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1、RepeatedGames(III)15.FolkTheorem5.1Theory2InfiniteRepetitionsAswehaveshownthatthestrategysetsininfinitelyrepeatedgamesarehugeandcomplicated.Toprovethefolktheorem,werestrictourattentionheretothosestrategiesthatcanberepresentedbyfiniteautomata.3Theone-shotPrisoners’DilemmaisdovehawkshowninTable.dove2,
2、2-1,3Itscooperativepayoffregionoftheonehawk3,-10,0shotgameistheshadedarea.Wehaveseenthattheinfinitely(-1,3)repeatedversionofthegamehas(2,2)manyNashequilibria,butthefullcountisimpossible.EverypointinthedeeplyshadedareaisaNashequilibriumoutcomeofthe(0,0)infinitelyrepeatedgame.(3,-1)4Intheearlydaysofga
3、metheory,itseemsthateverybodyknewthefolktheorem,butnobodywaswillingtoclaimcreditasitsauthor.However,RobertAumannwasthefirsttorecognizethefullsignificanceoftheFolkTheorem.Itsaysthat:ThesetofallNashequilibriumoutcomesofanindefinitelyrepeatedgameconsistsofallpointsinthecooperativepayoffregionofthestage
4、gameatwhichallplayersgettheirsecuritylevelsormore.5Thefolktheoremisoffundamentalimportanceforpoliticalphilosophy.Withoutanexternalenforcementagencytodetercontractviolations,mostoftheoutcomesinthecooperativepayoffregionofaone-shotgamelieoutsideourreach.Butwhenweconsidercooperationinsocietyasawhole,th
5、ereisnoexternalenforcementagencytowhichwecanappeal.Allearthlysourcesofauthority–kings,presidents,judges,policemen,andthelike–arethemselvesbutplayersinthegameoflife.Theytoomustbeincentivizediftheyaretocarryouttheirspecifiedrolesproperly.6Theonlystableagreementsavailabletosocietyasawholemustthereforep
6、olicethemselves.PoliticalphilosophersbeforeDavidHumesawnosolutiontothisconundrum.Eventoday,philosopherstryingtogetaroundtheproblemvainlyinventreasonwhyitisrationaltocooperateintheone-shotPrisoners’Dilemma.Butasocietydoesn’tplayaone-shotgame.Itplaysarepeatedgame,inwhichthefolktheoremtellsusthatweneed
7、losenoneofthefruitsofcooperationbyrestrictingourselvestoagreementsonequilibriainthegameoflife.7Anycontract(thatrationalplayersmightsigninthepresenceofanexternalenforcementagencyintheone-shotcase)isals
