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Convergence in the Finite Cournot Oligopoly with Social and Individual Learning

Author

Listed:
  • Thomas Vallée

    () (LEMNA - Laboratoire d'économie et de management de Nantes Atlantique - UN - Université de Nantes)

  • Murat Yildizoglu

    () (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - ECM - Ecole Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique - AMU - Aix Marseille Université - EHESS - École des hautes études en sciences sociales)

Abstract

Convergence to the Nash equilibrium in a Cournot oligopoly is a question that recurrently arises as a subject of controversy in economics. The development of evolutionary game theory has provided an equilibrium concept more directly connected with adjustment dynamics, and the evolutionary stability of the equilibria of the Cournot game has been extensively studied in the literature. Several articles show that the Walrasian equilibrium is the stable ESS of the Cournot game. But no general result has been established for the difficult case of simultaneous heterogenous mutations.Authors propose specific selection dynamics to analyze this case. Vriend (2000) proposes using a genetic algorithm for studying learning dynamics in this game and obtains convergence to Cournot equilibrium with individual learning. The resulting convergence has been questioned by Arifovic and Maschek (2006). The aim of this article is to clarify this controversy: it analyzes the mechanisms that are behind these contradictory results and underlines the specific role of the spite effect. We show why social learning gives rise to the Walrasian equilibrium and why, in a general setup, individual learning can effectively yield convergence to the Cournot equilibrium. We also illustrate these general results by systematic computational experiments.

Suggested Citation

  • Thomas Vallée & Murat Yildizoglu, 2009. "Convergence in the Finite Cournot Oligopoly with Social and Individual Learning," Working Papers halshs-00368274, HAL.
  • Handle: RePEc:hal:wpaper:halshs-00368274
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00368274
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    References listed on IDEAS

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    1. Stegeman, Mark & Rhode, Paul, 2004. "Stochastic Darwinian equilibria in small and large populations," Games and Economic Behavior, Elsevier, vol. 49(1), pages 171-214, October.
    2. Arifovic, Jasmina, 1994. "Genetic algorithm learning and the cobweb model," Journal of Economic Dynamics and Control, Elsevier, vol. 18(1), pages 3-28, January.
    3. Schaffer, Mark E., 1989. "Are profit-maximisers the best survivors? : A Darwinian model of economic natural selection," Journal of Economic Behavior & Organization, Elsevier, vol. 12(1), pages 29-45, August.
    4. Jasmina Arifovic & Michael Maschek, 2006. "Revisiting Individual Evolutionary Learning in the Cobweb Model – An Illustration of the Virtual Spite-Effect," Computational Economics, Springer;Society for Computational Economics, vol. 28(4), pages 333-354, November.
    5. Fernando Vega-Redondo, 1997. "The Evolution of Walrasian Behavior," Econometrica, Econometric Society, vol. 65(2), pages 375-384, March.
    6. R. D. Theocharis, 1960. "On the Stability of the Cournot Solution on the Oligopoly Problem," Review of Economic Studies, Oxford University Press, vol. 27(2), pages 133-134.
    7. Carlos Alós-Ferrer & Ana Ania, 2005. "The evolutionary stability of perfectly competitive behavior," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(3), pages 497-516, October.
    8. James Bergin & Dan Bernhardt, 2004. "Comparative Learning Dynamics," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 45(2), pages 431-465, May.
    9. Vallee, Thomas & Basar, Tamer, 1999. "Off-Line Computation of Stackelberg Solutions with the Genetic Algorithm," Computational Economics, Springer;Society for Computational Economics, vol. 13(3), pages 201-209, June.
    10. Vriend, Nicolaas J., 2000. "An illustration of the essential difference between individual and social learning, and its consequences for computational analyses," Journal of Economic Dynamics and Control, Elsevier, vol. 24(1), pages 1-19, January.
    11. Thomas Riechmann, 2006. "Cournot or Walras? Long-Run Results in Oligopoly Games," Journal of Institutional and Theoretical Economics (JITE), Mohr Siebeck, Tübingen, vol. 162(4), pages 702-720, December.
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    Cited by:

    1. Yıldızoğlu, Murat & Sénégas, Marc-Alexandre & Salle, Isabelle & Zumpe, Martin, 2014. "Learning The Optimal Buffer-Stock Consumption Rule Of Carroll," Macroeconomic Dynamics, Cambridge University Press, vol. 18(04), pages 727-752, June.
    2. Isabelle SALLE (GREThA, CNRS, UMR 5113) & Martin ZUMPE (GREThA, CNRS, UMR 5113) & Murat YILDIZOGLU (GREThA, CNRS, UMR 5113) & Marc-Alexandre SENEGAS (GREThA, CNRS, UMR 5113), 2012. "Modelling Social Learning in an Agent-Based New Keynesian Macroeconomic Model," Cahiers du GREThA 2012-20, Groupe de Recherche en Economie Théorique et Appliquée.
    3. Bischi, Gian Italo & Lamantia, Fabio & Radi, Davide, 2015. "An evolutionary Cournot model with limited market knowledge," Journal of Economic Behavior & Organization, Elsevier, vol. 116(C), pages 219-238.
    4. repec:eee:jeborg:v:141:y:2017:i:c:p:64-82 is not listed on IDEAS
    5. Efe Postalci, 2010. "Learning by observing," Working Papers 1007, Izmir University of Economics.

    More about this item

    Keywords

    Cournot oligopoly; Learning; Evolution; Selection; Evolutionary stability; Nash equilibrium; Genetic algorithms;

    JEL classification:

    • C - Mathematical and Quantitative Methods

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