in the interaction of the two players’ strategies.When thereceiver isbetter at returningbackhands, the servergoes to the forehandmoreoften(43percentinsteadof40percent).Inresponse, thereceivermovestohisforehand more often, too. A better backhand unlocks the power of yourforehand.SimilarlyforLarryBird,animprovementinhisleft-handedshootingchanges the way he is defended and allows him to shoot right-handed moreoften.

Asanotherexampleofthesamephenomenon,supposethereceivertrainstobecomemoreagile,sothathecanshiftfromaninitialforehandmovetoreturnabackhandservicemoreaccurately.Hissuccessfigureof20percentforthisshotrisesto25percent.Onceagain,hisproportionofforehandmoveswillincreasefrom30percentto31.6percent(usingWilliams’smethod,theratioofforehandtobackhandmoves increases from30:70 to30:65).The receivermoves to theforehand side more often since this is the source of his improved skill. Inresponse,theserverdiminishesthereceiver’sgainbygoingtotheforehandlessoften.

6.HOWTOACTRANDOMLYWhat shouldyoudo ifyouare told tomix forkballsand fastballs randomly inequalproportions?Onewayistopickanumberatrandombetween1and10.Ifthenumberis5orlessthenyouthrowafastball;ifthenumberis6orabovethengofortheforkball.Ofcourse,thisonlyreducestheproblemonelayer.Howdoyougoaboutpickingarandomnumberbetween1and10?

Letusstartwiththesimplerproblemoftryingtowritedownwhatarandomsequence of coin tosses will look like. If the sequence is truly random, thenanyonewhotriestoguesswhatyouwritedownwillbecorrectnomorethan50percent on average. But writing down such a “random” sequence is moredifficultthanyoumightimagine.

Psychologists have found that people tend to forget that a head is just aslikely to be followed by a head as by a tail; therefore they have too manyreversals,andtoofewstringsofheads,intheirsuccessiveguesses.Ifafaircointosscomesupheadsthirtytimesinarow,thenexttossisstillequallylikelytobeheadsortails.Thereisnosuchthingas“beingdue”foratails.Similarly,inthelottery,lastweek’snumberisjustaslikelytowinagainasanyothernumber.To avoid getting caught putting order into the randomness, you need a moreobjectiveorindependentmechanism.

Onesuchtrickistochoosesomefixedrule,butonethatisbothsecretandsufficientlycomplicatedthatitisdifficulttodiscover.Look,forexample,atthelengthof our sentences. If the sentencehas anoddnumberofwords, call it aheads;ifthesentencelengthiseven,callitatails.Thatshouldbeagoodrandomnumbergenerator.Workingbackwardover theprevious tensentencesyieldsT,H,H,T,H,T,H,H,H,T.Ifourbookisn’thandy,don’tworry;wecarryrandomnumbersequenceswithusall the time.Takea successionofyour friends’andrelatives’birthdates.Forevendates,guessheads; forodd, tails.Or lookat thesecondhandonyourwatch.Providedyourwatchisnottooaccurate,nooneelsewillknowthecurrentpositionofthesecondhand.Ouradvicetothepitcherwhomustmixinproportionsof50:50istoglanceathiswrist-watchjustbeforeeachpitch.Ifthesecondhandpointstowardanevennumber,thenthrowafastball;anoddnumber,thenthrowaforkball.Thesecondhandcanbeusedtoachieveanyratio.Tothrowfastballs40percentofthetimeandforkballs60percent,choosefastballifthesecondhandisbetween1and24,andforkballifitisbetween25and60.

7.UNIQUESITUATIONSAllofthisreasoningmakessenseingameslikefootballorbaseballortennis,inwhichthesamesituationarisesmanytimesinonegame,andthesameplayersconfront each other from one game to the next. Then there is time andopportunity to observe any systematic behavior, and respond to it.Correspondingly,itisimportanttoavoidpatternsthatcanbeexploited,andsticktothebestmix.Butwhataboutgamesthatareplayedjustonce?

Consider the choices of points of attack and defense in a battle.Here thesituationisusuallysouniquethatnosystemfromyourpreviousactionscanbeinferred by the other side. But a case for random choice arises from thepossibilityofespionage.Ifyouchooseadefinitecourseofaction,andtheenemydiscoverswhatyouaregoing todo,hewill adapthiscourseofaction toyourmaximumdisadvantage.Youwanttosurprisehim;thesurestwaytodosoistosurpriseyourself.Youshouldkeeptheoptionsopenaslongaspossible,andatthe last moment choose between them by an unpredictable and thereforeespionage-proof device. The relative proportions of the device should also besuch that if the enemy discovered them, he would not be able to turn theknowledge to his advantage. But that is just the best mix calculated in thedescriptionabove.

Finally, awarning. Evenwhen you are using your bestmix, therewill beoccasionswhenyouhaveapooroutcome.EvenifDaveSmithisunpredictable,sometimes Lenny Dykstra will still guess right and knock the ball out of thepark. In football, on third down and a yard to go, a run up themiddle is thepercentage play; but it is important to throw an occasional bomb to keep thedefensehonest.Whensuchapasssucceeds,fansandsportscasterswillmarvelatthe cunning choice of play, and say the coach is a genius.When it fails, thecoachwillcome in fora lotofcriticism:howcouldhegambleona longpassinsteadofgoingforthepercentageplay?

The time to justify thecoach’sstrategy isbeforeusing itonanyparticularoccasion.Thecoachshouldpublicizethefactthatmixingisvital;therunupthemiddle remainssuchagoodpercentageplaypreciselybecausesomedefensiveresources must be diverted to guard against the occasional costly bomb.However, we suspect that even if the coach shouts this message in allnewspapers and televisionchannelsbefore thegame, and thenuses abomb insuchasituationandit fails,hewillcomeinfor justasmuchcriticismas ifhehadnottriedtoeducatethepublicintheelementsofgametheory.

8.BODYGUARDOFLIESIf you are using your best mix, then it does not matter if the other playerdiscovers this fact, so long as he does not find out in advance the particularcourseofactionthatisindicatedbyyourrandomdeviceinaparticularinstance.Hecandonothing to takeadvantageofyour randomstrategy: theequilibriumstrategyischosentodefendagainstbeingexploitedinjustthisway.However,ifforwhatever reason you are doing something other than using your bestmix,

thensecrecyisvital.Leakageofthisknowledgewouldreboundtoyourcost.Bythe same token, you cangainbygettingyour rival tobelieve thewrong thingaboutyourplan.

InpreparationfortheirlandingsontheNormandybeachesinJune1944,theAlliesusedmanydevicestomaketheGermansbelievetheinvasionwouldbeatCalais.OneofthemostingeniouswastoturnaGermanspyintoadoubleagent—butnoordinarydoubleagent.TheEnglishmadesurethattheGermansknewthattheiragenthadbeenturned,butdidnotlettheGermansknowthatthiswasintentional. To build up his (lack of) credibility as a double agent, the spytransmittedhomesomeof theworst informationpossible.TheGermans foundthisinformationusefulsimplybyreversingthatwhichtheyweretold.Thiswasthesetupforthebigsting.WhenthedoubleagenttoldthetruththattheAlliedlandingwouldoccuratNormandy,theGermanstookthistobefurtherevidencethatCalaiswasthechosenspot.

Thisstrategyhadthefurtheradvantage thatafter the landing, theGermanswerenolongersurethattheirspywasreallyadoubleagent.Hehadbeenoneoftheir only sources of correct information. With his credibility restored, theEnglishcouldnowsendfalseinformationandhaveitbelieved.4

Theproblemwith this story is that theGermansshouldhavepredicted theEnglish strategy and thus calculated that therewas someprobability that theiragenthadbeenturned.Whenplayingmixedorrandomstrategies,youcan’tfooltheoppositioneverytimeoronanyoneparticulartime.Thebestyoucanhopeforistokeepthemguessingandfoolthemsomeofthetime.Inthisregard,whenyouknowthatthepersonyouaretalkingtohasinhisinterestadesiretomisleadyou,itmaybebesttoignoreanystatementshemakesratherthanacceptthematfacevalueortoinferthatexactlytheoppositemustbethetruth.

There is the story of the two rival businessmenwhomeet in theWarsawtrainstation.

“Whereareyougoing?”saysthefirstman.“ToMinsk,”repliestheother.“ToMinsk,eh?Whatanerveyouhave!Iknowthatyouaretellingmethat

youaregoing toMinskbecauseyouwantme tobelieve thatyouaregoing toPinsk.ButitsohappensthatIknowyoureallyaregoingtoMinsk.Sowhyareyoulyingtome?”5

Actionsdospeakalittlelouderthanwords.Byseeingwhatyourrivaldoes,youcan judge the relative likelihoodofmatters thathewants to conceal fromyou. It is clear from our examples that you cannot simply take a rival’sstatementsatfacevalue.Butthatdoesnotmeanthatyoushouldignorewhathedoeswhentryingtodiscernwherehistrueinterestslie.Therightproportionstomixone’sequilibriumplaycriticallydependonone’spayoffs.Thusobservingaplayer’s move gives some information about the mixing being used and isvaluable evidence to help infer the rival’s payoffs.Bidding strategies in pokerprovideaprimeexample.

Poker players are well acquainted with the need to mix their plays. JohnMcDonald gives the following advice: “The poker hand must at all times beconcealedbehindthemaskofinconsistency.Thegoodpokerplayermustavoidset practices and act at random, going so far, on occasion, as to violate theelementaryprinciplesofcorrectplay.”6A“tight”playerwhoneverbluffsseldomwinsalargepot;nobodywilleverraisehim.Hemaywinmanysmallpots,butinvariablyendsupaloser.A“loose”playerwhobluffstoooftenwillalwaysbecalled,andthushetoogoesdowntodefeat.Thebeststrategyrequiresamixofthesetwo.

Suppose you know that a regular poker rival raises two-thirds of the timeandcallsone-thirdofthetimewhenhehasagoodhand.Ifhehasapoorhand,hefoldstwo-thirdsofthetimeandraisestheotherthirdofthetime.(Ingeneral,itisabadideatocallwhenyouarebluffing,sinceyoudonotexpecttohaveawinninghand.)Thenyoucanconstructthefollowingtablefortheprobabilitiesofhisactions.

Before he bids, you believe that good and poor hands are equally likely.

Because his mixing probabilities depend on his hand, you get additionalinformation from the bid. If you see him fold, you canbe sure he had a poorhand.Ifhecalls,youknowhishandisgood.Butinboththesecases,thebettingisover.Ifheraises,theoddsare2:1thathehasagoodhand.Hisbiddoesnotalways perfectly reveal his hand, but you knowmore than when you started.Afterhearingaraise,youincreasethechancethathishandisgoodfrom1/2to2/3.*

9.SURPRISESo far, our applications of randomized strategies have focused exclusively ongames in which the players’ interests are strictly opposed. Somewhat moresurprisingisthepossibilityoffindinganequilibriumwithrandombehaviorevenwhentheplayershavecommoninterests.Inthiscase,mixingone’splaysleadsto an inferior outcome for all parties.But just because theoutcome is inferiordoesnotmeanthestrategiesarenotanequilibrium:equilibriumisadescriptionnotaprescription.

The reason for mixing one’smoves arises from a failure of coordination.Thisproblemonlyariseswhenthere isnotauniqueequilibrium.Forexample,twopeopledisconnectedduringaphonecalldon’talwaysknowwhoshouldcallwhomback.Withouttheabilitytocommunicate,theplayersdon’tknowwhichequilibriumtoexpect.Inaloosesense,theequilibriumwithrandomizationisawayofplayingacompromisebetweenthecoordinatedequilibria.Thenatureofthiscompromiseisillustratedinthestorybelow.

Dellaand Jimare the sortof coupleyou readabout in fiction,O.Henry’sTheGift of theMagi, to beprecise. “Nobody could ever count” their love foreach other, and each was willing, even eager, to make any sacrifice to get areallyworthyChristmasgiftfortheother.DellawouldsellherhairtogetJimachainforhisheirloomwatch,andJimwouldsell thewatch tobuyacombforDella’sbeautifulhair.

If they know each other well enough, they should both recognize thepossibilitythateachwillsellhisorheronetreasuretobuytheotheragift,andthe resultwillbea tragicmistake.Della shouldpauseandconsiderwhether itwould be better to keep her hair and await Jim’s gift. Likewise, Jim shouldconsider not selling hiswatch.Of course, if they both refrain, neither gives agift,whichwouldbeadifferentmistake.

Thisstorycanberepresentedasagame.

Payoffsto[Della,Jim]

Thecouple’sstrategiesinteracteventhoughtheirinterestslargelycoincide.Foreach,bothkindsofmistakewouldbeabadoutcome.Forconcreteness,wegivethisapointscoreofzero.Asbetweenthetwooutcomesinwhichonegivesagiftandtheotherreceivesit,supposeeachthinksitbettertogive(2points)thantoreceive(1point).

The situation in which Della keeps her hair and Jim sells his watch is apossibleequilibrium;eachspouse’sstrategy is thebest response to theother’s.ButthesituationinwhichDellasellsherhairandJimkeepshiswatchisalsoanequilibrium.Isthereamutuallyunderstoodconventiontoselectoneequilibriumover theother?Surprise isan importantaspectofagift; therefore theycannotcommunicateinadvancetoestablishaconvention.

Mixingcanhelppreservethesurprise,althoughatacost.Itiseasytocheckthatthestrategiesinwhicheachchoosestogivewithprobability2/3andreceivewith probability 1/3 also constitute an equilibrium.SupposeDella uses such amixture.IfJimsellshiswatch,thereisa1/3chancethatDellahaskeptherhair(2points)anda2/3chancethatshehassoldit(0point).Theaverageoutcomeis2/3point.Asimilarcalculationshows that if Jimkeepshiswatch, theaverageoutcome is again2/3point.So Jimhasnoclear reason tochooseone strategyrather than another, or indeed anymix. Once again, note that the function ofDella’sbestmixistokeepJimwillingtomix,andviceversa.

Theprobabilitiesofmistakesarequite large:4 times in9 thecouple findsthateachhassoldtheitemforwhichtheotherhasboughtthegift(asintheO.Henrystory),and1timein9neithergetsanygift.Becauseofthesemistakes,theaverage score (2/3 point for each) is worse than that of either of the two

equilibriainwhichonegivesandtheotherreceives(2pointsforthegiverand1forthereceiver).Thisisunlikethetennisexample,inwhicheachcouldactuallyraisehissuccessratebymixing.

Why the difference? Tennis is a zero-sum game, in which the players’interests are strictly opposed. They do better when they choose the mixingprobabilitiesindependently.InouraccountofTheGiftoftheMagi,thecouple’sinterests are largely aligned. They need, therefore, to coordinate theirmixing.Theyshouldtossonecoin,anddependingontheoutcomedecidewhogivesandwhoreceives.Thecouplehasaslightconflictofinterest;Jimprefersthetopleftoutcome, and Della the bottom right. Coordinated mixing can offer them acompromise, splitting the difference.When a common coin toss decides whogivesandwho receives, theaverageoutcome for eachbecomes1.5points.Ofcoursetheelementofsurpriseislost.

10.CATCHASCATCHCANSofartherehavebeenveryfewexamplesofmixedstrategyoutsidethesportingworld.Whyaretheresofewinstancesofbusinessesusingrandomizedbehavioroutintherealworld?First,itmaybedifficulttobuildintheideaofleavingtheoutcometochanceinacorporateculturethatwantstomaintaincontrolovertheoutcome. This is especially true when things go wrong, as they mustoccasionallywhenmovesarechosenrandomly.Whilesomepeopleunderstandthat a football coach has to fake a punt once in a while in order to keep thedefensehonest,asimilarlyriskystrategyinbusinesscangetyoufiredifitfails.But thepoint isn’t that theriskywillalwayswork,butrather that itavoids thedangerofsetpatternsandpredictability.

Oneapplicationinwhichmixedstrategiesimprovebusinessperformanceispricecouponing.Companiesusepricediscountcoupons tobuildmarketshare.The idea is to attract new customers, and not just to give a discount to yourpresent market. If competitors simultaneously offer coupons, then customersdon’thaveanyspecial incentive toswitchbrands. Instead, theystaywith theircurrent brand and take the discount. Onlywhen one company offers couponswhiletheothersdon’tarenewcustomersattractedtotrytheproduct.

ThepricecouponstrategicgameforcompetitorssuchasCokeandPepsiisthen quite analogous to the coordination problem of Jim and Della. Bothcompanies want to be the one to give coupons. But if they try to do thissimultaneously, the effects cancel out and both are worse off. One solutionwouldbetofollowapredictablepatternofofferingcouponseverysixmonths,

andthecompetitorscouldlearntoalternate.TheproblemwiththisapproachisthatwhenCokepredictsPepsiisjustabouttooffercoupons,Cokeshouldstepinfirst to preempt. The onlyway to avoid preemption is to keep the element ofsurprisethatcomesfromusingarandomizedstrategy.*

There are other cases in which businesses must avoid set patterns andpredictability.Someairlinesofferdiscountticketstotravelerswhoarewillingtobuyticketsatthelastminute.Buttheywon’ttellyouhowmanyseatsareleftinorder to help you estimate the chances of success. If last-minute ticketavailability were more predictable, then there would be a much greaterpossibility of exploiting the system, and the airlineswould losemore of theirotherwiseregularpayingcustomers.

Themostwidespreaduseofrandomizedstrategiesinbusinessistomotivatecompliance at a lower monitoring cost. This applies to everything from taxaudits to drug testing to parkingmeters. It also explains why the punishmentshouldnotnecessarilyfitthecrime.

Thetypicalfineforillegalparkingatameterismanytimesthemeterfee.Ifthemeter rate is a dollar per hour, would a fine of $1.01 not suffice to keeppeoplehonest?Itwould,providedthetrafficpoliceweresuretocatchyoueachtimeyouparkedwithoutputtingmoney in themeter.Suchenforcementwouldbeverycostly.Thesalariesofthetrafficwardenswouldbethelargestitem,butthe cost of administering the collectionmechanism needed to keep the policycrediblewouldbequitesubstantial,too.

Theauthoritieshaveanequallyeffectiveandlesscostlystrategy,namelytohavelargerfinesandrelaxtheenforcementefforts.Whenthefineis$25,a1in25 risk of being caught is enough to keep you honest.Amuch smaller policeforcewill do the job, and the fines collectedwill come closer to covering theadministrativecosts.

Thisisanotherinstanceoftheusefulnessofmixedstrategies.Itissimilartothetennisexampleinsomeways,anddifferentinotherrespects.Onceagain,theauthorities choose a random strategy because it is better than any systematicaction:noenforcementatallwouldmeanmisuseofscarceparkingplaces,anda100 percent enforcement would be too costly. However, the other side, theparking public, does not necessarily have a random strategy. In fact theauthoritieswant tomake thedetectionprobabilityand thefine largeenough toinducethepublictocomplywiththeparkingregulations.

Random drug testing has many of the same features as parking meterenforcement. It is too time-consumingandcostly to testeveryemployeeeverydayforevidenceofdruguse.Itisalsounnecessary.Randomtestingwilluncover

thosewhoareunabletoworkdrugfreeanddiscourageothersfromrecreationaluse. Again, the probability of detection is small, but the fine when caught ishigh.ThatisoneoftheproblemswiththeIRSauditstrategy.Thepenaltiesaresmallgiventhechancesofgettingcaught.Whenenforcementisrandom,itmustbe that the punishment is worse than the crime. The rule should be that theexpected punishment should fit the crime, where the expectation takes intoaccountthechanceofbeingcaught.

Thosehopingtodefeatenforcementcanalsouserandomstrategiestotheirbenefit. They can hide the true crime in the midst of many false alarms ordecoys,andtheenforcer’sresourcesbecomespreadtoothintobeeffective.Forexample, an air defense must be able to destroy nearly 100 percent of allincomingmissiles.A cost-effectivewayof defeating the air defense is for theattacker to surround the real missile with a bodyguard of decoys. It is muchcheaper to build a decoymissile than the real thing. Unless the defender canperfectly distinguish among them, he will be required to stop all incomingmissiles,realandfake.

The practice of shooting dud shells began in World War II, not by theintentionaldesignofbuildingdecoymissiles,butasaresponsetotheproblemofquality control. As John McDonald explained in his book Strategy in Poker,Business, and War, “The elimination of defective shells in production isexpensive.Someonegottheideathenofmanufacturingdudsandshootingthemonarandombasis.Amilitarycommandercannotaffordtohaveadelayedtimebombburiedunderhisposition,andheneverknewwhichwaswhich.Thebluffmadehimworkateveryunexplodedshellthatcameover.”

Whenthecostofdefenseisproportionaltothenumberofmissilesthatcanbe shotdown,attackerscanmake this enforcementcostunbearablyhigh.Thisproblemisoneofthemajorchallengesfacingthoseinvolvedinthe“StarWars”defense;itmayhavenosolution.

11.CASESTUDY#7:OPERATIONOVERLORDIn1944,theAllieswereplanninganoperationfortheliberationofEurope,andtheNaziswereplanningtheirdefenseagainstit.Thereweretwopossibilitiesfortheinitiallanding—theNormandybeachesandPasdeCalais.Alandingwouldsurely succeed against a weak defense, so the Germans would have toconcentratetheirattentionononeofthesetwoplaces.Calaiswasmoredifficulttoinvade,butmorevaluabletowin,beingclosertotheAllies’ultimatetargetsinFrance,Belgium,andGermanyitself.

Suppose theprobabilitiesof successareas follows:ProbabilitiesofAlliedSuccess

Thepayoffsaregivenonascaleof0to100.TheAlliescountasuccessful

landingatCalaisas100,asuccessfullandingatNormandyas80,andafailureateitherplaceas0(andtheGermansgetthenegativeofthesepayoffs).

PutyourselfsimultaneouslyinthebootsofGeneralEisenhower,theAlliedSupremeCommander, andFieldMarshalRommel, theGermancommanderoftheircoastaldefensesinFrance.Whatstrategieswouldyouchoose?

CaseDiscussionFirstcombinetheinformationontheprobabilitiesofsuccessandthepointscorevalue of success to construct a table of the average point scores. The scoreslisted are from theAllied perspective; theGerman scores can be taken as thenegativeofthesenumbers,asthesides’interestsarestrictlyopposed.

AlliedPointScores

There is no equilibrium in the basic strategies, and we must look for

mixtures. Using Williams’s method, the Allies should choose to land atNormandy or Calais with the odds of (100-20):(80-60), or 4:1, while theGermansshoulddeploytheirdefensesatNormandyorCalaiswiththeodds(80-20):(100-60),or3:2.TheaveragepointscorefortheAllieswhenbothusetheirbestmixturesis68.

Theprobabilitiesandpointscoreswechoseareplausible,butitishardtobeprecise or dogmatic about such matters. Therefore let us compare our resultswith what actually happened. In retrospect, we know that the Allies’ mixingproportionswereoverwhelminglyweightedtowardNormandy,andthatiswhatthey in fact chose. For theGermans, itwas a closer call. It is less surprising,therefore, that theGermandecision-makingwasswayedby theAllies’double-agent trick, differencesof opinion in their commanding ranks, and someplainbadluck,suchasRommelbeingawayfromthefrontat thecrucial time.Theyfailed to commit their reserves on the afternoon of D-Day when the AlliedlandingsatNormandyseemedtobesucceeding,believingthatabiggerlandingatCalaiswouldcome.Eventhen, thefateofOmahaBeachwasin thebalanceforawhile.ButtheAlliesgainedandconsolidatedtheirfootholdonNormandy.Therestyouknow.

EpiloguetoPartII

1.HISTORICALNOTEGametheorywaspioneeredbythePrincetonpolymath,JohnvonNeumann.Intheearlyyears,theemphasiswasongamesofpureconflict(zero-sumgames).Othergameswereconsideredinacooperativeform,thatis,theparticipantsweresupposedtochooseandimplementtheiractionsjointly.Theseapproachescouldnot encompass most of the games played in reality, in which people chooseactions separately but their links to others are not ones of pure conflict. Forgeneral games combining conflict and cooperation, our concept of anequilibrium is due to JohnNash. Thomas Schelling broadened the analysis ofsequential-movegames,developingtheideasofstrategicmoves.

2.FURTHERREADINGPioneeringbooksareoftenenjoyabletoread.Inthisspirit,werecommendvonNeumann and Morgenstern’s Theory of Games and Economic Behavior(PrincetonUniversityPress,1947)eventhoughthemathematicsmaybehardtofollowinplaces.Schelling’sTheStrategyofConflict(HarvardUniversityPress,1960) ismore than a pioneering book; it continues to provide instruction andinsight.

For an entertaining exposition of zero-sum games, J. D. Williams’s TheCompleatStrategyst (revisededition,McGraw-Hill, 1966) still cannotbebeat.The most thorough and highly mathematical treatment of pre-Schelling gametheory is in Duncan Luce and Howard Raiffa,Games and Decisions (Wiley,1957).

Amonggeneralexpositionsofgametheory,MortonDavis,GameTheory:ANontechnical Introduction (secondedition,BasicBooks,1983) isprobably the

easiest to read. A far more detailed and mathematically harder treatment isMartinShubik’sGameTheoryintheSocialSciences(MITPress,1982).

There are also several valuable books applying game theory to particularcontexts. In the field of politics, the noteworthy books include StevenBrams,GameTheoryandPolitics(FreePress,1979),WilliamRiker,TheArtofPoliticalManipulation(YaleUniversityPress,1986),andthemoretechnicalapproachofPeter Ordeshook’sGame Theory and Political Theory (Cambridge UniversityPress,1986).Forapplicationstobusiness,MichaelPorter’sCompetitiveStrategy(Free Press, 1982) and Howard Raiffa’s The Art and Science of Negotiation(HarvardUniversityPress,1982)aretwoexcellentresources.

3.OURSINSOFOMISSIONWe have blurred the distinction between zero-sum and non-zero-sum games.Equilibriaofzero-sumgameshavesomespecialpropertiesthatdonotcarryovertonon-zero-sumgames;thereforerigoroustreatmentsofthesubjectaredividedalongthisdimension.

Wehavesimplifiedmanysituationstothepointwhereeachplayerhadonlytwo strategies. This was done when the most basic ideas could be conveyedwithout serious lossof content. Inmost cases thecomplications introducedbymorestrategiesarepurelycomputational.Forexample,randomizationoverthreeormorebasicstrategiescanbedoneusingasimplecomputerprogram.Thereisa new aspect: only a subset of the strategiesmight be active (be playedwithpositiveprobability)inequilibrium.Onthispoint,seeLuceandRaiffa.

Wehaveignoredtheso-called“cooperativegames”inwhichplayerschooseandimplement theiractions jointly,andproduceequilibria like theCoreor theShapleyValue.Thiswasdonebecausewethinkanycooperationshouldemergeas the equilibrium outcome of a noncooperative game in which actions arechosen separately. That is, individuals’ incentive to cheat on any agreementshould be recognized and made a part of their strategy choice. However,interested readers can find treatments of cooperative games in the books byDavis,LuceandRaiffa,andShubik.

4.FROMHEREONPartIIItakestheconceptsandtechniquesdevelopedthusfartoseveraltypesofstrategic interactions. These include bargaining, voting, brinkmanship, and the

design of incentives. Once again we illustrate the strategic principles throughexamplesandcasestudiesandsuggestfurtherreadingsinfootnotesforreaderswhowishtopursuesometopicsinmoredetail.

PartIII

Brinkmanship

InOctober1962,theCubanmissilecrisisbroughttheworldtothebrinkofnuclearwar. The SovietUnion, under itsmercurial leaderNikitaKhrushchev,had begun to install nuclear missiles on Cuba, 90 miles from the Americanmainland. On October 14, our reconnaissance airplanes brought backphotographs of missile sites under construction. After a week of tensediscussionswithinhisadministration,onOctober22PresidentJohnF.Kennedyannounced a naval quarantine of Cuba. Had the Soviet Union taken up thechallenge, the crisis could have escalated to the point of all-out nuclear warbetweenthesuperpowers.Kennedyhimselfestimatedtheprobabilityof thisas“between one out of three and even.” But after a few anxious days of publicposturingandsecretnegotiation,Khrushchevshiedawayfromtheconfrontation.In return for a face-saving compromise involving eventualwithdrawal ofU.S.missiles in Turkey, he ordered the Soviet missiles in Cuba dismantled andshippedback.1

Khrushchev looked over the nuclear brink, did not likewhat he saw, andpulledback.Thename“brinkmanship”seemsaptforthestrategyoftakingyouropponenttothebrinkofdisaster,andcompellinghimtopullback.*Kennedy’saction in the Cuban missile crisis is generally accepted as an instance ofsuccessfulexerciseofbrinkmanship.

Therestofusalsopracticebrinkmanship,butwithlessthanglobalstakes.Amanagement team and a trade union facing a devastating strike, stubbornspouseswhose failure tocompromise is leading towarddivorce,andadividedCongress risking a government shutdown if it fails to ratify a budget are allengaged in brinkmanship.They are deliberately creating andmanipulating theriskofamutuallybadoutcomeinordertoinducetheotherpartytocompromise.

Brinkmanship isasubtlestrategyfraughtwithdangers,and ifyouwant topracticeitsuccessfully,youmustfirstunderstanditthoroughly.Weaimtohelpyougraspthesubtleties,usingtheCubanmissilecrisisasacasestudy.

UpondiscoveringthattheSovietshadsecretlyplacedmissilesinCuba,the

Kennedy administration contemplated a range of options: do nothing; take acomplaint to the United Nations (in practice, almost the same thing as doingnothing);imposeaquarantineorblockade(thecourseactuallyadopted);launchan air strike on the missile sites in Cuba; or—at the extreme end—make animmediatepreemptivetotalnuclearstrikeontheSovietUnion.

After theUnitedStates imposed anaval quarantine, theSoviets hadmanypossible responses.Theycouldbackdownand remove themissiles; stop theirshipscarryingmissilesinmid-Atlantic(thecourseactuallyadopted);trytoruntheblockade eitherwithout orwith naval support; or take the extreme stepoflaunchingapreemptivestrikeontheUnitedStates.

In thisspectrumofmovesandcountermoves,someof thepossibleactionswere clearly safe (such as the United States doing nothing or the Sovietsremoving themissiles)whileotherswereclearlydangerous(suchas launchinganairstrikeonCuba).Butinthelargemiddlerange,wheredoessafetyendanddanger begin? In other words, just wherewas the brink in the Cubanmissilecrisis?Wasthereaborderlinesuchthattheworldwassafetotheonesideofit,anddoomedassoonasthelinewascrossed?

The answer, of course, is that there was no such precise point, only agradually increasing risk of uncontrollable future escalation. Had the Sovietstriedtodefytheblockade,forexample,theUnitedStateswasunlikelytolaunchits strategic missiles at once. But events and tempers would have heated upanother notch, and the risk ofArmageddonwould have increased perceptibly.Thekeytounderstandingbrinkmanshipistorealizethatthebrinkisnotasharpprecipice,butaslipperyslope,gettinggraduallysteeper.

Kennedytooktheworldsomewaydownthisslope;Khrushchevdidnotriskgoingfarther,andthenthetwoarrangedapullbacktothesafegroundabove.IfthiswastheeffectofKennedy’sactions,itisatleastplausiblethatitwasalsohisintention.*Letusexaminethestrategyofbrinkmanshipinthislight.

The essence of brinkmanship is the deliberate creation of risk. This riskshouldbesufficientlyintolerabletoyouropponenttoinducehimtoeliminatetheriskbyfollowingyourwishes.Thismakesbrinkmanshipastrategicmove,ofthekindweintroducedinChapter5.Likeanystrategicmove, itaims to influencetheother’sactionsbyalteringhisexpectations.Infactbrinkmanshipisathreat,but of a special kind. To use it successfully, you must understand its specialfeatures.

Weapproachthesefeaturesthroughthreequestions.First,whynotthreatenyouropponentwiththecertaintyofadireoutcome,insteadofamereriskthatitwould happen? Second, what is the mechanism that ultimately determines

whethertheriskcomestopass?Third,justwhatistherightdegreeofthisrisk?Wetrytoanswereachofthesequestionsinturn.

1.WHYUNCERTAINTY?

Given that the United States wanted the Soviets to pull their missiles out ofCuba,whycouldKennedynothavethreatenedthathewouldannihilateMoscowunless Khrushchev removed the missiles? In the terminology we introducedbefore(Chapter5),thiswouldbeacompellentthreat;itmustspecifythepreciseconditions of compliance (missiles back to Russia, or in crates on a ship inHavanaharbor?)andadeadlineforcompliance.

Theproblemisthatinpracticesuchathreatwouldnotbebelieved,eitherbyKhrushchevorbyanyoneelse.Thethreatenedaction,surelyleadingtoaglobalthermonuclearwar,issimplytoodrastictobecredible.Ifthemissileswerenotoutbythedeadline,ratherthanannihilatetheworld,Kennedywouldsurelybetemptedtoextendthedeadlinebyaday,andthenanotherday.

InChapter6wesawseveralwaysoflendingcredibilitytothreats.Theuseofanautomaticdeviceseemsthemostpromisinginthiscontext.*ThisapproachisthebasisforthemoviesFailsafeandDr.Strangelove.InDr.Strangelove theSoviets have installed a “doomsday machine” that monitors AmericantransgressionsandautomaticallylaunchesSovietretaliationundercircumstancesspecified in a tamperproof computer program. InFailsafe it is theAmericanswhohavethedoomsdaymachine.Thosewhohaveseenthesemovies(whichwerecommendhighly)knowwhyKennedyshouldnotuseasimilardevicetomakehisthreatcredible.

Intheory,underidealcircumstances,everythingworksjustasplanned.Theveryknowledge thatanautomaticdevice is inplacemakes the threatcredible.Khrushchevbacksdown, the threat doesnot have to be carriedout, and all iswell.Ifathreatissuretosucceed,itneedneverbecarriedout,anditdoesnotmatterhowbigordireitis,orhowmuchitwouldhurtyoutootocarryitout.Butinpractice,youcannotbeabsolutelysurethatitwillworkasplanned.

Thereareinfacttwokindsoferrorsthatcanoccur.First,thethreatmaynotsucceed. SupposeKennedy has totallymisjudgedKhrushchev’smindset.ThenKhrushchevdoesnotbackdown,andthedoomsdaydeviceannihilatestheworldjust as Kennedy is regretting having installed it. Second, the threat may becarried out evenwhen it should not. Suppose the Soviets back down, but the

newsreachesthedoomsdaycomputerjusttoolate.Becausesucherrorsarealwayspossible,Kennedydoesnotwanttorelyon

threats that are too costly to carry out. Knowing this, Khrushchev will notbelievethethreats,andtheywillnotdeterorcompelhim.KennedymayclaimthatanautomaticlauncherhasthesoleauthoritytofireatMoscowiftheSovietmissiles are not out of Cuba by Monday, but Khrushchev can be sure thatKennedycontrolsanoverridebutton.

Although the threat of certainty of war is not credible, one of a risk orprobabilityofwarcanbecredible.IfKhrushchevfailstocomply,thereisarisk,but not a certainty, that themissileswill fly. The uncertainty scales down thethreat.The scalingdownmakes the threatmore tolerable to theUnitedStates,andthereforemorecredibletotheSoviets.

This isa lot likeanotherdeviceforcredibilitywementionedinChapter6,namelymovinginsmallsteps.Thereweconsideredbreakingupalargepromiseinto a succession of small ones. If I am trying to sell you a valuable piece ofinformationfora thousanddollars,Imaynotbewillingtodiscloseit inreturnforyourpromisetopay,butmaybewillingtorevealinstallmentsonebyoneinreturn for corresponding payments.A similar principle applies to threats.Andherethestepsconsistofdegreesofrisk.EachstageofescalationbytheUnitedStates or the Soviet Union increases the risk of global war; each smallconcessionreducestherisk.Thecalculationforeachsideishowfartoproceedorretreatalongthisroute.IfKennedyiswillingtogofartherthanKhrushchev,thenKennedy’sbrinkmanshipwillsucceed.

Kennedycannotcrediblythreatenanimmediateall-outnuclearstrike,buthecan credibly raise the risks to some degree by taking some confrontationalactions.Forexample,hemaybewillingtoriskonechanceinsixofnuclearwartoensuretheremovalofthemissiles.ThenKhrushchevcannolongerconcludethatKennedy’sthreatisvacuous;itisinKennedy’sinteresttoexposehimselftothis risk if it willmotivate the Soviets to remove themissiles. IfKhrushchevfindsthisdegreeofriskintolerable,thenthebrinkmanshiphasaccomplisheditsobjective:toallowKennedytochooseamoreappropriatelysizedthreat,onebigenoughtoworkandyetsmallenoughtobebelieved.

Westillhave toaskhowKennedycangoabout threateningarisk ofwar,shortofacertainty.Thisiswheretheslipperyslopecomesin.

2.THEMECHANISMOFRISKJusthowdoesonegoaboutgeneratingathreatthatinvolvesarisk?InChapter7

we studied the idea of mixing one’s moves, and suggested several randommechanisms that could be usedwhen selecting one from the range of actionsbeingmixed.Wemighttrythesameideahere.Forexample,supposethatduringthe Cuban missile crisis, one in six is the right risk of war for Kennedy tothreaten. Then he might tell Khrushchev that unless the missiles were out ofCubabyMonday, hewould roll a die, and if six cameuphewouldorder theU.S.missilestobelaunched.

Quite apart from thehorror thispicture conjuresup, it justwon’twork. IfKhrushchevrefusestocomply,andKennedyrollsthedieandsixcomesup,theactualdecisionisstillinKennedy’shands.HestillhasthepowerfulurgetogiveKhrushchevjustonemorerollofthedie(“let’smakeittwooutofthree”)beforeArmageddon.Khrushchevknowsthis,andknowsthatKennedyknowsthat,too.The credibility of the threat collapses just as surely as if the elaboratemechanismofrollingthediehadneverbeenmentioned.

Anessentialinsightisthatwhenasharpprecipiceisreplacedbyaslipperyslope, evenKennedydoesnotknowwhere safety lies. It is as ifhe isplayingnuclearRussian roulette insteadof rolling adie.Onenumber leads todisasterbut he does not knowwhich one that is. If the number comes up, he cannotchangehismindandrollagain.

Withrationalopponents,noonewouldevercrossthenuclearbrink.Butitispossible to fall down a slippery slope by mistake. Brinkmanship deliberatelyhidestheprecipicebycreatingasituationthatisslightlyoutofcontrol.

The risk in brinkmanship is therefore fundamentally different from theelementofchanceinmixingyourmoves.Ifthebestproportionsofyourtennisserve are50:50between forehandandbackhand, andyou toss a coinbefore aparticularserveanditcomesupheads,youhavenoreasontofeelhappyorsorryaboutthefact.Youareindifferentastoyouractiononeachoccasion;itisonlytheunpredictabilityofindividualoccasions,andtherightproportionsofchance,thatmatter.Withbrinkmanship,youarewillingtocreatetheriskbeforethefact,but remain unwilling to carry out the threatened act if the occasion arises. Toconvince your rival that the threatened consequencewill occur, you still needotherdevices.

Themostcommonistotaketheactualactionoutofyourcontrol.Itisnotamatterof“Ifyoudefyme,thenthereisariskthatIwillchoosetodosuchandsuch.” Instead, it is “If you defy me, there is a risk that such and such willhappen, howevermuch both of usmay regret it then.”Thus the credibility ofbrinkmanship still needs a device of commitment; only that device containswithinitacointossoradiethatgovernswhathappens.

This conjures up the image of an automaton or computer that will act in

responsetotherollofadie—anunlikelyscenario.Butinmanycircumstances,ageneralized fear that “things may get out of hand” serves the same purpose.KennedydoesnothavetospelloutexactlyhowachanceofArmageddonwillbecreated.

Soldiersandmilitaryexpertsspeakofthe“fogofwar”—asituationinwhichbothsidesactwithdisruptedlinesofcommunication,individualactsoffearorcourage,andagreatdealofgeneraluncertainty.Thereistoomuchgoingontokeepeverythingundercontrol.Thisservessomeofthepurposeofcreatingrisk.TheCubanmissilecrisisitselfprovidedinstancesofthis.Forexample,eventhepresidentfounditverydifficulttocontroltheoperationsofthenavalblockadeofCubaonceputintoplay.Kennedytriedtobringtheblockadefrom500milesoutto800milesofftheshoreofCubainordertogiveKhrushchevmoretime.Yetevidence based on the first ship boarded, theMarcula (a Lebanese freighterunderchartertotheSoviets),indicatesthattheblockadewasnevermoved.2

NordidDefenseSecretaryMcNamarasucceedinpersuadingChiefofNavalOperationsAnderson tomodify theNavy’s standardoperatingprocedure for ablockade. As recorded in Graham Allison’s book, Essence of Decision,McNamaraexplainedtoAnderson:

By theconventional rules,blockadewasanactofwarand the firstSovietship that refused to submit to boarding and search risked being sent to thebottom. But this was a military action with a political objective. Khrushchevmustsomehowbepersuadedtopullback,ratherthangoadedintoretaliation.3

Allisoncontinueswithhisportraitof themeeting:“Sensing thatAndersonwas not moved by this logic, McNamara returned to the line of detailedquestioning. Who would make the first interception? Were Russian-speakingofficersonboard?Howwouldsubmarinesbedealtwith?…WhatwouldhedoifaSovietcaptainrefusedtoanswerquestionsabouthiscargo?At thatpoint theNavy man picked up the Manual of Naval Regulations and, waving it inMcNamara’s face, shouted, ‘It’s all in there.’ TowhichMcNamara replied, ‘Idon’tgiveadamnwhatJohnPaulJoneswouldhavedone.Iwanttoknowwhatyouaregoing todo,now.’TheencounterendedonAnderson’s remark: ‘Now,Mr.Secretary,ifyouandyourDeputywillgobacktoyouroffices,theNavywillruntheblockade.’”

ThestandardoperatingproceduresforanavalblockademayhaveimposedamuchgreaterriskthanKennedydesired.Thisiswhereitisimportanttorealize

that the crisis was not a two-person game; neither the United States nor theSovietUnionwasoneindividualplayer.Thefact thatKennedy’sdecisionshadtobecarriedoutbypartieswiththeirownprocedures(andsometimestheirownagenda)providedamethodforKennedy tocrediblycommit to takingsomeofthecontroloutofhishands.Thewaysinwhichabureaucracytakesonalifeofitsown, thedifficultyofstoppingmomentum,and theconflictinggoalswithinan organization were some of the underlying ways in which Kennedy couldthreatentostartaprocessthathecouldnotguaranteetostop.

