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Unformatted text preview: ECN 712 Fall 2009 Professor Schlee Problem Set XIIa, not to be turned in 1. Evaluate : In a finitely repeated prisoners dilemma, the strategy of defect in every period, no matter what the history is dominant for each player. 2. Prove that in a repeated prisoners dilemma with finite horizon T , the unique Nash equilibrium outcome is DDDD DD  {z } 2 T times (that is, DD chosen T times, the number of times the stage game is played). 3. Strategic LearningbyDoing . Consider the following twoperiod duopoly game. The firms produce identical goods with market inverse demand of p ( ) at each date, with p ( q ) < 0 whenever p ( q ) > and p (0) > 0. At date 1, firm 1 is a monopolist. At date 2, firms 1 and 2 play a Cournot game, after observing the date1 output of firm 1, x . Firm 2 produces at a constant unit cost of k (0 ,p (0)). Firm 1 produces at a constant unit cost of k at date 1 and of c ( x ) at date 2, where c ( ) is strictly decreasing and convex. Firm 2s profit in the Cournot game is 2 ( q 1 ,q 2 ) and firm 1s profit from the two dates (in date 2 dollars) is 1 ( q 1 ,q 2 ,x ). Finally, let R 1 ( q 2 ,x...
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 Spring '10
 schlee
 Microeconomics

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