201Midterm1Answers-2006spring - SABANCI UNIVERSITY ECON 201...

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Unformatted text preview: SABANCI UNIVERSITY ECON 201 ÔÇô B GAMES AND STRATEGY FIRST MIDTERM EXAMINATION ANSWERS March 22, 2006 Instructor: Mehmet Ba├ž Time allowed: 90 minutes, 105 points 1. ( 30 points ). Two players, I and II, will vote over three alternatives, A, B and C. The rules are: (a) the alternative that gets two votes is chosen , but (b) if no alternative gets two votes, then alternative C is chosen . Player I prefers A the most, followed by B, and last, C. Player II prefers B most, followed by C, and last, A. Payoffs are as follows: A player gets ÔÇť2ÔÇŁ if her most preferred alternative is chosen, the payoff ÔÇť1ÔÇŁ if her second-best is chosen, and ÔÇť0ÔÇŁ otherwise. Suppose that the players will vote simultaneously. (i) Represent this game fully in its strategic (normal) form. (ii) Which strategies (if any) are strictly dominated? weakly dominated? Answer for both players. (iii) In class, we mentioned that the play of weakly dominated strategies can form a Nash equilibrium. Is this the case in this game? Verify. (iv) Identify all Nash equilibria of this game. Verify. (v) Identify the efficient one among these Nash equilibria and explain why it is efficient. ANSWER.. (i) To build the game matrix, we use the fact that if the votes match, then that alternative is chosen, and otherwise alternative C is chosen. II I A B C A 2 , 0 , 1 0 , 1 B 0 , 1 1 , 2 0 , 1 C 0 , 1 0 , 1 0 , 1 (ii) There are no strictly dominated strategies. For player I, voting B weakly dominates voting C, and voting A weakly dominates voting C. Neither voting A nor voting B weakly dominates the other. For player II, voting C weakly dominates voting A, and voting B weakly dominates both voting A and voting C. (iii) For player I, voting C is weakly dominated, for player II, voting A and voting C are both weakly dominated (by voting B). ÔÇťI votes C, II votes CÔÇŁ is a Nash equilibrium and the strategies of both players are weakly dominated....
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This note was uploaded on 03/16/2012 for the course FENS 101 taught by Professor Sel├žukerdem during the Fall '12 term at Sabanc─▒ University.

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201Midterm1Answers-2006spring - SABANCI UNIVERSITY ECON 201...

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