Consider a two player game with the following payoff matrix Player 1 Player 2 A B A 4, 4 2, 8

B 8, 2 3, 3

(a) Identify the Nash Equilibrium of the game above if it is played once.

(b) Suppose the game is infinitely repeated, each player discounts future payoffs with discount factor , and both players play Trigger Strategies. For what values of will both players be willing to play (A, A) in every period as a Subgame Perfect Nash Equilibrium?

(c) Present a pair of strategies and a range of values for that give each player a payoff strictly larger than 4 1 as a Subgame Perfect Nash equilibrium. Hint: You might find the following tricks useful: i) 1 + 2 + 4 + 6 + = 1 1 2 ii) 1 2 = (1 )(1 + )