IDEAS home Printed from https://ideas.repec.org/a/wsi/igtrxx/v08y2006i01ns0219198906000795.html
   My bibliography  Save this article

Rationalization In Signaling Games: Theory And Applications

Author

Listed:
  • PIERPAOLO BATTIGALLI

    (Bocconi University and IGIER, Via Salasco, 5, 20136, Milano, Italy)

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.

Suggested Citation

  • Pierpaolo Battigalli, 2006. "Rationalization In Signaling Games: Theory And Applications," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 8(01), pages 67-93.
    • Handle: RePEc:wsi:igtrxx:v:08:y:2006:i:01:n:s0219198906000795
    DOI: 10.1142/S0219198906000795
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219198906000795
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219198906000795?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Masahiro Okuno-Fujiwara & Andrew Postlewaite & Kotaro Suzumura, 1990. "Strategic Information Revelation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 57(1), pages 25-47.
    2. Dirk Bergemann & Stephen Morris, 2005. "Robust Implementation: The Role of Large Type Spaces," Levine's Bibliography 784828000000000116, UCLA Department of Economics.
    3. Patrick Bolton & Mathias Dewatripont, 2005. "Contract Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262025760, April.
    4. Grossman, Sanford J, 1981. "The Informational Role of Warranties and Private Disclosure about Product Quality," Journal of Law and Economics, University of Chicago Press, vol. 24(3), pages 461-483, December.
    5. Dirk Bergemann & Stephen Morris, 2012. "Robust Mechanism Design," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 2, pages 49-96, World Scientific Publishing Co. Pte. Ltd..
    6. Battigalli Pierpaolo & Siniscalchi Marciano, 2003. "Rationalization and Incomplete Information," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 3(1), pages 1-46, June.
    7. 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.
    8. Adam Brandenburger & Eddie Dekel, 2014. "Rationalizability and Correlated Equilibria," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 3, pages 43-57, World Scientific Publishing Co. Pte. Ltd..
    9. 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.
    10. In-Koo Cho & David M. Kreps, 1987. "Signaling Games and Stable Equilibria," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 102(2), pages 179-221.
    11. Kreps, David M. & Wilson, Robert, 1982. "Reputation and imperfect information," Journal of Economic Theory, Elsevier, vol. 27(2), pages 253-279, August.
    12. In-Koo Cho, 2004. "Monotonicity and Rationalizability in Large Uniform Price and Double Auctions," Theory workshop papers 658612000000000076, UCLA Department of Economics.
    13. Ben-Porath, E., 1992. "Rationality, Nash Equilibrium and Backward Induction in Perfect Information Games," Papers 14-92, Tel Aviv - the Sackler Institute of Economic Studies.
    14. Giacomo Bonanno & Klaus Nehring, 1999. "How to make sense of the common prior assumption under incomplete information," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(3), pages 409-434.
    15. Elchanan Ben-Porath, 1997. "Rationality, Nash Equilibrium and Backwards Induction in Perfect-Information Games," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 64(1), pages 23-46.
    16. Eddie Dekel & Drew Fudenberg & Stephen Morris, 2005. "Interim Rationalizability," Levine's Bibliography 666156000000000526, UCLA Department of Economics.
    17. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, April.
    18. 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.
    19. Eddie Dekel & Asher Wolinsky, 2000. "Rationalizable Outcomes of Large Independent Private-Value First Price Discrete Auctions," Discussion Papers 1308, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    20. Grossman, S J & Hart, O D, 1980. "Disclosure Laws and Takeover Bids," Journal of Finance, American Finance Association, vol. 35(2), pages 323-334, May.
    21. Pierpaolo Battigalli & Joel Watson, 1997. "On "Reputation" Refinements with Heterogeneous Beliefs," Econometrica, Econometric Society, vol. 65(2), pages 369-374, March.
    22. 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.
    23. Dekel, Eddie & Wolinsky, Asher, 2003. "Rationalizable outcomes of large private-value first-price discrete auctions," Games and Economic Behavior, Elsevier, vol. 43(2), pages 175-188, May.
