game theory question

QUESTION B2 (7 marks total) Consider a two-period repeated game with the following stage game. C D E C 4, 4 0,0 1, 5 D 0,0 2, 2 0,0 E 5, 1 0,0 0,0 This stage game is played twice and the repeated-game payoffs are simply the sum of the payoffs in each of the two periods. A strategy of each player is to choose one of C', D, E in stage 1, and for each possible outcome of stage 1, choose one of C, D, E in stage 2. Show that, for each player, playing 0' in period 1 be sustained in a subgame perfect equilibrium of this game. [In your answer, provide the relevant SPE strategy profile and show that it is indeed a SPE.]