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

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Unformatted text preview: 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) Heres 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 3s to in order to arrange this? 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...
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This note was uploaded on 02/06/2011 for the course ORIE 4350 at Cornell University (Engineering School).

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

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