Stanford Encyclopedia of PhilosophyEvolutionaryGameTheory

FirstpublishedMonJan14,2002substantiverevisionSunJul 19,2009

Evolutionary game theory originated as an application of the mathematical theory of games to biological contexts, arising from the realization that frequency dependent fitness introduces a strategic aspect to evolution. Recently, however, evolutionary game theory has become of increased interest to economists,sociologists, and anthropologists--and social scientists in general--as well as philosophers. The interest among social scientists in a theory with explicit biological roots derives from threefacts.First,theevolutiontreatedbyevolutionarygametheoryneednotbebiologicalevolution. Evolutionmay,inthiscontext,oftenbeunderstoodasculturalevolution,wherethisrefersto changesinbeliefsandnormsovertime.Second,therationalityassumptionsunderlyingevolutionary gametheoryare,inmanycases,moreappropriateforthemodellingofsocialsystemsthanthose assumptionsunderlyingthetraditionaltheoryofgames.Third,evolutionarygametheory,asan explicitlydynamictheory,providesanimportantelementmissingfromthetraditionaltheory.Inthe prefacetoEvolutionandtheTheoryofGames,MaynardSmithnotesthat[p]aradoxically,ithas turnedoutthatgametheoryismorereadilyappliedtobiologythantothefieldofeconomicbehaviour forwhichitwasoriginallydesigned.Itisperhapsdoublyparadoxical,then,thatthesubsequent developmentofevolutionarygametheoryhasproducedatheorywhichholdsgreatpromiseforsocial scientists,andisasreadilyappliedtothefieldofeconomicbehaviourasthatforwhichitwas originallydesigned.

1. HistoricalDevelopment2. TwoApproachestoEvolutionaryGameTheory

2.1Definitionsofevolutionarystability2.2Specifyingdynamicsforthepopulation

3. WhyEvolutionaryGameTheory?3.1Theequilibriumselectionproblem3.2Theproblemofhyperrationalagents3.3Thelackofadynamicaltheoryinthetraditionaltheoryofgames

4. ApplicationsofEvolutionaryGameTheory4.1Asenseoffairness4.2Theemergenceoflanguage.

5. PhilosophicalProblemsofEvolutionaryGameTheory5.1Themeaningoffitnessinculturalevolutionaryinterpretations5.2Theexplanatoryirrelevanceofevolutionarygametheory5.3Thevalueladennessofevolutionarygametheoreticexplanations

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1. HistoricalDevelopment

EvolutionarygametheorywasfirstdevelopedbyR.A.Fisher[seeTheGeneticTheoryofNaturalSelection(1930)]inhisattempttoexplaintheapproximateequalityofthesexratioinmammals.ThepuzzleFisherfacedwasthis:whyisitthatthesexratioisapproximatelyequalinmanyspecieswherethemajorityofmalesnevermate?Inthesespecies,thenonmatingmaleswouldseemtobeexcessbaggagecarriedaroundbytherestofthepopulation,havingnorealuse.Fisherrealizedthatifwemeasureindividualfitnessintermsoftheexpectednumberofgrandchildren,thenindividualfitnessdependsonthedistributionofmalesandfemalesinthepopulation.Whenthereisagreaternumberoffemalesinthepopulation,maleshaveahigherindividualfitnesswhentherearemoremalesinthepopulation,femaleshaveahigherindividualfitness.Fisherpointedoutthat,insuchasituation,theevolutionarydynamicsleadtothesexratiobecomingfixedatequalnumbersofmalesandfemales.Thefactthatindividualfitnessdependsupontherelativefrequencyofmalesandfemalesinthepopulationintroducesastrategicelementintoevolutions.

Fisher'sargumentcanbeunderstoodgametheoretically,buthedidnotstateitinthoseterms.In1961,R.C.LewontinmadethefirstexplicitapplicationofgametheorytoevolutionarybiologyinEvolutionandtheTheoryofGames(nottobeconfusedwiththeMaynardSmithworkofthesamename).In1972,MaynardSmithdefinedtheconceptofanevolutionarilystablestrategy(hereafterESS)inthearticleGameTheoryandtheEvolutionofFighting.However,itwasthepublicationofTheLogicofAnimalConflict,byMaynardSmithandPricein1973thatintroducedtheconceptofanESSintowidespreadcirculation.In1982,MaynardSmith'sseminaltextEvolutionandtheTheoryofGamesappeared,followedshortlythereafterbyRobertAxelrod'sfamousworkTheEvolutionofCooperationin1984.Sincethen,therehasbeenaveritableexplosionofinterestbyeconomistsandsocialscientistsinevolutionarygametheory(seethebibliographybelow).

2.TwoApproachestoEvolutionaryGameTheory

Therearetwoapproachestoevolutionarygametheory.ThefirstapproachderivesfromtheworkofMaynardSmithandPriceandemploystheconceptofanevolutionarilystablestrategyastheprincipaltoolofanalysis.Thesecondapproachconstructsanexplicitmodeloftheprocessbywhichthefrequencyofstrategieschangeinthepopulationandstudiespropertiesoftheevolutionarydynamicswithinthatmodel.

Thefirstapproachcanthusbethoughtofasprovidingastaticconceptualanalysisofevolutionarystability.Staticbecause,althoughdefinitionsofevolutionarystabilityaregiven,thedefinitionsadvanceddonottypicallyrefertotheunderlyingprocessbywhichbehaviours(orstrategies)changeinthepopulation.Thesecondapproach,incontrast,doesnotattempttodefineanotionofevolutionarystability:onceamodelofthepopulationdynamicshasbeenspecified,allofthestandardstabilityconceptsusedintheanalysisofdynamicalsystemscanbebroughttobear.

2.1Definitionsofevolutionarystability

Asanexampleofthefirstapproach,considertheproblemoftheHawkDovegame,analyzedbyMaynardSmithandPriceinTheLogicofAnimalConflict.Inthisgame,twoindividualscompeteforaresourceofafixedvalueV.(Inbiologicalcontexts,thevalueVoftheresourcecorrespondstoanincreaseintheDarwinianfitnessoftheindividualwhoobtainstheresourceinaculturalcontext,thevalueVoftheresourcewouldneedtobegivenanalternateinterpretationmoreappropriatetothespecificmodelathand.)Eachindividualfollowsexactlyoneoftwostrategiesdescribedbelow:

Hawk Initiateaggressivebehaviour,notstoppinguntilinjuredoruntilone'sopponentbacksdown.

Dove Retreatimmediatelyifone'sopponentinitiatesaggressivebehaviour.

Ifweassumethat(1)whenevertwoindividualsbothinitiateaggressivebehaviour,conflicteventually

resultsandthetwoindividualsareequallylikelytobeinjured,(2)thecostoftheconflictreducesindividualfitnessbysomeconstantvalueC,(3)whenaHawkmeetsaDove,theDoveimmediatelyretreatsandtheHawkobtainstheresource,and(4)whentwoDovesmeettheresourceissharedequallybetweenthem,thefitnesspayoffsfortheHawkDovegamecanbesummarizedaccordingtothefollowingmatrix:

Hawk DoveHawk (VC) VDove 0 V/2

Figure1:TheHawkDoveGame

(Thepayoffslistedinthematrixareforthatofaplayerusingthestrategyintheappropriaterow,playingagainstsomeoneusingthestrategyintheappropriatecolumn.Forexample,ifyouplaythestrategyHawkagainstanopponentwhoplaysthestrategyDove,yourpayoffisVifyouplaythestrategyDoveagainstanopponentwhoplaysthestrategyHawk,yourpayoffis0.)

