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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
Contact details of provider: Postal: Center for Mathematical Studies in Economics and Management Science, Northwestern University, 580 Jacobs Center, 2001 Sheridan Road, Evanston, IL 60208-2014
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  1. Fudenberg, Drew & Levine, David K, 1993. "Self-Confirming Equilibrium," Econometrica, Econometric Society, vol. 61(3), pages 523-45, May.
  2. 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.
  3. Marco Battaglini, 1999. "Multiple Referrals and Multidimensional Cheap Talk," Discussion Papers 1295, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  4. E. Kohlberg & J.-F. Mertens, 1998. "On the Strategic Stability of Equilibria," Levine's Working Paper Archive 445, David K. Levine.
  5. 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.
  6. Myerson, Roger B., 1989. "Credible negotiation statements and coherent plans," Journal of Economic Theory, Elsevier, vol. 48(1), pages 264-303, June.
  7. Spence, A Michael, 1973. "Job Market Signaling," The Quarterly Journal of Economics, MIT Press, vol. 87(3), pages 355-74, August.
  8. Riley, John G, 1979. "Informational Equilibrium," Econometrica, Econometric Society, vol. 47(2), pages 331-59, March.
  9. Grossman, Sanford J. & Perry, Motty, 1986. "Perfect sequential equilibrium," Journal of Economic Theory, Elsevier, vol. 39(1), pages 97-119, June.
  10. Crawford, Vincent P & Sobel, Joel, 1982. "Strategic Information Transmission," Econometrica, Econometric Society, vol. 50(6), pages 1431-51, November.
  11. Takahashi, Satoru & Ambrus, Attila, 2008. "Multi-Sender Cheap Talk with Restricted State Spaces," Scholarly Articles 3200263, Harvard University Department of Economics.
  12. Blume Andreas, 1994. "Equilibrium Refinements in Sender-Receiver Games," Journal of Economic Theory, Elsevier, vol. 64(1), pages 66-77, October.
  13. Farrell, Joseph, 1986. "Meaning and Credibility in Cheap-Talk Games," Department of Economics, Working Paper Series qt4968n3fz, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
  14. Cho, In-Koo & Kreps, David M, 1987. "Signaling Games and Stable Equilibria," The Quarterly Journal of Economics, MIT Press, vol. 102(2), pages 179-221, May.
  15. Vijay Krishna & John Morgan, 2001. "A Model Of Expertise," The Quarterly Journal of Economics, MIT Press, vol. 116(2), pages 747-775, May.
  16. van Damme, Eric, 1989. "Stable equilibria and forward induction," Journal of Economic Theory, Elsevier, vol. 48(2), pages 476-496, August.
  17. Rabin, Matthew, 1990. "Communication between rational agents," Journal of Economic Theory, Elsevier, vol. 51(1), pages 144-170, June.
  18. Banks, Jeffrey S & Sobel, Joel, 1987. "Equilibrium Selection in Signaling Games," Econometrica, Econometric Society, vol. 55(3), pages 647-61, May.
  19. Navin Kartik, 2005. "Information Transmission with Cheap and Almost-Cheap Talk," NajEcon Working Paper Reviews 666156000000000650, www.najecon.org.
  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. David Kreps & Robert Wilson, 1999. "Reputation and Imperfect Information," Levine's Working Paper Archive 238, David K. Levine.
  22. 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.
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