Beyond the Prisoners Dilemma - McAdams

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BEYONDTHEPRISONERSDILEMMA:COORDINATION,GAMETHEORYANDTHELAW

RichardH.McAdams

THE LAW SCHOOL THE UNIVERSITY OF CHICAGO

October2008

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ESSAY

BEYONDTHEPRISONERSDILEMMA:COORDINATION,GAMETHEORY,ANDLAW

RichardH.McAdams

TableofContentsINTRODUCTION.....................................................2I.ALLTHEPRISONERSDILEMMAALLTHETIME........................6II.WHATTHEPRISONERSDILEMMAOBSCURES:THESIMPLEGAMESOFCOORDINATION.............................11 A.TheAssuranceorStagHuntGame.......................13 B.TheBattleoftheSexesGame............................15 C.TheHawkDoveorChickenGame........................16III.WHATLEGALSCHOLARSHIPNEGLECTS:THEIMPORTANCEOFCOORDINATIONPROBLEMSTOLAW............19

A.TheFrequencyofCoordinationGames.......................19B.ThreeReasonsWhyCoordinationMatterstoLaw.............25 1.Inequality......................................25

2.TheInfluenceofHistoryandCultureonBehavior.......263.TheFocalPointPowerofLegalExpression............28

C.LegalApplicationsoftheThreeCoordinationGames...........31 1.BattleoftheSexes...............................31 2.Hawk/Dove...................................38 3.Assurance....................................43IV.INTELLECTUALEXCHANGEBETWEENLAWANDSOCIETYANDLAWANDECONOMICSSCHOLARSHIP.........................50CONCLUSION......................................................54

BernardD.MeltzerProfessor,UniversityofChicagoLawSchool, 1111E. 60thStreet,Chicago, IL 60637 (773)8342520, [email protected]. I thankDouglasBaird,LeeFennell, Ehud Gattel, Keith Hylton, Randy Picker and the participants in the BostonUniversityLaw&EconomicsworkshopandtheConferenceonBehavioralApproachestoLegalCompliance,BarIlanandHebrewUniversities,forthoughtfulcommentsonearlierdrafts.


September 15, 2008 GAME THEORY AND LAW 2

INTRODUCTION

Inreviewingagametheorytextalmosttwentyyearsago,IanAyrescomplained that countless law review articles rearticulate thePrisoners Dilemma, but few even proceed to the simplest of othergames.1Severalyearslater,instillthemostsignificantbooktreatmentofgametheoryfor law,DouglasBaird,RobertGertner,andRandallPickerbeganbylamentinghowlegalscholarshadneglectedgametheoryuptothat point other than to invoke a simple game such as the prisonersdilemma as a metaphor for a collective action problem.2 All of thesescholarsassertedthegreatvalueofgametheorytolegalanalysisandthehopethatitwouldtransformlegaltheoryasithastransformedeconomictheory.

That transformation has not occurred, at least not in the lawreview literature.Tothecontrary,thediagnosisofAyres,Baird,GertnerandPickerremainsexactlytruetoday:legalscholarsarenearlyobsessedwith the Prisoners Dilemma, mentioning the game in a staggeringnumber of law review articles (over 3000), but virtually ignoring otherequallysimplegamesofferingequallysharpinsightsintolegalproblems.One has to guess that the former obsession contributes to the latterneglect.Havinglearnedonetoolverywell,legalscholarseithershoehornsituations that are not Prisoners Dilemmas into that framework or,recognizing that the problem is not a PrisonersDilemma, give up ongame theory. For certain, this diagnosis does not apply to the formalmodelers,manywithPh.D.s ineconomics,whopublishpredominantlyinpeerreviewed lawandeconomics journals.But,asIshowbelow, thefarmore typical story for legal scholars is touse game theory only byusing thePrisonersDilemma.And thisoutcome, Icontend, is likeonlyusing mathematics when the problem involves odd numbers betweentwelveandtwohundred.

1 IanAyres, PlayingGameswith the Law, 42 STAN. L. REV. 1291, 129596 (1990) (bookreviewofERICRASMUSEN,GAMESAND INFORMATION:AN INTRODUCTIONTOGAMETHEORY(1989)) (Law review articles continued to be mindlessly mired in the game theorytechnologyofthefifties.).2DOUGLASG.BAIRD,ROBERTH.GERTNER&RANDALC.PICKER,GAMETHEORYAND THELAW1(1996).


Game theory contains many tools and insights beyond thePrisonersDilemma,toomanytobethesubjectofanessay.Nodoubttheformalmodelerswouldpointoutthegreaterrealismofusinggameswithcontinuous rather than discrete strategies,3 sequential rather thansimultaneous moves,4 asymmetric information,5 as well as models ofevolutionaryemergenceofequilibrium.6Mostcontemporarygametheoryisnotaboutgameswithpreexistingnames like thePrisonersDilemmaor the alternatives I discuss below, but concerns games the modelerconstructs to fit the situation being studied. Yet this is the kind ofcomplaint that Baird, Gertner, and Picker raised previously. I want totakeadifferent,morepracticalpathincriticizingthelawprofessorsuseof game theory, one that borrows from another applied field, politicalscience. That work demonstrates that in situations just as basic as thePrisonersDilemmawithtwoplayers,twodiscretestrategies,completeinformation, and simultaneous moves there is a world of value ingamesotherthanthePrisonersDilemma.7Ifocusonthreesuchgames,allinvolvingproblemsofcoordination8thatdonotariseinthePrisonersDilemma,andallhavinggreatvalueforlegaltheory.

WhywouldlegalscholarsfocusonthePrisonersDilemmatothepointwhereitobscuresotherinsightsofgametheory?Whatisthegamesallure? Two features that narrow the games application also make ittempting to a legal scholar. When played just once, the PrisonersDilemma is one of the few games with a single equilibrium. Anequilibrium is central to game theory; it is an outcome where each

3See,e.g.,ERICRASMUSEN,GAMESANDINFORMATION74106(4thed.2006).4Seee.g.,DREWFUDENBERG&JEANTIROLE,GAMETHEORY65206(2002).5 See, e.g., ERIC RASMUSEN, GAMES AND INFORMATION 169369 (4th ed. 2006); DREWFUNDENBERG&JEANTIROLE,GAMETHEORY207434(2002).6See,e.g.,H.PEYTONYOUNG,STRATEGICLEARNINGANDITSLIMITS(2004);DREWFUDENBERG&DAVIDK.LEVINE,THETHEORYOFLEARNINGINGAMES(1998).7Atthesametime,onemustbeawareofthelimitstosimplemodels,situationswhereomitting certain complexities to the game leads to the wrong conclusions. See, e.g.,DOUGLASG.BAIRD,ROBERTH.GERTNER&RANDALC.PICKER,GAMETHEORYANDTHELAW188218(1996)(chapteronCollectiveActionandtheLimitsofSimpleModels).8 Some essential works on coordination are THOMAS C. SCHELLING, THE STRATEGY OFCONFLICT (1960); DAVID LEWIS, CONVENTION (1969); EDNA ULLMANNMARGALIT, THEEMERGENCE OF NORMS 74133 (1977); ROBERT SUGDEN, THE ECONOMICS OF RIGHTS,COOPERATION, AND WELFARE 55103 (1986); BRIAN SKYRMS, THE STAG HUNT AND THEEVOLUTIONOFSOCIALSTRUCTURE(2004).


individualisplayingherbestresponsetowhateveryoneelseisdoing.Atsuchapoint,noonewantstoswitchstrategies.9Singleequilibriumgamesprovidea tidyanddefinitivepredictionof thebehavioraloutcome.Onecan therefore ignorecultureandhistorybecause,once factored into thepayoffs, their influence is fullyexhausted.10A second temptationof thePrisonersDilemma isauniquenormativefeature:everyonecanbemadebetteroffbylegalsanctionsthatsolvethegame.SoiftheproblemisaPrisonersDilemma,thecaseforalegalsolutionisunusuallystrong.

By contrast, coordination games have multiple equilibria andtherefore lack these allures. There being more than one equilibriummeansthatthepayoffsalonedonotdeterminethebehavioraloutcome.Inthis case, the economist concedes that history and culture (or otherfactors)mayaffectbehaviorindependentofinadditiontotheireffectonpayoffs.11Predictionismessy.Second,gamesotherthanthePrisonersDilemma frequently present no opportunity for a solution makingeveryone better off. Instead, coordination games oftenpresent a choicebetween conflictingpreferencesofdifferent individuals,whichmustbemadeonthebasisofsomecomplexandcontestablenormativetheory.12

9Moreprecisely,anequilibriumreferstoaNashequilibrium,which

is the central solution concept in game theory. It is based on theprinciple that the combination of strategies that players are likely tochooseisoneinwhichnoplayercoulddobetterbychoosingadifferentstrategygiventheonestheotherschoose.Apairofstrategieswillforma Nash equilibrium if each strategy is one that cannot be improvedupon given the other strategy. We establish whether a particularstrategy combination forms a Nash equilibrium by asking if eitherplayerhasanincentivetodeviatefromit.

DOUGLASG.BAIRD,ROBERTH.GERTNER&RANDALC.PICKER,GAMETHEORYANDTHELAW310(1996)(emphasisdeleted).10Forexample,ifanindividualgainssomeextrabenefitfromanoutcomebecauseofanemotionalattachmenttoaparticularculturalidentity,thegametheoristwillaccordinglyraise the payoffs to that individual for that outcome. If there remains only oneequilibrium,thentheeffectofcultureisentirelylimitedtothewayitaffectspayoffs.11Incontrasttothepriorfootnote,ifthepayoffspermitmultipleequilibria,culturemaynotonlyaffectthepayoffs,butalsoaffectthechoicebetweenthemultipleequilibria.Forexample,ifthepayoffsdontdetermineauniqueequilibrium,individualswiththesamepayoffsbutdifferentculturalidentitiesmayplaythegamedifferently.Seethediscussionoffocalpointsandcultureatinfratextaccompanyingnotes____.12See, e.g.,LEWISKAPLOW&STEVENSHAVELL,FAIRNESSVS.WELFARE1537 (2002); JOHNRAWLS, JUSTICEASFAIRNESS:ARESTATEMENT (2001);MARTHAC.NUSSBAUM,WOMENANDHUMANDEVELOPMENT:THECAPABILITIESAPPROACH(2000).


Inshort, there isastrong temptation todescribeasituationasaPrisoners Dilemma because it renders the problem amenable to anuncontroversiallegalsolution.Thisessay,however,describesthebenefitsof resisting this temptation,ofopeningoneseyes tomoregame theorythanthatonetrick,howeverclever.Coordinationproblemsarecommonandimportanttolaw,andthereismuchtobelearnedfromusingsimplegames to analyze them. Unlike the Prisoners Dilemma, coordinationgamesdescribe situations involving inequality, reveal how culture andhistory powerfully affect behavior, and demonstrate how law worksexpressively. These games provide unique insights into bargaining,constitutional law, democratic stability, international law, standardsetting, traffic regulation, property norms, gender roles, and socialmovements.Politicalscientists,economists,philosophers,and justa fewlegal scholars have begun exploring these matters. The theoreticalinsights alreadymade, however, no doubt only scratch the surface forwhatispossibleiflegalscholarsweretoengagethesealternativegamesasintensely as they have explored the Prisoners Dilemma. The mainpurposeofthisessayistoencouragelegalscholarstoexploitthepotentialof this sort of game theory and to correct the imbalance that currentlyoveremphasizesthePrisonersDilemma.

I also explain how coordination games provide a bridge forintellectual exchangebetween two rival schools of thought that largelyignore each other: Law & Economics and Law & Society. Though thelatter group mostly shuns game theory, it turns out that the socialproblemsLaw&Societyscholarsexploreareoverwhelmingcoordinationproblems,notPrisonersDilemmas.Eachgroupmightunderstandbetterthecontributionsoftheotheriflegalscholarsusinggametheoryweretofocusmoreattentiononthesealternativegames.