    24. Watson, Joel, 1993. "A "Reputation" Refinement without Equilibrium," Econometrica, Econometric Society, vol. 61(1), pages 199-205, January.
    25. , C. & ,, 2006. "Hierarchies of belief and interim rationalizability," Theoretical Economics, Econometric Society, vol. 1(1), pages 19-65, March.
    26. Harsanyi, John C, 1995. "Games with Incomplete Information," American Economic Review, American Economic Association, vol. 85(3), pages 291-303, June.
    27. In-Koo Cho, 1994. "Stationarity, Rationalizability and Bargaining," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(2), pages 357-374.
    28. MERTENS, Jean-François & ZAMIR, Shmuel, 1985. "Formulation of Bayesian analysis for games with incomplete information," LIDAM Reprints CORE 608, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    29. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2003. "Rationalizable bidding in first-price auctions," Games and Economic Behavior, Elsevier, vol. 45(1), pages 38-72, October.
    30. Feinberg, Yossi, 2000. "Characterizing Common Priors in the Form of Posteriors," Journal of Economic Theory, Elsevier, vol. 91(2), pages 127-179, April.
    31. Joel Watson, 1998. "Alternating-Offer Bargaining with Two-Sided Incomplete Information," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 573-594.
    32. Morris, Stephen, 1995. "The Common Prior Assumption in Economic Theory," Economics and Philosophy, Cambridge University Press, vol. 11(2), pages 227-253, October.
    33. Watson, Joel, 1996. "Reputation in Repeated Games with No Discounting," Games and Economic Behavior, Elsevier, vol. 15(1), pages 82-109, July.
    34. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    35. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2002. "Strong Belief and Forward Induction Reasoning," Journal of Economic Theory, Elsevier, vol. 106(2), pages 356-391, October.
    36. Battigalli, Pierpaolo, 2003. "Rationalizability in infinite, dynamic games with incomplete information," Research in Economics, Elsevier, vol. 57(1), pages 1-38, March.
    37. John C Harsanyi, 1997. "Games with incomplete information played by "bayesian" players," Levine's Working Paper Archive 1175, David K. Levine.
    38. Faruk Gul, 1998. "A Comment on Aumann's Bayesian View," Econometrica, Econometric Society, vol. 66(4), pages 923-928, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Burkhard Schipper & Hee Yeul Woo, 2012. "Political Awareness and Microtargeting of Voters in Electoral Competition," Working Papers 124, University of California, Davis, Department of Economics.
    2. Pierpaolo Battigalli & Pietro Tebaldi, 2019. "Interactive epistemology in simple dynamic games with a continuum of strategies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(3), pages 737-763, October.
    3. Dominiak, Adam & Lee, Dongwoo, 2023. "Testing rational hypotheses in signaling games," European Economic Review, Elsevier, vol. 160(C).
    4. Weng, Xi & Wu, Fan & Yin, Xundong, 2023. "Linear Riley equilibria in quadratic signaling games," Journal of Economic Theory, Elsevier, vol. 213(C).
    5. Schipper, Burkhard C. & Woo, Hee Yeul, 2019. "Political Awareness, Microtargeting of Voters, and Negative Electoral Campaigning," Quarterly Journal of Political Science, now publishers, vol. 14(1), pages 41-88, January.
    6. Heifetz Aviad & Meier Martin & Schipper Burkhard C., 2021. "Prudent Rationalizability in Generalized Extensive-form Games with Unawareness," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 21(2), pages 525-556, June.
    7. Manili, Julien, 2024. "Order independence for rationalizability," Games and Economic Behavior, Elsevier, vol. 143(C), pages 152-160.
    8. Burkhard Schipper & Hee Yeul Woo, 2014. "Political Awareness, Microtargeting of Voters, and Negative Electoral Campaigning," Working Papers 148, University of California, Davis, Department of Economics.
    9. repec:use:tkiwps:2727 is not listed on IDEAS
    10. Li, Ying Xue & Schipper, Burkhard C., 2020. "Strategic reasoning in persuasion games: An experiment," Games and Economic Behavior, Elsevier, vol. 121(C), pages 329-367.
    11. Burkhard Schipper & Hee Yeul Woo, 2012. "Political Awareness and Microtargeting of Voters in Electoral Competition," Working Papers 46, University of California, Davis, Department of Economics.
