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1、Eco514-GameTheoryLecture5：GameswithPayoUncertainty(2)Eco514—GameTheoryLecture5:GameswithPayoffUncertainty(2)MarcianoSiniscalchiSeptember30,1999IntroductionThislecturecontinuesouranalysisofgameswithpayoffuncertainty1>.Thethreemainobjec-tivesare:(1)toillustratetheflexibilityoftheHarsanyiframewo
2、rk(orourversionthereof);(2)tohighlighttheassumptionsimplicitintheconventionalusageoftheframework,andthepossibledepartures;(3)todiscussitspotentialproblems,aswellassomesolutionstothelatter.CournotRevisitedRecallourCournotmodelwithpayoffuncertainty.Firm2’scostisknowntobezero;Firm1’scostisuncert
3、ain,andwillbedenotedbyc∈{01,2}.DemandisgivenbyP(Q)=2??Qandeachfirmcanproduceqi∈[0,1].Werepresentthesituationasagamewithpayoffuncertaintyasfollows:let??={01,2},T1={{0},{12}},T2={??}andp2(0)=pi.Itiseasytoseethatspecifyingp1isnotrelevantforthepurposesofBayesianNashequilibriumanalysis:whatmatters
4、therearethebeliefsconditionaloneacht1∈T1,butthesewillobviouslybedegenerate.ThefollowingequalitiesdefineaBayesianNashequilibrium(doyouseewherethesecomefrom?):q1(0)=1??1q2211q1()=3??q2242[]1q2=1??1piq1(0)+(1??pi)q1()221Eco514-GameTheoryLecture5：GameswithPayoUncertainty(2)Eco514—GameTheoryLectur
5、e5:GameswithPayoffUncertainty(2)MarcianoSiniscalchiSeptember30,1999IntroductionThislecturecontinuesouranalysisofgameswithpayoffuncertainty1>.Thethreemainobjec-tivesare:(1)toillustratetheflexibilityoftheHarsanyiframework(orourversionthereof);(2)tohighlighttheassumptionsimplicitintheconventiona
6、lusageoftheframework,andthepossibledepartures;(3)todiscussitspotentialproblems,aswellassomesolutionstothelatter.CournotRevisitedRecallourCournotmodelwithpayoffuncertainty.Firm2’scostisknowntobezero;Firm1’scostisuncertain,andwillbedenotedbyc∈{01,2}.DemandisgivenbyP(Q)=2??Qandeachfirmcanproduce
7、qi∈[0,1].Werepresentthesituationasagamewithpayoffuncertaintyasfollows:let??={01,2},T1={{0},{12}},T2={??}andp2(0)=pi.Itiseasytoseethatspecifyingp1isnotrelevantforthepurposesofBayesianNashequilibriumanalysis:whatmatterstherearethebeliefsconditi
