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A Nonparametric Analysis of the Cournot Model

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  • John Quah
  • Andres Carvajal

Abstract

An observer makes a number of observations of an industry producing a homogeneous good. Each observation consists of the market price, the output of individual firms and perhaps information on each firm's production cost. We provide various tests (typically, linear programs) with which the observer can determine if the data set is consistent with the hypothesis that firms in this industry are playing a Cournot game at each observation. When cost information is wholly or partially unavailable, these tests could potentially be used to derive cost information on the firms. This paper is a contribution to the literature that aims to characterize (in various contexts) the restrictions that a data set must satisfy for it to be consistent with Nash outcomes in a game. It is also inspired by the seminal result of Afriat (and the subsequent literature) which addresses similar issues in the context of consumer demand, though one important technical difference from most of these results is that the objective functions of firms in a Cournot game are not necessarily quasiconcave.

Suggested Citation

  • John Quah & Andres Carvajal, 2009. "A Nonparametric Analysis of the Cournot Model," Economics Series Working Papers 465, University of Oxford, Department of Economics.
    • Handle: RePEc:oxf:wpaper:465
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    References listed on IDEAS

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    1. Andrés Carvajal, 2003. "Testable Restrictions of Nash Equilibrium in Games with Continuous Domains," Borradores de Economia 3555, Banco de la Republica.
    2. Forges, Françoise & Minelli, Enrico, 2009. "Afriat's theorem for general budget sets," Journal of Economic Theory, Elsevier, vol. 144(1), pages 135-145, January.
    3. Ray, Indrajit & Zhou, Lin, 2001. "Game Theory via Revealed Preferences," Games and Economic Behavior, Elsevier, vol. 37(2), pages 415-424, November.
    4. Felix Kubler, 2008. "Observable Restrictions of General Equilibrium Models with Financial Markets," Lecture Notes in Economics and Mathematical Systems, in: Computational Aspects of General Equilibrium Theory, pages 93-108, Springer.
    5. Robert R. Routledge, 2009. "Testable implications of the Bertrand model," Economics Discussion Paper Series 0918, Economics, The University of Manchester.
    6. Andrés Carvajal, 2010. "The testable implications of competitive equilibrium in economies with externalities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 45(1), pages 349-378, October.
    7. Donald J. Brown & Rosa L. Matzkin, 2008. "Testable Restrictions on the Equilibrium Manifold," Lecture Notes in Economics and Mathematical Systems, in: Computational Aspects of General Equilibrium Theory, pages 11-25, Springer.
    8. Sprumont, Yves, 2000. "On the Testable Implications of Collective Choice Theories," Journal of Economic Theory, Elsevier, vol. 93(2), pages 205-232, August.
    9. Carvajal, Andres, 2004. "Testable restrictions on the equilibrium manifold under random preferences," Journal of Mathematical Economics, Elsevier, vol. 40(1-2), pages 121-143, February.
    10. Carvajal, Andres & Ray, Indrajit & Snyder, Susan, 2004. "Equilibrium behavior in markets and games: testable restrictions and identification," Journal of Mathematical Economics, Elsevier, vol. 40(1-2), pages 1-40, February.
    11. Bresnahan, Timothy F., 1989. "Empirical studies of industries with market power," Handbook of Industrial Organization, in: R. Schmalensee & R. Willig (ed.), Handbook of Industrial Organization, edition 1, volume 2, chapter 17, pages 1011-1057, Elsevier.
    12. Matzkin, Rosa L, 1991. "Axioms of Revealed Preference for Nonlinear Choice Sets," Econometrica, Econometric Society, vol. 59(6), pages 1779-1786, November.
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    Cited by:

    1. Cherchye, Laurens & Demuynck, Thomas & De Rock, Bram, 2011. "Testable implications of general equilibrium models: An integer programming approach," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 564-575.

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    More about this item

    Keywords

    Revealed preference; Observable restrictions; Linear programming; Cournot game; Increasing marginal costs;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection

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