Advances in Decision Sciences
Volume 2010 (2010), Article ID 573107, 18 pages
Research Article

Coevolutionary Genetic Algorithms for Establishing Nash Equilibrium in Symmetric Cournot Games

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.


We use coevolutionary 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 coevolutionary algorithms we introduce establish Nash Equilibrium in those models, in contrast to the “individual learning” versions which, do not imply the convergence of the players' strategies to the Nash outcome. When players use “canonical coevolutionary genetic algorithms” as learning algorithms, the process of the game is an ergodic Markov Chain; we find that in the “social” cases 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; and finally we show that a large fraction of the games played are indeed at the Nash Equilibrium.