3.THECONTROLOFRISKIf you are trying to extract some exclusive information from someone, yourthreattokillhimunlessherevealsthesecretwillnotbecredible.Heknowsthatwhen the time comes, youwill realize that the secret dieswith him, andwillhavenoincentivetocarryoutthethreat.Hollywoodfilmsprovidetwoexcellentillustrationsofthisproblem,andofhowtodealwithit.Schellingusesascenefrom the filmHigh Wind in Jamaica.4 “The pirate captain Chavez wants hiscaptivetotellwherethemoneyishidden,andputshisknifetotheman’sthroattomakehimtalk.Afteramomentortwo,duringwhichthemankeepshismouthshut,thematelaughs.‘Ifyoucuthisthroathecan’ttellyou.Heknowsit.Andheknowsyouknowit.’Chavezputshisknifeawayandtriessomethingelse.”

Chavezmighthavekepttheknifeoutandtriedbrinkmanship,ifonlyhehadseen The Maltese Falcon. There Spade (Humphrey Bogart) has hidden thevaluablebird,andGutman(SydneyGreenstreet)istryingtofindoutwhereitis.

SpadesmiledattheLevantineandansweredhimevenly:“Youwantthebird.I’vegotit….Ifyoukillmehowareyougoingtogetthebird?IfIknowthatyoucan’taffordtokillmetillyouhaveit,howareyougoingtoscaremeintogivingittoyou?”

Inresponse,Gutmanexplainshowheintendstomakehisthreatcredible.

“Iseewhatyoumean.”Gutmanchuckled.“Thatisanattitude,sir,thatcallsforthemostdelicatejudgementonbothsides,becauseasyouknow,sir,menare

likelytoforgetintheheatoftheactionwheretheirbestinterestliesandlettheiremotionscarrythemaway.”5

Gutmanconcedesthathecan’tthreatenSpadewithcertaindeath.Instead,hecanexposeSpadetoarisk,aprobabilitythatthingsmightgetoutofcontrolinthe heat of the moment. The outcome is left to chance. It’s not that Gutmanwould actually want to kill Spade, but accidents do occur. And death isirreversible.GutmancannotcommittokillingSpadeforsureifSpaderefusestotalk. But he can threaten to put Spade in a position inwhichGutman cannotguaranteethathewillbeabletopreventSpadefromgettingkilled.*Thisabilityto expose someone to aprobabilityofpunishment canbe enough tomake thethreateffectiveifthepunishmentisbadenough.

Thegreater the riskofSpadegettingkilled in thisway, themoreeffectivethethreat.Butatthesametime,theriskbecomeslesstolerabletoGutman,andthereforethethreatbecomeslesscredible.Gutman’sbrinkmanshipwillworkif,andonlyif,thereisanintermediaterangeofprobabilitieswheretheriskislargeenoughtocompelSpadetorevealthebird’slocation,andyetsmallenoughtobeacceptable to Gutman. Such a range exists only if Spade values his own lifemorethanGutmanvaluesthebird,inthesensethattheprobabilityofdeaththatwillfrightenSpadeintotalkingissmallerthantheriskoflosinghisinformationthat gives Gutman pause. Brinkmanship is not just the creation of risk, but acarefulcontrolofthedegreeofthatrisk.

Nowwehave a problem.Manyof themechanisms that generate risk alsoprevent a sufficiently accurate control of the degree of that risk.We sawhowKennedycoulduseinternalpoliticsandstandardoperatingprocedurestoensurethat the situation would get somewhat outside his control, and therefore notaffectedbyKennedy’s temptationtobackdown.But thoseverythingsmakeitdifficult for him to ensure that the risk does not climb to a degree that isintolerable to theUnitedStates.Kennedy’sownestimateof the risk—betweenone out of three and even—is a wide range of risk, to the point where oneworries if the risk is being controlled at all.We have no perfect or generallyvalid answer to this dilemma. Brinkmanship is often an effective device, butequallyoftenitremainssomethingofanadventure.

4.GETTINGOFFTHEBRINK

Thereisafinalaspectofcontrolthatisessentialforeffectivebrinkmanship.Thethreatenedpartymustbeabletoreducetherisksufficiently,oftenallthewaytozero,byagreeing to thebrinkman’s terms.Spademusthave theassurance thatGutman’stemperwillcooldownsufficientlyquicklyonceheknowsthesecret,andKhrushchevmustbesurethattheUnitedStatesforceswillwithdrawassoonashecomplies.Otherwiseyouaredamnedifyoudoanddamnedifyoudon’t,andthereisnoincentivetocomply.

TheconductofAmerica’stradepolicyillustratesbrinkmanshipwithoutthecontrolmechanism.TheUnitedStates trade administration tries to compel theJapaneseandtheKoreanstoopentheirmarketstoAmericanexports(andalsotoexport less to the United States) by pointing out the risk of more seriousprotectionistactionsbytheCongress.“Ifwecan’treachamoderateagreement,theCongresswill enact restrictions thatwill be a lotworse for you.”The so-called voluntary export restraints on automobiles agreed to by Japan in 1981weretheresultofjustsuchaprocess.Theproblemwiththeregularuseofsuchtactics in trade negotiations is that they can create risk, but cannot control itwithin the requisite range. When other issues are occupying the legislators’attention, the risk of protectionist action by Congress is too low to be aneffectivethreat.Ontheotherhand,whentheCongressisexercisedabouttradedeficits,theriskiseithertoohightobeacceptabletoourownadministration,orsimply unresponsive to amodest foreign restraint and therefore an ineffectivethreat. Inotherwords, theAmericansystemofchecksandbalancescancreaterisk,butcannotcontroliteffectively.

5.FALLINGOFFTHEBRINKWithanyexerciseofbrinkmanship,thereisalwaysthedangeroffallingoffthebrink.WhilestrategistslookbackattheCubanmissilecrisisasasuccessfuluseof brinkmanship, our evaluation would be very different if the risk of asuperpower war had turned into a reality.6 The survivors would have cursedKennedy for recklesslyandunnecessarily flamingacrisis intoaconflagration.Yet in an exercise of brinkmanship, the risk of falling off the brink willsometimesturnintoareality.ThemassacreoftheChinesestudentsinJune1989isasadexample.ThestudentsoccupyingBeijing’sTiananmenSquarewereonacollisioncoursewiththehard-linersintheirgovernment.Onesidewouldhavetolose;eitherthehard-linerswouldcedepowertomorereform-mindedleadersorthe students would compromise on their demands. During the confrontation,therewasacontinualriskthat thehard-linerswouldoverreactanduseforceto

squelch the democracy movement. When two sides are playing a game ofbrinkmanship and neither side is backing down, there is a chance that thesituationwillgetoutofcontrol,withtragicconsequences.

In the aftermath of Tiananmen Square, government leaders became moreaware of the dangers in brinkmanship—for both sides. Faced with similardemocracyprotestsinEastGermanyandCzechoslovakia,thecommunistleadersdecidedtogiveintopopulardemands.InRomania,thegovernmenttriedtoholdfirm against a reformmovement, using violent repression to maintain power.Theviolenceescalatedalmosttothelevelofacivilwar,andintheendPresidentNicolaeCeausescuwasexecutedforcrimesagainsthispeople.

6.NUCLEARBRINKMANSHIPLetusput someof these ideas togetherand lookathow theUnitedStateshasused nuclear brinkmanship as an effective deterrent.Now that the coldwar isoverandthearmsraceiswindingdown,wecanexaminenuclearbrinkmanshipinacoolanalyticalwaythatwashardtoachieveearlier.Manyarguethatthereisaparadoxinnuclearweaponsbecausetheyposetoobigathreatevertouse.Iftheirusecannotberational,thenthethreatcannotberationaleither.Thisisjustthe Gutman-Spade exchange writ large. Without the threat value, nuclearweaponsareimpotentindeterringminorconflicts.

ThisiswhytheEuropeansfearedthatNATO’snuclearumbrellamightproveapoorshieldagainsttherainofsuperiorSovietconventionalforces.EveniftheUnited States is resolved to defend Europe, the argument went, the threat ofnuclearresponseisnotcredibleagainstsmallSoviettransgressions.TheSovietscanexploit thisusing“salami tactics,”asliceata time. Imagine that thereareriots inWest Berlin and some fires. East German fire brigades come to help.Does theU.S.presidentpress thenuclearbutton?Ofcoursenot.EastGermanpolice arrive in support. The button?No. They stay, and a few days later arereplacedbyEastGermantroops.Ateachpoint,theincrementalaggressionistoosmall to merit a drastic response. NATO keeps on redrawing the line of itstolerance. Eventually, the Soviets could be at Trafalgar Square, and NATOheadquartersinexilewouldbewonderingjustwhenitwasthattheymissedtheirchance.7

This conclusion was mistaken. The threat of a U.S. nuclear response toconventionalSoviet aggression inEuropewasoneofbrinkmanship.There aretwoways for getting around the problemof redrawing the line.Brinkmanshipusesboth.First,youarrangetotakethecontrolforpunishmentoutofyourhands

soastodenyyourselftheopportunitytoredrawtheline.Second,youtransformtheprecipiceintoaslipperyslope.Witheachstepfurtherdowntheslopethereistheriskoflosingcontrolandfallingintotheabyss.Inthisway,anopponentwhotriestoavoidyourthreatthroughsalamitacticsfindshimselfconstantlyexposedtoasmallchanceofdisaster.Eachslicehetakes,nomatterhowsmall,maybetheproverbial last straw.Theessential ingredient inmaking this typeof threatcredible is thatneitheryounoryourrivalknowsjustwhere thebreakingpointlies.

Asmallriskofdisastercanhavethesamethreatvalueasthecertaintyofasmallerpunishment.TheUnitedStateshasusedthenuclearthreatbycreatingarisk that themissileswill fly even thoughat that time thegovernmentwill betryingashardasitcantopreventtheattack.TheUnitedStates’sthreatwouldbecarriedoutonlyinspiteofitself.Thethreatofnuclearweaponryisthatitwillbeused inadvertently.Nuclear deterrence becomes crediblewhen there exists thepossibilityforanyconventionalconflicttoescalateoutofcontrol.Thethreatisnotacertaintybutratheraprobabilityofmutualdestruction.

As a conflict escalates, the probability of a chain of events leading to anuclear confrontation increases. Eventually the probability of war will besufficientlyhighthatonesidewillwanttobackdown.Butthewheelsofwarsetinmotionhaveamomentumall theirown,and theconcessionsmaycome toolate.Unanticipated, inadvertent,perhapsaccidentalor irrationalactionsbeyondtheleaders’controlwillprovidethepathofescalationtonuclearweapons.M.I.T.politicalscienceprofessorBarryPosenputthiswell:

Escalationhasgenerallybeenconceivedofaseitherarationalpolicychoice,in which the leadership decides to preempt or to escalate in the face of aconventional defeat, or as an accident, the result of a mechanical failure,unauthorizeduse,orinsanity.Butescalationarisingoutofthenormalconductofintense conventional conflict fallsbetween these twocategories: it isneither apurposeful act of policy nor an accident. What might be called “inadvertentescalation” is rather the unintended consequence of a decision to fight aconventionalwar.8

Nuclear deterrence involves a fundamental trade-off. There is a value inbeingabletomakethethreatofmutualdestruction.Thenuclearagehasenjoyedfortyyearswithoutaworldwar.Butthereisacostinleavingourfatetochance.Nucleardeterrencerequiresacceptingsomeriskofmutualdestruction.Muchof

thedebateaboutnucleardeterrencecentersonthisrisk.Whatcanwedotolowertheprobabilityofnuclearwarwithoutlosingthevalueofdeterrence?

The trick, as usual, is to keep such generalized riskwithin the bounds ofeffectivenessandacceptability. In thischapterwehavegivensomepointers tohowthiscanbedone,butultimatelysuccessfulbrinkmanshipremainssomethingofanartandanadventure.

7.CASESTUDY#8:BRINKMANSHIPINTHEATLANTIC

“At the outbreak of war, the Navy would move aggressively into theNorwegian Sea, first with submarines and then with several aircraft carriers.TheywouldrollbacktheSovietfleet,andattackitshomebasestations,strikingports and any bastions within reach of the carriers’ attack planes.”—JohnLehman,U.S.NavySecretary(1981-87)

“TothreatenSovietnuclearmissilesubmarinesistowagenuclearwar.Itisveryescalatory.”—BarryPosen,ProfessorofPoliticalScience,MIT9

Posen argues that the U.S. Navy is following a very dangerous andescalatorypolicyintheAtlantic.IntheeventofanyconventionalconflictwiththeU.S.S.R.,theU.S.NavywillattempttosinkallSovietsubsintheAtlantic.The problem with this strategy is that, at present, the United States cannotdistinguishnuclear fromnonnucleararmedsubmarines.Hence there is therisktheUnitedStateswillcrossthenuclearthresholdunknowinglybyinadvertentlysinkingaSovietsubmarinewithnuclearweapons.AtthatpointtheSovietswillfeel justified in attackingAmericannuclearweapons, andwewill beone steptooclosetoanall-outexchange.

SecretaryoftheNavyJohnLehmandefendsthepolicyjustasvigorouslyasPosen attacks it. He recognizes the increased chance that a conventional warwould escalate into a nuclear conflict. But he reasons that the Soviets shouldrecognize this too!The increasedchanceof escalationwas justifiedbecause itwoulddecreasethechanceofaconventionalconflictinthefirstplace.

Onwhichsideofthefencedoesbrinkmanshiplie?

CaseDiscussionOurunderstandingofbrinkmanship isunlikely topleaseeither side.When the

goal is to prevent a nuclear war, the policy should not have any effect. Theincreasedchanceofaconventionalconflictescalatingshouldbeexactlyoffsetbyadecreaseintheprobabilityofinitiatingaconventionalconflict.

Ananalogymightprovehelpful.Supposewe try tomakeduelingsaferbyreducingtheaccuracyof thepistols.The likelyoutcomeis that theadversarieswillcomecloser tooneanotherbefore firing.Suppose that theadversariesareequallygoodshots,andthatkillingtheotherpersonearnstherewardof1,andthatbeingkilledincursthepenaltyof-1.Thentheoptimalstrategyisforthetwotokeeponapproachingeachother,andfirethemomenttheprobabilityofhittingreaches 1/2.Theprobability of a fatal hit is the same (3/4) irrespective of theaccuracyofthepistols.Achangeintherulesneednotaffecttheoutcome;alltheplayerscanadjusttheirstrategiestooffsetit.

TodetertheSovietsfrominitiatingaconventionalattack,theUnitedStatesmust expose them to some risk that the conflict will escalate to a nuclearexchange.Iftheriskalongoneroutegrowslarger,thentheSovietswilladvancedownthatroutemoreslowly.AndtheAmericanswillbemorelikely(aswilltheSoviets)toofferaconcession,knowingthatbothcountriesfacethisbiggerrisk.

BoththeAmericansandtheSovietsshouldevaluatetheirstrategiesbytheirconsequences,nottheactionsperse.Foranotherhelpfulwaytothinkaboutthis,imaginethatthetwopartiesareengagedinanauction.Insteadofbiddingdollarsor rubles, they arebiddingprobabilitiesofdisaster.At somepoint thebiddinggets too rich.One sidedecides tobackdown rather thanescalate to a twenty-threepercent chanceofmutual loss.But itmayhavewaited too long, and theprobabilityofalosscouldalreadyhaveturnedintothebadoutcome.

InaconflictbetweentheUnitedStatesandtheSovietUnion,thebidsaretheprobabilitythattheconflictwillescalate.Howthetwosidescommunicatetheirbids depends critically on the rules of the game.But changing the rules alonecannotmake brinkmanship a safer game to play. If theUnited Stateswere tochange itspolicy in theAtlantic, theSovietscould simplyadjust theirbiddingstrategytorestorethesamepressureontheUnitedStates.Inasaferworld,thecountries can takemore escalatory steps.When the threat is a probability, theSovietscanalwaysadjusttheiractionssoastokeeptheprobabilitythesame.

Thisconclusiondoesnotmeanthatyoushouldgiveupandberesigned totheriskofnuclearwar.Toreducetherisks,youhavetoattacktheproblematamorefundamentallevel—thegamemustbechanged.WereFrenchandGermanaristocratstohaveusedlessaccurateduelingpistols,thatwouldnothavehelpedthemtolivelonger.Rather,theywouldhavetohavechangedthehonorcodethatinitiatedaduelatthedropofaglove.AstheUnitedStatesandtheSovietUnionbegintosharethesameobjectives,thatchangesthegame,notjusttherules.

CooperationandCoordination

“Itisnotfromthebenevolenceofthebutcher,thebrewerorthebakerthatweexpectourdinner,butfromtheirregardtotheirownselfinterest….[Everyindividual]intendsonlyhisownsecurity,onlyhisowngain.Andheisinthisledbyaninvisiblehandtopromoteanendwhichwasnopartofhis intention.Bypursuing his own interest, he frequently promotes that of society moreeffectuallythanwhenhereallyintendstopromoteit.”

AdamSmithwrotethisin1776inTheWealthofNations.Eversince,thesewordshavebeenmusic to theearsof free-marketadvocates.Theefficiencyofthe economic marketplace is then interpreted to suggest that a governmentshouldnotinterferewithindividuals’selfishattemptstomaximizetheirinterests.Some free-marketers are inclined to take this ideabeyond the economic realmandlikeDr.PanglossinCandideclaimthat“everythingisforthebestinthis,thebestofallpossibleworlds.”

The sad reality is thatAdamSmith’s invisible hand has a relatively smallspan.Thereisnogeneralpresumptionthatwheneverypersonpursueshisowninterest,theoutcomewillbethebestofallpossibleworlds.Eveninthenarrowersphereofeconomicaffairs,thereareimportantcaveatsandexceptionstotheruleoftheinvisiblehand.

Game theory provides a natural way to think about social interactions ofindividuals. Every person has his own aims and strategies; we bring themtogether and examine the equilibrium of the game in which these strategiesinteract. Remember that there is no presumption that an equilibriummust begood;wehavetofindoutineachsituationwhethertheoutcomeisawarofeachagainst all, or the best of all possible worlds, or something between theseextremes.

Why did Adam Smith think the invisible hand would produce goodeconomicresultsforsociety?Verybriefly,hisargumentwentasfollows.WhenI

buyaloafofbread,Iamusingupsomesociallyvaluableresources—thewheat,thefuel,theservicesoftheoven,thelabor,andsoon—thatgointomakingtheloaf.What stopsme fromover-using these resources is thepriceof the loaf. IwillbuytheloafonlyifitsvaluetomeexceedsthepriceIhavetopay.Inawell-functioningmarket the price equals the cost of all these resources—the bakerwillnotsellmetheloafunlessthepricecoversallhiscosts,andcompetitionwillprecludehischargingmeahigherprice.ThusIwillbuytheloafonlyifitsvalueto me exceeds the cost of the resources to the rest of society. The marketmechanism, therefore, controls my desire to buymore bread to just the rightextent.It isasif thepricewerea“fine”Ihadtopaytocompensatetherestofsociety for using up its resources.On the other side of the picture, the baker,representing the rest of society, is compensated for his costs in supplying thebreadthatIvalue,andthereforehasjusttherightincentivetoproduceit.

Thesimplicity,theclarity,wedaresaythebeautyofthisargumentexplainitsappeal. In fact the clarity carries with it an equally clear message about itslimitations. The invisible hand at best applies only to situations in whicheverything has a price. In many instances outside of economics, and even inmanywithin,peoplearenotchargedafinefordoingharmtotherestofsociety,norgivenarewardfordoinggoodtosomeoneelse.Forexample,manufacturersarerarelychargedanadequatepriceforusingupcleanair,norcompensatedfortraining a worker who might then quit and find other employment. Herepollutionisanunpricedgood(actuallyabad),andtheproblemisthatthereisnoeconomic incentive to temper the firm’s selfish interest in supplying a largeamountofpollution.Whenafirmtrainsaworker, thisgoodisnot tradedonamarket,so there isnoprice toguidethefirm’saction; thefirmmustequate itsowncostswithbenefitsandcannotcapturethewillingnessofotherstopayforthisservice. In theprisoners’dilemma,whenoneprisonerconfesses,heharmshiscolleaguebutisnotfined.Becausemanyunpricedornon-marketedactivitiesmatter,itisnowonderthatindividualsactingselfishlyoftendotoomuchharmtoothers,andtoolittlegood.

Withinthisbroadtheme,thefailuresoftheinvisiblehandcanoccurinmanyways.Everyonemightdotheindividuallybestthing,butthisendsupworstfromtheircollectiveviewpoint,asintheprisoners’dilemma.Toomanypeoplemightdothewrongthing,oreveryonemightdotoomuchofthewrongthing.Someoftheseproblemsareamenable tosocialpolicies;others, lessso.Thesections inthischapterdiscussthedifferenttypesoffailuresinturn.Foreach,wedevelopone central example, and then showhow the sameproblemarisesmuchmorewidelyandsuggesthowitmaybesolved.

1.FORWHOMTHEBELLCURVETOLLSIn the1950s the IvyLeaguecollegeswere facedwithaproblem.Each schoolwanted to produce a winning football team. The colleges found themselvesoveremphasizingathleticsandcompromising theiracademicstandards inordertobuildachampionship team.Yet,nomatterhowoften theypracticedorhowmuchmoney they spent, at the end of the season the standingsweremuch asthey had been before. The average win/loss record was still 50/50. Theinescapablemathematicalfactisthatforeverywinnertherehadtobealoser.Alltheextraworkcanceleditselfout.

The excitement of college sports depends as much on the closeness andintensity of the competition as on the level of skill.Many fans prefer collegebasketball and football to the professional versions;while the level of skill islower,thereisoftenmoreexcitementandintensitytothecompetition.Withthisidea inmind, the colleges got smart.They joined together and agreed to limitspringtrainingtooneday.Althoughthereweremorefumbles, thegameswereno less exciting. Athletes had more time to concentrate on their studies.Everyonewasbetteroff,exceptsomealumniwhowantedtheiralmamaters toexcelatfootballandforgetaboutacademicwork.

Many students would like to have a similar agreement with their fellowstudents before examinations. When grades are based on a traditional “bellcurve,”one’srelativestandingintheclassmattersmorethantheabsolutelevelofone’sknowledge.Itmattersnothowmuchyouknow,onlythatothersknowlessthanyou.Thewaytogainanadvantageovertheotherstudentsistostudymore.Iftheyalldoso,theyallhavemoreknowledge,buttherelativestandingsand therefore the bottom line—the grades—are largely unchanged. If onlyeveryone in the class could agree to limit spring studying to one (preferablyrainy)day,theywouldgetthesamegradeswithlesseffort.

The feature common to these situations is that success is determined byrelative rather than absolute performance.When one participant improves hisownranking,henecessarilyworsenseveryoneelse’s ranking.But the fact thatone’svictoryrequiressomeoneelse’sdefeatdoesnotmakethegamezero-sum.Inazero-sumgameitisnotpossibletomakeeveryonebetteroff.Here,itis.Thescopeforgaincomesfromreducingtheinputs.Whiletheremightalwaysbethesamenumberofwinnersandlosers,itcanbelesscostlyforeveryonetoplaythegame.

The sourceof theproblemofwhy (some) students study toomuch is thattheydo not have to pay a price or compensation to the others.Each student’s

studying is akin to a factory’s polluting: it makes it more difficult for all theother students to breathe. Because there is no market in buying and sellingstudyingtime,theresultisa“ratrace”:eachparticipantstrivestoohard,withtoolittletoshowforhisefforts.Butnooneteamorstudentiswillingtobetheonlyone,or the leader, in reducing theeffort.This is just likeaprisoners’dilemmawithmorethantwoprisoners.Escapefromthehornsofthisdilemmarequiresanenforceablecollectiveagreement.

AswesawwithOPECand theIvyLeague, the trick is to formacartel tolimitcompetition.Theproblemforhigh-schoolstudentsisthatthecartelcannoteasily detect cheating. For the collectivity of students, a cheater is one whostudiesmoretosneakanadvantageovertheothers.Itisveryhardtotellifsomearesecretlystudyinguntilaftertheyhave“aced”thetest.Bythenitistoolate.In some small towns, high-school students do have a way to enforce “no-studying”cartels.Everyonegets togetherandcruisesMainStreetatnight.Theabsenceofthosehomestudyingisnoticed.Punishmentcanbesocialostracismorworse.

Toarrangeaself-enforcingcartelisdifficult.Itisallthebetterifanoutsiderenforces the collective agreement limiting competition. This is just whathappened for cigarette advertising, although not intentionally. In the old days,cigarette companies used to spend money to convince consumers to “walk amile”fortheirproductorto“fightratherthanswitch.”Thedifferentcampaignsmade advertising agencies rich, but their main purpose was defensive—eachcompany advertised because the others did, too. Then, in 1968, cigaretteadvertisements were banned from TV by law. The companies thought thisrestrictionwouldhurtthemandfoughtagainstit.But,whenthesmokecleared,they saw that the ban helped them avoid mutually damaging and costlyadvertisingcampaignsandthusimprovedtheirprofits.

2.THEROUTELESSTRAVELEDThereare twomainways tocommute fromBerkeley toSanFrancisco.One isdriving over theBayBridge, and the other is taking public transportation, theBayAreaRapidTransit train calledBART.Crossing thebridge is the shortestroute,andwithnotraffic,acarcanmakethetripin20minutes.Butthatisrarelythecase.Thebridgehasonly four lanesand is easilycongested.*We supposethateachadditional2,000cars(perhour)causesa10minutedelayforeveryoneontheroad.Forexample,with2,000carsthetraveltimerisesto30minutes;at4,000cars,to40minutes.

TheBARTtrainmakesanumberofstops,andonehastowalktothestationandwait for the train. It is fair to say that the trip takes closer to 40minutesalong this route,but the trainnever fights traffic.When trainusage rises, theyputonmorecars,andthecommutingtimestaysroughlyconstant.

If,duringtherushhour,10,000commuterswanttogofromBerkeleytoSanFrancisco, how will the commuters be distributed over the two routes? Eachcommuter will act selfishly, choosing the route that minimizes his owntransportation time. Left to their own devices, 40 percent will drive and 60percentwilltakethetrain.Thecommutingtimewillbe40minutesforeveryone.Thisoutcomeistheequilibriumofagame.

We can see this result by asking what would happen if the split weredifferent.Supposeonly2,000driverstooktheBayBridge.Withlesscongestion,the tripwould take less time (30minutes) along this route. Then some of the8,000BARTcommuterswouldfindoutthattheycouldsavetimebyswitching,andwould do so. Conversely, if therewere, say, 8,000 drivers using the BayBridge,eachspending60minutes, someof themwouldswitch to the train forthe faster trip itprovides.Butwhen thereare4,000driverson theBayBridgeand 6,000 on the train, no one can gain by switching: the commuters havereachedanequilibrium.

Wecanshowtheequilibriumusingasimplechart,whichisquitesimilarinspirit to the one in Chapter 4 describing the classroom experiment of theprisoners’ dilemma. The line AB represents the 10,000 commuters, with thenumberusingtheBayBridgemeasuredfromAandthenumberonthetrainfromB.Verticalheightsmeasuretraveltimes.TherisinglineDEFshowshowthetriptimeontheBayBridgeincreasesas thenumberofdriversonit increases.Theflatlineshowstheconstanttimeof40minutesforthetrain.ThelinesintersectatE,showingthat the trip timesonthe tworoutesareequalwhenthenumberofdrivers on the Bay Bridge, namely the length AC, is 4,000. This graphicdepictionofequilibriumisaveryusefultooltodescribetheequilibrium;wewilluseitofteninthischapter.

Isthisequilibriumgoodforthecommutersasawhole?Notreally.Itiseasy

tofindabetterpattern.Supposeonly2,000taketheBayBridge.Eachofthemsaves10minutes.The2,000whoswitchtothetrainarestillspendingthesametimeas theydidbefore,namely40minutes.Soare the6,000whocontinue totakethetrain.Wehavejustsaved20,000person-minutes(oralmosttwoweeks)fromthetotaltraveltime.

Whyisthissavingpossible?Orinotherwords,whywerethedriverslefttothemselves not guided by an invisible hand to the best mix of routes? Theanswer again lies in the cost that each user of the Bay Bridge inflicts on theothers.Whenanextradrivertakesthisroad,thetraveltimeofalltheotherusersgoes up by a little bit. But the newcomer is not required to pay a price thatreflectsthiscost.Hetakesintoaccountonlyhisowntraveltime.

Whattrafficpatternisbestforthegroupofdriversasawhole?Infact,theoneweconstructed,with2,000carsontheBayBridgeandatotaltimesavingof20,000minutes,isbest.Toseethis,tryacoupleofothers.Ifthereare3,000carson theBayBridge, the travel time is 35minutes,with a saving of 5minuteseach, or 15,000 minutes in all. With only 1,000 cars, the travel time is 25minutes, and each saves 15minutes, but the total saving is again only 15,000minutes.The intermediatepointwith2,000drivers,eachsaving10minutes, isbest.

How can the best pattern be achieved? Devotees of central planning willthinkofissuing2,000licensestousetheBayBridge.Iftheyareworriedaboutthe inequity of allowing thosewith licenses to travel in 30minuteswhile theother 8,000 must take the train and spend 40 minutes, they will devise aningenioussystemofrotatingthelicensesamongthepopulationeverymonth.

Amarket-based solutionchargespeople for theharm theycause toothers.Suppose each person values an hour of time at $12, that is, each would bewilling to pay$12 to save an hour.Then charge a toll for drivingon theBayBridge;setthetoll$2abovetheBARTfare.Byoursupposition,peopleregard

an extra $2 cost as equivalent to 10 minutes of time. Now the equilibriumcommutingpatternwillhave2,000carsontheBayBridgeand8,000ridersonBART. Each user of the Bay Bridge spends 30 minutes plus an extra $2 incommutingcosts;eachBARTriderspends40minutes.Thetotaleffectivecostsare thesame,andnoonewants toswitch to theotherroute. In theprocesswehave collected $4,000 of toll revenue (plus an additional 2,000 BART fares),which can then go into the county’s budget, thus benefiting everyone becausetaxescanbelowerthantheywouldotherwisebe.

A solution even closer to the spirit of free enterprise would be to allowprivateownershipoftheBayBridge.Theownerrealizesthatpeoplearewillingtopayfortheadvantageofafastertriponalesscongestedroad.Hechargesaprice, therefore, for the privilege. How can he maximize his revenue? Bymaximizingthetotalvalueofthetimesaved,ofcourse.

The invisible hand guides people to an optimal commuting pattern onlywhenthegood“commutingtime”ispriced.Withtheprofit-maximizingtollonthebridge, timereally ismoney.ThosecommuterswhorideBARTaresellingtimetothosewhousethebridge.

Finally,werecognizethatthecostofcollectingthetollsometimesexceedstheresultingbenefitofsavingpeople’stime.Creatingamarketplaceisnotafreelunch.Thetollboothsmaybeaprimarycauseofthecongestion.Ifso,itmaybebesttotoleratetheinitialinefficientroutechoices.

3.CATCH-22?

Chapter3offeredthefirstexamplesofgameswithmanyequilibria.Conventionsfor driving on one side of the road orwho should return disconnected phonecallswere the twocases. In those examples itwasnot importantwhichof theconventionswas chosen, so long as everyone agreed on the same convention.Butsometimesoneconventionismuchbetterthananother.Evenso,thatdoesn’tmeanitwillalwaysgetadopted.Ifoneconventionhasbecomeestablishedandthen some change in circumstances makes another one more desirable, it isespeciallyhardtobringaboutthechange.

Thekeyboarddesignonmosttypewritersisacaseinpoint.Inthelate1800s,therewas no standard pattern for the arrangement of letters on the typewriterkeyboard.Then in 1873ChristopherScholes helpeddesign a “new improved”layout.The layoutbecameknownasQWERTY,after the letterarrangementof

thesixlettersinthetopleftrow.QWERTYwaschosentomaximizethedistancebetweenthemostfrequentlyusedletters.Thiswasagoodsolutioninitsday;itdeliberatelysloweddownthetypist,andreducedthejammingofkeysonmanualtypewriters.By1904, theRemingtonSewingMachineCompanyofNewYorkwas mass-producing typewriters with this layout, and it became the de factoindustrystandard.Butwithtoday’selectrictypewritersandwordprocessors,thisjammingproblemisnowcompletelyirrelevant.Engineershavedevelopednewkeyboardlayouts,suchasDSK(Dvorak’sSimplifiedKeyboard),whichreducethedistancetypists’fingers travelbyoverfiftypercent.Thesamematerialcanbetypedin5–10percentlesstimeusingDSKthanQWERTY.1ButQWERTYistheestablishedsystem.Almostall typewritersuse it, soweall learn itandarereluctant to learn a second keyboard. Typewriter and keyboardmanufacturerscontinue,therefore,withQWERTY.Theviciouscircleiscomplete.2

Ifhistoryhadworkeddifferently,andiftheDSKstandardhadbeenadoptedfrom theoutset, thatwouldhavebeenbetter for today’s technology.However,givenwhereweare,thequestionofwhetherornotweshouldswitchstandardsinvolves a further consideration. There is a lot of inertia, in the form ofmachines,keyboards,andtrainedtypists,behindQWERTY.Isitworthwhiletoretool?

Fromthepointofviewofsocietyasawhole,theanswerwouldseemtobeyes.During theSecondWorldWar, theU.S.NavyusedDSKtypewritersonalargescale,andretrainedtypiststousethem.Itfoundthatthecostofretrainingcouldbefullyrecoupedinonlytendaysofuse.

Wouldprivateemployersdotheretraining?Theymightiftheyknewitwascost-effective.DiscoveringtheinformationabouttheefficacyofDSKisacostlyendeavor. No wonder that few private employers are willing to perform thisservice,andittooksomeoneaslargeastheU.S.Navytotryitfirst.

Asmechanicaltypewritersarereplacedbyelectroniconesandbycomputerkeyboards,eventheexistingstockofQWERTYkeyboards isa lesssignificantbarrier to change; the keys can be reassigned by changing just one chip orrewriting some software.However, it has proved impossible to get out of theviciouscircle.No individualuserwouldwant tobear thecostofchanging thesocial convention. Uncoordinated decisions of individuals keep us tied toQWERTY.

Theproblem is calledabandwagoneffect andcanbe illustratedusing thefollowing chart. On the horizontal axis we show the fraction of typists usingQWERTY. The vertical axis details the chance that a new typist will learnQWERTY as opposed to DSK. As drawn, if 85 percent of typists are using

QWERTY,thenthechancesare95percentthatanewtypistwillchoosetolearnQWERTYandonly5percent that thenewtypistwill learnDSK.Thewaythecurve is drawn is meant to emphasize the superiority of the DSK layout. Amajority of new typists will learn DSK rather than QWERTY provided thatQWERTY has anything less than a 70 percent market share. In spite of thishandicap,itispossibleforQWERTYtodominateinequilibrium.

Thechoiceofwhichkeyboardtouseisastrategy.Whenthefractionusing

each technology is constant over time,we are at an equilibrium of the game.Showing that this game converges to an equilibrium is not easy. The randomchoice of each new typist is constantly disrupting the system. Recent high-powered mathematical tools, namely stochastic approximation theory, haveallowed economists and statisticians to prove that this dynamic game doesconvergetoanequilibrium.3Wenowdescribethepossibleoutcomes.

If the fraction of typists usingQWERTY exceeds 72 percent, there is theexpectation that an even greater fraction of people will learn QWERTY. ThespanofQWERTYexpandsuntilitreaches98percent.Atthatpoint,thefractionofnewtypistslearningQWERTYjustequalsitspredominanceinthepopulation,98percent,andsothereisnomoreupwardpressure.*

Conversely,ifthefractionoftypistsusingQWERTYfallsbelow72percent,

thenthereistheexpectationthatDSKwilltakeover.Fewerthan72percentofthenewtypists learnQWERTY,andthesubsequentfall in itsusagegivesnewtypistsanevengreater incentive to learn thesuperior layoutofDSK.OncealltypistsareusingDSKthereisnoreasonforanewtypisttolearnQWERTY,andQWERTYwilldieoutaltogether.

Themathematicssaysonlythatwewillendupatoneofthesetwopossibleoutcomes:everyoneusingDSKor98percentusingQWERTY.Itdoesnotsaywhichwilloccur.Ifwewerestartingfromscratch,theoddsareinfavorofDSKbeing the predominant keyboard layout. Butwe are not.Historymatters. ThehistoricalaccidentthatledtoQWERTYcapturingnearly100percentoftypistsends up being self-perpetuating, even though the original motivation forQWERTYislongsinceobsolete.

Since bad luck or the convergence to an inferior equilibrium is self-perpetuating, there is the possibility of making everyone better off. But itrequirescoordinatedaction.Ifthemajorcomputermanufacturerscoordinateona new keyboard layout or a major employer such as the federal governmenttrainsitsemployeesonanewkeyboard, thiscanswitchtheequilibriumall thewayfromoneextremetotheother.Theessentialpointisthatitisnotnecessarytoconverteveryone, justacriticalmass.Givenenoughofa toehold, thebettertechnologycantakeitfromthere.

The QWERTY problem is but one minor example of a more widespreadproblem.Ourpreferenceforgasolineenginesoversteamandlight-waternuclearreactorsovergas-cooled isbetter explainedbyhistorical accidents thanby thesuperiorityoftheadoptedtechnologies.BrianArthur,aneconomistatStanfordandoneof thedevelopersof themathematical toolsused to studybandwagoneffects,tellsthestoryofhowweendedupwithgasoline-poweredcars.4

In1890therewerethreewaystopowerautomobiles—steam,gasoline,andelectricity—andoftheseonewaspatentlyinferiortotheothertwo:gasoline….[A turning point for gasoline was] an 1895 horseless carriage competitionsponsoredby theChicagoTimes-Herald.Thiswaswonbyagasoline-poweredDuryea—oneofonlytwocarstofinishoutofsixstarters—andhasbeencitedasthepossibleinspirationforR.E.Oldstopatentin1896agasolinepowersource,whichhesubsequentlymass-producedinthe“Curved-DashOlds.”Gasolinethusovercameitsslowstart.Steamcontinuedviableasanautomotivepowersourceuntil 1914, when there was an outbreak of hoof-and-mouth disease in NorthAmerica. This led to thewithdrawal of horse troughs—which iswhere steamcars could fill with water. It took the Stanley brothers about three years todevelopacondenserandboilersystemthatdidnotneedtobefilledeverythirtyorfortymiles.Butbythenitwastoolate.Thesteamengineneverrecovered.

While there is little doubt that today’s gasoline technology is better thansteam, that’snot the rightcomparison.Howgoodwould steamhavebeen if ithadhad thebenefit of seventy-fiveyearsof researchanddevelopment?Whilewemayneverknow,someengineersbelievethatsteamwasthebetterbet.5

In theUnited States, almost all nuclear power is generated by light-waterreactors. Yet there are reasons to believe that the alternative technologies ofheavy-waterorgas-cooled reactorswouldhavebeensuperior, especiallygiventhesameamountof learningandexperience.Canada’sexperiencewithheavy-waterreactorsallowsthemtogeneratepowerfor25percentlesscostthanlight-waterreactorsofequivalentsizeintheUnitedStates.Heavy-waterreactorscanoperatewithouttheneedtoreprocessfuel.Perhapsmostimportantisthesafetycomparison. Both heavy-water and gas-cooled reactors have a significantlylowerriskofameltdown—heavywaterbecausethehighpressureisdistributedovermanytubesratherthanasinglecorevessel,andgas-cooledbecauseofthemuchslowertemperatureriseintheeventofacoolantloss.6

Thequestionofhowlight-waterreactorscametodominatehasrecentlybeenstudiedbyRobinCowen, ina1987StanfordUniversityPh.D. thesis.ThefirstconsumerfornuclearpowerwastheU.S.Navy.In1949,thenCaptainRickovermade the pragmatic choice in favor of light-water reactors. He had two goodreasons.Itwasthenthemostcompacttechnology,animportantconsiderationforsubmarines,anditwasthefurthestadvanced,suggestingthatitwouldhavethe

quickestroutetoimplementation.In1954,thefirstnuclear-poweredsubmarine,Nautilus,waslaunched.Theresultslookedverypositive.

Atthesametimeciviliannuclearpowerbecameahighpriority.TheSovietshad exploded their first nuclear bomb in 1949. In response, Atomic EnergyCommissioner T. Murray warned, “Once we become fully conscious of thepossibilitythat[energy-poor]nationswillgravitatetowardstheUSSRifitwinsthenuclearpowerrace,itwillbequiteclearthatthisraceisnoEverest-climbing,kudos-providing contest.”7 General Electric and Westinghouse, with theirexperience producing light-water reactors for the nuclear-powered submarines,were the natural choice to develop civilian power stations. Considerations ofprovenreliabilityandspeedofimplementationtookprecedenceoverfindingthemostcost-effectiveandsafesttechnology.Althoughlight-waterwasfirstchosenasaninterimtechnology, thisgaveitenoughofaheadstartdownthelearningcurvethattheotheroptionshaveneverhadthechancetocatchup.

TheadoptionofQWERTY,gasolineengines,andlight-waterreactorsarebutthreedemonstrationsofhowhistorymatters indetermining today’s technologychoices. But the historical reasons may be irrelevant considerations in thepresent.Typewriter-keyjamming,hoof-and-mouthdisease,andsubmarinespaceconstraints are not relevant to today’s trade-offs between the competingtechnologies.The important insight fromgame theory is to recognizeearlyonthe potential for future lock-in—once one option has enough of a head start,superior technological alternativesmay never get the chance to develop.Thusthere is apotentiallygreatpayoff in theearly stages fromspendingmore timefiguringoutnotonlywhat technologymeets today’sconstraints,butalsowhatoptionswillbethebestforthefuture.

4.FASTERTHANASPEEDINGTICKETJust how fast should you drive? In particular, should you abide by the speedlimit?Again the answer is foundby looking at the gamewhere your decisioninteractswiththoseofalltheotherdrivers.

Ifnobodyisabidingbythelaw,thenyouhavetworeasonstobreakittoo.First,someexpertsarguethatitisactuallysafertodriveatthesamespeedastheflowoftraffic.8Onmosthighways,anyonewhotriestodriveatfifty-fivemilesper hour creates a dangerous obstacle that everyone else must go around.Second,when you tag alongwith the other speeders, your chances of gettingcaught are almost zero.Thepolice simply cannot pull overmore than a smallpercentageofthespeedingcars.Aslongasyougowiththeflowoftraffic,there

issafetyinnumbers.As more people become law-abiding, both reasons to speed vanish. It

becomesmoredangeroustospeed,sincethiswillrequireweavinginandoutoftraffic.Andyourchancesofgettingcaughtincreasedramatically.

WeshowthisinachartsimilartotheoneforcommutersfromBerkeleytoSanFrancisco.Thehorizontallinemeasuresthepercentageofdriverswhoabideby the speed limit. The lines A and B show each driver’s calculation of hisbenefitfrom(A)abidingbyand(B)breakingthelaw.Ourargumentsaysthatifno one else is keeping under the limit (the left-hand end), neither should you(lineB is higher than lineA); if everyone else is law-abiding (the right-handend),youshouldbetoo(lineAishigherthanlineB).Onceagaintherearethreeequilibria,ofwhichonlytheextremeonescanarisefromtheprocessofsocialdynamicsasdriversadjusttooneanother’sbehavior.

