Exercise 1. Two individuals go out on a hunt. Each can individually choose to hunt a stag or hunt a hare. Each hunter must choose an action without knowing the choice of the other. The only way of hunting a stag is that both hunters choose to hunt it. An individual can always get a hare by himself, but a hare is worth less than a stag. To be precise, each hunter will get a payoff equal to two for successfully hunting a stag. A hunter will get a payoff equal to one for hunting a hare. Finally, a hunter will get a payoff equal to zero if she does not hunt anything.

(i) Identify the set of pure strategies for each player. (ii) Write down the normal form game.

(iii) Compute the set of pure strategy Nash equilibria.

Exercise 2. Provide an example of a 2-player normal form game where each player has 3 (pure) strategies such that:

(i) There is exactly one pure strategy Nash equilibrium. (ii) There are exactly two pure strategy Nash equilibria.

(iii) There are exactly three pure strategy Nash equilibria. (iv) There are exactly nine pure strategy Nash equilibria.

Exercise 3. Consider the following 3-player normal form game L R L R T 8,8,8 7,7,7 T m 1,1,8 3 7,7,7 8 W E (i) For each player, write his set of best responses against every strategy prole of his opponents. 90 DO to l \"H 00 (ii) Find every Nash equilibrium in the game