Inorderforastrategytobeevolutionarilystable,itmusthavethepropertythatifalmosteverymemberofthepopulationfollowsit,nomutant(thatis,anindividualwhoadoptsanovelstrategy)cansuccessfullyinvade.Thisideacanbegivenaprecisecharacterizationasfollows:LetF(s1,s2)denotethechangeinfitnessforanindividualfollowingstrategys1againstanopponentfollowingstrategys2,andletF(s)denotethetotalfitnessofanindividualfollowingstrategysfurthermore,supposethateachindividualinthepopulationhasaninitialfitnessofF0.Ifisanevolutionarilystablestrategyandamutantattemptingtoinvadethepopulation,then

F()=F0+(1p)F(,)+pF(,)

F()=F0+(1p)F(,)+pF(,)

wherepistheproportionofthepopulationfollowingthemutantstrategy.

Sinceisevolutionarilystable,thefitnessofanindividualfollowingmustbegreaterthanthefitnessofanindividualfollowing(otherwisethemutantfollowingwouldbeabletoinvade),andsoF()>F().Now,aspisverycloseto0,thisrequiresthateitherthat

F(,)>F(,)

orthat

F(,)=F(,)andF(,)>F(,)

(ThisisthedefinitionofanESSthatMaynardSmithandPricegive.)Inotherwords,whatthismeansisthatastrategyisanESSifoneoftwoconditionsholds:(1)doesbetterplayingagainstthananymutantdoesplayingagainst,or(2)somemutantdoesjustaswellplayingagainstas,butdoesbetterplayingagainstthemutantthanthemutantdoes.

Giventhischaracterizationofanevolutionarilystablestrategy,onecanreadilyconfirmthat,fortheHawkDovegame,thestrategyDoveisnotevolutionarilystablebecauseapurepopulationofDovescanbeinvadedbyaHawkmutant.IfthevalueVoftheresourceisgreaterthanthecostCofinjury(sothatitisworthriskinginjuryinordertoobtaintheresource),thenthestrategyHawkisevolutionarilystable.Inthecasewherethevalueoftheresourceislessthanthecostofinjury,thereisnoevolutionarilystablestrategyifindividualsarerestrictedtofollowingpurestrategies,althoughthereisanevolutionarilystablestrategyifplayersmayusemixedstrategies.[1]

IntheyearsfollowingtheoriginalworkofMaynardSmithandPrice,alternateanalyticsolutionconceptshavebeenproposed.Ofthese,twoimportantonesaretheideaofanevolutionarilystableset(seeThomas1984,1985a,b),andtheideaofalimitESS(seeSelten1983,1988).Theformerprovidesasetwisegeneralizationoftheconceptofanevolutionarilystablestrategy,andthelatterextendstheconceptofanevolutionarilystablestrategytothecontextoftwoplayerextensiveformgames.

2.2Specifyingdynamicsforthepopulation

Asanexampleofthesecondapproach,considerthewellknownPrisoner'sDilemma.Inthisgame,individualschooseoneoftwostrategies,typicallycalledCooperateandDefect.Hereisthegeneralformofthepayoffmatrixfortheprisoner'sdilemma:

Cooperate DefectCooperate (R,R) (S,T)Defect (T,S) (P,P)

Figure2:PayoffMatrixforthePrisoner'sDilemma.Payoffslistedas(row,column).

whereT>R>P>SandT>R>P>S.(Thisformdoesnotrequirethatthepayoffsforeachplayerbesymmetric,onlythattheproperorderingofthepayoffsobtains.)Inwhatfollows,itwillbeassumedthatthepayoffsforthePrisoner'sDilemmaarethesameforeveryoneinthepopulation.

HowwillapopulationofindividualsthatrepeatedlyplaysthePrisoner'sDilemmaevolve?Wecannotanswerthatquestionwithoutintroducingafewassumptionsconcerningthenatureofthepopulation.First,letusassumethatthepopulationisquitelarge.Inthiscase,wecanrepresentthestateofthepopulationbysimplykeepingtrackofwhatproportionfollowthestrategiesCooperateandDefect.Letpcandpddenotetheseproportions.Furthermore,letusdenotetheaveragefitnessofcooperatorsanddefectorsbyWCandWD,respectively,andletWdenotetheaveragefitnessoftheentirepopulation.ThevaluesofWC,WD,andWcanbeexpressedintermsofthepopulationproportionsandpayoffvaluesasfollows:

WC=F0+pcF(C,C)+pdF(C,D)WD=F0+pcF(D,C)+pdF(D,D)W=pcWC+pdWD

Second,letusassumethattheproportionofthepopulationfollowingthestrategiesCooperateandDefectinthenextgenerationisrelatedtotheproportionofthepopulationfollowingthestrategiesCooperateandDefectinthecurrentgenerationaccordingtotherule:

Wecanrewritetheseexpressionsinthefollowingform:

Ifweassumethatthechangeinthestrategyfrequencyfromonegenerationtothenextaresmall,thesedifferenceequationsmaybeapproximatedbythedifferentialequations:

TheseequationswereofferedbyTaylorandJonker(1978)andZeeman(1979)toprovidecontinuousdynamicsforevolutionarygametheoryandareknownasthereplicatordynamics.

ThereplicatordynamicsmaybeusedtomodelapopulationofindividualsplayingthePrisoner'sDilemma.ForthePrisoner'sDilemma,theexpectedfitnessofCooperatingandDefectingare:

WC =F0+pcF(C,C)+pdF(C,D)=F0+pcR+pdS

and

WD =F0+pcF(D,C)+pdF(D,D)

=F0+pcT+pdP.

SinceT>RandP>S,itfollowsthatWD>WCandhenceWD>W>WC.Thismeansthat

and

SincethestrategyfrequenciesforDefectandCooperateinthenextgenerationaregivenby

and

respectively,weseethatovertimetheproportionofthepopulationchoosingthestrategyCooperateeventuallybecomesextinct.Figure3illustratesonewayofrepresentingthereplicatordynamicalmodeloftheprisoner'sdilemma,knownasastatespacediagram.

Figure3:TheReplicatorDynamicalModelofthePrisoner'sDilemma

Weinterpretthisdiagramasfollows:theleftmostpointrepresentsthestateofthepopulationwhereeveryonedefects,therightmostpointrepresentsthestatewhereeveryonecooperates,andintermediatepointsrepresentstateswheresomeproportionofthepopulationdefectsandtheremaindercooperates.(OnemapsstatesofthepopulationontopointsinthediagrambymappingthestatewhenN%ofthepopulationdefectsontothepointofthelineN%ofthewaytotheleftmostpoint.)Arrowsontheline

representtheevolutionarytrajectoryfollowedbythepopulationovertime.Theopencircleattherightmostpointindicatesthatthestatewhereeverybodycooperatesisanunstableequilibrium,inthesensethatifasmallportionofthepopulationdeviatesfromthestrategyCooperate,thentheevolutionarydynamicswilldrivethepopulationawayfromthatequilibrium.ThesolidcircleattheleftmostpointindicatesthatthestatewhereeverybodyDefectsisastableequilibrium,inthesensethatifasmallportionofthepopulationdeviatesfromthestrategyDefect,thentheevolutionarydynamicswilldrivethepopulationbacktotheoriginalequilibriumstate.

