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Coevolutionary Genetic Algorithms for Establishing Nash Equilibrium in Symmetric Cournot Games

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  • Protopapas, M.K.
  • Kosmatopoulos, E.B.
  • Battaglia, F.

Abstract

We use co-evolutionary genetic algorithms to model the players' learning process in several Cournot models, and evaluate them in terms of their convergence to the Nash Equilibrium. The ``social-learning'' versions of the two co-evolutionary algorithms we introduce, establish Nash Equilibrium in those models, in contrast to the ``individual learning'' versions which, as we see here, do not imply the convergence of the players' strategies to the Nash outcome. When players use ``canonical co-evolutionary genetic algorithms'' as learning algorithms, the process of the game is an ergodic Markov Chain, and therefore we analyze simulation results using both the relevant methodology and more general statistical tests, to find that in the ``social'' case, states leading to NE play are highly frequent at the stationary distribution of the chain, in contrast to the ``individual learning'' case, when NE is not reached at all in our simulations; to find that the expected Hamming distance of the states at the limiting distribution from the ``NE state'' is significantly smaller in the ``social'' than in the ``individual learning case''; to estimate the expected time that the ``social'' algorithms need to get to the ``NE state'' and verify their robustness and finally to show that a large fraction of the games played are indeed at the Nash Equilibrium.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 15375.

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Date of creation: 22 May 2009
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Handle: RePEc:pra:mprapa:15375

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Keywords: Genetic Algorithms; Cournot oligopoly; Evolutionary Game Theory; Nash Equilibrium;

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  1. Carlos Alós-Ferrer & Ana Ania, 2005. "The evolutionary stability of perfectly competitive behavior," Economic Theory, Springer, vol. 26(3), pages 497-516, October.
  2. Michael Kopel & Herbert Dawid, 1998. "On economic applications of the genetic algorithm: a model of the cobweb type," Journal of Evolutionary Economics, Springer, vol. 8(3), pages 297-315.
  3. Arifovic, Jasmina, 1994. "Genetic algorithm learning and the cobweb model," Journal of Economic Dynamics and Control, Elsevier, vol. 18(1), pages 3-28, January.
  4. 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.
  5. Thomas VALLEE (LEN - IAE Nantes) & Murat YILDIZOGLU (GREThA), 2007. "Convergence in Finite Cournot Oligopoly with Social and Individual Learning," Cahiers du GREThA 2007-07, Groupe de Recherche en Economie Théorique et Appliquée.
  6. Dubey, Pradeep & Haimanko, Ori & Zapechelnyuk, Andriy, 2006. "Strategic complements and substitutes, and potential games," Games and Economic Behavior, Elsevier, vol. 54(1), pages 77-94, January.
  7. Riechmann, Thomas, 2001. "Genetic algorithm learning and evolutionary games," Journal of Economic Dynamics and Control, Elsevier, vol. 25(6-7), pages 1019-1037, June.
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Cited by:
  1. Johannes Paha, 2010. "Simulation and Prosecution of a Cartel with Endogenous Cartel Formation," MAGKS Papers on Economics 201007, Philipps-Universität Marburg, Faculty of Business Administration and Economics, Department of Economics (Volkswirtschaftliche Abteilung).

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