國外博弈論課件lecture(6)-wenkub.com
2024-10-15 12:48 本頁面
【正文】 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。 , si+ 1, . .., sn) ui( s1, s2, ... si 1, si , si+ 1, ... , sn) fo r all s1? S1, s2? S2, . . ., si 1? Si 1, si+ 1? Si + 1, ..., sn? Sn. Definition: strictly dominated strategy regardless of other players’ choices si” is strictly better than si’ Prisoner 2 Mum Confess Prisoner 1 Mum 1 , 1 9 , 0 Confess 0 , 9 6 , 6 May 21, 2021 73347 Game TheoryLecture 3 7 Review: iterated elimination of strictly dominated strategies ? If a strategy is strictly dominated, eliminate it ? The size and plexity of the game is reduced ? Eliminate any strictly dominated strategies from the reduced game ? Continue doing so successively May 21, 2021 73347 Game TheoryLecture 3 8 Iterated elimination of strictly dominated strategies: an example 1 , 0 1 , 2 0 , 1 0 , 3 0 , 1 2 , 0 Player 1 Player 2 Middle Up Down Left 1 , 0 1 , 2 0 , 3 0 , 1 Player 1 Player 2 Middle Up Down Left Right May 21, 2021 73347 Game TheoryLecture 3 9 New solution concept: Nash equilibrium ? The bination of strategies (B’, R’) has the following property: ? Player 1 CANNOT do better by choosing a strategy different from B’, given that player 2 chooses R’. ? Player 2 CANNOT do better by choosing a strategy different from R’, given that player 1 chooses B’. ? (B’, R’) is called a Nash equilibrium Player 2 L’ C’ R’ Player 1 T’ 0 , 4 4 , 0 3 , 3 M’ 4 , 0 0 , 4 3 , 3 B’ 3 , 3 3 , 3 , May 21, 2021 73347 Game TheoryLecture 3 10 Nash Equilibrium: idea ? 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 corresponding strategies, or ? A stable situation that no player would like to dev
教學課件相關推薦
鄂ICP備17016276號-1