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Cournot Oligopoly and Concavo-Concave Demand

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  • Christian Ewerhart

Abstract

The N-firm Cournot model with general technologies is reviewed to derive generalized and unified conditions for existence of a pure strategy Nash equilibrium. Tight conditions are formulated alternatively (i) in terms of concavity of two-sided transforms of inverse demand, or (ii) as linear constraints on the elasticities of inverse demand and its first derivative. These conditions hold, in particular, if a firm’s marginal revenue decreases in other firms’ aggregate output, or if inverse demand is logconcave. The analysis relies on lattice-theoretic methods, engaging both cardinal and ordinal notions of supermodularity. As a byproduct, a powerful test for strict quasiconcavity is obtained.

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Bibliographic Info

Paper provided by Institute for Empirical Research in Economics - University of Zurich in its series IEW - Working Papers with number 427.

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Date of creation: Sep 2009
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Handle: RePEc:zur:iewwpx:427

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Keywords: Cournot competition; existence of Nash equilibrium; concavity of demand; supermodular games; strict quasiconcavity;

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Cited by:
  1. Pierre von Mouche & Federico Quartieri, 2013. "On the uniqueness of Cournot equilibrium in case of concave integrated price flexibility," Journal of Global Optimization, Springer, vol. 57(3), pages 707-718, November.

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