IDEAS home Printed from https://ideas.repec.org/a/bla/jecrev/v63y2012i1p57-67.html
   My bibliography  Save this article

Robust Rationalizability Under Almost Common Certainty Of Payoffs

Author

Listed:
  • STEPHEN MORRIS
  • SATORU TAKAHASHI
  • OLIVIER TERCIEUX

Abstract

An action is robustly rationalizable if it is rationalizable for every type who has almost common certainty of payoffs. We illustrate by means of an example that an action may not be robustly rationalizable even if it is weakly dominant, and argue that robust rationalizability is a very stringent refinement of rationalizability. Nonetheless, we show that every strictly rationalizable action is robustly rationalizable. We also investigate how permissive robust rationalizability becomes if we require that players be fully certain of their own payoffs.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Stephen Morris & Satoru Takahashi & Olivier Tercieux, 2012. "Robust Rationalizability Under Almost Common Certainty Of Payoffs," The Japanese Economic Review, Japanese Economic Association, vol. 63(1), pages 57-67, March.
    • Handle: RePEc:bla:jecrev:v:63:y:2012:i:1:p:57-67
    DOI: j.1468-5876.2011.00553.x
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1111/j.1468-5876.2011.00553.x
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/j.1468-5876.2011.00553.x?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. Drew Fudenberg & David M. Kreps & David K. Levine, 2008. "On the Robustness of Equilibrium Refinements," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 5, pages 67-93, World Scientific Publishing Co. Pte. Ltd..
    2. Vincent J. Vannetelbosch & P. Jean-Jacques Herings, 2000. "The equivalence of the Dekel-Fudenberg iterative procedure and weakly perfect rationalizability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 15(3), pages 677-687.
    3. Jonathan Weinstein & Muhamet Yildiz, 2007. "A Structure Theorem for Rationalizability with Application to Robust Predictions of Refinements," Econometrica, Econometric Society, vol. 75(2), pages 365-400, March.
    4. 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).
    5. Frank Schuhmacher, 1999. "Proper rationalizability and backward induction," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(4), pages 599-615.
    6. Atsushi Kajii & Stephen Morris, 1997. "The Robustness of Equilibria to Incomplete Information," Econometrica, Econometric Society, vol. 65(6), pages 1283-1310, November.
    7. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    8. , & , & ,, 2007. "Interim correlated rationalizability," Theoretical Economics, Econometric Society, vol. 2(1), pages 15-40, March.
    9. Vincent J. Vannetelbosch & P. Jean-Jacques Herings, 2000. "The equivalence of the Dekel-Fudenberg iterative procedure and weakly perfect rationalizability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 15(3), pages 677-687.
    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. Annie Liang, 2019. "Games of Incomplete Information Played By Statisticians," Papers 1910.07018, arXiv.org, revised Jul 2020.
    2. Annie Liang, 2016. "Games of Incomplete Information Played by Statisticians," PIER Working Paper Archive 16-028, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 01 Jan 2016.
    3. Takahashi, Satoru & Tercieux, Olivier, 2020. "Robust equilibrium outcomes in sequential games under almost common certainty of payoffs," Journal of Economic Theory, Elsevier, vol. 188(C).
    4. Chen, Yi-Chun & Takahashi, Satoru & Xiong, Siyang, 2022. "Robust refinement of rationalizability with arbitrary payoff uncertainty," Games and Economic Behavior, Elsevier, vol. 136(C), pages 485-504.

    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. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications,, Elsevier.
    2. Frick, Mira & Romm, Assaf, 2015. "Rational behavior under correlated uncertainty," Journal of Economic Theory, Elsevier, vol. 160(C), pages 56-71.
    3. Oyama, Daisuke & Tercieux, Olivier, 2010. "Robust equilibria under non-common priors," Journal of Economic Theory, Elsevier, vol. 145(2), pages 752-784, March.
    4. Chen, Yi-Chun & Takahashi, Satoru & Xiong, Siyang, 2014. "The robust selection of rationalizability," Journal of Economic Theory, Elsevier, vol. 151(C), pages 448-475.
    5. Chen, Yi-Chun & Takahashi, Satoru & Xiong, Siyang, 2022. "Robust refinement of rationalizability with arbitrary payoff uncertainty," Games and Economic Behavior, Elsevier, vol. 136(C), pages 485-504.
    6. Kota Murayama, 2020. "Robust predictions under finite depth of reasoning," The Japanese Economic Review, Springer, vol. 71(1), pages 59-84, January.
    7. Kota Murayama, 2015. "Robust Predictions under Finite Depth of Reasoning," Discussion Paper Series DP2015-28, Research Institute for Economics & Business Administration, Kobe University.
    8. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2007. "Interactive epistemology in games with payoff uncertainty," Research in Economics, Elsevier, vol. 61(4), pages 165-184, December.
    9. Chen, Yi-Chun & Mueller-Frank, Manuel & Pai, Mallesh M., 2022. "Continuous implementation with direct revelation mechanisms," Journal of Economic Theory, Elsevier, vol. 201(C).
    10. 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.
    11. ,, 2013. "On the structure of rationalizability for arbitrary spaces of uncertainty," Theoretical Economics, Econometric Society, vol. 8(2), May.
    12. Tang, Qianfeng, 2015. "Hierarchies of beliefs and the belief-invariant Bayesian solution," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 111-116.
    13. Perea Andrés, 2003. "Rationalizability and Minimal Complexity in Dynamic Games," Research Memorandum 047, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    14. Weinstein, Jonathan & Yildiz, Muhamet, 2017. "Interim correlated rationalizability in infinite games," Journal of Mathematical Economics, Elsevier, vol. 72(C), pages 82-87.
    15. Weinstein, Jonathan & Yildiz, Muhamet, 2007. "Impact of higher-order uncertainty," Games and Economic Behavior, Elsevier, vol. 60(1), pages 200-212, July.
    16. Perea ý Monsuwé, A., 2003. "Proper rationalizability and belief revision in dynamic games," Research Memorandum 048, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    17. Yildiz, Muhamet, 2015. "Invariance to representation of information," Games and Economic Behavior, Elsevier, vol. 94(C), pages 142-156.
    18. Chen, Yi-Chun, 2012. "A structure theorem for rationalizability in the normal form of dynamic games," Games and Economic Behavior, Elsevier, vol. 75(2), pages 587-597.
    19. Ronald Stauber, 2014. "A framework for robustness to ambiguity of higher-order beliefs," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(3), pages 525-550, August.
    20. Jain, Ritesh & Lombardi, Michele, 2022. "Continuous virtual implementation: Complete information," Journal of Mathematical Economics, Elsevier, vol. 99(C).

    More about this item

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

    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:bla:jecrev:v:63:y:2012:i:1:p:57-67. 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: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/jeaaaea.html .

    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.