PartIintroducesthePrisonersDilemmaandgivessomemeasureof itsenormous influenceover legalscholarship.PartII introducesthreesimplegamesAssurance,HawkDove,andBattleoftheSexesthatareat least as common as the Prisoners Dilemma, but that are virtuallyneglectedby legal scholarship. InPart III, Idescribe someof themanywaysthesegamesilluminatelegalproblems,showingthemtobeatleastas important to law as the Prisoners Dilemma. Part IV discusses


opportunities for intellectual exchange between Law&Economics andLaw&Society.PartVconcludes.

I.ALLTHEPRISONERSDILEMMAALLTHETIME

The problem of cooperation exemplified by the PrisonersDilemma (PD) is one of the most dominant paradigms of recenttheoreticalworkineconomics,politics,andlaw.AsRobertAxelrodputsit:ThetwopersoniteratedPrisonersDilemmaistheE.coliofthesocialsciences.13 Legal scholars make great use of the concept, havingmentioned it an astonishingnumber of law reviewpublications over3000according tomyWestlawsearch14 toexplore topicsrangingfromcontracts15 and property,16 to international law,17 race discrimination,18feminism,19 social norms,20 the federal judiciary,21 and, indeed, actual

13ROBERTAXELROD,THECOMPLEXITYOFCOOPERATIONii(1997).14 I searched on August 12, 2008 in the JLS database for prisoners dilemma orprisonersdilemmaandtheresultwas3,051documents.Prisonersdilemma isnotavalidsearchtermbecauseofthewayWestlawreadsanapostropheattheendofaword,but the search I ranpicksup thisusageanyway. Ifweadd to the search thePrisonersDilemmas multiparty cousin the Social Dilemma, the yield is 3376 documents,althoughsomeoftheseusetheterminanonstrategicsense(asasynonymforthetermsocialproblem).15 See, e.g., Wayne Eastman, How Coasean Bargaining Entails a Prisoners Dilemma, 72NOTRE DAME L. REV. 89 (1996); Robert L. Birmingham, The Duty to Disclose and thePrisonersDilemma: Laidlawv.Organ,29WM.&MARYL.REV.249(1988);RobertE.Scott,ConflictandCooperationinLongTermContracts,75CAL.LAWREV.2005(1987).16See, e.g.,ELINOROSTROM,GOVERNINGTHECOMMONS:THEEVOLUTIONOF INSTITUTIONSFOR COLLECTIVE ACTION 2338 (1990); Wendy J. Gordon, AsymmetricMarket Failure andPrisonersDilemmainIntellectualProperty,17U.DAYTONL.REV.853(1992).17See,e.g.,GeorgeNorman&JoelP.Trachtman,TheCustomaryInternationalLawGame,99 AMER. J. INTL. LAW 541 (2005); John K. Setear, Responses to Breach of a Treaty andRationalistInternationalRelationsTheory,83VA.L.REV.1,2732(1997)18See,e.g.,RichardH.McAdams,CooperationandConflict:TheEconomicsofGroupStatusProductionandRaceDiscrimination,108Harv.L.Rev.1003(1995).19See,e.g.,CarolM.Rose,WomenandProperty:GainingandLosingGround,78VA.L.REV.421 (1992); H.E. Baber, Tomboys, Femmes and PrisonersDilemmas, 9 J. CONTEMP. LEGALISSUES37(1998).20See,e.g.,ROBERTAXELROD,THEEVOLUTIONOFCOOPERATION(1984);ERICA.POSNER,LAWANDSOCIALNORMS(2000);PaulG.Mahoney&ChrisW.Sanchirico,CompetingNormsandSocialEvolution:IstheFittestNormEfficient?,149U.PA.L.REV.2027(2001).21See, e.g.,ThomasW.Merrill,Pluralism, thePrisonersDilemma, and theBehavior of theIndependentJudiciary,88NW.U.L.REV.396(1993);DavidS.Law,AppointingFederalJudges:ThePresident,TheSenate,andThePrisonersDilemma,26CARDOZOLAWREV.479(2005).


prisoners.22LegaltheoristsusethePDtoexplainothermajorconceptsinlawe.g.,thetragedyofthecommons,23thepublicgoodsproblem,24andtrust,25allwhicharethemselvesrelevanttomanyareasoflaw.

Givenmythesis,thePDneedsalmostnointroduction,yetitwillhelpgreatly toreview the iconicnarrativefromwhich thegamegets itsname.Aprosecutorsuspectstwoprisonersofafelony,butcancurrentlyprove their involvement only in amisdemeanor.The prosecutor offerseachprisonerthesameinducementtoconfesstothefelony,summarizedbelowinFigure1:Ifyouaretheonlyonetoconfess,Iwillrewardyoubydroppingallcharges,whichisrepresentedinFigure1bythepayoffof0.Ifyouaretheonlyonenottoconfess,Iwilluseyourconfederatestestimonytoconvictyouofthefelonyandobtainforyouthemaximumfiveyearsinprison(5);ifneitherofyouconfesses,youeachgetoneyearfor themisdemeanor (1); ifbothconfess, Iwillconvictyoubothof thefelonybutgiveyouan intermediatesentenceofthreeyears(3).Inthiscontext, toselect thestrategyofnotconfessing is tocooperateand toselect the strategy of confessing is to defect.Altruism can of coursechangethegame,butthestandardassumption isthattheprisonerscareonlyabouttheirownpunishment.

Prisoner2

22See,e.g.,RussellDeanCovey,BeatingthePrisoneratPrisonersDilemma:TheEvidentiaryValueofaWitnesssRefusaltoTestify,47AM.U.L.REV.105(1997).23See,HanochDagan&MichaelA.Heller,TheLiberalCommons,110YALEL.J.549,555(2001)(Most lawyers,economists,andothersocialscientists learnof the tragedyof thecommons in the firstweeksofschool,andallare taught thatcommonsproperty is theaxiomaticexampleofaprisonersdilemma.).24See,e.g.,RichardA.Epstein,AFarewelltoPragmatism,71U.CHI.L.REV.675,677(2004)(referring to the creationofpublicgoods asoccurring when statepowerblocks thedegenerative outcomes of the standard prisoners dilemma game.); Sean J. Griffith,SpinningandUnderpricing:LegalandEconomicAnalysisofthePreferentialAllocationofSharesinInitialPublicOfferings,69BROOK.L.REV.583,610n.91(2004)(Themostfamiliarofthese[socialdilemmas] is the prisonersdilemma,butother termsare commonlyapplied tothe same general problem, including social traps, the tragedy of the commons, andpublicgoods/freeridingproblems.).25 See, e.g., Karen Eggleston, Eric A. Posner & Richard Zeckhauser, The Design andInterpretationofContracts:WhyComplexityMatters,95Nw.U.L.Rev.91,115(2000)(Oneusefulmodelof trust treats itasanattributeof relationships inwhich twoparties inarepeatedprisonersdilemmacooperateratherthanriskretaliation.).


Prisoner1 Cooperate Defect

Cooperate 1,1 5,0

Defect 0,5 3,3

Figure1:TheClassicPrisonersDilemma

Withthesepayoffs, ifPrisoner2cooperates,Player1 isbetteroffdefecting (receiving a payoff of 0) than cooperating (1).26 If Player 2defects, Player 1 is better off defecting (3) than cooperating (5).Therefore,Player1hasadominantstrategyofdefecting; it isherbestmove regardlessofwhatPlayer2does.Because thepayoffs shownaresymmetric, Player 2 has the same dominant strategy. Thus, the onlyequilibrium is Defect/Defect. In Figure 1, and subsequent matrices, Iindicateanequilibriumbyunderliningthepayoffs.Thegameistermedadilemmabecausethistheoreticallyinevitableoutcomeisworseforeachprisonerthananotherpossibleoutcome,Cooperate/Cooperate.

A simple Westlaw search reveals a staggering 3000+ articlesreferring to the PD,27 which contrasts with only trivial attention tocoordinationgamesofequal legalsignificance (asdemonstratedbelow).OnewaytotellthatlegalscholarsgiveexcessiveattentiontothePDistonote how scholars misdescribe and misapply the game. First, scholarssometimes attempt to shoehorn a nonPD situation into the PDmodeltheyfindsoalluring.Asimpleexampleisarunonabank.Quiteafewarticlesclaimthat[b]ankrunsrepresentaclassicprisonersdilemma.28

26NoticethatinFigure1asineverymatrixthepayoffsforPlayer1areontheleftineachcellandthepayoffsforPlayer2areontheright.27Seesupranote__.28 SeeMarkE.VanDerWeide& SatishM.Kini, SubordinatedDebt:ACapitalMarketsApproachtoBankRegulation,41B.C.L.Rev.195,204(2000).SeealsoR.NicholasRodelli,TheNewOperatingStandardsforSection20Subsidiaries:TheFederalReserveBoardsPrudentmarchTowardFinancialServicesModernization,2N.C.BANKINGINST.311,31516(1998);DanielR.Fischel,Andrew M. Rosenfield & Robert S. Stillman, The Regulation of Banks and BankHoldingCompanies,73VA.L.REV.301,30708 (1987); JonathanR.Macey,TheBusiness ofBanking:BeforeandAfterGrammLeachBliley,25J.CORP.L.691,696(2000).OnAugust12,2008,myWestlawsearchintheJLRdatabasefor(run/3bank)/p(prisoner/2dilemma)yielded tendocuments.Bycontrast,aparallelsearch forarticles involving themostaptcoordinationgame(staghuntorassurance,explainedbelow)todescribeabankrun,theyieldwaszero.IthankKeithHyltonforsuggestingthisexample.


On thisview, [d]epositorswillbebetteroff individually if they couldbeat their fellow depositors to the bank and reclaim their depositswhenever there is the slightest bit of uncertainty about the value of abanks assets.29Yet a PrisonersDilemma is surely a poormodel of abank run.Abettermodelwould includeboth theequilibriumoutcomewherethebankisstableasbanksusuallyareandalsotheequilibriumwherethereisarun.ThePrisonersDilemmagamecanatbestapplyonlyaftersomeuncertaintyarisesaboutthebank.Bycontrast,thesimplegame of Assurance, discussed below,30 describes both the efficientdepositequilibriumandtheinefficientrunequilibriumandthewaythat uncertainty or a lack of assurance tips the situation from theformertothelatter.

ThePrisonersDilemmagameisalsoapoormodelofabankrunbecause,evenaftertheslightestbitofuncertaintyarisesinabank,itisnot necessarily the best strategy for each depositor to reclaim herdeposit.Depositorsincurcostsinremovingdeposits.Ifsomeuncertaintyarises about person As bank, and yet others will not reclaim theirdeposits,thenAwillhavenointerestinincurringthecostsofreclaiminghers. It isonlywhensheexpectsothers towithdraw theirdeposits thatshe wants to withdraw hers. The difference between wanting to takesomeactionnomatterwhattheothersdoandwantingtotakesomeactiononlyifothersalsodothesamemayseemsmall,butthePrisonersDilemmaisstrictlylimitedtotheformercase.Asweshallsee,thelattersituationisaboutcoordinatingonesbehaviorwithothers.

