Social Learning Algorithms Reaching Nash Equilibrium in Symmetric Cournot Games

The series of studies about the convergence or not of the evolutionary strategies of players that use co-evolutionary genetic algorithms in Cournot games has not addressed the issue of individual players' strategies convergence, but only of the convergence of the aggregate indices (total quantity and price) to the levels that correspond either to the Nash or Walrash Equilibrium. Here we discover that while some algorithms lead to convergence of the aggregates to Nash Equilibrium values, this is not the case for the individual players' strategies (i.e. no NE is reached). Co-evolutionary programming social learning, as well as a social learning algorithm we introduce here, achieve this goal (in a stochastic sense); this is displayed by statistical tests, as well as "NE stages" evaluation, based on ergodic Markov chains.