Learning Nash Equilibria in Large Populations With Constrained Strategy Switching

We consider a large population of learning agents that interact noncooperatively by selecting strategies from a common set. Each strategy has a payoff, assigned by a strictly concave potential game. The agents repeatedly revise their strategies according to a learning rule that models how they seek alternatives with higher payoffs. Our objective is to determine when the population learns the Nash equilibrium of the game, meaning its strategy profile asymptotically converges to this equilibrium. Unlike previous work assuming unrestricted strategy switching, here we tackle the case where only certain strategies are accessible from certain others, characterized by a strategy graph that is connected but possibly incomplete. Through Lyapunov’s method, we prove that modifications based on KL-divergence to either the payoffs or the learning rules ensure the strategy profile’s near-global convergence to the Nash equilibrium. We highlight the practical significance of our findings and provide a numerical validation.