a) Explain why the selfish type 2 player will always play D, while the nice type 2 player might play C or D. b) Let p be the probability that a player 1 faces a selfish player 2. Draw the incomplete information game in extensive form. c) Suppose that player 1 is expected to play D. What is a nice player 2's best response? d) For what values of p (if any) is it Bayesian-Nash equilibrium (BNE) for player 1 to play D in response to D by both types of player 2s? Explain. e) For what values of p (if any) is it a Bayesian-Nash equilibrium (BNE) for player 1 to play C in response to D by a selfish player 2 and C by a nice player 2? Explain. PROBLEM 6. There is a dispute in a local saloon in the Wild West, the Marshal arrives to restore order when one of the men steps back and pulls his hand away from his body as if he's ready to draw. The decision faced by the Marshal and the stranger is whether to draw immediately or instead wait and draw only in response to the other's pulling out his gun. The shooting talents of the Marshal are known by everyone, but the Marshal doesn't know the skill of the stranger: is he a gunslinger or just a plain cowpoke? The payoffs for the game in which the Marshal faces a gunslinger are represented in matrix a, and the payoffs for the game in which the Marshal faces a cowpoke are represented in matrix b.
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