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Unformatted text preview: MS&E 246: Game Theory with Engineering Applications Feryal Erhun Winter, 2010 Problem Set # 1 Due: January 21, 2010 1. Consider the following bargaining game. Players 1 and 2 are bargaining over how to split one dollar. Both players simultaneously name shares they would like to have, s 1 and s 2 , where 0 s 1 , s 2 1. If s 1 + s 2 1, then the players receive the shares they named; if s 1 + s 2 > 1, then both players receive zero. i. What are each players strictly dominated strategies? ii. What are each players weakly dominated strategies? iii. What are the pure strategy Nash equilibria of this game? 2. (a) Argue that if a player has two weakly dominant strategies, then for every strategy choice by his opponents, the two strategies yield him equal payoffs. (b) Provide an example of a two-player game in which a player has two weakly dominant pure strategies but his opponent prefers that he play one of them rather than the other. 3. Consider the following game: Player 2 LL L M R U (100,2) (-100,1) (0,0) (-100,-100) Player 1 D (-100,-100) (100,-49) (1,0) (100,2) i. If you were player 2 in this game and you were playing it once without the ability to engage in preplay communication with player 1, what strategy would you choose? ii. What are all the Nash equilibria (pure and mixed) of this game?...
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