Atthispoint,onemayseelittledifferencebetweenthetwoapproachestoevolutionarygametheory.Onecanconfirmthat,forthePrisoner'sDilemma,thestatewhereeverybodydefectsistheonlyESS.Sincethisstateistheonlystableequilibriumunderthereplicatordynamics,thetwonotionsfittogetherquiteneatly:theonlystableequilibriumunderthereplicatordynamicsoccurswheneveryoneinthepopulationfollowstheonlyESS.Ingeneral,though,therelationshipbetweenESSsandstablestatesofthereplicatordynamicsismorecomplexthanthisexamplesuggests.TaylorandJonker(1978),aswellasZeeman(1979),establishconditionsunderwhichonemayinfertheexistenceofastablestateunderthereplicatordynamicsgivenanevolutionarilystablestrategy.Roughly,ifonlytwopurestrategiesexist,thengivena(possiblymixed)evolutionarilystablestrategy,thecorrespondingstateofthepopulationisastablestateunderthereplicatordynamics.(IftheevolutionarilystablestrategyisamixedstrategyS,thecorrespondingstateofthepopulationisthestateinwhichtheproportionofthepopulationfollowingthefirststrategyequalstheprobabilityassignedtothefirststrategybyS,andtheremainderfollowthesecondstrategy.)However,thiscanfailtobetrueifmorethantwopurestrategiesexist.

TheconnectionbetweenESSsandstablestatesunderanevolutionarydynamicalmodelisweakenedfurtherifwedonotmodelthedynamicsbythereplicatordynamics.Forexample,supposeweusealocalinteractionmodelinwhicheachindividualplaystheprisoner'sdilemmawithhisorherneighbors.NowakandMay(1992,1993),usingaspatialmodelinwhichlocalinteractionsoccurbetweenindividualsoccupyingneighboringnodesonasquarelattice,showthatstablepopulationstatesfortheprisoner'sdilemmadependuponthespecificformofthepayoffmatrix.[2]

WhenthepayoffmatrixforthepopulationhasthevaluesT=2.8,R=1.1,P=0.1,andS=0,theevolutionarydynamicsofthelocalinteractionmodelagreewiththoseofthereplicatordynamics,andleadtoastatewhereeachindividualfollowsthestrategyDefectwhichis,asnotedbefore,theonlyevolutionarilystablestrategyintheprisoner'sdilemma.Thefigurebelowillustrateshowrapidlyonesuchpopulationconvergestoastatewhereeveryonedefects.

Generation1 Generation2 Generation3

Generation4 Generation5 Generation6

Figure4:Prisoner'sDilemma:AllDefect[Viewamovieofthismodel]

However,whenthepayoffmatrixhasvaluesofT=1.2,R=1.1,P=0.1,andS=0,theevolutionarydynamicscarrythepopulationtoastablecycleoscillatingbetweentwostates.Inthiscyclecooperatorsanddefectorscoexist,withsomeregionscontainingblinkersoscillatingbetweendefectorsandcooperators(asseeningeneration19and20).

Generation1 Generation2 Generation19 Generation20

Figure5:Prisoner'sDilemma:Cooperate[Viewamovieofthismodel]

Noticethatwiththeseparticularsettingsofpayoffvalues,theevolutionarydynamicsofthelocalinteractionmodeldiffersignificantlyfromthoseofthereplicatordynamics.Underthesepayoffs,thestablestateshavenocorrespondinganalogueineitherthereplicatordynamicsnorintheanalysisofevolutionarilystablestrategies.

AphenomenonofgreaterinterestoccurswhenwechoosepayoffvaluesofT=1.61,R=1.01,P=0.01,andS=0.Here,thedynamicsoflocalinteractionleadtoaworldconstantlyinflux:underthesevaluesregionsoccupiedpredominantlybyCooperatorsmaybesuccessfullyinvadedbyDefectors,andregionsoccupiedpredominantlybyDefectorsmaybesuccessfullyinvadedbyCooperators.Inthismodel,thereisnostablestrategyinthetraditionaldynamicalsense.[3]

Generation1 Generation3 Generation5 Generation7

Generation9 Generation11 Generation13 Generation15

Figure6:Prisoner'sDilemma:Chaotic[viewamovieofthismodel]

Thesemodelsdemonstratethat,althoughnumerouscasesexistinwhichbothapproachestoevolutionarygametheoryarriveatthesameconclusionregardingwhichstrategiesonewouldexpecttofindpresentinapopulation,thereareenoughdifferencesintheoutcomesofthetwomodesofanalysistojustifythedevelopmentofeachprogram.

3. WhyEvolutionaryGameTheory?

Althoughevolutionarygametheoryhasprovidednumerousinsightstoparticularevolutionaryquestions,agrowingnumberofsocialscientistshavebecomeinterestedinevolutionarygametheoryinhopesthatitwillprovidetoolsforaddressinganumberofdeficienciesinthetraditionaltheoryofgames,threeofwhicharediscussedbelow.

3.1Theequilibriumselectionproblem

TheconceptofaNashequilibrium(seetheentryongametheory)hasbeenthemostusedsolutionconceptingametheorysinceitsintroductionbyJohnNashin1950.AselectionofstrategiesbyagroupofagentsissaidtobeinaNashequilibriumifeachagent'sstrategyisabestresponsetothestrategieschosenbytheotherplayers.Bybestresponse,wemeanthatnoindividualcanimproveherpayoffbyswitchingstrategiesunlessatleastoneotherindividualswitchesstrategiesaswell.ThisneednotmeanthatthepayoffstoeachindividualareoptimalinaNashequilibrium:indeed,oneofthedisturbingfactsoftheprisoner'sdilemmaisthattheonlyNashequilbriumofthegamewhenbothagentsdefectissuboptimal.[4]

YetadifficultyariseswiththeuseofNashequilibriumasasolutionconceptforgames:ifwerestrictplayerstousingpurestrategies,noteverygamehasaNashequilbrium.ThegameMatchingPenniesillustratesthisproblem.

Heads TailsHeads (0,1) (1,0)Tails (1,0) (0,1)

Figure7:PayoffmatrixforthegameofMatchingPennies(Rowwinsifthetwocoinsdonotmatch,whereasColumnwinsifthetwocoinsmatch).

WhileitistruethateverynoncooperativegameinwhichplayersmayusemixedstrategieshasaNashequilibrium,somehavequestionedthesignificanceofthisforrealagents.Ifitseemsappropriatetorequirerationalagentstoadoptonlypurestrategies(perhapsbecausethecostofimplementingamixedstrategyrunstoohigh),thenthegametheoristmustadmitthatcertaingameslacksolutions.

