HW2-answer - Dr. Huanxing Yang Econ 601 Game Theory...

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Dr. Huanxing Yang Econ 601 Game Theory Homework Assignment 1 Due April 16, Wednesday 1. Chapter 4, Problem 5 a) Since b is optimal when player 2 uses x , c is optimal when player 2 uses y , and d is optimal when player 2 uses z , player 1's strategies of b , c , and d are not strictly dominated. Next note that a is strictly dominated by c . Thus, the strategies of player 1 that survive one round of the iterative deletion of strictly dominated strategies (IDSDS) are b , c , and d . Turning to player 2, z is optimal when player 1 uses a and y is optimal when player 1 uses b . z strictly dominates x . Thus, the strategies of player 2 that survive one round of the IDSDS are y and z . The reduced game is then as shown in Figure SOL4.5.1. Figure SOL4.5.1 Player 2 1,3 0,2 Player 1 2,1 1,2 0,1 2,4 y z b c d For player 1, c strictly dominates b . Neither c nor d are strictly dominated. Thus, the strategies of player 1 that survive two rounds of the IDSDS are c and d . Turning to player 2, neither strategy is strictly dominated. After two rounds, the reduced game is as shown in Figure SOL4.5.2. Figure SOL4.5.2 Player 2 Player 1 2,1 1,2 0,1 2,4 y z c d Though neither of player 1's strategies are strictly dominated, z strictly dominates y for player 2. After three rounds, the reduced game is as shown in Figure SOL4.5.3. Figure SOL4.5.3 Player 2 Player 1 1,2 2,4 z c d
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d strictly dominates c for player 1. We conclude that the IDSDS implies that player 1 uses d and player 2 uses z . b) The unique Nash equilibrium is ( d , z ). 2. Chapter 4, Problem 8 a) Figure SOL4.8.1 Sheikh 2468 1 0 1 0,5 0,3 0,1 0,-1 0,-3 3 5,0 0,3 0,1 0,-1 0,-3 Sultan 5 3,0 3,0 0,1 0,-1 0,-3 7 1,0 1,0 1,0 0,-1 0,-3 9 -1,0 -1,0 -1,0 -1,0 0,-3 b) The unique Nash equilibrium is (7, 6). 3. Chapter 4, Problem 9 The Nash equilibria are ( b, x, A ), ( a ,z, B ), ( c, x, C ), ( c, z, C ). 4. Chapter 4, Problem 10 (a) The resulting performance is 1 for player 1, -1 for player 2, and -1 for player 3 so player 1 wins the promotion. Player 1's strategy is clearly optimal since he receives the maximal payoff of 1. If player 2 switches
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This note was uploaded on 07/17/2008 for the course ECON 601 taught by Professor Yang during the Spring '08 term at Ohio State.

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HW2-answer - Dr. Huanxing Yang Econ 601 Game Theory...

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