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# prel2 - Prelim II 2 hours OR&IE 435 Game Theory Fall 04 You...

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Prelim II OR&IE 435 Fall ’04 2 hours. Game Theory You may use one sheet of notes (8 1/2 x 11, both sides). Give brief justifications for your answers. 1. (25 points: 10, 10, 5) Here’s a “die-matching” game: II - 3 1 1 1 1 1 3 - 1 - 1 - 1 - 1 - 1 1 - 3 1 1 1 1 - 1 3 - 1 - 1 - 1 - 1 1 1 - 3 1 1 1 - 1 - 1 3 - 1 - 1 - 1 I 1 1 1 - 3 1 1 - 1 - 1 - 1 3 - 1 - 1 1 1 1 1 - 3 1 - 1 - 1 - 1 - 1 3 - 1 1 1 1 1 1 - 3 - 1 - 1 - 1 - 1 - 1 3 (a) Write down a linear programming problem whose solution would allow you to obtain a security strategy for I and the value of the game. Explain how to obtain these from the optimal solution of your LP. (b) Guess security strategies for both players. Compute the payoff to each if they use these strategies. Check that these two strategies form a Nash equilibrium. (c) You want to design a “fair” die-matching game, with value 0. What could you change all the 3’s to in order to arrange this?

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2. (30 points: 6, 6, 7, 4, 4, 3) Alice and Bob and the players in the penny-matching game: Bob H T - 1 1 H 1 - 1 Alice 1 - 1 T - 1 1
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