國(guó)外博弈論課件lecture(8)(已改無(wú)錯(cuò)字)
2022-11-19 13:59:03 本頁(yè)面
【正文】 ion three) cont’d ? Now we h ave four e qu ati ons with four u nknown s. 2)()|()()|()(212121211LHLHHHHHcqccccpcqccccpcacq???????? 2)()|()()|()(212121211LLLHLHLLcqccccpcqccccpcacq???????? 2)()|()()|()(121212122LHLHHHHHcqccccpcqccccpcacq???????? 2)()|()()|()(121212122LLLHLHLLcqccccpcqccccpcacq???????? ? Solv i ng t h ese giv e s us t h e foll ow in g B ayes ia n N ash equilibri um . ? ?)( ),( *1*1 LH cqcq ? ?)( ),( *2*2 LH cqcq June 23, 2021 73347 Game TheoryLecture 24 16 Cournot duopoly model of inplete information (version three) cont’d ? The Bayes i an Nash eq uilib rium: (( )(*1 Hcq, )(*1 Lcq), ( )(*2 Hcq, )(*2 Lcq)) ? If firm 139。s mar gin al c ost is HIGH t hen it cho oses )(*1 Hcq wh ic h is its best response to f irm 239。s ( )(*2 Hcq, )(*2 Lcq) (and the p robabili ty) . ? If firm 139。s mar gin al c ost is LOW t hen it cho oses )(*1 Lcq whi c h is its best response to f irm 239。s ( )(*2 Hcq, )(*2 Lcq) (and the p robabili ty) . ? I f firm 2 39。s mar gin al c ost is HIGH t hen it cho oses )(*2 Hcq whi c h is its best response to f irm 1 39。s ( )(*1 Hcq, )(*1 Lcq) (an d t he probab i li ty) . ? If firm 239。s mar gin al c ost is LOW t hen it cho oses )(*2 Lcq whi c h is its best response to f irm 139。s ( )(*1 Hcq, )(*1 Lcq) (and the p robabili ty) . June 23, 2021 73347 Game TheoryLecture 24 17 Normalform representation of static Bayesian games ? T he normal form r epre sentation o f an n pla yer static ga me G of in ple te in form ation specifie s: ? A fini te set o f pla yers {1, 2, .. ., n }, ? pla yers’ act io n sets nAAAA . . . , , , , 321 and ? their payoff f unctio ns ? mor e ? Re mar k: a pla yer39。s pa yoff functio n d epe nds on not only the n player s39。 actions but also he r TY PE . ? iT is playe r i 39。s type set . ? Exa mple: } ,{1 LH ccT ?, } ,{2 LH ccT ? June 23, 2021 73347 Game TheoryLecture 24 18 Normalform representation of static Bayesian games: payoffs ? Pl ayer i 39。s p ayoff functi on is represented as : . , ..., , ,f or ) 。 ..., , ,(221121 iinnini TtAaAaAataaau ???? ? Exa mple: ])([) 。 ,(211211 HH cqqaqcqqu ???? ])([) 。 ,(211211 LL cqqaqcqqu ???? ? Ea ch pla y e r know s her own t ype. Equi va le nt ly, she knows her own payoff f unctio n. ? Ea ch pla y e r may be u ncertain ab out ot her play ers39。 t ypes. Eq uivalen tl y, she is uncertain about ot
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