HO8F10 - GAME THEORY IN THE SOCIAL SCIENCES Political...

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G AME T HEORY IN THE S OCIAL S CIENCES Political Science 135/Economics 110 Hand out on: Folk Theorems for Infintely Repeated Games Some notation: Let G be the stage game, be one of I ’s strategies, S I S II be one of II ’s strategies, and be a strategy profile with payoffs . Let be a Nash equilibrium of the stage game with payoffs , be j ’s minmax strategy and m ) , ( II I S S ) , ( II I v v ) , ( II I N N ) , ( II I n n j M j be j ’s minmax payoff. An outcome is individually rational if and . I I m v > II II m v > Nash Folk Theorem for Infinitely Repeated Games : If the players are sufficiently patient, then we can find strategies that are Nash in the infinitely repeated game and in which the individually rational outcome is played in each round. Player I ’s (Grim-Trigger) strategy is: - play in the first round. I S - play in the current round as long as the other player play has always played in the past; otherwise minmax the other player forever (i.e., play in each future round). I
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This note was uploaded on 12/25/2010 for the course PO 137 taught by Professor Power during the Fall '10 term at University of California, Berkeley.

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HO8F10 - GAME THEORY IN THE SOCIAL SCIENCES Political...

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