Suppose the following Prisoner's Dilemma is repeated infinitely:

Player 2 C D Player 1 C (2,2) (0, 4) D (4,0) (1, 1) Let n be the payoff to player i in period t, fort = 1,2, . .. . Player i maximizes her discounted sum of payoffs given by: DO where o, is the discount factor of Player i, for i = 1,2. Suppose the players try to sustain (C, C) in each period by the Grim Trigger strat- egy. That is, each player plays the following strategy: . Play C in the first period. . In any other period, play C if both players have played C in all previous pe- riods; and play D otherwise (i.e., if any one player has ever played D before) Suppose 61 = ; and 62 = #, is both players adopting the above grim trigger strat- egy a subgame perfect Nash equilibrium of the infinitely repeated game? Show your calculation and reasoning