Abstract
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.
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We thank David Austen-Smith, Drew Fudenberg, Johannes Hörner, Navin Kartik, Marcin Peski, Phil Reny, Marciano Siniscalchi, Jeroen Swinkels, and anonymous reviewers for helpful comments. We are particularly indebted to Sidartha Gordon and Joel Sobel for their insights. We are also grateful to seminar participants at Columbia, Northwestern, Penn State, Rochester, and the 2006 N. American Econometric Society Meetings.
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Eső, P., Schummer, J. Credible deviations from signaling equilibria. Int J Game Theory 38, 411–430 (2009). https://doi.org/10.1007/s00182-009-0161-x
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DOI: https://doi.org/10.1007/s00182-009-0161-x