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Two identical firms have MC = $2 and face a market demand function of QD = 8 – P. The firms compete on the basis of (continuous) price; if their prices are equal they split the market but if one has a lower price it gains the entire market. If the game is repeated, a discount factor δ applies to each firm, and the discounted value of profits is maximized.

a) If this game is played once, and the firms cooperate (collude), what is the maximum profit they can make together, and how much will each firm make?

What is the Nash Equilibrium of this game, and why?

b) If this game is repeated a very large finite number of times, what is the Nash Equilibrium, and why?

c) If the game is infinitely repeated, for what values of δ will the firms be able to sustain a cooperative Nash Equilibrium, and why?