Yetthedistinctionisoftenoverlooked.Evenwhendescribingtheoriginal PD scenario, quite a few scholars posit payoffs where the bestoutcome for a player freedom from prison occurs when neither partyconfesses.31This is an error.Bypositing thatmutual silence allowsboth

29SeeJonathanR.Macey,TheBusinessofBanking:BeforeandAfterGrammLeachBliley,25J.CORP.L.691,696(2000).30Seeinfratextaccompanyingnotes__.31 Some smart scholars make this error. Robert Birmingham observes that JudgeEasterbrookmisdescribesaPrisonersDilemmainPagev.UnitedStates,884F.2d300,301(7thCir.1989)(emphasisadded),whenhesays:

Twoprisoners,unabletoconferwithoneanother,mustdecidewhetherto take theprosecutorsoffer:confess, inculpate theother,andserveayear in jail,orkeep silentand serve fiveyears. If theprisoners could


prisoners to avoid any penalty, these scholars create a situationwhereeachprisonerwants toconfessonly if theotherconfesses;eachwants toremain silent if the other remains silent. As a result, there are twoequilibria(Confess/ConfessandSilence/Silence)andthesituationisnotaPD,butoneof thecoordinationgamesdiscussedbelow. Isuspect thesescholarsmake this error despite knowing the game theory because, intrying quickly to recall the PD scenario frommemory, they imagine aprosecutor/prisoner bargaining situation that seems realistic and typical,which iswheremutualsilence isbest.It just turnsoutsurprise! thatmanyrealisticandtypicallegalsituationsarenotPDs.BelowweseehowadifferentgameAssurancehelpstounderstandtheseinteractions.

makea(binding)bargainwitheachother,theywouldkeepsilentandbothwouldgofree.Buttheycantcommunicate,andeachfearsthattheotherwilltalk.Sobothconfess.

Butifmutualsilenceequalmutualfreedom,whileasoleconfessorservesoneyear(andasolenonconfessorgetsfive),thenthebestresponsetosilence issilence.TocreateaPD,theprosecutormustensurethateitherprisonercanobtainherbestoutcomenoprisononlyifsheisthesoleconfessor.Soifbotharesilent,theymustbothservesometime,asfor a minor crime the prosecutor can already prove. See Robert Birmingham, TellingAlternative Stories: Heterodox Versions of the Prisoners Dilemma, the Coase Theorem, andSupplyDemandEquilibrium,29CONN.L.REV.827,84245(1997)(firstmakingthiscriticism).

LeeFennellcatchesthesameerrorinherreviewofROBINPAULMALLOY,LAWINAMARKETCONTEXT:ANINTRODUCTIONTOMARKETCONCEPTSINLEGALREASONING(2004).SeeLeeAnneFennell,BookNote,55 J.LEGALED.295,30001 (2005). Ihave found fiveotherexamples just in thepast threeyears:DavidMcGowan,Politics,OfficePolitics, andLegalEthics:ACaseStudyintheStrategyofJudgment,20GEO.J.LEGALETHICS1057,1072(2007)(Ifthey cooperate with one another by remaining silent, each receives no penalty (or arelatively light one).); Jonathan T. Schmidt,Note,KeepingU.S.CourtsOpen to ForeignAntitrustPlaintiffs:AHybridApproach to theEffectiveDeterrenceof InternationalCartels,31YALE J. INTLL.211,234 (2006)(showingchartwithoutcome formutualsilencebeingnopenalty,whilethesoleconfessorgetsalightpenaltyofoneyear);GlennHarrison&Matthew Bell, Recent Enhancements in Antitrust Criminal Enforcement: Bigger Sticks andSweeterCarrots,6HOUS.BUS.&TAXL.J.207,216(2006)(Ifneitherprisonerconfesses,bothgofree);GeoffreyP.Miller,TheLegalFunctionofRitual,80CHI.KENTL.REV.1181,1185(2005)(Ifneitherconfesses,bothwillgofree,while ifonlyoneconfesses,theconfessorwillserveonlyashortsentence(say,oneyear));PamelaH.Bucy,GameTheoryandtheCivilFalseClaimsAct:IteratedGamesandCloseKnitGroups,35LOY.U.CHI.L.J.1021,1028n.46(2004)(Ifbothprisonersrefusetoconfess,theybothgofree.Otherwise,theprisonerwhoconfessesfirstgetsashortprisonsentence...).


Inanyevent,theseexamplesarenotalone.32LegalscholarsseemtowearPDcoloredlensesthattrickthemintoseeingsomethingthatisntthere.Letusnowconsiderwhattheyarefailingtosee.

II.WHATTHEPRISONERSDILEMMAOBSCURES:THREESIMPLEGAMESOFCOORDINATION

ThePrisonersDilemmagameisabrilliantwayofillustratingtheproblem of cooperation. Where selfish pursuits lead individuals tooutcomes thatareworse for each than someotherachievableoutcome,theyneed to findhow to cooperate to reach thebetteroutcome.Tobeclear, Ihavenoquarrelwith the remarkablepowerof thisanalysis:PDproblems are prevalent, their solution frequently offers anuncontroversialway to improve socialwelfare, and legal sanctions areoften necessary and sufficient to solve such problems. But cooperationfailuresarenottheonlyobstaclesindividualsfacetoachievingtheirends.Gametheoryidentifiesanotherpervasiveproblem:theneedtocoordinate.Usinggamesassimpleas thePD, the theorydemonstrateswhysocietyneedsmechanismsforcoordinationasmuchas itneedsmechanismsforcooperation.Asweshallsee, lawservestheformerfunctionasmuchasthelatter.

To illustrateacoordinationproblem,considerasimplevariationon the canonicalnarrativeof thePD.Theprosecutorplaces indifferentinterrogation rooms two prisonerswho jointly committed some crime.Suppose,however,thattheprosecutorscaseissoweakthattheprisonerscoulddefeat theprosecutorand free themselves if,butonly if, theycangive a consistent alibi for theirwhereabouts at the time of the crime. Itwontworkfortheprisonerstosaytheywereeachaloneatthetime;theyeach need someone to confirm their alibi and, because they are guilty, 32Bankruptcy issimilar.Whenuncertaintyarises,creditorscanmakearunon theirdebtorjustasdepositorsmakearunonabank.ThomasJacksondescribesthissituationasa PrisonersDilemma, see ThomasH. Jackson, Bankruptcy,NonBankruptcy Entitlements,and theCreditorsBargain,91YALEL.J.857 (1982),but thesameproblemsarise.First, thegame describes the situation that exists only after the perception of insolvency arises,where a game discussed below (Assurance) also captures the original situation ofperceivedsolvency.Second,becausecallinginaloaniscostly,creditorAmaynotwanttobearthiscostifnoneoftheothercreditorscallintheirloan.


eachknows that she can rely onno one except the otherprisoner.Buttheydidnotagreeonanalibiinadvance.Eachprisonerthinksofvariouspossibilities:theywereatoneoftheirhomesortheother,atthemovies,outhunting,etc.Theproblem isthatneitherknowswhatalibitheotherwillchoose.Moregenerally, theproblemofcoordinationarisesbecausethere is more than one path to some desired outcome, both want tochoose compatible paths, but neither knowswhich path the otherwilltake.LetuscalltheexamplethePrisoners(Pure)Coordinationgame.33

Coordination is a pervasive concern of law. There are manycoordination games, but I limit myself here to three classics: (1) theAssuranceorStagHuntgame,(2)theHawk/DoveorChickengame,andthe (3) Battle of the Sexes. Unlike the PD, these games require anintroductionbecausetheyareroutinelyignoredbythelegalscholarship.Incontrastto3051hitsforPD,34aWestlawsearchreveals121referencestotheAssuranceorStagHuntgame,35101referencestotheHawk/DoveorChickengame,36and75referencesoftheBattleoftheSexesgame.37Inotherwords,theseothergamesarementioned,respectively,4%,3%,and2.5%asoftenasthePDgame.Thenumberofarticlesmentioninganyofthese three games is 243, or 8% of the PD total.38 So let usmeet theseneglectedtoolsoflegalanalysis.

33Thegameisapurecoordinationgamebecausethereisnoelementofconflict.Eachplayer is indifferentamong theequilibriaandcaresonlyaboutcoordinating.Theclassicexampleisthechoiceofdrivingontheleftortherightsideoftheroad.34Seesupratextaccompanyingnotes__.35My search termswere:staghuntorassurancegame.All the searches reportedherewereconductedonAugust12,2008intheJLRdatabase.36Mysearchtermswere:chickengameor(hawk/sdove/sgame).37Mysearchtermswere:(battle/ssexes/sgame).38My search combined the above three searches,disjunctively. The combined searchresultof243yieldsfewerdocumentsthanaddingthethreeindividualgametotalsbecausesomedocumentsmentionmorethanoneofthegames.Yetthesegamesarethemostlikelycoordination games to be mentioned. Indeed, my search for the generic termcoordination game yielded only 238 documents. There is, however, some slightmovementintherightdirection.Limitingthepriorsearchestopublicationssince2002,Ifound 1048 articles referencing the PD and 104 referencing any one of the threecoordinationgame,whichis10%ofthePDtotal.


A.TheAssuranceorStagHuntGame

Figure 2 depicts what is known as a Stag Hunt or Assurancegame.39Here, if Player 2 selects StrategyA, then Player 1 is better offselecting Strategy A and receiving 4 than selecting Strategy B andreceiving3.IfPlayer2selectsStrategyB,however,thenPlayerAisbetteroffselectingStrategyB(receiving3insteadof0).Becausethepayoffsaresymmetric,Player2hasthesamepreferences.Thus,theplayerswanttomatch strategiesand thegamehas two (pure strategy)40equilibria:A/AandB/B.

Player2

Player1 StrategyA StrategyB

StrategyA 4,4 0,3

StrategyB 3,0 3,3

Figure2:AnAssuranceorStagHuntGame

The players have the same preferences, each preferring A/A toB/B. This common interest might make it trivially easy to reach themutually desired outcome. But the problem here is the riskiness ofStrategyA.SelectingStrategyBguaranteesareturnof3,whileStrategyAwillearneither4or0.Forthisreason,bothPlayersmightselecttheless

39 See, e.g., BRIAN SKYRMS, THE STAG HUNT AND THE EVOLUTION OF SOCIAL STRUCTURE(2004);DENNISCHONG,COLLECTIVEACTIONANDTHECIVILRIGHTSMOVEMENT10340(1991);GaryBornstein&ZoharGilula,BetweenGroupCommunication andConflictResolution inAssurance and Chicken Games, 47 J. CONFLICT RES. 326 (2003); Amartya Sen, Isolation,Assurance, and the Social Rate ofDiscount, 81 QUART. J. ECON. 112 (1967). For technicaldifferences inAssuranceandStagHunt,whichneednotconcernushere,seeBAIRD,GERTNER&PICKER,supranote16,at301,315.40Apure strategy isone that selects (inagiven circumstance)a certainmoveorbehavior with certainty. This approach is contrasted with a mixed strategy, whichinvolves (in a given circumstance) selecting among at least two moves with someprobabilitiesthatsumtoone.Concordantly,inapurestrategyequilibrium,eachplayeradoptsaparticularstrategywithcertainty,whereasinamixedstrategyequilibriumoneor more of the players adopts a strategy that randomizes among a number of purestrategies.SeeDOUGLASG.BAIRD,ROBERTH.GERTNER&RANDALC.PICKER,GAMETHEORYANDTHELAW313(1996).Tokeepthingssimple,Ifocusonpurestrategyequilibria.


riskyStrategyBandwindupinequilibriumB/Bdespitethefactthateachregards B/B as worse than A/A. The players thus face a problem ofcoordination.

ThegamedrawsoneofitsnamesAssurancefromthefactthateachneedstoassuretheotherthatsheisgoingtoplaytheriskierstrategyAso theothershouldaswell.41ThenameStagHuntcomes fromRousseausillustration42ofthechoicebetweenhuntingstagandhuntinghare,where one succeeds inhunting stag only if the otherhunter alsohunts stag, where sharing a stag with the other hunter is the bestoutcome, butwhere hunting hare is safer because one can succeed ononesown.