Inthecaseofthecommuterschoosingbetweenthetworoads,thedynamics

convergedontheequilibriuminthemiddle.Herethetendencyistowardoneoftheextremes.Thedifferencearisesbecauseofthewayinteractionswork.Withcommuting,eitherchoicebecomeslessattractivewhenmoreoftheothersfollowyou,whereaswithspeeding,additionalcompanymakesitmoreattractive.

Thegeneralthemeofoneperson’sdecisionaffectingtheothersapplieshere,too.Ifonedriverspeedsup,hemakesitalittlesaferfortheotherstospeed.Ifno one is speeding, no one iswilling to be the first to do so and provide this“benefit”totheotherswithoutbeing“rewarded”fordoingso.Butthereisanewtwist: if everyone is speeding, then no one wants to be the only one to slowdown.

Can this situationbeaffectedbychanging thespeed limit?Thecurvesaredrawnforaspecificspeedlimit,say55m.p.h.Supposethelimitisraisedto65.The value of breaking the limit falls, since beyond a point, higher speeds dobecomedangerous,andtheextraadvantageofgoing75insteadof65islessthan

the gain of going 65 over 55. Furthermore, above 55miles an hour, gasolineconsumptiongoesupexponentiallywithspeed.Itmaybetwentypercentmoreexpensive to drive at 65 than at 55, but it could easily be 40 percent moreexpensivetodriveat75ratherthanat65.

What can lawmakers learn from this if they want to encourage people todrive at the speed limit? It is not necessary to set the speed limit sohigh thateveryoneishappytoobeyit.Thekeyistogetacriticalmassofdriversobeyingthe speed limit. Thus a short phase of extremely strict enforcement and harshpenaltiescanchangethebehaviorofenoughdriverstogeneratethemomentumtoward full compliance. The equilibrium moves from one extreme (whereeveryone speeds) to the other (where everyone complies). With the newequilibrium, the police can cut back on enforcement, and the compliancebehavior is self-sustaining.Moregenerally,what this suggests is that shortbutintenseenforcementcanbesignificantlymoreeffectivethanthesametotaleffortappliedatamoremoderatelevelforalongertime.9

5.WHYDIDTHEYLEAVE?

Americancitieshavefewraciallyintegratedneighborhoods.Iftheproportionofblackresidentsinanarearisesaboveacriticallevel,itquicklyincreasesfurtherto nearly one hundred percent. If it falls below a critical level, the expectedcourse is for the neighborhood to become all white. Preservation of racialbalancerequiressomeingeniouspublicpolicies.

Isthedefactosegregationofmostneighborhoodstheproductofwidespreadracism?Thesedays, a largemajorityof urbanAmericanswould regardmixedneighborhoodsasdesirable.*Themore likelydifficulty is that segregation canresultas theequilibriumofagame inwhicheachhouseholdchooseswhere tolive,evenwhentheyallhaveameasureofracialtolerance.ThisideaisduetoThomas Schelling.10 We shall now outline it, and show how it explains thesuccess of the Chicago suburb, Oak Park, in maintaining an integratedneighborhood.

Racialtoleranceisnotamatterofblackorwhite;thereareshadesofgray.Differentpeople,blackorwhite,havedifferentviewsaboutthebestracialmix.For example, very fewwhites insist on a neighborhood that is 99 or even 95percentwhite;yetmostwillfeeloutofplaceinonethatisonly1or5percentwhite.Themajoritywouldbehappywithamixsomewhereinbetween.

We can illustrate the evolution of neighborhood dynamics using a chartsimilar to the one from the QWERTY story. On the vertical axis is theprobabilitythatanewpersonmovingintotheneighborhoodwillbewhite.Thisisplottedinrelationshiptothecurrentracialmix.Thetoprightendofthecurveshowsthatonceaneighborhoodbecomescompletelysegregated,allwhite, theoddsareoverwhelmingthat thenextpersonwhomoves into theneighborhoodwillalsobewhite.Ifthecurrentmixfallsto95percentor90percentwhite,theoddsarestillveryhighthatthenextpersontomoveinwillalsobewhite.Ifthemixchangesmuchfurther, thenthereisasharpdrop-offintheprobabilitythatthe next person to join the communitywill bewhite; the curve is steep in itsmiddleregion.Finally,astheactualpercentageofwhitesdropstozero,sothattheneighborhoodisnowsegregatedattheotherextreme,theprobabilityisveryhighthatthenextpersontomoveinwillbeblack.

In this situation, the equilibrium will be where the racial mix of the

populationjustexactlyequalsthemixofnewentrantstothecommunity.Onlyinthis event are the dynamics stable. There are three such equilibria: two at theextremes where the neighborhood is all white and all black, and one in themiddlewherethereisamix.Thetheorysofardoesnottelluswhichofthethreeequilibriaisthemostlikely.Inordertoanswerthisquestion,weneedtoexaminetheforcesthatmovethesystemtowardorawayfromanequilibrium,thatis,thesocialdynamicsofthesituation.

The social dynamics will always drive the neighborhood to one of theextremeequilibria.Schellinglabeledthisphenomenon“tipping.”Letusseewhyitoccurs.

Supposethemiddleequilibriumhas70percentwhitesand30percentblacks.

By chance, let one black familymove out and be replaced by awhite family.Then theproportionofwhites in thisneighborhoodbecomesslightlyabove70percent.Lookingat the chart, theprobability that thenext entrantwill alsobewhite is thenabove70percent.Theupwardpressure is reinforcedby thenewentrants. Say the racial mix shifts to 75:25 percent. The tipping pressurecontinues.Thechance thatanewentrantwillbewhite isabove75percent,sothe expectation is that the neighborhoodwill become increasingly segregated.This goes on until the mix of new entrants is the same as the mix in theneighborhood.Asdrawn, that occurs again onlywhen the neighborhood is allwhite.Iftheprocesshadstartedwithonewhitefamilymovingoutandoneblackfamily moving in, there would have been a chain reaction in the oppositedirection,andtheoddsarethattheneighborhoodwouldhavebecomeallblack.

Theproblemisthatthe70:30percentmixisnotastableequilibrium.Ifthismixissomehowdisrupted,aschanceissuretodo,thereisatendencytomovetoward one of the extremes. Sadly, from the extremes there is no similartendencytomovebacktowardthemiddle.Althoughsegregationisthepredictedequilibrium, that does not mean that people are better off at this outcome.Everyonemight prefer to live in amixedneighborhood.But they rarely exist,andevenwhenfoundtendnottolast.

Onceagain,thesourceoftheproblemistheeffectofonehousehold’sactionontheothers.Startingata70:30percentmix,whenonewhitefamilyreplacesablack family, thismaymake theneighborhooda little lessattractive for futureblackstomovein.Butitisnotassessedafineforthis.Byanalogywiththeroadtolls, perhaps there should be a departure tax.But thatwould be counter to amorebasicprinciple,namelythefreedomtolivewhereonechooses.Ifsocietywantstopreventtipping,itmustlookforsomeotherpolicymeasures.

Ifwecannotfineadepartingfamilyforthedamageitcauses,bothtothosewho remain and those who now might choose not to come, we must takemeasures thatwill reduce the incentives forothers to followsuit. Ifonewhitefamily leaves, the neighborhood should not become less attractive to anotherwhite family. Ifoneblack family leaves, theneighborhoodshouldnotbecomelessattractivetoanotherblackfamily.Publicpolicycanhelppreventthetippingprocessfromgatheringmomentum.

The racially integratedChicagosuburbofOakParkprovidesan ingeniousexampleofpoliciesthatwork.Itusestwotools:first, thetownbanstheuseof“For Sale” signs in front yards, and secondly, the town offers insurance thatguarantees homeowners that they will not lose the value of their house andpropertybecauseofachangeintheracialmix.

If by chance two houses on the same street are for sale at the same time,

“ForSale”signswouldspreadthisnewsquicklytoallneighborsandprospectivepurchasers. Eliminating such signsmakes it possible to conceal the news thatwouldbeinterpretedasbad;nobodyneedknowuntilafterahousehasbeensoldthatitwasevenupforsale.Theresultisthatpanicsareavoided(unlesstheyarejustified, inwhich case they are just delayed).By itself, the first policy is notenough.Homeownersmight stillworry that they should sell their housewhilethegoingisgood.Ifyouwaituntiltheneighborhoodhastipped,you’vewaitedtoolongandmayfindthatyou’velostmostofthevalueofyourhome,whichisalargepartofmostpeople’swealth.Oncethetownprovidesinsurance,thisisnolonger an issue. In otherwords, the insurance removes the economic fear thataccelerates tipping. In fact, if the guarantee succeeds in preventing tipping,propertyvalueswillnotfallandthepolicywillnotcostthetaxpayersanything.

Tippingtoanall-blackequilibriumhasbeenthemorecommonprobleminurbanAmerica.Butinrecentyearsgentrification,whichisjusttippingtoanall-richequilibrium,hasbeenontherise.Leftunattended,thefreemarketwilloftenhead to these unsatisfactory outcomes. But public policy, combined with anawareness of how tippingworks, canhelp stop themomentum toward tippingandpreservethedelicatebalances.

6.ITCANBELONELYATTHETOPTop law firms generally choose their partners from among their juniorassociates.Thosenotchosenmustleavethefirm,andgenerallymovetoalower-rankedone.AtthemythicalfirmJustin-Case,thestandardsweresohighthatformanyyearsnonewpartnerswereselected.Thejuniorassociatesprotestedaboutthislackofadvancement.Thepartnersrespondedwithanewsystemthatlookedverydemocratic.

Here iswhat they did.At the time of the annual partnership decision, theabilitiesofthetenjuniorassociateswereratedfrom1to10,with10beingthebest. The junior associates were told their rating privately. Then they wereushered into ameeting roomwhere theywere to decide bymajority vote thecutofflevelforpartnership.

Theyallagreedthateveryonemakingpartnerwasagoodideaandcertainlypreferable to the old days when nobody made partner. So they began with acutoffof1.Thensomehigh-ratedjuniorassociatesuggestedthattheyraisethecutoff to 2. He argued that this would improve the average quality of thepartnership.Nine juniorassociatesagreed.Thesoledissentingvotecamefromtheleastablemember,whowouldnolongermakepartner.

Next, someone proposed that they raise the standard from 2 to 3. Eightpeoplewerestillabovethisstandard,andtheyallvotedforthisimprovementinthequalityof thepartnership.Thepersonranked2votedagainst,as thismovedeprived him of partnership. What was surprising was that the lowest-ratedjunior associate was in favor of this raising of the standards. In neither casewould he make partner. But at least in the latter he would be grouped withsomeone who has ability 2. Therefore, upon seeing that he was not selected,other law firmswouldnotbeable to inferhisexactability.Theywouldguessthathe iseithera1ora2,a levelofuncertainty that is tohisadvantage.Theproposaltoraisethestandardto3passed9:1.

With eachnewcutoff level someoneproposed raising it byone.All thosestrictlyabovevotedinfavorsoastoraisethequalityofthepartnership(withoutsacrificingtheirownposition),whileallthosestrictlybelowjoinedinsupportofraising the standard so as to make their failure less consequential. Each timetherewasonlyonedissenter,theassociaterightatthecutofflevelwhowouldnolongermakepartner.Buthewasoutvoted9:1.

Andsoitwent,until thestandardwasraisedall thewayupto10.Finally,someoneproposedthattheyraisethestandardto11sothatnobodywouldmakepartner.Everybodyrated9andbelowthoughtthatthiswasafineproposal,sinceoncemorethisimprovedtheaveragequalityofthoserejected.Outsiderswouldnottakeitasabadsignthattheydidn’tmakepartner,asnobodymakespartneratthislawfirm.Thesolevoiceagainstwasthemostablejuniorassociate,wholosthischancetomakepartner.Buthewasoutvoted9:1.

Theseriesofvotesbringseverybodybacktotheoldsystem,whichtheyallconsidered worse than the alternative of promotion for all. Even so, eachresolutionalongthewaypassed9:1.Therearetwomoralstothisstory.

Whenactionsaretakeninapiecemealway,eachstepofthewaycanappearattractivetothevastmajorityofdecision-makers.Buttheendisworsethanthebeginning for everyone. The reason is that voting ignores the intensity ofpreferences.Inourexample,allthoseinfavorgainaverysmallamount,whiletheonepersonagainstlosesalot.Intheseriesoftenvotes,eachjuniorassociatehas nine small victories and one major loss that outweighs all the combinedgains. We saw a similar example in Chapter 1 involving trade tariffs oramendmentstothetaxreformbill.

Just because an individual recognizes the problem does not mean anindividualcanstoptheprocess.Itisaslipperyslope,toodangeroustogetonto.Thegroupasawholemust lookaheadand reasonback inacoordinatedway,andsetuptherulessoastopreventtakingthefirststepsontheslope.Thereissafetywhenindividualsagreetoconsiderreformsonlyasapackageratherthan

asaseriesofsmallsteps.Withapackagedeal,everyoneknowswherehewillendup.Aseriesofsmallstepscan lookattractiveat first,butoneunfavorablemovecanmorethanwipeouttheentireseriesofgains.

In1989,Congresslearnedthisdangerfirst-handinitsfailedattempttovoteitselfa50percentpayraise.Initially,thepayraiseseemedtohavewidesupportin both houses. When the public realized what was about to happen, theyprotested loudly to their representatives. Consequently, each member ofCongresshadaprivateincentivetovoteagainstthepayhike,providedheorshethought that the hike would still pass. The best scenario would be to get thehigher salary while having protested against it. Unfortunately (for them) toomanymembersofCongresstookthisapproach,andsuddenlypassagenolongerseemedcertain.Aseachdefectionmovedthemfurtherdowntheslipperyslope,therewasallthemorereasontovoteagainstit.Ifthepayhikeweretofail,theworstpossiblepositionwouldbetogoonrecordsupportingthesalaryhike,paythepoliticalprice,andyetnotgettheraise.Atfirst,therewasthepotentialforafew individuals to selfishly improve their own position. But each defectionincreasedtheincentivetofollowsuit,andsoonenoughtheproposalwasdead.

There isasecond,quitedifferentmoral to theJustin-Casestory.Ifyouaregoing to fail,youmightaswell failatadifficult task.Failurecausesothers todowngrade their expectations of you in the future. The seriousness of thisproblem depends on what you attempt. Failure to climb Mt. Everest isconsiderably less damning than failure to finish a 10K race. The point is thatwhenotherpeople’sperceptionofyourabilitymatters,itmightbebetterforyouto do things that increase your chance of failing in order to reduce itsconsequence.PeoplewhoapplytoHarvardinsteadofthelocalcollege,andaskthemostpopularstudentforapromdateinsteadofamorerealisticprospect,arefollowingsuchstrategies.

Psychologists see this behavior in other contexts. Some individuals areafraidtorecognizethelimitsoftheirownability.Inthesecasestheytakeactionsthat increase the chance of failure in order to avoid facing their ability. Forexample,amarginalstudentmaynotstudyforatestsothatifhefails,thefailurecan be blamed on his lack of studying rather than intrinsic ability. Althoughperverse and counterproductive, there is no invisible hand to protect you ingamesagainstyourself.

7.POLITICIANSANDAPPLECIDERTwo political parties are trying to choose their positions on the liberal-

conservative ideological spectrum. First the challenger takes a stand; then theincumbentresponds.

Suppose the voters range uniformly over the spectrum. For concreteness,numberthepoliticalpositionsfrom0to100,where0representsradicalleftand100representsarch-conservative.Ifthechallengerchoosesapositionsuchas48,slightly more liberal than the middle of the road, the incumbent will take apositionbetweenthatandthemiddle—say,49.Thenvoterswithpreferencesof48 and under will vote for the challenger; all others, making up just over 51percentofthepopulation,willvotefortheincumbent.Theincumbentwillwin.

If thechallenger takesapositionabove50, then the incumbentwill locatebetweenthatand50.Againthiswillgethimmorethanhalfthevotes.

By the principle of looking ahead and reasoning backward, the challengercanfigureoutthathisbestbetistolocaterightinthemiddle.*Atthislocation,the forces pulling for more conservative or more liberal positions have equalnumbers. The best the incumbent can do is imitate the challenger. The twopartiestakeidenticalstands,soeachgetsfiftypercentofthevotesifissuesaretheonlythingthatcounts.Thelosersinthisprocessarethevoters,whogetanechoratherthanachoice.

Inpractice,thepartiesdonottakeidenticalhardpositions,buteachfudgesits standaround themiddleground.Thisphenomenonwas first recognizedbyColumbia University economist Harold Hotelling in 1929. He pointed outsimilar examples in economic and social affairs: “Our cities becomeuneconomicallylargeandthebusinessdistrictswithinthemaretooconcentrated.Methodist and Presbyterian churches are too much alike; cider is toohomogeneous.”11

Would theexcesshomogeneitypersist if therewere threeparties?Supposethey take turns to choose and revise their positions, and have no ideologicalbaggagetotiethemdown.Apartylocatedontheoutsidewilledgeclosertoitsneighbor to chip away some of its support. Thiswill squeeze the party in themiddle to suchanextent thatwhen its turncomes, itwillwant to jump to theoutsideandacquireawholenewandlargerbaseofvoters.Thisprocesswillthencontinue, and there will be no equilibrium. In practice, parties have enoughideologicalbaggage,andvotershaveenoughpartyloyalty,topreventsuchrapidswitches.

Inothercases,locationswon’tbefixed.ConsiderthreepeopleallwaitingforataxiinManhattan.Theoneatthemostuptownpositionwillcatchthefirsttaxigoing downtown, and the one located farthest downtown will catch the firstuptowncab.Theone in themiddle is squeezedout. If themiddleperson isn’t

willing to wait, he will move to one of the outside positions. Until the taxiarrives, there may not be an equilibrium; no individual is content to remainsqueezedinthemiddle.Herewehaveyetanother,andquitedifferent,failureofanuncoordinateddecisionprocess;itmaynothaveadeterminateoutcomeatall.In such a situation, society has to find a different and coordinated way ofreachingastableoutcome.

8.THESTOCKMARKETANDBEAUTYCONTESTSInoftenquoted lines,JohnMaynardKeynescompared thestockmarket to thenewspaperbeautycontestsofhistime.

Professionalinvestmentmaybelikenedtothosenewspapercompetitionsinwhich competitors have to pick out the six prettiest faces from one hundredphotographs, the prize being awarded to the competitor whose choice mostnearlycorresponds to theaveragepreferenceof thecompetitorsasawhole;sothateachcompetitorhastopick,notthosefaceswhichhehimselffindsprettiest,butthosewhichhethinkslikeliesttocatchthefancyoftheothercompetitors,allofwhomarelookingattheproblemfromthesamepointofview.Itisnotacaseofchoosingthosewhich, to thebestofone’s judgment,arereally theprettiest,nor even thosewhich average opinion genuinely thinks the prettiest.We havereachedthethirddegreewherewedevoteourintelligencestoanticipatingwhataverageopinionexpectstheaverageopiniontobe.12

Itmattersnotwho theprettiestwoman is in truth.Whatyoucareabout istrying topredictwhoeveryoneelsewill think is theprettiestorwhoeveryoneelsewillthinkeveryoneelsewillthinkisprettiest….

WhenonehearsKeynes’comparisonofthestockmarkettoabeautycontest,it is essential to emphasize his beauty contestwas no ordinary pageant. In anordinarypageant themostbeautifulcontestantshouldwin; thejudgesneednotbehave strategically. Similarly, in a stockmarket, one imagines that the stockwith the highest earnings should have the highest price.Keynes’ great insightwastoexplainhowstrategicplaycouldoutweighrealityindeterminingwinnersinthestockmarketandnewspaperbeautycontests.

In thenewspapercontest, readershave toput themselves intoall theother

readers’ shoes simultaneously.At thispoint their choiceofawinnerhasmuchlesstodowithanytrueorabsolutestandardofbeautythanwithtryingtofindsome focal point on which expectations converge. If one contestant wassignificantlymorebeautifulthanalltheothers,thiscouldprovidethenecessaryfocal point.But the reader’s jobwas rarely that easy. Imagine instead that thehundredfinalistswerepracticallyindistinguishableexceptforthecoloroftheirhair.Ofthehundred,onlyoneisaredhead.Wouldyoupicktheredhead?

The taskof the reader is to figure out the realized conventionwithout thebenefitofcommunication.“Pickthemostbeautiful”mightbethestatedrule,butthat could be significantly more difficult than picking the skinniest or theredhead, or the one with an interesting gap between her two front teeth.Anything that distinguishes becomes a focal point and allows people’sexpectationstoconverge.Forthisreason,weshouldnotbesurprisedthatmanyof theworld’smostbeautifulmodelsdonothaveperfect features; rather, theyare almost perfect but have some interesting flaw that gives their look apersonalityandafocalpoint.

Investinginthestockmarkethasmanyofthesameproperties.Astockpriceriseswhenthedemandattheoldpriceexceedsthesupply.*Tomakemoneyinthemarket,yourgoalistofigureoutwhatstocksotherpeoplethinkaregoingtoappreciate.As always, they aremaking this calculation by putting themselvesintoeverybody’sshoesallatonce.Whenthishappens,anythinggoes.

Stockprices can escalate to absurd levels and then comecrashingback toreality. The crash of October 1987 is only a bump compared to some of thespeculative bubble crashes in history. From 1634 to 1638 the prices of tulipbulbs inHolland shot up several thousand percent and thenwilted away evenmorequickly.Theepisodeisknowntothisdayasthetulipbulbmania.13

Thepointofallthisisthatequilibriumcaneasilybedeterminedbywhimorfad.Thereisnothingfundamentalthatguaranteesthemostbeautifulcontestantwillbechosenorthebeststockwillappreciatethefastest.Therearesomeforcesthatworkintherightdirection.Highforecastearningsaresimilartothebeautycontestant’scomplexion—oneofthemanynecessarybutbynomeanssufficientconditionsneededtoanchorotherwisearbitrarywhimsandfads.

9.ARECAPITULATIONIn this chapter we describedmany instances in which the games people playhavemorelosersthanwinners.Uncoordinatedchoicesinteracttoproduceapooroutcomeforsociety.Letussummarizetheproblemsbriefly,andyoucanthentry

outtheideasonthecasestudy.Firstwelookedatgamesinwhicheachpersonhadaneither-orchoice.One

problemwas the familiarmulti-personprisoners’ dilemma: everyonemade thesamechoice,anditwasthewrongone.Nextwesawexamplesinwhichsomepeoplemadeonechoicewhiletheircolleaguesmadeanother,buttheproportionswere not optimal from the standpoint of the group as awhole.This happenedbecauseoneofthechoicesinvolvedgreaterspillovers,i.e.,effectsonothers,thatthechoosersfailedtotakeintoaccount.Thenwehadsituationsinwhicheitherextreme—everyonechoosingonethingoreveryonechoosingtheother—wasanequilibrium. To choose one, ormake sure the right onewas chosen, requiredsocial conventions, penalties, or restraints on people’s behavior. Even then,powerful historical forces might keep the group locked into the wrongequilibrium.

Turningtosituationswithseveralalternatives,wesawhowthegroupcouldvoluntarilyslidedownaslipperypathtoanoutcomeitwouldcollectivelyregret.In other examples, we found a tendency toward excessive homogeneity.Sometimes there might be an equilibrium held together by people’s mutuallyreinforcingexpectationsaboutwhatothersthink.Instillothercases,equilibriummightfailtoexistaltogether,andanotherwaytoreachastableoutcomewouldhavetobefound.

Thepointofthesestoriesisthatthefreemarketdoesn’talwaysgetitright.There are two fundamental problems.One is that historymatters.Our greaterexperiencewithgasolineengines,QWERTYkeyboards,andlight-waternuclearreactors may lock us in to continued use of these inferior technologies.Accidents of history cannot necessarily be corrected by today’smarket.Whenone looks forward to recognize that lock-in will be a potential problem, thisprovidesareasonforgovernmentpolicytoencouragemorediversitybeforethestandardisset.Orifweseemstuckwithaninferiorstandard,publicpolicycanguide a coordinated change from one standard to another. Moving frommeasurements in inches and feet to the metric system is one example;coordinatingtheuseofdaylightsavingtimeisanother.

Inferior standards may be behavioral rather than technological. Examplesincludeanequilibrium inwhicheveryonecheatsonhis taxes,ordrives abovethespeedlimit,orevenjustarrivesatpartiesanhourafterthestatedtime.Themovefromoneequilibriumtoabetteronecanbemosteffectivelyaccomplishedviaashortandintensecampaign.Thetrickistogetacriticalmassofpeopletoswitch, and then the bandwagon effect makes the new equilibrium self-sustaining.Incontrast,a littlebitofpressureoveralongperiodof timewouldnothavethesameeffect.

Theothergeneralproblemwithlaissezfaireisthatsomuchofwhatmattersin life takes place outside the economic marketplace. Goods ranging fromcommon courtesy to clean air are frequently unpriced, so there is no invisiblehand to guide selfish behavior. Sometimes creating a price can solve theproblem, as with the congestion problem for the Bay Bridge. Other times,pricing the good changes its nature. For example, donated blood is typicallysuperior to blood that is purchased, because the types of individualswho sellblood for the money are likely to be in a much poorer state of health. Thecoordination failures illustrated in this chapter aremeant to show the role forpublicpolicy.Butbeforeyougetcarriedaway,checkthecasebelow.

10.CASESTUDY#9:APRESCRIPTIONFORALLOCATING

DENTISTSIn this case study, we explore the coordination problem of how the invisiblehandallocates (ormisallocates) the supplyofdentistsbetweencities and ruralareas. Inmanyways the problemwill seem closely related to our analysis ofwhether to drive or take the train from Berkeley to San Francisco. Will theinvisiblehandguidetherightnumberstoeachplace?

It is often argued that there is not so much a shortage of dentists as aproblemofmisallocation.Justas toomanydrivers, left to theirownresources,wouldtaketheBayBridge,isitthecasethattoomanydentistschoosethecityover thecountryside?And if so,does thatmeansocietyshouldplacea tollonthosewhowanttopracticecitydentistry?

Forthepurposesofthiscasestudy,wegreatlysimplifythedentists’decisionproblem. Living in the city or in the countryside are considered equallyattractive.Thechoiceisbasedsolelyonfinancialconsiderations—theygowheretheywillearnthemostmoney.LikethecommutersbetweenBerkeleyandSanFrancisco, the decision is made selfishly; dentists maximize their individualpayoffs.

Sincetherearemanyruralareaswithoutenoughdentists,thissuggeststhatthere is room for an increased number of dentists to practice in rural areaswithoutcausinganycongestion.Thusruraldentistryislikethetrainroute.Atitsbest,beingaruraldentistisnotquiteaslucrativeashavingalargecitypractice,butitisamorecertainroutetoanabove-averageincome.Boththeincomesandthe value to society of rural dentists stays roughly constant as their numbersgrow.

BeingacitypractitionerismoreakintodrivingovertheBayBridge—itis

wonderfulwhenyouarealoneandnotsogreatwhenthecitygetstoocrowded.Thefirstdentistinanareacanbeextremelyvaluable,andmaintainaverylargepractice.Butwithtoomanydentistsaround,thereisthepotentialforcongestionand price competition. If the number increases too far, city dentists will becompetingforthesamepatientpool,andtheirtalentswillbeunderutilized.Ifthepopulationofcitydentistsgrowsevenfurther,theymayendupearninglessthantheir rural counterparts. In short, as thenumberofcitypractices increases, thevalueofthemarginalservicethattheyperformfalls,asdoestheirincome.

We depict this story in a simple chart, again quite similar to the drivingversustrainexample.Supposethereare100,000newdentistschoosingbetweencityand ruralpractices.The lengthof the lineAB represents the100,000.ThenumberofnewcitydentistsisthedistancetotherightofA,andthenumberofnewruraldentistsisthedistancetotheleftofB.Forexample,lookatpointC.AsthelengthACisaquarterofAB,Ccorrespondsto25,000newcitydentistsand75,000newruraldentists.

Thefallingline(citydentists)andtheflatline(ruraldentists)representthe

financialadvantagesoftakingtherespectiveroads.AtpointA,whereeveryonechooses rural practices, city dentists’ incomes are above the incomes of thosewithruralpractices.ThisisreversedatB,whereeveryonechoosescitydentistry.

TheequilibriumforcareerchoicesisatE,wherethetwooptionsprovidethesame financial rewards. To verify this, suppose that the distribution of careerchoiceresults inapoint likeC to the leftofE.SinceatpointC, city dentists’incomes are higher than rural dentists’ incomes, we expect that more newdentistsshouldchoosecityoverruralpractices.Thiswillmovethedistributionofcityvs.ruraltotherightofC.ThereverseadjustmentwouldtakeplaceifwestartedatapointtotherightofE,wherecitydentistswerethelowerpaidofthetwo.OnlywhenE is reachedwill next year’s career choices broadly replicatethoseofthisyear,andthesystemwillsettledowntoanequilibrium.

Isthisoutcomethebestforsociety?

CaseDiscussionAs in the case of the commuters, the equilibrium does not maximize thecombinedincomeofdentists.Butsocietycaresabouttheconsumersofdentistryaswellasthepractitioners.Infact,leftalone,themarketsolutionatEisthebestforsocietyasawhole.

Thereasonisthattherearetwosideeffectscreatedwhenonemorepersondecidestobeacitydentist.Theadditionalcitydentistlowersallotherdentists’incomes,imposingacostontheexistingcitydentists.Butthisreductioninpriceisabenefittoconsumers.Thetwosideeffectsexactlycanceleachotherout.Thedifference between this story and our commuting example is that no onebenefited from the extra commuting time when the Bay Bridge becamecongested. When the side effect is a change in price (or income), then thepurchasersbenefitattheproducers’cost.Thereiszeroneteffect.

From society’s viewpoint, a dentist should not worry about loweringcolleagues’incomes.Eachdentistshouldpursuethehighest-payingpractice.Aseachpersonmakesaselfishchoice,weareinvisiblyledtotherightdistributionof dentists between city and rural areas.And, the two careerswill have equalincomes.*

Ofcourse, theAmericanDentalAssociationmaylookatthisdifferently.Itmayplacemoreweightonthelosstocitydentists’incomesthanonthesavingtoconsumers. From the dental profession’s perspective there is indeed amisallocation,withtoomanydentistspracticinginthecity.Ifmoredentiststookrural practices, then the potential advantages of a city practice would not be“wasted” by competition and congestion. Taken as a whole, the income ofdentistswouldriseifitwerepossibletokeepthenumberofcitydentistsbelowthefree-marketlevel.Althoughdentistscannotplaceatollonthosewhowanttopractice in the city, it is in the profession’s self-interest to create a fund thatsubsidizesdentalstudentswhocommittoestablisharuralpractice.

10

TheStrategyofVoting

Thefoundationofademocraticgovernmentisthatitrespectsthewillofthepeopleasexpressedthroughtheballotbox.Unfortunately,theseloftyidealsarenotsoeasily implemented.Strategic issuesarise invoting, justas inanyothermultipersongame.Voterswilloftenhaveanincentivetomisrepresenttheirtruepreferences.Neithermajority rule nor any other voting scheme can solve thisproblem, for there does not exist any one perfect system for aggregating upindividuals’preferencesintoawillofthepeople.*

What this means is that the structure of the game matters. For example,whenCongresshastochoosebetweenmanycompetingbills,theorderinwhichvotes are taken canhave a great influenceon the final outcome.Webeginbylooking at the voting process more carefully, figuring out just when anindividual’svotematters.

1.THETIEOFPOWERRecentpresidentialelectionshaveemphasizedtheimportanceoftheselectionofthevicepresident.Thispersonwillbejustaheartbeatawayfromthepresidency.Butmostcandidatesforpresidentspurnthesuggestionofthesecondspotontheticket, and most vice presidents do not seem to enjoy the experience. Theprospectoftwiddlingone’sthumbsforfouroreightyears,waitingforthebosstodie,ishardlyafitoccupationforanyone.*JohnNanceGarner,FDR’sfirstVP,expressed this succinctly: “The vice-presidency ain’tworth a pitcher ofwarmspit.”

OnlyoneclauseoftheConstitutionspecifiesanyactualactivityforthevicepresident.Article I,Section3.4says:“TheVice-Presidentof theUnitedStatesshallbePresidentof theSenate,butshallhavenovote,unless theybeequallydivided.”Thepresidingis“ceremony,idleceremony,”andmostofthetimethevicepresidentdelegatesthisresponsibilitytoarotationofjuniorsenatorschosenbythesenatemajorityleader.Isthetiebreakingvoteimportant,orisitjustmore

ceremony?At first glance, both logic and evidence seem to support the ceremonial

viewpoint.Thevicepresident’svotejustdoesnotseemimportant.Thechanceofa tievote issmall.Themostfavorablecircumstancesfora tiearisewheneachsenator is just as likely to vote oneway as the other, and an even number ofsenators vote. The result will be roughly one tie vote in twelve.† Of coursesenators’ votes are far from random. Only when the two parties are roughlyequalorwhenthereisanespeciallydivisiveissuethatsplitssomeofthepartylinesdoesthevicepresident’svotegetcounted.

Themost active tiebreaking vice presidentwas our first, JohnAdams.Hecast29tiebreakingvotesduringhiseightyears.Thisisnotsurprising,sincehisSenate consisted of only 20members, and a tiewas almost three timesmorelikely than it is today,withour100-memberSenate. In fact,over the first200years, therehavebeenonly222occasionsfor thevicepresident tovote.Morerecently,RichardNixon,underEisenhower,wasthemostactivevicepresident,casting a total of 8 tiebreaking votes—out of 1,229 decisions reached by theSenateduringtheperiod1953–61.Thisfallintiebreakingvotesalsoreflectsthefactthatthetwo-partysystemismuchmoreentrenched,sothatfewerissuesarelikelytocrosspartylines.

Butthisceremonialpictureofthevicepresident’svoteismisleading.Moreimportant than how often the vice president votes is the impact of the vote.Measuredcorrectly, thevicepresident’svote is roughlyequal in importance tothatofanysenator.

One reason that the vice president’s votematters is that it tends to decideonlythemostimportantanddivisiveissues.Forexample,GeorgeBush,asvicepresident, voted to save both the administration’s chemical weapons program(twice) and theMXmissile program.This suggests thatwe should lookmorecloselyatjustwhenitisthatavotematters.

Avotecanhaveoneoftwoeffects.Itcanbeinstrumentalindeterminingtheoutcome,or it canbea“voice” that influences themarginofvictoryordefeatwithoutalteringtheoutcome.Inadecision-makingbodyliketheSenate,thefirstaspectisthemoreimportantone.

To demonstrate the importance of the vice president’s current position,imaginethatthevicepresidentisgivenaregularvoteasPresidentoftheSenate.When does this have any additional impact? For important issues, all 100senators will try to be present.* If the 100 senators are split 51–49 or morelopsidedly,thentheoutcomeisthesamenomatterwhichwaythevicepresidentvotes.The only time the outcome hinges on the vice president’s 101st vote is

whentheSenateissplit50–50,justthesameasnow,whenthevicepresidenthasonlyatiebreakingvote.

Werecognizethatouraccountofavicepresident’svotingpowerleavesoutaspectsofreality.Someoftheseimplylesspowerforthevicepresident;others,more.Muchofasenator’spowercomesfromtheworkincommittees,inwhichthevicepresidentdoesnotpartake.Ontheotherhand,thevicepresidenthasthevetopowerofthepresidentonhisside.

Our illustrationof thevicepresident’svote leads toan importantmoralofwider applicability: anyone’s vote affects the outcome onlywhen it creates orbreaksa tie.Thinkhowimportantyourownvote is indifferentcontexts.Howinfluentialcanyoubeinapresidentialelection?Yourtown’smayoralelection?Yourclub’ssecretarialelection?

Aswith theSenate, thechance that the restof theelectorate reachesa tie,leavingyoudecisive,isatamaximumwheneachvoterisjustaslikelytovoteonewayas theother.Mathematicalcalculationshows that thechancesofa tieare proportional to the square root of the number of voters: increasing theelectorateamillionfoldreducesthechancesofatiebyafactorofathousand.IntheSenate,with100voters,wesawthatthechanceofatieinthemostfavorablecircumstanceswas1in12.Inapresidentialelectionwith100millionvoters,itdropsto1in12,000.Becauseoftheelectoralcollegesystem,thereisagreaterchancethatyouwillbedecisiveinaffectingtheelectoralvotesofyourstate.Butthe fact that the population is rarely split so evenlyworks the otherway, andevenaslightadvantageforonecandidateortheotherreducesthechancesofatiedrastically.Soyoumight take1 in12,000asanoptimisticestimateofyourinfluence in a presidential election. Considering these odds, is it worth yourwhiletovote?

To explore this question, let us take a concrete example. Suppose onecandidate,Mr.SoftHeart,haspromisedtoraisetheminimumwagefrom$3.50to$5.00,andtheother,Mr.HardHead,isopposedtoanyincrease.Ifyouholdaminimum-wagejob,work2,000hoursayear,andexpecttokeepthejobwhenthewagerises,Mr.Heartwillmean$3,000ayearmoreinyourpocketthanMr.Head.Overthefouryears,thiswillamountto$12,000.Butthechancethatyourvotewill bring this about is only1 in 12,000.The expected advantage to youfromyourvoteisonlyadollar.Itisnotworthyourwhiletovoteiftodosoyoumust sacrifice even 20minutes of paidworking time. Surveys find thatmostpeoplevaluetheirleisuretimeatabouthalftheirwagerate.Thereforevotingisnotworth40minutesofyourleisuretime.

Evenifyouareunlikelytochangetheoutcome,youcanstilladdyourvoiceto the crowd.Butwill it beheard?While it is clear that 100million to0 is a

landslide, there is no apparent line where the change in one vote causes alandslide to become a simple victory. And yet if enough people change theirvote,thelandslidewillbecomeatieandthenalossandfinallyalandslideintheother direction. This absence of a “bright line” dates back to the Greekphilosopher Zeno, who tells the paradox in terms of creating a mound fromgrains of sand one at a time. It seems true that no one grain can turn a non-mound into a mound. And yet, enough grains will turn a molehill into amountain.Avote ismuch like a grain of sand. It is hard to imagine howoneadditionalvotewillchangeanyone’sperceptionoftheoutcome.*

Whatthistellsusisthatcalculationsofpersonalgainsandcostscannotbedecisiveinmotivatingpeopletovote.Fortheproperfunctioningofdemocracy,however, it is very important that people do so. That is why we need socialconditioning.Fromcivicsclassesinelementaryschooltoelection-eveappealstoone’spatrioticduty,societiesworktogetoutthevote—evenifindividualvotersdon’t have any major impact on the election.* Where patriotic duty is foundinsufficient, people are sometimes legally required to vote, as is the case inseveralcountries,includingAustralia.

2.THEMEDIANVOTERSofarouremphasishasbeenonpairwiseelections.Insuchcasesthereislittlestrategyotherthanwhetherornottovote.Ifyouvote,youshouldalwaysvoteforthecandidatewhomyoumostprefer.Becauseyourvotemattersmostwhenitbreaks a tie, you want your vote to reflect your preferences honestly.† Forelectionswithmorethantwoalternatives,thedecisionisbothwhetherornottovoteandwhat tovote for. It isno longer true thatone shouldalwaysvote forone’sfavoritecandidate.

In the1984Democraticpartyprimary,supportersofJesseJacksonhad theproblem of trying to send a signal with their vote. They could predict thatJackson was unlikely to win. The polls told them that Gary Hart andWalterMondalewere the clear front-runners. Therewas a great incentive to vote forthoseat theheadof thepackinordernot towasteone’svote.Thisbecameanevenbiggerproblemwhenthereweresevencandidatescompetingforthe1988Democraticpartypresidentialnomination.Supportersdidn’twanttowastetheirvoteorcampaigncontributionsonanonviablecandidate.Thuspollsandmediacharacterizationsthatpronouncedfront-runnershadtherealpotentialtobecomeself-fulfillingprophecies.

Thereisanotherreasonwhyvotesmaynotreflectpreferences.Onewaytohelpkeepyourvotefromgettinglostinthecrowdistomakeitstandout:takeanextremepositionawayfromthecrowd.Someonewhothinksthatthecountryis too liberalcouldvote foramoderatelyconservativecandidate.OrshecouldgoallthewaytotheextremerightandsupportLyndonLaRouche.Totheextentthat candidates compromise by taking central positions, it may be in somevoters’ interests to appearmore extreme than they are. This tactic is effectiveonlyuptoapoint.Ifyougooverboard,youarethoughtofasacrackpot,andtheresultisthatyouropinionisignored.Thetrickistotakethemostextremestandconsistentwithappearingrational.

To make this a little more precise, imagine that we can align all thecandidatesona0 to100scaleof liberal toconservative.TheYoungSpartacusLeague is way on the left, around 0, while Lyndon LaRouche takes themostconservativestance,somewherenear100.

Voters express their preferencebypicking somepoint along the spectrum.Supposethewinneroftheelectionisthecandidatewhosepositionistheaverageof all voters’ positions. The way you might think of this happening is thatthrough negotiations and compromises, the leading candidate’s position ischosentoreflecttheaveragepositionoftheelectorate.Theparallelinbargainingistosettledisputesbyofferingto“splitthedifference.”

Consider yourself a middle-of-the-roader: if it were in your hands, youwouldpreferacandidatewhostandsattheposition50onourscale.Butitmayturnout that thecountry isabitmoreconservative than that.Withoutyou, theaverage is 60. For concreteness, you are one of a hundred voters polled todeterminetheaverageposition.

Ifyou stateyouractualpreference, thecandidatewillmove to [99×60+50]/100 = 59.9. If, instead, you exaggerate and claim to want 0, the finaloutcome will be at 59.4. By exaggerating your claim, you are six times aseffectiveininfluencingthecandidate’sposition.Here,extremisminthedefenseofliberalismisnovice.

Ofcourse,youwon’tbetheonlyonedoingthis.Allthosemoreliberalthan60willbeclaimingtobeat0,whilethosemoreconservativewillbearguingfor100.Intheend,everyonewillappeartobepolarized,althoughthecandidatewillstilltakesomecentralposition.Theextentofthecompromisewilldependontherelativenumberspushingineachdirection.

Theproblemwiththisaveragingapproachisthatittriestotakeintoaccountbothintensityanddirectionofpreferences.Peoplehaveanincentiveto tell thetruth about direction but exaggerate when it comes to intensity. The sameproblemariseswith“splitthedifference”:ifthatistheruleforsettlingdisputes,

everyonewillbeginwithanextremeposition.One solution to this problem dates back to the twenties and Columbia

University economistHaroldHotelling. Instead of taking themeanor averageposition,thecandidatechoosesthemedianposition,theplatformwherethereareexactlyasmanyvoterswhowant thecandidate tomove left as tomove right.Unlike themean, themedian position does not depend on the intensity of thevoters’ preferences, only their preferred direction. To find themedian point, acandidate could start at 0 and keepmoving to the right as long as amajoritysupportsthischange.Atthemedian,thesupportforanyfurtherrightwardmoveisexactlybalancedbytheequalnumberofvoterswhopreferashiftleft.

