Answer Happy

1. (Three hunter stag hunt) Three hunters play a stag hunt game. There are two possible strategies, Stag and Hare. Anyone who plays Hare will get a payoff of 1, no matter what the others do. If at least two hunters play the strategy Stag, then each player who played Stag will get a payoff of S/n where n is the number of hunters who played Stag. If one hunter plays Stag and the other two play Hare, then the hunter who played Stag gets 0. (a) (5 points) If S > 3, find all of the pure-strategy Nash equilibria for this game. If 2<s<3, find all of the pure-strategy Nash equilibria for this game. (b) (5 points) Suppose that there is a symmetric mixed strategy equilibrium where each hunter plays Stag with probability p such that 0 < p<1. Find a quadratic equation in p that must be satisfied at such an equilibrium. (c) (5 points) Looking at the solution to (c) find the range of values of S for which there is a symmetric mixed strategy equilibrium with 0<p<1. (To solve for the roots of a quadratic, ax2 +bx+c= 0, the quadratic formula is x= -b+62-4ac d) (5 points) If S = 3, find a symmetric mixed strategy equilibrium that is not a pure-strategy equilibrium. 20