Evolution in Bayesian Supermodular Population Games

We study evolution in Bayesian supermodular population games. We define such games in the context of large populations of agents and establish the existence of a maximum and a minimum pure strategy Nash equilibria which are monotone in types. To study evolution in such games, we introduce Bayesian perturbed best response dynamics and the corresponding aggregate perturbed best response dynamic. Using the theory of cooperative dynamical systems, we show that solution trajectories of the aggregate perturbed best response dynamic converge to the set of perturbed equilibrium distributions. Using results from Ely and Sandholm (2005), we then conclude that the L1 solution trajectories of the Bayesian perturbed best response dynamic also converge to the set of Bayesian perturbed equilibria.