Whenacandidateadopts themedianposition,novoterhasan incentive todistortherpreferences.Why?Thereareonlythreecasestoconsider:(i)avotertotheleftofthemedian,(ii)avoterexactlyatthemedian,and(iii)avotertotherightofthemedian.Inthefirstcase,exaggeratingpreferencesleftwarddoesnotalter themedian, and therefore the position adopted, at all.Theonlyway thatthis voter can change the outcome is to support amove rightward.But this isexactly counter tohis interest. In the second case, thevoter’s ideal position isbeing adopted anyway, and there is nothing to gain by a distortion ofpreferences.The thirdcaseparallels thefirst.Movingmore to therighthasnoeffect on the median, while voting for a move left is counter to the voter’sinterests.

The way the argument was phrased suggested that the voter knows themedianpointforthevotingpopulation,andwhethersheistotherightortheleftof it.Yet the incentive to tell the truthhadnothing to dowithwhichof thoseoutcomes occurred. You can think about all three of the above cases aspossibilitiesandthenrealizethatwhicheveroutcomematerializes,thevoterwillwant to revealherpositionhonestly.Theadvantageof the rule that adopts themedian position is that no voter has an incentive to distort her preferences;truthfulvotingisthedominantstrategyforeveryone.

The only problemwith adopting themedian voter’s position is its limitedapplicability.Thisoptionisavailableonlywheneverythingcanbereducedtoaone-dimensionalchoice,asinliberalversusconservative.Butnotallissuesareso easily classified. Once voters’ preferences are more than one-dimensional,there will not be a median. At that point, the possibility of manipulating thesystembecomesreal.

3.NAIVEVOTING

Themostcommonlyusedelectionprocedureissimplemajorityvoting.Andyettheresultsof themajority-rulesystemhaveparadoxicalproperties,aswasfirstrecognizedovertwohundredyearsagobyFrenchRevolutionherotheMarquisdeCondorcet.

In his honor,we illustrate his fundamental paradox ofmajority rule usingrevolutionaryFranceasthesetting.AfterthefalloftheBastille,whowouldbethenewpopulist leaderofFrance?Suppose threecandidates,Mr.Robespierre,Mr. Danton, and Madame Lafarge, are competing for the position. Thepopulationisdividedintothreeequallysizedgroups,left,middle,andright,withthefollowingpreferences:

Left’sRanking Middle’sRanking Right’sRanking

1stDanton Lafarge Robespierre

2ndLafarge Robespierre Danton

3rdRobespierre Danton Lafarge

InavoteofRobespierreagainstDanton,Robespierrewinstwotoone.TheninavoteofRobespierreagainstLafarge,LafargebeatsRobespierretwotoone.But then in a vote of Lafarge againstDanton,Dantonwins two to one. Thusthereisnooverallwinner.Whoendsupontopdependsonwhichvotewasthelasttaken.Moregenerally,thispossibilityofendlesscyclesmakesitimpossibletospecifyanyofthealternativesasrepresentingthewillofthepeople.

Thingsbecomeevenmoreinsidiouswhenvotingcyclesareembeddedinalargerproblem.Thewillofthemajoritycanleaveeveryoneworseoff.Toshowthisproblem,weupdateandexpandthepreferencesabove.SupposetheSevenDwarfs are candidates in an election.* The voters are split into three equalfactions—call themLeft,Middle,andRight.Therankingsof thegroupsareasfollows.

Left’sRanking Middle’sRanking Right’sRanking

1stHappy Grumpy Dopey

2ndSneezy Dopey Happy

3rdGrumpy Happy Sleepy

4thDopey Bashful Sneezy

5thDoc Sleepy Grumpy

6thBashful Sneezy Doc

7thSleepy Doc Bashful

Note that thecyclicorderingoverHappy,Dopey,andGrumpyisequivalent tothecyclicorderingofRobespierre,Danton,andMadameLafargeabove.

If we start with Happy versus Dopey, Dopey wins. Then Grumpy beatsDopey. And Sneezy beats Grumpy. Next Sleepy beats Sneezy. Then BashfulbeatsSleepy,andDocbeatsBashful.Thisisremarkable.Asequenceofmajorityvoteshas takenusfromHappy,Dopey,andGrumpyall thewaytoDoc,whenevery voter agrees that any one of Happy, Dopey, andGrumpy is better than

Doc.How did this happen? The elections were all decided by two-thirds

majorities. Those on the winning side gained a position, while those on thelosingendwentdownfourslotsonaverage.Allvotershadfourwinsand twolosses,whichonnetputsthemfourplacesworsethanwheretheystarted.

At this point you would be justified in objecting that these voters wereresponsible for their ownmisfortunes; they voted in a shortsightedway. Eachpairwisecontestwasdecidedasifitweretheonlyone,insteadofbeingapartofa chain of votes. If the voters had only looked ahead and reasoned backwardtheyneverwouldhaveallowedthemselvestoendupwithDoc.That’strue.Butthepresenceofavotingcyclemakestheoutcomehighlysensitivetothevotingprocedure.Thenextsectionshowshowcontrollingtheagendacandeterminetheoutcome.

4.ORDERINTHECOURTThewaytheU.S.judicialsystemworks,adefendantisfirstfoundtobeinnocentorguilty.Thepunishmentsentenceisdeterminedonlyafteradefendanthasbeenfoundguilty.Itmightseemthatthisisarelativelyminorproceduralissue.Yet,the order of this decision-making can mean the difference between life anddeath,orevenbetweenconvictionandacquittal.Weusethecaseofadefendantchargedwithacapitaloffensetomakeourpoint.

There are three alternative procedures to determine the outcome of acriminalcourtcase.Eachhas itsmerits,andyoumightwant tochooseamongthembasedonsomeunderlyingprinciples.

1. StatusQuo:Firstdetermineinnocenceorguilt,thenifguiltyconsidertheappropriatepunishment.2. Roman Tradition: After hearing the evidence, start with the mostserious punishment andworkdown the list. First decide if the deathpenaltyshouldbeimposedforthiscase.Ifnot,thendecidewhetheralifesentenceisjustified.If,afterproceedingdownthelist,nosentenceisimposed,thenthedefendantisacquitted.3. MandatorySentencing:Firstspecifythesentenceforthecrime.Thendeterminewhetherthedefendantshouldbeconvicted.

The difference between these systems is only one of agenda: what gets

decided first.To illustrate how important this canbe,we consider a casewithonly three possible outcomes: the death penalty, life imprisonment, andacquittal.* This story is based on a true case; it is a modern update of thedilemmafacedbyPlinytheYounger,aRomanlawyerworkingunderEmperorTrajanaroundA.D.100.1

The defendant’s fate rests in the hands of three judges. Their decision isdeterminedbyamajorityvote.Thisisparticularlyusefulsincethethreejudgesaredeeplydivided.

Onejudge(JudgeA)holdsthatthedefendantisguiltyandshouldbegiventhemaximumpossiblesentence.This judgeseeks to impose thedeathpenalty.Lifeimprisonmentishersecondchoiceandacquittalisherworstoutcome.

The second judge (Judge B) also believes that the defendant is guilty.However, this judge adamantly opposes the death penalty.Hermost preferredoutcome is life imprisonment. The precedent of imposing a death sentence issufficiently troublesome that she would prefer to see the defendant acquittedratherthanexecutedbythestate.

Thethirdjudge,JudgeC,isaloneinholdingthatthedefendantisinnocent,and thusseeksacquittal.She ison theothersideof the fence fromthesecondjudge, believing that life in prison is a fate worse than death. (On this thedefendant concurs.) Consequently, if acquittal fails, her second-best outcomewouldbe to see thedefendant sentenced todeath.Life inprisonwouldbe theworstoutcome.

JudgeA’sRanking JudgeB’sRanking JudgeC’sRankingBest DeathSentence LifeinPrison AcquittalMiddle LifeinPrison Acquittal DeathSentenceWorst Acquittal DeathSentence LifeinPrison

Underthestatusquosystem,thefirstvoteistodetermineinnocenceversusguilt.But these judgesaresophisticateddecision-makers.Theylookaheadandreasonbackward.Theycorrectlypredictthat,ifthedefendantisfoundguilty,thevotewillbetwotooneinfavorofthedeathpenalty.Thiseffectivelymeansthattheoriginalvoteisbetweenacquittalandthedeathpenalty.Acquittalwinstwo

toone,asJudgeBtipsthevote.It didn’t have to turnout thatway.The judgesmight decide to follow the

Romantraditionandworktheirwaydownthelistofcharges,startingwith themostseriousones.Theyfirstdecidewhetherornottoimposeadeathpenalty.Ifthedeathpenaltyischosen,therearenomoredecisionstobemade.Ifthedeathpenaltyisrejected,theremainingoptionsarelifeimprisonmentoracquittal.Bylookingforward,thejudgesrecognizethatlifeimprisonmentwillbetheoutcomeofthesecondstage.Reasoningbackward,thefirstquestionreducestoachoicebetweenlifeanddeathsentences.Thedeathsentencewinstwotoone,withonlyJudgeBdissenting.

A third reasonable alternative is to first determine the appropriatepunishment for the crime at hand. Here we are thinking along the lines of amandatorysentencingcode.Oncethesentencehasbeendetermined,thejudgesmustthendecidewhetherthedefendantinthecaseathandisguiltyofthecrime.In this case, if the predetermined sentence is life imprisonment, then thedefendantwillbefoundguilty,asJudgesAandBvoteforconviction.Butifthedeathpenaltyistoberequired,thenweseethatthedefendantwillbeacquitted,as Judges B and C are unwilling to convict. Thus the choice of sentencingpenalty comes down to the choice of life imprisonment versus acquittal. Thevoteisforlifeimprisonment,withJudgeCcastingthelonedissent.

You may find it remarkable and perhaps troubling that any of the threeoutcomes ispossiblebased solelyon theorder inwhichvotes are taken.Yourchoice of a judicial systemmight then depend on the outcome rather than theunderlyingprinciples.

5.THESOPHISTICATESTheproblemswithmajority rulegobeyondmanipulating theoutcomethroughcontrol of the agenda. Even sophisticated voters who exercise foresight cancollectivelyoutsmartthemselves.Wetellastorythatillustratesthepoint,freelyadaptingthesagaofPresidentReagan’snomineesfortheSupremeCourt.

Judge Bork was the first nominee. Judges Ginsberg and Kennedy wereknown to be high on the list, and likely to be nominated shouldBork not beconfirmedbytheSenate.IftheSenateturneddownallthree,thelikelihoodwasthattheseatwouldstayvacantforthenextpresidenttofill.

Imagine that thedecision rests in thehandsof threepowerful senators.Toavoidimpugningthereputationofanyactualpersons,wewillcall thethreeA,B,andC.Theirrankingsofthefourpossibleoutcomesareasfollows:

A’sRanking B’sRanking C’sRanking

1stKennedy Ginsberg Vacant

2ndVacant Kennedy Bork

3rdBork Vacant Ginsberg

4thGinsberg Bork Kennedy

The first thing to observe is that leaving the seat vacant is unanimouslypreferred to nominating Judge Bork. Yet if these are the preferences and thesenators correctly predict the order of nominations as Bork, Ginsberg, andKennedy,theresultwillbethatBorkisconfirmed.

Wefigureoutthevotingpatternsbyworkingbackwardupthetree.

If the vote comes down to appointing Kennedy versus leaving the seat

vacant, Kennedy will win. By looking ahead and reasoning backward thesenatorscanpredictavictoryforKennedyifGinsbergisdefeated.Therefore,if

BorkisturneddownthecontestbecomesGinsbergorKennedy.IntheGinsbergversusKennedycontest,Ginsbergwinstwotoone.

Reasoningbackwardagain,rightatthestartthesenatorsshouldrealizethattheir choice is Bork or Ginsberg. Here, Bork wins two to one. Everyone islooking ahead and correctly figures out the consequences of their action. Yettheycollectivelyendupwithacandidatewhosenomination,everyoneagrees,isworsethanleavingtheseatvacant.

Nowinfactitdidn’tturnoutthatway,andthereareseveralreasons.Noonewasquitecertainwhothenextnomineewouldbe.Preferenceschangedasmoreinformationwaslearnedaboutthenominees.Thesenators’preferencesmaynothave been as we represented them. Equally important, we have ignored anypossibilityforlogrolling.

Thiswasaperfectopportunityforlogrollingtoarise.Therewerethree2:1votes.Eachofthesenatorswasonthewinningsidetwiceandonthelosingsideonce.Thegainfromeachwinwasworthoneposition in their ranking,but thelosspushedthemdownthree.Itdoesn’thelptowintwosmallbattlesandlosethebigwar.Thepossibility formutualgainopens thedoor for logrolling, andwiththesepreferencesweexpectBorkwouldbedefeated.

6.ALL-TIMEGREATSAftertheWhiteHouse,electiontoCooperstownmaybethenextmostcovetednationalhonor.Membership in theBaseballHallofFame isdeterminedbyanelection.Thereisagroupofeligiblecandidates—forexample,aplayerwithtenyears of experience becomes eligible five years after retirement.*The electorsarethemembersoftheBaseballWritersAssociation.Eachvotermayvoteforupto tencandidates.Allcandidatescapturingvotesfrommore than75percentofthetotalnumberofballotsreturnedareelected.

One problem with this system is that the electors don’t have the rightincentivestovotefortheirtruepreferences.Therulethatlimitseachvotertotenchoices forces the voters to consider electability as well as merit. Somesportswritersmaybelieveacandidateisdeserving,butdon’twanttothrowawaythevote if theplayer isunlikely tomake thecutoff.This same issuearose forvoting in presidential primaries, and it appears in any election in which eachvoterisgivenafixednumberofvotestodistributeamongthecandidates.

Two experts in game theory propose an alternative way to run elections.Steven Brams and Peter Fishburn, one a political scientist and the other aneconomist, argue that “approval voting” allows voters to express their true

preferenceswithoutconcernforelectability.2Underapprovalvoting,eachvotermayvoteforasmanycandidatesashewishes.Votingforonepersondoesnotexcludevotingforanynumberofothers.Thusthereisnoharminvotingforacandidatewhohasnohopeofwinning.Ofcourseifpeoplecanvoteforasmanycandidates as they wish, who gets elected? Like the Cooperstown rule, theelectoralrulecouldspecifyinadvanceapercentageof thevoteneededtowin.Oritcouldpre-specifythenumberofwinningcandidates,andthenthepositionsarefilledbythosewhogatherthemostvotes.

Approval voting has begun to catch on, and is used bymanyprofessionalsocieties.HowwoulditworkfortheBaseballHallofFame?WouldCongressdobetter if it used approval voting when deciding which expenditure projectsshould be included in the annual budget? We look at the strategic issuesassociated with approval voting when a cutoff percentage determines thewinners.

Imagine that election to the different sports halls of famewas decided byapprovalvoting, inwhichallcandidatescapturingabovea fixedpercentageofthe votes are elected.At first glance, the voters have no incentive tomisstatetheir preferences. The candidates are not in competitionwith one another, butonlywithanabsolute standardofquality implicit in the rule that specifies therequired percentage of approval. If I think Reggie Jackson should be in theBaseball Hall of Fame, I can only reduce his chances by withholding myapproval,andifIthinkhedoesn’tbelongthere,Icanonlymakehisadmissionmorelikelybyvotingcontrarytomyview.

However,candidatesmaycompeteagainstoneanotherinthevoters’minds,eventhoughnothingintherulesmandatesit.Thiswillusuallyhappenbecausevotershavepreferencesconcerningthesizeorthestructureofthemembership.SupposeDanMarinoandJohnElwaycomeupforelectiontotheFootballHallof Fame. I thinkMarino is the better quarterback, although I will admit thatElway also meets the standard for a Hall of Fame berth. However, I think itoverridinglyimportantthattwoquarterbacksnotbeelectedinthesameyear.MyguessisthattherestoftheelectorateregardsElwaymorehighlyandhewouldgetinnomatterhowIvote,butthatMarino’scasewillbeaveryclosecall,andmyapproval is likely to tiphimover.Voting truthfullymeansnamingMarino,which is likely to lead to theoutcome inwhichbothareadmitted.Therefore IhavetheincentivetomisstatemypreferenceandvoteforElway.

Twoplayersmaycomplementeachother,ratherthancompete,inthevoters’minds.IthinkneitherGeoffBoycottnorSunilGavaskarbelongsintheCricketHallofFame,butitwouldbeagrossinjusticetohaveoneandnottheother.IfinmyjudgmenttherestoftheelectoratewouldchooseBoycottevenifIdon’tvote

forhim,whilemyvotemaybecrucialindecidingGavaskar’sselection,thenIhaveanincentivetomisstatemypreferenceandvoteforGavaskar.

Incontrast,aquotaruleexplicitlyplacescandidatesincompetitionwithoneanother.Suppose theBaseballHallofFame limits admission toonly twonewpeopleeachyear.Leteachvoterbegiventwovotes;hecandividethembetweentwo candidates or give both to the same candidate. The candidates’ votes aretotaled,andthetoptwoareadmitted.Nowsupposetherearethreecandidates—JoeDiMaggio,MarvThroneberry,andBobUecker.*EveryoneratesDiMaggioat thetop,but theelectorsaresplitequallybetweentheother two.IknowthatDiMaggioissuretogetin,soasaMarvThroneberryfanIgivemytwovotestohimtoincreasehischancesoverBobUecker.Ofcourseeveryoneelseisequallysubtle. The result: Throneberry andUecker are elected andDiMaggio gets novotes.

Government expenditure projects naturally compete with one another solong as the total budget is limited, or congressmen and senators have strongpreferencesoverthesizeofthebudget.Wewillleaveyoutothinkwhich,ifany,is theDiMaggioproject, andwhichonesare theThroneberrysandUeckersoffederalspending.

7.“LOVEALOATH’DENEMY”Incentives to distort one’s preferences appear in other situations, too. Oneinstanceoccurswhenyoucanmove first anduse thisopportunity to influenceothers.3 Take for example the case of charitable contributions by foundations.Suppose there are two foundations, eachwith a budget of $250,000.They arepresented with three grant applications: one from an organization helping thehomeless, one from the University of Michigan, and one from Yale. Bothfoundationsagreethatagrantof$200,000tothehomelessisthetoppriority.Ofthetwootherapplications,thefirstfoundationwouldliketoseemoremoneygotoMichigan,while the secondwouldprefer to fundYale.Suppose the secondstealsamarchandsendsacheckforitstotalbudget,$250,000,toYale.Thefirstisthenleftwithnoalternativebuttoprovide$200,000tothehomeless,leavingonly $50,000 for Michigan. If the two foundations had split the grant to thehomeless, thenMichiganwould have received $150,000, aswouldYale.Thusthesecondfoundationhasengineereda transferof$100,000fromMichigan toYale through the homeless. In a sense, the foundation has distorted itspreferences—ithasnotgivenanythingtoitstopcharitypriority.Butthestrategiccommitment does serve its true interests. In fact, this typeof fundinggame is

quitecommon.*Byactingfirst,smallfoundationsexercisemoreinfluenceoverwhich secondary priorities get funded. Large foundations and especially thefederalgovernmentarethenlefttofundthemostpressingneeds.

This strategic rearranging of priorities has a direct parallel with voting.Before the 1974 Budget Act, Congress employed many of the same tricks.Unimportantexpenditureswerevotedonandapprovedfirst.Lateron,whenthecrunchappeared,theremainingexpendituresweretooimportanttobedenied.Tosolve this problem,Congress now votes first on budget totals and thenworkswithinthem.

When you can rely on others to save you later, you have an incentive todistort your priorities by exaggerating your claim and taking advantage of theothers’ preferences. You might be willing to gain at the expense of puttingsomethingyouwantatrisk,ifyoucancountonsomeoneelsebearingthecostoftherescue.

Theprincipleofforcingotherstosaveyoucanturntheoutcomeallthewayaround,fromyourworsttoyourbestalternative.Hereweshowhowthisisdoneusingthevotesofacorporateboardoftrusteesfacingahostiletakeover.Theirimmediateproblem ishow to respond.Fouroptionshavebeenproposed, eachwithitsownchampion.

Thefoundingpresidentislookingforawaytokeepthecompanyintact.Hisfirst preference is to initiate a poison-pill provision into the company charter.Thepoisonpillwouldbedesigned topreventanyoutsideparty fromattainingcontrolwithoutboardapproval.

The twoyoungmembersof theboard feel the situation ismoredesperate.Theybelievethatatakeoverisinevitableandareconcentratingonfindingawaytomakethepresenttransactionmoreacceptable.Theirpreferredactionistolookforawhiteknight,abuyerwhoisacceptabletomanagementandtheboard.Themanagementrepresentationontheboardsuggestsathirdpossibility.Thepresentmanagerswouldliketheopportunitytobuythecompanythroughamanagementbuyout,anMBO.

The fifth member of the board is an outside director. He is cautiouslyoptimisticabout thepresentraiderandargues that there is timetoseehowtheofferdevelops.

Afterthesefouroptionshavebeendiscussed,everyoneendsupwithaclearpictureofwheretheothersstand(orsit)onthefourproposals.Forexample,thefounder isamanofaction;hisworstoutcomeis theWait&Seeposition.Thetwo young board members agree with the fifth that the MBO option isunattractive; whenevermanagement competeswith an outside bidder it opens

thedoortoconflictofinterestandinsidertrading,formanagersaretheultimateinsiders.Thecompletesetofpreferencesispresentedbelow.

Founder’sRanking

TwoYoungDirectors’Rankings

Management’sRanking

OutsideDirector’sRanking

1stPoisonPill WhiteKnight MBO Wait&See

2ndMBO PoisonPill PoisonPill WhiteKnight

3rdWhiteKnight

Wait&See Wait&See PoisonPill

4thWait&See MBO WhiteKnight MBO

Faced with these options, the board must make a decision. Everyonerecognizesthatthevotingproceduremaywellinfluencetheoutcome.Evenso,they decide there is a natural order to the decision-making process: begin bycomparingtheactivecoursesofactionandthendecidewhetherthebestoneisworth doing.They first compare anMBOwith aWhiteKnight, and themorepreferredalternativeisthencomparedwiththePoisonPilloption.Havingfoundthebestactiveresponse,theydecidewhetherthisisworthdoingbycomparingitwithWait&See.

Thisvotingproblemisrepresentedbythetreebelow.

This treeshouldremindyouofa tennis tournament inwhichsomeplayers

are seeded.We are seeding “Wait&See” all theway into the finals, “PoisonPill”intothesemifinals,andgivingnoseedto“MBO”and“WhiteKnight.”

Boxing and chessbothwork thisway, too.There is a series of challengesthatyoumustwininordertogoagainstthepresidingworldchampion.TheU.S.presidential electionprocess alsoworks thisway.When there is an incumbentpresident, that person is typically a shoo-in for his party’s nomination. Theopposingpartyrunsaprimarytodecidewhowillgoagainsttheincumbentinthefinal elections. The primary process, the ensuing party nomination, and thepresidentialelectioncanbe thoughtofasaseriesofeliminationelections.Butbacktotheboardroom.

Wesupposethatthefiveboardmembershaveenoughforesighttorealizetheconsequencesof theiractions insuccessiverounds,andvoteaccordingto theirtruepreferences.Backwardreasoningmakesthisproblemeasytosolve.Youcanwork out the solution and see that theWhiteKnight optionwins (or you canjump to the next paragraph), but that is not the point of this story. We areinterested in showing how the founder can improve the outcome from hisperspectivebymakingacommitmenttodistortedpreferences.

HowisitthattheWhiteKnightoptionwinsunderforesightedvoting?Thelast election must be Wait & See versus something. In this final electioneveryonehasan incentive tovotehonestly,since thiswilldetermine theactualoutcome.Thethreepossibilitiesareeasytocalculate:

Wait&Seevs.PoisonPill,PoisonPillwins4–1.Wait&Seevs.MBO,Wait&Seewins3–2.Wait&Seevs.WhiteKnight,WhiteKnightwins3–2.

Nowwegobackonepreviousround.ThecontestwillbeeitherPoisonPillvs.WhiteKnightorPoisonPillvs.MBO.Inthefirstcase,bothPoisonPillandWhiteKnightarepreferredtoWait&See.Sowhateverwinsthesecondroundwillbeimplemented.TheboardmemberspreferWhiteKnighttoPoisonPill,3–2.

Inthesecondcase,avoteforMBOisinrealityavoteforWait&See.Boardmembers cananticipate that ifMBObeatsPoisonPill for the active course, itwillloseoutinthenextcomparisonwithWait&See.SowhendecidingbetweenPoisonPillandMBO,boardmemberswillactasifdecidingbetweenPoisonPillandWait&See,withtheresult thatPoisonPillwins4–1.Thusthefirst-roundcomparison is truly between Poison Pill and White Knight. White Knight ischosen by a 3–2 margin and is then selected in each of the subsequentcomparisons.

Once the founder recognizeswhatwill happen, there is a strategy he canemploytogethismostpreferredoption, thePoisonPill.Lookwhathappensifthefounder“adopts”thepreferencesoftheoutsideboardmember.Ofcourseitisessentialthatthischangeofpreferencesiscredibleandismadeknowntoalltheothervoters.Suppose the founder simplygiveshisvote to theoutsidedirectorandleavesthemeeting.

Atfirstglancethisseemsnothingshortofcrazy;theadoptedpreferencesarealmosttheoppositeofhistrueones.Butlookattheeffect.Thevoteswillnowgoasfollows:

Wait&Seevs.PoisonPill,PoisonPillwins3–2.Wait&Seevs.MBO,Wait&Seewins4–1.Wait&Seevs.WhiteKnight,Wait&Seewins3–2.

TheonlyactiveoptionthatcanbeatWait&SeeisPoisonPill.Rightfromthe start the board members should predict that if Poison Pill ever loses, theoutcomewillbeWait&See.YetbothMBOandWhiteKnightsupporterspreferPoisonPill toWait&See.TheyareforcedtovoteforPoisonPillasit is theironlyviablealternative;thusPoisonPillwins.

Bytransferringhissupporttotheopposition,thefounderisabletomakeacrediblethreatthatitiseitherPoisonPillorWait&See.Asaresult,allbutthedie-hardWait&See supportersdump theWhiteKnightoption (which cannolongerbeatWait&See)infavorofthePoisonPill.Superficially,thistransferofavotedoublesthestrengthoftheWait&Seesupporters.Actually,itleadstoan

outcome that is worse from their viewpoint—Poison Pill rather than WhiteKnight. Invoting, strength canbeweakness.Of course, if theoutsidedirectorseesthroughthegame,heshouldrefusetoacceptthefounder’sproxy.

Ifyouregardthisstoryasfarfetched,somethingquitelikeitdidoccurinthe1988Wisconsinpresidentialprimary.TheRepublicangovernorofthestatesaidthatoftheDemocraticcandidates,JesseJacksonwasthemostinteresting.Manycommentators thought thiswas aMachiavellian attempt to getRepublicans tocross over and vote for Jackson in the Democratic primary, thereby helpingproduce amore easily beatable opponent for Bush in the November election.Apparently, Michael Dukakis was sufficiently easy for George Bush to beat,evenwithoutthishelp.

8.CASESTUDY#10:ALLORNOTHINGGin and vermouth: some prefer them straight, while others only drink themmixed, i.e., a martini. We’ve seen examples of both types of preferences. InelectiontotheFootballHallofFame,somewouldbehappywitheitherElwayorMarino,butnotboth,whileincricketothersfindonlythemartinicombinationofBoycottandGavaskarpalatable.

Is thebudgetapprovalprocessall thatdifferent?Howcan itbe improved?Onesuggestionistogivethepresidentthepowerofaline-itemveto.

Weask theCongress,onceagain:Giveus thesametool that43governorshave, a line-item veto, sowe can carve out the boondoggles and pork—thoseitemsthatwouldneversurviveontheirown.

—RonaldReagan,StateoftheUnionAddress,January27,1987.

Yet,itispossiblethatthismaybeatoolthepresidentisbetteroffwithout.Howcouldthatbe?

CaseDiscussionOnereasonisthatwithoutaline-itemveto,thepresidentiscommittedtotakingwhat theCongress gives him; he cannotmodify it piecemeal to better suit hispreferences. Consequently, compromises made in Congress will be honored

withoutfearthatthepresidentwillpickandchoosewhatsegmentstokeep.OnceCongresspredictstheywillloseallofthepartsthatwouldnotsurviveontheirown,theprocessofagreeingonabudgetwillbecomemuchmorecontentious,and a consensus compromisemay not be found. Congressmay bemuch lesswillingtoservethepresidentamartiniifhecanremixitbeforepresentingittothenation.

Thusapresidentwithaline-itemvetomightendupwithlesspower,simplybecause theCongress is lesswilling (or able) to put proposals on his desk.Asimple example helps illustrate the point. President Reagan wanted funds forStarWars.Unfortunately forReagan, theRepublicanparty did not control theCongress. TheDemocrats’ approval had to be bought. The budget offered theDemocrats a package of social programs that made the defense spendingtolerable. The willingness of the Democrats to approve the budget wascontingent on the complete package. If they thought that Reagan could use aline-itemveto tocut thesocialprograms(in thenameofpork), theywouldbeunwillingtogivehimtheStarWarsfunds.

Thedebateabouttheeffectivenessoftheline-itemvetoforreducingdeficitsis best settled by looking at the experience at the state level. ColumbiaUniversity economist Douglas Holtz-Eakin has examined the historicalevidence:

Gubernatorialvetopowerisquiteold.ThePresidentoftheConfederacyhad(butdidnotexercise)itemvetopowerduringtheCivilWarand28states(outofatotalof45)adoptedalineitemvetobetween1860and1900.By1930,41ofthe48 stateshadaprovision for line itemvetopower.Thegovernorsof IowaandWestVirginiaacquiredlineitemvetopowerin1969.4

Andyet,afterlookingatallthesecases,ProfessorHoltz-Eakinwasunabletoseeanyreductionin thebudgetdeficitsofstateswhosegovernorhadtheline-itemveto.

11

Bargaining

Anewlyelectedtradeunionleaderwenttohisfirsttoughbargainingsessionin thecompanyboardroom.Nervousand intimidatedby thesetting,heblurtedout his demand: “We want ten dollars an hour or else.” “Or else what?”challengedtheboss.Theunionleaderreplied,“Ninedollarsfifty.”

Fewunionleadersaresoquicktobackdown,andbossesneedthethreatofJapanesecompetition,nottheirownpower,tosecurewageconcessions.Butthesituation poses several important questions about the bargaining process.Willtherebeanagreement?Willitoccuramicably,oronlyafterastrike?Whowillconcedeandwhen?Whowillgethowmuchofthepiethatistheobjectofthehaggling?

InChapter2,wesketcheda simplestoryof twochildrenarguingover thedivision of an ice-cream pie. Because the pie melted while the exchange ofoffers and counteroffers went on, the two sides were motivated to reach animmediateagreement.Yettheagreeddivisionwasbasedonwhatwouldhappenifeitherside let thepiemelt.Theexample illustrated thestrategicprincipleoflookingaheadandreasoningback.Manyrealitiesofthebargainingprocessweresacrificedinordertomakethatprinciplestandout.Thischapterusesthesameprinciple, but with more attention to issues that arise during bargaining inbusiness,politics,andelsewhere.

We begin by recapitulating the basic idea in the context of union-managementnegotiationoverwages.Tolookaheadandreasonback,ithelpstostartatafixedpointinthefuture,soletusthinkofanenterprisewithanaturalconclusion,suchasahotelinasummerresort.Theseasonlasts101days.Eachday the hotel operates, it makes a profit of $1,000. At the beginning of theseason,theemployees’unionconfrontsthemanagementoverwages.Theunionpresentsitsdemand.Themanagementeitheracceptsthis,orrejectsitandreturnsthenextdaywithacounteroffer.Thehotelcanopenonlyafteranagreementisreached.

Firstsupposebargaininghasgoneonforsolongthatevenifthenextroundleadstoanagreement,thehotelcanopenforonlythelastdayoftheseason.In

fact bargaining will not go on that long, but because of the logic of lookingahead and reasoning back, what actually happens is governed by a thoughtprocess that starts at this logical extreme. Suppose it is the union’s turn topresent its demand. At this point the management should accept anything asbeingbetterthannothing.Sotheunioncangetawaywiththewhole$1,000.*

Now look at the day before the last,when it is themanagement’s turn tomakeanoffer.Itknowsthattheunioncanalwaysrejectthis,lettheprocessgoonto the lastday,andget$1,000.Therefore themanagementcannotofferanyless.Andtheunioncannotdoanybetterthanget$1,000onthelastday,sothemanagement need not offer any more on the day before. Therefore themanagement’sofferat thisstageisclear:of the$2,000profitoverthelast twodays,itaskshalf.Eachsidegets$500perday.

Next let the reasoning move back one more day. By the same logic, theunionwillofferthemanagement$1,000,andaskfor$2,000;thisgivestheunion$667 per day and the management $333. We show the full process in thefollowingtable:

Table1:SuccessiveRoundsofWageBargaining Union’sShare Management’sShareDaystoGo Offerby Total PerDay Total PerDay1 Union $1,000 $1,000 $0 $02 Management 1,000 500 1,000 5003 Union 2,000 667 1,000 3334 Management 2,000 500 2,000 5005 Union 3,000 600 2,000 400…100 Management 50,000 500 50,000 500101 Union 51,000 505 50,000 495

Eachtimetheunionmakesanoffer,ithasanadvantage,whichstemsfromitsabilitytomakethelastall-or-nothingoffer.Buttheadvantagegetssmallerasthenumberofroundsincreases.Atthestartofaseason101dayslong,thetwosides’positionsarealmostidentical:$505versus$495.Almostthesamedivisionwouldemergeifthemanagementweretomakethelastoffer,orindeedifthere

werenorigidruleslikeoneofferaday,alternatingoffers,etc.1Theappendixtothis chapter shows how this framework generalizes to include negotiations inwhichthereisnopredeterminedlastperiod.Ourrestrictionstoalternatingoffersand a known finite horizonwere simply devices to help us look ahead. Theybecome innocuous when the time between offers is short and the bargaininghorizonislong—inthesecases,lookingaheadandreasoningbackwardleadstoaverysimpleandappealingrule:splitthetotaldownthemiddle.

Whatismore,theagreementoccursontheveryfirstdayofthenegotiationprocess.Becausethetwosideslookaheadtopredictthesameoutcome,thereisno reasonwhy they should fail to agreeand jointly lose$1,000aday.Not allinstances of union-management bargaining have such a happy beginning.Breakdownsinnegotiationsdooccur,strikesorlockoutshappen,andsettlementsfavoronesideortheother.Byrefiningourexampleandringingsomechangesonitspremises,wecanexplainthesefacts.

1.THEHANDICAPSYSTEMINNEGOTIATIONSOne importantelement thatdetermineshow thepiewillbe split is eachside’scostofwaiting.Althoughbothsidesmay loseanequalamountofprofits,onepartymayhaveotheralternativesthathelppartiallyrecapturethisloss.Supposethat themembers of theunion can earn$300 a day in outside activitieswhilenegotiations with the hotel management go on. Now each time themanagement’sturncomes,itmustoffertheunionnotonlywhattheunioncouldgetadaylater,butalsoatleast$300forthecurrentday.Theentriesinourtablechange in the union’s favor; we show this in a new table. Once again theagreement occurs at the season opening andwithout any strike, but the uniondoesmuchbetter.

Table2:SuccessiveRoundsofWageBargaining

Union’sShare Management’sShareDaystoGo Offerby Total PerDay Total PerDay1 Union $1,000 $1,000 $0 $02 Management 1,300 650 700 3503 Union 2,300 767 700 233

4 Management 2,600 650 1,400 3505 Union 3,600 720 1,400 280…100 Management 65,000 650 35,000 350101 Union 66,000 653 35,000 347

The result can be seen as a naturalmodification of the principle of equaldivision, to allow for the possibility that the parties start the process withdifferent“handicaps,”asingolf.Theunionstartsat$300,thesumitsmemberscouldearnontheoutside.Thisleaves$700tobenegotiated,andtheprincipleisto split it evenly, $350 for each side. Therefore the union gets $650 and themanagementonly$350.

In other circumstances the management could have an advantage. Forexample,itmightbeabletooperatethehotelusingscabswhilethenegotiationswith theuniongoon.But because thoseworkers are less efficient ormust bepaidmore,orbecausesomeguestsarereluctanttocrosstheunion’spicketlines,themanagement’sprofitfromsuchoperationwillbeonly$500aday.Supposetheunionmembershavenooutsideincomepossibilities.Onceagaintherewillbe an immediate settlement with the union without an actual strike. But theprospect of the scab operationwill give themanagement an advantage in thenegotiation,anditwillget$750adaywhiletheuniongets$250.

If the unionmembers have an outside income possibility of $300and themanagementcanoperatethehotelwithaprofitof$500duringnegotiations,thenonly$200remainsfreetobebargainedover.Themanagementgets$600andtheuniongets$400.Thegeneralideaisthatthebetterapartycandobyitselfintheabsenceofanagreement,thehigherwillbeitsshareofthepiethatisthesubjectofthebargaining.

2.“THISWILLHURTYOUMORETHANITHURTSME”Whenastrategicbargainerobserves thatabetteroutsideopportunity translatesintoabettershareinabargain,hewilllookforstrategicmovesthatimprovehisoutsideopportunities.Moreover,hewillnotice thatwhatmatters ishisoutsideopportunityrelativetothatofhisrival.Hewilldobetterinthebargainingevenif he makes a commitment or a threat that lowers both parties’ outsideopportunities,solongasthatoftherivalisdamagedmoreseverely.

In our example, when the union members could earn $300 a day on theoutside while themanagement couldmake a profit of $500 a day using scablabor, the result of the bargaining was $400 for the union and $600 for themanagement.Nowsuppose theunionmembersgiveup$100adayofoutsideincometointensifytheirpicketing,andthisreducesthemanagement’sprofitby$200aday.Thenthebargainingprocessgivestheunionastartingpointof$200($300-$100)andthemanagement$300($500-$200).Thetwostartingpointsaddupto$500,andtheremaining$500ofdailyprofitfromregularoperationofthehotel is split equallybetween them.Therefore theuniongets$450and themanagement gets $550. The union’s threat of hurting both (but hurting themanagementmore)hasearneditanextra$50.

The major league baseball players used just such a tactic in their wagenegotiationsin1980.Theywentonstrikeduringtheexhibitionseason,returnedtoworkatthestartoftheregularseason,andthreatenedtostrikeagainstartingonMemorialDayweekend.Toseehowthis“hurttheteamownersmore,”notethatduring the exhibition season theplayersgotno salaries,while theownersearned revenue from vacationers and locals. During the regular season theplayersgot thesamesalaryeachweek.For theowners, thegateand televisionrevenues are low initially and rise substantiallyduring and after theMemorialDayweekend.ThereforethelossoftheownersrelativetothatoftheplayerswashighestduringtheexhibitionseasonandagainstartingMemorialDayweekend.Itseemstheplayersknewtherightstrategy.2

The owners gave in just before the second half of the threatened baseballstrike. But the first half actually occurred. Our theory of looking ahead andreasoningback isclearly incomplete.Whyis it thatagreementsarenotalwaysreachedbeforeanydamageisdone—whyaretherestrikes?

3.BRINKMANSHIPANDSTRIKESBeforeanoldcontractexpires,theunionandthefirmbeginthenegotiationsforanewlaborcontract.Butthereisnosenseofurgencyduringthisperiod.Workgoeson,nooutputissacrificed,andthereisnoapparentadvantagetoachievinganagreementsoonerratherthanlater.Itwouldseemthateachpartyshouldwaituntil the lastmoment and state its demand just as the old contract is about toexpireandastrikelooms.Thatdoeshappensometimes,butoftenanagreementisreachedmuchsooner.

In fact, delaying agreement can be costly even during the tranquil phasewhentheoldcontractstilloperates.Theprocessofnegotiationhasitsownrisk.

There can be misperception of the other side’s impatience or outsideopportunities, tension, personality clashes, and suspicion that the other side isnotbargainingingoodfaith.Theprocessmaybreakdowndespitethefactthatbothpartieswantittosucceed.

Although both sides may want the agreement to succeed, they may havedifferent ideas about what constitutes success. The two parties do not alwayslookforwardandseethesameend.Theymaynothavethesameinformationorsharethesameperspective,sotheyseethingsdifferently.Eachsidemustmakeaguessabouttheother’scostofwaiting.Sinceasidewithalowwaitingcostdoesbetter,itistoeachside’sadvantagetoclaimitscostislow.Butthesestatementswillnotbetakenatfacevalue;theyhavetobeproven.Thewaytoproveone’swaitingcostsarelowistobeginincurringthecostsandthenshowyoucanholdout longer, or to take a greater risk of incurring the costs—lower costsmakehigher risks acceptable. It is the lack of a common view about where thenegotiationswillendthatleadstothebeginningofastrike.

The situation is tailor-made for the exercise of brinkmanship. The unioncouldthreatenanimmediatebreakdownoftalksfollowedbyastrike,butstrikesareverycostlytounionmembersaswell.Whiletimeforcontinuednegotiationremains, such a dire threat lacks credibility. But a smaller threat can remaincredible:tempersandtensionsaregraduallyrising,andabreakdownmayoccureventhoughtheuniondoesn’treallywantitto.Ifthisbothersthemanagementmorethanitbotherstheunion,itisagoodstrategyfromtheunion’sperspective.Theargumentworkstheotherwayaroundtoo;thestrategyofbrinkmanshipisaweapon for the stronger of the two parties—namely, the one that fears abreakdownless.

Sometimeswage negotiations go on after the old contract has expired butwithout a strike, andwork continues under the termsof the old contract.Thismightseemtobeabetterarrangement,becausethemachineryandtheworkersarenot idleandoutput isnot lost.Butoneof theparties,usually theunion, isseeking a revision of the terms of the contract in its favor, and for it thearrangement is singularly disadvantageous. Why should the managementconcede?Why should it not let the negotiations spin on foreverwhile the oldcontractremainsinforcedefacto?

Againthethreatinthesituationistheprobabilitythattheprocessmaybreakdownandastrikemayensue.Theunionpracticesbrinkmanship,butnowitdoesso after the old contract has expired. Time for routine negotiations is past.Continuedwork under an expired contractwhile negotiations go on iswidelyregardedasasignofunionweakness.Theremustbesomechanceofastriketomotivatethefirmtomeettheunion’sdemands.

