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1、InternationalJournalofGameTheory,Vol.17,Issue3,page177-186ANoteonReactiveEquilibriaintheDiscountedPrisoner'sDilemmaandAssociatedGamesByE.Kalai1,D.Samet2,andW.Stanford3Abstract:NecessaryandsufficientconditionsarederivedunderwhichtheTit-for-Tatstrategypairisasubgameperfectequilibriumint
2、hestandarddiscountedprisoner'sdilemma.Thesensi-tivityoftheequilibriumtochangesinthediscountparametersisshowntobeacommonfeatureofallsuchnontrivial"reactive"equilibria.Thisappearstorulethemoutasreasonablesolutionstothediscountedprisoner'sdilemma.Inremarks,weindicatehowtheseresultscanbee
3、xtendedtoafairlygeneralclassofgames.1IntroductionThepurposeofthisnoteistoinvestigatethesubgameperfection(seeSelten[7])propertiesofcertainpurestrategyequilibriaininfinitelyrepeatedversionsoftheclassicprisoner'sdilemmaandrelatedclassesofgames.Concentratingontheprisoner'sdilemmaforthemom
4、ent,theequilibriaweconsiderconsistofstrategypairsinwhichatleastoneoftheplayersbasescurrentperiodactiononlyontheprioractionsofhisopponent,ignoringthehistoryofhisownactionsinthesupergame.Astrategyofthistypeiscalledreactiveforobviousreasons.Thecorrespondingequilibriawillalsobecalledreact
5、ive.Intheexamplebelow,wedemonstratetheexistenceofaperfectreactiveequilibriuminwhichthecollusiveoutcomeobtainsalongtheequilibriumpath.Thisequilibriumisseentobequitespecial,however;beingextremelysensitivetovariationsinthediscountratesoftheplayers.Weshowthatthisisafeaturecom-montoallsuch
6、nontrivialreactiveequilibria.Inparticular,theclassofperfectreactiveequilibriawhicharerobusttochangesinthediscountratesconsistsofthesingletrivialequilibriuminwhichbothplayerschoosetheirnoncooperativeactioninevery1EhudKalai,NorthwesternUniversity,Evanston,Illinois,USA.2DovSamet,Bar-Ilan
7、University,Ramat-Gan,Israel.3WilliamStanford,UniversityofIllinoisatChicago,Chicago,Illinois,USA.0020-7276[88[3/177-186$2.5091988Physiea-Verlag,Heidelberg178E.Kalaietal.period,independentofpriorhistory.ThisresultisdemonstratedintheProposition.Theinherentsensitivityofnontrivialreactive
8、equil
