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Convergence in the Finite Cournot Oligopoly with Social and Individual Learning

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  • Thomas Vallée

    ()
    (LEMNA - Laboratoire d'économie et de management de Nantes Atlantique - Université de Nantes : EA4272)

  • Murat Yildizoglu

    ()
    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - Université de la Méditerranée - Aix-Marseille II - Université Paul Cézanne - Aix-Marseille III - Ecole des Hautes Etudes en Sciences Sociales (EHESS) - CNRS : UMR6579)

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.

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Bibliographic Info

Paper provided by HAL in its series Working Papers with number halshs-00368274.

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Date of creation: 15 Mar 2009
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Handle: RePEc:hal:wpaper:halshs-00368274

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

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References

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  1. 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.
  2. 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.
  3. Vallee, Thomas & Basar, Tamer, 1999. "Off-Line Computation of Stackelberg Solutions with the Genetic Algorithm," Computational Economics, Society for Computational Economics, vol. 13(3), pages 201-09, June.
  4. Fernando Vega Redondo, 1996. "The evolution of walrasian behavior," Working Papers. Serie AD 1996-05, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  5. 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.
  6. 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.
  7. 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, 05.
  8. Arifovic, Jasmina, 1994. "Genetic algorithm learning and the cobweb model," Journal of Economic Dynamics and Control, Elsevier, vol. 18(1), pages 3-28, January.
  9. Carlos Alós-Ferrer & Ana Ania, 2005. "The evolutionary stability of perfectly competitive behavior," Economic Theory, Springer, vol. 26(3), pages 497-516, October.
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Cited by:
  1. Murat YILDIZOGLU (GREQAM, CNRS, UMR 6579) & Marc-Alexandre SENEGAS (GREThA, CNRS, UMR 5113) & Isabelle SALLE (GREThA, CNRS, UMR 5113) & Martin ZUMPE (GREThA, CNRS, UMR 5113), 2011. "Learning the optimal buffer-stock consumption rule of Carroll," Cahiers du GREThA 2011-11, Groupe de Recherche en Economie Théorique et Appliquée.
  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.

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