AmoresignificantproblemwithinvokingtheNashequilibriumastheappropriatesolutionconceptarisesbecausegamesexistwhichhavemultipleNashequilibria(seethesectiononSolutionConceptsandEquilibria,intheentryongametheory).WhenthereareseveraldifferentNashequilibria,howisarationalagenttodecidewhichoftheseveralequilibriaistherightonetosettleupon?[5]AttemptstoresolvethisproblemhaveproducedanumberofpossiblerefinementstotheconceptofaNashequilibrium,eachrefinementhavingsomeintuitivepurchase.Unfortunately,somanyrefinementsofthenotionofaNashequilibriumhavebeendevelopedthat,inmanygameswhichhavemultipleNashequilibria,eachequilibriumcouldbejustifiedbysomerefinementpresentintheliterature.TheproblemhasthusshiftedfromchoosingamongmultipleNashequilibriatochoosingamongthe

variousrefinements.Some(seeSamuelson(1997),EvolutionaryGamesandEquilibriumSelection)hopethatfurtherdevelopmentofevolutionarygametheorycanbeofserviceinaddressingthisissue.

3.2Theproblemofhyperrationalagents

Thetraditionaltheoryofgamesimposesaveryhighrationalityrequirementuponagents.Thisrequirementoriginatesinthedevelopmentofthetheoryofutilitywhichprovidesgametheory'sunderpinnings(seeLuce(1950)foranintroduction).Forexample,inordertobeabletoassignacardinalutilityfunctiontoindividualagents,onetypicallyassumesthateachagenthasawelldefined,consistentsetofpreferencesoverthesetoflotteriesovertheoutcomeswhichmayresultfromindividualchoice.Sincethenumberofdifferentlotteriesoveroutcomesisuncountablyinfinite,thisrequireseachagenttohaveawelldefined,consistentsetofuncountablyinfinitelymanypreferences.

Numerousresultsfromexperimentaleconomicshaveshownthatthesestrongrationalityassumptionsdonotdescribethebehaviorofrealhumansubjects.Humansarerarely(ifever)thehyperrationalagentsdescribedbytraditionalgametheory.Forexample,itisnotuncommonforpeople,inexperimentalsituations,toindicatethattheypreferAtoB,BtoC,andCtoA.Thesefailuresofthetransitivityofpreferencewouldnotoccurifpeoplehadawelldefinedconsistentsetofpreferences.Furthermore,experimentswithaclassofgamesknownasabeautypageantshow,quitedramatically,thefailureofcommonknowledgeassumptionstypicallyinvokedtosolvegames.[6]Sinceevolutionarygametheorysuccessfullyexplainsthepredominanceofcertainbehaviorsofinsectsandanimals,wherestrongrationalityassumptionsclearlyfail,thissuggeststhatrationalityisnotascentraltogametheoreticanalysesaspreviouslythought.Thehope,then,isthatevolutionarygametheorymaymeetwithgreatersuccessindescribingandpredictingthechoicesofhumansubjects,sinceitisbetterequippedtohandletheappropriateweakerrationalityassumptions.

3.3Thelackofadynamicaltheoryinthetraditionaltheoryofgames

AttheendofthefirstchapterofTheoryofGamesandEconomicBehavior,vonNeumannandMorgensternwrite:

Werepeatmostemphaticallythatourtheoryisthoroughlystatic.Adynamictheorywouldunquestionablybemorecompleteandthereforepreferable.Butthereisampleevidencefromotherbranchesofsciencethatitisfutiletotrytobuildoneaslongasthestaticsideisnotthoroughlyunderstood.(VonNeumannandMorgenstern,1953,p.44)

Thetheoryofevolutionisadynamicaltheory,andthesecondapproachtoevolutionarygametheorysketchedaboveexplicitlymodelsthedynamicspresentininteractionsamongindividualsinthepopulation.Sincethetraditionaltheoryofgameslacksanexplicittreatmentofthedynamicsofrationaldeliberation,evolutionarygametheorycanbeseen,inpart,asfillinganimportantlacunaoftraditionalgametheory.

Onemayseektocapturesomeofthedynamicsofthedecisionmakingprocessintraditionalgametheorybymodelingthegameinitsextensiveform,ratherthanitsnormalform.However,formostgamesofreasonablecomplexity(andhenceinterest),theextensiveformofthegamequicklybecomesunmanageable.Moreover,evenintheextensiveformofagame,traditionalgametheoryrepresentsanindividual'sstrategyasaspecificationofwhatchoicethatindividualwouldmakeateachinformationsetinthegame.Aselectionofstrategy,then,correspondstoaselection,priortogameplay,ofwhatthatindividualwilldoatanypossiblestageofthegame.Thisrepresentationofstrategyselectionclearlypresupposeshyperrationalplayersandfailstorepresenttheprocessbywhichoneplayerobserveshisopponent'sbehavior,learnsfromtheseobservations,andmakesthebestmoveinresponsetowhathehaslearned(asonemightexpect,forthereisnoneedtomodellearninginhyperrationalindividuals).Theinabilitytomodelthedynamicalelementofgameplayintraditionalgametheory,andtheextenttowhichevolutionarygametheorynaturallyincorporatesdynamical

considerations,revealsanimportantvirtueofevolutionarygametheory.

4. ApplicationsofEvolutionaryGameTheory

Evolutionarygametheoryhasbeenusedtoexplainanumberofaspectsofhumanbehavior.Asmallsamplingoftopicswhichhavebeenanalysedfromtheevolutionaryperspectiveinclude:altruism(FletcherandZwick,2007Gintisetal.,2003SanchezandCuesta,2005Trivers,1971),behaviorinpublicgoodsgame(ClemensandRiechmann,2006Hauert,2006Hauertetal.,2002,2006HubermanandGlance,1995),empathy(PageandNowak,2002Fishman,2006),humanculture(EnquistandGhirlanda,2007Enquistetal.,2008),moralbehaviour(Alexander,2007Boehm,1982HarmsandSkyrms,2008Skyrms1996,2004),privateproperty(Gintis,2007),signalingsystemsandotherprotolinguisticbehaviour(Barrett,2007HauskenandHirshleirfer,2008Hurd,1995Jager,2008Nowaketal.,1999Pawlowitsch,2007,2008Skyrms,forthcomingZollman,2005),sociallearning(KamedaandNakanishi,2003Nakahashi,2007Rogers,1988WakanoandAoki,2006Wakanoetal.,2004),andsocialnorms(Axelrod,1986Bicchieri,2006BinmoreandSamuelson,1994Chalubetal.,2006Kendaletal.,2006Ostrum,2000).

Thefollowingsubsectionsprovideabriefillustrationoftheuseofevolutionarygametheoreticmodelstoexplaintwoareasofhumanbehavior.Thefirstconcernsthetendencyofpeopletoshareequallyinperfectlysymmetricsituations.Thesecondshowshowpopulationsofprelinguisticindividualsmaycoordinateontheuseofasimplesignalingsystemeventhoughtheylacktheabilitytocommunicate.Thesetwomodelshavebeenpointedtoaspreliminaryexplanationsofoursenseoffairnessandlanguage,respectively.Theywereselectedforinclusionhereprimarilybecauseoftherelativesimplicityofthemodelandapparentsuccessatexplainingthephenomenoninquestion.

