Protopapas, M.K. and Kosmatopoulos, E.B. and Battaglia, F. (2009): Coevolutionary Genetic Algorithms for Establishing Nash Equilibrium in Symmetric Cournot Games. Published in: Advances in Decision Sciences , Vol. 2010, No. 2010 (May 2010)
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Abstract
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 ``sociallearning'' versions of the two coevolutionary 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 coevolutionary 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.
Item Type:  MPRA Paper 

Commentary on:  Protopapas, M.K. and Kosmatopoulos, E.B. and Battaglia, F. (2009): Coevolutionary Genetic Algorithms for Establishing Nash Equilibrium in Symmetric Cournot Games. 
Original Title:  Coevolutionary Genetic Algorithms for Establishing Nash Equilibrium in Symmetric Cournot Games 
Language:  English 
Keywords:  Genetic Algorithms; Cournot oligopoly; Evolutionary Game Theory; Nash Equilibrium 
Subjects:  C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C73  Stochastic and Dynamic Games ; Evolutionary Games ; Repeated Games 
Item ID:  22851 
Depositing User:  Mattheos Protopapas 
Date Deposited:  22. May 2010 22:36 
Last Modified:  02. Jan 2016 20:13 
References:  Alkemade F, La Poutre H, Amman H (2007) On Social Learning and Robust Evolutionary Algorithm Design in the Cournot Oligopoly Game. Comput Intell 23: 162175. AlosFerrer C, Ania A (2005) The Evolutionary Stability of Perfectly Competitive Behavior. Econ Theor 26: 497516. Arifovic J (1994) Genetic Algorithm Learning and the Cobweb Model. J Econ Dynam Contr 18: 328. Basawa IV, Rao P (1980) Statistical Inference for Stochastic Processes. Academic Press, London. Dawid H, Kopel M (1998) On Economic Applications of the Genetic Algorithm: A Model of the Cobweb Type. J Evol Econ 8: 297315. Dubey P, Haimanko O, Zapechelnyuk A (2006) Strategic Complements and Subtitutes and Potential Games. Game Econ Behav 54: 7794. Franke R (1998) Coevolution and Stable Adjustments in the Cobweb Model. J Evol Econ 8: 383406. Goldberg DE (1989) Genetic Algorithms in Search, Optimization and Machine Learning. Addison  Wesley, Reading MA. Kemeny J, Snell J (1960) Finite Markov Chains. D.Van Nostrand Company Inc., Princeton MA. Price TC (1997) Using CoEvolutionary Programming to Simulate Strategic Behavior in Markets. J Evol Econ 7: 219254. Riechmann T (1999) Learning and Behavioral Stability. J Evol Econ 9: 225242. Riechmann T (2001) Genetic Algorithm Learning and Evolutionary Games. J Econ Dynam Contr 25: 10191037. Son YS, Baldick R (2004) Hybrid Coevolutionary Programming for Nash Equilibrium Search in Games with Local Optima. IEEE Trans Evol Comput 8: 305315. Vallee T, Yildizoglou M (2007) Convergence in Finite Cournot Oligopoly with Social and Individual Learning. Working Papers of GRETha, 200707. Available by GRETha ( http://www.gretha.fr ) Accessed 10 November 2007. Vriend N (2000) An Illustration of the Essential Difference between Individual and Social Learning, and its Consequences for Computational Analyses. J Econ Dynam Contr 24: 119. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/22851 
Available Versions of this Item

Coevolutionary Genetic Algorithms for Establishing Nash Equilibrium in Symmetric Cournot Games. (deposited 25. May 2009 09:46)
 Coevolutionary Genetic Algorithms for Establishing Nash Equilibrium in Symmetric Cournot Games. (deposited 22. May 2010 22:36) [Currently Displayed]
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Protopapas, M.K. and Kosmatopoulos, E.B. and Battaglia, F.
Coevolutionary Genetic Algorithms for Establishing Nash Equilibrium in Symmetric Cournot Games. (deposited 25. May 2009 09:46)
 Protopapas, M.K. and Kosmatopoulos, E.B. and Battaglia, F. Coevolutionary Genetic Algorithms for Establishing Nash Equilibrium in Symmetric Cournot Games. (deposited 22. May 2010 22:36) [Currently Displayed]