1. Grim Trigger in the Repeated Prisoner's Dilemma In one instance of the prisoner's dilemma, each player chooses whether to pay some cost c > 0 in order to confer a benet I) > c onto the other player. The payoffs from a single iteration of this prisoner's dilemma are therefore: Cooperate Defect ' (b, c) The repeated prisoner's dilemma is built out of several stages, each of which is a copy of the above game. At the end of each stage, the two players repeat the prisoner's dilemma again with probability 6, where 0 S 6 g 1. A strategy in the repeated prisoner's dilemma is a rule which determines whether a player will cooperate or defect in each given stage. This rule may depend on which round it is, and on either player's actions in previous rounds. For example, the grim trigger strategy is described by the following rule: cooperate if both players have never defected, and defect otherwise. The goal of this problem is to show that the strategy pair in which both players play grim trigger is a Nash equilibrium if 6 > g. (a) Suppose that player 1 and player 2 are both following the grim trigger strategy. What actions will be played in each stage of the repeated game? What are the payoffs to players 1 and 2 in each stage? (b) Using your result from part 1a, write down the expected payoff to player 1 from the entire repeated prisoner's dilemma in terms of c, b, and 6