Robust Equilibria of Potential Games

Potential games, as considered by Monderer and Shapley (1996), are games with potential functions. Potential functions are functions of action profiles such that the difference induced by a single deviation is equal to that of the deviator's payoff function. Monderer and Shapley (1996) demonstrated that the set of action profiles maximizing the potential function is a subset of Nash equilibria and that this subset does not depend upon a particular potential function. Monderer and Shapley (1996) wrote, at least technically, the potential defines a refinement concept. The observation of Monderer and Shapley (1996) brings up the question of what can justify this refinement concept. The purpose of this paper is to provide a possible justification, using the notion of robustness of equilibria to incomplete information considered by Kajii and Morris (1997, 1997). It is shown that Nash equilibria that maximize potential functions are generically robust in the sense of Kajii and Morris (1997).