question is provided in image attached solution is also provided, but need explanation

1. Recall the two-by-two coordination game: 1/2 S B S 2, 1 0,0 B 0,0 1,2 as om Suppose that this stage game is played repeatedly for T = co periods by the same players. The common discount factor is o e (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: 1/2 L R 1/2 L R A : U 2, 2, 0 5, 5,5 B : U 4, 4, 1 4,2, 8 D 8, 6,8 0, 7,4 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 o = 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. Solution: a) Each player can be guaranteed the minmar average payoff of } by miring between S and B; b) Any combination of the stage game NEs (U, L, B) and (D, R, B) constitutes SPNE. A SPNE with (U, R, A) played in the first round is : a $2 = (D, R, B) if s' = (U, R, A) (U, L, B) if not