Econ 367 PS2 - 1 Kaushik Basu Spring 2008 Econ 367...

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Kaushik Basu Spring 2008 Econ 367 Game-Theoretic Methods Problem Set 2 Solutions 1. Consider the normal-form game described below. [Here and elsewhere, player 1 chooses rows, and 2 chooses columns.] L R U 2,2 0,0 D 0,0 1,1 (a) Describe the set of players N. N = {1,2} (b) For each player i N, describe the set of strategies, S i , open to i. S 1 = {U,D} and S 2 = {L,R} (c) Describe each player, i's, payoff function, i π . That is, write down what ) , ( 1 L U π is and likewise for other strategy pairs. Π 1 (U,L) = Π 2 (U,L) = 2; Π 1 (U,R) = Π 1 (D,L) = Π 2 (U,R) = Π 2 (D,L) = 0; Π 1 (D,R) = Π 2 (D,R) = 1 (d) What are the Nash equilibria of this game? Two Nash Equilibria: (U,L) and (D,R) 2. Consider the following game. N = {1,2}. S 1 = {U,D}, S 2 = {L}. 0 ) , ( ; 2 ) , ( 1 1 = = L D L U π π . 10 ) , ( ; 1 ) , ( 2 2 = - = L D L U π π Represent this game in a payoff matrix. What is the Nash equilibrium of this game? Answer: L U (2,-1) D (0,10) Nash Equilibrium: (U,L) 1
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3. Three friends, Anna (A), Berlin (B) and Churchill (C) plan to meet at the cinema. However, they forget to decide whether to meet for the matinee show (M) or the night show (N). Each must choose independently between M and N.
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