| The standard model of a Bayesian game assumes that players' beliefs are derived from a common knowledge prior on preference parameters. I analyze the robustness of equilibrium strategies of such games to perturbations in the information structure.; In a type space environment (Harsanyi, 1967--68), I embed types corresponding to this information structure into an appropriately defined larger type space. I then perturb the embedded set using the notion of common p-belief (Monderer and Samet, 1989), by considering all types for which it is common p-belief that all players derive their beliefs about preference parameters from similar priors. I examine the equilibrium correspondence that maps priors on preference parameters to corresponding equilibria, and derive conditions on selections that guarantee that the selections define epsilon-equilibria for types in the perturbed set. By definition, such epsilon-equilibria require each player to play an equilibrium strategy for the game where his individual prior is a common knowledge prior.; Based on the properties of such epsilon-equilibria, I propose a notion of robustness that is invariant to small changes in second and higher order beliefs, and which implies that the potential payoff gains from deviating from a robust strategy are uniformly bounded by a small number whenever beliefs are "close" to the beliefs of the standard model. The definition of robustness yields a non-trivial equilibrium refinement for the standard model. Since the characterization of robustness only relies on the structure of the equilibrium correspondence, it is independent of the specification of the underlying type space, which significantly simplifies identifying robust equilibria.; For finite games, I derive additional characterizations for the selections that define robust equilibria. Specifically, I show that an admissible selection can be discontinuous and does not require lower hemicontinuity of the equilibrium correspondence for existence.; As an application, I show how the mechanism design problem is altered by allowing perturbations in the information structure. |
