The Stag Hunt game is based on a story told by Jean Jacques Rousseau in his bookDiscourses on the Origin and Foundation of Inequality Among Men (1754). The story goessomething like this: "Two hunters set out to kill a stag. One has agreed to drive the stag1 through the forest, and the other to post at a place where the stag must pass. If bothfaithfully perform their assigned stag-hunting tasks, they will surely kill the stag and eachwill get an equal share of this large animal. During the course of the hunt, each hunter hasan opportunity to abandon the stag hunt and to pursue a hare. If a hunter pursues the hareinstead of the stag he is certain to catch the hare and the stag is certain to escape. Eachhunter would rather share half of a stag than have a hare to himself." The matrix belowshows payoffs in a stag hunt game. If both hunters hunt stag, each gets a payoff of 4. If bothhunt hare, each gets 3. If one hunts stag and the other hunts hare, the stag hunter gets 0and the hare hunter gets 3. Hunter B
Hunt Stag Hunt Hare
Hunter A Hunt Stag 4,4 0,3
Hunt Har 3,0 3,3
(a) If you are sure that the other hunter will hunt stag, what is the best thing for you to do?
(b) If you are sure that the other hunter will hunt hare, what is the best thing for you to do?
(c) Does either hunter have a dominant strategy in this game? If so, what is it? If not explain why not.
(d) This game has two pure strategy Nash equilibria. What are they?
(e) is one Nash equilibrium better for both hunters than the other? If so, which is the better equilib- rium?
(f) If a hunter believes that with probability 1/2 the other hunter will hunt stag and with probability 1/2 he will hunt hare, what should this hunter do to maximize his expected payoff?