Robust Deviations from Signaling Equilibria

In Sender-Receiver games with costly signaling, some equilibria are vulnerable to deviations which could be "unambiguously" interpreted by the Receiver as coming from a unique set of possible Sender-types. The vulnerability occurs when the types in this set are the ones who gain from the deviation, regardless of the posterior beliefs the Receiver forms over that set. We formalize this idea and use it to characterize a unique equilibrium outcome in two classes of games. First, in mono- tonic signaling games, only the Riley outcome is immune to this sort of deviation. Our result therefore provides a plausible story behind the selection made by Cho and Kreps' (1987) D1 criterion on this class of games. Second, we examine a version of Crawford and Sobel's (1982) model but with costly signaling and finite type sets, where standard refinements have no effect. We show that only a Riley-like separating equilibrium is immune to these deviations.