國(guó)外博弈論課件lecture(6)-資料下載頁(yè)
2024-10-18 12:48本頁(yè)面
【正文】 r 2’s best response to Player 1’s strategy Tail ? Tail is Player 1’s best response to Player 2’s strategy Head ? Head is Player 2’s best response to Player 1’s strategy Head ? Hence, NO Nash equilibrium 1 , 1 1 , 1 1 , 1 1 , 1 Player 1 Player 2 Tail Head Tail Head May 21, 2021 73347 Game TheoryLecture 3 24 In th e no rm al fo rm g a me { S 1 , S 2 , ..., S n , u 1 , u 2 , . .., u n }, if p la y er 1 , 2 , .. ., i 1, i +1, ... , n choose strategi es nii ssss ,...,..., 111 ??, r espectively , th en p la y er i 39。 s b est respo nse fu nctio n is defin ed by } a l lf o r ), . . . , . . . ,( ), . . . , . . . ,(:{ ) , . . . , . . . , (111111111iiniiiiniiiiiiniiiSssssssusssssuSsssssB???????????? Definition: best response function Player i’s best response Given the strategies chosen by other players May 21, 2021 73347 Game TheoryLecture 3 25 An a lternati ve d efinitio n: Play er i 39。 s stra tegy ), . . ., . . . ,(111 niiii ssssBs ??? if and onl y if it solv es (o r it is an o pt im al so lu tio n to) Ma xi miz e ), . . . , . . . ,(111 niiii sssssu ?? ? Sub ject to ii Ss ?? where nii ssss ..., , , ..., , 111 ?? are g iv en. Definition: best response function Player i’s best response to other players’ strategies is an optimal solution to May 21, 2021 73347 Game TheoryLecture 3 26 Using best response function to define Nash equilibrium ? A set of strategies, one for each player, such that each player’s strategy is best for her, given that all other players are playing their strategies, or ? A stable situation that no player would like to deviate if others stick to it In the nor m al f orm ga m e { S 1 , ..., S n , u 1 , ..., u n }, a binati on of str ategies ), . . . ,( **1 nss is a Na sh equili b rium if f or ever y player i , ) . . . , , , , . . . , ( ** 1* 1*1* niiii ssssBs ??? May 21, 2021 73347 Game TheoryLecture 3 27 Summary ? Nash equilibrium ? Best response function ? Using best response function to define Nash equilibrium ? Using best response function to find Nash equilibrium ? Next time ? Concave function and maximization ? Applications ? Reading lists ? Sec and of Gibbons
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