????????II???????III??????Simultaneous-MoveGameswithMixedStrategiesII:Non-Zero-SumGamesandIII:GeneralDiscussion?8?Chapter08??????????????Simultaneous-MoveGameswithMixedStrategies:Non-Zero-SumGames????????????????????????????????????????????Innon-zero-sumgames,playerdonothaveclearlyconflictinginterestsandhavenogeneralreasontowanttoconcealtheirinterestsfromothers.???????????????Asaresult,thereisnogeneralargumentforkeepingtheotherplayerguessing.Slide21???????????????MixingSustainedbyUncertainBeliefs????????????????????????????????????????????????????????However,Simultaneousplaycanstillleadplayerstohaveuncertainbeliefsabouttheactionsofarivalplayerandthereforetobeuncertainabouttheirownbestactions.Slide3??????????WillHarryMeetSally?SALLYStarbucksLocalLatteStarbucks1,10,0HARRYLocalLatte0,02,2Slide42??????????WillHarryMeetSally?Sally’sPayoffs2LocalLatteSally’sbest-response1Starbucks02/31Harry’sp-mixSlide5??????????WillHarryMeetSally?1Sally’sq-mix2/33NashEquilibriaHarry’sbestresponse012/3Harry’sp-mixSally’sbestresponseSlide63??????????WillHarryMeetSally?????????????????2/3?????????????2?1??Theexpectedpayoffofeachinthemixed-strategyequilibriumis(4/9*1)+(1/9)*2+(4/9*0)=2/3,worsethanbothpure-strategyNashequilibrium(2or1).?????????????????????????4/9???????????????Whentheychooserandomlyandindependently,thereissomepositiveandoftensignificantprobability(here4/9)thattheymakemutuallyinconsistentchoicesandgetalowpayoff.Slide7????DicedChicken?DEANSwerveStraight(Chicken)(Though)JAMESSwerve0,0-1,1(Chicken)Straight1,-1-2,-2(Though)Slide84????DicedChicken?1Dean’sq-mix1/23NashEquilibriaJames’sbestresponse011/2James’sp-mixDean’sbestresponseSlide9??????Best-ResponseAnalysis????????????????????????????????????Best-responseanalysiswiththemixtureprobabilitiesonthetwoaxesisacomprehensivewayoffindingallNashequilibria.????????????????????????????Themoresimplyopponent’sindifferencemethodcanfindonlythegenuinelymixedstrategyequilibrium.Slide105????????????Non-Zero-SumMixingWithThreeStrategi