1. Consider the following game (a variant of the prisoner's dilemma): 2 C d 1 4,4 8, 2 D 2, 8 6,6 Suppose both players play the game repeatedly. What is the minimum value of S for the grim trigger strategy to be a Nash equilibrium? 2. Give three interpretations of what the S coefficient represents. 3. Consider a duopoly market with an inverse demand function P(Q) = 24 -Q and C(q) = 0 for each firm. The firms must choose production levels yearly, and every year there is only a fifty percent chance the other firm survives. Suppose firm one decides to choose a trigger strategy where it produces half the monopoly output as long as the other firm produces half the monopoly output. However, if firm two chooses to produce anything other than the monopoly output, firm one produces the Cournot output in every subsequent period. a) Suppose firm two decides to use the same strategy. What is the payoff to each firm? b) Suppose firm two decides to deviate from this strategy and choose a different level of output in the first period. What should firm two produce in the first period and each subsequent period? Find the payoffs for firm two. c) Compare the payoffs to a) and b). It turns out the strategy in b) is the optimal deviation if a) is not a Nash equilibrium. Given this fact, is a) a Nash equilibrium