3. [25 points] Consider a modified version of the Prisoners' Dilemma game as represented by the following payoff matrix: P2 n 7,-2 5,5 0,6 p -1,3 6,0 3,3 P1 n 0, 0 -2, 7 3,-1 Check if the following strategy profile is a subgame-perfect equilibrium of this modified PD game repeated for two periods, with both players knowing that they will interaction for two periods and then the game will end. Strategy Profile: Player 1: Play n in the first period. In the second period, play p if (n, c) has been played in the first period, otherwise play c. Player 2: Play c in the first period. In the second period, play p if (n, c) has been played in the first period, otherwise play c. [Note that the first component of each pair is the strategy for player 1, and the second component is that of player 2, e.g. "(n,c)" indicates player 1 playing n and player 2 playing c.]