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slide24-Oct26 - ECON 401: Game theory: solution concepts...

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Unformatted text preview: ECON 401: Game theory: solution concepts Siyang Xiong Rice University October 27, 2011 Xiong (Rice University) ECON 401 October 27, 2011 1 / 13 mixed strategies: normal-form games for any game (normal-form or extensive-form), suppose S i is the set of strategies available to player i . A mixed strategy is a probability over S i . a mixed strategy is denoted by & i 24 . S i / . for example: prisoner&s dilemma: don&t confess confess don&t confess & 2 , & 2 & 10 , & 1 confess & 1 , & 10 & 5 , & 5 a mixed strategy & 1 : [with probability 2 3 , take [ don&t confess ] , and with probability 1 3 , take [ confess ] ], denoted by 2 3 [ don&t confess ] C 1 3 [ confess ] . a mixed strategy & 2 : [with probability 1 4 , take [ don&t confess ] , and with probability 3 4 , take [ confess ] ], denoted by 1 4 [ don&t confess ] C 3 4 [ confess ] . Xiong (Rice University) ECON 401 October 27, 2011 2 / 13 with players taking mixed strategy, their returns in this game are the expected payo/s induced by the mixed strategies: suppose player 1 takes & 1 and player 2 takes & 2 , then player 1 gets 2 3 1 4 U 1 [ don&t confess , don&t confess ] C 2 3 3 4 U 1 [ don&t confess , confess ] C 1 3 1 4 U 1 [ confess , don&t confess ] C 1 3 3 4 U 1 [ confess , confess ] D 1 6 . & 2 / C 1 2 . & 10 / C 1 12 . & 1 / C 1 4 . & 5 / D & 4 & 60 & 1 & 15 12 D& 80 12 D& 20 3 player 2 gets 2 3 1 4 U 2 [ don&t confess , don&t confess ] C 2 3 3 4 U 2 [ don&t confess , confess ] C 1 3 1 4 U 2 [ confess , don&t confess ] C 1 3 3 4 U 2 [ confess...
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slide24-Oct26 - ECON 401: Game theory: solution concepts...

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