    12. Pierpaolo Battigalli & Carlo Chiarella & Stefano Gatti & Tommaso Orlando, 2017. "M&A negotiations with limited information: how do opaque firms buy and get bought?," Working Papers 596, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    13. Burkhard Schipper & Ying Xue Li, 2018. "Strategic Reasoning in Persuasion Games: An Experiment," Working Papers 181, University of California, Davis, Department of Economics.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Battigalli Pierpaolo & Siniscalchi Marciano, 2003. "Rationalization and Incomplete Information," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 3(1), pages 1-46, June.
    2. Battigalli, Pierpaolo, 2003. "Rationalizability in infinite, dynamic games with incomplete information," Research in Economics, Elsevier, vol. 57(1), pages 1-38, March.
    3. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications,, Elsevier.
    4. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2007. "Interactive epistemology in games with payoff uncertainty," Research in Economics, Elsevier, vol. 61(4), pages 165-184, December.
    5. Battigalli Pierpaolo & Di Tillio Alfredo & Grillo Edoardo & Penta Antonio, 2011. "Interactive Epistemology and Solution Concepts for Games with Asymmetric Information," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 11(1), pages 1-40, March.
    6. , & , & ,, 2007. "Interim correlated rationalizability," Theoretical Economics, Econometric Society, vol. 2(1), pages 15-40, March.
    7. Müller, Christoph, 2016. "Robust virtual implementation under common strong belief in rationality," Journal of Economic Theory, Elsevier, vol. 162(C), pages 407-450.
    8. Guarino, Pierfrancesco, 2020. "An epistemic analysis of dynamic games with unawareness," Games and Economic Behavior, Elsevier, vol. 120(C), pages 257-288.
    9. Cappelletti Giuseppe, 2010. "A Note on Rationalizability and Restrictions on Beliefs," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 10(1), pages 1-13, September.
    10. , & , & ,, 2006. "Topologies on types," Theoretical Economics, Econometric Society, vol. 1(3), pages 275-309, September.
    11. Battigalli, P. & Catonini, E. & Manili, J., 2023. "Belief change, rationality, and strategic reasoning in sequential games," Games and Economic Behavior, Elsevier, vol. 142(C), pages 527-551.
    12. Shimoji, Makoto & Schweinzer, Paul, 2015. "Implementation without incentive compatibility: Two stories with partially informed planners," Games and Economic Behavior, Elsevier, vol. 91(C), pages 258-267.
    13. Catonini, Emiliano, 2019. "Rationalizability and epistemic priority orderings," Games and Economic Behavior, Elsevier, vol. 114(C), pages 101-117.
    14. Amanda Friedenberg, 2006. "Can Hidden Variables Explain Correlation? (joint with Adam Brandenburger)," Theory workshop papers 815595000000000005, UCLA Department of Economics.
    15. Adam Brandenburger & Amanda Friedenberg, 2014. "Intrinsic Correlation in Games," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 4, pages 59-111, World Scientific Publishing Co. Pte. Ltd..
    16. Catonini, Emiliano, 2020. "On non-monotonic strategic reasoning," Games and Economic Behavior, Elsevier, vol. 120(C), pages 209-224.
    17. Pomatto, Luciano, 2022. "Stable matching under forward-induction reasoning," Theoretical Economics, Econometric Society, vol. 17(4), November.
    18. Perea, Andrés, 2017. "Forward induction reasoning and correct beliefs," Journal of Economic Theory, Elsevier, vol. 169(C), pages 489-516.
    19. Jonathan Weinstein & Muhamet Yildiz, 2004. "Finite-Order Implications of Any Equilibrium," Levine's Working Paper Archive 122247000000000065, David K. Levine.
    20. Zuazo-Garin, Peio, 2017. "Uncertain information structures and backward induction," Journal of Mathematical Economics, Elsevier, vol. 71(C), pages 135-151.

    More about this item

    Keywords

    Incomplete information; signaling; rationalization; Subject Classification: C72; Subject Classification: D82;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wsi:igtrxx:v:08:y:2006:i:01:n:s0219198906000795. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/igtr/igtr.shtml .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.