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【正文】 her players39。 payoff functions. June 23, 2021 73347 Game TheoryLecture 24 19 Normalform representation of static Bayesian games: beliefs (probabilities) ? Pl ayer i ha s beli ef s on ot her players39。 types, den oted by . ..., , ,f or ) | ..., , , ..., , ,( 22111121 nniniii TtTtTtttttttp ????? or . ..., , , ), ..., , , ..., , ,( w he r e) |( 22111121 nnniiiiii TtTtTtttttttttp ???? ???? ? Pl ayer i 39。s b el ie fs are conditional p robabi l itie s ? Exa mple: )|( 121 HH ccccp ?? )|(121 LH ccccp ?? )|( 121 HL ccccp ?? )|(121 LL ccccp ?? June 23, 2021 73347 Game TheoryLecture 24 20 Strategy ? In a st atic Ba yesian g ame, a stra tegy f or p la yer i is a f u nction iiii Ttts ?e a c h f or ) (. ? ) (ii ts specifie s what player i does f or h er each t ype ii Tt ? ? Exa mple: ( )(1 Hcq, )(1 Lcq) is a str ate gy f or firm 1 in t he Co urnot model of inco mplete informat io n (ve rsion thr ee). June 23, 2021 73347 Game TheoryLecture 24 21 Bayesian Nash equilibrium: 2player ? In a st atic Ba yesian 2 pla yer game } , 。 , 。 , 。 ,{21212121 uuppTTAA, the st rategies )( ),( *2*1 ?? ss are pure st rategy B ayesian N ash equ i li bri um if ? for each of p la yer 139。s types 11 Tt ?, )(1*1 ts solves ???2211)|() )。( ,( 12112*211TtAattpttsauM a x ? and f or each of playe r 239。s types 22 Tt ?, )(2*2 ts s olve s ???1122)|() 。 ),(( 212221*12TtAattptatsuM a x June 23, 2021 73347 Game TheoryLecture 24 22 Bayesian Nash equilibrium: 2player ? In a st atic Ba yesian 2 pla yer game } , 。 , 。 , 。 ,{ 21212121 uuppTTAA, the str ategi es )( ),( *2*1 ?? ss are pure strategy Bayesian Na sh equ i li bri um if for each i a nd j , ( assume .... } , ,{ .... } , , ,{2221212111 ttTttT ??) )( 11*1 ts )(21*2 ts )( 12*1 ts )(22*2 ts ? ? ? )(2*2 jts )( 1*1 its ? ? )(2*2 nts )( 1*1 nts ? ? player 1’s best response if her type is t1i player 2’s best response if her type is t2j In the sense of expectation based on her belief In the sense of expectation based on her belief June 23, 2021 73347 Game TheoryLecture 24 23 Summary ? Cournot duopoly model of inplete information (version three) ? Bayesian Nash equilibrium ? Next time ? Battle of sexes with inplete information (version two) ? Auction ? Reading lists ? Chapter of Gibbons ? Chapter of Gibbons
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