7. (10 pts.) Consider a prisoner's dilemma game of the following. Ben Confess Deny Confess (1, 1) (20, 0) Alex Deny (0, 20) (4, 4) a) Find all pure strategy nash equilibria. (2 pts.)b) Suppose that the prisoner's dilemma game is repeated once every year, forever. Firm i's payoff of the repeated game of the repeated game is a discounted sum of each year, starting with year 0. The payoff of the repeated game for Firm i is, n,- = 2120,81 TIL j, where It\" is Firm i's jth year specific payoff. Suppose further that ,8 = 0.9. Explain what a grim trigger strategy is in this game. Then, show (with calculations) how both firms using grim-trigger strategies is N_OT a nash equilibrium. (4 pts.) Continuing from part b), what is the lowest value of B that can support a grim-trigger strategy equilibrium? (4 pts.)