10.3 Fudenberg and Tirole (1992) develop a game of stag-hunting based on an observation originally made by Rousseau. The two players in the game may either cooperate in catching a stag or each may set out on his own to catch a hare. The payoff matrix for this game is given by

a. Describe the Nash equilibria in this game.

b. Suppose B believes that A will use a mixed strategy in choosing how to hunt. How will B’s optimal strategy choice depend on the probability A will play stag?

c. Suppose this game is expanded to n players (the game Rousseau had in mind) and that all n must cooperate in order for a stag to be caught. Assuming that the payoffs for one specific player, say B, remain the same and that all the other n
1 players will opt for mixed strategies, how will B’s optimal strategy depend on the probabilities with which each of the other players plays stag? Explain why cooperation seems less likely in this larger game.