4.1Asenseoffairness

Onenaturalgametouseforinvestigatingtheevolutionoffairnessisdividethecake(thisisthesimplestversionoftheNashbargaininggame).Inchapter1ofEvolutionoftheSocialContract,Skyrmspresentstheproblemasfollows:

Herewestartwithaverysimpleproblemwearetodivideachocolatecakebetweenus.Neitherofushasanyspecialclaimasagainsttheother.Outpositionsareentirelysymmetric.Thecakeisawindfallforus,anditisuptoustodivideit.Butifwecannotagreehowtoshareit,thecakewillspoilandwewillgetnothing.(Skyrms,1996,pp.34)

Moreformally,supposethattwoindividualsarepresentedwitharesourceofsizeCbyathirdparty.Astrategyforaplayer,inthisgame,consistsofanamountofcakethathewouldlike.Thesetofpossiblestrategiesforaplayeristhusanyamountbetween0andC.IfthesumofstrategiesforeachplayerislessthanorequaltoC,eachplayerreceivestheamountheaskedfor.However,ifthesumofstrategiesexceedsC,noplayerreceivesanything.Figure8illustratesthefeasiblesetforthisgame.

Figure8:ThefeasiblesetforthegameofDividetheCake.Inthisfigure,thecakeisofsizeC=10butallstrategiesbetween0and10inclusivearepermittedforeitherplayer(includingfractionaldemands).

WehaveaclearintuitionthattheobviousstrategyforeachplayertoselectisC/2thephilosophicalproblemliesinexplainingwhyagentswouldchoosethatstrategyratherthansomeotherone.Evenintheperfectlysymmetricsituation,answeringthisquestionismoredifficultthanitfirstappears.Toseethis,firstnoticethatthereareaninfinitenumberofNashequilibriaforthisgame.Ifplayer1asksforpofthecake,where0pC,andplayer2asksforCp,thenthisstrategyprofileisaNashequilibriumforanyvalueofp[0,C].(Eachplayer'sstrategyisabestresponsegivenwhattheotherhaschosen,inthesensethatneitherplayercanincreaseherpayoffbychangingherstrategy.)However,theequalsplitisonlyoneofinfinitelymanyNashequilibria.

OnemightproposethatbothplayersshouldchoosethatstrategywhichmaximizestheirexpectedpayoffontheassumptiontheyareuncertainastowhethertheywillbeassignedtheroleofPlayer1orPlayer2.Thisproposal,Skyrmsnotes,isessentiallythatofHarsanyi(1953).Theproblemwiththisisthatifplayersonlycareabouttheirexpectedpayoff,andtheythinkthatitisequallylikelythattheywillbeassignedtheroleofPlayer1orPlayer2,thenthis,too,failstoselectuniquelytheequalsplit.Considerthestrategyprofilep,CpwhichassignsPlayer1pslicesandPlayer2Cpslices.IfaplayerthinksitisequallylikelythathewillbeassignedtheroleofPlayer1orPlayer2,thenhisexpectedutilityisp+(Cp)=C/2,forallvaluesp[0,C].

Nowconsiderthefollowingevolutionarymodel:supposewehaveapopulationofindividualswhopairupandrepeatedlyplaythegameofdividethecake,modifyingtheirstrategiesovertimeinawaywhichisdescribedbythereplicatordynamics.Forconvenience,letusassumethatthecakeisdividedinto10equallysizedslicesandthateachplayer'sstrategyconformstooneofthefollowing11possibletypes:Demand0slices,Demand1slice,,Demand10slices.Forthereplicatordynamics,thestateofthepopulationisrepresentedbyavectorp0,p1,,p10whereeachpidenotesthefrequencyofthestrategyDemandislicesinthepopulation.

Thereplicatordynamicsallowsustomodelhowthedistributionofstrategiesinthepopulationchangesovertime,beginningfromaparticularinitialcondition.Figure9belowshowstwoevolutionaryoutcomesunderthecontinuousreplicatordynamics.Noticethatalthoughfairdivisioncanevolve,asinFigure9(a),itisnottheonlyevolutionaryoutcome,asFigure9(b)illustrates.

(a)Theevolutionoffairdivision.

(b)Theevolutionofanunequaldivisionrule.

Figure9:Twoevolutionaryoutcomesunderthecontinuousreplicatordynamicsforthegameofdividethecake.Oftheelevenstrategiespresent,onlythreearecolourcodedsoastobeidentifiableintheplot(seethelegend).Theinitialconditionsforthesolutionshownin(a)wasthepoint0.0544685,0.236312,0.0560727,0.0469244,0.0562243,0.0703294,0.151136,0.162231,0.0098273,0.111366,0.0451093,andtheinitialconditionsforthesolutionshownin(b)wasthepoint0.410376,0.107375,0.0253916,0.116684,0.0813494,0.00573677,0.0277155,0.0112791,0.0163166,0.191699,0.00607705.

Recallthatthetaskathandwastoexplainwhywethinktheobviousstrategychoiceinaperfectly

symmetricresourceallocationproblemisforbothplayerstoaskforhalfoftheresource.Whattheaboveshowsisthat,inapopulationofboundedlyrationalagentswhomodifytheirbehavioursinamannerdescribedbythereplicatordynamics,fairdivisionisone,althoughnottheonly,evolutionaryoutcome.Thetendencyoffairdivisiontoemerge,assumingthatanyinitialconditionisequallylikely,canbemeasuredbydeterminingthesizeofthebasinofattractionofthestatewhereeveryoneinthepopulationusesthestrategyDemand5slices.Skyrms(1996)measuresthesizeofthebasinofattractionoffairdivisionusingMonteCarlomethods,findingthatfairdivisionevolvesroughly62%ofthetime.

However,itisimportanttorealisethatthereplicatordynamicsassumesanypairwiseinteractionbetweenindividualsisequallylikely.Inreality,quiteofteninteractionsbetweenindividualsarecorrelatedtosomeextent.Correlatedinteractioncanoccurasaresultofspatiallocation(asshownaboveforthecaseofthespatialprisoner'sdilemma),thestructuringeffectofsocialrelations,oringroup/outgroupmembershipeffects,tolistafewcauses.

Whencorrelationisintroduced,thefrequencywithwhichfairdivisionemergeschangesdrastically.Figure10illustrateshowthebasinofattractionofAllDemand5changesasthecorrelationcoefficientincreasesfrom0to0.2.[7]Oncetheamountofcorrelationpresentintheinteractionsreaches=0.2,fairdivisionisvirtuallyanevolutionarycertainty.Notethatthisdoesnotdependonthereonlybeingthreestrategiespresent:allowingforsomecorrelationbetweeninteractionsincreasestheprobabilityoffairdivisionevolvingeveniftheinitialconditionscontainindividualsusinganyoftheelevenpossiblestrategies.

(a)=0 (b)=0.1

(c)=0.2

Figure10:Threediagramsshowinghow,astheamountofcorrelationamonginteractionsincreases,fairdivisionismorelikelytoevolve.

What,then,canweconcludefromthismodelregardingtheevolutionoffairdivision?Italldepends,ofcourse,onhowaccuratelythereplicatordynamicsmodelstheprimaryevolutionaryforces(culturalorbiological)actingonhumanpopulations.Althoughthereplicatordynamicsareasimplemathematicalmodel,itdoessufficeformodellingbothatypeofbiologicalevolution(seeTaylorandJonker,1978)andatypeofculturalevolution(seeBrgersandSarin,1996Weibull,1995).AsSkyrms(1996)notes:

Inafinitepopulation,inafinitetime,wherethereissomerandomelementinevolution,somereasonableamountofdivisibilityofthegoodandsomecorrelation,wecansaythatitislikelythatsomethingclosetoshareandsharealikeshouldevolveindividingthecakesituations.Thisis,perhaps,abeginningofanexplanationoftheoriginofourconceptofjustice.

