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

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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 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 . 10 ) , ( ; 1 ) , ( 2 2 = - = L D L U (2,-1) D (0,10) Nash Equilibrium: (U,L) 1
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Econ 367 PS2 - 1 Kaushik Basu Spring 2008 Econ 367...

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