Policy “Games”

Strategic Decisions Strategic Decisions & Game Theory& Game Theory

2

Outline Defining strategic gamesDefining strategic games Considering some common examples of strategic games in Considering some common examples of strategic games in

policy settingspolicy settings Working through solution concepts and mechanicsWorking through solution concepts and mechanics

Simultaneous gamesSimultaneous games Sequential gamesSequential games

Understanding and countering strategic movesUnderstanding and countering strategic moves Advantages and disadvantages of going firstAdvantages and disadvantages of going first Bargaining games & experimental outcomesBargaining games & experimental outcomes

3

Defining “Strategic Decisions” In narrow sense used here, strategic decisions (games) In narrow sense used here, strategic decisions (games)

meanmean Decisions where optimal strategies of 2 (or more) Decisions where optimal strategies of 2 (or more)

players are actively interdependentplayers are actively interdependent Optimal strategy depends on predictions of other Optimal strategy depends on predictions of other

participant(s) best strategyparticipant(s) best strategy Not just “playing against nature or world” with Not just “playing against nature or world” with

fixed prices, probabilities, behaviorfixed prices, probabilities, behavior Think chess, poker, or rock-paper-scissors, not Think chess, poker, or rock-paper-scissors, not

roulletteroullette

Some Policy-related Games

Prisoner’s dilemmaPrisoner’s dilemma Hostage’s dilemmaHostage’s dilemma Samaritan’s dilemmaSamaritan’s dilemma Agenda ControlAgenda Control Fed Time ConsistencyFed Time Consistency Median Voter Model (Location Game)Median Voter Model (Location Game) BargainingBargaining Terms limits & unravelingTerms limits & unraveling

Prisoner’s Dilemma 2 criminals arrested for crime2 criminals arrested for crime

Interrogated separately Interrogated separately Choices: Confess/Don’t confessChoices: Confess/Don’t confess

Confession by one leads to low/high Confession by one leads to low/high sentencessentences

Confession by both leads to moderate Confession by both leads to moderate sentencessentences

Confession by neither leads to acquittalConfession by neither leads to acquittal Not Confess = “cooperative”, positive sum (for Not Confess = “cooperative”, positive sum (for

participants) solutionparticipants) solution Confess = competitive solutionConfess = competitive solution

5

Prisoner’s Dilemma-like Games

Hostage’s DilemmaHostage’s Dilemma Multi-person version of PDMulti-person version of PD Positive sum through cooperationPositive sum through cooperation Non-cooperative solution often Non-cooperative solution often

dominatesdominates Oligopoly Games (pricing, ads, entry, …)Oligopoly Games (pricing, ads, entry, …)

Cooperation (maybe implicit) leads to Cooperation (maybe implicit) leads to higher profits than competitionhigher profits than competition

6

Samaritan’s Dilemma

Giver-RecipientGiver-Recipient Giver: I’ll give you $X, when that’s gone, you Giver: I’ll give you $X, when that’s gone, you

are on your own (or if you do Y, the money are on your own (or if you do Y, the money stops)stops)

Recipient: knows giver’s preferences -- Recipient: knows giver’s preferences -- recipient “starvation” is “worst case”recipient “starvation” is “worst case”

Equilibrium: recipient abuses gift, gets moreEquilibrium: recipient abuses gift, gets more Ex: Parent-child; gov’t-recipient; moral Ex: Parent-child; gov’t-recipient; moral

hazard & catastropheshazard & catastrophes

7

Fed Money Game Strategic setupStrategic setup

Fed money-inflation policyFed money-inflation policy Citizens form inflation expectationsCitizens form inflation expectations Sequence of actions/reactions/anticipationsSequence of actions/reactions/anticipations

If citizens think Fed is keeping inflation low, Fed can spur If citizens think Fed is keeping inflation low, Fed can spur sluggish economy with more money; citizens treat as more sluggish economy with more money; citizens treat as more income/output rather than as lower dollar valueincome/output rather than as lower dollar value

Citizens adjust expectations, expect higher inflationCitizens adjust expectations, expect higher inflation Less money creation to slow inflation now leads to slower Less money creation to slow inflation now leads to slower

income/output but inflation doesn’t respond quicklyincome/output but inflation doesn’t respond quickly Fed must rebuild reputation for low inflation policyFed must rebuild reputation for low inflation policy

“Location” Games Where to setup shop if consumer/voters positioned along a Where to setup shop if consumer/voters positioned along a

road or distributed about a point uniformly or normal road or distributed about a point uniformly or normal distribution, given that competitor is trying to setup shop distribution, given that competitor is trying to setup shop in best location also?in best location also?