Thisclaim,ofcourse,hasnotgonewithoutcomment.Foraselectionofsomediscussionsee,inparticular,D'Arms(1996,2000)D'Armsetal.,1998Danielson(1998)Bicchieri(1999)Kitcher(1999)Gintis(2000)Harms(2000)Krebs(2000)AlexanderandSkyrms(1999)andAlexander(2000,2007).

4.2Theemergenceoflanguage.

InhisseminalworkConvention,DavidLewisdevelopedtheideaofsenderreceivergames.Suchgameshavebeenusedtoexplainhowlanguage,andsemanticcontent,canemergeinacommunitywhichoriginallydidnotpossessanylanguagewhatsoever.[8]Hisoriginaldefinitionisasfollows(withportionsofextraneouscommentarydeletedforconcisionandpointsenumeratedforclarityandlaterreference):

AtwosidedsignalingproblemisasituationSinvolvinganagentcalledthecommunicatorandoneormoreotheragentscalledtheaudience,suchthatitistruethat,anditiscommonknowledgeforthecommunicatorandtheaudiencethat:

1. Exactlyoneofseveralalternativestatesofaffairss1,,smholds.Thecommunicator,butnottheaudience,isinagoodpositiontotellwhichoneitis.

2. Eachmemberoftheaudiencecandoanyoneofseveralalternativeactionsr1,,rmcalledresponses.Everyoneinvolvedwantstheaudience'sresponsestodependinacertainwayuponthestateofaffairsthatholds.ThereisacertainonetoonefunctionFfrom{si}onto{rj}suchthateveryoneprefersthateachmemberoftheaudiencedoF(si)onconditionthatsiholds,foreachsi.

3. Thecommunicatorcandoanyoneofseveralalternativeactions1,,n(nm)calledsignals.Theaudienceisinagoodpositiontotellwhichonehedoes.NooneinvolvedhasanypreferenceregardingtheseactionswhichisstrongenoughtooutweighhispreferenceforthedependenceFofaudience'sresponsesuponstatesofaffairs.[]

4. Acommunicator'scontingencyplanisanypossiblewayinwhichthecommunicator'ssignalmaydependuponthestateofaffairsthatheobservestohold.ItisafunctionFcfrom{si}into{k}.[]

5. Similarly,anaudience'scontingencyplanisanypossiblewayinwhichtheresponseofamemberoftheaudiencemaydependuponthesignalheobservesthecommunicatortogive.ItisaonetoonefunctionFafrompartof{k}into{rj}.

[]

WheneverFcandFacombine[]togivethepreferreddependenceoftheaudience'sresponseuponthestateofaffairs,wecallFc,Faasignalingsystem.(Lewis,1969,pp.130132)

SincethepublicationofConvention,itismorecommontorefertothecommunicatorasthesenderandthemembersoftheaudienceasreceivers.Thebasicideabehindsenderreceivergamesisthefollowing:Natureselectswhichstateoftheworldobtains.ThepersonintheroleofSenderobservesthisstateoftheworld(correctlyidentifyingit),andsendsasignaltothepersonintheroleofReceiver.TheReceiver,uponreceiptofthissignal,performsaresponse.IfwhattheReceiverdoesisthecorrectresponse,giventhestateoftheworld,thenbothplayersreceiveapayoffof1iftheReceiverperformedanincorrectresponse,thenbothplayersreceiveapayoffof0.Noticethat,inthissimplifiedmodel,nochanceoferrorexistsatanystage.TheSenderalwaysobservesthetruestateoftheworldandalwayssendsthesignalheintendedtosend.Likewise,theReceiveralwaysreceivesthesignalsentbytheSender(i.e.,thechannelisnotnoisy),andtheReceiveralwaysperformstheresponseheintendedto.

WhereasLewisallowedtheaudiencetoconsistofmorethanoneperson,itismorecommontoconsidersenderreceivergamesplayedbetweentwopeople,sothatthereisonlyasinglereceiver(or,inLewisianterms,asinglememberoftheaudience).[9]Forsimplicity,inthefollowingwewillconsideratwoplayer,senderreceivergamewithtwostatesoftheworld{S1,S2},twosignals{1,2},andtworesponses{r1,r2}.(Weshallseelaterwhylargersenderreceivergamesareincreasinglydifficulttoanalyse.)

Noticethat,inpoint(2)ofhisdefinitionofsenderreceivergames,Lewisrequirestwothings:thattherebeauniquebestresponsetothestateoftheworld(thisiswhatrequiringFtobeonetooneamountsto)andthateveryoneintheaudienceagreesthatthisisthecase.Sinceweareconsideringthecasewherethereisonlyasingleresponder,thesecondrequirementisotiose.Forthecaseoftwostatesoftheworldandtworesponses,thereareonlytwowaysofassigningresponsestostatesoftheworldwhichsatisfyLewis'srequirement.Theseareasfollows(whereXYdenotesinstateoftheworldX,thebestresponseistodoY):

1. S1r1,S2r2.2. S1r2,S2r1.

Itmakesnorealdifferenceforthemodelwhichoneofthesewechoose,sopicktheintuitiveone:instateoftheworldSi,thebestresponseisri(i.e.,function1).

Astrategyforthesender(whatLewiscalledacommunicator'scontingencyplan)consistsofafunctionspecifyingwhatsignalhesendsgiventhestateoftheworld.Itis,asLewisnotes,afunctionfromthesetofstatesoftheworldintothesetofsignals.Thismeansthatitispossiblethatasendermaysendthesamesignalintwodifferentstatesoftheworld.Suchastrategymakesnosense,fromarationalpointofview,becausethereceiverwouldnotgetenoughinformationtobeabletoidentifythecorrectresponseforthestateoftheworld.However,wedonotexcludethesestrategiesfromconsiderationbecausetheyarelogicallypossiblestrategies.

Howmanysenderstrategiesarethere?Becauseweallowforthepossibilityofthesamesignaltobesentformultiplestatesoftheworld,therearetwochoicesforwhichsignaltosendgivenstateS1andtwochoicesforwhichsignaltosendgivenstateS2.Thismeanstherearefourpossiblesenderstrategies.Thesestrategiesareasfollows(where'XY'meansthatwhenthestateoftheworldisXthesenderwillsendsignalY):

Sender1:S11,S21.Sender2:S11,S22.Sender3:S12,S21.Sender4:S12,S22.

Whatisastrategyforareceiver?Here,itprovesusefultodeviatefromLewis'soriginaldefinitionoftheaudience'scontingencyplan.Instead,letustakeareceiver'sstrategytobeafunctionfromthesetofsignalsintothesetofresponses.Asinthecaseofthesender,weallowthereceivertoperformthesameresponseformorethanonesignal.Bysymmetry,thismeansthereare4possiblereceiverstrategies.Thesereceiverstrategiesare:

Receiver1:1r1,2r1.Receiver2:1r1,2r2.Receiver3:1r2,2r1.Receiver4:1r2,2r2.

