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Problem-Set-3 - Problem Set 3 Game Theory Instructor Todd...

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Problem Set 3 — Game Theory Instructor: Todd Sarver Econ 310-2, Fall 2011 TA: Esteban Petruzzello (Any email questions regarding this PS should be sent to this TA.) Complete all problems and explain your answers carefully. This problem set is due on Thursday, October 27 at 4:45pm in the mailbox labeled Todd Sarver in the Economics Department main office (302 Andersen Hall). At the top of your assignment, please include the TA whose discussion session you attend (Guannan, Robert, Esteban) and the day that you attend (Monday, Friday). 1 Mixed Strategies in the Coordination Game In class, we discussed the following coordination game: Player 2 P C Player 1 P 5 , 5 0 , 0 C 0 , 0 2 , 2 Recall that the pure-strategy Nash equilibria of this game are ( P, P ) and ( C, C ). In the language of mixed strategies, the equilibrium strategy profile ( P, P ) can be written as ( σ P 1 , σ P 2 ) = (1 , 1), and the strategy profile ( C, C ) can be written as ( σ P 1 , σ P 2 ) = (0 , 0) (since σ C i = 1 - σ P i ). There is also another mixed-strategy equilibrium of this game. Find the mixed strategies ( σ P 1 , σ P 2 ) in this third Nash equilibrium. 2 Mixed Strategies and Weakly Dominated Strategies
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