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Problem Set 4 Economics 703 Spring 2016 Due: Friday February 19 1. Consider a monopolist facing the demand curve p = 10 − Q. The monopolist can choose either of the following cost functions: c1 (q) = 3q or c2 (q) = 10 + q. a) Which cost function does the monopolist choose? b) Now suppose that there is a second firm with cost function c1 (q) above. Whichever cost function firm 1 chooses, the second firm will observe this choice and then have the option of entering the market or not. If he does not enter, firm 1 remains a monopolist with the chosen cost function. If firm 2 does enter, he pays an entry cost of $4 and the two firms compete as Cournot duopolists. More precisely, whichever cost function firm 1 chose, we have a pure strategy Nash equilibrium in quantity choices. What is the pure subgame perfect equilibrium of this game? 2. For games (a) through (d) on question 3 of Problem Set 3, find all (pure) weak perfect Bayesian equilibria and sequential equilibria. 3. For games (a) and (b) on the following page, find the sets of pure strategy Nash, subgame perfect, weak perfect Bayesian, and sequential equilibria. 1 1 a) b a 2 c c d d 3 2 2 2 f e 4 3 1 e 0 0 0 e f 0 0 0 3 0 1 f 1 0 1 3 1 0 Figure 1: (a) 1 b) b a 1 2 0 2 c c d d 3 e -1 1 0 f e 0 3 2 0 3 1 Figure 2: (b) 2 f 1 -1 0 2 1 3