HO9F10 - GAME THEORY IN THE SOCIAL SCIENCES Political...

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1 G AME T HEORY IN THE S OCIAL S CIENCES Political Science 135/Economics 110 Hand out on Subgame Perfect Equilibria in Repeated Games In this handout we will consider the infinitely repeated game in which the players discount factor is .9 and in which the stage game is: II W X Y Z A 6, 6 -1, 10 -2,5 -5,-3 B I 10, -1 3, 3 -1, 4 -1, -3 C 5, -2 4, -1 0, 0 -3, -3 D -3, -5 -3, -4 -3, -3 -2, -2 Grim Trigger Strategies are not subgame perfect: Consider the following grim trigger strategies in which each player minmaxes the other forever following a defection. The strategies are: I: Play A in round one. Play A in the current round as long as II has always played W in all previous rounds; otherwise play D. II: Play W in round one. Play W in the current round as long as I has always played A in all previous rounds; otherwise play Z. It is straight forward to verify that these strategies form a Nash equlibrium. But are they subgame perfect? The answer is no. To show this, we must find a subgame in which the
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HO9F10 - GAME THEORY IN THE SOCIAL SCIENCES Political...

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