00solution - Prof. William H. Sandholm Department of...

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–1– Prof. William H. Sandholm Department of Economics University of Wisconsin Spring 2000 Final Exam Solutions 1. Since we are only assuming common knowledge of rationality, we need to look for the rationalizable strategies. Since this is a two player game, it is equivalent to look for strategies which survive iterated removal of strictly dominated strategies. It turns out to be easiest to first use iterated strict dominance to get rid of pure strategies, and then to get rid of mixed strategies which are never a best response. We can first remove c , which is strictly dominated by d . After this, we can remove A , which is then strictly dominated by B . Then, we can remove a , which is strictly dominated by 2 5 b + 3 5 d . No other pure strategies can be removed. Since pure strategies B and C are both best responses to b , these strategies and all mixtures between them are rationalizable. If player 1 plays B , then d and e are both best responses for player 2; if σ 1 ( B ) ( 3 5 , 1), then d is the unique best response; if 1 ( B ) = 3 5 , then b and d are both best responses; if 1 ( B ) [0, 3 5 ), b is the unique best response. Thus, it is never a best response for player 2 to put positive weight on both b and e ; but all other mixtures between b , d , and e are best responses. Thus: Rationalizable strategies for 1: All mixtures of B and C . Rationalizable strategies for 2: All mixtures of b , d , and e which do not put positive weight on both b and e .
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This note was uploaded on 08/08/2008 for the course ECON 713 taught by Professor Sandholm during the Spring '08 term at Wisconsin.

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00solution - Prof. William H. Sandholm Department of...

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