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1、DynamicGamesofCompleteInformationDynamicGamesofCompleteandImperfectInformationJune18,2003173-347GameTheory--Lecture21OutlineofdynamicgamesofcompleteinformationDynamicgamesofcompleteinformationExtensive-formrepresentationDynamicgamesofcompleteandperfectinforma
2、tionGametreeSubgame-perfectNashequilibriumBackwardinductionApplicationsDynamicgamesofcompleteandimperfectinformationMoreapplicationsRepeatedgamesJune18,2003273-347GameTheory--Lecture21Today’sAgendaReviewofpreviousclassInfinitelyrepeatedgamesJune18,2003373-347
3、GameTheory--Lecture21InfinitelyrepeatedgameAinfinitelyrepeatedgameisadynamicgameofcompleteinformationinwhicha(simultaneous-move)gamecalledthestagegameisplayedinfinitely,andtheoutcomesofallpreviousplaysareobservedbeforethenextplay.Precisely,thesimultaneous-mov
4、egameisplayedatstage1,2,3,...,t-1,t,t+1,.....Theoutcomesofallprevioust-1stagesareobservedbeforetheplayatthetthstage.Eachplayerdiscountsherpayoffbyafactor,where0<<1.Aplayer’spayoffintherepeatedgameisthepresentvalueoftheplayer’spayoffsfromthestagegames.June18
5、,2003473-347GameTheory--Lecture21PresentvalueJune18,2003573-347GameTheory--Lecture21Infinitelyrepeatedgame:exampleThefollowingsimultaneous-movegameisrepeatedinfinitelyTheoutcomesofallpreviousplaysareobservedbeforethenextplaybeginsEachplayer’spayofffortheinfin
6、itelyrepeatedgameispresentvalueofthepayoffsreceivedatallstages.Question:whatisthesubgameperfectNashequilibrium?Player2L2R2Player1L11,15,0R10,54,4June18,2003673-347GameTheory--Lecture21Everysubgameofaninfinitelyrepeatedgameisidenticaltothegameasawhole1L1R12L2R
7、22L2R2L1R12L2R22L2R2L1R12L2R22L2R2L1R12L2R22L2R2L1R12L2R22L2R2115005441111(1,1)(5,0)(0,5)(4,4)115005441150054411500544TOINFINITYJune18,2003773-347GameTheory--Lecture21Example:strategyAstrategyforaplayerisacompleteplan.Itcandependonthehistoryoftheplay.Astrateg
8、yforplayeri:playLiateverystage(orateachofherinformationsets)Anotherstrategycalledatriggerstrategyforplayeri:playRiatstage1,andatthetthstage,iftheoutcomeofeachofallt-1previousstagesis(R1,R
