3. Consider two firms forming a duopoly. If the two firms collude and choose low quantity, they each earn a profit equal to 1500 in each round. If the two firms choose to produce a high quantity, they each earn a profit equal to 1200 in each round. If one firm defects and chooses high quantity while the other selects low quantity, the firm that defects earns 1900 and the one that cooperates earns 1000 in each round. The game is simultaneous. a. Find the Nash equilibrium of the one-shot game. (2 marks) b. If both firms know that the game will be repeated exactly 2 rounds, can collusion be sustained? Explain. (3 marks) c. Suppose that the game is infinitely repeated. If both firms adopt the Grim strategy, what discount rate will sustain collusion? Explain. (5 marks) d. Suppose that, each round, the probability that the game is played another round is p=0.8. What discount rate will sustain collusion? How does the value of p impact the incentive to collude? (5 marks) e. Suppose that firms can only detect defection after two rounds, and the probability that the game is played in the next round is 1. What discount rate will sustain collusion? Explain how delayed detection impact the possibilities of collusion. (5 marks)