Please help with this question. (Game theory)

2. Innitely Repeated Prisoner's Dilemma Consider the Prisoners' dilemma discussed in class. Defect Cooperate Defect 1, 1 5,0 Cooperate 0, 5 4, 4 Suppose the game is innitely repeated with a common discount factor 6 = 0.9. As usual, at the beginning of each period, players observe all actions chosen in all previous periods. (a) Consider the following "tit-fortat" strategy: 0 Play Cooperate in the rst period. 0 Starting from the second period, play the action chosen by the other player in the previous period. Is it a subgameperfect Nash equilibrium (SPNE) for both players to adopt the titfortat strategy? (b) Consider a strategy that forgives the opponent once. Given any history, we can count the total number of times Defect has been played in the past. Denote this number by n. For example, if the history is such that (Cooperate, Defect) is played in the rst period; and (Defect, Cooperate) is played in the second period, then n = 2. Specically, the strategy under consideration is as follows. 0 Play Cooperate in the rst period. c If n = 0 or 1, play Cooperate this period. c If n > 1, play Defect this period. Is it a SPNE for both players to adopt the strategy above