Protopapas, M.K. and Kosmatopoulos, E.B. and Battaglia, F. (2009): Coevolutionary Genetic Algorithms for Establishing Nash Equilibrium in Symmetric Cournot Games.
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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 

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:  15375 
Depositing User:  Mattheos Protopapas 
Date Deposited:  25. May 2009 09:46 
Last Modified:  12. Feb 2013 07:43 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/15375 
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 Coevolutionary Genetic Algorithms for Establishing Nash Equilibrium in Symmetric Cournot Games. (deposited 25. May 2009 09:46) [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) [Currently Displayed]