Cournot Oligopoly and Concavo-Concave Demand

Christian Ewerhart

No 427, IEW - Working Papers from Institute for Empirical Research in Economics - University of Zurich

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.

Keywords: Cournot competition; existence of Nash equilibrium; concavity of demand; supermodular games; strict quasiconcavity (search for similar items in EconPapers)
JEL-codes: C62 C72 L13 (search for similar items in EconPapers)
Date: 2009-09
New Economics Papers: this item is included in nep-bec, nep-com, nep-ind and nep-mic
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:zur:iewwpx:427

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