Whenthestrikehappens,whatkeepsitgoing?Thekeytocommitmentistoreduce the threat in order tomake it credible.Brinkmanship carries the strikealongon a day-by-daybasis.The threat never to return toworkwouldnot becredible, especially if the management comes close to meeting the union’sdemands.Butwaitingonemoredayorweekisacrediblethreat.Thelossestothe workers are smaller than their potential gains. Provided they believe theywillwin(andsoon),itisworththeirwhiletowait.Iftheworkersarecorrectintheirbeliefs,managementwillfinditcheapertogiveinandinfactshoulddosoimmediately.Hencetheworkers’threatwouldcostthemnothing.Theproblemisthat the firm may not perceive the situation the same way. If it believes theworkersareabouttoconcede,thenlosingjustonemoreday’sorweek’sprofitsisworthgetting amore favorable contract. In thisway, both sides continue toholdout,andthestrikecontinues.

Earlier, we talked about the risk of brinkmanship as the chance that bothsideswouldfalltogetherdowntheslipperyslope.Astheconflictcontinues,bothsides risk a large loss with a small but increasing probability. It was thisincreasingexposuretoriskthatinducedonesidetobackdown.Brinkmanshipintheformofastrikeimposescostsdifferently,buttheeffectisthesame.Insteadof a small chance of a large loss, there is a large chance, even certainty, of asmall losswhen a strike begins.As the strike continues unresolved, the smalllossgrows,justasthechanceoffallingoffthebrinkincreases.Thewaytoprovedeterminationistoacceptmoreriskorwatchstrikelossesescalate.Onlywhenone side discovers that the other is truly the stronger does it decide to backdown. Strength can takemany forms.One sidemay suffer less fromwaiting,perhaps because it has valuable alternatives; winningmay be very important,perhapsbecauseofnegotiationswithotherunions;losingmaybeverycostly,sothatthestrikelosseslooksmaller.

Thisapplicationofbrinkmanshipappliestothebargainingbetweennationsaswellasthatbetweenfirms.WhentheUnitedStatestriestogetitsalliestopayagreatershareofthedefensecosts,itsuffersfromtheweaknessofnegotiatingwhile working under an expired contract. The old arrangement in which theAmericansbearthebruntoftheburdencontinuesinthemeantime,andtheU.S.allies are happy to let the negotiations dragon.Can—and should—theUnitedStatesresorttobrinkmanship?

Risk andbrinkmanship change theprocessofbargaining in a fundamentalway.Intheearlieraccountsofsequencesofoffers, theprospectofwhatwouldcomelaterinducedthepartiestoreachanagreementontheveryfirstround.Anintegral aspect of brinkmanship is that sometimes the parties do go over thebrink.Breakdownsand strikes canoccur.Theymaybegenuinely regrettedby

both parties, butmay acquire amomentum of their own and last surprisinglylong.

4.SIMULTANEOUSBARGAININGOVERMANYISSUESOuraccountofbargaininghassofarfocusedonjustonedimension,namelythetotal sumofmoneyand its splitbetween the twosides. In fact therearemanydimensionstobargaining:theunionandmanagementcarenotjustaboutwagesbut health benefits, pension plans, conditions ofwork, and so on. TheUnitedStates and its NATO allies care not just about total defense expenditures, buthow theyareallocated. Inprinciple,manyof theseare reducible toequivalentsumsofmoney,butwithanimportantdifference—eachsidemayvaluetheitemsdifferently.

Suchdifferencesopenupnewpossibilitiesformutuallyacceptablebargains.Suppose the company is able to secure group health coverage on better termsthan the individual workerswould obtain on their own—say, $1,000 per yearinsteadof$2,000peryear fora familyof four.Nowtheworkerswould ratherhave health coverage than an extra $1,500 a year inwages, and the companywouldratherofferhealthcoveragethananextra$1,500inwages,too.3

It would seem that the negotiators should throw all the issues of mutualinterestintoacommonbargainingpot,andexploitthedifferenceintheirrelativevaluationstoachieveoutcomesthatarebetterforeveryone.Thisworksinsomeinstances; for example, broad negotiations toward trade liberalization in theGeneralAgreementonTariffsandTrade (GATT)havehadbetter success thanonesnarrowlyfocusedonparticularsectorsorcommodities.

Butjoiningissuestogetheropensupthepossibilityofusingonebargaininggame to generate threats in another. For example, theUnitedStatesmayhavehad more success in extracting concessions in negotiations to open up theJapanese market to its exports if it threatened a breakdown of the militaryrelationship, therebyexposingJapan toa riskofSovietorChineseaggression.TheUnited States had no interest in actually having this happen; itwould bemerely a threat that would induce Japan to make the economic concession.Therefore, Japan would insist that the economic and military issues benegotiatedseparately.

5.CASESTUDY#11:’TISBETTERTOGIVETHANTO

RECEIVE?

Recallourbargainingprobleminwhichahotel’smanagementanditslaborwerenegotiatingover how todivide the season’s profits.Now, insteadof labor andmanagementalternatingoffers,imaginethatonlythemanagementgetstomakeoffers,andlaborcanonlyacceptorreject.

Asbefore,theseasonlasts101days.Eachdaythehoteloperates,itmakesaprofitof$1,000.Negotiationsstartatthebeginningoftheseason.Eachday,themanagementpresents itsoffer,which iseitheracceptedor rejectedby labor. Ifaccepted,thehotelopensandbeginsmakingmoney.Ifrejected,thenegotiationscontinueuntileitheranofferisacceptedortheseasonendsandtheentireprofitsarelost.

Table3illustratesthedecliningpotentialprofitsastheseasonprogresses.Ifbothlaborandmanagement’sonlyconcernistomaximizeitsownpayoff,whatdoyouexpectwillhappen(andwhen)?

Table3:WageBargaining—ManagementMakesAllOffers

DaystoGo Offerby TotalProfitstoDivide AmountOfferedtoLabor1 Management $1,000 ?2 Management 2,000 ?3 Management 3,000 ?4 Management 4,000 ?5 Management 5,000 ?…100 Management 100,000 ?101 Management 101,000 ?

CaseDiscussionIn this case, we expect the outcome to differ radically from 50:50. Because

managementhasthesolepowertopropose,itisinthemuchstrongerbargainingposition.Managementshouldbeabletogetclosetotheentireamountandreachagreementonthefirstday.

Topredictthebargainingoutcome,westartattheendandworkbackward.On the last day there is no value in continuing, so labor should bewilling toacceptanypositiveamount,say$1.00.Onthepenultimateday,laborrecognizesthatrejectingtoday’sofferwillbringonly$1.00tomorrow;hence,theyprefertoaccept $2.00 today. The argument continues right up to the first day.Managementproposestogivelabor$101,andlabor,seeingnobetteralternativeinthefuture,accepts.

Table4:WageBargaining—ManagementMakesAllOffers

DaystoGo Offerby TotalProfitstoDivide AmountOfferedtoLabor1 Management $1,000 $12 Management 2,000 23 Management 3,000 34 Management 4,000 45 Management 5,000 5…100 Management 100,000 100101 Management 101,000 101

This story clearly exaggerates management’s true bargaining power.Postponingagreement,evenbyoneday,costsmanagement$999andlaboronly$1.Totheextentthatlaborcaresnotonlyaboutitspaymentsbutalsohowthesepaymentscomparetomanagement’s,thistypeofradicallyunequaldivisionwillnot be possible. But that does not mean we must return to an even split.Management still has all the bargaining power. Its goal should be to find theminimallyacceptableamount togive to labor so that laborprefersgetting thatamountovernothing,eventhoughmanagementmaygetmore.Forexample,inthe last period, labormight bewilling to accept $334whilemanagement gets

$666iflabor’salternativeiszero.Ifso,managementcanperpetuatethat1:2splitthroughouteachof the101daysandcapture two-thirdsof the totalprofit.Thevalueofthistechniqueforsolvingbargainingproblemsisthatitsuggestssomeof the different sources of bargaining power. Splitting the difference or evendivisionisacommonbutnotuniversalsolutiontoabargainingproblem.Lookforward and reason backward provides a reasonwhywemight expect to findunequaldivision.Inparticular,itsuggeststhatinthecaseofmakingoffers,“’Tisbettertogivethantoreceive.”

6.APPENDIX:PATIENCEISITSOWNREWARDIt is possible to apply backward reasoning even when problems lack a fixedendpoint.*Thisisanimportantfeatureofmostbargainingproblems.Letuslooktherefore at a more typical setting, such as a steel company. A strike is inprogress.Ifitissettled,thecompanycanmakeanoperatingprofitof$3millioneachweek.Theunionandthemanagementarebargainingover thedivisionofthis sum.Negotiation sessions are heldweekly, and the two sides alternate inmakingoffers.

Every week that goes by without an agreement, the two sides togethersacrifice$3million.Asusual,timeismoney.Animmediatesettlementisintheirjoint best interest.But onwhat terms? Intuition suggests that the party that ismoreimpatientforasettlementwillmaketheearlierorthelargerconcessions.Amore detailed look at the process confirms this intuition, and converts it intomoreprecisepredictionsaboutthetwoparties’shares.

Timeismoneyinmanydifferentways.Mostsimply,adollarreceivedearlierisworthmorethanthesamedollarreceivedlater,becauseitcanbeinvestedandearninterestordividendsinthemeantime.Iftherateofreturnoninvestmentsis5percentayear,thenadollarreceivedrightnowisworth$1.05receivedayearlater.

The same idea applies to our union andmanagement, but there are someadditional features that may add to the impatience factor. Each week theagreementisdelayed,thereisariskthatold,loyalcustomerswilldeveloplong-term relationships with other suppliers, and the firm will be threatened withpermanent closure.Theworkers and themanagerswill have tomove to otherjobs that pay less well, the union leaders’ reputation will suffer, and themanagement’sstockoptionswillbecomeworthless.Animmediateagreementisbetter than one aweek later precisely to the extent of the probability that thiswillcometopassinthecourseofthatweek.

Of course the union and the management may assess the risks and theirconsequencesdifferently.Justtomakethingsprecise,supposetheunionregards$1.00rightnowasequivalentto$1.01aweeklater,andforthemanagementthefigure is$1.02. Inotherwords, theunion’sweekly“interest rate” is1percent;the management’s, 2 percent. The management is twice as impatient as theunion.

This difference in the two sides’ impatiencehas a dramatic effect on theirbargaining settlement: the two sides’ shares are in inverse proportion to theirrates of interest, so the union gets two-thirds ($2 million per week) and themanagementone-third($1millionperweek).

The fact that the greater share in bargaining agreements goes to themorepatientsideisveryunfortunatefortheUnitedStates.Oursystemofgovernment,anditscoverage in themedia, foster impatience.Whennegotiationswithothernationsonmilitaryandeconomicmattersaremakingslowprogress, interestedlobbyistsseeksupportfromcongressmen,senators,andthemedia,whopressuretheadministrationforquickerresults.Ourrivalnationsinthenegotiationsknowthisverywell,andareabletosecuregreaterconcessionsfromus.

12

Incentives

Why have socialist economic systems failed so miserably? The best laidFiveYearPlansofStalinandhissuccessors“gangagley”becausetheworkersand the managers lacked adequate incentives. Most importantly, the systemoffered no reward for doing a good job rather than a merely adequate one.Peoplehadno reason toshow initiativeor innovation,andevery reason tocutcornerswherevertheycould—fulfillingquantityquotasandslackingonquality,forexample.

Amarket economy has a better natural incentive mechanism, namely theprofitmotive.A company that succeeds in cutting costs, or introducing a newproduct,makesagreaterprofit;onethat lagsbehindstandstolosemoney.Buteven thisdoesnotworkperfectly.Eachemployeeormanager inacompany isnot fully exposed to the chill wind of competition in themarket, and the topmanagementofthefirmhastodeviseitsowninternalcarrotsandstickstoobtainthe desired standards of performance from those below.When two firms joinforces for a particular project, they have the added problem of designing acontractthatwillsharetheincentivesbetweenthemintherightway.

1.HOWTOREWARDWORKEFFORTWebringouttheimportantideasforthedesignofincentiveschemesthroughaseries of examples. Imagine yourself as the owner of a high-tech company inCaliforniatryingtodevelopandmarketanewcomputerchessgame,Wizard1.0.Ifyousucceed,youwillmakeaprofitof$200,000 from thesales. Ifyou fail,you make nothing. Success or failure hinges on what your expert player-programmerdoes.She can either put her heart and soul into thework, or justgive it a routine shot.With high-quality effort, the chances of success are 80percent,butforroutineeffort,thefiguredropsto60percent.

Chessprogrammerscanbehiredfor$50,000,buttheyliketodaydream,andwillgiveonlytheirroutineeffortforthissum.Forhigh-qualityeffort,youhave

topay$70,000.Whatshouldyoudo?

ChanceofSuccess

AverageRevenue

SalaryPayments

AverageProfit=Revenue—Salary

Low-QualityEffort

60% $120,000 $50,000 $70,000

High-QualityEffort

80% $160,000 $70,000 $90,000

A routine effort will get you $200,000 with a 60 percent chance, whichcomes out to $120,000 on average. Subtracting the $50,000 salary leaves anaverageprofitof$70,000.Thecorrespondingcalculationifyouhireahigh-effortexpert is 80 percent of $200,000 - $70,000, that is, $90,000. Clearly you dobettertohireahigh-effortexpertatthehighersalary.

Butthereisaproblem.Youcan’ttellbylookingattheexpert’sworkingdaywhether she ismaking routine effort or quality effort. The creative process ismysterious.Thedrawingsonyourprogrammer’spadmaybethekeytoagreatgraphicsdisplay thatwill ensure the successofWizard1.0, or just doodlesofpawnsandbishopstoaccompanyherdaydreaming.Knowingthatyoucan’ttellthe difference between routine effort and quality effort,what is to prevent theexpert from accepting the salary of $70,000 appropriate for high effort, butmakingroutineeffortjustthesame?Eveniftheprojectfails,thatcanalwaysbeblamedonchance.Afterall,evenwithgenuinequalityeffort,theprojectcanfail20percentofthetime;thiswasjustthatkindofbadluck.

Whenyoucan’tobservethequalityofeffort,youhavetobaseyourrewardschemeonsomethingyoucanobserve.Inthepresentinstancethatcanbeonlytheultimateoutcome,namelysuccessorfailureoftheprogrammingeffort.Thisdoes have a link to effort, albeit an imperfect one—higher quality of effortmeans a greater chance of success. This link can be exploited to generate anincentivescheme.

Whatyoudoisoffertheexpertaremunerationthatdependsontheoutcome:a larger sum upon success and a smaller sum in the event of failure. Thedifference, or the bonus for success, should be just enough to make it in theemployee’s own interest to provide high-quality effort. In this case, the bonusmustbebigenoughsothattheexpertexpectsahigheffortwillraiseherearnings

by$20,000,from$50,000to$70,000.Hencethebonusforsuccesshastobeatleast$100,000:a20percentincreaseinthechanceofgettinga$100,000bonusprovides the necessary $20,000 expected payment formotivating high-qualityeffort.

It remains to find the separate sums to be paid in the event of success orfailure. That needs a little calculation. The answer is that you should pay theemployee$90,000forsuccess,andsheshouldpayyouafineof$10,000intheevent of failure. With this incentive scheme, the programmer’s incrementalreward for success is $100,000, the minimum necessary for inducing qualityeffort.Theaveragepaymenttoheris$70,000(an80percentchanceof$90,000anda20percentchanceof-$10,000).This leavesyou, theowner,anaverageprofit of $90,000 (an 80 percent chance of $200,000 - the average salary of$70,000). This is exactly what you could have gotten if you could observequalityofeffortbydirectsupervision.Theincentiveschemehasdoneaperfectjob;theunobservabilityofefforthasn’tmadeanydifference.

In essence, this incentive scheme sells 50 percent of the firm to theprogrammerinexchangefor$10,000andhereffort.Hernetpaymentsaretheneither $90,000 or—$10,000, and with so much riding on the outcome of theproject it becomes in her interest to supply high-quality effort in order toincrease the chance of success (and her profit share of $100,000). The onlydifferencebetweenthiscontractandthefine/bonusschemeisinthename.Whilethenamemaymatter,we see there ismore thanoneway to achieve the sameeffect.

But thesesolutionsmaynotbepossible,eitherbecauseassessingafineonan employeemaynot be legal or because theworker does not have sufficientcapital topaythe$10,000forher50percentstake.Whatdoyoudothen?Theansweristogoasclosetothefinesolutionorequity-sharingasyoucan.Sincetheminimumeffectivebonusis$100,000,theworkergets$100,000intheeventof success and nothing upon failure. Now the employee’s average receipt is$80,000, andyourprofit falls to$80,000.With equity-sharing, theworkerhasonlyherlaborandnocapitaltoinvestintheproject.Butshestillhastobegivena50percentsharetomotivatehertosupplyhigh-qualityeffort.Sothebestyoucandoissellher50percentofthecompanyforherlaboralone.Theinabilitytoenforcefinesorgetworkerstoinvesttheirowncapitalmeansthattheoutcomeisless good from your point of view—in this case, by $10,000. Now theunobservabilityofeffortmakesadifference.

Another difficulty with the fine/bonus scheme or equity-sharing is theproblem of risk. The worker’s incentives arise from her taking a $100,000gamble.Butthislargeriskmaynotbeevaluatedbythestatisticalaverageofthe

outcomes. In this case, the worker has to be compensated both for supplyinghigh-quality effort and for bearing risk. The bigger the risk, the bigger thecompensation. This extra compensation is another cost of a firm’s inability tomonitor its workers’ efforts. Often the best solution is a compromise; risk isreduced by giving theworker less than ideal incentives and consequently thismotivateslessthananidealamountofeffort.

Inotherinstancesyoumayhaveotherindicatorsofthequalityofeffort,andyou can and should use themwhen designing your incentive scheme. Perhapsthemostinterestingandcommonsituationisoneinwhichthereareseveralsuchprojects. Even though success is only an inexact statistical indicator of thequality of effort, it can bemademore precise if there aremore observations.Therearetwowaysinwhichthiscanbedone.Ifthesameexpertworksforyouonmany projects, then you can keep a record of her string of successes andfailures.Youcanbemoreconfidentinattributingrepeatedfailuretopooreffortquality rather than the working of chance. The greater accuracy of yourinferenceallowsyoutodesignabetterincentivescheme.Thesecondpossibilityis thatyouhaveseveralexpertsworkingonrelatedprojects,and there issomecorrelation in the success or failure of the projects. If one expert fails whileothersaroundheraresucceeding, thenyoucanbemoreconfident thatsheisashirkerandnotjustunlucky.Thereforerewardsbasedonrelativeperformance—inotherwords,prizes—willgeneratesuitableincentives.

Whenanemployerdesignsincentivestomotivateaworker,theproblemsareonlyone-sided.Morecomplicatedandmoreinterestingaretheproblemsofjointventures inwhicheachsidehas toprovide the right incentives tomotivate theother.

2.HOWTOORGANIZEAJOINTVENTUREIn the late1960s,BensonandHedges launched their new100-millimeter-longcigarettes with a memorable television commercial, in which “Hedges”described his search for “Benson.” Hedges had the idea for an extra-longcigarette, and was sure that it would be a success if he could use the greattobacco from an obscure brand called Benson’s. After many adventures, hefoundBenson.“Icanseeitnow,”heexclaimed,“HedgesandBenson100s!”Ofcourse,heconcluded,“Bensonsawitalittledifferent.”

Bycombiningtheirresources,BensonandHedgescouldincreasetheirtotalprofit. They had to agree on its division. PresumablyBensonwon that round.Nowwewanttothinkofwhathappensnext.

Oncetheirpartnershipagreementismadeandthenewbrandislaunched,thetwoaretoaconsiderableextentstuckwitheachother.Neithercanreturntotheoldindependentpursuitwithoutsacrificingsomeprofit.Hedges’innovationhasbecometiedinthepublic’smindtooneparticularbrandoftobacco,andBensonhaslosthispreviousbrandidentificationandcustomerbase.Knowingthis,eachwouldbetemptedtoreopenthepartnershipagreementandextractalittlemoreadvantageattheexpenseoftheother,threateningtowalkoutofthewholedealifthedemandisrefused.

Butifthetwoaregoodstrategists,thisdoesnotcomeasasurprise.Eachcanforeseethepossibility,andbecomesreluctanttoenterintoadealthatleaveshimopentosuchfutureexploitation.Thewholeprofitableschemeisthreatened.Thesolution is to provide, in the original deed of partnership, enforceable penaltyclausesthatremovethetemptationtorenege.Thischapterisaboutthedesignofsuchclauses.

Theissuearisesinpersonalpartnershipsjustasinbusinessones.Imagineaworkingcouple,bothofwhomdislikecookingbutcannotaffordtoeatoutmorethanonceaweek.Theystartwithanimplicitorexplicitunderstandingthattheywillsplitthecookingchoresequally—threedaysaweekeach.Butthewife,say,knowsthatthehusbandisnotlikelytowalkoutjustbecauseshecutshersharedownto twodays.She is tempted todiscoveressentialwork thatdemandsherpresenceattheofficeforanextrahouronsomedays,makingitimpossibleforhertogethomeintimetofixdinnereventhoughitisherturn.Thehusbandinturnshould lookahead to thisand try toarrange the initialdeal insuchawaythatthewife’sfuturetemptationisreduced.

Ofcoursethepersonalandlong-termaspectsofamarriageoftensufficetoensurethat thepartiesdonot trysuchtricks,or that theyresolvesuchdisputesamicably when they do arise. Business partnerships are less influenced bypersonalemotions,and thedollaramountsof the temptation tocheatareoftenhigher.Thereforethekindsofcontractswewilldiscussaremorerelevantinthissetting, even though themarriage analogy sometimesmakes formore strikingandamusingstories.

What are the essential features of this class of situations? First, thesesituations involve projects that require simultaneous participation by two ormorepeopleorfirms.Eachsidemustmakesomeinvestmentupfront—astakeitstandstoloseiftherelationshipisterminated—orelsetheotherside’swalkingout will be no threat at all. Second, there must be some uncertainty aboutsubsequenteventsthatactsasajustificationforreopeningoftheagreement,orelse a simple clause that provides large punitive damages for any breachwillservethepurpose.

Infactboththeseconditionsexisttosomedegreeinmanyactualinstances.Wewill highlight them by constructing an example that ismodeled on a realcase,butisolatessomefeaturesofitforemphasis.

When IBM chose Microsoft’s operating system (MS-DOS) for its firstgeneration of personal computers, thiswas a big factor inMicrosoft’s growthandprofits. In turn, thefuturedevelopmentofIBM’sfamilyofcomputerswasconstrained by their dependence on features of MS-DOS. Let us stylize thisexample.

Suppose the development of a computer system involves separatedevelopment of a compatible pair of hardware and software components.Twofirms, each specializing inone area, are contemplating this project.The initialexploration will require $2.2 million of investment in the hardware part, and$1.1million in the software. This initial investmentwill reveal the additionalcostsofcompletingthedevelopment.Forthemoment, theprospectivepartnersknowonlythelow,middle,andhighvaluesofthelikelycosts.Supposetheseare$18,$24,and$30millionforthehardwareand$9,$12,and$15millionforthesoftware.Thefinishedcomputersystemisexpectedtogenerateoperatingprofitsof$39million.

TheUnifiedDecisionBeforeweaskwhatkindofcontractthesetwofirmscanagreeto,andabideby,let us pose a simpler question. Suppose instead of two separate firmsspecializing in hardware and software, there is just one integrated firm. Itsmanagement is appraising a project with two components, hardware andsoftware, whose costs and revenues are exactly as above. How will themanagementproceed?

Thedecisioninvolvestwostages.Thefirstiswhethertogoaheadwiththeexploration; the second, depending on what the exploration has shown, iswhether to proceed with the further development. As usual, the managementmust lookaheadandreasonback, that is,start thinkingabout thesecondstagefirst.

With three possible values of the cost for each component, there are ninecases thatcanarise.Each isequally likely; thus theprobabilityofeach is1/9.Thechart shows the total costs for eachof thesecases.The initial explorationrevealswhichofthesecasesisgoingtoarise.Atthatpointtheexplorationcostshave already been incurred, and the only question is whether furtherdevelopmentisworthwhile,thatis,whethertheoperatingprofitswillcoverthe

costsofdevelopment.DevelopmentCosts—Hardware+Software(inmillionsofdollars)

Intwoofthecases,namely,thoseinwhichthehardwarecoststurnouttobe

at the high end and the software costs are either medium or high, the totaldevelopment costs exceed the $39 million operating profit. If the initialexplorationrevealsthatoneofthesecasesisgoingtoarise,theprojectshouldbecanceled. In two other cases, one inwhich high hardware costs combinewithlowsoftwarecostsandoneinwhichmediumhardwarecostscombinewithhighsoftwarecosts,theoperatingprofitsonlyjustcoverthedevelopmentcosts.Themanagement has no preference between going ahead and canceling; let ussuppose it goes ahead, perhaps because it can thus show its concern for theworkerssolongasnoactuallossisentailed.

We can show the net profit (operating profit minus development cost) ineachof thesenine cases.The twoentries at thebottom right are zerobecausecancellationispossible.Withoutthisoption,thesecaseswouldhaveentailedthelossesshowninparentheses.

Profits(inmillionsofdollars)

Thenineentriesaddupto$36million,butsinceeachcasehasaprobabilityofonly1/9,theirstatisticalaverageisonly36/9=$4million.

Nowlookatthefirststageofdecision,namelywhetherornottoundertakethe initial exploration. This costs $3.3 million, and the expected profit is $4million. Therefore the decision is to go ahead. Without the option ofcancellation,thestatisticalaverageofsubsequentprofitswouldhavebeenonly$3million,and thewholeprojectwouldhavebeenrejected.Thepossibilityofdivorce if thingsdon’tworkoutmakes iteasier toenter intoamarriage in thefirstplace.

ContractsLetusabandonthefictionofanintegratedfirm,andseehowseparatesoftwareandhardwarefirmstacklethesamedecision.Therangeofcostsforthehardwarefirm is exactly twice that for the software firm, so the answer would seemsimple.Leteachbearitsownexplorationcosts.Goaheadwiththedevelopmentexcept in the two cases identified in the chart above. If the project continues,reimburseeachfirmforitsdevelopmentcosts,andthensplittheremainingsum(the net profit) between them in the ratio of two (for hardware) to one (forsoftware).

Unfortunately this won’t work. Suppose the hardware firm’s initialexploration reveals that its development costs are going to be low. Then itbenefits by lying and claiming to havemiddle costs.Whether the firm lies ortellsthetruth,theprojectwillalwaysproceed.Butexaggeratingcostsresultsinanextra$6millioncostreimbursementbutonlya$4millionreductioninprofit-sharing.Thisistruenomatterwhatthesoftwarefirmannounces.Thusclaimingmiddlecostswhenactualcostsarelowisadominantstrategyforthehardware

firm.Thesoftwarefirmhasasimilartemptation;itwantstopretendtohavehigh

costs.Butwhentheybothengageinsuchpretense, thedevelopmentstagewillnever show an operating profit, and when both of them know this at theexplorationstage,theywilldecidenottoproceedwiththeprojectatall.

Howcanafirmlieaboutitscosts?Infactitisveryeasytooverstatecosts.Eachfirmprobablyhasseveral linesofbusinesswithcommonoverheadcosts,andcanapplyadisproportionateshareoftheoverheadtothisproject.Afirmcanactually increase its costs—for example, by paying the managers inflatedsalariesandpaddingotherexpenses.Whenthepaddedcostsmustbepaidoutofone’s own revenue, there is no temptation to do so. But when the costs arereimbursedfromajointrevenuepool,eachpartnerfirmistemptedtocheattheother. “Cost plus” contracts awardedbygovernments suffer largeoverruns forthesamereason.*

Let us therefore think of an alternative. Simply split the operating profitbetweenthemintheratiooftwo(forhardware)toone(forsoftware),andhaveeach firm bear its own development costs. Now there is no incentive to padcosts.Butwehavelosttheprocedureformakingtherightcancellationdecision.The software firmgets $13millionof the operatingprofit.When its costs arehigh($15million),itwantstocancelthedevelopment,eventhoughcontinuationwould be jointly profitable if the hardware firm’s costswere low at the sametime.Ontheotherhand,ifthesoftwarefirm’scostsaremedium($12million),itwants togoahead, even thoughcancellationwouldbe jointlypreferable if thehardware firm’s costs were high at the same time. Should the contract allowcancellation at the request of one party (divorce on demand), or should bothpartieshavetoconcur(divorcebymutualconsentonly)?Eitherrulewillleadtoundesirableoutcomesinsomeofthecases.Thisisthedilemmaofdesigninganidealcontract—howtocombineefficientgo-aheaddecisionswiththeincentivetotruthfullyrevealprivateinformationaboutcostsorrevenues.

PayingWhatItCostsWe begin by focusing on the incentives for the hardware firm. The simplestsolution is tohave thehardware firm reimburse the software firm for its costsandkeepall the remainingprofits if it decides toproceed.Whenever the jointcosts are less than the profit opportunity, the hardware firm will decide toproceed—itgets the total revenueminus itsowndevelopment costsminus thecost reimbursement to the software firm. This incentive scheme gives the

hardwarefirmtheincentivetomaketheefficientdecision.How does the hardware firm know the software firm’s cost? Both sides

could simultaneously announce their costs and agree that the project proceedsonlyifthesumoftheannouncedcostsisbelowtheprofitopportunity.Sincethehardware firm keeps all the profits after reimbursing the software firm for itsdevelopmentcosts,itwantstoproceedwhenevertheseresidualprofitsexceeditstrue costs. The only way to ensure this outcome is for the hardware firm toannouncethetruth.Ifthesoftwarefirmexaggeratesitscosts,thenthego-aheaddecisionswon’talwaysbecorrect.Butthehardwarefirmstillwantstomakeatruthfulannouncementnomatterwhichstrategythesoftwarefirmfollows:truth-tellingisthehardwarefirm’sdominantstrategy.

To see this, consider eachof the cases.Thehardware firmknows that thesoftwarefirmcouldannounceoneofthreenumbers.Ifthatnumberis$9million(thelowend),theprojectwillgoaheadnomatterwhatcostfigurethehardwarefirmannounces,and its revenuewillbe39-9=$30million,enough tocoveranyofitscosts.Nextsupposethesoftwarefirmsays$12million.Ifthehardwarefirm’s true costs are $18 million (low) or $24 million (middle), truthfulrevelation will let the project proceed and result in $27 million, which stillcoversthetruecostof$18or$24million.Pretendingthecostsarehighresultsincancellation,whichpassesupaprofitableopportunity.Ontheotherhand,ifthehardwarefirm’scostsaretruly$30million(high),anditpretendstheyarelowormedium,theprojectgoesaheadandthehardwarefirmgets$27million,whichisanetlossof$3million.

To sum up, inflating costs has no effect on profits when the project goesahead, but can result in cancellation and missed profitable opportunities.Deflatingcostsmakesnodifferencewhentheprojectiscanceled,butmayresultinago-aheaddecisionexactlywhenitmeansaloss.Thereforetruth-tellingisthedominant strategy for the hardware firm. The incentive scheme alters thestrategic environment for the hardware firm to the point where its moral is“Neitheraninflatornoradeflatorbe.”

Adifferentpointofviewshedsusefulnewlightontheincentivemechanism.Whenthehardwarefirmtriestogetago-aheaddecision,itisaskingthesoftwarefirm to incur somecost.Suchcosts inflictedonothers are calledexternalities,andthepurposeofincentiveschemesistoinducepeopletotakeintoaccounttheexternalitiestheyimposeonothers.Thisisjustwhathappenswhenthehardwarefirm receives as payment the operating profit minus the software firm’s cost.When the project goes ahead, the hardware firm’s total cash flow equals theoperatingprofit,minusthesoftwarefirm’scosts,minusitsowncosts.Thereforethehardwarefirmisjustasconcernedtoreducecostsforthesoftwarefirmasit

isforitself.Inotherwords,itisactinginthejointinterest,orhasinternalizedtheexternality.

Thuswehavesolvedthehardwarefirm’sincentiveproblem.Theexactsametrickalsosolvesthesoftwarefirm’sincentiveproblem,ifthesituationissetuptheotherwayaround—i.e.,thesoftwarefirmgetsthetotalprofitsminusitsowncosts and the costs announced by the hardware firm. As above, the projectproceeds whenever profits exceed the sum of the two announced costs. Aparallel argument shows that a truthful announcement is thedominant strategyforthesoftwarefirm.

Butallisnotyetwell.Westillhavetocombinethetwoincentiveschemessothat theycanoperatesimultaneously.Otherwiseweonlyget truth-tellingbyonesideandthennoguaranteeofanyefficiencyintheoutcomes.Theproblemwith running both incentive schemes simultaneously is that in every case inwhichtheprojectgoesahead,thetotalpaymentsexceedthetotalrevenues!Allthatisavailableforpayoutistheoperatingprofit.Butthecombinedschemespayout twice the operating profit, minus the sum of the two costs. The shortfallequals theoperatingprofitminus thesumof the twocosts,and this ispositivewhenevertheprojectgoesahead.

One way to get around this problem is for the two firms to bank somesuitable sum up front and use this to cover shortfalls. If the firms bank thestatisticalaverageof theexpectedshortfalls, theywillcomeoutaheadinsomecases and lose in others, but break even on the average. In our example thebankedamountworksoutat$4million.

Butit ispossibletodoevenbetter.Wecandeviseacontract that(1)givesboth firms the incentive to reveal their costs truthfully, (2) always ensuresefficientgo-aheadorcancellationdecisions,and(3)guaranteesthatthecontractbreaksevenonacase-by-casebasis,notjustontheaverage.

Theprinciplebehindtheefficientcontractistogetfirmstotakeintoaccountthecoststheyimposeonothersbytheiractions.Wejustsawthatwheneachfirmpaystheother’scost,theyareeachmotivatedtoannouncethetruthandmakeanefficientgo-aheaddecision.But this leads toaproblemwithbudgetbalancing.Soinsteadofpayingtheactualcostoftheotherfirm,eachcanpaytheexpectedorstatisticalaverageofthecostsitsactionwillimpose.Wheneachfirmdeclaresa low cost, this increases the chance that the project will proceed andcorrespondinglythechancethattheotherfirmwillhavetobearsomeproductioncosts.Tomakeeachfirmtakeintoaccounttheaverageexternalityitwillinflictontheothertypeoffirm,itshouldreceivethestatisticalaverageoftheproject’soperatingprofitminustheaverageofthecostsoftheothertypeoffirmitwillbedealingwithwhen the project goes ahead. If the firm inflates its own cost, it

riskscancelingtheprojectmorefrequentlyandgettingsmallerreceipts,whileifit deflates costs this leads to a higher “externality” payment for the expectedcostsimposedontheotherfirm.

Twoexampleswillclarifythis.Ifthehardwarefirmdeclaresitscoststobelow($18million),thentheprojectwillgoaheadnomatterwhatthecostsofthesoftware firm, which can be $9, $12, or $15 million, each with a one-thirdchance.The statistical average is$12million.This is the sumsubtracted fromtheoperatingprofitof$39millionincalculatingthehardwarefirm’sreceipt.Ifthehardwarefirmdeclareshighcost($30million),thentheprojectwillgoaheadonlyifthesoftwarefirmdeclareslowcost($9million),whichhappensone-thirdof the time. So the hardware firm should receive one third of $39 minus $9million,or$10million.Thechartbelowshowsthereceiptfiguressocalculated.Ineachcell thereceiptsof thehardwarefirmareshowninthebottomleftandthereceiptsforthesoftwarefirmareinthetopright.

ReceiptCalculations—-FirstStage(inmillionsofdollars)

Software

But the receipts socalculateddonotbalance thebudgetonacase-by-case

basis.Forexample,inthebottomleftcasetheprojectcollectsarevenueof$39millionbutpaysoutonly$25million,whileinthetwoothercasesinthebottomrow there isno revenuegenerated (because theprojectdoesnotgoahead)butthereisapayoutof$22million.Thereforeasecondstageofthecalculationmustadjustthepayoutsandachievebalance.Thismustbedonewithoutupsettingthe

firms’incentivestorevealtheirtruecosts.Wecanchangeeachfirm’sreceiptsinresponse towhat theother firmsays; forexample,wecanaddor subtractanynumberfromthehardwarefirm’sreceiptsinthefirstcolumnwithoutalteringitsincentive togiveoneansweror theother.Eachcolumnof thehardware firm’sreceiptsandeach rowof thesoftware firm’s receiptscanbeadjusted thisway.We can also rearrange the hardware firm’s payoffs along each row so long astheir statistical average is preserved, and similarly for the software firm alongeachcolumn.Alltheseadjustmentsgiveusmorethanenoughfreedomtoensurecase-by-casebalance.WeofferonepossibleanswerinScheme1.

Scheme1withCorrectIncentivesandBudgetBalance(inmillionsofdollars)

Thishas theniceproperty that thehardware firm’s receipts,averagedover

allninepossibilities,are$20.33million,whilethoseofthesoftwarefirmare$10million;theratioof2:1isalmostexactlytheratiooftheirgeneralcoststructure,and therefore the scheme seems to offer the fairest division of the returnsbetweenthetwo.Butinthecasesinwhichtheprojectiscanceled,thehardwarefirmmustpaythesoftwarefirm$3million.Thiscanbeacauseofdisputesafterthefact.Analternativescheme,Scheme2thatfollows,haszeropaymentswhenthereisacancellation.Thismightbeeasiertoenforce.Butitgivesthehardwarefirm an overall better deal: an average of $23.33 million as against only $7millionforthesoftwarefirm,aratioofmorethanthreetoone.

Scheme 2withCorrect Incentives and Budget Balance (inmillions ofdollars)

If one side,when terminating a partnership, is required tomake the other

side whole, then this side will have just the right incentive to maintain thepartnership.Sometimesitwillbedissolved,butthegaintoonesideisnotattheexpenseoftheother.

Theideaofpayingthecostyouimposeonothersisusefulinmanycontexts.Itevenhelpsusunderstandbiddingstrategyinauctions.

3.THESTRATEGYOFAUCTIONSManyproductionorsupplycontracts,especiallygovernmentonesbutsometimesalsoprivateones,areawardedbyasealed-bidauction.Eachfirmsubmits inasealedenvelopethepriceforwhichitiswillingtodothejob.Thenallthebidsarecompared,andthelowestbidderwins,andreceivesthepricethatshebid.

Imagineyourselfasabidderforsuchacontract,sayconstructionofastretchof highway. Your cost (which includes the normal return you require oninvestment)is$10million.Youdonotknowthecostsofyourcompetitors,andmay not even know their identities. But you have reason to believe that theircostswill range somewhere between $5million and $15million. The best ofthemwillhaveacost figure that isequally likely to lieanywherebetween theextremes—onechanceintenforeachmillioninthisrange.Whatbidshouldyousubmit?

You will never submit a bid that is lower than your cost. For example,supposeyoubid$9million.Thismakesnodifference ifyoudon’twin,but ifyou dowin, youwill be paid a price that is less than your cost.*Youwill bepavingthewaytoyourownbankruptcy.

Whataboutsubmittingabid that ishigher thanyourcost?Supposeall the

othersbidhonestly,andseewhathappensifyousubmitthebidof$11million.Youmustconsiderthreepossibilitiesseparately.Fivetimesoutoften,somerivalwillhavebidlessthan$10million,andyourinflatedbidwillmakenodifferenceatall.Fourtimesoutoften,thebestrivalbidwillexceed$11million.Youcouldhavewon thecontractwithabidof either$10millionor$11million,but thehigherbidgetsyou$1millionmoreprofit.There isonechance in ten that thebest rival bid falls between $10 million and $11 million. Now youroverstatement costs you the contract. But at $10 million the price only justcoveredyourcosts,sothecontractwasonlybarelyworthhavinganyway.

Puttingthethreecasestogether,youseethatsubmittinganinflatedbidisagood strategy for you; in the language of game theory, it dominates truthfulbidding.Theotherparticipantsare thinkingalongthesamelines.Thereforeallbidsgetinflated.

When the bids reveal the true costs, society can make an accurate cost-benefit analysis of the road, and the decision to build itwill be economicallyefficient.Arethereotherbiddingschemesthatremovethestrategictemptationtoinflatethebids?

Yes.Onesimpleschemeawardsthecontract tothelowestbidder,butpaysherapriceequaltothesecond-lowestbid,ratherthanherown.Letusseehowthisworks.Supposeagainthatyourcostis$10million,andthatyouarethinkingofbidding$11million.Asbefore, thereare threecases toconsider. If thebestrivalbidisunder$10million,thenyourstrategymakesnodifference.Ifthebestrivalbidismorethan$11million,youstillwinthecontract,butnowthepriceyougetequalsthebestrivalbid,sotheinflationhasnotgainedyouanything.Ifthebestrivalbidfallsbetween$10and$11million,yourstrategyhascostyouthecontract,whenthetruthwouldhavegottenyouatleastalittleprofit,namelytheexcessofthebestrivalbidover$10million.

To sum up, inflating your bid gains you nothing in two of the cases, andloses a little in one case. Therefore you have a dominant strategy, namelysubmittingabidthatequalsyourcost.

Wecanlookatitinanotherway,andtherebyshedsomeusefulnewlightonthescheme.Whenyouinflateyourbidfrom$10millionto$11million,youareinflictingacostonsociety,namelycreatingthepossibilitythatthecontractwillgotoafirmthathasahighercost—usesupmoreresources—thanyours.Hereagain,thiscostinflictedbyonepersononothersiscalledanexternality.Agoodincentive schememust induce you to take into account the true social cost ofyouraction,includinganyexternalityyouimposeonothers.Thiscanbedonebychargingyouthecosts,orpayingyouarewardforavoidingthem.Inthepresentinstance, thesecondmethod is theoneatwork.Bynot inflatingyourbid,you

save society the risk of an unnecessarily costly undertaking, and are rewardedwithapriceequaltothehighercost.

Thisisjustlikethefirstincentiveschemewedescribedforthejointventure.Inthiscase,theefficientsolutionistohavethefirmwiththelowestcostgetthecontract.By takingon theproject, it saves the firmwith thenext lowest costsfromincurringitscosts.Thissavingsisapositiveexternality.Whenthewinningbidderispaidforincurringthisexternality,ithastheincentivetoannouncethetruth, and efficient decisions will bemade. But the ability to elicit true costsfromthebiddersdoesnotcomeforfree.TheDepartmentofTransportationhasto pay the lowest biddermore than his own cost, namely the cost of the nextlowestbidder.

Items can be sold as well as purchased using this type of auction. Eachpersonplaceshisbidinasealedenvelope,andthehighestbidderissoldtheitemat the second highest bidder’s price. Developed by Columbia Universityeconomist William Vickrey, this procedure is sometimes called a Vickreyauction or a philatelist auction (stamp journals use this procedure to auctionstamps through themail). Once again, each person should bid his or her truevaluation.Biddingmorethanone’svalueriskswinningtheauctionwhenitisnotworthwhile, while underbidding never saves you money but risks losing theprizewhenyouwerestillwillingtopaythesecondhighestbid.

