國(guó)外博弈論課件lecture(6)(參考版)
2024-10-21 12:48本頁(yè)面
【正文】 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 。 Natives Bar 2 $2 $4 $5 Bar 1 $2 10 , 10 14 , 12 14 , 15 $4 12 , 14 20 , 20 28 , 15 $5 15 , 14 15 , 28 25 , 25 Payoffs are in thousands of dollars Use best response function to find the Nash equilibrium. May 21, 2021 73347 Game TheoryLecture 3 22 Example: The battle of the sexes ? Opera is Player 1’s best response to Player 2’s strategy Opera ? Opera is Player 2’s best response to Player 1’s strategy Opera ? Hence, (Opera, Opera) is a Nash equilibrium ? Fight is Player 1’s best response to Player 2’s strategy Fight ? Fight is Player 2’s best response to Player 1’s strategy Fight ? Hence, (Fight, Fight) is a Nash equilibrium 2 , 1 0 , 0 0 , 0 1 , 2 Chris Pat Prize Fight Opera Prize Fight Opera May 21, 2021 73347 Game TheoryLecture 3 23 Example: Matching pennies ? Head is Player 1’s best response to Player 2’s strategy Tail ? Tail is Player 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
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