Problem 3 (Bayesian Games) Consider the following Bayesian game played by two pl

Question

Problem 3 (Bayesian Games) Consider the following Bayesian game played by two players (1 and 2) who are deciding whether to cooperate, C, or defect, D. Two states are possible, Good and Bad. Suppose that Player 2 knows the state, while Player 1 thinks that the state is Good with probability p. Payoffs in each state respectively satisfy 112 C D State Good: C0,0 1,1 DI 1,1 0,0 112 C D State Bad: C0,0 0,1. DI 1,0 3,3 Player 1 is the row player, and his payoff is the first to appear in each entry. Player 2 is the column player and his payoff is the second to appear in each entry. 1. What is the set of possible strategies for the two players in this game? 2. Find the pure strategy Bayes-Nash equilibria for all values of p E (0,1)

Explanation / Answer

1. The Nash equilibria in pure strategies in the good state would be (D,C) and (C,D), with payoffs of (1,1) in each case. This can happen with probability p. In the bad state the Nash equilibrium is given by (D,D) with payoffs of (3,3). This occurs with probability of 1-p.

2. The Bayes Nash equilibrium takes into consideration the 2 states giving the best expected outcome.

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