Please write the solution of this question(a)

4. [16 points] Two players, 1 and 2, play the following game repeatedly. The values in the table are the monetary rewards to the players for every possible combination of their actions. At any point in time, the actions taken by both players in the past (i.e. the history of play) are commonly known by both players. C D Player 2 C (2, 2) (0,3) D (3, 0) (l, 1) Player 1 Here the first component is Player 1's reward and the second component is Player 2's reward. Both players want to maximize the discounted present value of their per-period rewards, with the same discount factor 5 = 0.9. In other words, if Player 1 receives a stream of monetary rewards (X0,X1, X2, Xt, ) over time, his lifetime payoff is U= x0 +Xl 5 + X2 5 2 + + xt 5t+w Player 2 evaluates her lifetime payoff similarly. (a) Suppose it is common knowledge that the game is repeated for exactly 100 periods, t = O, 1, 2, , 99. Is there a Subgame Perfect Equilibrium of the repeated game in which the action proflle (C, C) is played in period t = 99? Why or why not? Is there a Subgame Perfect Equilibrium of the repeated game in which the action prole (C, C) is played in period t = 0? Why or why not