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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.

Suggested Citation

  • Christian Ewerhart, 2009. "Cournot Oligopoly and Concavo-Concave Demand," IEW - Working Papers 427, Institute for Empirical Research in Economics - University of Zurich.
    • Handle: RePEc:zur:iewwpx:427
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    File URL: https://www.econ.uzh.ch/apps/workingpapers/wp/iewwp427.pdf
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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.

    More about this item

    Keywords

    Cournot competition; existence of Nash equilibrium; concavity of demand; supermodular games; strict quasiconcavity;
    All these keywords.

    JEL classification:

    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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