Informational Robustness and Solution Concepts

We discuss four solution concepts for games with incomplete information. We show how each solution concept can be viewed as encoding informational robustness. For a given type space, we consider expansions of the type space that provide players with additional signals. We distinguish between expansions along two dimensions. First, the signals can either convey payoff relevant information or only payoff irrelevant information. Second, the signals can be generated from a common (prior) distribution or not. We establish the equivalence between Bayes Nash equilibrium behavior under the resulting expansion of the type space and a corresponding more permissive solution concept under the original type space. This approach unifies some existing literature and, in the case of an expansion without a common prior and allowing for payoff relevant signals, leads us to a new solution concept that we dub belief-free rationalizability.