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Robust Deviations from Signaling Equilibria

  • Peter Eso
  • James Schummer

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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  1. Banks, Jeffrey S & Sobel, Joel, 1987. "Equilibrium Selection in Signaling Games," Econometrica, Econometric Society, vol. 55(3), pages 647-61, May.
  2. Marco Battaglini, 2002. "Multiple Referrals and Multidimensional Cheap Talk," Econometrica, Econometric Society, vol. 70(4), pages 1379-1401, July.
  3. Navin Kartik, 2005. "Information Transmission with Cheap and Almost-Cheap Talk," NajEcon Working Paper Reviews 666156000000000650, www.najecon.org.
  4. Farrell Joseph, 1993. "Meaning and Credibility in Cheap-Talk Games," Games and Economic Behavior, Elsevier, vol. 5(4), pages 514-531, October.
  5. van Damme,Eric, 1987. "Stable equilibria and forward induction," Discussion Paper Serie A 128, University of Bonn, Germany.
  6. KOHLBERG, Elon & MERTENS, Jean-François, . "On the strategic stability of equilibria," CORE Discussion Papers RP 716, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. Kreps, David M. & Wilson, Robert, 1982. "Reputation and imperfect information," Journal of Economic Theory, Elsevier, vol. 27(2), pages 253-279, August.
  8. Ambrus, Attila & Takahashi, Satoru, 2008. "Multi-sender cheap talk with restricted state spaces," Theoretical Economics, Econometric Society, vol. 3(1), March.
  9. Fudenberg, Drew & Levine, David K, 1993. "Self-Confirming Equilibrium," Econometrica, Econometric Society, vol. 61(3), pages 523-45, May.
  10. In-Koo Cho & David M. Kreps, 1997. "Signaling Games and Stable Equilibria," Levine's Working Paper Archive 896, David K. Levine.
  11. Rabin, Matthew, 1990. "Communication between rational agents," Journal of Economic Theory, Elsevier, vol. 51(1), pages 144-170, June.
  12. Blume, A., 1992. "Equilibrium Refinements in Sender-Receiver Games," Working Papers 92-12, University of Iowa, Department of Economics.
  13. Myerson, Roger B., 1989. "Credible negotiation statements and coherent plans," Journal of Economic Theory, Elsevier, vol. 48(1), pages 264-303, June.
  14. Michael Spence, 1973. "Job Market Signaling," The Quarterly Journal of Economics, Oxford University Press, vol. 87(3), pages 355-374.
  15. John G. Riley, 1976. "Informational Equilibrium," UCLA Economics Working Papers 071, UCLA Department of Economics.
  16. 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.
  17. 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.
  18. Krishna, V. & Morgan, J., 1999. "A Model of Expertise," Papers 206, Princeton, Woodrow Wilson School - Public and International Affairs.
  19. V. Crawford & J. Sobel, 2010. "Strategic Information Transmission," Levine's Working Paper Archive 544, David K. Levine.
  20. Fudenberg, Drew & Tirole, Jean, 1991. "Perfect Bayesian equilibrium and sequential equilibrium," Journal of Economic Theory, Elsevier, vol. 53(2), pages 236-260, April.
  21. Matthews, Steven A. & Okuno-Fujiwara, Masahiro & Postlewaite, Andrew, 1991. "Refining cheap-talk equilibria," Journal of Economic Theory, Elsevier, vol. 55(2), pages 247-273, December.
  22. Grossman, Sanford J. & Perry, Motty, 1986. "Perfect sequential equilibrium," Journal of Economic Theory, Elsevier, vol. 39(1), pages 97-119, June.
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