Simple Solution: Move to the middle (median), otherwise, Simple Solution: Move to the middle (median), otherwise, competitor can locate just to the “busier” side and capture competitor can locate just to the “busier” side and capture everyone on that sideeveryone on that side

Examples: Median voter model and evidence such as Examples: Median voter model and evidence such as primary & general election races; retail shopsprimary & general election races; retail shops

Complications: multiple dimensions to choiceComplications: multiple dimensions to choice

9

Political Chess

Tom Hanks directed a 12 part HBO series-- Tom Hanks directed a 12 part HBO series-- From the Earth to the From the Earth to the MoonMoon– dramatizing the U.S. space program from Mercury through – dramatizing the U.S. space program from Mercury through the Apollo moon landings. One segment depicts the events of Apollo the Apollo moon landings. One segment depicts the events of Apollo 1 in which three astronauts died in a capsule fire during a routine test. 1 in which three astronauts died in a capsule fire during a routine test. The fire resulted from a spark in wiring causing the highly The fire resulted from a spark in wiring causing the highly pressurized, pure oxygen air in the capsule to ignite and reach pressurized, pure oxygen air in the capsule to ignite and reach temperatures over 1000 degrees 15 seconds. The capsule contractor -- temperatures over 1000 degrees 15 seconds. The capsule contractor -- North American and its executive in charge of the Apollo – learned North American and its executive in charge of the Apollo – learned that NASA would likely lay substantial blame on North American.  that NASA would likely lay substantial blame on North American.  The NA executive, a hardworking and upstanding person, is outraged The NA executive, a hardworking and upstanding person, is outraged and explains to his boss how NA should expose NASA by providing and explains to his boss how NA should expose NASA by providing Congress with documentation of the written warnings to NASA about Congress with documentation of the written warnings to NASA about the dangers of a pure oxygen gas system as well as pressurized tests at the dangers of a pure oxygen gas system as well as pressurized tests at sea level. His boss says , no,we’re not and goes on to respond. Can sea level. His boss says , no,we’re not and goes on to respond. Can you make sense of the boss’ decision?you make sense of the boss’ decision?

The boss looked ahead to the Congress/NASA relationship should The boss looked ahead to the Congress/NASA relationship should NASA be exposed or not, and worked backward to the effect on NANASA be exposed or not, and worked backward to the effect on NA

10

Changing the game: Fight or Die

Upon arriving in Mexico, Cortez burned his Upon arriving in Mexico, Cortez burned his shipsships

His crew now had strongest possible His crew now had strongest possible incentive to fight as hard as possibleincentive to fight as hard as possible

Example of changing the nature of the game Example of changing the nature of the game by changing player optionsby changing player options

Ex: Limiting rival options through big, Ex: Limiting rival options through big, irreversible investmentsirreversible investments

11

12

A Sampler of Strategic Decisions

Strategic SituationsStrategic Situations Bidding-Negotiation; Auctions; Bidding-Negotiation; Auctions;

(homes, cars, yard sales, …) (homes, cars, yard sales, …) Employment: Job Market; Employment: Job Market;

Board-Management; Board-Management; Management-Labor; Management-Labor;

Politics/Group DynamicsPolitics/Group Dynamics Pricing, Ad, … CompetitionPricing, Ad, … Competition Dating, MarriageDating, Marriage Families: Parent-Child, Families: Parent-Child,

Spouses, SiblingsSpouses, Siblings Games: Poker, … Games: Poker, …

Strategic-Related Strategic-Related BehaviorBehavior

Signaling & Filtering Signaling & Filtering InformationInformation

Altering Perceptions-BeliefsAltering Perceptions-Beliefs Promises/ThreatsPromises/Threats Changing “Rules” (nature of Changing “Rules” (nature of

game)game) Repeated IDsRepeated IDs Mixing ActionsMixing Actions Incentives for CooperationIncentives for Cooperation Cooperation-Compete Cooperation-Compete

DilemmasDilemmas Free-RidingFree-Riding

13

Six Essentials Questions of SDs Who are Key Decision makers (units)? Who are Key Decision makers (units)?

Who are the decision entities?Who are the decision entities? What is the Timing of DecisionsWhat is the Timing of Decisions??

Sequences or simultaneous? Sequences or simultaneous? One-shot or repeated?One-shot or repeated?

What Information is Available?What Information is Available? What do players know/believe?What do players know/believe?