One illustrationof thegame is thebank rundiscussedabove,although that obviously involves more than two players.43 Everyonewants to keep their money in the bank if everyone else does, but toremove theirmoney if enough others are going to remove theirs. Theefficient equilibrium iswheredepositorsgain theadvantageofpoolingtheir resources, but the inefficient equilibrium results when everyoneseekstoavoidtheriskofpoolingandgoitalone.Thegamecapturesthefactthat,intimesofuncertainty,thedepositorsneedtoassureeachotherthattheywillnotpanic.UnlikethePD,ifnooneelsewillwithdrawtheirdepositinfear,thereisnoreasonforyoutodoso.

As another example of Assurance, consider again a prosecutorbargainingwithprisoners. Suppose that,unlike thePD, theprosecutorhassolittleevidencethatshecannotconvicteitherprisonerofanycrimeifneitherconfesses.Unlike theaboveexample, theyneednotevengivean alibi to avoid punishment; they need merely remain silent to bothwalkfree.Againstthisbestoutcome,theprosecutoroffersaprisontermof7yearseachifbothconfess,1yearforbeingthesoleconfessor,and12yearsforbeingthesolenonconfessor.Ifso,theneachprisonerwantstoassure theother that shewill remain silent;neitherwants to confess if

41See,e.g.,DENNISCHONG,COLLECTIVEACTIONANDTHECIVILRIGHTSMOVEMENT10340(1991);AmartyaSen,Isolation,Assurance,andtheSocialRateofDiscount,81QUART.J.ECON.112(1967).42JEANJACQUESROUSSEAU,ADISCOURSEONINEQUALITYIII(Trans.M.Cranston1984).43Seetextaccompanyingnotes__.


they expect that the otherwill not confess.44The PrisonersAssurancegamemust behighlyplausible because it is the set of facts bywhichsomescholarsmisdescribethePD.45Indeed,ChristopherLeslieconfirmsthat this result is common in antitrust conspiracies: if the prosecutorcantprovetheconspiracy,shecantproveanyoffense.46

B.TheBattleoftheSexesGame

Figure 3 illustrates theBattleof the Sexes (BOS)game,wheretheworstoutcome foreachplayer is the failure tomatchstrategies,butwhereoneplayerprefersmatching at StrategyA and theotherprefersmatchingatStrategyB.47Specifically,ifPlayer2selectsstrategyA,Player1 isbetteroff selectingStrategyA (receiving3 insteadof0). IfPlayer2selectsStrategyB,Player1 isbetteroffselectingStrategyB (receiving1insteadof0).Player2spreferencesareparallel, so thereare two (purestrategy)equilibria:A/AandB/B.UnlikeAssurance,thereisconflictherebecausePlayer1prefersA/AandPlayer2prefersB/B.LikeAssurance,theplayersagreeon theneed toavoid certainoutcomes,B/AandA/B,eachofwhichisworseforbothplayersthaneitherequilibrium.

Player2

44OnemightchallengetheexamplebysayingthataprosecutorwouldalwayschoosetomakethegameaPDbyofferingzeroyearsifadefendantistheonlyonewhoconfesses(insteadof1).Inthatcase,itseemstobeweaklydominanttoconfess,whichisbetterfortheprosecutor.Yet the reality is thatmostdefendantswillnever regardanoutcomeofconfessing and avoiding criminal sanctions as being as good as not confessing andavoidingcriminalsanctions.First,confessingmayforcetheconfessortostopengaginginprofitable illegal activities, such as an ongoing pricefixing scheme. Second, there is areputationalcost tobeinga snitch.Third, thedefendantmayhave some smallaltruismtowards her criminal confederates. However small these effects are, the best outcomewhentheprosecutorcantconvicteitherwithoutaconfessionismutualsilence,inwhichcasethegameisAssuranceandnotPD.45Seesupranote__.46 SeeChristopherR. Leslie, Trust,Distrust, andAntitrust, 82 TEX. L. REV. 515, 63839(2004) (Yet in most criminal antitrust prosecutions, the authorities do not have solidevidenceof aminor crime. . . .Without sufficient evidenceof aminor crime, antitrustauthoritiesneed some leverage to convince cartelists to confess.Otherwise, there isnoPrisonersDilemma.). 47See,e.g.,RussellCooper,etal.,ForwardInductionintheBattleoftheSexesGames83Amer.Econ.Rev.1303(1993).



StrategyA 3,1 0,0

StrategyB 0,0 1,3

Figure3:ABattleoftheSexesGame

Althoughanygamethissimplewillmissmuchnuance,theBOSisausefulmodelofbargaining.Thegamealsomodelsstandardsetting,aswhere different firms or industries need to agree to certain technicalstandards to allow their products to interact. I explore these examplesbelow.

We can also return to prosecutorial bargaining with prisoners.Supposetheprosecutorhasenoughinformationtochargebothprisonerswithasubstantiveoffenseandwithaconspiracytocommitthatoffense.In response, A and B could each assert that a particular one of themcommittedtheoffensealone.Ifso,thenneitherprisonercanbeconvictedof the crime of conspiracy; the confessorwill be convicted only of thesubstantive offense and the other prisoner will go free. The strategyobviouslyrequirescoordinationbecausetheywillfailtobecredibleandfail todefeat the conspiracy charge if they eachpoint the finger at theotheroreachpointthefingeratthemselves.BeingaBOS,eachprefersadifferent equilibrium the one where the other prisoner takesresponsibility. InsteadofaPrisonersDilemma,wehave thePrisonersBattleoftheSexesgame.

C.TheHawkDoveorChickenGame

TheChickenorHawkDove(HD)posesacoordinationproblembut onewith even greater conflict than the BOS.48 Figure 4 illustrates.Giventhosepayoffs,ifPlayer2selectsthestrategyDove,thenPlayer1sbest response isHawk (receiving 4 insteadof 2 fromplayingDove). IfPlayer2selectsHawk,thenPlayer1sbestresponseisDove(receiving0 48See,e.g.,ROBERTSUGDEN,THEECONOMICSOFRIGHTS,COOPERATION,ANDWELFARE55103(1986);GaryBornstein,DavidBudescu&ShmuelZamir,CooperationinIntergroup,NPerson,andTwoPersonGamesofChicken,41 J.CONFLICTRES.384 (1997);HughWard,TheRisksofaReputation forToughness:Strategy inPublicGoodsProvisionProblemsModelledbyChickenSupergames,17BRIT.J.POL.SCI.23(1987).


insteadof1fromplayingHawk).Becausethepayoffsaresymmetric,theconverse is trueforPlayer2,whichmeansthereare two(purestrategy)equilibria:Dove/HawkandHawk/Dove.

Player2

Player1 Dove Hawk

Dove 2,2 0,4

Hawk 4,0 1,1

Figure4:AHawkDoveGame

Most obviously, there is conflict because each equilibrium hasdramatically unequal payoffs, one favoring Player 1 and the otherfavoringPlayer2.Butthereisalsoaproblemofcoordinationbecausetheplayers have a common interest in avoidingwhat each regards as theworstpossibleoutcomeHawk/Hawk.Eventhoughthatoutcomeisnotanequilibrium(becauseatthatpointaplayerwouldprefertounilaterallyswitch strategies), ifbothplayers aim for theirpreferredoutcomebysimultaneouslyplayingHawk, that is exactlywhat results.49 Indeed, inthe alternative name Chicken comes from a fictional game betweenteenagerswhodrivetheircarsdirectlyateachother,wheretheonewhoswervesfirstlosesface,butthefailureofeithertoswerveiscatastrophic.50

Inthenextpart,IclaimthatdisputesoftenhavethestructureofaHD game. For now, consider again the setting of prosecutorialbargaining. Suppose that theprosecutorhas somuch evidence that shecanconvictbothprisonersofaseriousoffensewithoutaconfession.Butimaginethateitherprisonercan,bysnitching,revealevidencethatthetrue perpetrator is a previously unsuspected person C, therebyexoneratingbothprisoners.Theproblemisthattheprisonerseachprefer 49TheothernonequilibriumoutcomeisDove/Dove.InFigure4,thejointpayoffsatthisoutcome(2+2=4)arethesameasthejointoutcomeatthetwoequilibria(4+0=4).Thisis not necessary; the joint Dove/Dove payoffs could be less or more than the jointequilibriapayoffs.Iftheyaremore,thenwealsohaveacooperationprobleminreachingthisefficientoutcome.50SeeRebelWithoutaCause(WarnerBrothers1955).


that theotheroneactasasnitchbecauseeachknows thatasnitchmaysufferretaliationbyCorothercriminals.Eachprisonerthereforeregardsthe best outcome as to remain silent while the other snitches, but theworstoutcometobewhereneithersnitchesandbothareimprisonedforacrime theydidnotcommit.51But theonly two (purestrategy)equilibriainvolve exactly one snitcher: Snitch/Be Silent and Be Silent/Snitch.52InsteadofthePD,thisisthePrisonersHDgame.

*****

In thePD,aprisoneralwaysdoesbetterbyconfessinganddoesbestbybeingtheonlyonetoconfess.Butinfourotherequallyplausiblecases ofprosecutorial bargaining, that isnot the case. In thePrisoners(Pure)Coordinationgame,onedoesbestbymatchingwhateveralibitheotherprisonergives.InthePrisonersAssurancegame,aprisonerwantstoreciprocatetheotherprisonersdecisionandonedoesbestbymutualsilence. In the Prisoners BOS game, one wants to cast all blame onwhicheverprisonertheotherprisonerblames;onedoesbestbymutuallyblamingtheotherprisoner.InthePrisonersChickengame,onewantstobesilentiftheotherprisonersnitchesonthethirdpartywhocommittedthe crime but to snitch if the otherprisoner is silent; onedoes bestbyhavingtheotherprisonersnitch.

Thisessay isnot justaboutprosecutorialbargaining,as thenextsectiondemonstrates.But takingseriously the iconicscenarioof thePDtellsus something of the excessive influence of thatgame.Because thelegal/game theory literature discusses prisoner/prosecutor bargainingonly in terms of the PD, onemight think that the PD is the standardsituationthatactualconspiratorsface,i.e.,thatprosecutorsalwayscreateadilemmaforthem.ButtheconditionsallowingthePDarespecificandnarrow. Collectively, the other four situations seem at least equallyplausible, probably more so. No doubt, legal scholars recognize thisempirical fact,but fail to imagine thatgame theoryalsonicelycaptures

51Eachwouldalsopreferthatbothsnitchtobeingtheonlysnitch,becausethereissomesafetyinnumbers.52ThiskindofHDorChickengameissometimescalledtheVolunteersDilemma,butit isnotaPD (because it isnotadominantstrategy toavoidvolunteering).SeeWILLIAMPOUNDSTONE:PRISONERSDILEMMA:JOHNVONNEUMANN,GAMETHEORY,ANDTHEPUZZLEOFTHEBOMB20104(1992).


the situations that are not PDs. In the next section, we see how theproblemgeneralizes.

III.WHATLEGALSCHOLARSHIPNEGLECTS:THEIMPORTANCEOFCOORDINATIONPROBLEMSTOLAW

There is nothing exotic about the three coordination gamesintroduced in the last part Stag Hunt, Battle of the Sexes, andHawk/Dove.Theywereidentifiedandnameddecadesago,havebeenthesubjectofenormous theoreticalandempiricalwork,andare thoughtbygame theorists to typifymany situationsof social interaction. Indeed, Ihavechosenthembecause,amongthegamesassimpleasthePD,thesethreehavethemostobvioususefulnessforlaw.Yetthedegreetowhichlegalscholarshipusesthesegamesisutterlytrivialwhencomparedtotheattention (obsession?) given to the PD. No one of these games ismentioned inmore than 4% of the number of articles that cite the PDgame;collectivelytheyreceive8%ofthereferencesasthePD.53

I can only imagine two possible justifications for this disparity:thatonebelievesthatthePDgameisfarmorecommonthanthesethreecoordinationgamesorthatonebelievesthatthecoordinationgamesarenot relevant to the situations law addresses. As I show in this part,neitheristrue.SectionAlooksattheissueabstractly,identifyingseveralreasonstobelievethatcoordinationproblemsareatleastaspervasiveasPDs. Section B explains three ways that coordination problems mattergenerally for law. Finally, SectionC considers individually each of thethree games (BOS, HD, and Assurance) and reviews some literature,published almost entirely outside of law reviews, that uses them toilluminate legal issues. The point here is not to be exhaustive animpossible task in an essay but to show something of the untappedpotentialforgamesotherthanthePD.

