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Rationalization in Signaling Games: Theory and Applications

  • Pierpaolo Battigalli

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. Eddie Dekel & Asher Wolinsky, 2001. "Rationalizable outcomes of large independent private-value first-price discrete auctions," Discussion Papers 1321, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  2. 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.
  3. Sobel, Joel & Stole, Lars & Zapater, Inigo, 1990. "Fixed-equilibrium rationalizability in signaling games," Journal of Economic Theory, Elsevier, vol. 52(2), pages 304-331, December.
  4. J. Watson, 2010. "A ‘Reputation’ Refinement without Equilibrium," Levine's Working Paper Archive 580, David K. Levine.
  5. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2003. "Rationalizable bidding in first-price auctions," Games and Economic Behavior, Elsevier, vol. 45(1), pages 38-72, October.
  6. 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.
  7. P. Battigalli & M. Siniscalchi, 2002. "Rationalization and Incomplete Information," Princeton Economic Theory Working Papers 9817a118e65062903de7c3577, David K. Levine.
  8. Perry, M. & Reny, P.J., 1995. "A General Solution to King Solomon's Dilemma," Papers 9581, Tilburg - Center for Economic Research.
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  13. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
  14. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2002. "Strong Belief and Forward Induction Reasoning," Journal of Economic Theory, Elsevier, vol. 106(2), pages 356-391, October.
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  19. Faruk Gul, 1998. "A Comment on Aumann's Bayesian View," Econometrica, Econometric Society, vol. 66(4), pages 923-928, July.
  20. J. Watson & P. Battigalli, 2010. "On 'Reputation' Refinements with Heterogeneous Beliefs," Levine's Working Paper Archive 582, David K. Levine.
  21. Eddie Dekel & Drew Fudenberg & Stephen Morris, 2005. "Interim Rationalizability," Harvard Institute of Economic Research Working Papers 2064, Harvard - Institute of Economic Research.
  22. Harsanyi, John C., 1994. "Games with Incomplete Information," Nobel Prize in Economics documents 1994-1, Nobel Prize Committee.
  23. Dirk Bergemann & Stephen Morris, 2005. "Robust Implementation: The Role of Large Type Spaces," Levine's Bibliography 784828000000000116, UCLA Department of Economics.
  24. John C Harsanyi, 1997. "Games with incomplete information played by "bayesian" players," Levine's Working Paper Archive 1175, David K. Levine.
  25. Okuno-Fujiwara, Masahiro & Postlewaite, Andrew & Suzumura, Kotaro, 1990. "Strategic Information Revelation," Review of Economic Studies, Wiley Blackwell, vol. 57(1), pages 25-47, January.
  26. Jeffrey C. Ely & Marcin Peski, . "Hierarchies Of Belief And Interim Rationalizability," Discussion Papers 1388, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  27. In-Koo Cho & David M. Kreps, 1997. "Signaling Games and Stable Equilibria," Levine's Working Paper Archive 896, David K. Levine.
  28. Morris, Stephen, 1995. "The Common Prior Assumption in Economic Theory," Economics and Philosophy, Cambridge University Press, vol. 11(02), pages 227-253, October.
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  30. 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.
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