IftherolesofSenderandReceiverarepermanentlyassignedtoindividualsasLewisenvisagedthenthereareonlytwopossiblesignalingsystems:Sender2,Receiver2andSender3,Receiver3.Allotherpossiblecombinationsofstrategiesresultintheplayersfailingtocoordinate.ThecoordinationfailureoccursbecausetheSenderandReceiveronlypairtheappropriateactionwiththestateoftheworldinoneinstance,aswithSender1,Receiver1,ornotatall,aswithSender2,Receiver3.

WhatiftherolesofSenderandReceiverarenotpermanentlyassignedtoindividuals?Thatis,whatifnatureflipsacoinandassignsoneplayertotheroleofSenderandtheotherplayertotheroleofReceiver,andthenhasthemplaythegame?Inthiscase,aplayer'sstrategyneedstospecifywhathewilldowhenassignedtheroleofSender,aswellaswhathewilldowhenassignedtheroleofReceiver.SincetherearefourpossiblestrategiestouseasSenderandfourpossiblestrategiestouseasReceiver,thismeansthatthereareatotalof16possiblestrategiesforthesenderreceivergamewhenrolesarenotpermanentlyassignedtoindividuals.Here,aplayer'sstrategyconsistsofanorderedpair(SenderX,ReceiverY),whereX,Y{1,2,3,4}.

ItmakesadifferencewhetheroneconsiderstherolesofSenderandReceivertobepermanentlyassignedornot.Iftherolesareassignedatrandom,therearefoursignalingsystemsamongsttwoplayers[10]:

1. Player1:(Sender2,Receiver2),Player2:(Sender2,Receiver2)2. Player1:(Sender3,Receiver3),Player2:(Sender3,Receiver3)3. Player1:(Sender2,Receiver3),Player2:(Sender3,Receiver2)4. Player1:(Sender3,Receiver2),Player2:(Sender2,Receiver3)

Signalingsystems3and4arecurious.System3isacasewhere,forexample,IspeakinFrenchbutlisteninGerman,andyouspeakGermanbutlisteninFrench.(System4swapsFrenchandGermanforbothyouandme.)Noticethatinsystems3and4theplayersareabletocorrectlycoordinatetheresponsewiththestateoftheworldregardlessofwhogetsassignedtheroleofSenderorReceiver.

Theproblem,ofcourse,withsignalingsystems3and4isthatneitherPlayer1norPlayer2woulddowellwhenpittedagainstacloneofhimself.Theyarecaseswherethesignalingsystemwouldnotworkinapopulationofplayerswhoarepairwiserandomlyassignedtoplaythesenderreceivergame.Infact,itisstraightforwardtoshowthatthestrategies(Sender2,Receiver2)and(Sender3,Receiver3)aretheonlyevolutionarilystablestrategies(seeSkyrms1996,8990).

Asafirstapproachtothedynamicsofsenderreceivergames,letusrestrictattentiontothefour

strategies(Sender1,Receiver1),(Sender2,Receiver2),(Sender3,Receiver3),and(Sender4,Receiver4).Figure11illustratesthestatespaceunderthecontinuousreplicatordynamicsforthesenderreceivergameconsistingoftwostatesoftheworld,twosignals,andtworesponses,whereplayersarerestrictedtousingoneofthepreviousfourstrategies.Onecanseethatevolutionleadsthepopulationinalmostallcases[11]toconvergetooneofthetwosignalingsystems.[12]

Figure11:Theevolutionofsignalingsystems.

Figure12illustratestheoutcomeofonerunofthereplicatordynamics(forasinglepopulationmodel)whereallsixteenpossiblestrategiesarerepresented.Weseethateventuallythepopulation,forthisparticularsetofinitialconditions,convergestooneofthepureLewisiansignallingsystemsidentifiedabove.

Figure12:Theevolutionofasignallingsystemunderthereplicatordynamics.

Whenthenumberofstatesoftheworld,thenumberofsignals,andthenumberofactionsincreasefrom2,thesituationrapidlybecomesmuchmorecomplex.IfthereareNstatesoftheworld,Nsignals,andNactions,thetotalnumberofpossiblestrategiesequalsN2N.ForN=2,thismeansthereare16possiblestrategies,aswehaveseen.ForN=3,thereare729possiblestrategies,andasignallingproblemwhereN=4has65,536possiblestrategies.Giventhis,onemightthinkthatitwouldprovedifficultforevolutiontosettleuponanoptimalsignallingsystem.

Suchanintuitioniscorrect.HofbauerandHutteger(2008)showthat,quiteoften,thereplicatordynamicswillconvergetoasuboptimaloutcomeinsignallinggames.Inthesesuboptimaloutcomes,apoolingorpartialpoolingequilibriumwillemerge.ApoolingequilibriumoccurswhentheSenderusesthesamesignalregardlessofthestateoftheworld.ApartialpoolingequilibriumoccurswhentheSenderiscapableofdifferentiatingbetweensomestatesoftheworldbutnotothers.Asanexampleofapartialpoolingequilibrium,considerthefollowingstrategiesforthecasewhereN=3:SupposethattheSendersendssignal1instateoftheworld1,andsignal2instatesoftheworld2and3.Furthermore,supposethattheReceiverperformsaction1uponreceiptofsignal1,andaction2uponreceiptofsignals2and3.Ifallstatesoftheworldareequiprobable,thisisapartialpoolingequilibrium.GiventhattheSenderdoesnotdifferentiatestatesoftheworld2and3,theReceivercannotimprovehispayoffsbyrespondingdifferentlytosignal2.GiventheparticularresponsebehaviouroftheReceiver,theSendercannotimproveherpayoffsbyattemptingtodifferentiatestatesoftheworld2and3.

5.PhilosophicalProblemsofEvolutionaryGameTheory

Thegrowinginterestamongsocialscientistsandphilosophersinevolutionarygametheoryhasraisedseveralphilosophicalquestions,primarilystemmingfromitsapplicationtohumansubjects.

5.1Themeaningoffitnessinculturalevolutionaryinterpretations

Asnotedpreviously,evolutionarygametheoreticmodelsmayoftenbegivenbothabiologicalandaculturalevolutionaryinterpretation.Inthebiologicalinterpretation,thenumericquantitieswhichplayaroleanalogoustoutilityintraditionalgametheorycorrespondtothefitness(typicallyDarwinianfitness)ofindividuals.[13]Howdoesoneinterpretfitnessintheculturalevolutionaryinterpretation?

Inmanycases,fitnessinculturalevolutionaryinterpretationsofevolutionarygametheoreticmodelsdirectlymeasuressomeobjectivequantityofwhichitcanbesafelyassumedthat(1)individualsalwayswantmoreratherthanlessand(2)interpersonalcomparisonsaremeaningful.Dependingontheparticularproblemmodeled,money,slicesofcake,oramountoflandwouldbeappropriateculturalevolutionaryinterpretationsoffitness.Requiringthatfitnessinculturalevolutionarygametheoreticmodelsconformtothisinterpretativeconstraintseverelylimitsthekindsofproblemsthatonecanaddress.Amoreusefulculturalevolutionaryframeworkwouldprovideamoregeneraltheorywhichdidnotrequirethatindividualfitnessbealinear(orstrictlyincreasing)functionoftheamountofsomerealquantity,likeamountoffood.

