Advances in Decision Sciences
Volume 2010 (2010), Article ID 573107, 18 pages
doi:10.1155/2010/573107
Research Article

Coevolutionary Genetic Algorithms for Establishing Nash Equilibrium in Symmetric Cournot Games

Mattheos K. Protopapas,1 Francesco Battaglia,1 and Elias B. Kosmatopoulos2

1Department of Statistics, University of Rome “La Sapienza”, Aldo Moro Square 5, 00185 Rome, Italy
2Department of Production Engineering and Management, Technical University of Crete, Agiou Titou Square, Chania 73100, Crete, Greece

Received 12 June 2009; Accepted 16 February 2010

Academic Editor: Stephan Dempe

Copyright © 2010 Mattheos K. Protopapas et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. Arifovic, “Genetic algorithm learning and the cobweb model,” Journal of Economic Dynamics and Control, vol. 18, no. 1, pp. 3–28, 1994.
  2. C. Alós-Ferrer and A. B. Ania, “The evolutionary stability of perfectly competitive behavior,” Economic Theory, vol. 26, no. 3, pp. 497–516, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. T. Vallee and M. Yildizoglou, “Convergence in finite cournot oligopoly with social and individual learning,” Working Papers of GRETha, 2007, http://www.gretha.fr.
  4. H. Dawid and M. Kopel, “On economic applications of the genetic algorithm: a model of the cobweb type,” Journal of Evolutionary Economics, vol. 8, no. 3, pp. 297–315, 1998.
  5. R. Franke, “Coevolution and stable adjustments in the cobweb model,” Journal of Evolutionary Economics, vol. 8, no. 4, pp. 383–406, 1998.
  6. N. J. Vriend, “An illustration of the essential difference between individual and social learning, and its consequences for computational analyses,” Journal of Economic Dynamics & Control, vol. 24, no. 1, pp. 1–19, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. F. Alkemade, H. La Poutré, and H. M. Amman, “On social learning and robust evolutionary algorithm design in the Cournot oligopoly game,” Computational Intelligence, vol. 23, no. 2, pp. 162–175, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  8. P. Dubey, O. Haimanko, and A. Zapechelnyuk, “Strategic complements and substitutes, and potential games,” Games and Economic Behavior, vol. 54, no. 1, pp. 77–94, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. T. C. Price, “Using co-evolutionary programming to simulate strategic behaviour in markets,” Journal of Evolutionary Economics, vol. 7, no. 3, pp. 219–254, 1997.
  10. Y. S. Son and R. Baldick, “Hybrid coevolutionary programming for Nash equilibrium search in games with local optima,” IEEE Transactions on Evolutionary Computation, vol. 8, no. 4, pp. 305–315, 2004. View at Publisher · View at Google Scholar
  11. D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley, Reading, Mass, USA, 1989.
  12. T. Riechmann, “Genetic algorithm learning and evolutionary games,” Journal of Economic Dynamics and Control, vol. 25, no. 6-7, pp. 1019–1037, 2001. View at Publisher · View at Google Scholar
  13. T. Riechmann, “Learning and behavioral stability: an economic interpretation of genetic algorithms,” Journal of Evolutionary Economics, vol. 9, no. 2, pp. 225–242, 1999.
  14. J. G. Kemeny and J. L. Snell, Finite Markov Chains, The University Series in Undergraduate Mathematics, D. Van Nostrand, Princeton, NJ, USA, 1960. View at MathSciNet
  15. I. V. Basawa and B. L. S. Prakasa Rao, Statistical Inference for Stochastic Processes, Probability and Mathematical Statistics, Academic Press, London, UK, 1980. View at MathSciNet
  16. M. K. Protopapas and E. B. Kosmatopoulos, “Determination of sequential best replies in n-player games by Genetic Algorithms,” International Journal of Applied Mathematics and Computational Sciences, vol. 5, no. 1, 2009.