A.TheFrequencyofCoordinationGames

53Seesupratextaccompanyingnote__.


In the real world, coordination games occur no less frequentlythan PD games. In later sections, I argue for this proposition withconcrete examples. Initially, however, consider three abstractobservations.First,thePDrepresentsonlyasmallfractionofthepossiblegames that arise in the simple twobytwo setting. Second, the payoffstructure that gives rise to the PD game is trivially different from thestructure that produces the HD and Assurance games, thus making itlikely that all threegames are equally common.Third, evenwithin theiteratedPD,thereisfrequentlyastrongelementofcoordination.

In itssimple form, thePDgamehas twoplayers,eachofwhomhave twodiscrete actions they can take,where thedecisions aremadesimultaneously. Long ago, game theoristsmapped out all the possiblegames that have this twobytwo structure. If the players only makeordinal rankingsandarenever indifferentbetweenoutcomes, thereare78strategicallydistinctgames.54ThePDgame representsoneof thesepossibilities. According to political scientist Katherina Holzinger, threemorecasesareclosevariantsonthePD.55Bycontrasttothesefourgames,she counts fivedistinct cases of theAssurance (or StagHunt)game orvariations she calls degenerate coordination,56 one case of theHawk

54AnatolRapoportandMelvinGuyerwerethefirsttonotethatthereare78strategicallydistinct twobytwogames (assuming strictordinal rankings)of the576possiblepayoffcombinations. See Anatol Rapoport & Melvin Guyer, A Taxonomy of 2 X 2 Games,11GENERALSYSTEMS:YEARBOOKOFTHESOCYFORADVANCEMENTOFGEN.SYSTEMSTHEORY203,204 (1966). See alsoANATOLRAPOPORT, MELVIN J. GUYER& DAVID G. GORDON, THE 2X2GAME 17 (1976). Each player can ordinally rank the four outcomes in the twobytwosettingin24ways,whichmeansthetwoplayerscanranktheoutcomesin24X24=576ways.But[t]hegamematricesarestrategicallyequivalentwheneveronlytherows,thecolumns,bothrowsandcolumns,or,insymmetricgames,theplayersareinterchanged.SeeKatharinaHolzinger,TheProblemsofCollectiveAction:ANewApproach,Preprintsausder MaxPlanckProjektgruppe Recht der Gemeinschaftsguter 5 (2003), available athttp://www.coll.mpg.de/pdf_dat/2003_2.pdf (last accessed 8/26/07). For example, if twoplayersmutuallyprefertheoutcomewherebothplayStrategyX,thenthegamewhereStrategyX isplaced in the firstrowand firstcolumn isstrategicallyequivalent to thegamewhereStrategyXisplacedinthesecondrowandsecondcolumn.55Id.at9,14.TheAsymmetricDilemmadiffersfromthePDinthatonlyoneofthetwoplayershasadominantstrategytodefect,whiletheotherplayersbestmoveistomatchwhateverthefirstplayerdoes.ButtheresultisstillaDilemmabecause,knowingthatthefirstplayerwilldefect,thesecondplayerwillalsodefect.56 In these games, there are multiple equilibria, where some favor one or the otherplayer,buttheefficientequilibriumhasequalpayoffs.Thus,thegamesshouldbeeasytosolve,butstillrequiresomeassuranceofhowtheotherplayerisgoingtoproceed.


Dove(orChicken)game,andfivedistinctcasesoftheBattleoftheSexesgame.57Thereis,therefore,nothingintheabstractnatureofthePDgamethatmakes itmore likely tooccur than these threecoordinationgames.Wedontknowthatnatureproducespayoffsrandomly,butifitdid,wewould actually expect these three coordination games to occur almostthreetimesasfrequentlyasthePDgame(givenelevenoccurrencesofthecoordination game variants, compared to four occurrences of the PDgamevariants).

Second,minorchanges in thepayoffsofaPDgamecanproducetwoofourcoordinationgames:AssuranceandHD.Toillustrate,Figure5represents a generic twobytwo game, where specific payoffs arereplacedbythevariablesa,b,c,andd.TheparticulargamethatexistsinFigure 5 depends on the relationship between those variables. The PDarises if, forbothplayers, b > a > d > c.58 If b > a, eachplayerwants torespond to Strategy A (which we can here call Cooperation) withStrategyB(Defection).Becaused>c,eachplayerwantstorespond toDefectionwithDefection.So eachplayerwill chooseDefectionand thesoleequilibrium isDefect/Defect.Yetbecausea>d,eachplayerregardsthis outcome as worse than the outcome Cooperate/Cooperate. ThatswhatmakesthegameaDilemma.

Player2


StrategyA a,a c,b

StrategyB b,c d,d

Figure5:AGenericSymmetric2X2Game:PD b>a>d>cAssurance: a>b>d>cHD: b>a>c>d

57Id.at9,1415.58 If thegame isrepeated,anotherstandardcondition is thatb+c


Yet Figure 5 also represents theAssurance game if the payoffstaketheforma>b>d>c.Ifa>b,theneachplayerwantstorespondtoStrategyAwithStrategyA.Ifd>c,theneachplayerwantstorespondtoStrategyBwithStrategyB.Asaresult,therearetwoequilibria:A/AandB/B, where both players prefer A/A (because a > d), but each regardsStrategy B as safer (it necessarily avoids theworst outcome c). This isAssurance.YetthedifferencefromthePDistrivial;allthatdiffersistherelativepositionsofpayoffsaandb.Ifbisslightlygreaterthana,wehaveaPD;ifaisslightlygreaterthanb,wehaveAssurance.

Similarly,theHDGamearisesifthepayoffstaketheformb>a>c>d.Ifb>a,theneachplayerwantstorespondtoStrategyAwithStrategyB.Ifc>d,theneachplayerwantstorespondtoStrategyBwithStrategyA. The two equilibria are A/B and B/A; each player prefers to playStrategyBagainstStrategyA(becausebisthehighestpayoff),butifbothplay B they get the worst possible outcome (d is the lowest). This isHawkDove.Again,thedifferenceistrivial;allthatisrequiredtoflipthePDgametoHDisachangeintherelativepositionsofpayoffcandpayoffd.Ifdisslightlygreaterthanc,wehaveaPD;ifcisslightlygreaterthand,wehaveHD.

Thus, ifone takes thePD tobeapervasive featureofsocial life,thenthereisgoodreasontothinkthattheAssuranceandHDgamesarealsoapervasivefeatureofsociallife,givenhowlittlethepayoffshavetochange to flip one game into the other. If cooperation is a commonproblem,soiscoordination.

Coordination is pervasive for a final reason: the problemfrequently arises within an iterated PD. In the real world, the PD isusuallycomplicatedbythefactthatthereismorethanoneplausiblewayforthepartiestogoaboutcooperating.Ifthepartiesattempttocooperateusing different understandings of cooperation, then it is likely that atsomepointapartywillengageinbehaviorshebelievesiscooperativebutthat theothersideviewsasnoncooperative.Onesidepunisheswhat itviews asdefection, the other side views the punishment as unjustifieddefectionrequiringretaliatorydefection.Theresultingrecriminationsendcooperation. Thus, one step to solving the iterated PD game, almost


always neglected by existing legal literature, is coordinating on oneparticularmeansofcooperation.

Theresultinggameisnow,Iadmit,slightlymorecomplexthanatwobytwo game. Instead of each player choosing one of two actions,there are three choices: Defect, Cooperate According to Plan A, orCooperateAccordingtoPlanB.Theresultisathreebythreegame,asinFigure6,adaptedfromGarrettandWeingast,thepoliticalscientistswhofirstnotedthelegalsignificanceofcoordinationwithinaniteratedPD.59

Player2:

Player1: CooperateA CooperateB Defect

CooperateA 3,2* 1,1 0,4

CooperateB 1,1 2,3* 0,4

Defect 4,0 4,0 1,1

Figure6:PDwithEmbeddedBOSGame*EquilibriumPossibleOnlyWithIteration

Figure6 isaPD.60But if thegame is repeated, the folk theoremsaysthatitispossibletosustaincooperation;eachpartymaycooperatetoavoid theothersides futuredefection.But inFigure6, there isnogainovermutual defection and no chance of sustaining cooperation unlessthey twoplayersuse thesame formofcooperation,AorB.Theneed tomatch cooperative form is a matter of coordination. The type ofcoordinationcanvary,butthecoordinationproblemembeddedinFigure6isaBOSgame.Ifiterationmakescooperationpossible,thentherearetwocooperativeequilibria:A/AandB/B.Eachplayerpreferseitherequilibria

59SeeGeoffreyGarrett&BarryR.Weingast,Ideas,Interests,andInstitutions:Constructingthe European Communitys Internal Market, in IDEAS AND FOREIGN POLICY: BELIEFS,INSTITUTIONS,ANDPOLITICALCHANGE(J.Goldstein&R.O.Keohane,eds.1993).60EachplayersdominantstrategyisDefect.IfPlayer2cooperatesineitherway,AorB,Player1gainsmorebydefecting(4)thanbyeitherformofcooperation(3or1).Ifplayer2defects, then player 1 gainsmore bydefecting (1) than either form of cooperating (0).Player 2 faces the same incentives so in the oneshot game, the only equilibrium isDefect/Defect.


to any other outcome, but Player 1 prefers cooperating at A/A, whilePlayer 2 prefers B/B (each receives a payoff of 3 at her preferredequilibriumand2attheotherequilibrium).

Garrett and Weingast use the embedded BOS game to modeltreaties.61 Two nations, for example, may agree to limit their tariffs(against domestic interest groups that push for them) and sustain thisagreementbythreateningtobreachiftheotherbreaches.Butthepartiesmustdefinepreciselywhattradingbehaviorconstitutescooperationforpurposes of their conditionally cooperative strategies. If one nationeliminates its tariffs but enacts health or labor legislation that impedesimportsfromtheothernation,isthatdefection?Moreprecisely,underwhatcircumstancesisnontarifflegislationthatimpedestradeconsistentwithcooperation?Perhapsthereisasingleanswertothisquestion,butif thereare twoormoreways todefineacceptablenontariff legislationand each nation prefers a different standard, they face a situation likeFigure6.UnlesstheyfirstsolvetheirBOSgamebyagreeingonStandardAorStandardB,theywilleventuallybeinapositionwhereonenationsefforttocooperateunderStandardAisperceivedbytheothernationasadefectionunderStandardB.Thelatternationretaliatesbydefectingandcooperationunravels.

The example generalizes because cooperation is rarely selfdefining. Two neighboring farmer/ranchers may face a variety ofcooperationproblems, e.g., theneed for joint repairofborder fencesorconservationofasharedwatersource.Butoneneighborwantstorepairborder fences annually and base water conservation measures on anassumptionofaverageannualrainfall,whiletheotherneighborwantstorepair fences every threemonths and savewater for possible droughtyears. Unless they first coordinate on these matters, they will neversustain cooperation. Those using the PD usually simplify by ignoringthese embedded coordination problems, but they may constitute thebiggestobstacletolongtermcooperation.

