1. Suppose two players play the following prisoner's dilemma stage game in every period t = 1. ..T. You can think of this as two firms choosing either a High price or Low price. Player 2 H L Player 1 L (11,0) (1,1) H (10,10) (0,15) a. If T is finite, what is the unique subgame perfect equilibrium? Why? b. If T is infinite and players discount the future using discount factor 6, is the equilibrium in part a still a subgame perfect equilibrium? Explain. c. If T is infinite, what is the smallest value of o such that each player can obtain a payoff of 10 each period in a subgame perfect equilibrium? d. Now suppose that the stage game is played in period 1 and that, conditional on the game being played in a given period t, there is probability 1-p that the stage game is played in period t + 1 and probability p that the repeated game ends after period t. For simplicity, assume now that firms do not discount future payments (i.e., that p = 0). Show that for p sufficiently small, each player can obtain the payoff 10 in a subgame perfect equilibrium