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 “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.
Highlights
The “Cournot Game” models an oligopoly of two or more firms that simultaneously define the quantities they supply to the market, which in turn define both the market price and the equilibrium quantity in the market
In contrast to the classical genetic algorithms used for optimization, the co-evolutionary versions are distinct at the issue of the objective function
In a classical genetic algorithm the objective function for optimization is given before hand, while in the co-evolutionary case, the objective function changes during the course of play as it is based on the choices of the players
Summary
Online at https://mpra.ub.uni-muenchen.de/22851/ MPRA Paper No 22851, posted 22 May 2010 22:36 UTC. We 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.
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