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Unformatted text preview: Problem Set 2 . Ben Polak Econ 159a/MGT522a Four questions, due September 26, 2007. 1. Penalty Shots Revisited. Player 1 has to take a soccer penalty shot to decide the game. She can shoot L eft, M iddle, or R ight. Player 2 is the goalie. He can dive to the l eft, m iddle, or r ight. Actions are chosen simultaneously. The payo&s (which here are the probabilities in tenths of winning) are as follows. 2 l m r L 4 ; 6 7 ; 3 9 ; 1 1 M 6 ; 4 3 ; 7 6 ; 4 R 9 ; 1 7 ; 3 4 ; 6 (a) For each player, is any strategy dominated by another (pure) strategy? (b) For what beliefs about player 1’s strategy is m a best response for player 2? For what beliefs about player 2’s strategy is M a best response for player 1? [Hint: you do not need to draw a 3-dimensional picture!]. (c) Suppose player 2 \puts himself in player 1’s shoes" and assumes that player 1, what ever is her belief, will always choose a best-response to that belief. Should player 2 ever choose m ? (d) Show that this game does not have a (pure-strategy) Nash Equilibrium? 2. Partnerships Revisited. (Adapted from Watson.) Recall the partnership game we discussed in class. Two law partners jointly own a ¡rm and share equally in its revenues. Each law partner individually decides how much e&ort to put into the ¡rm. The ¡rm’s revenue islaw partner individually decides how much e&ort to put into the ¡rm....
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This note was uploaded on 02/13/2012 for the course ECON 159 taught by Professor Benjaminpolak during the Fall '08 term at Yale.
- Fall '08
- Game Theory