Infact,thisone-stepprocedureshouldleadtoexactlythesameoutcomeasatraditionalEnglishauction.IntheEnglishauction,allthebiddersareinthesameroom and an auctioneer calls out successively higher prices. The biddingprogresses until only one bidder is left—going once, going twice, sold. Thepenultimatebidder shoulddropoutonlywhen thepriceexceedshisvaluation.Thusthepersonwhovalues the itemmosthighlyshouldwintheprize,andhepaysapriceequaltothevalueofthenexthighestbidder.*ButthatisexactlytheoutcomeoftheVickreyauction!

ComparetheVickreyauctiontothemorestandardwaytorunasealed-bidauction—thehighestbidderwinstheprizeandpayshisbid,oriftheauctionisusedtosellacontract,thelowestbidderisawardedthecontractandispaidhisbid.Whichschemeworksbetterfortheseller(orbuyer)?

Itisremarkablebuttruethat,onaverage,thetwoschemesleadtoexactlythesameoutcomes. In thecaseofagovernmentcollectingbidsforaroadproject,theseemingbudgetaryadvantageofpaying the lowestbidrather than thenextlowest bid disappears when we understand how the bidders respond to itstrategically,namelybyinflatingtheirbids.Thelowestbidderwinsandispaidan amount equal to his own bid, but thatwill be an inflated bid. A complete

mathematicalanalysisoftheproblemshowsthatthebudgetaryeffectofthebidinflationundertheconventionalmethodisexactlythesameasthatofpayingthewinnerthebidofthenextbidder.Thereforetheschemewedescribeddoesnotcost any more than the conventional one. The intuitive reason for thisequivalence is that both types of auctions should always lead to an efficientoutcome: the person with the lowest costs should always win. But efficiencyarisesonlywhenpeople takeaccountof theexternality they imposeonothers.Thus a firm’s optimal bid is the expected cost on the next best competitorconditionalonwinningtheauction.Thisisjustlikethebalanced-budgetversionofthejoint-ventureincentive;inthiscase,thewinningfirmbidstheexpectedoraverageexternalityratherthantheactualexternality.

4.CASESTUDY#12:THERISKOFWINNINGOne of the more unusual features of a Vickrey sealed-bid auction is that thewinningbidderdoesnotknowhowmuchshewillhavetopayuntiltheauctionis over and she haswon.Remember, in aVickrey auction thewinning bidderpaysonlythesecondhighestbid.Incontrast,thereisnouncertaintyinthemorestandard sealed-bid auction, inwhich thewinnerpaysherbid.Since everyoneknowsherownbid,noonehasanydoubtsastohowmuchshewillhavetopayifshewins.

The presence of uncertainty suggests that we might want to consider theeffect of risk on the participants’ bidding strategies. The typical response touncertainty isnegative: thebiddersareworseoff inaVickreyauctionbecausetheydonotknowhowmuch theywill have topay if theyhave submitted thewinningbid.Isitreasonablethatabidderwillrespondtothisuncertaintyorriskbyloweringherbidbelowthetruevaluation?

CaseDiscussionItistruethatthebiddersdisliketheuncertaintyassociatedwithhowmuchtheymighthavetopayiftheywin.Eachisinfactworseoff.Yet,inspiteoftherisk,participantsshouldstillbidtheirtruevaluations.Thereasonisthatatruthfulbidis adominant strategy.As longas the sellingprice isbelow thevaluation, thebidderwantstobuythegood.Theonlywaytoensurethatyouwinwheneverthepriceisbelowyourvalueistobidthetruevalue.

InaVickreyauction,biddingthetruevaluationdoesn’tmakeyoupaymore—exceptwhensomeoneelsewouldhaveoutbidyou,inwhichcaseyouwould

havewanted to raise your bid until the selling price exceeded your valuation.TheriskassociatedwithaVickreyauctionislimited;thewinnerisneverforcedtopayanamountgreaterthanherbid.Whilethereisuncertaintyaboutwhatthewinner will pay, this uncertainty is only over the degree of good news. Eventhoughthegoodnewsmightbevariable,thebeststrategyistowintheauctionwheneverit’sprofitable.Thatmeansbiddingyourtruevalue.Younevermissaprofitableopportunityandwheneveryouwinyoupaylessthanyourtruevalue.

13

CaseStudies

1.THEOTHERPERSON’SENVELOPEISALWAYSGREENERThe inevitable truth about gambling is that one person’s gainmust be anotherperson’sloss.Thusitisespeciallyimportanttoevaluateagamblefromtheotherside’s perspective before accepting. For if they are willing to gamble, theyexpect towin,whichmeanstheyexpectyouto lose.Someonemustbewrong,butwho?Thiscasestudylooksatabetthatseemstoprofitbothsides.Thatcan’tberight,butwhere’stheflaw?

Therearetwoenvelopes,eachcontaininganamountofmoney;theamountofmoney iseither$5,$10,$20,$40,$80,or$160andeverybodyknows this.Furthermore, we are told that one envelope contains exactly twice as muchmoneyastheother.Thetwoenvelopesareshuffled,andwegiveoneenvelopetoAli and one to Baba. After both the envelopes are opened (but the amountsinsidearekeptprivate),AliandBabaaregiventheopportunitytoswitch.Ifbothpartieswanttoswitch,weletthem.

SupposeBabaopenshisenvelopeandsees$20.Hereasonsasfollows:Aliisequally likely to have $10 or $40. Thus my expected reward if I switchenvelopes is (10 + 40)/2 = $25 > $20. For gambles this small, the risk isunimportant,soitisinmyinteresttoswitch.

Byasimilarargument,Aliwillwanttoswitchwhethershesees$10(sinceshefiguresthathewillgeteither$5or$20,whichhasanaverageof$12.50)or$40(sinceshefigurestogeteither$20or$80,whichhasanaverageof$50).

Something is wrong here. Both parties can’t be better off by switchingenvelopessincetheamountofmoneytogoaroundisnotgettinganybiggerbyswitching. What is the mistaken reasoning? Should Ali and/or Baba offer toswitch?

CaseDiscussionAswitchshouldneveroccurifAliandBabaarebothrationalandassumethattheotheristoo.Theflawinthereasoningistheassumptionthattheotherside’swillingness to switchenvelopesdoesnot revealany information.Wesolve theproblem by looking deeper and deeper into what each side thinks about theother’sthoughtprocess.FirstwetakeAli’sperspectiveaboutwhatBabathinks.ThenweusethisfromBaba’sperspectivetoimaginewhatAlimightbethinkingabouthim.Finally,wegobacktoAliandconsiderwhatheshouldthinkabouthowBaba thinksAli thinks about Baba. Actually, this all soundsmuchmorecomplicatedthanitis.Usingtheexample,thestepsareeasiertofollow.

SupposethatAliopenshisenvelopeandsees$160.Inthatcase,sheknowsthatshehasthegreateramountandhenceisunwillingtoparticipateinatrade.Since Ali won’t trade when she has $160, Baba should refuse to switchenvelopeswhenhehas$80,for theonlytimeAlimight tradewithhimoccurswhenAlihas$40, inwhichcaseBabaprefers tokeephisoriginal$80.But ifBabawon’tswitchwhenhehas$80,thenAlishouldn’twanttotradeenvelopeswhenshehas$40, sincea tradewill resultonlywhenBabahas$20.Nowwehavearrivedat thecaseinhand.IfAlidoesn’twant toswitchenvelopeswhenshe has $40, then there is no gain from trade when Baba finds $20 in hisenvelope; he doesn’t want to trade his $20 for $10. The only person who iswillingtotradeissomeonewhofinds$5intheenvelope,butofcoursetheothersidedoesn’twanttotradewithhim.

2.THELASTSHALLBEFIRSTTheU.S. government had amajor problem trying tomotivate severalmillionteenagerstoregisterforthemilitarydraft.Large-scalecivildisobediencewouldmake it impossible to punish everyone who violated the law. Still, thegovernmenthadabigadvantage:itsettherules.

Tosee theadvantageofmoving first, imagine that thegovernment isonlyallowedtopunishonepersonwhofailstoregister.Howcantheyusethissinglethreattoinduceeveryonetoregister?

CaseDiscussionThe government announces that it will go after evaders in alphabetical order.The person with surname Aaron knows that he would be singled out for

punishmentifhefailedtoregister.Thecertaintyofpunishmentisthenenoughtomotivatehimtoregister.ThentheAbramsconcludethatsincealloftheAaronswill surely register, it is theywhowill be punished.And so on down the linerightthroughtotheZhukovsandtheZweibels.

A lawyer might argue that it is unconstitutional to single out people forpunishmentbecauseof thealphabeticalorderingof theirnames.Butnothingisspecialaboutthealphabet.Thekeypointisthattheorderofpunishmentispre-specified. A randomly chosen and announced order of birthdates, or socialsecuritynumbers,doesjustaswell.Afewselectivepunishmentsgoalongwayinkeepingeveryoneinline,andaremuchcheaperthanofferingmarketwagestoattractanequalnumberandqualityofrecruits.

Forexample,ifCongressmistookappearancesforreality,itmightforbidtheDraftBoard tousealphabeticalorderas themeansbywhich theychoosewhogets punished first, leaving open other equivalentmethods.What is needed tostopthepracticeistoforbidthepre-announcementofanyorder.

Whentheparticipantsinagamearerankedinsomeorder,itisoftenpossibleto predictwhat the person at one endwill do. This knowledge influences theactionofthenextperson,whichinturninfluencesthethird,andsoondowntheline.

Thestorywehavetoldisabitextreme.BythetimewegettotheZhukovs,someonewillsurelynotregisterandthenbepunished.TheZhukovsdon’treallyhave to worry. With so many individuals, one expects a small amount ofslippage. The point is that the number of punishments available need not beanywherenearthenumberofpeopletomotivate.Thecapacity(andwillingness)tojailathousandprotestorscandeterseveralmillionwould-be’s.

3.THETHREE-WAYDUELThreeantagonists,Larry,Mo,andCurly,areengagedinathree-wayduel.Therearetworounds.Inthefirstround,eachplayerisgivenoneshot:firstLarry,thenMo,andthenCurly.Afterthefirstround,anysurvivorsaregivenasecondshot,againbeginningwithLarry,thenMo,andthenCurly.

Foreachduelist,thebestoutcomeistobethesolesurvivor.Nextbestistobe one of two survivors. In third place is the outcome in which no one getskilled.Deadlastisthatyougetkilled.

Larry is a poor shot,with only a 30 percent chance of hitting a person atwhomheaims.Moisamuchbettershot,achieving80percentaccuracy.Curlyisaperfectshot—henevermisses.

What is Larry’s optimal strategy in the first round?Who has the greatestchanceofsurvivalinthisproblem?

CaseDiscussionAlthoughbackwardreasoningisthesafewaytosolvethisproblem,wecanjumpaheadalittlebyusingsomeforward-lookingarguments.Westartbyexaminingeach of Larry’s options in turn. What happens if Larry shoots at Mo?WhathappensifLarryshootsatCurly?

If Larry shoots at Mo and hits, then he signs his own death warrant. ItbecomesCurly’s turn toshoot,andhenevermisses.Curlywillnotpassat thechance toshootLarry,as this leads tohisbestoutcome.LarryshootingatModoesnotseemtobeaveryattractiveoption.

IfLarryshootsatCurlyandhits,thenitisMo’sturn.MowillshootatLarry.[Think about how we know this to be true.] Hence, if Larry hits Curly, hischanceofsurvivalislessthan20percent(thechancethatMomisses).

So far,neitherof theseoptions looks tobeveryattractive. In fact,Larry’sbeststrategyistofireupintheair!Inthiscase,MowillshootatCurly,andifhemisses,CurlywillshootandkillMo.ThenitbecomesthesecondroundanditisLarry’sturntoshootagain.Sinceonlyoneotherpersonremains,hehasatleasta30percentchanceofsurvival,since that is theprobability thathekillshisoneremainingopponent.

The moral here is that small fish may do better by passing on their firstchancetobecomestars.Weseethiseveryfouryearsinpresidentialcampaigns.When there is a largenumberof contenders, the leader of thepackoftengetsderailed by the cumulative attacks of all the medium-sized fish. It can beadvantageous to wait, and step into the limelight only after the others haveknockedeachotherandthemselvesoutoftherunning.

Thus,yourchancesofsurvivaldependonnotonlyyourownabilitybutalsowhomyouthreaten.Aweakplayerwhothreatensnoonemayendupsurvivingifthestrongerplayerskilleachotheroff.Curly,althoughheisthemostaccurate,hasthelowestchanceofsurvival—only14percent.Somuchforsurvivalofthefittest!Mohasa56percentchanceofwinning.Larry’sbeststrategyturnshis30percentaccuracyintoa41.2percentchanceofwinning.1

Today’s duels aremore likely to be fought between takeover specialist T.BoonePickensandthetargetmanagementoverwhowillendupwithcontrolofthe board of directors.Our next case presents the story of a firm that tried topreemptatakeoverduelthroughtheuseofapoisonpill.Butthingsdon’talways

comeoutasplanned,especiallyifyoudon’tthinkfarenoughahead.

4.THESHARKREPELLENTTHATBACKFIREDInrecentyears,corporationshaveadoptedmanynewandinnovativeways,oftencalled shark repellents, to prevent outside investors from taking over theircompany.Withoutcommentingontheefficiencyorevenmoralityoftheseploys,we present a new and as yet untested variety of poison pill and ask you toconsiderhowtoovercomeit.

ThetargetcompanyisPiper’sPickledPeppers.Althoughnowpubliclyheld,theoldfamilytiesremain,asthefive-memberboardofdirectorsiscompletelycontrolled by five of the founder’s grandchildren. The founder recognized thepossibility of conflict between his grandchildren as well as the threat ofoutsiders.Toguardagainstboth familysquabblesandoutsiderattacks,he firstrequiredthattheboardofdirectorelectionsbestaggered.Thistrickmeansthateven someone who owns 100 percent of the shares cannot replace the entireboard—rather, only the members whose terms are expiring. Each of the fivemembershadastaggeredfive-yearterm.Anoutsidercouldhopetogetatmostoneseatayear.Takenatfacevalue,itappearedthatitwouldtakesomeonethreeyearstogetamajorityandcontrolofthecompany.

Thefounderwasworriedthathisideaofstaggeredtermswouldbesubjecttochangeifahostilepartywrestedcontroloftheshares.Asecondprovisionwasthereforeadded.Theprocedureforboardelectioncouldbechangedonlybytheboard itself.Anyboardmembercouldmakeaproposalwithout theneed foraseconder.Buttherewasamajorcatch.Theproposerwouldberequiredtovoteforhisownproposal.Thevotingwouldthenproceedinclockwiseorderaroundtheboardroomtable.Topass,aproposalneededatleast50percentofthetotalboard(absenceswerecountedasvotesagainst).Giventhattherewereonlyfivemembers,thatmeantatleast3outof5.Here’stherub.Anypersonwhomadeaproposaltochangeeitherthemembershipoftheboardortherulesbyhowthatmembershipwasdeterminedwouldbedeprivedofhispositionontheboardandhis stock holdings if his proposal failed. The holdings would be distributedevenly among the remaining members of the board. In addition, any boardmember who voted for a proposal that failed would also lose his seat on theboardandhisholdings.

Forawhile thisprovisionprovedsuccessful in fendingoffhostilebidders.ButthenSeaShellsbytheSeaShoreLtd.bought51percentofthesharesinahostile takeover attempt.SeaShells votedherself one seat on theboard at the

annualelection.Butitdidnotappearthatlossofcontrolwasimminent,asshewasonelonevoiceagainstfour.

At their firstboardmeeting,SeaShellsproposeda radical restructuringoftheboardmembership.Thiswasthefirstsuchproposalthattheboardhadevervoted on. Not only did the Sea Shells proposal pass, amazingly, it passedunanimously!Asaresult,SeaShellsgottoimmediatelyreplacetheentireboard.Theolddirectorsweregivenaleadparachute(whichisstillbetterthannothing)andthenwereshownthedoor.

Howdidshedo it?Hint: Itwasprettydevious.Backwardreasoning is thekey.Firstworkonaschemetogettheresolutiontopass,andthenyoucanworryaboutunanimity.Toensurethat theSeaShellsproposalpasses,startat theendand make sure that the final two voters have an incentive to vote for theproposal.Thiswillbeenoughtopasstheresolution,sinceSeaShellsstartstheprocesswithafirstyesvote.

CaseDiscussionMany proposals do the trick. Here’s one of them. Sea Shells’ restructuringproposalhasthefollowingthreecases:

If the proposal passes unanimously, then Sea Shells chooses anentirely new board. Each board member replaced is given a smallcompensation.Iftheproposalpasses4to1,thenthepersonvotingagainstisremovedfromtheboard,andnocompensation ismade.If theproposalpasseswith a voteof 3 to2, thenSeaShells transfers the entiretyof its 51percentshareofPeter’sPickledPepperstotheothertwoyesvotersinequalproportion.Thetwonovotersareremovedfromtheboardwithnocompensation.

At thispoint, backward reasoning finishes the story. Imagine that thevote

comesdowntothewire:thelastvoterisfacedwitha2–2count.Ifhevotesyes,itpassesandhegets25.5percentofthecompany’sstock.Ifitfails,SeaShells’assets(andtheotheryes-voter’sshares)aredistributedevenlyamongthethreeremainingmembers,sohegets(51+12.25)/3=21.1percentofthecompany’sstock.He’llsayyes.

Everyone can thereby use backward reasoning to predict that if it comes

downtoa2–2tie-breakingvote,SeaShellswillwinwhenthefinalvoteiscast.Now lookat the fourthvoter’sdilemma.When it ishis turn tovote, there areeither

(i)1yesvote(bySeaShells),(ii)2yesvotes,or(iii)3yesvotes.

Iftherearethreeyesvotes,theproposalhasalreadypassed.Thefourthvoter

wouldprefertogetsomethingovernothing,andthereforevotesyes.Iftherearetwoyesvotes,hecanpredict that thefinalvoterwillvoteyesevenifhevotesno.The fourthvoter cannot stop theproposal frompassing.Hence, again it isbettertobeonthewinningside,sohewillvoteyes.Finally,ifheseesonlyoneyesvote,thenhewouldbewillingtobringthevotetoa2–2tie.Hecansafelypredictthatthefinalvoterwillvoteyes,andthetwoofthemwillmakeoutverynicelyindeed.

The first two Piper’s board members are now in a true pickle. They canpredictthateveniftheybothvoteno,thelasttwowillgoagainstthemandtheproposalwillpass.Given that theycan’tstop it frompassing, it isbetter togoalongandgetsomething.

Thiscasedemonstratesthepowerofbackwardreasoning.Ofcourseithelpstobedevioustoo.

5.WINNINGWITHOUTKNOWINGHOWChapter 2 introduced games in which players move in sequence and whichalwaysendsafterafinitenumberofmoves.Intheory,wecouldexamineeverypossible sequence of moves and thereby discover the best strategy. This isrelativelyeasyfortic-tac-toeandimpossible(atpresent)forchess.Inthegamebelow, thebeststrategy isunknown.Yet,evenwithoutknowingwhat it is, theveryfactthatitexistsisenoughtoshowthatitmustleadtoawinforthefirstplayer.

ZECKisadot-gamefortwoplayers.Theobjectistoforceyouropponenttotakethelastdot.Thegamestartswithdotsarrangedinanyrectangularshape,for

examplea7×4:

Each turn, a player removes a dot and with it all remaining dots to thenortheast.Ifthefirstplayerchoosesthefourthdotinthesecondrow,thisleaves

hisopponentwithEachperiodatleastonedotmustberemoved.Thepersonwhoisforcedtotakethelastdotloses.

Foranyshapedrectanglewithmorethanonedot,thefirstplayermusthaveawinningstrategy.Yetthisstrategyisnotcurrentlyknown.Ofcoursewelookatallthepossibilitiesandthenfigureitoutforanyparticulargame,suchasthe7x4above—butwe don’t know the best strategy for all possible configurations ofdots.Howcanweshowwhohasthewinningstrategywithoutknowingwhatitis?

CaseDiscussionIf the second player has a winning strategy, that means that for any openingmoveof the firstplayer, the secondhasa response thatputshim inawinningposition.Imaginethatthefirstplayerjusttakestheupperright-handdot.

No matter how the second player responds, the board will be left in a

configurationthatthefirstplayercouldhavecreatedinhisfirstmove.Ifthisistrulyawinningposition,thefirstplayershouldhaveandcouldhaveopenedthegamethisway.Thereisnothingthesecondplayercandotothefirstthatthefirst

playercan’tdountohimbeforehand.

6.ASEASONFOREVERYTHINGANDEVERYTHINGINITSSEASON

Consider the problem faced by the former United States Football League(USFL)indecidingwhethertoplayinthefallorthespring.Thefallmarketisthebiggest,andconsequently,theUSFL’sidealwouldbetohaveamonopolyinthefallandhavetheNationalFootballLeague(NFL)movetothespring.But,iftheNFL remains in the fall, theUSFL does better to take amonopoly in thespring. The worst possible outcome for the USFL would be if both leaguesmovedtoaspringschedule.

TheNFL,evenwithitsstrongerreputation,stillprefersthattheUSFLplayduring its off season. However, its reputation is strong enough and the fallmarketissufficientlybiggerthanthespringthattheNFLpreferstogohead-to-headagainsttheUSFLinthefallthantakethespringbyitself.

Tomaketheseideasmoreprecise,supposethatthereare100millionpeoplewhowouldwatchfootballinthefall,and50millioninthespring.Ifoneleaguehasamonopolyduringaseason,itgetstheentiremarketforthatseason.Ifthetwogohead-to-headduringaseason, theNFLgetsa70percentshareand theUSFLa30percentshareduringthatseason;thepotentialviewersfortheotherseasongounserved.

The following table gives the viewer figures for both leagues for the fourpossible combinations of their choices. To save space,we have combined thetablesoftheirseparateyieldsintoone.Ineachbox,thebottomleftentryistheUSFL’smarket,andthetoprightistheNFL’smarket.

TableofMarketSizesfor[USFL,NFL]

Whatdoweexpecttohappen?

CaseDiscussionTheUSFLdoesnothave adominant strategy. Its bestmove is always toplayduring theNFL’s off season.Clearly this is not independent ofwhat theNFLdoes. The NFL, however, does have a dominant strategy. It prefers the fallseason independentof theUSFL’schoice;observe that thenumbers in its firstcolumn,70and100,areuniformlybigger than thecorrespondingnumbers,50and35,inthesecondcolumn.

What should happen in this game? The NFL should pick its dominantstrategy,namelythefall.TheUSFL,byputtingitselfintheNFL’scleats,shouldbe able to predict that the NFLwill play in the fall. Then, the USFL shouldchoosethespring.

Thesepredictions remain true forawide rangeofpotential fall andspringmarket sizes.Givena70:30market splitbetween theNFLandUSFL, the fallmarketcanbeanywherefrom43percentto233percentbiggerthanthespringmarketandthesamepredictionsfallout.Giventhisrobustnessofourresult,weconclude that theUSFL’smove toa fall schedulewasamistake, andone thatmayverywellhavecostthemtheirexistence.

7.HEWHOLASTSLASTLASTSBEST?

Managers generally take a rosy view of time: markets expand, bettertechnologies become available, information improves. But where there isgrowth, there is also decay. More than 10 percent of the United States’

manufacturing output was accounted for by industries whose real output hadshrunk during the 1970s. These declining industries range from coremanufacturing such as steel, tire, and rubber to fibers and chemicals, to babyfoods andvacuum tubes.The reasons for thedecline are varied, ranging fromtechnological progress (transistors over vacuum tubes) to improved foreigncompetition (steel) to regulation (chemicals) to changing demographics (babyfoods).

Inthesedecliningindustries,someonemustreducecapacityinorderfortheindustry to remainprofitable.Each firmwould like itscompetitors toshoulderthereduction; thatway theycancapture theremainingmarketby themselves.2This case examines the question ofwhether survivability is related to size. Indecliningmarkets,doDavidscutGoliathsdowntosizeordo theygetsteppedon?

We lookat competitionbetweenDavidandGoliath,bothproducers in thedeclining slingshot industry. David is a small producer. Hemanufactures oneslingshotperquarter.GoliathistwiceDavid’ssize.Heproducestwoslingshotsperquarter.Thetwocompetitorshavenoflexibilityinchoosingoutput.Iftheyarein,theyarein;oncetheystop,theycan’tcomeback.*

TheirbattlehassomeofthesamecharacteristicsasTimeversusNewsweek.Eachquarter theydecidewhether toproduceor toexit,withoutknowing theircompetitor’scoevalchoice.Butthentheyfindoutlastperiod’smoveandgettorepeatthebattlenextquarter(providedneitherexited).

The price chart on the next page details the market price (net of cost)depending on howmuch is produced. Starting in the first quarter of 1988, ifDavidisamonopolist,hecanexpecttomake$3onhisoneslingshot.IfDavidexitsandleavesGoliathasamonopolist,Goliathgetsalowerunitpricesincehisoutput is bigger; in this case, he gets $2 per slingshot. (Of course, $2 on twoslingshotsisbetterthan$3onDavid’sone.)IfbothDavidandGoliathproduce,theyaresaidtobeduopolists.Inthatcasetheysaturatethemarket,andtheprice(netofcost)fallsto50cents.

Thedecliningmarketisevidentfromthepricechart.Thefirstcolumnshowsthe price net of cost if David captures the market for himself. The secondcolumndetailsthepricenetofcostifGoliathisamonopolist.Thethirdcolumndetailsthepricenetofcostifbothfirmscontinuetoproduceinaduopoly.

IneachquarterafterJanuary1988,thepricefallsby25centsforanyoutputlevel brought to market. As can be seen from the chart, the pressure to exitbegins in the third quarter of 1988, when the duopolists first losemoney. ByJanuary1990,Goliathisnolongerprofitableevenasamonopolist.Ayearlater,

evenDavidcannolongerexpecttomakeanymoney.

TableofPrice(NetofCost) DavidAlone GoliathAlone David&GoliathJan. 1988

3.00 2.00 0.50

Apr.2.75 1.75 0.25

July2.50 1.50 0.00

Oct.2.25 1.25 -0.25

Jan. 19892.00 1.00 -0.50

Apr.1.75 0.75 -0.75

July1.50 0.50 -1.00

Oct.1.25 0.25 -1.25

Jan. 19901.00 0.00 -1.50

Apr. 0.75 -0.25 -1.75

July0.50 -0.50 -2.00

Oct.0.25 -0.75 -2.25

Jan. 19910.00 -1.00 -2.50

Apr.-0.25 -1.25 -2.75

July-0.50 -1.50 -3.00

Oct.-0.75 -1.75 -3.25

Over the twelve quarters from 1988 to 1991 the slingshot industry willbecomeextinct.Butwhendothefirmsexit?Whogivesupfirst?Whendotheyexit?

Thisproblemcanbesolvedusingthetechniqueofsequentiallyeliminatingdominatedstrategies.Togetyoustarted,notethatstayingpastJanuary1990isadominatedstrategy forGoliath,ashe forevermore losesmoney, irrespectiveofwhetherDavidstaysorexits.Nowworkbackwardandaskwhatyouwoulddoifyou were David and it was the third quarter of 1989 and Goliath was stillproducing.*

CaseDiscussionIn thisproblem, itdoesnotmatterhowmuchmoneyyoumake, justhowlongyoucanmake it.The firm thatcanhangon the longestcan forceout itsmoreprofitablerivalassoonasduopolyprofitsbegintoturnnegative.

Assuggestedinthehint,ifDavidcanholdonuntilthethirdquarterof1989heishomefree.Fromthenon,theworstpossibilityisthatGoliathstaysinthemarketthroughthefourthquarterof1989.ThiswillcostDavid$2.25induopolylosses.Butwhen1990comes,Goliathmustexit,sincehesufferslosseseitherasa duopolist or as a monopolist. Thus, David can count on making $2.50 inmonopoly profits during the 1990s, which is enough to tide him over anypossiblelossesduringthefinaltwoquartersof1989.

Now,thepowerofbackwardreasoningpicksupsteam.GiventhatDavidiscommittedtostayinguponreachingJuly1989(exitingisadominatedstrategy),GoliathcanexpecttoearnonlylossesfromJuly1989onward.Thus,hewillexitimmediatelyifheeverfindshimselfasaduopolistonthatdate.ThatmeansthatDavid can expect tomake the $2.50 as amonopolist in 1990 and $2.75 as amonopolist inthefinal twoquartersof1989.Thiswindfallof$5.25morethancovers the maximum duopoly losses up until that date ($1.50), and thereforeDavidshouldneverexitbeforeJanuary1991.GiventhatDavidiscommittedtostaying, Goliath should leave as soon as duopoly profits turn negative, July1988.

NotethatGoliathcannotmakethesamecommitmenttostayinthemarketfor the same length of time. That commitment breaks down first in January1990,andthentheguaranteedexitbyJanuary1990translatesintoaforcedexitby July 1989. The slippery slope for Goliath brings him back all the way toOctober1988,thefirstinstancewhenthemarketisn’tbigenoughforthetwoofthem.

This simple story of fighting formarket share in declining industriesmayhelpexplain theobservation that large firmsareoften the first toexit.CharlesBadenFuller,anexpertinthedeclineofBritishmarkets,reportsthatwhenthedemand for U.K. steel casing fell by 42 percent over the period 1975-1981,executivesof the two largest firms,F.H.Lloydand theWeirGroup,“felt thattheyhadborne thebrunt of the costs of rationalization; they accounted for 41percent of the industry output in 1975, but for 63% of the capacity that waswithdrawnoverthe1975-1981period,reducingtheircombinedmarketshareto24percent.”

Remember that size is not always an advantage: in judo and here in exitstrategies, the trick is to use your rival’s bigger size and consequently

inflexibilityagainsthim.

8.NOBLESSEOBLIGEAn important feature ofOPEC is that itsmembers are of unequal size. SaudiArabiaispotentiallyamuchlargerproducerthananyoftheothers.Dolargeandsmallmembersofacartelhavedifferentincentivestocheat?

Wekeepmatters simpleby looking at just one small country, sayKuwait.Supposethatinacooperativecondition,Kuwaitwouldproduce1millionbarrelsperday,andSaudiArabiawouldproduce4.Foreach,cheatingmeansproducing1millionextrabarrelsaday.SoKuwait’schoicesare1and2;SaudiArabia’s,4and5.Dependingonthedecisions,totaloutputonthemarketcanbe5,6,or7.Suppose the corresponding profit margins (price minus production cost perbarrel)wouldbe$16,$12,and$8respectively.Thisleadstothefollowingprofittable.Ineachbox,thebottomleftnumberistheSaudiprofit,andthetoprightnumberistheKuwaitiprofit,eachmeasuredinmillionsofdollarsperday.

Profits(MillionsofDollars/Day)for[SaudiArabia,Kuwait]

Kuwaithasadominantstrategy:cheatbyproducing2.SaudiArabiaalsohas

a dominant strategy, but this is the cooperative output level of 4. The Saudiscooperate even though Kuwait cheats. The prisoners’ dilemma has vanished.Why?

CaseDiscussionSaudi Arabia has an incentive to cooperate for purely selfish reasons. If theyproducealowoutput,themarketpricerisesandtheprofitmarginsgoupforallmembersofOPEC.IftheyhadonlyasmallshareinOPEC’stotaloutput,theywouldnotfinditprofitabletoprovidethis“publicservice”tothewholecartel.But if their share is large, then a large part of the benefit of the higher profitmargincomestothem,anditmaybeworththecostofsufferingsomereductioninvolume.This iswhathappens for the illustrativenumberswechoseabove.3Hereisanotherwayoutoftheprisoners’dilemma:findalargebenefactorwhoactscooperativelyandtoleratesothers’cheating.

The same thing happens in many alliances. In many countries, a largepoliticalparty andoneormore smallpartiesmust formagoverningcoalition.The large party commonly takes the responsible positions and makes thecompromises that hold the alliance together, while the small parties insist ontheir special concerns andget their often extremeway.The influenceof smallreligious parties in Israel’s coalition government is a prime example. Anotherexample arises in the NATO alliance; the United States provides adisproportionate amount of the defense expenditure whose benefits go toWestern Europe and Japan.MancurOlson has aptly labeled this phenomenon“theexploitationofthegreatbythesmall.”

9.FILL’ERUPManygasoline stations advertiseonly thepriceof their leaded gasoline.Whatmakes this peculiar is that very few of their customers actually buy leadedgasoline;onlycarsmanufacturedbefore1976areabletouseleadedgas.

It is clear how this practice began.Originally, therewas only one type ofgasoline.Itwasn’tuntil1911,whenLewisandJacobBlausteininventedawayto boost gasoline octanewithout using lead additives, that unleaded gas evenbecameavailable.Anothersixtyyearspassedbeforeitbecamethestandard.

Now stations continue to advertise the price of a product bought by fewcustomers.Thestationsdisplayonlyonenumbertocatchtheeyeofthepassingmotoristandcontinuetousetheonetheyusedbefore.Mostmotoristsmustinferthe unleaded price they need to know from the leaded price. Why does thispracticepersist?

CaseDiscussionWhatwouldhappenifonegasolinestationdecidedtoadvertiseitsunleadedgasprice in big numbers?Motorists find it too difficult to read anything but thenumbers.As a result, they assume it is the leaded gas price being advertised.Typically,unleadedgasisaboutfivecentsagallonmoreexpensiveatthepumps,anddriversthereforewouldmistakenlyaddaboutanickeltomaketheirguessoftheunleadedprice.Thismaverickgasolinestationputsitselfatadisadvantage,asmotoristsoverestimateitsprice.Interestinglyenough,unleadedgasischeaperwholesale.Thissuggeststhatleadedgasplaystheroleofalossleader.*

A maverick station advertising its unleaded price puts itself at a furtherdisadvantage: it competes on its bread-and-butter product. It ismuch better toengageinpricewarsongoodsthataccountforonlyasmallfractionofsales.Apricewarwithunleadedgasthreatenstheprofitabilityofthewholestation.

The bottom line is that stations go on advertising the leaded price. Thislocked-in equilibrium is different in one respect from that of the QWERTYtypewriterkeyboardinChapter9:therewecouldfindnowinnersfromthestatusquo;herethegasstationsbenefitfromthelackofcompetitionoverthepriceofunleaded gas. But the consumers are stuck in a bad equilibrium, and no gasstationhas any incentive to change it. If societywants to improvematters forconsumers, onewaywouldbe to legislate a change in the convention; requirethat if only oneprice is posted, this pricemust be that of unleaded.A secondsolutionistorequirethatgasolinestationsadvertiseinbignumbersalloftheirbasicgrades,leaded,unleaded,andsuperunleaded.Soonenoughthiswillallbemoot; the sale of leaded gas is being phased out, so stations will have toadvertisethepriceoftheirunleadedgas—itstheonlytypetheywillbeselling.

10.BAYBRIDGEThemorningtrafficfromOaklandtoSanFranciscoacrosstheBayBridgegetsbackedupfrom7:30to11:00A.M.Untilthejamclearsat11:00,eachadditionalcarthatentersthetrafficmakesallthosewhocomelaterwaitjustalittlelonger.The right way tomeasure this cost is to sum up the additional waiting timesacrosseveryonewhoisdelayed.Whatisthetotalwaiting-timecostimposedbyoneadditionalcarthatcrossesthebridgeat9:00A.M.?

You may be thinking you don’t know enough information. A remarkablefeaturetothisproblemisthattheexternalitycanbecalculatedbasedonthelittleamountyou’vebeentold.Youdon’tneedtoknowhowlongittakesthecarsto

crossthetollplaza,northedistributionofcarsthatarriveafter9:00.Theansweristhesamewhetherthelengthofthetrafficjamstaysconstantorvarieswidelyuntilitclears.

CaseDiscussionThetrickistoseethatallthatmattersisthesumofthewaitingtime.Wearenotconcernedwithwhowaits.(Inothercircumstances,wemightwanttoweighthewaiting timesby themonetaryvalueof timefor thosecaught in the jam.)Thesimplestwaytofigureoutthetotalextrawaitingtimeistoshufflearoundwhowaits,puttingalltheburdenononeperson.Imaginethattheextradriver,insteadofcrossingthebridgeat9:00A.M.,pullshiscarovertothesideandletsalltheotherdriverspass.Ifhepassesuphisturninthisway,theotherdriversarenolongerdelayedbytheextracar.Ofcourse,hehastowaittwohoursbeforethetraffic clears and the road is clear.But these twohours exactly equal the totalwaitingtimeimposedonalltheotherdriversifheweretocrossthebridgeratherthanwaitonthesidelines.Thereasonisstraightforward.Thetotalwaitingtimeisthetimeit takesforeveryonetocrossthebridge.Anysolutionthatinvolveseveryonecrossing thebridgegives thesame totalwaiting time,butdistributeddifferently. Looking at the solution in which the extra car does all the extrawaitingistheeasiestwaytoaddupthenewtotalwaitingtime.

11.THETRAGEDYOFTHECOMMONSInanimportantandinfluentialarticle,UniversityofCaliforniabiologistGarrettHarding described how untrammeled choices of individuals could lead todisasterforsociety:

Pictureapastureopentoall.Itistobeexpectedthateachherdsmanwilltrytokeepasmanycattleaspossibleon thiscommons….Therein is the tragedy.Eachmanislockedintoasystemthatcompelshimtoincreasehisherdwithoutlimit, in aworld that is limited.Ruin is the destination towardwhich allmenrush,eachpursuinghisownbestinterestinasocietythatbelievesinthefreedomofthecommons.4

Hediscussedoverpopulation,pollution,excessivefishing,anddepletionofexhaustibleresourcesintheseterms.Heconcludedthatpeopleworldwidemust

recognize the necessity of restricting individual freedom in these choices, andacceptsome“mutualcoercionmutuallyagreedupon.”

Weareaskingyouto identify thenatureof theproblem.Try torelate it toone or more of the examples we gave in this chapter. You can then identifyalternativesolutionsandexaminetheirmerits.

CaseDiscussionDepending upon the circumstances, the tragedy of the commons could be amany-person prisoners’ dilemma (each person grazes too many cows) or aspilloverproblem(toomanypeoplechoosetobecomeherdsmen).

The economist’s favorite solution would be the establishment of propertyrights.ThisiswhatactuallyhappenedinthefifteenthandsixteenthcenturiesinEngland:thecommonlandwasenclosedandclaimedbythelocalaristocratsorlandlords.Whenlandisprivateproperty,theinvisiblehandwillshutthegatetojusttherightextent.Theownerwillchargegrazingfeestomaximizehisrentalincome, and this will cut back the use. This will enhance overall economicefficiency, but alter the distribution of income; the grazing feeswillmake theownerricher,andtheherdsmenpoorer.

Thisapproachisnotfeasibleinsomeinstances.Propertyrightsoverthehighseas are hard to define and enforce in the absence of an internationalgovernment, as is control over air that moves from one country to anothercarryingpollutants.For this reason,whalingandacid rainmustbehandledbymoredirect controls,but securing thenecessary international agreements isnoeasymattereither.

Population is an even harder problem, as Harding noted. The right ofdecision about one’s family, including its size, is enshrined in the UnitedNations’UniversalDeclarationofHumanRightsandinmanycountries’billsofrights.CountrieslikeChinaandIndiathathaveattimesusedsomecoercionintheirpopulation-controleffortshaveevokedwidespreaddisapproval.

Sometimes,when thegroup is small enough, voluntary cooperation solvestheproblem.When twooilorgasproducershavewells that tap into the sameundergrounddeposit,eachhastheincentivetospeeduphisuptake,togetmoreoftheresourcebeforetheotherdoes.Whenbothofthemfollowthispolicy,theexcessive speed of depletion can actually lower the total amount that can berecoveredfromthedeposit.Inpractice,drillersrecognizetheproblemandseemable toreachproduction-sharingarrangements thatkeepat theproper level thetotalflowfromallwellstappingonedeposit.All’swellthatendswell?

12.WHATPRICEADOLLAR?Professor Martin Shubik of Yale University designed the following game ofentrapment.Anauctioneerinvitesbidsforadollar.Biddingproceedsinstepsoffivecents.Thehighestbiddergetsthedollar,butboththehighestandthesecondhighestbidderspaytheirbidstotheauctioneer.5

Professorshavemadetidyprofits—enoughforalunchortwoatthefacultyclub—from unsuspecting undergraduates playing this game in classroomexperiments.Supposethecurrenthighestbidis60centsandyouaresecondwith55.Theleaderstandstomake40cents,butyoustandtoloseyour55.Byraisingto65,youcanputthebootontheotherfoot.Thelogicisnodifferentwhentheleading bid is $3.60 and yours is $3.55. If you do not raise the bidding stillfurther,the“winner”loses$2.60,butyoulose$3.55.

Howwouldyouplaythisgame?

CaseDiscussionThis is an example of the slippery slope.Once you start sliding, it is hard torecover. It is better not to take the first step unless you knowwhere you aregoing.

Thegamehasoneequilibrium,inwhichthefirstbidisadollarandtherearenofurtherbids.Butwhathappensifthebiddingstartsatlessthanadollar.Theescalationhasnonaturallimitotherthantheamountofmoneyinyourwallet.Atleast,thebiddingmuststopwhenyourunoutofmoney.ThatisallweneedtoapplyRule1:Lookforwardandreasonbackward.

Imagine that Eli and John are the two students in Shubik's auction of adollar.Eachhas$2.50inhiswallet,andeachknowstheother'scashsupply.6Tokeepthingssimple,biddingtakesplaceindimeunits.

Tostartattheend,ifElieverbids$2.50,he'llwinthedollar(andbedown$1.50).Ifhebids$2.40,thenJohnmustbid$2.50inordertowin.Sinceitisnotworth spendingadollar towinadollar, anEli bidof$2.40willwin if John'scurrentbidisat$1.50orless.

ThesameargumentworksifElibids$2.30.Johncan'tbid$2.40andexpecttowin,becauseEliwouldcounterwith$2.50.Tobeat$2.30,Johnneedstogoall theway up to $2.50.Hence a $2.30 bid beats $1.50 and below.So does a$2.20bid,a$2.10bid,allthewaydowntoa$1.60bid.IfElibids$1.60,JohnshouldpredictthatEliwon'tgiveupuntilthebiddingreaches$2.50.Eli'sdollarsixty is already lost; but it isworthhiswhile to spendanotherninety cents to

capturethedollar.The first person to bid $1.60 wins, because that establishes a credible

commitment to go up to $2.50. In ourmind,we should think of $1.60 as thesamesortofwinningbidas$2.50.Inordertobeat$1.50,itsufficestobid$1.60,and nothing lesswill do. Thatmeans $1.50will beat all bids at 60 cents andbelow.Even a bid of 70 centswill beat all bids at 60 cents andbelow.Why?Oncesomeonebids70cents,itisworthwhileforthemtogoupto$1.60andbeguaranteedvictory.Withthiscommitment,noonewithabidof60centsorlessfindsitworthwhiletochallenge.

