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problemset5 - Problem Set 5 Ben Polak Econ 159a/MGT522a...

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Problem Set 5. Ben Polak Econ 159a/MGT522a Three questions due October 24, 2007 (N.B. This is after the midterm.) 1. Evolutionary Stability and Weak Domination (Osborne). Suppose that the pure strategy s ° is evolutionarily stable. Is it possible that there is some other pure strategy that weakly dominates s ° ? Is it possible that there is some other pure strategy that is not weakly dominated by s ° ? Brie°y explain your answer. 2. Evolutionary Stability and Pareto Ranked Equilibria (adapted from Osborne). Con- sider the following symmetric two-player game. Each player can ‘demand’ an amount 1, 2 or 3. If both players demand the same amount then they each get that amount. If they demand di±erent amounts then the player who demands less gets the amount demanded by the player who demanded more, and the player who demands more gets 1/4 of her demand. That is, u 1 ( s 1 ; s 2 ) = 8 < : s 2 if s 1 < s 2 s 1 if s 1 = s 2 s 1 4 if s 1 > s 2 .
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