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We use co-evolutionary genetic algorithms to model the players' learningprocess in several Cournot models, and evaluate them in terms of theirconvergence to the Nash Equilibrium. The "social-learning" versions of the twoco-evolutionary algorithms we introduce, establish Nash Equilibrium in thosemodels, in contrast to the "individual learning" versions which, as we seehere, do not imply the convergence of the players' strategies to the Nashoutcome. When players use "canonical co-evolutionary genetic algorithms" aslearning algorithms, the process of the game is an ergodic Markov Chain, andtherefore we analyze simulation results using both the relevant methodology andmore general statistical tests, to find that in the "social" case, statesleading to NE play are highly frequent at the stationary distribution of thechain, in contrast to the "individual learning" case, when NE is not reached atall in our simulations; to find that the expected Hamming distance of thestates at the limiting distribution from the "NE state" is significantlysmaller in the "social" than in the "individual learning case"; to estimate theexpected time that the "social" algorithms need to get to the "NE state" andverify their robustness and finally to show that a large fraction of the gamesplayed are indeed at the Nash Equilibrium.

Coevolutionary Genetic Algorithms for Establishing Nash Equilibrium in Symmetric Cournot Games