Consider a two-period repeated game. Thestage gameis the following:

L C R

T 4, 4 0, 1 0, 0

M 1, 0 1, 2 7, 0

B 0, 0 0, 7.5 6, 6

(a) (4pts) Find all pure-strategy Nash equilibria when the stage game is played only once. What are

the Nash equilibrium payoffs?

(b) (6pts) Now consider the two-period repeated game. Suppose the discount factors d1 = d2 = 1

for both players. Find a pair of subgame-perfect-equilibrium strategies in which player 1 plays B

and player 2 plays R in the first period. Explain why the pair of strategies is a subgame perfect

equilibrium. Note that the game is not symmetric so you need to separately verify for each player.

(c) (4pts) Now assume that Player 1's discount factor d11 and Player 2 's discount factor d21.

Find the entire ranges of values of d1 and d2 so that the pair of strategies in Part (b) remain subgame

perfect equilibrium.