资源描述：
《Advanced Micro (2) 16a2 Repeated Games英文文献资料》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。
1、RepeatedGames(II)11.Introduction2Single-ShotGameExample:Twoplayergameofimperfectinformation.Eachplayerhasoneinformationsetandtwooptionsatthatinformationset.1CD2CDCDTwostrategiesforeachplayer:{C,D}3Let’sRepeat…Assumeeachplayerhasthe1sametwooptionsateachinfoset:{C,D}2FirstIterat
2、ionsubgame11112222SecondIterationWhatisPlayer1’sstrategyset?(Crossproductofallchoicesetsatallinformationsets…){C,D}x{C,D}x{C,D}x{C,D}x{C,D}25=32possiblestrategies4OneMoreTime…121111222211111111111111112222222222222222Eachplayernowhas221=2,097,152possiblestrategies!5Shorthandfo
3、rStrategiesSimilarly,onemayuseshorthandforstrategies:ALLC“AlwaysCooperate”AlwaysplayCALLD“AlwaysDefect”AlwaysplayDGRIM“GrimTrigger”PlayCatfirst.IfanyplayereverplaysD,playDforeverafter.TFT“TitforTat”Cooperateinfirstround.Ineachsubsequentround,dowhatevertheotherplayerdidinthepre
4、viousroundDEV1L“DeviateonceinL”TFTuntilperiodL.PlayDonce.PlayCtwice.ThenTFTthereafter.GRIMDEV1LGRIMuntilperiodL.PlayDinperiodLandthereafter.6CalculatingUtilities•GiventwostrategiesSandS12--Determinethe“pathofplay”thatresultsfromthosestrategies.--Foreachstage,determinethe“pathp
5、lay”actionofeachplayer,andthendeterminetheresultingpayofftoeachplayer.--Foreachplayer,sumtheirstagegamepayoffs,discountingifappropriate.7CalculatingUtilities“Onthepath”actionsLetSspecify1’smovesforallrounds{C,D,D,D,C}1Streamround01234ofpayoffsS2specify2’smovesforallrounds{C,C,
6、C,D,D}Mbei’spayoffinthestagegamei,tinroundt,givenS1andS2CDCEx:M=U(D,D)1,31DNTotalutilityisU(S,S)=M+M+M+…+M=∑Mi12i,0i,1i,2i,Ni,tt=08CalculatingUtilitiesLetSspecify1’smovesforallrounds{C,D,D,D,C}1Streamround01234ofpayoffsSspecify2’smovesforallrounds{C,C,C,D,D}2Example:Prisoner’s
7、DilemmaU(S,S)=3+5+5+1+0=14112CD35C30U(S,S)=3+0+0+1+5=921201D519TypesofRepeatedGames•Finitelyrepeatedwithaknownend--Backwardsinductionoftenuseful•Finitelyrepeatedwithanunknownend--Probabilityofgameending•Infinitelyrepeated--Payoffsdiscounted101.1WhatwillHappeninFinitelyRepeated
8、Games?11SomerepeatedgamescanbesolvedviabackwardsinductionExam
