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Abstract: This paper studies uniqueness of equilibrium in symmetric Bayesian games. It shows that if signals are highly but not perfectly dependent, then players play their risk-dominant actions for all but a vanishing set of signal realizations. In contrast to the literature on global games, noise is not assumed to be additive. Dependence is modeled using the theory of copulas.

This paper considers a simple adaptive learning rule in Bayesian games with binary actions where players employ threshold strategies. Global convergence results are given for supermodular games and potential games. If there is a unique equilibrium, players' strategies converge almost surely to it. Even if there is not, in potential games and in the two-player case in supermodular games, any limit point of the learning process must be an equilibrium. In particular, if equilibria are isolated, the learning process converges to one of them almost surely.