61SeeGeoffreyGarrett&BarryR.Weingast,Ideas,Interests,andInstitutions:Constructingthe European Communitys Internal Market, in IDEAS AND FOREIGN POLICY: BELIEFS,INSTITUTIONS,ANDPOLITICALCHANGE(J.Goldstein&R.O.Keohane,eds.1993).


Insum,thereisnoreasontothinkthatthePDismorecommonaproblemthancoordination.

B.ThreeReasonsWhyCoordinationMatterstoLaw

Coordinationproblemsarenotonlypervasive,but important tothe social conflict law addresses. I consider specific games in the nextsection,buttherearethreegeneralfeaturesofthesegamesthatIexplainfirst. Unlike the PD game, coordination games model situations ofinequality,theymakehistoryandculturerelevant,andtheyexplainonewaythatlawworksexpressively,independentofsanctions.

1.Inequality

Everyone gains from solving a PD. Yet it is obvious that lawfrequently deals with social conflict where one person or group gainsonlybecauseanotherpersonorgroup loses.Theconceptsofsocialrolesbased on race, gender, or other factors usually arise in the context ofsocial norms that impose unequal burdens on different groups.Correctinginjusticeusuallymeansraisingthewealth(orotherprivileges)ofthevictimbycompensationthat lowersthewealthofthewrongdoer.But the PD game does not capture these issues of distribution. If theproblem is a PD, the solution makes everyone better off. There is nonormativecomplexityandnocontroversy.

Bycontrast,coordinationgamesfrequentlycapturedistributionalconflict.Notalways:thereneedbenoinequalityintheAssurancegame.The twoequilibriamay involveequalpayoffsbetween the twoplayers.Yet theBOS andHD gamesdo reflectdistributional struggle.The twoequilibriaoutcomesineachgamenecessarilyhaveunequalpayoffswhereoneplayerprefersoneequilibriumandtheotherplayerpreferstheotherequilibrium. When discussing these games below, I point out someliterature that uses the BOS game to model certain sexist norms indifferentpartsoftheworld,suchasthosethatrequiregenitalcutting.62I

62Seeinfratextaccompanyingnotes__.


haveused theBOSandHDgames tomodeldiscriminatorynorms,63 inwaysIdiscussbelow.64

2.TheInfluenceofHistoryandCultureonBehavior

Asecond implicationofcoordinationgames is the importanceofhistoryandculture.Inasingleequilibriumgame,aneconomicmodelcanclaim to account for the influence of history and culture by makingadjustments to the payoffs, which then uniquely determine howindividualswillbehave.Butthesurprisingresultofacoordinationgame,oranygamewithmultipleequilibria, is that thepayoffs,whatever theyinclude,donotuniquelydeterminethebehavior.Somethingelsebesidespayoffscananddoesinfluencehowpeopleact.

The game theory term for those other influences is a focalpoint.65Decades ago,Nobel Laureate Thomas Schelling first observedthat,insituationsrequiringcoordination,anythingthatmakessalientonebehavioral means of coordinating tends to produce selffulfillingexpectations that this equilibrium will occur.66 Schelling notes how, inmanyrealworldsettings,somethinginthesituationnotcapturedbytheformal mathematic structure draws the mutual attention of theindividualswhoneedtocoordinate.

The simplest examples involve pure coordination games. Forexample,Schelling askedpeople tonameaplace and timeofday theywouldgotomeetanotherpersoninNewYorkCityiftheyhadplannedadaytomeetbuthadfailedtopickaparticularplaceortime.Thereareavery largenumberof choices; random selection shouldproducealmostzero matches. But Schelling found that a majority identified GrandCentral Station and almost everyone selected noon.67 When he asked

63 See Richard H. McAdams, Conformity to Inegalitarian Conventions and Norms: TheContributionofCoordinationandEsteem,88THEMONIST238(2005).64Seeinfratextaccompanyingnotes__. 65See,e.g.,MaartenC.W.Jaanssen,RationalizingFocalPoints,50THEORY&DECISION119(2001); Maarten C.W. Janssen, (1998), Focal points, in NEW PALGRAVE DICTIONARY OFECONOMICSANDTHELAW(VOL. II)150 (P.Newman,ed.1998);RobertSugden,TowardsaTheoryofFocalPoints,105ECON.J.533(1995).66THOMASC.SCHELLING,THESTRATEGYOFCONFLICT5467(1960).67Id.at5556.


individuals to name apositive number named by anotherpersonwhowanted to match the number they named, despite the infinity ofequilibria,fortypercentnamedthenumberone.68Whenhemodifiedtheproblem to ask individuals to match a number on the (hypothetical)assumption that theywould receive thenumberofdollars equal to thenumberonwhichtheymatched,twentyninepercentselectednotonebutone million.69 In each case, the players solve a difficult coordinationproblembygravitatingtowardstheprominentorconspicuousoutcome.Schelling called the salient solution the focal point.70 Later researchfinds that individuals do not just thoughtlessly choose the salientsolution,butreasonaboutwhatislikelytobemutuallysalient.71

What makes a particular outcome focal? Among other things,Schellingmentionsprecedent,analogy,andwhothepartiesareandwhattheyknowabouteachother.72Precedentreferstohistory.Whatis focaldependsonwhat the individuals in the situationbelieve abouthow they or others they know have solved the same or analogoussituations in thepast. If theyoungestor theoldestpresentalwaysboresomeburdeninthepast,everyoneislikelytoexpectthatsolutioninthepresent.Itiscriticalwhothepartiesareandwhattheyknowabouteachother not only because different pairs of individuals share differentexperiences,butalsobecause theymaysharedifferent framesbywhichthey judgepasteventsasanalogous.Thus,focalpointsreflectculture.TheonlyreasonSchellingsrespondentsidentifiedGrandCentralStationasameetingspotisthattheylivedinNewHaven,Connecticutandsuchpeople frequently arrive in New York City at that location. That hisrespondents named one million as a quantity of money was entirelycontingentonthesalienceofthatquantityinAmericanculture.

Economiststhusdiscussculture,especiallycorporateculture,as the conceptual tools common language, beliefs, and frames that 68Id.69Id.70Id.71 See Judith Mehta, Chris Starmer & Robert Sugden. The Nature of Salience: AnExperimental Investigation of Pure Coordination Games, 84 AMER. ECON. REV. 658 (1994);JudithMehta,ChrisStarmer&RobertSugden,FocalPointsinPureCoordinationGames:AnExperimentalInvestigation,36THEORYANDDECISION163(1994).72THOMASC.SCHELLING,THESTRATEGYOFCONFLICT57(1960).


social groups have used to solve past coordination games and arethereforelikelytouseinattemptingtosolvefuturecoordinationgames.73ThepoliticalscientistMichaelChweexplainsthefunctionofsocialritualsascreating focalpointsolutions tocoordinationproblems.74 Indeed,oneof the pathbreaking earlyworks on coordinationwas the philosopherDavidLewisseffort toexplain languageasaconventionalsolution toarecurrent coordination game.75 None of this is possible with the PD,wherehistoryandcultureaffectbehavioronly to thedegree theyaffectpayoffs.

3.TheFocalPointPowerofLegalExpression

Besides precedent and analogy, Schelling also identifiedcommunication as ameansof creating a focalpoint.Evennonbindingcheap talk can make the discussed solution salient.76 Suchcommunicationmayoccurbetweenthepartiesinthecoordinationgame,but Schelling observed how a thirdparty someone not in thecoordinationgamecanuseexpression toconstructa focalpoint.77Thethirdpartycanrecommendthattheindividualscoordinateinaparticular

73SeeAVNERGREIF,INSTITUTIONSANDTHEPATHTOTHEMODERNECONOMY(2006);AvnerGreif,CulturalBeliefsandtheOrganizationofSociety:AHistoricalandTheoreticalReflectiononCollectivistand IndividualistSocieties,102 J.POL.ECON.912 (1994);BenjaminE.Hermalin,Economics and Corporate Culture in THE INTERNATIONAL HANDBOOK OF ORGANIZATIONALCULTUREANDCLIMATE(S.Cartwrightetal.,eds.,2001);DavidM.Kreps,CorporateCultureandEconomicTheory,inPERSPECTIVESONPOSITIVEPOLITICALECONOMY(Alt&Shepsle,eds.,1990); Roberto A. Weber & Colin F. Camerer, Cultural Conflict andMerger Failure: AnExperimentalApproach,49ManagementSci.400(2003).74MICHAELSUKYOUNGCHWE,RATIONALRITUAL:CULTURE,COORDINATION,ANDCOMMONKNOWLEDGE(2001).75SeeDAVIDLEWIS,CONVENTION (1969).SeealsoBrianSKYRMS,THESTAGHUNTANDTHEEVOLUTIONOFSOCIALSTRUCTURE4981(2004)(ontheevolutionofsignalingandinference);BRIAN SKYRMS, EVOLUTION OF THE SOCIAL CONTRACT 80104 (1996)(on the evolution ofmeaning).76 Cheap talk refers to statements that are costless to make, nonbinding, andnonverifiable. BAIRD, GERTNER & PICKER, supra note 16, at 303. For the theory of howcheaptalkcannonethelessinfluencebehavior,seeJosephFarrell&MatthewRabin,CheapTalk,10J.ECON.PERSP.103(1996).Forareviewoftheexperimentalliterature,seeVincentCrawford,ASurveyofExperimentsonCommunicationviaCheapTalk,78J.ECON.THEORY286(1998).77SeeTHOMASC.SCHELLING,THESTRATEGYOFCONFLICT66(1960)(departmentstoresignforwhere lostpartiesshouldreunitecreatesa focalpointsolution to theircoordinationproblem).


way,andtherebycreateselffulfillingexpectationsthattherecommendedbehaviorwilloccur.Ifthegovernment inanewsociety(withoutapriorcustom)announces thatdriverswilldriveon the rightsideof the road,the salience of that solution is likely to cause that result, regardless ofwhetherthegovernmentwillusesanctionstoenforcetheannouncementorwhetherthecitizensfeelamoralobligationtoobeythelaw.

Of greatest significance to law, Schelling proposed that thirdpartiescancreatefocalpointsinthemorecommonmixedmotivegamesthatinvolvebothcoordinationandconflict.Suppose,Schellingasks,thatthe traffic light fails at somebusy intersection and abystander not apoliceofficersteps in todirect traffic.78As twodriversapproach fromdifferentstreets,eachpreferstoproceedaheadoftheother,althougheachregardstheworstoutcomeasacollision.Thus,thesituationislikeaHDor BOS game. Schelling conjectured that the bystanders hand signalswould influence thedriversbehavior. Ifhandsignalare in fullviewofbothdrivers, then thedrivermotioned to stopwill now have strongerreasontoexpectthattheotherdriverwillproceed(andviceversa).Giventhatexpectation,herbestresponseistostop,whichistocomplywiththethirdpartysexpression.Bycreatingafocalpoint,thethirdpartywieldsapurelyexpressiveinfluenceonbehavior.79

Severaltheoristshavenotedthatlawcanworkinthismanner,aslegalrulesareaformofthirdpartyexpression(of legislators, judges,orexecutive branch officials) making focal the form of behavior the lawdemands.80 Like the bystanderinthe intersection, legal actors caninfluencebehaviormerelybycreatingselffulfillingexpectationsthatthelegally obligatorybehaviorwill occur.Anumber of experimentsprove

78Id.at144.79Nothing intheexamplerequiresthatthebystanderthreatennoncompliancedriverswith sanctions or possess what drivers consider to be legitimate authority. [H]isdirections have only the power of suggestion, but coordination requires the commonacceptanceofsomesourceofsuggestion.Id.at144.80SeeRichardH.McAdams,AFocalPointTheoryofExpressiveLaw,86VA.LAWREV.1649(2000);RichardH.McAdams,TheExpressivePowerofAdjudication,2005U. ILL.LAWREV.1043;RogerB.Myerson,Justice,Institutions,andMultipleEquilibria,5CHI.J.INTLLAW91(2004);RobertCooter,ExpressiveLawandEconomics,27J.LEGALSTUD.585(1998);RobertB.Ahdieh,LawsSignal:ACueingTheoryofLawinMarketTransition,77S.CAL.LAWREV.215(2004).


