Problem Set V Fall, 2010 1. Consider an industry characterized by Bertrand competition with di f erentiated prod-ucts in which two f rms choose prices p 1 and p 2 . Demand for f rm i ’s output is q i ( p i ,p j )= 12 − p i + 1 2 p j ,wh e r e p i and p j are respectively f rm i’s price and the competitor’s price;marginal cost for each f rm is 0 . Consider the in f nitely repeated game with this as the stage game. a. Solve for the joint pro f t maximizing price and pro f tforeach f rm. b. Solve for the Bertrand equilibrium price and equilibrium pro f tforeach f rm. c. Formally describe trigger strategies in which f rms choose identical prices which maximize joint pro f ts in the f rst stage, and continue to do so as long as both have chosen this price in all previous stages, and choose the one-shot Nash equilibrium prices if either has ever deviated. d. For what discount factors δ ∈ (0 , 1)
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