國外博弈論課件lecture(7)-資料下載頁
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【正文】 on ]1 ,0[ . Bid der 2 bel ie ves t h at 1v is uniformly distr ib uted on ]1 ,0[ . 1v and 2v are inde pe nd ent. ? Bi dd er 1 and 239。s p ayoff functions: ??????????????????????1212221222221221211121111211 if0 if2 if)。,( if0 if2 if)。,(bbbbbvbbbvvbbubbbbbvbbbvvbbu June 24, 2021 73347 Game TheoryLecture 25 19 Firstprice sealedbid auction ( of Gibbons) cont’d ? A str ategy for bidd er 1 is a f unctio n )( 11 vb, fo r all ]1 ,0[1 ?v. ? A str ategy for bidd er 2 is a f unctio n )( 22 vb, fo r all ]1 ,0[2 ?v. ? Given bid d er 139。s bel ie f on bidd er 2, f or each ]1 ,0[1 ?v, b id der 1 sol ves )}({P r o b)(21)}({P r o b)( 221112211101vbbbvvbbbvM a xb?????? ? Given bid d er 239。s bel ie f on bidd er 1, f or each ]1 ,0[2 ?v, bid der 2 sol ves )}({P r o b)(21)}({P r o b)( 112221122202vbbbvvbbbvM a xb?????? June 24, 2021 73347 Game TheoryLecture 25 20 Firstprice sealedbid auction ( of Gibbons) cont’d ? Ch eck whet her ????????2)( ,2)(22*211*1vvbvvb is Bayesi an Nash equi l ib rium . ? Given bid d er 139。s bel ie f on bidd er 2, f or each ]1 ,0[1 ?v, b id der 1 39。s best response to )(2*2 vb sol ves )}({P r o b)(21)}({P r o b)( 2*21112*211101vbbbvvbbbvM a xb?????? }2{P r o b)(21}2{P r o b)( 2111211101vbbvvbbvM a xb?????? }2{P r o b)(21}2{P r o b)( 1211121101bvbvbvbvM a xb?????? 111012)( bbvM a xb?? FOC: 04211 ?? bv 2)( 111vvb ?? June 24, 2021 73347 Game TheoryLecture 25 21 Firstprice sealedbid auction ( of Gibbons) cont’d ? He nce, f or e ach ]1 ,0[1 ?v, 2)(11*1vvb ? is bi dde r 139。s best r espo nse to bid der 239。s 2)(22*2vvb ? . ? By symm et ry, for each ]1 ,0[2 ?v, 2)(22*2vvb ? is bidd er 239。s best r e spon se to bid der 139。s 2)(11*1vvb ? . ? The refor e, ????????2)( ,2)(22*211*1vvbvvb is Bayesi a n Nash equil i brium. June 24, 2021 73347 Game TheoryLecture 25 22 Summary ? Battle of sexes with inplete information (version two) ? Firstprice sealedbid auction ? Next time ? Reading lists ? Chapter of Gibbons ? Chapter of Gibbons
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