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week9_answ - Department of Economics University of...

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Page 1 of 4 Department of Economics, University of California, Davis Ecn 122 - Game Theory - Professor Giacomo Bonanno ANSWERS TO PRACTICE PROBLEMS for WEEK 9 1. Since B is strictly dominated, it cannot be assigned positive probability at a Nash equilibrium. Let p be the probability of T and q the probability of L. Then p must satisfy the condition: 4 p + 0 (1 - p ) = 3 p + 2(1 - p ) while q must satisfy the condition: 1 q + 4 (1 - q ) = 2 q + 1(1 - q ). Thus p = 2 3 and q = 3 4 . Hence the mixed-strategy equilibrium is given by: T C B L R 2 3 1 3 3 4 1 4 0 F H G I K J 2. (a) The normal form is as follows: PLAYER 2 AC AD BC BD LEG 2 , 0 2 , 0 0 , 2 0 , 2 LEH 2 , 0 2 , 0 0 , 2 0 , 2 LFG 0 , 6 0 , 6 4 , 1 4 , 1 LFH 0 , 6 0 , 6 4 , 1 4 , 1 REG 1 , 4 4 , 3 1 , 4 4 , 3 REH 2 , 0 1 , 2 2 , 0 1 , 2 RFG 1 , 4 4 , 3 1 , 4 4 , 3 P L A Y E R 1 RFH 2 , 0 1 , 2 2 , 0 1 , 2
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Page 2 of 4 (b) There are no pure-strategy Nash equilibria. (c) First let us solve the subgame on the left: Player 2 A B E 2 , 0 0 , 2 Player 1 F 0 , 6 4 , 1 There is no pure-strategy equilibrium. Let us find the mixed-strategy equilibrium. Let p be
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