Credible deviations from signaling equilibria

In games with costly signaling, some equilibria are vulnerable to deviations which could be "unambiguously" interpreted as coming from a unique set of Sender-types. This occurs when these types are precisely the ones who gain from deviating for any beliefs the Receiver could form over that set. We show that this idea characterizes a unique equilibrium outcome in two classes of games. First, in monotonic 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's (Q J Econ 102:179-221, 1987) D1 criterion on this class of games. Second, we examine a version of Crawford and Sobel (Econometrica 50:1431-1451, 1982) model with costly signaling, where standard refinements have no effect. We show that only a Riley-like separating equilibrium is immune to these deviations.