1.3 Mixed Strategy Equilibrium-exe

1.3 Mixed Strategy Equilibrium-exe - AMS 335/ECO 355 Game...

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AMS 335/ECO 355 Game Theory Fall 2010 Exercise of 1.3 Mixed Strategy Equilibrium Zhen Xu Page 1 of 3 Exercise 1.3.1 the Prisoners’ Dilemma Table 1 shows Aumann version of the Prisoner's Dilemma, where the units of the payoff are thousands of dollars. Find the max-min strategies and the mixed strategy Nash equilibrium if any. Table 1 The Prisoner's Dilemma Player 2 Cooperate Defect Player 1 Cooperate 3, 3 0, 4 Defect 4, 0 1, 1 We know from the practice in chapter 1.1 Normal Form Game that both players have dominant strategy Defect and the game has a unique pure strategy Nash equilibrium ( Defect , Defect ). We can also discuss the game by assuming that the two players prepare for the worst, that is, choose a max-min strategy, which maximizes the player’s worst payoff against all possible choices of the opponent. For the above game, the worst scenario for Player 1 is that the opponent chooses Defect , thus Player 1 will also choose Defect in order to better off the worst case. Since this is a symmetric game, Player 2 has the same max-min strategy choice – Defect . Suppose Player 1 players
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1.3 Mixed Strategy Equilibrium-exe - AMS 335/ECO 355 Game...

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