What Actions are Possible?What Actions are Possible? Aggressive/passive; high/low; fold/bluff; …Aggressive/passive; high/low; fold/bluff; … CooperationCooperation

Payoffs to decisions?Payoffs to decisions? Fixed sum, positive sum, or negative sum?Fixed sum, positive sum, or negative sum? Quantitative & qualitativeQuantitative & qualitative

Manipulation Possibilities? Manipulation Possibilities? Can players alter rules or beliefs of others? Can players alter rules or beliefs of others?

Practicing Essentials: PD Decision Makers?Decision Makers? Timing?Timing? Info?Info? Actions?Actions? Payoffs?Payoffs? Manipulation?Manipulation?

Decision Makers: 2 Accused (police in background)Decision Makers: 2 Accused (police in background) Timing: Effectively simultaneous because of lack of info even if Timing: Effectively simultaneous because of lack of info even if

sequential in real timesequential in real time Info: Not aware of other’s choice until no return/police info not Info: Not aware of other’s choice until no return/police info not

reliable reliable Actions: Confess or not (highly simplified)Actions: Confess or not (highly simplified) Payoffs: Variable sum, higher if cooperationPayoffs: Variable sum, higher if cooperation Manipulation: Not in simple versionManipulation: Not in simple version

Solution Concepts ““Nash Equilibrium”: outcome where Nash Equilibrium”: outcome where

opponent doing best possible opponent doing best possible Sequential Sequential

““Rollback”: Look ahead to last period Rollback”: Look ahead to last period and work backand work back

Simultaneous Simultaneous Iterative: step-by-step analysis of best Iterative: step-by-step analysis of best

choice given a decision by otherchoice given a decision by other Repeated SimultaneousRepeated Simultaneous

Rollback + IterativeRollback + Iterative 15

Solution Mechanics: “Classic PD” Example• Payoffs = (jail time for #1, jail time for #2)

Prisoner 2Prisoner 2CC NCNC

Prisoner 1Prisoner 1CC 1010,10,10 11,,2020NCNC 2020,,11 33,,33

Solution Mechanics: “Classic PD” Example

• Iterative: prisoner 1 considers best choice if #2 confesses (column 1) & chooses C (time = 10); #1 considers best choice if #2 not confess & chooses C (payoff = 1); NC is dominant strategy for #1

Prisoner 2Prisoner 2CC

Prisoner 1Prisoner 1CC 1010,10,10 NCNC 2020,,11

Best outcome for #1, if # 2 Confesses

Solution Mechanics: “Classic PD” Example

• #1 considers best choice if #2 not confess & chooses C (payoff = 1);

• C is dominant strategy for #1; always better than NC

Prisoner 2Prisoner 2NCNC

Prisoner 1Prisoner 1CC 11,,2020NCNC 33,,33

Best outcome for #1, if#2 no confess

Samaritan’s Dilemma • Recipient Chooses High Effort (HE) or Low Effort (LE);

Giver Chooses Pay or No Pay; Payoffs (Recipient; Giver)

• Can you find the typical solution: consider Giver’s payoffs in view of recipient’s choices

GiverGiverPayPay No PayNo Pay

RecipientRecipientHEHE 1010,100,100 00,,2020LELE 100100,,1010 2020,,00

Samaritan’s Dilemma • Iterative solution: If Recipient HE, Giver Pay; If Recipient

LE, Giver Pay – Pay dominant for Giver (the dilemma); recipient exploits this information and chooses LE

GiverGiverPayPay No PayNo Pay

RecipientRecipientHEHE 1010,100,100 00,,2020LELE 100100,,1010 2020,,00

Dominant outcome

Sequential Mechanics: Agenda Control byLooking Ahead and Working Back Rules of order may seem trivial, but where they are strictly Rules of order may seem trivial, but where they are strictly

followed, they empower strategic decision makersfollowed, they empower strategic decision makers Suppose a committee made up of members who favor Suppose a committee made up of members who favor

proposal s (E), (M), and (R). They must decide on a single proposal s (E), (M), and (R). They must decide on a single proposal and the mix of members creates the following likely proposal and the mix of members creates the following likely voting outcomes:voting outcomes: E prefers: E > M > RE prefers: E > M > R M prefers: M > R > EM prefers: M > R > E R prefers: R > E > MR prefers: R > E > M So, E beats M, M beat R, and R beats ESo, E beats M, M beat R, and R beats E

How should chairperson structure the vote if wants M to How should chairperson structure the vote if wants M to win? win?

