Midterm Examination I: Solutions ECON 504 - Microeconomics II
نویسنده
چکیده
Solution We know that a strictly dominated action is played with zero probability in any Nash equilibrium. There are two pure strategy equilibria (M,L), (B,R). There is no equilibrium in which only one of the players completely mix. The only remaining possibility is both of them completely mixing. Let p be player 1’s probability of playing M and q be player 2’s probability of playing L. As we know, an action receives positive probability in an equilibrium if and only if it is a best response to other players’ strategies. Therefore, given q player 1 must be indifferent between M and B, and given p player 2 must be indifferent between L and R. In other words,
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Midterm Examination Solutions ECON 504 - Microeconomics II
Solution The following is a Nash equilibrium: Player 1 calls and the other players do not call. Player 1’s payoff in this action profile is equal to v− c, and is greater than 0, which is the payoff he would get if he deviated and did not call. All the other players get a payoff of v, which is greater than the payoff that they would get if they were to deviate and call: v − c. Therefore, no play...
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