Recall the two-by-two coordination game: 1/2 S B S 2,1 0, 0 B 0, 0 1, 2 Suppose that this stage game is played repeatedly for T = infinity periods by...

Recall the two-by-two coordination game:

1/2 S B

S 2,1 0, 0

B 0, 0 1, 2

Suppose that this stage game is played repeatedly for T = infinity periods by the same

players. The common discount factor is  2 (0,1) :

(a) What is the lowest average payoff that player one can be assured of receiving in

this infinitely repeated game? Indicate in a graph all payoff profiles that can be

sustained as subgame perfect Nash equilibria (SPNE).

(b) Now suppose that the following stage game is played by three players:

A :

1/2 L R

U 2, 2, 0 5, 5, 5

D 8, 6,8 0,7,4

B :

1/2 L R

U 4, 4,1 4,2,8

D 0, 2, 9 4, 2, 5

That is, player one chooses U or D; player two chooses L or R; and player three

chooses matrix A or B: Suppose that the common discount factor is d = 1, and

that the stage game is played exactly twice. Carefully report three different pure-

strategy SPNE, including one in which (U,R,A) is played in the first period.