The Stag-Hunt Game - A group of 10 hunters are hunting, where the games include a stag and several hares. Each hunter can choose whether to hunt the stag or go after a hare. It takes the joint effort of all n players to catch the stag, but each hunter on their own is able to catch one hare. Suppose that a stag is worth $100 and a hare is worth $9. When answering the following questions, assume that players' payoffs are given by their financial gains.

(a) Suppose that if all players hunt the stag, they will catch the stag and split the gain evenly amongst themselves. Formulate this situation as a strategic game and find the Nash equilibria.

(b) Now suppose that if all players hunt the stag, they can catch the stag and then allocate the $100 anyway they like amongst themselves. Formulate this situation as a coalitional game and find the core of the game.