hw12 - in the game Let p(t denote the proportion of the...

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S'11 Prof. Stahl ECO 354K - Problem Set No. 12 Due Thursday, May 4. 1. Consider the following symmetric normal-form game: L R . L | 60, 60 | 0, 40 | R | 40, 0 | 40, 40 | (a) Find all the Nash equilibria. (b) Suppose this game is played by boundedly rational players. What is the most likely choice of Level-1 players, Level-2 players? (c) Given the first period choices identified in (b), what is the most likely choice of Level-1 and Level-2 players in the second period and beyond? 2. Suppose the previous game is played in a very large single population consisting of L and R types. Every period players are randomly matched and play the previous game; i.e. L types always play L, and R types always play R
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Unformatted text preview: in the game. Let p(t) denote the proportion of the population consisting of L types in period t, so 1-p(t) is the proportion consisting of R types. (a) What is the expected payoff of each type as a function of p(t)? (b) What is the average payoff in the population? (c) If the population of types evolves according to replicator dynamics, write down the first-order differential equation that defines the population dynamics: dp/dt = ? (d) Sketch a graph of dp/dt. (e) Identify all the values of p for which dp/dt = 0. These points are called the “dynamic rest points”. (f) If p(0) = 0.5, what will be the limit of p(t) as t goes to infinity?...
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This note was uploaded on 06/09/2011 for the course ECON 354 taught by Professor Econ during the Spring '11 term at University of Texas.

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