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Convergence in the Finite Cournot Oligopoly with Social and Individual Learning

Author

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  • Thomas Vallée

    (LEMNA - Laboratoire d'économie et de management de Nantes Atlantique - IEMN-IAE Nantes - Institut d'Économie et de Management de Nantes - Institut d'Administration des Entreprises - Nantes - UN - Université de Nantes)

  • Murat Yildizoglu

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

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://shs.hal.science/halshs-00368274
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    References listed on IDEAS

    as
    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. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, April.
    5. Thomas Riechmann, 2006. "Mixed motives in a Cournot game," Economics Bulletin, AccessEcon, vol. 4(29), pages 1-8.
    6. 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.
    7. Fernando Vega-Redondo, 1997. "The Evolution of Walrasian Behavior," Econometrica, Econometric Society, vol. 65(2), pages 375-384, March.
    8. R. D. Theocharis, 1960. "On the Stability of the Cournot Solution on the Oligopoly Problem," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 27(2), pages 133-134.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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. Salle, Isabelle & Yildizoglu, Murat & Zumpe, Martin & Sénégas, Marc-Alexandre, 2017. "Coordination through social learning in a general equilibrium model," Journal of Economic Behavior & Organization, Elsevier, vol. 141(C), pages 64-82.
    2. 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(4), pages 727-752, June.
    3. Efe Postalci, 2010. "Learning by observing," Working Papers 1007, Izmir University of Economics.
    4. Arifovic, Jasmina & Yıldızoğlu, Murat, 2019. "Learning the Ramsey outcome in a Kydland & Prescott economy," Journal of Economic Behavior & Organization, Elsevier, vol. 157(C), pages 191-208.
    5. César García-Díaz & Gábor Péli & Arjen van Witteloostuijn, 2020. "The coevolution of the firm and the product attribute space," PLOS ONE, Public Library of Science, vol. 15(6), pages 1-25, June.
    6. Isabelle SALLE & Martin ZUMPE & Murat YILDIZOGLU & Marc-Alexandre SENEGAS, 2012. "Modelling Social Learning in an Agent-Based New Keynesian Macroeconomic Model," Cahiers du GREThA (2007-2019) 2012-20, Groupe de Recherche en Economie Théorique et Appliquée (GREThA).
    7. Gian Italo Bischi & Fabio Lamantia, 2022. "Evolutionary oligopoly games with cooperative and aggressive behaviors," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 17(1), pages 3-27, January.
    8. Anufriev, Mikhail & Kopányi, Dávid, 2018. "Oligopoly game: Price makers meet price takers," Journal of Economic Dynamics and Control, Elsevier, vol. 91(C), pages 84-103.
    9. Gergely Varga & János Vincze, 2019. "Saver Types: An Evolutionary-Adaptive Approach," Society and Economy, Akadémiai Kiadó, Hungary, vol. 41(2), pages 263-287, June.
    10. Jasmina Arifovic & Liang Dia & Nobuyuki Hanaki, 2023. "An individual evolutionary learning model meets Cournot," ISER Discussion Paper 1200, Institute of Social and Economic Research, Osaka University.
    11. Mattheos Protopapas & Francesco Battaglia & Elias Kosmatopoulo, 2008. "Coevolutionary Genetic Algorithms for Establishing Nash Equilibrium in Symmetric Cournot Games," Working Papers 004, COMISEF.
    12. 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.
    13. Gian Italo Bischi & Fabio Lamantia & Davide Radi, 2018. "Evolutionary oligopoly games with heterogeneous adaptive players," Chapters, in: Luis C. Corchón & Marco A. Marini (ed.), Handbook of Game Theory and Industrial Organization, Volume I, chapter 12, pages 343-370, Edward Elgar Publishing.

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    Keywords

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