1. (10 points) Consider a variant of the Stag Hunt game. There are 10 hunters. In the following, assume only a minimum of six hunters are needed to capture the stag. A captured stag is equally shared only by the hunters who chose to hunt the stag. As before, a player gets payoff zero if he chooses Stag but the stag is not caught, and gets a payoff 1 if he chooses Hare regardless of other players' strategies. Other things equal, every player prefers a larger share of the stag.
2. Find all Nash equilibria for the following two cases. Note that each case is a different game! For each game you need to find Nash equilibria and then explain why they are Nash equilibria; you also need to explain why the other strategy profiles are not Nash. Let V be the total value of the stag.
3. (a) (4 points) Assume V/10 > 1, namely, each hunter prefers 1/10 of the stag to a hare. (b) (6 points) Assume V8 > 1 > V9 , namely, each hunter prefers 1/8 of the stag to a hare,
4. but would prefer a hare to 1/9 or smaller share of the stag.

1. (10 points) Consider a variant of the Stag Hunt game. There are 10 hunters. In the following, assume only a minimum of si_x hunters are needed to capture the stag. A captured stag is equally shared only by the hunters who chose to hunt the stag. As before, a player gets payoff zero if he chooses Stag but the stag is not caught, and gets a payoff 1 if he chooses Hare regardless of other players' strategies. Other things equal, every player prefers a larger share of the stag. Find all Nash equilibria for the following two cases. Note that each case is a different game! For each game you need to nd Nash equilibria and then explain why they are Nash equilibria; you also need to explain why the other strategy proles are not Nash. Let V be the total value of the stag. (a) (4 points) Assume V/ 10 > 1, namely, each hunter prefers 1/10 of the stag to a hare. (b) (6 points) Assume % > 1 > %, namely, each hunter prefers 1/8 of the stag to a hare, but would prefer a hare to 1 / 9 or smaller share of the stag