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slide23-Oct24 - ECON 401: Game theory: strategies Siyang...

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ECON 401: Game theory: strategies Siyang Xiong Rice University October 23, 2011 Xiong (Rice University) ECON 401 October 23, 2011 1 / 19
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normal-form representation of games a normal-form game is composed of: a set of players, I I a set of actions A i for each player i . 2 I / ; . a i / i 2 I . interpretation: players simultaneously choose some actions available to them; it is usually represented by a game matrix. for example: prisoner±s dilemma: don±t confess confess don±t confess 2 , 2 10 , 1 confess 1 , 10 5 , 5 meet in new york empire state building grand central station empire state building 10 , 10 0 , 0 grand central station 0 , 0 10 , 10 Xiong (Rice University) ECON 401 October 23, 2011 2 ² 19
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extensive-form games an extensive-form is composed of: a set of players, I I a set of histories for each player i . 2 I / , H i I terminal histories: the game ends at terminal histories; non-terminal histories: the game continues at non-terminal histories; a set of actions available for player i at each H i I payo/s for both players at each terminal history; there are two kinds of extensive-form games; perfect-information extensive form games; imperfect-information extensive form games; an extensive form game is usually represented by a tree. Xiong (Rice University) ECON 401 October 23, 2011 3 ± 19
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matching penny version B: there are two players, 1 and 2; player 1 moves &rst, and he chooses head and tail; after observing player 1±s choice, player 2 moves and he choosed hea and tail, which ends the game, if the faces of the pennies match, player 1 gets 1 and player 2 gets -1; if the faces of the pennies do not match, player 1 gets -1 and player 2 gets 1. Xiong (Rice University)
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This note was uploaded on 02/09/2012 for the course ECON 401 taught by Professor Siyang during the Spring '11 term at Rice.

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slide23-Oct24 - ECON 401: Game theory: strategies Siyang...

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