Coevolutionary Genetic Algorithms for Establishing Nash Equilibrium in Symmetric Cournot Games
AbstractWe 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.
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 15375.
Date of creation: 22 May 2009
Date of revision:
Genetic Algorithms; Cournot oligopoly; Evolutionary Game Theory; Nash Equilibrium;
Other versions of this item:
- Mattheos Protopapas & Francesco Battaglia & Elias Kosmatopoulo, 2008. "Coevolutionary Genetic Algorithms for Establishing Nash Equilibrium in Symmetric Cournot Games," Working Papers 004, COMISEF.
- C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-05-30 (All new papers)
- NEP-CMP-2009-05-30 (Computational Economics)
- NEP-EVO-2009-05-30 (Evolutionary Economics)
- NEP-GTH-2009-05-30 (Game Theory)
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