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Problem Set I

Problem Set I - P denote the market-clearing price and...

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Problem Set I The fi rst two problems are from Gibbons, Game Theory for Applied Eco- nomics. 1. (Gibbons 1.3) Players 1 and 2 are bargaining over how to split one dollar. Both players simultaneously name shares they would like to have, s 1 and s 2 , where 0 s 1 , s 2 1 . If s 1 + s 2 1 , then the players receive the shares they named; if s 1 + s 2 > 1 , then both players receive zero. What are the pure-strategy Nash equilibria of this game? 2. (Gibbons 1.4) Suppose there are n fi rms in the Cournot oligopoly model. Let q i denote the quantity produced by fi rm i , let Q = q 1 + · · · + q n denote the aggregate quantity on the market. Let
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Unformatted text preview: P denote the market-clearing price and assume that inverse demand is given by P ( Q ) = a − Q (assuming Q < a , else P = 0 ). Assume that the total cost of f rm i from producing quantity q i is C i ( q i ) = cq i . That is, there are no f xed costs and the marginal cost is constant at c , where we assume c < a . Following Cournot, suppose that the f rms choose their quantities simultaneously. What is the Nash equilibrium? What happens as n approaches in f nity? 3. Osborne 18.1 4. Osborne 30.1 1...
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