thepoint.81Forexample,JaniceNadlerandIshowthatmereexpression,evenwhenselectedrandomlybyamechanicaldevice,affectsbehaviorinaHDgame.82

Fora realworldexampleof laws focalpointpower, ithelps tolook to history, where some legal institutions lacked the power ofsanctions.Considermedieval Iceland,which forseveralcenturieshadarobust legal culture, elaborate legal codes, and courts that generatedsubstantial compliance,83 all despite the absence of any coercive stateinstitutions.84Therewasno stateapparatus topretend tomonopolizethe legitimateuseof force,nosheriff to issueasummons toahostileparty, to keep the peace in the court, or to execute the judgment.85Instead,[i]twasuptothelitigantstoserveprocessontheiropponents,maintain order in court, and enforce court judgments in their favor.Ultimately,thesanctionbehindlegaljudgmentandarbitratedsettlementwasselfhelp,mostoftenappearingintheguiseofthebloodfeud.86

How did the law work without state enforcement? By makingfocal the outcome the courts judgment declared. Individual litigantscouldenforceorresistajudgmentonlybygatheringthesupportoftheirkin. [Power]meant having others think one had the ability tomusterbodiestoassistinthevariousproceduresthatmadeupalegalaction.87The situation was not a PD, but a coordination game like HD, whereneitherwantedtobackdownbutneitherwantedthedisputetocontinueto the death. In this setting, it is easy to believe that a court couldinfluencethebehaviorofthepartiesbyprovidingafocalpoint.Oncethe

81See,e.g.,RichardH.McAdams&JaniceNadler,CoordinatingintheShadowoftheLaw:TwoContextualizedTestsoftheFocalPointTheoryofLegalCompliance,forthcomingin42LAW& SOCIETYREVIEW (2008); JeanRobertTyran&LarsP. Feld,AchievingCompliancewhenLegalSanctionsareNonDeterrent,108SCAND.J.ECON.135(2006);RobertoGalbiati&PietroVertova,Obligations and Cooperative Behavior in PublicGoodsGames, 64GAMES & ECON.BEHAV.146(2008).82 See Richard H. McAdams & Janice Nadler, Testing the Focal Point Theory of LegalCompliance:TheEffectofThirdPartyExpressioninanExperimentalHawk/DoveGame,2J.EMP.LEGALSTUD.87(2005).83SeeWILLIAM I.MILLER,BLOODTAKINGANDPEACEMAKING:FEUD,LAW,ANDSOCIETY INSAGAICELAND22257(1990).84Id.at224.85Id.at232.86Id.at2021.87Id.at245(emphasisadded).


courtannouncedawinner, itappeared that thewinnerwouldfightandthisexpectationmadeitmoredifficultforthelosertogatherorretainkintofightonhisbehalf.88

C.LegalApplicationsoftheThreeCoordinationGames

Now let us turn to our three coordination games and considerhoweachofthembearsonvarious legal issues.Theultimatepoint istoaskwhether the legal literature is justified ingiving twenty timesmoreattentiontothePDthananyoneofthesegames.

1.BattleoftheSexes

The BOS game is useful for understanding bargaining, thecreationofconstitutionsandtreaties,standardsetting,theharmonizationoflaw,andgenderroles.

Bargaining. Coordination is central to bargaining. Admittedly,whennegotiationsconclude,theremaybeaPDregardingcompliance.Ifenforcement is insufficient, eachpartymighthave adominant strategynot toupholdherendof thebargain.But inmanysituations, formalorinformal sanctions make contractual compliance likely. If so, theimportant issue is whether the parties reach agreement. Givenenforcement,whateverproblembargainingis,itisnotaPD.89Abargainispossible only because two ormore parties canmutually gain by someagreement. Where being the only one to defect in a PD is the bestoutcome, being the only one to withhold agreement in a bargainingsituation is not the best outcome because it prevents the gain of the

88Foranotherhistoricexample,seeAndreaMcDowell,RealProperty,SpontaneousOrder,andNormsintheGoldMines,29LAW&SOCIALINQ.771(2004)(findingthatthefocalpointtheory of adjudication explains third party resolution of frontiermining disputes). SeegenerallyRichardH.McAdams,TheExpressivePower ofAdjudication,2005 ILL.LAWREV.1043,110103.89PoliticalscientistJamesFearonmakesthispointinthecontextoftreatynegotiations.SeeJamesFearon,Bargaining,Enforcement,andInternationalCooperation,52INTLORG.269(1998). He says that after two states conclude an agreement, there is frequently anenforcementproblem that takes the form of an iteratedPD (because each side finds itcheaper in theshort runnot tocomply regardlessofwhat theothersidedoes).But theinitialstageofcreatinganagreementinvolvescoordination.


bargain.Instead,theproblemisoneofcoordinationbecausethereismorethanonewaytoconcludeagreementandeachpartysharesthedesiretoavoid an impasse that may result when each party presses for itspreferreddistribution.90

Any twobytwo game will miss much of the problem ofbargaining.91Nonetheless,becausethereisinsightinsimplemodels,onemayreasonablyaskwhattwobytwogamebestmodelsbargaining.TheansweristheBOSgame.WemightthinkofBOSascapturingwhatbothsidesknowisthelastroundofbargaining,whereeachsidewillmakeitsfinalofferandtherearejusttwounequalwaysfortheofferstomatch.Ifthetwooffersmatch,thereisacontractandbothpartiesgain.Ifthereisnomatch, the bargaining endswithout an agreement and both partieslose.Buteachpreferstomatchtermsinadifferentway.

International Law. A large political science literature usescoordination games to explore international relations and international

90Schellingdiscussedfocalpointsinthecontextofbargainingbasedontheideathatabargainerwilltrytoidentifyorcreatefocalpointsthatdrawshercounterparttowardthebargainingoutcomesheseeks.That ideahasgenerallybeenneglected in thebargainingliterature,butseeMaartenC.W. Janssen,On theStrategicUseofFocalPoints inBargainingSituations,27 J.ECON.PSYCH.622 (2006). In the legal literature,a fewscholarshaveusedfocal points to explain the effect of nonbinding rules orprecedent on bargaining. SeeRobertAhdeih,TheStrategyofBoilerplate,104MICH.L.R.1033,105355(2006)(usingfocalpoints toexplainhowboilerplate terms incontract forms influencebargaining);RussellKorobkin, Inertia andPreference inContractNegotiation:ThePsychologicalPower ofDefaultRules andFormTerms,51VAND.L.REV.1583 (1998)(exploring similareffects fordefaultcontractrules).SeealsoRichardH.McAdams&JaniceNadler,CoordinatingintheShadowoftheLaw:TwoContextualizedTestsoftheFocalPointTheoryofLegalCompliance,forthcoming42LAW&SOCYREV.(2008)(findingcontractdefaultrulesaffectdecisionsinaBOSgame).91Suchasimplegamenarrowsthenumberofpossiblemovestotwo,wherethereareusuallymanywaysonecouldreachagreement.Second,asimultaneousgameignoresthebackandforthnatureofbargaining.Finally,simplegamesassumecompleteinformation,where bargaining usually occurs in the presence of asymmetric information. For thisreason, game theorists have explored various complex models of bargaining. Oneapproach is the Rubenstein alternating offers model. See Ariel Rubinstein, PerfectEquilibriuminaBargainingModel,50ECONOMETRICA1151(1982);MARTINOSBORNE&ARIELRUBINSTEIN, BARGAINING AND MARKETS (1990). For discussions, see DOUGLAS G. BAIRD,ROBERTH.GERTNER&RANDALC.PICKER,GAMETHEORYANDTHELAW21941(1996);ERICRASMUSEN, GAMES AND INFORMATION 299303 (3d ed. 2001). Another approach is theaxiomaticbargainingmodel.SeeJohnNash,TheBargainingProblem,18ECONOMETRICA155(1950). Fordiscussions, seeAVINASHDIXIT& SUSAN SKEATH,GAMES OF STRATEGY 52149(1999);RASMUSEN,supra,at29699.


law.92 As noted above, Garrett & Weingast view international law asarising in an iterated PD game, but they make the embeddedcoordinationpointdiscussedabove.93Because thenationsmustsolveaBOS game in order to solve their PD, the nations must bargain.Cooperation is sustainable only if the states agree to a singleunderstanding of cooperation. Garrett and Weingast propose that thetreaty and subsequent judicial interpretations of it make focal onesolution to theembeddedBOSgame,soeachnation thereafteruses theagreedupondefinitionstojudgewhethertheothernationcooperatedordefected in the prior round. With such a mutual understanding, thenations may then sustain cooperation (by threatening to respond todefectionwithfuturedefection).

Standard Setting and Uniform Laws. When different firms orindustries need to agree to certain technical standards to allow theirproducts to interact (e.g., automotive parts, computers and addons,hardwareandsoftware),theyengageinstandardsetting.TheBOSgamemodelsstandardsettingbecauseallpartieswishtoreachsomestandard,butdisagreeas towhatstandard isbest.Each firmprefers thestandardclosesttothespecificationsofitscurrentproduct,buteveryonestillwantstheirproduct to match everyone elsesproduct.Unlike thePD, onceeveryone else starts to use a given technical standard, there is noincentivetodefectbuteveryincentivetoconform.

Therearesomeobvious legalexamplesofstandardsetting,suchas treaties establishing standardized weights and measures,communications protocols for air traffic control, the internationalexchangeofmailedandtelephoniccommunications,andtheexchangeof

92 See, e.g., Judith Goldstein & Robert O. Keohane, Ideas and Foreign Policy: AnAnalyticalFramework,inIDEASANDFOREIGNPOLICY:BELIEFS,INSTITUTIONS,ANDPOLITICALCHANGE3,1720(J.Goldstein&R.O.Keohane,eds.1993);JamesD.Morrow,ModelingtheFormsofInternationalCooperation,48INTL.ORG.387(1994);ArthurStein,CoordinationandCollaboration: Regimes in an AnarchicWorld, 36 INTL. ORG. 299 (1982); Duncan Snidal,CoordinationVersusPrisonersDilemma:ImplicationsforInternationalCooperationandRegimes,79AMER.POL.SCI.REV.923(1985).Forlegaldiscussions,seeJACKL.GOLDSMITH&ERICA.POSNER,THELIMITSOFINTERNATIONALLAW(2005).93GeoffreyGarrett&BarryR.Weingast,Ideas,Interests,andInstitutions:ConstructingtheEuropeanCommunitysInternalMarket,inIDEASANDFOREIGNPOLICY:BELIEFS,INSTITUTIONS,ANDPOLITICALCHANGE(J.Goldstein&R.O.Keohane,eds.1993).


fingerprints by police departments.94 In each case, the central issue iscoordination;despitedisagreementastowhatstandardisbest,thereisastrongincentivetomatchstandardsandnoincentivetodeviatefromthestandardeveryoneelseadopts.

