discussion_of_duel

discussion_of_duel - Discussion of \Duel" Econ 159a/MGT522a...

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Discussion of \Duel" Econ 159a/MGT522a Ben Polak November 1, 2007 The argument below is a little more formal (and a little less direct) than the one we used in class, but The Rules. There are two players, each with a wet sponge. They start at either side of the room. The players have alternate turns. Each turn, the player can either shoot or take a step forward. If she shoots and hits then she wins. If she misses, then the game continues so The Strategic Decision. When to shoot? Extra structure to make the analysis tractable. Assume that the abilities of the players are known. In particular, let P 1 ( d ) be player 1’s probability of hitting if she shoots at distance d ; and let P 2 ( d ) be player 2’s probability of hitting if she shoots at distance d ; In addition, let us make two plausible assumptions: P 1 (0) = P 2 (0) = 1; that is, they hit for sure from point blank. Both P 1 and P 2 are decreasing; that is, the probabilities of hitting go down with distance. Notice we do need not assume that the players are equally good shots, or even that one is better than the other at all distances, just that their abilities are known. Speculations. We might think that a better shot will shoot ±rst since she has a better chance of hitting. Alternatively, we might think that a worse shot will try to pre-empt the better shot. In fact, the right way to solve this game is:
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This note was uploaded on 02/13/2012 for the course ECON 159 at Yale.

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discussion_of_duel - Discussion of \Duel" Econ 159a/MGT522a...

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