IDEAS home Printed from https://ideas.repec.org/p/bdi/wptemi/td_757_10.html
   My bibliography  Save this paper

A note on rationalizability and restrictions on belief

Author

Listed:
  • Giuseppe Cappelletti

    (Bank of Italy)

Abstract

Rationalizability is a widely accepted solution concept in the study of strategic form game with complete information and is fully characterized in terms of assumptions on the rationality of the players and common certainty of rationality. Battigalli and Siniscalchi extend rationalizability and derive the solution concept called ?-rationalizability. Their analysis is based on the following assumptions: (a) players are rational; (b) their first-order beliefs satisfy some restrictions; and (c) there is common belief of (a) and (b). In this note I focus on games with complete information and I characterize ?-rationalizability with a new notion of iterative dominance which is able to capture the additional hypothesis on players' beliefs.

Suggested Citation

  • Giuseppe Cappelletti, 2010. "A note on rationalizability and restrictions on belief," Temi di discussione (Economic working papers) 757, Bank of Italy, Economic Research and International Relations Area.
    • Handle: RePEc:bdi:wptemi:td_757_10
    as

    Download full text from publisher

    File URL: http://www.bancaditalia.it/pubblicazioni/temi-discussione/2010/2010-0757/en_tema_757.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Dirk Bergemann & Stephen Morris, 2005. "Robust Implementation: The Role of Large Type Spaces," Levine's Bibliography 784828000000000116, UCLA Department of Economics.
    2. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    3. , C. & ,, 2006. "Hierarchies of belief and interim rationalizability," Theoretical Economics, Econometric Society, vol. 1(1), pages 19-65, March.
    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 & 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.
    6. Vincent P. Crawford, 2003. "Lying for Strategic Advantage: Rational and Boundedly Rational Misrepresentation of Intentions," American Economic Review, American Economic Association, vol. 93(1), pages 133-149, March.
    7. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
    8. 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.
    9. Dirk Bergemann & Stephen Morris, 2007. "Belief Free Incomplete Information Games," Cowles Foundation Discussion Papers 1629, Cowles Foundation for Research in Economics, Yale University.
    10. John C. Harsanyi, 1967. "Games with Incomplete Information Played by "Bayesian" Players, I-III Part I. The Basic Model," Management Science, INFORMS, vol. 14(3), pages 159-182, November.
    11. 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..
    12. Battigalli, Pierpaolo, 1997. "On Rationalizability in Extensive Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 40-61, May.
    13. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2002. "Strong Belief and Forward Induction Reasoning," Journal of Economic Theory, Elsevier, vol. 106(2), pages 356-391, October.
    14. Battigalli, Pierpaolo, 2003. "Rationalizability in infinite, dynamic games with incomplete information," Research in Economics, Elsevier, vol. 57(1), pages 1-38, March.
    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. Battigalli Pierpaolo & Prestipino Andrea, 2013. "Transparent Restrictions on Beliefs and Forward-Induction Reasoning in Games with Asymmetric Information," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 13(1), pages 79-130, May.

    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 & 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.
    2. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications,, Elsevier.
    3. 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.
    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. 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.
    6. Manili, Julien, 2024. "Order independence for rationalizability," Games and Economic Behavior, Elsevier, vol. 143(C), pages 152-160.
    7. Guarino, Pierfrancesco, 2020. "An epistemic analysis of dynamic games with unawareness," Games and Economic Behavior, Elsevier, vol. 120(C), pages 257-288.
    8. Perea, Andrés, 2017. "Forward induction reasoning and correct beliefs," Journal of Economic Theory, Elsevier, vol. 169(C), pages 489-516.
    9. Burkhard C. Schipper & Hang Zhou, 2022. "Level-k Thinking in the Extensive Form," Working Papers 352, University of California, Davis, Department of Economics.
    10. Perea, Andrés, 2022. "Common belief in rationality in games with unawareness," Mathematical Social Sciences, Elsevier, vol. 119(C), pages 11-30.
    11. De Magistris, Enrico, 2024. "Incomplete preferences or incomplete information? On Rationalizability in games with private values," Games and Economic Behavior, Elsevier, vol. 144(C), pages 126-140.
    12. V. K. Oikonomou & J. Jost, 2020. "Periodic Strategies II: Generalizations and Extensions," Papers 2005.12832, arXiv.org.
    13. Zuazo-Garin, Peio, 2017. "Uncertain information structures and backward induction," Journal of Mathematical Economics, Elsevier, vol. 71(C), pages 135-151.
    14. Müller, Christoph, 2016. "Robust virtual implementation under common strong belief in rationality," Journal of Economic Theory, Elsevier, vol. 162(C), pages 407-450.
    15. Andrés Perea & Elias Tsakas, 2019. "Limited focus in dynamic games," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(2), pages 571-607, June.
    16. , & , & ,, 2007. "Interim correlated rationalizability," Theoretical Economics, Econometric Society, vol. 2(1), pages 15-40, March.
    17. Amanda Friedenberg & H. Jerome Keisler, 2021. "Iterated dominance revisited," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(2), pages 377-421, September.
    18. Giacomo Bonanno & Elias Tsakas, 2017. "Qualitative analysis of common belief of rationality in strategic-form games," Working Papers 181, University of California, Davis, Department of Economics.
    19. Amanda Friedenberg, 2006. "Can Hidden Variables Explain Correlation? (joint with Adam Brandenburger)," Theory workshop papers 815595000000000005, UCLA Department of Economics.
    20. 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..

    More about this item

    Keywords

    rationalizability; strategic form game; complete information;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:bdi:wptemi:td_757_10. 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: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/bdigvit.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.