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1. Pepsi (Firm 1) and Coke (Firm 2) are playing a version of Cournot duopoly. If they choose quantities q1, q2, their profits are π1 = q1(24 - q1 - q2), π2 = q2(24 - q1 - q2)
(a) Find the unique Nash equilibrium of the game.
(b) Specify quantities for Pepsi and Coke such that they both make higher profits than in (1a). Explain why these are not an equilibrium.
(c) Now suppose the game will be repeated for, potentially, many periods. The firms don't know how many periods; there is no definite ending date, but at each date there is a .01 chance that the game ends. Describe strategies for Pepsi and Coke that are in equilibrium, and such that they will always choose the quantities in 1b. Please note that your strategies must explain how each firm will respond to each possible action of the other, and must be such that, when told Pepsi's strategy, Coke will want to keep to its plan, and vice versa. (Hint: Grim Trigger.)
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