Please Show All Work

1. There's a market with two rms who are contemplating acting collusively. If they cut production so that each is making half the monopoly quantity, they each get am = 2. If they act as competitors, they both get are = 1. If one player plays the monopoly quantity, the other player can take advantage of the situation and increase output, getting a larger share of the market for himself at the expense of his partner, who gets 0 if this occurs; call this value ad, for 'optimal deviation'. Here's a strategic form for the game: Pla er2 _ collude Player 1 Collude um." a. For what values of 1rd does this have the form of a prisoner's dilemma, i.e., each player has a strictly dominant strategy to play competitively? b. Assume the game is repeated innitely with discount factor 5 and 1rd= 4. Show that for sufciently patient players, it is a subgame perfect Nash equilibrium to collude in every period. What is the minimum 5 that achieves cooperation