Voting Possibilities: Game Tree

Vote 1 Vote 2Vote 1 Vote 2 WinnerWinner R v. MR v. M M v. EM v. E E E

M v. EM v. E E v. RE v. R R R

E v. R E v. R R v. MR v. M M M

22

Sequential Solutions: Looking Ahead

Vote 2Vote 2 WinnerWinnerM v. EM v. E E E

E v. RE v. R R R

R v. MR v. M M M For M to win in the second vote, the matchup must be For M to win in the second vote, the matchup must be

R v. M, so eliminate other options R v. M, so eliminate other options 23

Sequential Solutions: Looking Ahead and Working Back Vote 1 Vote 2Vote 1 Vote 2 WinnerWinner R v. MR v. M

M v. EM v. E

E v. R E v. R R v. MR v. M M M

With options in vote 2 paired down, the choice for vote 1 becomes clearWith options in vote 2 paired down, the choice for vote 1 becomes clear

24

25

Strategic Moves: Manipulating the Game Changing order of movesChanging order of moves

Agenda control exampleAgenda control example Changing information or beliefs Changing information or beliefs

Threats, promises, credibility Threats, promises, credibility Poker examples (info sending & receiving)Poker examples (info sending & receiving) nuclear deterrencenuclear deterrence

Changing available strategiesChanging available strategies CortezCortez

Changing payoffs or beliefs about themChanging payoffs or beliefs about them Negotiation & “salami tactics” Negotiation & “salami tactics” Use of agents, e.g. retailUse of agents, e.g. retail

26

Countering Strategic Moves:Manipulating Manipulators Order counter-measuresOrder counter-measures

Amendments, coalitions, …Amendments, coalitions, … Information-Extraction countermeasuresInformation-Extraction countermeasures

Signal-Jamming, e.g. vaguenessSignal-Jamming, e.g. vagueness Threat/promise countermeasuresThreat/promise countermeasures

Brinksmanship; salamiBrinksmanship; salami Option/payoff-limiting countermeasuresOption/payoff-limiting countermeasures

Expand Options, e.g., Exclude Agents-Non-Expand Options, e.g., Exclude Agents-Non-decision makersdecision makers

Salami (more increments/consistency in Salami (more increments/consistency in payoffs, e.g. Hawken research)payoffs, e.g. Hawken research)

27

Misc. SD Observations:First or Second Mover Advantage? First Mover Advantage if manipulation of game First Mover Advantage if manipulation of game

possible through changing game or beliefs of rivalpossible through changing game or beliefs of rival – – Princess BridePrincess Bride

Second Mover Advantage if information becomes Second Mover Advantage if information becomes available by rival’s move available by rival’s move

Sailing; NCAA Football Overtime; Sailing; NCAA Football Overtime; What about “Hold-em” Poker?What about “Hold-em” Poker?

Tradeoff: manipulation v. info gatheringTradeoff: manipulation v. info gathering

28

Misc. SD Observations:Bargaining Ultimatum Game (and related) theory and experimentationUltimatum Game (and related) theory and experimentation

UG = split of pot if 2 parties agree on split; 1 makes offer-UG = split of pot if 2 parties agree on split; 1 makes offer-1 accepts or declines offer; 1 accepts or declines offer;

Variations: size of pot; depreciation of pot; anonymity; Variations: size of pot; depreciation of pot; anonymity; repetitionrepetition

Money matters but not all that mattersMoney matters but not all that matters Typical outcomes: bigger than 99:1, less than 50:50Typical outcomes: bigger than 99:1, less than 50:50

Time Values Time Values Patience is a virtue Patience is a virtue Patience is the best signal of patiencePatience is the best signal of patience

29

Misc SD Observations:Bargaining Tradeoffs Custom Home ProjectCustom Home Project

Builder-HomeownerBuilder-HomeownerBuilder info advantageBuilder info advantage

Options: Options: Flex Price w/fixed percentageFlex Price w/fixed percentageFixed-Price w/negotiated changesFixed-Price w/negotiated changes

Info/Incentive TradeoffsInfo/Incentive TradeoffsFlex: flexibility of changes; no “hold-out Flex: flexibility of changes; no “hold-out

problem”; wrong incentive for info problemproblem”; wrong incentive for info problemFixed: Incentive to monitor & control expenses; Fixed: Incentive to monitor & control expenses;

“hold-out” problem on changes; incentive to cut “hold-out” problem on changes; incentive to cut cornerscorners