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Gibbons Problems for PS I

Gibbons Problems for PS I - denote the market-clearing...

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From Gibbons, Game Theory for Applied Economics 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 ,wh e r e 0 s 1 ,s 2 1 .I f 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? 1.4 Suppose there are n f rms in the Cournot oligopoly model. Let q i denote the quantity produced by f rm i ,le t Q = q 1 + ··· +
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Unformatted text preview: 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? 1...
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