please show work

1. There's a market with two firms 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 me = 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 na, for 'optimal deviation'. Here's a strategic form for the game: Player 2 Collude Compete Player 1 Collude 2, 2 0, Ad Compete 1, 1 a. For what values of na 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 infinitely with discount factor 8 and Tta = 4. Show that for sufficiently patient players, it is a subgame perfect Nash equilibrium to collude in every period. What is the minimum 8 that achieves cooperation