Coevolutionary Genetic Algorithms for Establishing Nash Equilibrium in Symmetric Cournot Games
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.
|Date of creation:||22 May 2009|
|Date of revision:|
|Contact details of provider:|| Postal: |
Web page: http://mpra.ub.uni-muenchen.de
More information through EDIRC
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Carlos Alós-Ferrer & Ana Ania, 2005. "The evolutionary stability of perfectly competitive behavior," Economic Theory, Springer, vol. 26(3), pages 497-516, October.
- Arifovic, Jasmina, 1994. "Genetic algorithm learning and the cobweb model," Journal of Economic Dynamics and Control, Elsevier, vol. 18(1), pages 3-28, January.
- 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.
- repec:hal:journl:hal-00394413 is not listed on IDEAS
- 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.
- repec:hal:journl:hal-00293948 is not listed on IDEAS
- Riechmann, Thomas, 2001. "Genetic algorithm learning and evolutionary games," Journal of Economic Dynamics and Control, Elsevier, vol. 25(6-7), pages 1019-1037, June.
- 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.
- 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.
- repec:hal:journl:hal-00293929 is not listed on IDEAS
When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:15375. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Ekkehart Schlicht)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.