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Rationalization in Signaling Games: Theory and Applications

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Pierpaolo Battigalli

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Abstract

Focusing on signaling games, I illustrate the relevance of the rationalizability approach for the analysis multistage games with incomplete information. I define a class of iterative solution procedures, featuring a notion of “forward induction”: the Receiver tries to explain the Sender’s message in a way which is consistent with the Sender’s strategic sophistication and certain given restrictions on beliefs. The approach is applied to some numerical examples and economic models. In a standard model with verifiable messages a full disclosure result is obtained. In a model of job market signaling the best separating equilibrium emerges as the unique rationalizable outcome only when the high and low types are sufficiently different. Otherwise, rationalizability only puts bounds on the education choices of different types.

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Paper provided by IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University in its series Working Papers with number 275.

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Date of creation: 2004
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Handle: RePEc:igi:igierp:275

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  1. Grossman, Sanford J, 1981. "The Informational Role of Warranties and Private Disclosure about Product Quality," Journal of Law & Economics, University of Chicago Press, vol. 24(3), pages 461-83, December.
  2. Joel Sobel, 1990. "Fixed-Equilibrium Rationalizability in Signaling Games," University of California at San Diego, Economics Working Paper Series 90-13, Department of Economics, UC San Diego.
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  3. Grossman, S J & Hart, O D, 1980. " Disclosure Laws and Takeover Bids," Journal of Finance, American Finance Association, vol. 35(2), pages 323-34, May. [Downloadable!] (restricted)
  4. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2002. "Strong Belief and Forward Induction Reasoning," Journal of Economic Theory, Elsevier, vol. 106(2), pages 356-391, October. [Downloadable!] (restricted)
  5. Feinberg, Yossi, 2000. "Characterizing Common Priors in the Form of Posteriors," Journal of Economic Theory, Elsevier, vol. 91(2), pages 127-179, April. [Downloadable!] (restricted)
  6. 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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  7. Battigalli, Pierpaolo & Siniscalchi, Marciano, 1999. "Hierarchies of Conditional Beliefs and Interactive Epistemology in Dynamic Games," Journal of Economic Theory, Elsevier, vol. 88(1), pages 188-230, September. [Downloadable!] (restricted)
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  8. Dirk Bergemann & Stephen Morris, 2005. "Robust Implementation: The Role of Large Type Spaces," Levine's Bibliography 784828000000000116, UCLA Department of Economics. [Downloadable!]
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  9. Battigalli, Pierpaolo, 2003. "Rationalizability in infinite, dynamic games with incomplete information," Research in Economics, Elsevier, vol. 57(1), pages 1-38, March. [Downloadable!] (restricted)
  10. Faruk Gul, 1998. "A Comment on Aumann's Bayesian View," Econometrica, Econometric Society, vol. 66(4), pages 923-928, July.
  11. Dirk Bergemann & Stephen Morris, 2003. "Robust Mechanism Design," Cowles Foundation Discussion Papers 1421R, Cowles Foundation, Yale University, revised Apr 2004. [Downloadable!]
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  12. Okuno-Fujiwara, Masahiro & Postlewaite, Andrew & Suzumura, Kotaro, 1990. "Strategic Information Revelation," Review of Economic Studies, Blackwell Publishing, vol. 57(1), pages 25-47, January. [Downloadable!] (restricted)
  13. Dekel, E. & Wolinsky, A., 2000. "Rationalizable Outcomes of Large Independent Private-Value First-Price Discrete Auctions," Papers 2000-13, Tel Aviv.
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  14. N. M. Kiefer, 1998. "Reply," Econometric Reviews, Taylor and Francis Journals, vol. 7(2), pages 161-163. [Downloadable!] (restricted)
  15. Harsanyi, John C, 1995. "Games with Incomplete Information," American Economic Review, American Economic Association, vol. 85(3), pages 291-303, June.
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  16. In-Koo Cho, 2004. "Monotonicity and Rationalizability in Large Uniform Price and Double Auctions," Theory workshop papers 658612000000000076, UCLA Department of Economics. [Downloadable!]
  17. Watson, Joel, 1996. "Reputation in Repeated Games with No Discounting," Games and Economic Behavior, Elsevier, vol. 15(1), pages 82-109, July. [Downloadable!] (restricted)
  18. Eddie Dekel & Drew Fudenberg & Stephen Morris, 2005. "Interim Rationalizability," Levine's Bibliography 666156000000000526, UCLA Department of Economics. [Downloadable!]
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  19. Tai-Wei Hu, 2004. "General Rationalizability and Its Robustness for Strategic Form Games with Incomplete Information," Econometric Society 2004 Far Eastern Meetings 771, Econometric Society.
  20. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July. [Downloadable!] (restricted)
  21. Ely, Jeffrey C. & Peski, Marcin, 2006. "Hierarchies of belief and interim rationalizability," Theoretical Economics, Society for Economic Theory, vol. 1(1), pages 19-65, March. [Downloadable!]
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  22. Pierpaolo Battigalli & Joel Watson, 1997. "On "Reputation" Refinements with Heterogeneous Beliefs," Econometrica, Econometric Society, vol. 65(2), pages 369-374, March.
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  23. 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. [Downloadable!] (restricted)
  24. repec:bep:theadv:v:3:y:2003:i:1:p:1073-1073 is not listed on IDEAS
  25. Giacomo Bonanno & Klaus Nehring, 1999. "How to make sense of the common prior assumption under incomplete information," International Journal of Game Theory, Springer, vol. 28(3), pages 409-434. [Downloadable!] (restricted)
  26. Brandenburger, Adam & Dekel, Eddie, 1987. "Rationalizability and Correlated Equilibria," Econometrica, Econometric Society, vol. 55(6), pages 1391-1402, November. [Downloadable!] (restricted)
  27. Watson, Joel, 1993. "A "Reputation" Refinement without Equilibrium," Econometrica, Econometric Society, vol. 61(1), pages 199-205, January. [Downloadable!] (restricted)
  28. Cho, In-Koo, 1994. "Stationarity, Rationalizability and Bargaining," Review of Economic Studies, Blackwell Publishing, vol. 61(2), pages 357-74, April. [Downloadable!] (restricted)
  29. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2003. "Rationalizable bidding in first-price auctions," Games and Economic Behavior, Elsevier, vol. 45(1), pages 38-72, October. [Downloadable!] (restricted)
  30. Perry, Motty & Reny, Philip J., 1999. "A General Solution to King Solomon's Dilemma," Games and Economic Behavior, Elsevier, vol. 26(2), pages 279-285, January. [Downloadable!] (restricted)
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  31. Watson, Joel, 1998. "Alternating-Offer Bargaining with Two-Sided Incomplete Information," Review of Economic Studies, Blackwell Publishing, vol. 65(3), pages 573-94, July. [Downloadable!] (restricted)
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  32. L. G. Godfrey & A. R. Tremayne, 1998. "Reply," Econometric Reviews, Taylor and Francis Journals, vol. 7(1), pages 63-64. [Downloadable!] (restricted)
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