WeekofFeb23

WeekofFeb23 - the batter is more likely to get a hit than...

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W3211 Spring 2009 Professor Vogel Recitation Week of 02/23/09 L R T a 1 ;b 1 a 2 ;b 2 B a 3 ;b 3 a 4 ;b 4 1. Suppose this is a simultaneous move game (i.e. both players move at the same time) (a) What are the weakest conditions under which both ( T;L ) and ( B;R ) are pure strategy Nash Equilibria? (b) Can both ( T;L ) and ( B;R ) be dominant strategy Nash Equilibria? (c) Under what condition is there a strict mixed strategy Nash Equilibrium? 2. Suppose that the following simultaneous move game is being played [ PLAYERS ] between a pitcher (Player 1 ) and a batter (Player 2 ). [ ACTIONS ] The pitcher can throw two pitches, a fastball ( F ) and a cutter ( C ) and the batter can look for either the fastball ( A ) or the cutter ( B ). [ PAYOFFS ] If the pitcher throws either F or C , only a good fastball (if the batter guesses correctly and the pitcher throws a fastball,
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Unformatted text preview: the batter is more likely to get a hit than if the batter guesses correctly and the pitcher throws a cutter; if the batter guesses incorrectly and the pitcher throws a fastball, the batter is more likely to get a hit than if the batter guesses incorrectly and the pitcher throws a cutter). The batter&s utility is increasing in the probability he gets a hit while the pitcher&s utility is decreasing in the probability the batter gets a hit. (a) Write out a payo/ matrix for this game with examples for payo/s that satisfy the above description of the game. (b) Given the description of this game, can there exist a dominant strategy equilib-rium? (c) Given the description of this game, can a pitcher ever be su¢ ciently good at throwing a cutter (or bad at throwing a fastball) that there is a Nash Equilibrium in pure strategies ( C;B ) ?...
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This note was uploaded on 12/21/2009 for the course ECON 1211 taught by Professor Govel during the Spring '08 term at Columbia.

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