  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. 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.