WeexpectthateitherJohnorEliwillbid70centsandthebiddingwillend.Although the numbers will change, the conclusion does not depend on therebeing just twobidders.Given thatbudgetsdiffer,backward reasoningcan stillfind the answer. But it is critical that everyone know everyone else's budget.Whenbudgetsareunknown,asonewouldexpect,anequilibriumwillexistonlyinmixedstrategies.

Of course there is a much simpler and more profitable solution for thestudents:collusion.Ifthebiddersagreeamongthemselves,adesignatedpersonwillbidadime,nooneelsewillbidatall,andtheclasswillsharetheprofitofninetycents.

YoumaytakethisstoryasproofofthefollyofYaleundergraduates.Butistheescalationofthesuperpowers'nucleararmsarsenalsallthatdifferent?Bothincurred costs in the trillions of dollars in quest of the "dollar" of victory.Collusion, which means peaceful coexistence, is a much more profitablesolution.

13.THEKINGLEARPROBLEM

Tellme,mydaughters,—Sincenowwewilldivestusbothofrule,Interestofterritory,caresofstate,—Whichofyoushallwesaydothloveusmost?ThatweourlargestbountymayextendWherenaturedothwithmeritchallenge.

—Shakespeare,KingLear

KingLearwasworried about howhis childrenwould treat him in his oldage.Muchtohisregret,hediscoveredthatchildrendonotalwaysdeliverwhattheypromise.

Inadditiontoloveandrespect,childrenarealsomotivatedbythepossibilityof an inheritance. Here we look at how a strategic use of inheritance canmanipulatechildrentovisittheirparents.

Imagine that parentswant their children eachweek to eachvisit once andphone twice. To give their children the right incentives, they threaten todisinherit any child who fails to meet this quota. The estate will be evenlydividedamongall thechildrenwhomeet thisquota. (Inaddition tomotivatingvisits, this scheme has the advantage of avoiding the incentive for children tosuffocatetheirparentswithattention.)Thechildrenrecognizethattheirparentsareunwillingtodisinheritallofthem.Asaresult,theygettogetherandagreetocutbackthenumberofvisits,potentiallydowntozero.

Theparentscallyouinandaskforsomehelpinrevisingtheirwill.Wherethereisawill,thereisawaytomakeitwork.Buthow?Youarenotallowedtodisinheritallofthechildren.

CaseDiscussionAsbefore,anychildwhofailstomeetthequotaisdisinherited.Theproblemiswhattodoifallofthemarebelowthequota.Inthatcase,givealloftheestatetothe child who visits the most. This will make the childrens' reduced visitingcartel impossible to maintain. We have put the children into a multipersondilemma.Thesmallestamountofcheatingbringsamassivereward.Achildwhomakes justonemorephonecall increaseshisorher inheritance fromanequalshare to100percent.Theonly escape is togo alongwith theparents'wishes.(Obviously,thisstrategyfailswithonlychildren.Thereisnogoodsolutionforcoupleswithanonlychild.Sorry.)14.UNITEDSTATESV.ALCOAAn established firm in an industry stands to gain by keeping out newcompetition. Then it can raise prices to monopoly levels. Since monopoly issociallyharmful, the antitrust authorities try todetect andprosecute firms thatemploystrategiestodeterrivalsfromenteringthebusiness.

In 1945, theAluminumCorporationofAmerica (Alcoa)was convictedofsuchapractice.AnappellatepanelofCircuitCourtjudgesfoundthatAlcoahadconsistentlyinstalledmorerefiningcapacitythanwasjustifiedbydemand.Inhisopinion,JudgeLearnedHandsaid:

Itwasnotinevitablethatit[Alcoa]shouldalwaysanticipateincreasesinthe

demandforingotandbepreparedtosupplythem.Nothingcompelledittokeepdoublingandredoublingitscapacitybeforeothersenteredthefield.Itinsiststhatitneverexcludedcompetitors;butwecanthinkofnomoreeffectiveexclusionthan progressively to embrace each new opportunity as it opened and to faceeverynewcomerwithnewcapacityalreadygearedintoagreatorganization.

This case has been debated at length by scholars of antitrust law andeconomics.7Hereweaskyoutoconsidertheconceptualbasisofthecase.Howcould the construction of excess capacity deter new competitors? Whatdistinguishesthisstrategyfromothers?Whymightitfail?

CaseDiscussionAn established firm wants to convince potential new competitors that thebusiness would not be profitable for them. This basically means that if theyentered, the price would be too low to cover their costs. Of course theestablishedfirmcouldsimplyputoutthewordthatitwouldfightanunrelentingpricewaragainstanynewcomers.Butwhywouldthenewcomersbelievesuchaverbalthreat?Afterall,apricewariscostlytotheestablishedfirmtoo.

Installing capacity in excess of the needs of current production givescredibilitytotheestablishedfirm'sthreat.Whensuchcapacityisinplace,outputcanbeexpandedmorequicklyandatlessextracost.Itremainsonlytostafftheequipmentandgetthematerials;thecapitalcostshavealreadybeenincurredandarebygones.Apricewarcanbefoughtmoreeasily,morecheaply,andthereforemorecredibly.

Thismakes sense in the logic of strategy, butwill such a devicework inpractice?Thereareatleasttwoqualificationsthatlimititssuccess.First,iftherearemanyfirmsalreadyintheindustry,thendiscouragingnewcomersgivesmoreprofit toallof them.Willanyonefirmbear thecostsofcapacitywhen itgetsonlyapartofthebenefit?Thisisastandardprisoners'dilemma.Ifonefirmislargeenough,itmayinitsowninterestprovidesuchaservicetotherestoftheindustry.Otherwisethefirmsmustcolludeinbuildingcapacity;thismaybehardtohidefromtheantitrustauthorities.

In the Alcoa case, one may not regard the dilemma of who will installcapacity as a serious problem, because Alcoa had a 90 percent share of theprimary aluminum ingotmarket.But—and this is the second qualification—isthattherelevantmarket?Eveniftherearenootherproducersofprimaryingots,

secondaryproductionfromscrapisasourceofcompetition.SoisAlcoa'sownfutureproduction.Manyaluminum-basedproductsarehighlydurable.IfAlcoaputsmorealuminumonthemarketinthefuture,thenthevaluesofthesedurablegoodswilldecrease. If thecompanycannotcrediblyguarantee theusers that itwillrestrictitsownfutureoutput,thentheywillfearsuchlosses,andthereforereduce the price they are willing to pay for aluminum now. This is just likeIBM'sproblemofpricingmainframecomputers.Thesolutionofrentingismuchharderhere: you can't rent aluminumas such;Alcoawouldhave to extend itsoperationsintoallsortsofaluminum-basedproducts.

15.TWOWRONGSKEEPTHINGSRIGHTParentsoftenfaceadifficultproblempunishingtheirchildrenforbadbehavior.Children have an uncanny sense that the parents' threat to punishmay not becredible.They recognize that thepunishmentmayhurt theparentsasmuchasthechildren(althoughforverydifferentreasons).Thestandardparentaldodgetothis inconsistency is that thepunishment is for thechild'sowngood.Howcanparentsdoabetterjobatmakingtheirthreattopunishbadbehaviorcredible?

CaseDiscussionWith twoparents andone child,wehave a three-persongame.Teamworkcanhelp theparentsmakeanhonest threat topunishamisbehavingchild.Say thesonmisbehaves,andthefatherisscheduledtocarryout thepunishment.If thesonattempts torescuehimselfbypointingout the"irrationality"ofhisfather'sactions, the father can respond that he would, given the choice, prefer not topunishhisson.But,werehetofailincarryingoutthepunishment,thatwouldbebreakinganagreementwithhiswife.Breakingthatagreementwouldbeworsethanthecostofpunishingthechild.Thusthethreattopunishismadecredible.

Even singleparents canplay thisgame,but the argumentgetsmuchmoreconvoluted, as the punishment agreementmust bemadewith the child. Onceagain, say the son misbehaves, and his father is scheduled to carry out thepunishment. If the son attempts to rescue himself by pointing out the"irrationality"ofhisfather'sactions,thefathercanrespondthathewould,giventhechoice,prefernottopunishhisson.But,werehetofailincarryingoutthepunishment, then thiswouldbeamisdeedonhispart,amisdeedforwhichheshould be punished. Thus, he is punishing his son only to prevent gettingpunishedhimself.Butwhoistheretopunishhim?It'stheson!Thesonreplies

that were his father to forgive him, he too would forgive his father and notpunishhisfatherforfailingtopunishhim.Thefatherrespondsthatwerehissonto fail to punish him for being lenient, this would be the second punishableoffensedonebythesoninthesameday!Andsoonandsoforthdotheykeepeachotherhonest.Thismayseemalittlefarfetched,butnolessconvolutedthanmostargumentsusedtojustifypunishingkidswhomisbehave.

16.WINNINGTHEHOMESTRETCHChapter1toldthestoryofhowtokeeptheleadintheAmerica'sCuprace.Sinceeachboat couldobserve theother, itwas relatively straightforward forDennisConner to follow John Bertrand's course. How to stay ahead gets morecomplicated when the moves are simultaneous: prediction rather thanobservationisneeded.

In duplicate bridge, a team is evaluated by how well it does playing aparticular hand when compared to a second team that plays the same handagainstadifferent setofopponents. Imagine thatyouareplaying forTeamA,andgoingintothefinalhandyouareleadingTeamB,GorenandZeck.

Yourhandisalmostbutnotquiteperfect.Youareguaranteedtomake6notrump.Youfigurethatyouhavea50percentchanceofmaking7notrump,butthensodoGorenandZeck, since theyareplaying the samehand in theotherroom.* Ifyoubid7andmake it, thatguarantees thatyouwin the tournament.Evenifyoubid7andfail,ifGorenandZeckhavemadethesamebidandalsofailed you stillwin. If both sides bid 6, you are guaranteed towin, since youwentintothefinalroundwiththelead.Ifyoubid6andtheybid7andmakeit,theywillovertakeyouandwin.

What should you do tomaximize your chance of winning?What do youthinkGorenandZeckwilldo?Howlikelyareyoutowin?

CaseDiscussionYouarelookingtomaximizeyourchanceofwinning.Thefollowingtablegivesyourprobabilitybasedonwhodoeswhat.

YourTeam'sChanceofWinning

Wheredidthesenumberscomefrom?Whenbothteamsbid7notrump,you

will win unless you fail and theymake it, which is a one-in-four possibility;hence you have a three-fourths chance ofwinning.When you alone bid 7 notrump,youwinifyoumakeitandloseifyoudon't;it'safifty-fiftyproposition.Whenyoubid6andtheybid7,youwinonlyiftheyfail;againit'safifty-fiftyproposition.Whenneitheroftheteamsbids7,youareguaranteedavictory.

Nowthatthetableisfilledout,calculatingtheequilibriumstrategyiseasy.UsingtheWilliamsmethodwefindthat7notrumpshouldbebidtwo-thirdsofthetimeand6notrumptheotherthird.*IfwetakeratiosbycolumnratherthanrowandrecognizethatyourchanceofwinningisthesameasGorenandZeck'schanceoflosing,thenwefindthattheyshouldplay7notrumpwithprobability2/3and6notrumpwithprobability1/3.

Whatareyourchancesofwinning the tournament?Youcanexpect towintwooutofthreetimesthatyouareinthissituation.Forexample,ifyoubid7notrump,thenwithprobability2/3GorenandZeckwillalsobeplaying7notrump,soyourchanceofwinningis0.75,andwith1/3probabilityGorenandZeckwillbid6notrump,sothatyouwinwithchance0.5:theweightedaverageis(2/3)(3/4)+ (1/3) (1/2)= 2/3.You can verify that bidding 6 no trump leads to thesamechanceofwinning.

In contrast, suppose you ignored the idea ofmixing and always bid 7 notrumpinthissituation.IfGorenandZeckfiguredthisoutthentheywouldneverbid 7 no trump and your chance of winning would be reduced to 0.5. Theadvantageoffollowingyourequilibriummixtureisthatyoucan'tbeoutfoxedbyyourrivals.

17.BRINKMANSHIPANDTHEJURYOnMarch25,1988,JudgeHowardE.Bell,presidingovertheRobertChambers

"Preppy Murder" trial, was facing a tough problem. According to New YorkTimesreports,"The12-memberjurywasfallingapart.Desperatenotescameoutfromindividualjurorsaskingtoberemovedfromthecase.Onemanburstintotearsinfrontofthejudgeandsaidhisemotionalhealthhadbeendestroyedbythe strain.At noon, two notes came out at the same time—one from the juryforewoman saying that the panel was 'at an impasse'; the other from anindividual juror saying there was no impasse and that a verdict was stillpossible."

Ahungjurywouldbeadefeatforallparties.JenniferLevin'sfamilywouldhavetosufferthroughasecondtrial,andRobertChamberswouldhavetobearseveralmoremonthsofuncertaintybeforebeingable toeithergetonwithhislifeorstartservinghissentence.Althoughtheremightbelittleelsetheycouldagreeon,bothsideswantedaverdict.

Afterninedaysofdeliberating,therewasincreasingevidencethatifthejurydid in fact come up with a decision, there would be no way to predict thedecision beforehand. "Jurors said later that the votes were swinging wildlybetweenconvictingandacquittingMr.Chambersofthemostseriouschargeofsecond-degreemurder."

HowcanJudgeBellusebrinkmanshiptohelpbothparties?

CaseDiscussionThe prosecutor, Ms. Fairstein, and the Levin family would prefer to see aguaranteethatChambersgetsomesentenceandbefoundguilty,thanleavetheoutcomein thehandsofanincreasinglyrandomjury,orworse,riskgettingnoresultandhavingtogothrougharetrial.

Thedefenseside,Chambers'sattorneyMr.LitmanandtheChambersfamily,alsohadreasontofear:anincreasinglydifficult-to-predictjurydecisionorretrialcouldbothbeworsethanreachingasettlementpleabargain.

JudgeBellusestheriskofthejuryactuallyreachingadecisionorbecominghopelesslydeadlockedasthethreattogetbothsidestonegotiate.Thejudgehasnocontroloverhowlongthejurytakestomakeupitsmind.Asthedefenseandprosecutionarenegotiatingasettlement, there is theconstant risk that the jurywillreachadecisionorapermanentimpasse.

There is no clear line saying that after ten days, six hours therewill be amistrialoradecision.Insteaditisaslipperyslope.JudgeBellhasanincentivetokeepthejurytogetherandusethistopressurethetwopartiestoreachterms.Evenifthejudgeknowsthatthejuryisatapermanentimpasse,hemightwant

tokeepthisfromthetwolawyers.Hecantell thejurytoplayMonopolyforadayortwo.

If the outcomewere known, then the riskwould be resolved and the twopartieswouldlosetheirincentivetocompromise.Itisonlybecausethetwosidesfeeldifferentlyabout therisk that theyarebrought together toseekacommonmiddleground.

When a case is brought before a jury,we create a risk that is beyond ourcontrol.Initially,wemaythinkweknowhowthejurywilldecide,andtheriskismanageable.Butasthedeliberationsproceed,theuncertaintyaboutthedecisionbecomes overwhelming. The two opposing sides begin to have more similarbeliefsaboutwhatthejurywilldecide,andthentheycaneliminatetheriskbyprovidingtheirownverdict.

WhetherJudgeBellknowinglyengaged inbrinkmanshipornot,hehelpedperpetuateaslipperyslopethatmadeeveryonelookforthesafehighgroundinapleabargain.

18.THEFREEDOMTOMEDDLELiberalorlibertariansocialphilosophieshaveabasictenetthateveryonehastherighttomakecertaindecisionswithoutoutsideinterference.Cansocialdecisionsbemadeinconformitywiththisprinciple?

Consideranissuethatmostpeoplewouldplaceinthisdomainofindividualsovereignty—the color of one’s bedroomwalls.Take twopeople,RosencrantzandGuildenstern,and twocolors, redandgreen.Thereare fourpossiblecolorcombinations.WriteRGforthecaseinwhichRosencrantz’sbedroomwallsareredandGuildenstern’saregreen,GRtheotherwayround,RRwhenbothwallsarered,andGGwhenbotharegreen.

Onewaytointerpretthelibertarianprincipleis,“Foranychoiceinwhichthealternatives differ only in the color of one person’s walls, that person’spreference should be accepted by society.”8 Suppose Rosencrantz is anonconformist; hewants hiswalls to be a different color fromGuildenstern’s.However,Guildensternisaconformist;hewantshiswallstobethesamecolorasRosencrantz’s.Withthesepreferences,thereisnodecisionthatabidesbythislibertarianprinciple—justtrythedifferentpossibilities.9

Youmightthinktheproblemisthateachperson’spreferencewas,properlyspeaking,notforthecolorofhisownwallsassuch,butforacolorthesameas,or the opposite of, the other person’s. Allowing such preferences to rule thesociety’s choice is tantamount to too much meddling in each other’s affairs.

Thereforeletuscreateasecondscenario,andrestrictthesenseoflibertarianism:“Ifapersonhasanunconditionalpreferenceforthecolorofhisownwalls,andtwoalternativesdifferonlyinthiscolor,thenthatperson’spreferenceshouldbeacceptedbysociety.”

SupposeRosencrantzhasanunconditionalpreferenceforhisbedroomwallsbeingred—heprefersRXtoGXwhetherX, thecolorofGuildenstern’swalls,equals R or G. While Rosencrantz prefers his own walls red, he also has ameddlesome interest and is evenmore strongly concerned that Guildenstern’swallsbered.Thushis rankingof thefourpossibilities isRRbest,GRsecond,RGthird,andGGlast.Guildensternhasasimilarpreferenceforgreen:GGbest,GRsecond,RGthird,RRlast.

RankingofOutcomesinSecondScenarioby[Rosencrantz,Guildenstern]

Showthatthelibertarianprinciplecanleadtoanoutcomethatisworsefrom

bothoftheirviewpointsthansomeotheroutcome.Whatcanmakelibertarianismworkable?

CaseDiscussionThe libertarian principle leads the players into a prisoners’ dilemma.Rosencrantz’s unconditional preference for having red bedroom walls is theanalogue of a dominant strategy. Whichever color Guildenstern picks,Rosencrantzdoesbetterchoosingred.Underlibertarianism,societyallowshimthischoice.Similarly,Guildensternhashisbedroomwallsgreenasadominantstrategy.Onceagain,aliberalistsocietygiveshimthischoice.

PuttingtheirindividualchoicestogetherleadstotheoutcomeRG.Butboth

RosencrantzandGuildensternpreferGR toRG.As in theprisoners’dilemma,wehaveanotherexamplewherebothplayers’followingtheirdominantstrategyleadsthemtoamutuallyinferioroutcome.

One solution might be to restrict the sense of libertarianism still further.Thus the social decision might accept Rosencrantz’s preference for red overgreenwallsonlyifitisevenlessmeddlesome,inthesensethatheprefersbothRGandRRoverbothGRandGG.Thisworks,butonlyinthesensethatsincepreferences are not actually of this kind, libertarianism doesn’t apply in thissituation.Philosophershavedebatedthisproblemendlessly,anddevisedfurtherrestrictions on libertarian rights.10 But most of these proposals imposelibertarianismasanoutside requirementon the socialdecisionsofpeoplewhocontinuetohavemeddlesomepreferencesaboutwhatothersdo.Atrulylastingandworkablesolutionrequiresgeneralagreementoverwhichmattersbelongtothe domain of privacy, and agreement to abandon our preferences (becomeindifferent) about one another’s choices in such matters. In other words,libertarianismshouldbeingrainedinourprivatepreferencesifitistosucceedasasocialnorm.

19.AMEDALLIONFORTHEMAYORIn1987,NewYorkCitymayorEdKochsucceededinincreasingthenumberoflicensedtaxicabsinManhattan.Overthepreviousfiftyyears,thepopulationofManhattanincreasedby3millionpeople,whilethenumberoftaxicabsgrewby100.Onesignoftheshortageisthattherighttolegallyoperateataxi(calledamedallion)soldintheopenmarketforjustover$125,000in1987.Atthesametime,taxiswererentedoutfortwotwelve-hourshiftsdailyatabout$60pershift(or$45,000peryear).

If the city just auctioned off the 100 newmedallions, they could bring in$12.5million.Theproblemisthatallthenewownersshouldbeworriedthatthecityhasdiscoveredsomethingtoogoodtobetrue.Whywon’ttheytrytoauctionoff100morenewmedallionsnextyear?Ifthecitycan’tpromisetorefrainfromincreasing the number of medallions until the point where they becomeworthless,nobodywillpayverymuchfortheminthefirstplace.

MayorKochhascalledyouinasaconsultant.Hewantsadviceonhowtoraiserevenuewhenheincreasesthenumberoftaxis.Heislookingforawaytocommithimself(andfutureadministrations)nottokeepdilutingthevalueoftheold medallions by continually printing new ones. The Taxi and LimousineCommission is inshambles,andnobody trustsapolitician’swordalone.What

doyousuggest?

CaseDiscussionThetrickissimplytorentratherthansellthenewmedallions.Thatway,nobodyispayingforanyfuturevaluewhichmightlaterbeappropriated.Themayorhasanincentivetorestrict thenumberofrentalmedallions,becauseifherentstoomany, the total rentwill fall, potentially all theway to zero if themedallionsbecomeworthless.

Note that this is really justanapplicationofmakingcommitments stepbystep.Here the steps are not the number ofmedallions but rather the length oftimeforwhichthemedallionsaregood.Peoplearewillingtotrustthemayorforaweekorayear. It takes time topassnewlegislation.And themost that isatrisk is oneyear’s valueof amedallion.Rather than sell this year’smedallion,next year’s medallion, and all future medallions rolled up into one eternalmedallion,themayorcanrestorecredibilitybysellingthesecommoditiesoneatatime.Thesimplewaytodothisisjusttorentratherthansell.

20.ARMSACROSSTHEOCEANIn the United Statesmany homeowners own guns for self-defense. In Britainalmost no one owns a gun. Cultural differences provide one explanation. Thepossibilityofstrategicmovesprovidesanother.

In both countries, amajority of homeowners prefer to live in an unarmedsociety. But they are willing to buy a gun if they have reason to fear thatcriminalswillbearmed.Manycriminalsprefertocarryagunasoneofthetoolsoftheirtrade.

Thetablebelowsuggestsapossiblerankingofoutcomes.Ratherthanassignspecificmonetarypayoffs to eachpossibility, theoutcomesare ranked1,2,3,and4foreachside.

RankingofOutcomes[Homeowners,Criminals]

If there were no strategic moves, we would analyze this as a game with

simultaneousmoves, anduse the techniques fromChapter3.We first look fordominantstrategies.Sincethecriminals’gradeincolumn2isalwayshigherthanthat in a corresponding row in column 1, criminals have a dominant strategy:theyprefertocarrygunswhetherornothomeownersarearmed.

Homeowners do not have a dominant strategy; they prefer to respond inkind.Ifcriminalsareunarmed,agunisnotneededforself-defense.

What is the predicted outcome when we model the game as one withsimultaneousmoves?FollowingRule2,wepredictthatthesidewithadominantstrategyusesit;theothersidechoosesitsbestresponsetothedominantstrategyof itsopponent.Sinceguns is thedominant strategy forcriminals, this is theirpredictedcourseofaction.Homeownerschoosetheirbestresponsetoguns;theytoo will own a gun. The resulting equilibrium is ranked [3,3], the third bestoutcomeforbothparties.

Inspiteof theirconflicting interests, the twosidescanagreeonone thing.Theybothprefertheoutcomeinwhichneithersidecarriesguns[1,2]tothecaseinwhich both sides are armed [3,3].What strategicmovemakes this possibleandhowcoulditbecredible?

CaseDiscussionImagine for amoment that criminals are able to preempt the simultaneity andmakeastrategicmove.Theywouldcommitnottocarryguns.Inthissequentialgame,homeownersdonothave topredictwhatcriminalswilldo.Theywouldsee that the criminals’ move has been made, and they are not carrying guns.Homeownersthenchoosetheirbestresponsetothecriminals’commitment;theytoogounarmed.Thisoutcomeisranked[1,2],animprovementforbothsides.

It isnotsurprising thatcriminalsdobetterbymakingacommitment.*But

homeownersarebetteroff,too.Thereasonforthemutualgainisthatbothsidesplace a greater weight on the others’ move than their own. Homeowners can

reversethecriminals’movebyallowingthemtomakeanunconditionalmove.†

In reality, homeownersdonot constituteoneunitedplayer, andneither docriminals.Eventhoughcriminalsasaclassmaygainbytakingtheinitiativeandgivingupguns,anyonememberofthegroupcangetanadditionaladvantagebycheating.Thisprisoners’dilemmawoulddestroythecredibilityofthecriminals’initiative. They need some way to bond themselves together in a jointcommitment.

If the country has a history of very strict gun-control laws, guns will beunavailable. Homeowners can be confident that criminals will be unarmed.Britain’s strict control of guns allows criminals to commit to work unarmed.Thiscommitment iscredible,as theyhavenoalternative. In theUnitedStates,the greater prevalence of guns denies criminals an ability to commit to workunarmed.Asaresult,manyhomeownersarearmedforself-defense.Bothsidesareworseoff.

Clearly this argument oversimplifies reality; one of its implications is thatcriminals should support gun-control legislation. Even in Britain, thiscommitmentisdifficulttomaintain.ThecontinuingpoliticalstrifeoverNorthernIreland has had the indirect effect of increasing the availability of guns to thecriminalpopulation.Asaconsequence,thecriminals’commitmentnottocarrygunshasbeguntobreakdown.

Inlookingback,notethatsomethingunusualhappenedinthetransitionfroma simultaneous-move to a sequential-move game. Criminals chose to foregowhat was their dominant strategy. In the simultaneous-move game it wasdominant for themtocarryguns. In thesequential-movegame, theychosenotto.Thereasonis that inasequential-movegame, theircourseofactionaffectsthehomeowners’choice.Becauseofthisinteraction,theycannolongertakethehomeowners’responseasbeyondtheirinfluence.Theymovefirst,sotheiractionaffectsthehomeowners’choice.Carryingagunisnolongeradominantstrategyinthesequentialrepresentationofthegame.

21.THELIMITSTOCHARITYMany public goods, such as educational television, are financed primarilythroughprivatecontributions.Sinceeveryonebenefitsfromtheprovision,thereisanimplicitbargainingproblemoverwhowillmakethecontributionsandwhowill get a free ride. A look at the similarities between fund-raising and

bargainingcanhelpdesignamoreeffectivefund-raisingcampaign.In a bargaining problem, labor and management face pressure to

compromise because of the potential for lost profits if a strike occurs. Theincentiveforcompromiseissimilartothetheincentivetocontribute.PublicTVfund-raising campaigns try to make their viewers recognize a cost ifcontributions are not forthcoming.They threaten that showsmay be canceled.Moreimmediately,thestationmayinterruptscheduledbroadcastsuntilacertainfund-raisinggoal ismet.Thedesiredprogramsareheldhostage; theransomisthenexttargetlevel.

Just as the workers want the best deal possible, public television stationswanttoraiseasmuchmoneyaspossible.Butiftheytrytopushbeyondwhatisfeasible, they risk alienating their viewers. The programs can be kept hostageonlysolongbeforetheyaregivenup.

Themaximumlevelofpotentialcontributionswillofcoursedependonthenumberofviewers andhowmuch theyvalue theprogramming. If thereareNpotentialcontributorsandeachhasabenefitB, thebestonemighthopeis thatthe fund-raisingwillbe successfulwhenever the target levelT is less than thecombinedbenefits,NB.Isthattrue?Toanswerthisquestion,welookatasimplecaseinwhichthereareonlytwopotentialcontributors.Thefund-raisinggoalis$10,000andeachvaluesasuccessfulcampaignat$7,500.Thenitshouldwork,shouldn’t it?Theproblem is thatneither sidewants togive$7,500and let theothercontributeonly$2,500andgetallthesurplus.Herewehaveabargainingproblem.Thetotalcombinedvalueis$15,000andthecostisonly$10,000.Howdothetwopartiesdividethe$5,000surplus?

Againwe use the idea of alternating offers to keepmatters simple. In thepresentcontext,thetwocontributorsareaskedinsequencetomakeadonationpledge. The solicitation continues until the goal is met. We expect bothindividualswillmakemorethanonepledge.Theyshouldemploythestrategyofmovinginsmallsteps.Thisensuresthatneithergets toofaraheadof theotherand thuscontributesanunfairshare.But there isacostofmovingslowly,andthismustbebalancedagainstthepotentialforexploitation.

Thecostofmovingslowlyisthatthecontributorsareimpatientandwouldprefer to see thegoal reached sooner rather than later.Abenefit ofB today isworthδBifwemustwaituntiltomorrowbeforethebenefitisreceived,whereδ< 1. This is just like lost interest onmoney; the difference in value betweentodayandtomorrowisB(1–δ),andifyouthinkoftheselostbenefitsasinterestforgone, then think of 1–δ as the interest rate. Finally, remember that thecontributionsaremadeintheformofapledge;theyneedbepaidonlyafterthefund-raisinggoal ismet.Nowall thefactsareon the table.Howmuchmoney

canthecampaignraise?

CaseDiscussionThisproblemwasrecentlysolvedbyeconomistsAnatAdmatiandMottyPerry.Aremarkablefeatureoftheiransweristhatthetotalcontributionsdonotdependontheinterest-ratevariableδ.Evenmoresurprisingisthatitispossibletoraiseanamountequaltothetotalvaluationofallthecontributors.Henceiftheprojectisworthwhile,itshouldbepossibletoraisethemoney.

Asalways,westartattheendandworkbackward.Whilethereisnonaturaltime period for an ending, there is a contribution level that ends the implicitbargaining:ifthefund-drivetargetis$T,thentheproblemisoverwhen$Thasbeen contributed. When the pledged amount is close enough to $T, then thepersonwhose turn it is should cap it off rather thanwait another round.Howcloseiscloseenough?Thebestthatonecanhopeforbywaitingisthattheotherpersonwillmakeupthedifference.Henceunlessyoubringthecontributionto$T,youcandonobetterthanδV, thefullvalueoftheprojectoneperiodlater.Ontheotherhand,ifyoucontributeanamountx today,thenyougetthevalueV–x, the value today net your contribution. It isworthwhile bringing the totalcontributionsupto$Tprovidedtheamountneededisthecontributionmustbelessthantheinterestlost.

Nowbothpartiescanlookaheadandreasonthatoncethecontributionsareupto$T–(1–δ)V,thegoalwillbereachedoneperiodlater.Ifthetotalpledgeiscloseenoughtothisamount,thenitisworthwhiletobringituptothattotalandspeed up the completion of the campaign. Note that there is no incentive tocontributeanamountthatbringsthetotalabovethatlevel,forthatjustreducesthenextparty’scontributionwithoutanysavingstoyourself.Norareyouwillingtobringthepledgetotalallthewayto$T,sincethatinvolvesmoremoneythanthecostofdelayingcompletionbyoneperiod.Thusifyoumakeacontributionofy thatbrings the total to$T–(1–δ)V,yourpayoff isδ(V–y):oneperiod lateryougetthepayoffVandpayyourpledgey.Alternatively,youcanwaitaperiodandswitchpositions.Thentheotherpersonmakesacontributionthatbringsyouup to$T–(1–δ)V, inwhichcase itbecomesworthyourwhile tocontributex=(1–δ)V.Yourpayoffisthisisthevalueofcompletingthecampaignintwoperiodsnetthecontributionyou make. Comparing the value of contributing to waiting, we see that it is

worthwhilecontributingratherthansufferinganextraperiodofdelayprovided

Note that our calculations did not take into account the amount that each

person has already contributed. The reason is that the contributors are alwayslooking forward to how much more they should contribute; their previouspledgesarenotarelevantpartofthiscalculationsincetheywillbepaidonewayortheotherandthusnetoutofanycost-benefitcalculation.

Sofarwehavefiguredouthowmuchmoneywillberaisedinthelasttwoperiods.Applyingthesamereasoningallowsustogobackfurtherandcalculatehow long the campaignwill take to reach its goal and howmuch people arewilling to contribute at each stage so as not to delay the process. The totalpotential for contributions is the sum of these amounts. They are

Notethatthefirsttwotermswerethecontributionsfromthelasttwoperiodsascalculatedabove.Whatisremarkableisthatthetotalpotentialforcontributionsdoesnotdependontheinterestrateδ.Thismaximumamountequalsthesumofthe two contributors’ valuations. It is possible to get individuals to contributetheirfullvalueoftheproject.Thissuggeststhattheoutcomeofthefund-raisingdriveisagoodreflectionofhowmuchthecontributorsvaluetheproject.

22.THELIMITSTOREDISTRIBUTIONThe political systems of many countries have economic equality as a centraltenet of their policy. Almost all governments use some form of redistributivetaxation.Forexample,theUnitedStateshadtopratesofincometaxexceeding70percentinthe1960sand1970s,whileinSwedenthemarginaltaxratecouldexceed100percent.Butinthelastdecadetheideahastakenholdthathightaxratesdestroyincentivestowork.Thusinthe1980s, thetoprateswerereduceddramatically, both by the United States and even by the more egalitariangovernmentofSweden.

Theprimemotivation to lower taxeswas thedeleteriouseffectof taxesonwork incentives.While there is nowa greater incentive to accumulatewealth,there is alsogreater inequalityof income.Of course there aremany causesofinequality,andataxonincomeisablunttoolforattackingthesymptom,notthecause.Thinkaboutthedifferentcausesofinequalityandhowtheyinfluencethedesignofanidealtaxsystem.Whataretheproblemsofimplementingthisideal

system?Howdoesitcomparewiththepresentsystem?

CaseDiscussionWebeginbylookingatsomeofthecausesofeconomicinequality.First,thereisluck.Thiscanbeoftwokinds.Somepeoplearebornwithsomeinnatetalentoradvantage over others. Even among those who start equal in these respects,fortunefavorstheendeavorsofsomemorethanothers.Manypeoplethinkthereis something unfair about inequality that arises from luck, and taxation thatequalizessuchadvantagesfindsfairlybroadsupport.

Then there is effort; some people just work harder or longer than others.Whenpeopleexpressagreementwiththeclaimthattaxationdestroysincentives,theyusuallymean the incentive to supply effort.Whowouldworkhard if thegovernment stands ready to takeawaya largepartof the result?Manypeoplealsothinkitmorallyrightthatoneshouldbeabletokeepthefruitsofone’sowneffort, althoughdie-hard egalitarians argue that one shouldbewilling to sharethegainswithothers.

Let us suppose that the governmentwants to collect at least a part of theeconomicfruitofeachcitizen’seffort,withoutdestroyingincentives.If thetaxcollectors can observe each individual’s effort, there is no problem. The taxscheduleforeachpersoncanbeexpresseddirectlyintermsofhiseffort,andareallypunitivetaxleviedforanyamountofeffortsmallerthantheideal.

Infactitisverydifficulttomonitortheeffortofmillionsofworkers.Theymayhavetoclockinandclockouteveryday,buttheycantakethingseasyandlower the quality of their work. Even the Soviet-type economies, which haveveryseverepenaltiesat theirdisposal,havefoundit impossible to improvethequality ofworkwithout offeringmaterial incentives. This has led them into aviciouscircleinwhichtheworkerssayofthegovernment:“Wepretendtowork,andtheypretendtopayus.”

Inpractice,effortmustbejudgedbyanindirectindicator,usuallytheincomethatresultsfromtheeffort.Butthisindicatorisnotperfect;ahighincomemaybetheresultofalargeamountorahighqualityofeffort,oritmaybeduetoastrokeofluck.Thenthetaxsystemcannolongerbefinelytunedtoelicitingtherighteffortfromeachperson.Insteadofaharshpunishmentforshirking,thetaxschedulewould have to impose a harsh punishment for realizing low income,andthatwillpunishtheunluckyalongwiththeshirkers.Thereisafundamentalconflictbetweentheegalitarianandtheincentiveeffectsofthetaxsystem,andtheschedulemuststrikeabalancebetweenthem.

Next consider differences in natural talent. The egalitarian might think itperfectlylegitimatetotaxawaytheeconomicgainsthatariseforthisreason.Butabilitytodosodependsonlocatingthetalented,andinducingthemtoexercisethat talentdespite theknowledge that theresulting incomewillbe taxedaway.Theproblemismadealltheworsebecausemucheffortisrequiredtobringeventhebestoftalenttofullfruition.Onceagain,pursuitofegalitarianismislimitedbecauseitrequiresthesocietytomakepooruseofitstalentpool.

Thebestexampleofthedifficultyofidentifyingandthentaxingthefruitsoftalentoccurs in the treatmentof topartistsandsport stars in theSovietUnionandothercommunistcountries.Theavowedpolicyofthesecountriesisthatallthewinningsofthesportstars,orreceiptsfromperformancesoftheartistsintheWest, go to the state, and the individuals get only salaries and expenses.Onewould think thatsuchpeoplewouldgive theirbestanyway,motivatedby theirpersonalprideandthepleasurethatcomesfromdoingone’sbest.Inpractice,thesalariesandotherperksplacetheseindividualsfarabovetheaveragestandardoflivingintheircountries.Eventhen,manyofthemdefecttotheWest.Recently,sometopSoviet tennisplayershavestartedtonegotiatethepercentageoftheirwinningstheymaykeep,anunusualinstanceofbargainingaboutanincometaxschedule.

Finally, even after a tax schedule that attempts to strike the right balancebetween equality and incentives has been established, the administrationmustthink about its enforcement strategy.Theultimate economic result of effort orluck, namely a person’s income or wealth, is not easily observed by thegovernment.Thepayersofitemslikewages,salaries,interest,anddividendsarerequired to report them to the tax authorities. But to a considerable extent,governmentsmustaskindividualstoreporttheirownincomes.Thereportscanbeaudited,butthatisacostlyprocess,andinpracticeonlyasmallpercentageoftaxreturnscanbeaudited.Howshouldthesebechosen?

Inourdiscussionoftheadvantagesofmixedstrategies,wepointedoutthatfixedandpubliclyknownrulesonauditinghaveaseriousflaw.Peoplewhoarethinkingofunderstating incomeor inflating theirdeductionswillmakesure tostayjustoutsidetheauditcriteria,andthosewhocannotavoidanauditwillbehonest.Exactlythewrongpeoplewillbeaudited.Thereforesomerandomnessintheauditingstrategyisdesirable.Theprobabilityofanauditshoulddependonthevariousitemsonataxreturn.Buthow?

Ifallpeoplewereotherwiseidentical,thentheoneswithlowincomeswouldbetheoneswhohadbadluck.Butanyonecanreportalowincomeandhopetobetakenforavictimofbadluck.Thisseemstoimplythattheprobabilityofanauditshouldbehigherforthetaxreturnsreportinglowerincomes.

Butpeoplearenototherwiseidentical,andthesedifferencesareoftenmuchbiggerthanthoseofluck.Ataxreturnreportinganincomeof$20,000ismorelikelytobefromanhonestfactoryworkerthanacheatinglawyer.Luckily,thetax authorities do have independent information about a person’s occupation.Thereforeabetterruleis,theprobabilityofanauditshouldbehighforareturninwhich the reported income is low compared towhat onewould expect forsomeone in that occupation. Similarly, audits should target those returnsclaimingdeductionsthatarehighcomparedwithwhatonewouldexpectgivenotheraspectsofthereturn.Andthatisinfactdone.

23.FOOLINGALLTHEPEOPLESOMEOFTHETIME:THE

LASVEGASSLOTSAnygamblingguideshouldtellyouthatslotmachinesareyourworstbet.Theoddsarewayagainstyou.Tocounterthisperceptionandencourageslotmachineplay,someLasVegascasinoshavebeguntoadvertisethepaybackratiofortheirmachines—the fraction of each dollar bet returned in prizemoney.Going onestep further, some casinos guarantee that they havemachines that are set to apaybackratiogreaterthan1!Thesemachinesactuallyputtheoddsinyourfavor.Ifyoucouldonlyfindthosemachinesandplaythem,youwouldexpecttomakemoney. The trick, of course, is that they don’t tell you which machines arewhich.Whentheyadvertisethattheaveragepaybackis90percentandthatsomemachinesaresetat120percent,thatalsomeansthatothermachinesmustbesetsomewherebelow90percent.Tomake itharderforyou, there isnoguaranteethatmachinesaresetthesamewayeachday—today’sfavorablemachinescouldbe tomorrow’s losers.Howmight you go about guessingwhichmachines arewhich?

CaseDiscussionSincethisisourfinalcase,wecanadmitthatwedonothavetheanswer—andeven ifwe did,we probablywouldn’t share it.Nonetheless, strategic thinkingcanhelpmakeamoreeducatedguess.Thetrickistoputyourselfintothecasinoowners’ shoes.Theymakemoneyonlywhenpeople play thedisadvantageousmachinesatleastasmuchasthefavorablemachines.

Is it really possible that the casinos could “hide” themachineswhich areofferingthefavorableodds?Ifpeopleplaythemachinesthatpayoutthemost,

won’ttheyfindthebestones?Notnecessarily,andespeciallynotnecessarilyintime!Thepayoffofthemachineisinlargepartdeterminedbythechanceofajackpotprize.Lookataslotmachinethattakesaquarterapull.Ajackpotprizeof$10,000witha1in40,000chancewouldgiveapayoffratioof1.Ifthecasinoraisedthechanceto1in30,000,thenthepayoffratiowouldbeveryfavorableat1.33.Butpeoplewatchingothersplay themachinewouldalmostalwaysseeapersondroppingquarterafterquarterwithnosuccess.Averynaturalconclusionwouldbethat this isoneoftheleastfavorablemachines.Eventually,whenthemachinepaysitsjackpotprize,itcouldberetooledandthensetatalowerrate.

In contrast, the least favorablemachines could be set to pay back a largefractionofthemoneywithaveryhighchance,andbasicallyeliminatethehopeof the big jackpot. Look at amachine setwith a payback of 80 percent. If itprovideda$1prizeonroughlyeveryfifthdraw,thenthismachinewouldmakealotofnoise,attractingattentionandpossiblymoregamblers’money.

Perhapstheexperiencedslotplayershavefiguredallthisout.Butifso,youcanbetthatthecasinosarejustdoingthereverse.Whateverhappens,thecasinoscanfindoutattheendofthedaywhichmachineswereplayedthemost.Theycanmakesurethatthepayoffpatternsthatattractthemostplayareactuallytheoneswiththelowerpayoffratio.Forwhilethedifferencebetweenapayoffratioof 1.20 and 0.80 may seem large—and determines the difference betweenmakingmoneyandlosingmoney—itcanbeextremelyhardtodistinguishbasedonthenumberofexperimentsanyoneslotplayerhastomake.Thecasinoscandesignthepayoffstomaketheseinferencesharderandevengothewrongwaymostofthetime.

The strategic insight is to recognize that unlike the UnitedWay, the LasVegascasinosarenotinthebusinesstogiveoutmoney.Intheirsearchforthefavorablemachines,themajorityoftheplayerscan’tberight.Forifthemajorityofthepeoplewereabletofigureitout,thecasinowoulddiscontinuetheirofferrather than lose money. Hence, don’t wait in line. You can bet that the mostheavilyplayedmachinesarenottheoneswiththehighestpayback.