Intraditionalgametheory,astrategy'sfitnesswasmeasuredbytheexpectedutilityithadfortheindividualinquestion.Yetevolutionarygametheoryseekstodescribeindividualsoflimitedrationality(commonlyknownasboundedlyrationalindividuals),andtheutilitytheoryemployedintraditionalgametheoryassumeshighlyrationalindividuals.Consequently,theutilitytheoryusedintraditionalgametheorycannotsimplybecarriedovertoevolutionarygametheory.Onemustdevelopanalternatetheoryofutility/fitness,onecompatiblewiththeboundedrationalityofindividuals,thatissufficienttodefineautilitymeasureadequatefortheapplicationofevolutionarygametheorytoculturalevolution.

5.2Theexplanatoryirrelevanceofevolutionarygametheory

Anotherquestionfacingevolutionarygametheoreticexplanationsofsocialphenomenaconcernsthekindofexplanationitseekstogive.Dependingonthetypeofexplanationitseekstoprovide,areevolutionarygametheoreticexplanationsofsocialphenomenairrelevantormerevehiclesforthepromulgationofpreexistingvaluesandbiases?Tounderstandthisquestion,recognizethatonemustaskwhetherevolutionarygametheoreticexplanationstargettheetiologyofthephenomenoninquestion,thepersistenceofthephenomenon,orvariousaspectsofthenormativityattachedtothephenomenon.Thelattertwoquestionsseemdeeplyconnected,forpopulationmemberstypicallyenforcesocialbehaviorsandruleshavingnormativeforcebysanctionsplacedonthosefailingtocomplywiththerelevantnormandthepresenceofsanctions,ifsuitablystrong,explainsthepersistenceofthenorm.Thequestionregardingaphenomenon'setiology,ontheotherhand,canbeconsideredindependentofthelatterquestions.

Ifonewishestoexplainhowsomecurrentlyexistingsocialphenomenoncametobe,itisunclearwhyapproachingitfromthepointofviewofevolutionarygametheorywouldbeparticularilyilluminating.Theetiologyofanyphenomenonisauniquehistoricaleventand,assuch,canonlybediscoveredempirically,relyingontheworkofsociologists,anthropologists,archaeologists,andthelike.Althoughanevolutionarygametheoreticmodelmayexcludecertainhistoricalsequencesaspossiblehistories(sinceonemaybeabletoshowthattheculturalevolutionarydynamicsprecludeonesequencefromgeneratingthephenomenoninquestion),itseemsunlikelythatanevolutionarygametheoreticmodelwouldindicateauniquehistoricalsequencesufficestobringaboutthephenomenon.Anempiricalinquirywouldthenstillneedtobeconductedtoruleouttheextraneoushistoricalsequencesadmittedbythemodel,whichraisesthequestionofwhat,ifanything,wasgainedbytheconstructionofanevolutionarygametheoreticmodelintheintermediatestage.Moreover,evenifanevolutionarygametheoreticmodelindicatedthatasinglehistoricalsequencewascapableofproducingagivensocialphenomenon,thereremainstheimportantquestionofwhyweoughttotake

thisresultseriously.Onemaypointoutthatsincenearlyanyresultcanbeproducedbyamodelbysuitableadjustingofthedynamicsandinitialconditions,allthattheevolutionarygametheoristhasdoneisprovideonesuchmodel.Additionalworkneedstobedonetoshowthattheunderlyingassumptionsofthemodel(boththeculturalevolutionarydynamicsandtheinitialconditions)areempiricallysupported.Again,onemaywonderwhathasbeengainedbytheevolutionarymodelwoulditnothavebeenjustaseasytodeterminetheculturaldynamicsandinitialconditionsbeforehand,constructingthemodelafterwards?Ifso,itwouldseemthatthecontributionsmadebyevolutionarygametheoryinthiscontextsimplyareaproperpartoftheparentsocialsciencesociology,anthropology,economics,andsoon.Ifso,thenthereisnothingparticularaboutevolutionarygametheoryemployedintheexplanation,andthismeansthat,contrarytoappearances,evolutionarygametheoryisreallyirrelevanttothegivenexplanation.

Ifevolutionarygametheoreticmodelsdonotexplaintheetiologyofasocialphenomenon,presumablytheyexplainthepersistenceofthephenomenonorthenormativityattachedtoit.Yetwerarelyneedanevolutionarygametheoreticmodeltoidentifyaparticularsocialphenomenonasstableorpersistentasthatcanbedonebyobservationofpresentconditionsandexaminationofthehistoricalrecordshencethechargeofirrelevancyisraisedagain.Moreover,mostoftheevolutionarygametheoreticmodelsdevelopedtodatehaveprovidedthecrudestapproximationsoftherealculturaldynamicsdrivingthesocialphenomenoninquestion.Onemaywellwonderwhy,inthesecases,weshouldtakeseriouslythestabilityanalysisgivenbythemodelansweringthisquestionwouldrequireoneengageinanempiricalstudyaspreviouslydiscussed,ultimatelyleadingtothechargeofirrelevanceagain.

5.3Thevalueladennessofevolutionarygametheoreticexplanations

Ifoneseekstouseanevolutionarygametheoreticmodeltoexplainthenormativityattachedtoasocialrule,onemustexplainhowsuchanapproachavoidscommittingthesocallednaturalisticfallacyofinferringanoughtstatementfromaconjunctionofisstatements.[14]Assumingthattheexplanationdoesnotcommitsuchafallacy,oneargumentchargesthatitmustthenbethecasethattheevolutionarygametheoreticexplanationmerelyrepackagescertainkeyvalueclaimstacitlyassumedintheconstructionofthemodel.Afterall,sinceanyargumentwhoseconclusionisanormativestatementmusthaveatleastonenormativestatementinthepremises,anyevolutionarygametheoreticargumentpurportingtoshowhowcertainnormsacquirenormativeforcemustcontainatleastimplicitlyanormativestatementinthepremises.Consequently,thisapplicationofevolutionarygametheorydoesnotprovideaneutralanalysisofthenorminquestion,butmerelyactsasavehicleforadvancingparticularvalues,namelythosesmuggledinthepremises.

Thiscriticismseemslessseriousthanthechargeofirrelevancy.Culturalevolutionarygametheoreticexplanationsofnormsneednotsmuggleinnormativeclaimsinordertodrawnormativeconclusions.Thetheoryalreadycontains,initscore,apropersubtheoryhavingnormativecontentnamelyatheoryofrationalchoiceinwhichboundedlyrationalagentsactinordertomaximize,asbestastheycan,theirownselfinterest.Onemaychallengethesuitabilityofthisasafoundationforthenormativecontentofcertainclaims,butthisisadifferentcriticismfromtheabovecharge.Althoughculturalevolutionarygametheoreticmodelsdoactasvehiclesforpromulgatingcertainvalues,theywearthoseminimalvaluecommitmentsontheirsleeve.Evolutionaryexplanationsofsocialnormshavethevirtueofmakingtheirvaluecommitmentsexplicitandalsoofshowinghowothernormativecommitments(suchasfairdivisionincertainbargainingsituations,orcooperationintheprisoner'sdilemma)maybederivedfromtheprincipledactionofboundedlyrational,selfinterestedagents.

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