Problem_set_5

# Problem_set_5 - Kaushik Basu Spring 2008 Econ 367...

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Kaushik Basu Spring 2008 Econ 367: Game-Theoretic Methods Problem Set 5 1. Neither John nor George wishes to show up at a public meeting wearing the same colored hat. Hats can be R (red), W or B. Represent the decision problem of John and George as a game. That is, selecting some appropriate numbers for payoffs, write down a pay-off matrix to describe this game. Locate all the Nash equilibria. 2. Let us define a new equilibrium concept, which I will call the asymmetric Nash equilibrium , for two-player games as follows: ( ) , * 2 * 1 s s is an asymmetric Nash equilibrium if and only if ) , ( ) , ( * 2 1 1 * 2 * 1 1 s s s s π π , for all s 1 * 1 s ), , ( ) , ( 2 * 1 2 * 2 * 1 2 s s s s π π for all s 2 (a) In the game described below, where player 1 chooses between U and D and 2 chooses between L and R , locate all Nash equilibria and asymmetric Nash equilibria L R U 2, 2 4, 2 D 1, 2 4, 4 (b) If an outcome is an asymmetric Nash equilibrium, does it have to be a Nash equilibrium? Briefly explain your answer. 3. Consider the Traveler’s Dilemma game. (a) Is strategy 100 (that is, for a player to write 100) weakly dominated by any other strategy (that is, writing some other number)? If so, which ones? Briefly explain your answer.

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