Notes

1TENTALESOFSTRATEGY1.Theirresearchisreportedin“TheHotHandinBasketball:OntheMisperceptionofRandomSequences,”CognitivePsychology17(1985):295–314.2.NewYorkTimes,Sept.22,1983,p.B19.3.ThesequotesarefromMartinLuther’sspeechattheDietofWormsonApril18,1521,asdescribedinRolandBainton,HereIStand:ALifeofMartinLuther(NewYork:Abingdon-Cokesbury).4.DonCook,CharlesdeGaulle:ABiography(NewYork:Putnam,1982).5.DavidSchoenbrun,TheThreeLivesofCharlesdeGaulle(NewYork:Athenaeum,1966).6.GaryHufbauer,DianeBerliner,andKimberleyAnnElliott,TradeProtectionintheUnitedStates:31CaseStudies(Washington,D.C.:InstituteforInternationalEconomics,1985).

2ANTICIPATINGYOURRIVAL’SRESPONSE1.RobertFrost’sPoems,ed.LouisUntermeyer(NewYork:WashingtonSquarePress,1971).2.Hecanmoveoneofeightpawnsforwardeitheronesquareortwo,orhecanmoveoneofthetwoknightsinoneoftwoways(tothesquareslabeledrook-3orbishop-3).

3SEEINGTHROUGHYOURRIVAL’SSTRATEGY

1.Alfred,LordTennyson,InMemoriam(NewYork:W.W.Norton,1973)pp.19–20.EvenbetterisSamuelButler’splayonTennyson:“Tisbettertohavelovedandlostthannevertohavelostatall,”fromTheWayofAllFlesh(NewYork:E.P.Dutton,1952)p.385.2.Quotedfrom“GameTheory:Reagan’sMove,”NewYorkTimes,April15,1981,p.D2.3.ResearchersatthefrontiersofgametheoryworryaboutthelimitationsoftheNashequilibriumconcept.TheyhavedevelopedgameswhereintuitivelyobviousoutcomesarenotNashequilibriaandviceversa.Buttheseissuesdonotaffectmostapplicationsofgametheory.ReaderswhoarecuriousaboutthelimitsofNashequilibriumcanfindexcellentdiscussionsinKenBinmore’sforthcomingtextFunandGames(Lexington,Mass.:D.C.Heath)andDavidKreps’sGameTheoryandEconomicModelling(Oxford:OxfordUniversityPress,1990).

4RESOLVINGTHEPRISONERS’DILEMMA1.ReportedintheWallStreetJournal,December4,1986.2.RobertAxelrod,TheEvolutionofCooperation(NewYork:BasicBooks,1984).3.Thiscasestudysummarizeshispaper“IssuesintheCoordinationofMonetaryandFiscalPolicy”inMonetaryIssuesinthe1980’s(KansasCity:FederalReserveBankofKansasCity,1983).

5STRATEGICMOVES1.InstitutionalInvestor(June1979).2.Theterminology,andmuchoftheanalysis,waspioneeredbyThomasSchellinginTheStrategyofConflict(Cambridge,Mass.:HarvardUniversityPress,1960).3.OscarWilde,LadyWindermere’sFan(London:Methuen,1909).4.“EconomicScene,”NewYorkTimesApril10,1981,p.D2andApril15,1981,p.D2.5.TheSunTzutranslationisfromLionelGiles,SunTzuontheArtofWar.6.SeeJohnNewhouse,TheSportyGame(NewYork:AlfredA.Knopf,1983).7.Wechosetheparticularnumbersforcostsandprofitstomakethepointsinthesimplestway;othernumberscanproducedifferentoutcomes.Formoreonthis

topicseeAvinashDixitandAlbertKyle,“TheUseofProtectionandSubsidiesforEntryPromotionandDeterrence,”AmericanEconomicReview(March1985):139–52.

6CREDIBLECOMMITMENTS1.Bartlett’sFamiliarQuotations(Boston,Mass.:Little,Brown&Co.,1968),p.967.2.DashiellHammett,TheMalteseFalcon(SanFrancisco:PanBooks,ArioPress,1983),p.15.3.Hobbes,Leviathan(London:J.M.Dent&Sons,1973),p.71.4.JohnF.KennedyspeakingonJuly25,1961.ThequoteistakenfromFredIkle’sbook,HowNationsNegotiate(NewYork:HarperandRow,1964),p.67.5.WallStreetJournal,August7,1986.6.WallStreetJournal,January2,1990,p.B1.7.Evenso,Mr.Russomightfinditdifficulttorenegotiatewithalargenumberofpeoplesimultaneously.Ifevenonepersonfailstoagree,therenegotiationisheldup.8.ThisexampleisfromhiscommencementaddresstotheRandGraduateSchool,laterpublishedas“StrategyandSelf-Command,”inNegotiationJournal(October1989).9.Prescott,TheHistoryoftheConquestofMexico,vol.1(London:GibbingsandCo.,1896),Chapter8.10.Ibid.11.ThisinterpretationandfurthermathematicalanalysisofstrategiccommitmentmaybefoundinJeremyBulow,JohnGeanakoplos,andPaulKlemperer’spaper“MultimarketOligopoly:StrategicSubstitutesandComplements,”JournalofPoliticalEconomy93(1985):488–511.12.ThisdescriptionandquotecomesfromMichaelPorter,CasesinCompetitiveStrategy(NewYork:FreePress,1983).13.Pudd’nheadWilson’sCalendar(NewYork:W.W.Norton,1980),Chapter15,p.73.14.ThomasSchelling,TheStrategyofConflict(Cambridge,Mass.:HarvardUniversityPress,1960),p.200.15.Forafascinatingaccountofincentivesusedtomotivatesoldiers,seeJohnKeegan’sbookTheFaceofBattle(NewYork:VikingPress,1976).16.SeeFisher,McGowan,andGreenwood’saccountinFolded,Spindled,andMutilated(Cambridge,Mass.:MITPress,1983).

17.RonaldCoase,“DurabilityandMonopoly,”JournalofLawandEconomics15(April1972).

7UNPREDICTABILITY1.NewYorkTimes,October12,1986,pp.5.1–2.2.DavidHalberstam,TheSummerof’49(NewYork:Morrow,1989).3.TheCompleatStrategyst,rev.ed.(NewYork:McGraw-Hill,1966).4.Foramoredetailedaccountofthisstory,seeChristopherAndrew’sbookHerMajesty’sSecretService(NewYork:Penguin,1986).5.ThisstoryistakenfromSigmundFreud’sJokesandTheirRelationshiptotheUnconscience(NewYork:W.W.Norton,1963).6.JohnMcDonald,StrategyinPoker,Business,andWar(NewYork:W.W.Norton,1950),p.30.

8BRINKMANSHIP1.Foradetailedaccountofthecrisis,seeElieAbel,TheMissileCrisis(NewYork:J.B.Lippincott,1966).GrahamAllisonoffersawonderfulgame-theoreticanalysisoftheCubanmissilecrisisinhisbookEssenceofDecision:ExplainingtheCubanMissileCrisis(Boston:Little,Brown&Co.,1971);weshallrefertothisatseveralpointsinthischapter.2.TheevidenceisinGrahamAllison’sEssenceofDecision,pp.129–30.3.Allison,EssenceofDecision,p.131.HeattributesittoElieAbel’sreconstructionofthemeeting.4.SeeSchelling’sbookArmsandInfluence(NewHaven,Conn.:YaleUniversityPress,1966),p.70.5.Theseexcerptsaretakenfromthebookonwhichthemoviewasbased:DashiellHammett’sTheMalteseFalcon(SanFrancisco:PanBooks,ArioPress,1983),p.169.6.SeeGrahamAllison’sEssenceofDecision.7.ThishypotheticalscenariowaspaintedinanepisodeoftheBritishtelevisioncomedyseries,“Yes,PrimeMinister.”8.“InadvertentNuclearWar?”InternationalSecurity7(1982):28–54.9.BothquotesarefromaNewYorkTimesMagazine(December15,1985,pp.31–69)articleonthenNavySecretaryLehman.

9COOPERATIONANDCOORDINATION1.ThisestimatefortheadvantageofDSKoverQWERTYisbasedonworkbyDavidRumelhart,apsychologyprofessoratStanfordUniversity.2.ThesadfactsofthisstorycomefromStanfordeconomistW.BrianArthur,“CompetingTechnologiesandEconomicPrediction,”Options,InternationalInstituteforAppliedSystemsAnalysis,Laxenburg,Austria,April1984.AdditionalinformationisprovidedbyPaulDavid,aneconomichistorianatStanford,in“ClioandtheEconomicsofQWERTY,”AmericanEconomicReview,PapersandProceedings,May1985.3.SeeWBrianArthur,YuriErmoliev,andYuriKaniovski’spaper“OnGeneralizedUrnSchemesofthePolyaKind.”OriginallypublishedintheSovietjournalKibernetika,ithasbeentranslatedandreprintedinCybernetics19(1983):61–71.SimilarresultsareshownthroughdifferentmathematicaltechniquesbyBruceHill,DavidLane,andWilliamSudderthintheirpaper“AStrongLawforSomeGeneralizedUrnProcesses,”publishedinAnnalsofProbability8(1980):214–26.4.W.BrianArthur,“CompetingTechnologiesandEconomicPrediction,”Options,InternationalInstituteforAppliedSystemsAnalysis,Laxenburg,Austria(April,1984):10–13.5.SeeR.Burton’s1976paper“RecentAdvancesinVehicularSteamEfficiency,”SocietyofAutomotiveEngineersPreprint760340,andW.Strack’spaper“CondensersandBoilersforSteam-poweredCars,”NASATechnicalNote,TND-5813(Washington,D.C.,1970).Whiletheoverallsuperioritymaybeindisputeamongengineers,astrongadvantageofsteamorelectricpoweredcarsisthereductioninpollutionemissions.6.ThesecomparisonsarecataloguedinRobinCowen’s1988NewYorkUniversityworkingpaper“NuclearPowerReactors:AStudyinTechnologicalLockIn.”TheexpertengineersourcesfortheseconclusionsincludeHughMclntyre’s1975ScientificAmericanarticle“Natural-UraniumHeavy-WaterReactors,”HaroldAgnew’s1981ScientificAmericanarticle“Gas-CooledNuclearPowerReactors,”andEliotMarshall’s1984Sciencearticle“TheGas-CooledReactorMakesaComeback.”7.ThequoteisfromM.Hertsgaard’sbookTheMenandMoneyBehindNuclearEnergy(NewYork:Pantheon,1983).Murrayusedthewords“power-hungry”ratherthan“energy-poor,”butofcoursehemeantpowerinthesenseofelectricratherthaninfluential.8.LesterLaveoftheUniversityofCalifornia,Irvine,findsstrongstatistical

evidencetosupportthis.Seehisarticle“Speeding,Coordinationandthe55m.p.h.SpeedLimit,”AmericanEconomicReview(December1985).9.CyrusChu,aneconomistattheNationalTaiwanUniversity,developsthisideaintoamathematicaljustificationforthecyclicbehaviorofcrackdownsfollowedbylaxenforcementinhisworkingpaper“JustifyingShort-livedEnthusiasminLawEnforcement.”10.SeehisbookMicromotivesandMacrobehavior(NewYork:W.W.Norton,1978),Chapter4.11.Seehisarticle“StabilityinCompetition,”EconomicJournal(March1929).12.TheGeneralTheory,vol.7(ofKeynes’collectedworks)(NewYork:St.Martin’sPress,1973),p.156.13.ForsomeamusingstoriesaboutthetulipbulbmaniaseeBurtMalkiel’sRandomWalkdownWallStreet(NewYork:W.W.Norton,1975),pp.27–29.CharlesKindleberger’sManias,PanicsandCrashes(NewYork:BasicBooks,1978)isahighlyinstructiveandentertainingexaminationofthehistoryofboomsandbustsinavarietyofmarkets.

10THESTRATEGYOFVOTING1.ThestoryofPlinytheYoungerisfirsttoldfromthestrategicviewpointinRobinFarquharson’s1957OxfordUniversitydoctoralthesis,whichwaslaterpublishedasTheoryofVoting(NewHaven,Conn.:YaleUniversityPress,1969).WilliamRiker’sTheArtofPoliticalManipulation(NewHaven,Conn.:YaleUniversityPress,1986)providesmuchmoredetailandformsthebasisforthismodernretelling.Riker’sbookisfilledwithcompellinghistoricalexamplesofsophisticatedvotingstrategiesrangingfromtheConstitutionalConventiontotherecentattemptstopasstheEqualRightsAmendment.2.TheargumentsarepresentedintheirbookApprovalVoting(Boston,Mass.:Birkhauser,1983).3.ThistopicisaddressedinrecenteconomicsworkingpapersbyPrincetonprofessorDouglasBernheimandUniversityofMichiganprofessorHalVarian.4.Thishistoryoftheline-itemvetoandtheempiricalresultsarereportedinDouglasHoltz-Eakin’spaper“TheLineItemVetoandPublicSectorBudgets,”JournalofPublicEconomics(1988):269–92.

11BARGAINING

1.ThegeneralizationtobargainingwithoutproceduresisbasedonrecentworkbyeconomistsMottyPerryandPhilipReny.2.ThiscaseisdiscussedbyLarryDeBrockandAlvinRothin“StrikeTwo:Labor-ManagementNegotiationsinMajorLeagueBaseball,”TheBellJournalofEconomics(Autumn1981).3.HowardRaiffa’sbookTheArtandScienceofNegotiation(Cambridge,Mass.:HarvardUniversityPress,1982)isanexcellentsourceforstrategyinmultiple-issuebargaining.

13CASESTUDIES1.Formoreonthisproblem,includingahistoricalperspective,seePaulHoffman’sinformativeandentertainingbookArchimedes’Revenge(NewYork:W.W.Norton,1988).2.ColumbiaBusinessSchoolprofessorKathrynHarriganexpressesthisprincipleinhermaxim“Thelasticemanalwaysmakesmoney.”(SeeForbes,“EndgameStrategy,”July13,1987,pp.81–204.)3.TheincentiveforSaudiArabiatocooperatealsodependsonthesizeofthemarket.Asthemarketexpands,cheatingbecomesmoreprofitable,andtheSaudismightnotbeabovesneakinginadefectioniftheythoughtitsafetodoso.Therewardstotheleaderofholdingthecarteltogetherarelargerinadversemarkets.ThisconclusionaccordswiththestoryofOPEC.Itwaswhenthemarketweakenedintheearly1980sthattheSaudisclearlycommittedthemselvestotheroleofthe“swingproducer,”promisingtoreducetheiroutputsoastoallowthesmallermembersbiggershares.4.GarrettHarding,“TheTragedyoftheCommons,”Science162(December13,1968):1243–48.5.MartinShubik,“TheDollarAuctionGame:AParadoxinNoncooperativeBehaviorandEscalation,”JournalofConflictResolution15(1971):109–111.6.ThisideaofusingafixedbudgetandthenapplyingbackwardlogicisbasedonresearchbypoliticaleconomistBarryO’Neill,whichisforthcomingintheJournalofConflictResolution.7.AsummaryoftheargumentsappearsinF.M.Scherer,IndustrialMarketStructureandEconomicPerformance(Chicago:RandMcNally,1980).8.BruceAckerman’sbookSocialJusticeintheLiberalState(NewHaven,Conn.:YaleUniversityPress,1980)providesseveralalternativedefinitionsofliberalisminhisdefenseoftheprinciple.9.StartwithRR,andcompareitwithGR.Thetwodifferonlyinthecolorof

Rosencrantz’swalls,andbeingthenonconformist,RosencrantzprefersGR.SoweacceptGR.NowintroduceGG.ThisdiffersfromGRonlyinthecolorofGuildenstern’swalls;GuildensternistheconformistandprefersGG.ComparethatinturnwithRG;hereRosencrantz’spreferenceforRGshouldberespected.Finally,bringbackRR,whichwinssinceitbelongstoGuildenstern’srealmofprivacy.Thecyclecancontinueindefinitely.10.AlanGibbard,“APareto-consistentLibertarianClaim,”JournalofEconomicTheory7(1974):388–410.

* There were also some pretty amusing suggestions,includingStrategyandYou.

*Thisstrategynolongerappliesoncetherearemorethantwocompetitors.Evenwiththreeboats,ifoneboattacksright and the other tacks left, the leader has to choosewhich(ifeither)tofollow.

* There is the story of the newcomer to theGulagwhowasaskedbytheresidents,“Howlongisyoursentence?”The answer was “Ten years.” “What did you do?”“Nothing.” “No, there must be some mistake. Thesentenceforthatisonlythreeyears.”

†This actuallymeant 3,653days: “The three extradayswere for leap years.” (A. Solzhenitsyn,OneDay in theLifeofIvanDenisovitch,1962.)

* Luther’s reputation extends beyond the Church andbehind the IronCurtain. TheWartburg, EastGermany’sdomesticallyproducedcar,isjokinglyreferredtoas“TheLuther”:apparentlyitcanbeequallyimmobile.

*TheSuezCanalisasea-levelpassage.Thediggingwasrelativelyeasysince the landwasalready low-lyinganddesert. Panama involved much higher elevations, lakesalongtheway,anddensejungle.Lesseps’attempttodigdown to sea level failed. Much later, the U.S. ArmyCorps of Engineers succeeded using a very differentmethod—a sequenceof locks, using the lakes along theway.

*Evenifeveryonepays,somedriverswillendupwithaclunker. But if the clunkers are randomly assigned, nodriver facesagreatchanceof thebaddraw. Incontrast,thefirstdriverwhorefusestopaycanexpecttodrivetheclunkerquiteregularly.

*ProfessorDouglasHoltz-EakinofColumbiaUniversityhas looked at the effects of line-item veto power at thestate level. His results fail to detect any differences inspending when a line-item veto is available. This isdiscussed in greater detail in case study #10, followingthechapteronvoting.

*Ifthedriverwantedtoprovethathewasgoingtochargelessthanthemeter,hecouldhaveturnedonthemeterasaskedandthencharged80percentoftheprice.Thefactthat he did not should have told something about hisintentions;seetheSkyMastersonstoryjustabove.

† The twowho learned this lesson in game theory, andlived to tell the tale, were John Geanakoplos of YaleUniversity,andoneofyourauthors,BarryNalebuff.

* You may have heard this expression as the “squeakywheel”—a stuck wheel needs even more grease. Ofcourse,sometimesitgetsreplaced.

*Iftruthbetold,thisiswhatBarrywishedhehaddone.Itwas3:00inthemorningandmuchtoomuchchampagnehadbeendrunkforhimtohavebeenthinkingthisclearly.Hebet$200ontheevennumbersfiguringthathewouldendupinsecondplaceonlyintheeventthathelostandshewon,theoddsofwhichwereapproximately5:1inhisfavor. Of course 5:1 events sometimes happen and thiswasoneofthosecases.Shewon.

*InGreene’sOurManinHavana, thesalesmanforoneofthesetwofirmschosetofight—withpoisonratherthanprices.

* The continuation, 2. N-KB3, P-Q3, 3. P-Q4, PxP, 4.NxP,N-KB3,5.N-QB3,P-QR3,6.B-KN5,P-K3,7.P-KB4,Q-N3, 8.Q-Q2,QxP, is called its PoisonedPawnVariation,whichsoundsasif itcamefromthepalaceoftheBorgias,orfromWallStreet.

* Although youmay think tic-tac-toe is a simple game,don’t try todraw thegame tree.Note that nogamecanend before the fifth move, since that is the first timesomeone will have three pieces on the board. By thistime,thenumberofbranchesisalreadyupto9×8×7×6×5=15,120.Evenso,thegamecanbesolvedeasilyas most of the branches are strategically identical. Forexample,althoughthereareninepossiblefirstmoves,thesymmetryof thegameallowsus to recognize that thereareessentiallyonlythreemoves:corner,side,ormiddle.It is tricks like this that help keep the game treemanageable.

* Some shoppers seem to be able to bargain anywhere(even including Sears). Herb Cohen’s book, You CanNegotiateAnything,hasmanyvaluabletipsinthisregard.

*Thesamesimplificationwillapplyasweconsidermoreroundsofofferandcounteroffer.Youcaneasilyturnouraccountintoamorerealisticbutmessiercalculationthatallowsforthecomplexitiesweareignoring.

*Thuswehave“Myenemy’senemy’senemyisnotmyfriend.”

* In fact, if there is any odd number of countries in thechain,thenAissafe.IfthechainhasanevenlengththenBwillattackA;afterB’sattack,thechainisreducedtoanoddlengthandBissafe.

*TherefrainfromthesongLochLomondgoes:“Oh,ye’lltak’thehighroadan’I’lltak’thelowroad,An’I’llbeinScotland afore ye.” Therefore we should point out thatthe Labor Party won most of the seats in Scotland,althoughtheConservativeswontheelectionintheUnitedKingdomasawholebyaverywidemargin.

*Furthermore, thiswouldbea tie that resulted fromthefailedattempttowin,sonoonewouldcriticizeOsborneforplayingtotie.

* Some people believe that nature, too, is a strategicgame-player,andamalevolentonethattakespleasureatupsettingourbest-laidplans.Forexample,whenyouhearthatthereisafortypercentchanceofrain,thatmeanssixtimesoutoftenyouwillremembertotakeyourumbrellaand it won’t rain, while the other four times out oftenyou’llforgetyourumbrellaandtherewillbeadownpour.

*Thisexamplealsopointsoutoneof theweaknessesofgame theory. Acts are judged by their consequencesalone. Nomoral value is placed on the act itself. Eventhough his father is already mortally wounded, Indianamight not want to take responsibility for the act thatcauseshisdeath.

* Inourexample theoffensive team is strongatpassingand weak at running. That is why the pass does betterthan the run even against a pass defense. The run doesbetteragainst theblitzonlybecause thedefensivebacksarenotinposition.

*Thisissoinall“zero-sum”games,inwhichoneside’sgainisexactlytheotherside’sloss.

* This story is an updated version of the cat-and-mousestoryinJ.D.Williams,TheCompleatStrategyst.PerhapsthecatwasPersian.

*Perhapsthemostoriginalalternativeanswerwasofferedby U.C.S.D. anthropology professor Tanya Luhrmann.Shereplied:“TheNewYorkPublicLibrarymainreadingroom.” When told that this was an uncommon if notuniqueanswer,sheimmediatelydefendedherchoice.Sheexplained thatalthoughherprobabilityof successmightbelow,shewasmuchmoreinterestedinmeetingthetypeofpersonwhowouldpick theNewYorkPublicLibraryrather than the type of person who would pick GrandCentral!

*Araiderwhogainscontrolofthecompanyhasarighttotakethecompanyprivateandthusbuyoutallremainingshareholders.Bylaw,theseshareholdersmustbegivena“fair market” price for their stock. Typically, the lowertierofatwo-tieredbidisstillintherangeofwhatmightbeacceptedasfairmarketvalue.

*Unfortunately,neitherisitanequilibriumforthebidbyMacy’s to succeed, for in that case, the two-tiered bidwouldattractlessthan50percentofthesharesandsotheprice per share offered would be above the bid byMacy’s. Alas, this is one of those cases with noequilibrium. Finding a solution requires the use ofrandomizedstrategies,whichisthetopicofChapter7.

* Of course it must be remembered that the dollar rosesharplyagainstothercurrencies from1981 to1985,andfell almost equally fast from 1985 to 1987. Thereforeneitherthedropinoilpricesinthefirsthalfofthe1980s,northerecoverysincethen,wereasdramaticintermsofanaverageofallcurrenciesastheywereindollarsalone.

* This way of representing both players’ payoffs in thesamematrixisduetoThomasSchelling.Withexcessivemodesty he writes, “If I am ever asked whether I evermade a contribution to game theory, I shall answer yes.Askedwhatitwas,Ishallsaytheinventionofstaggeredpayoffsinamatrix….Ididnotsupposethattheinventionwas patentable, so Imade it freely available and hardlyanybodyexceptmystudentstakesadvantage.Iofferittoyoufreeofcharge.”

*ThestatisticalliteraturedescribesfalsepositivesasTypeI errors and false negatives as Type II errors. Mostcommon of all is the Type III error: not being able torememberwhichiswhich.

* For example, quotas under themultifiber arrangementare levied by extremely complicated categories ofgarments and countries. Thismakes it very hard to seethe effect of the quota in raising the price of anyparticulargood.Economistshaveestimatedtheseeffectsandfoundpriceincreasesashighas100percent;atariffthishighwouldsurelyarouselouderconsumerprotests.

* This ruling was not without some controversy. TheCommission’s chairman, James Miller, dissented. Hewrote that the clauses “arguably reduce buyers’ searchcosts and facilitate their ability to find the best price-valueamongbuyers.”Formore information,see“In thematter of Ethyl Corporation et al.” FTC Docket 9128,FTCDecisions,pp.425–686.

*InExodus(21:22),wearetold,“Ifmenwhoarefightinghitapregnantwomanandshegivesbirthprematurelybutthere is no serious injury, the offender must be finedwhateverthewoman’shusbanddemands.Butifthereisaseriousinjury,youaretotakelifeforalife,eyeforeye,toothfor tooth,handforhand,burnforburn,woundforwound,bruise forbruise.”TheNewTestament suggestsmore cooperative behavior. InMatthew (5:38)wehave,“Youhaveheardthatitwassaid,‘EyeforEye,andToothforTooth.’ButItellyou,donotresistanevilperson.Ifsomeone strikesyouon the right cheek, turn tohim theotheralso.”Wemovefrom“Dountoothersastheyhavedoneontoyou”tothegoldenrule,“Dountoothersasyouwould have them do unto you” (Luke 6:31). If peoplewere to follow the golden rule, there would be noprisoners’ dilemma. And if we think in the largerperspective, although cooperation might lower yourpayoffsinanyparticulargame,thepotentialrewardinanafterlifemakes this a rational strategyeven for a selfishindividual.

*Alternatively, thesemisunderstandings could also ariseon the part of theMcCoys, and the effectwouldbe thesame.

* It takesaclevercarpenter to turna tree intoa table;acleverstrategistknowshowtoturnatableintoatree.

* Secrecy of the ballot is supposed to make the votersimmune from pressure in this way. But once again,inferencewilldothejobwithoutactualobservation.Itisnot sufficient that I canobserve thatyouhavemoved; Imust actually be able to infer what your move was.Althoughmyballotmaybesecretwhen itgoes into thebox,thefinalvotecannotbesecret.Ifacandidatebribes100 people and then receives only 47 votes, he knowsthatsomeone(actually,53someones)hascheatedhim.Ifhe punishes all 100 people whom he bribed, in theprocess he’ll get the right person. Although blunt, thistechnique can circumvent the secrecy of the ballot boxwhen theelectionhasonlyasmallnumberofvoters (ineachprecinct).

* Additionally, Silk noted that supporting Reagancompletely leaves the Republicans in a better positionthan the Democrats, no matter what strategy theDemocrats choose. In the top left compartment, theRepublicans’1stplaceisbetterthantheDemocrats’3rd,andinthebottomleftcompartment,theRepublicans’3rdis better than theDemocrats’ 4th.Thus theRepublicansalwayscomeoutontop.ButasweexplainedinChapter2, each player should attempt to maximize his ownposition, without concern for who ends up on top. Thecorrectsenseofdominance is thatastrategydoesbetterforyouthanotherstrategies,notthatitleavesyoubetteroff than an opponent. To the extent that players areconcerned about their relative position, these concernsshould already be included as part of the rankings orpayoffslistedinthetable.

† Since the Republicans are already at their mostpreferred outcome, there is nothing they can do toimprove their position.Their goal is simply tomaintainthe status quo. It is in their interest to prevent theDemocratsfrommakinganystrategicmovethatchangestheoutcomeofthegame.

* If the Republicans agree, the Democrats will have anincentive to renege on the deal. This promise must beirreversibleinordertohaveaneffect.

* In fact, just such a threat was used 1853. The blackwarships of Admiral Matthew C. Perry persuaded theshogunate to open the Japanese market to Americancommerce. Today, the Japanese describe excessiveU.S.pressure to open up Japanese markets as “the secondcomingoftheblackships.”

*Thereissomequestionastowhethercarrierpigeonsisamodern-dayembellishmentofthestory.FredericMortoninhisbookTheRothschilds, claims“OnJune19,1815,lateintheafternoonaRothschildagentnamedRothworthjumped into a boat at Oostend. In his hand he held aDutch gazette still damp from the printer. By the dawnlight of June 20 Nathan Rothschild stood at Folkstoneharbor and let his eye fly over the lead paragraphs. Amoment later he was on his way to London (beatingWellington’s envoy by several hours) to tell thegovernment that Napoleon had been crushed. Then heproceededtothestockmarket.”

*Even theIsraelishave lostsomeof their reputationfortoughness. Their willingness to swap 3,000 Arabprisoners for 3 of their air force pilots suggests thatexceptionswillsometimesbemade.

* Sadly, we must report that the Mayflower FurnitureCompany recently had its first sale, a going out ofbusinesssale.

*Ontheotherhand,amongcollegeprofessors,thereisasaying, “A handshake is good enough betweenbusinessmen.Butwhenyour university’s deanpromisesyousomething,getitinwriting.”

*AlthoughtheTrojansmayhavegottenitbackward,theGreekswereaheadofthegame.SchellingcitestheGreekgeneral Xenophon as an early example of this type ofstrategic thinking. Although Xenophon did not literallyburn his bridges behind him, he did write about theadvantages of fighting with one’s back against a gully.See Schelling’s “Strategic Analysis and SocialProblems,”publishedinhiscollectedessays,ChoiceandConsequence (Cambridge, Mass.: Harvard UniversityPress,1984).

*Polaroid’sstockactuallyfell inresponseto thisaward,as the market was expecting a judgment closer to $1.5billion.

*Apparently,Khrushchevattempted touse this strategy,threateningthatSovietrocketswouldflyautomaticallyintheeventofarmedconflictinBerlin;seeTomSchelling’sArmsandInfluencep.39.

* The motive for punishing deserters is made evenstrongerifthedeserterisgivenclemencyforkillingthosein line next to him who fail to punish him. Thus if asoldier fails tokill a deserter, there arenow twopeoplewhocanpunish:hisneighborandthedeserter,whocouldsavehisownlifebypunishingthosewhofailedtopunishhim.

*AccordingtotheU.S.DefenseDepartment,overafive-yearperiod sevenservicemenordependentswerekilledand39 injuredby soft-drinkmachines that toppledoverwhilebeingrockedinanattempttodislodgebeveragesorchange—The International Herald Tribune, June 15,1988.

* For the starting position, therewas a standard startingsalary which was pretty much identical acrosscompetitors.Hence, he could predictwhat hewould beacceptingevenbeforeitwasoffered.

*Tobeunpredictable,thepitchershouldmakearandomselection from accurate pitches. He should not throwinaccuratepitches.Aninaccuratepitcherisunpredictablebecausehehimselfdoesnotknowwheretheballwillgo.Withoutaccuracy,thereisnocontrolovertheplacementandrelativefrequenciesofthedifferenttypesofpitches.Thebestexampleofanaccuratebutunpredictablepitchis the knuckleball. Because the ball hardly spins, theseamsleadtosuddenmovementsthroughtheairandnoonecanquitepredict itsoutcome—but fewpitcherscanthrowgoodknuckleballs.

* Note that the receiver does better betting on hisforehandas soonas theoddsof a serve to the forehandare above 40 percent—not 50 percent. Even though theoddsmaybeagainstaservice to the forehand,his skillsare not equal. Anticipating a forehand is the right betwhenevertheoddsarebetterthan40percent.

*Wecanconfirm this resultusinga littlealgebra. If thetableofpayoffsfortheColumnplayerisasdrawnbelow,thentheequilibriumratioofLefttoRightis(D-B):(A-C). Column chooses a probability p of playing Left sothatRowisindifferentbetweenUpandDown;pA+(1-p)B=pC+(1-p)Dimpliesp/(1-p)=(D+B)/(A-C)asclaimed.SincetheRowplayer’spayoffsarethenegativeoftheColumnplayer’s,hisequilibriummixtureofUptoDownis(D-C):(A-B).

* The estimation of probabilities conditional on hearingthe bid is made using a mathematical technique calledBayes rule. The probability the other player has a goodhandconditionalonhearingthebid“X”isthechancethatthis person would both have a good hand and bid “X”divided by the chance that he ever bids “X.” Thus,hearinga“Fold”impliesthathishandmustbebad,sincea person with a good hand never “Folds.” Hearing a“Call”impliesthathishandmustbegood,sincetheonlytime a player calls is when his hand is good. Afterhearinga“Raise,”thecalculationsareonlyslightlymorecomplicated.Theoddsthataplayerbothhasagoodhandand raises is (1/2)(2/3) = 1/3,while the chance that theplayerbothhasabadhandandraises,i.e.,bluffs,is(1/2)(1/3)=1/6.Hence the total chanceofhearinga raise is1/3+1/6=1/2.AccordingtoBayesrule,theprobabilitythatthehandisgoodconditionalonhearingaraiseisthefractionof the totalprobabilityofhearinga raise that isduetothetimeswhentheplayerhasastronghand:inthiscasethatfractionis(l/3)/(l/2)=2/3.

*ThereissomestrongstatisticalevidencethatCokeandPepsireachedacooperativesolutionfortheircouponing.As reported on “60 Minutes,” there was a span of 52weeks in which Coke and Pepsi each offered 26 pricepromotions and there was no overlap. The chance thatthis would occur by luck if the two companies wereacting independently and each offered 26 weeks ofcouponing is 1/495918532948104—or less than 1 in1,000trillion.

* Thomas Schellingmore or less invented this concept,and certainly pioneered its analysis. Thiswhole chapterowesmorethanwecansaytohisbooks,TheStrategyofConflict(Chapters7,8)andArmsandInfluence(Chapter3). Many people erroneously say “brinksmanship”—which sounds more like the art of robbing an armoredtruck.

* In fact, it would be a mistake to think of the Cubanmissile crisis as a gamewith twoplayers,Kennedy andKhrushchev. On each side, there was another game ofinternal “politics,” with the civilian and militaryauthorities disagreeing among themselves and with oneanother.GrahamAllison’sEssenceofDecision (seenote2)makesacompellingcaseforregardingthecrisisasjustsuch a complex many-person game. Later we will seehowthepresenceoftheseotherplayers(andinstitutions)canplayanessentialpartinbrinkmanship.

* Reputation won’t work, because after the threat iscarriedout there isno tomorrow.Contractswon’twork,becauseeveryonewillfacetheoverwhelmingtemptationtorenegotiate.Andsoon.

* This can be viewed as the strategic rationality of anirrationalact,anotherdevicewediscussed inChapter6.But here it is the probability, not the certainty, of anirrationalactthatisthecrucialfeature.

*Sometimes,afterearthquakes,itisclosedaltogether.

* If the number of typists using QWERTY is above 98percent,thenumberisexpectedtofallbackto98percent.Therewillalwaysbeasmallnumber,somewhereupto2percent, of new typists who will choose to learn DSKbecausetheyareinterestedinthesuperiortechnologyandarenotconcernedwiththecompatibilityissue.

* Of course the fact that people have any preferencesabout the racial mix of their neighbors is a form ofracism,albeitalessextremeonethantotalintolerance.

*Aswithhighways,thepositioninthemiddleoftheroadis called the median. When voters’ preferences are notnecessarilyuniform,thechallengerlocatesatthepositionwhere fifty percent of the voters are located to the leftand fifty percent are to the right. This median is notnecessarily the averageposition.Themedianposition isdeterminedbywherethereareanequalnumberofvoicesoneachside,while theaveragegivesweight tohowfarthevoicesareaway.

* The evening news commentary that the stock marketfell owing to heavy selling tends to leave out thiscondition: remember, for every seller there must be abuyer.

*Or,totheextentthatlivinginacityisworthmorethanlivinginaruralarea,thisdifferentialwillbereflectedinincomedifferences.

*ThisdeepresultisduetoStanfordUniversityprofessorKenneth Arrow. His famous “impossibility” theoremshows that any system for aggregating unrestrictedpreferencesover threeormore alternatives into a groupdecision cannot simultaneously satisfy the followingminimally desirable properties: (i) transitivity, (ii)unanimity, (iii) independence of irrelevant alternatives,(iv) non-dictatorship. Transitivity requires that if A ischosenoverB andB is chosen overC, thenAmust bechosenoverC.UnanimityrequiresAtobechosenoverBwhenA isunanimouslypreferred toB. IndependenceofirrelevantalternativesrequiresthatthechoicebetweenAandBdoesnotdependonwhethersomeotheralternativeC isavailable.Non-dictatorship requires that there isnoindividual who always gets his way and thus hasdictatorialpowers.

* No doubt they console themselves by thinking of theevenworseplightofBritain’sPrinceCharles.

† The biggest chance that a fixed group of 50 SenatorsvotesAyeandtheremaining50voteNayis(½)50·(½)50.Multiplying this by the number of ways of finding 50supporters out of the total 100, we get approximately(1/12).

*Orsenatorsonoppositesidesoftheissuewilltrytopairofftheirabsences.

* Even though any single individual’s opinion of theoutcomeiseversoslightlychanged,asmallimpactonalargenumberofpeoplemaystilladduptosomething.

* A much cheaper and potentially more representativeway of deciding elections would be to run a poll. Thecurrentpractice isaglorifiedpoll;anyonewhowants toparticipate,doesso.Thetheoryofstatisticstellsusthatifthe vote from a random sample of 10,000 gives onecandidatea5%edge(5,250ormorevotes),thenthereisless than a one-in-a-million chance the outcomewill bereversed, even if 100million people vote. If the vote iscloser we have to continue expanding the survey size.While this process could greatly reduce the cost ofvoting,thepotentialforabuseisalsogreat.Theselectionofarandomvoterissubjecttoanightmareofproblems.

† Again, there is the qualification that you might careaboutthecandidate’smarginofvictory.Specifically,youmightwantyourcandidatetowin,butonlywithasmallmargin of victory (in order to temper hismegalomania,for example). In that case, you might choose to voteagainst your preferred alternative, provided you wereconfidentthathewouldwin.

*Anysimilaritybetweenthisstoryandtheearlystagesofthe 1988 Democratic presidential primaries is purelycoincidental.

* Similar results hold even when there are many moreoutcomes.

*However,iftheplayerhasbeenontheballotforfifteenyearsandfailedtogetelected,theneligibilityislost.Forotherwise ineligibleplayers, there is analternative routetoelection.AnOldTimers’committeeconsidersspecialcasesandsometimeselectsoneortwocandidatesayear.

*Marv Throneberry played first base for the ’62Mets,possibly the worst team in the history of baseball. Hisperformance was instrumental to the team’s reputation.BobUeckerismuchbetterknownforhisperformanceinMillerLitecommercialsthanforhisplayonthebaseballfield.

* One explicit example is the strategic game playedbetween the Marshall and Rhodes Scholarships. TheMarshall Fund’s objective is to have the maximuminfluence over who is given a scholarship to study inEngland. If someone has the potential to win both aMarshallandaRhodes,theMarshallFundpreferstohavethe person study as a Rhodes Scholar; that brings theperson to England at no cost to theMarshall Fund andthusallows theMarshallScholarship to selectonemoreperson.HencetheMarshallFundwaitsuntil theRhodesScholarships have been announced before making itsfinalselections.

*We couldmake themore realistic assumption that themanagementwillneedsomeminimalsharesuchas$100,but that will only complicate the arithmetic, and won’tchangethebasicideaofthestory.

* This approach was pioneered by the economist ArielRubinstein,andthesolutionwediscussisoftencalledtheRubinsteinbargainingsolutioninhishonor.Oneexampleof how to do this is provided in the case study “TheLimitstoCharity”offeredinChapter13.

* In fact the design of defense contracts would haveprovidedthebestexampleforthischapter,butforthefactthattheanalogueoftheoperatingprofitistooelusiveinthe case of defense to allow any numerical examples.Howdoesonevaluenationaldefense?

* Here we are supposing that the bid is a firmcommitment, and that you cannot later renegotiate ahigherprice.Inthenextsectionwewilllookatcontractswithrenegotiation.

* Actually, there is typically some minimum biddingincrement. Since the pricemoves upward in jumps, theexpected selling price in an English auction is theminimum bid above the value of the second highestbidder.ThedifferenceinsellingpricebetweenanEnglishand Vickrey auction is thus limited to the size of thebiddingunit.

*Infact,theseassumptionsareappropriateforindustriesinwhich themarginalcostofproducingup tohistoricalcapacityislow.Fortheseindustries,fixedcostsdominateand result in tremendous pressure to fill up excesscapacity. In alumina refining, for instance, operatingbelowfullcapacityutilizationistechnicallyinefficientinthat it altersproductcharacteristics.Operatingbelow70percentcapacity is infeasiblebecauseaminimalamountofchemicalshastobefedthroughthemachinerytokeepit running. A strategy of frequently shutting down andstarting up is not a viable option either. After eachshutdown, corrosive chemicals accumulate in themachinery (e.g., caustic soda in the digesters). Start-uprequirescleaningout themachineryand readjustingand“debottlenecking” it—a process that sometimes takesover a year. In effect, then, alumina refineries face achoice between operating at close to full capacity andshuttingdownpermanently.

*Incalculatingthevalueoftheworst-casescenario,youcansimplifythemathematicsbyassumingazerointerestrate; profits (losses) tomorrow and today are equallyvaluable.

* Economists can offer a second reason why leadedgasoline sells for less: it is bought by a different set ofcustomers. You might not be surprised to see smallermarkups on products bought by people who drive oldcars than on products bought by peoplewho drive newcars.A new owner of a $30,000BMW is less likely tobalkatatencentmarkupthansomeonedrivingabeat-up’74Pinto.

* It is important in this problem that your chance ofmaking 7 no trump is independent ofGoren andZeck'schances, even though both teams are playing the samecards.Thiscouldhappen ifyouwillmake7only if thelead isclubsandmake6otherwise.Basedon thecards,theleadisequallylikelytobeclubsordiamonds;inthiscase,yourchanceofmaking7willbeindependent.

*Inequilibrium,theratioof7notrumpto6notrumpis(l–0.5):(0.75–0.5)or2:1.

*Could the criminals have done even better?No.Theirbest outcome is the homeowners’ worst. Sincehomeowners can guarantee themselves 3 or better byowing guns, no strategic move by criminals can leavehomeownersat4.Hence,acommitmenttogounarmedisthe best strategic move for criminals. What about acommitmentbythecriminalstocarryarms?Thisistheirdominant strategy. Homeowners would anticipate thismove anyway. Hence, it has no strategic value. Byanalogywithwarningsandassurances,acommitmenttoadominantstrategycouldbecalleda“declaration”:it isinformationalratherthanstrategic.

† What happens if homeowners preempt and let thecriminalsrespond?Homeownerscanpredictthatforanyunconditional choice of action on their part, criminalswill respond by going armed. Hence, homeowners willwant to go armed, and the result is no better thanwithsimultaneousmoves.