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Convergence in Finite Cournot Oligopoly with Social and Individual Learning

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  • Thomas Vallée

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

  • Murat Yildizoglu

    (GREThA - Groupe de Recherche en Economie Théorique et Appliquée - UB - Université de Bordeaux - 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 have 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.
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Suggested Citation

  • Thomas Vallée & Murat Yildizoglu, 2007. "Convergence in Finite Cournot Oligopoly with Social and Individual Learning," Post-Print hal-00293948, HAL.
    • Handle: RePEc:hal:journl:hal-00293948
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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(4), pages 727-752, June.
    2. Gergely Varga & János Vincze, 2019. "Saver Types: An Evolutionary-Adaptive Approach," Society and Economy, Akadémiai Kiadó, Hungary, vol. 41(2), pages 263-287, June.
    3. Arifovic, Jasmina & Diao, Liang & Hanaki, Nobuyuki, 2025. "An individual evolutionary learning model meets Cournot," Journal of Economic Dynamics and Control, Elsevier, vol. 172(C).
    4. Mattheos Protopapas & Francesco Battaglia & Elias Kosmatopoulo, 2008. "Coevolutionary Genetic Algorithms for Establishing Nash Equilibrium in Symmetric Cournot Games," Working Papers 004, COMISEF.
    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 & Murat Yildizoglu & Martin Zumpe & Marc-Alexandre Sénégas, 2012. "Modelling social learning in an Agent-Based new keynesian macroeconomic model," Post-Print hal-00779045, HAL.
    7. 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.
    8. Efe Postalci, 2010. "Learning by observing," Working Papers 1007, Izmir University of Economics.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.

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