Butstandardsettingisfarmorecommonandcentraltolawthanthese examples suggest. Regarding private law, such as contracts,securitiesregulation,orarbitration,nationstatesarefrequentlyinterestedin harmonization95 or, as a lesser but even more common step, theconvergence of different domestic legal regimes.96 Within a federatednation state, the same desire exists for the unification of laws acrossjurisdictions, such as the adoption of the Uniform Commercial CodeacrossAmericanstates.97Theadvantageofpolicyconvergenceand legalharmonizationisthattheysavetransactioncostswhenprivatefirmsseektodobusiness acrossborders.Thegreater thedisparity in the lawsof,say, contracts, securities,or antitrust, themoredifficult it is to transactacrossborders. Inotherwords, legal rules themselves arestandardsand

94See,e.g.,LaurenceR.Helfer,ExitingTreaties,91VA.L.REV.1579,163336(2005)(usingtheBOSgametoexplorethe issueoftreatyexit).Forcoordinatingairtrafficcontrol,therelevanttreatyistheConventiononInternationalCivilAviation,Dec.7,1944,art.37,61Stat. 1180, 1190, 15 U.N.T.S. 295, 320. For an explanation, see Michael Gerard Green,ControlofAirPollutantEmissions fromAircraftEngines:LocalImpactsofNationalConcern,5ENVTL. LAW. 513 (1999) (authorizing the governing body of the ICAO . . . to adoptinternational standards and practices concerning communications systems; airportcharacteristics; air traffic control practices; personnel licensing; aircraft airworthiness;aircraftregistration;andothermattersdealingwiththesafety,regularityandefficiencyofairnavigation.).SeealsoConventionfortheEstablishmentofanInternationalBureauofWeightsandMeasures,May20,1875,20Stat.709.95See, e.g.,BethSimmons,The InternationalPoliticsofHarmonization:TheCase ofCapitalMarket Integration, 55 INTLORG. 589 (2001);FrancescoParisi,TheHarmonization ofLegalWarrantiesinEuropeanSalesLaw:AnEconomicAnalysis,52AM.J.COMP.L.403(2004).TheInternational Institute for the Unification of Private Law (UNIDROIT) works towardsharmonizationofprivate law.See, e.g.,KlausPeterBerger, InternationalArbitralPracticeand theUNIDROITPrinciplesof InternationalCommercialContracts,46AM. J.COMP.L.129(1998).96 See DANIEL W. DREZNER, ALL POLITICS IS GLOBAL: EXPLAINING INTERNATIONALREGULATORY REGIMES 11 (2007)(distinguishing three nested levels of internationalcoordination:[r]egulatorycoordinationiscodifiedadjustmentofnationalstandardsinordertorecognizeoraccommodateregulatoryframeworksfromothercountries;policyconvergence is the narrowing of gaps in national standards over time; and[h]armonizationispolicyconvergencetoasingleregulatorystandard.).97See,e.g.,JamesJ.Brudney,TheUniformStateLawProcess:WilltheUMAandRUAAbeAdoptedbytheStates?8DISP.RESOL.MAG.3(Summer2002).


there are costs savings to minimizing the differences between thestandards.At the same time, because a state incurs costs in switchingfrom one legal standard to another, each prefers that the other nationsshifttoitslegalstandard.TheresultisaBOSgame.98

Constitutions.Politicalscientistshaveappliedtheaboveanalysisofinternationallawtoconstitutionallaw.First,theinteractionofpartiestoaconstitutionfrequentlypresentsagameinvolvingcoordination.Second,awrittenarrangementoradjudicationbetweenthosepartiesmayinfluencetheirbehaviorbyvirtueofcreatingafocalpoint inacoordinationgame(and thereby creating selffulfilling expectations of how to behave).RussellHardininitiatedthisliteraturebyclaimingthatconstitutionsariseoutof,notthePD,butaBOSgame.99Hardinimaginestheconstitutionistheresultofabargainbetweenpowerful interestgroupswhoarebetteroff matching strategies, by agreeing to the same structure ofgovernment,thantheyareiftheyfailtoagreeandhavenogovernment.100Butat the same time the situation isobviouslynotapure coordinationgame because interest groups preferdifferent structures. JonElster, bycontrast,views theconstitutionassolvingan iteratedPDgamebetween

98 Dreznerprovidesaslightlymorecomplexstandardsgame for just thissituation.SeeDANIELW.DREZNER,ALLPOLITICSISGLOBAL5155(2007).Hisgameusesvariablesthatallow for the possibility that both parties are better off retaining their own nationalstandardbecausethegainstoeitherpartyfromcoordinationaresmallerthanthecostsofswitching legal standards.Butwhere thebenefitsof coordinating arehigh enough, theresult is aBOS game. See alsoAnuBradford, InternationalAntitrustNegotiations and theFalseHopeof theWTO,48HARV. INTLL.J.383 (2007)(usingDreznersapproach tomodelinternationalantitrustharmonization).99 Russell Hardin, Why a Constitution? in THE FEDERALIST PAPERS AND THE NEWINSTITUTIONALISM100,101,105(BernardGrofman&DonaldWittman,eds.,1989).SeealsoRussell Hardin, Constitutionalism, in HANDBOOK OF POLITICAL ECONOMY 289 (DonaldWittman&BarryWeingast,eds.,2006).Otherpoliticalscientists,suchasPeterOrdeshook,have explored the prescriptive implications of this theory for the creation of stableconstitutions. See Peter C. Ordeshook, Are Western Constitutions Relevant to AnythingOther than theCountries theyServe?,13CONSTLPOL.ECON.3 (2002);PeterC.Ordeshook,ConstitutionalStability,3CONSTLPOL.ECON.137(1992).100 See Russell Hardin,Why a Constitution? in THE FEDERALIST PAPERS AND THE NEWINSTITUTIONALISM 100, 105 (Bernard Grofman & Donald Wittman, eds., 1989)(game 3).Notethatinsteadofgivingpayoffnumbersthatrepresentutilities,wherehighernumbersarebetter,Hardingivespayoff ranks,where lowernumbersmeanhigher ranks.Thus,Game3isBOSwiththetwoequilibriabeingthepayoffranks(2,1)and(1,2),representingmatchesatI/IandII/II.


politicalparties,but(asGarrettandWeingastclaimforinternationallaw),hedescribesacoordinationproblemembeddedinthePD.101

Creatingaconstitutionconstructsafocalpoint.Writingdowntheallocationofpower in aparticular structureofgovernmentmakes thatallocation salientand creates selffulfillingexpectations that thevariousplayerswilldemand at least asmuchpower asgranted in thewriting,forcing other players to cede that much power. One of the fewconstitutionalscholars toexamine the focalpoint theory,DavidStrauss,explainsthatitsuggestsgivinggreatinterpretiveweighttoconstitutionaltextualism.102Thatfocalpointscanalternativelybebasedonprecedent(rather than communication) also explains the power of unwrittenconstitutionallaw,oncustomsthatcreatestrongexpectationsabouthowpartieswillcoordinate.103

Thefocalpointpoweralsoexplainsthe judiciarysinfluenceoverthe other branches of government in matters of constitutional conflict.The ultimate reason the executive and legislative branches defer to thejudiciary cannotbe that the judiciarywillbring legal sanctions tobear,given that the judiciary depends on other branches of government forthosesanctions.Butthecourtmaywieldexpressive influencesbyvirtueof its power tomake a particular resolution focal. The key is that thepoliticalbranchesorpartieswish tocoordinate toavoidaconstitutionalcrisisorbreakdown.104Buttheconstitutionaltextandtraditionleaveopengaps and ambiguities, which allows disruptive disputes. Judicialjudgmentsarefollowedmerelybecause,likeadriverintraffic,thelosing

101SeeJonElster,UnwrittenConstitutionalNorms(Oct.2007unpublisheddraft)(onfilewith author). Political parties expect to alternate control of government and thus findthemselvesinaniteratedPDgamewhereeachpartywillbenefitifbothpartiesadheretocertain restraints of power when in office. But there are many ways to definegovernmentalpowers;manywaysofdefining the restraint requiredofeachbranch.ToachievecooperationintheiteratedPDgame,thepartiesmustagreeontheboundariesofgovernmentalpowers.102DavidStrauss,CommonLawConstitutionalInterpretation,144CHI.LAWREV.877,91019(1996).103See,e.g.,ErnestA.Young,TheConstitutionOutside theConstitution,117YALEL.J.408(2007); JonElster,UnwrittenConstitutionalNorms (Oct.2007unpublisheddraft)(on filewithauthor).104Cf.MatthewC.Stephenson,When theDevilTurns . . .:ThePoliticalFoundationsofIndependentJudicialReview,32J.LEGALSTUD.59(2003).


partyexpectsthewinningpartytoinsistandviewsdeferringastheonlywaytoavoidtheworstoutcome.105

GenderRolesandInequality.Othertheoristsusecoordinationgamestoexplorehowsexrolenormsariseandpersist. Inseparatepapers, theeconomistGillianHadfieldandthepoliticalscientistGerryMackiepointtothecoordinationthatoccurswithinmarriage.Hadfieldexploreswhyitisthat,[r]egardlessofthelevelofeconomicdevelopment,itappearsthatalmost all tasks in a society tend to be gendered, that is, to be easilyidentifiable as either womens work or mans work.106 Biologicalexplanations founder because themajority of tasks divided along sexlinesarenotallocateduniformly toonesexworldwide.107 Instead, it iscommon thata taskgenderedmale inonesociety isgenderedfemale inanother.108Hadfieldpointstotheneedforindividualstocoordinatetheiracquisitionofhumancapitalbeforemarriagesoastobringtoamarriagethe skills that best compliment a future spouses skill.109 In a preindustrialsociety,forexample,ifmostmen(women)knowhowtomakeleatherproducts,butnotbaskets, then theywill seekwives (husbands)whohavetheskilltheylackbasketmaking.Oncemostmen(women)insocietydoacertainkindofwork,awoman(man)whohasthesameskillwillbeunattractiveasaspouse.Aswithallconventions, the individualwhodeviatespaysacost.110

105 See also TOM GINSBURG, JUDICIAL REVIEW IN NEW DEMOCRACIES: CONSTITUTIONALCOURTSINASIANCASES(2003).106GillianK.Hadfield,ACoordinationModel of theSexualDivision ofLabor,40 J.ECON.BEHAV.&ORG.125,125(1999).107Id.at130.108 In one large study of 50 economic activities in 185 preindustrial societies, themanufacturingofleatherproducts,forexample,wasanexclusivelymaleoccupationin35societiesandanexclusivelyfemaleoccupationin29,whilebasketmakingwasexclusivelymalein37societiesandexclusivelyfemalein51.Id.at12728(Table1).109Id.at130(thecoordinationmodelprovidesabasisforunderstandinghoweconomicconditionscangiverisetonorms,culture,ideologyandsoonwhichindependentlykeepthesexualdivisionoflaboralivelongaftereconomicconditionshavechanged).Seealso14348.110Id.at143(Tryingtobreakoutofthesegenderedcategories...putsanindividualatgreatriskofnotfindingapartnerwithwhomheorshecancombineskillssoastohavebreadtoconsume.).


Mackie identifies the same coordination dynamic in customs offemalefootbindingandgenitalcutting.111Iftheparentsofgirlsinavillagebindtheirdaughtersfeetandtheparentsofboyspermitmarriageonlytofemaleswhose feetwere bound, then individual deviations are costly.There is the risk that girls whose feet are not bound will beunmarriageable.112Mackie notes that the astonishingly quickdemise ofthecustomoffootbindinginChinaearlyinthe20thcenturytookaccountof this coordination dynamic.Whatworkedwere agreements betweenparentswithinvillagesthatthosewhohadgirlswouldnotbindtheirfeetand that thosewhohadboyswouldnotallow them tomarrygirlswithboundfeet.113Onceenoughparentsexpressedawillingnesstofollowthisnew behavior, everyone else wanted to follow it as well. Whereindividualdeviationiscostly,thiscollectiveactionworkedtounravelthenorm.

Finally,inequalitymayarisebecausehistoryandculturemakethegenderorraceofindividualsthefocalpointforcoordination.Ifeveryoneexpectsthewomanoraracialminoritytosettleforlessinabargainingsituation,thenawomanorminoritymem

Beyond the Prisoners Dilemma - McAdams

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