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Robust Deviations from Signaling Equilibria

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Author Info
Peter Eso
James Schummer

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Abstract

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.

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Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1406.

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Date of creation: Oct 2005
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Handle: RePEc:nwu:cmsems:1406

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Related research
Keywords: Signaling games; Sender-Receiver; robust equilibrium; re¯nements.;

Find related papers by JEL classification:
C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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  1. Fudenberg, Drew & Tirole, Jean, 1991. "Perfect Bayesian equilibrium and sequential equilibrium," Journal of Economic Theory, Elsevier, vol. 53(2), pages 236-260, April. [Downloadable!] (restricted)
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  3. Blume Andreas, 1994. "Equilibrium Refinements in Sender-Receiver Games," Journal of Economic Theory, Elsevier, vol. 64(1), pages 66-77, October. [Downloadable!] (restricted)
  4. Navin Kartik, 2005. "Information Transmission with Cheap and Almost-Cheap Talk," NajEcon Working Paper Reviews 666156000000000650, www.najecon.org. [Downloadable!]
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  8. David Austen-Smith & Jeffrey S. Banks, 1998. "Cheap Talk and Burned Money," Discussion Papers 1245, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
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  9. van Damme,Eric, 1987. "Stable equilibria and forward induction," Discussion Paper Serie A 128, University of Bonn, Germany.
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  10. Banks, Jeffrey S. & Sobel, Joel., 1985. "Equilibrium Selection in Signaling Games," Working Papers 565, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
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  11. Fudenberg, D. & Levine, D.K., 1991. "Self-Confirming Equilibrium ," Working papers 581, Massachusetts Institute of Technology (MIT), Department of Economics.
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  12. Cho, In-Koo & Sobel, Joel, 1990. "Strategic stability and uniqueness in signaling games," Journal of Economic Theory, Elsevier, vol. 50(2), pages 381-413, April. [Downloadable!] (restricted)
  13. Kreps, David M. & Wilson, Robert, 1982. "Reputation and imperfect information," Journal of Economic Theory, Elsevier, vol. 27(2), pages 253-279, August. [Downloadable!] (restricted)
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  14. Steven A. Matthews & M. Okuno-Fujiwara & Andrew Postlewaite, 1990. "Refining Cheap-Talk Equilibria," Discussion Papers 892R, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
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  15. Krishna, V. & Morgan, J., 1999. "A Model of Expertise," Papers 206, Princeton, Woodrow Wilson School - Public and International Affairs.
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  16. Ambrus, Attila & Takahashi, Satoru, 2008. "Multi-sender cheap talk with restricted state spaces," Theoretical Economics, Society for Economic Theory, vol. 3(1), pages 1-27, March. [Downloadable!]
  17. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-37, September. [Downloadable!] (restricted)
  18. Crawford, Vincent P & Sobel, Joel, 1982. "Strategic Information Transmission," Econometrica, Econometric Society, vol. 50(6), pages 1431-51, November. [Downloadable!] (restricted)
  19. Spence, A Michael, 1973. "Job Market Signaling," The Quarterly Journal of Economics, MIT Press, vol. 87(3), pages 355-74, August. [Downloadable!] (restricted)
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  21. Farrell Joseph, 1993. "Meaning and Credibility in Cheap-Talk Games," Games and Economic Behavior, Elsevier, vol. 5(4), pages 514-531, October. [Downloadable!] (restricted)
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