Abstract
The series of studies about the convergence or not of the evolutionary strategies of players that use co-evolutionary genetic algorithms in Cournot games has not addressed the issue of individual players’ strategies convergence, but only of the convergence of the aggregate indices (total quantity and price) to the levels that correspond either to the Nash or Walrash Equilibrium. Here we discover that while some algorithms lead to convergence of the aggregates to Nash Equilibrium values, this is not the case for the individual players’ strategies (i.e. no NE is reached). Co-evolutionary programming social learning, as well as a social learning algorithm we introduce here, achieve this goal (in a stochastic sense); this is displayed by statistical tests, as well as “NE stages” evaluation, based on ergodic Markov chains.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alkemade, F., La Poutre, H., Amman, H.: On Social Learning and Robust Evolutionary Algorithm Design in the Cournot Oligopoly Game. Comput. Intell. 23, 162–175 (2007)
Alos-Ferrer, C., Ania, A.: The Evolutionary Stability of Perfectly Competitive Behavior. Econ. Theor. 26, 497–516 (2005)
Arifovic, J.: Genetic Algorithm Learning and the Cobweb Model. J. Econ. Dynam. Contr. 18, 3–28 (1994)
Basawa, I.V., Rao, P.: Statistical Inference for Stochastic Processes. Academic Press, London (1980)
Dawid, H., Kopel, M.: On Economic Applications of the Genetic Algorithm: A Model of the Cobweb Type. J. Evol. Econ. 8, 297–315 (1998)
Dubey, P., Haimanko, O., Zapechelnyuk, A.: Strategic Complements and Subtitutes and Potential Games. Game Econ. Behav. 54, 77–94 (2006)
Franke, R.: Coevolution and Stable Adjustments in the Cobweb Model. J. Evol. Econ. 8, 383–406 (1998)
Goldberg, D.E.: Genetic Algorithms in Search, Optimization and Machine Learning. Addison - Wesley, Reading (1989)
Kemeny, J., Snell, J.: Finite Markov Chains. D.Van Nostrand Company Inc., Princeton (1960)
Price, T.C.: Using Co-Evolutionary Programming to Simulate Strategic Behavior in Markets. J. Evol. Econ. 7, 219–254 (1997)
Protopapas, M., Kosmatopoulos, E.: Two genetic algorithms yielding Nash Equilibrium in Symmetric Cournot Games. COMISEF Working Paper Series, WPS-04 (2008)
Riechmann, T.: Learning and Behavioral Stability. J. Evol. Econ. 9, 225–242 (1999)
Riechmann, T.: Genetic Algorithm Learning and Evolutionary Games. J. Econ. Dynam. Contr. 25, 1019–1037 (2001)
Son, Y.S., Baldick, R.: Hybrid Coevolutionary Programming for Nash Equilibrium Search in Games with Local Optima. IEEE Trans. Evol. Comput. 8, 305–315 (2004)
Vallee, T., Yildizoglou, M.: Convergence in Finite Cournot Oligopoly with Social and Individual Learning. Working Papers of GRETha, 2007-07 (2007), GRETha, http://www.gretha.fr (accessed November 10, 2007)
Vriend, N.: An Illustration of the Essential Difference between Individual and Social Learning, and its Consequences for Computational Analyses. J. Econ. Dynam. Contr. 24, 1–19 (2000)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Protopapas, M.K., Battaglia, F., Kosmatopoulos, E.B. (2010). Social Learning Algorithms Reaching Nash Equilibrium in Symmetric Cournot Games. In: Di Chio, C., et al. Applications of Evolutionary Computation. EvoApplications 2010. Lecture Notes in Computer Science, vol 6024. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12239-2_20
Download citation
DOI: https://doi.org/10.1007/978-3-642-12239-2_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-12238-5
Online ISBN: 978-3-642-12239-2
eBook Packages: Computer ScienceComputer Science (R0)