IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v110y2018icp248-257.html
   My bibliography  Save this article

Rationalizability and logical inference

Author

Listed:
  • Balkenborg, Dieter

Abstract

In a model of modal logic it is shown that the assumptions of rationality and intelligence of the players imply that only rationalizable strategies can be played. Nothing more can be inferred from these rules. Hereby the assumption of “intelligence” expresses that whatever an outside observer can deduce about the play of the game can be inferred by the players themselves, provided they have the same information. In our framework the assumption of intelligence is simply the familiar inference rule of necessitation in modal logic. Our approach contrasts with a hierarchical approach traditional in the literature, where assumption about knowledge about knowledge ... about rationality are added one by one.

Suggested Citation

  • Balkenborg, Dieter, 2018. "Rationalizability and logical inference," Games and Economic Behavior, Elsevier, vol. 110(C), pages 248-257.
    • Handle: RePEc:eee:gamebe:v:110:y:2018:i:c:p:248-257
    DOI: 10.1016/j.geb.2018.04.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899825618300617
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.geb.2018.04.006?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Borgers Tilman, 1994. "Weak Dominance and Approximate Common Knowledge," Journal of Economic Theory, Elsevier, vol. 64(1), pages 265-276, October.
    2. Ehud Kalai & Eitan Zemel, 1988. "On The Order of Eliminating Dominated Strategies," Discussion Papers 789, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. Dieter Balkenborg & Josef Hofbauer & Christoph Kuzmics, 2015. "The refined best-response correspondence in normal form games," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(1), pages 165-193, February.
    4. Perea,Andrés, 2012. "Epistemic Game Theory," Cambridge Books, Cambridge University Press, number 9781107401396, September.
    5. Dekel, Eddie & Fudenberg, Drew, 1990. "Rational behavior with payoff uncertainty," Journal of Economic Theory, Elsevier, vol. 52(2), pages 243-267, December.
    6. Balkenborg, Dieter G. & Hofbauer, Josef & Kuzmics, Christoph, 2013. "Refined best-response correspondence and dynamics," Theoretical Economics, Econometric Society, vol. 8(1), January.
    7. Bjorndahl, A. & Halpern, J.Y. & Pass, R., 2017. "Reasoning about rationality," Games and Economic Behavior, Elsevier, vol. 104(C), pages 146-164.
    8. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
    9. Adam Brandenburger & Amanda Friedenberg & H. Jerome Keisler, 2014. "Admissibility in Games," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 7, pages 161-212, World Scientific Publishing Co. Pte. Ltd..
    10. Perea,Andrés, 2012. "Epistemic Game Theory," Cambridge Books, Cambridge University Press, number 9781107008915, September.
    11. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
    12. Robert J. Aumann, 1999. "Interactive epistemology I: Knowledge," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(3), pages 263-300.
    13. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    14. Arieli, Itai & Aumann, Robert J., 2015. "The logic of backward induction," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 443-464.
    15. Apt Krzysztof R., 2007. "The Many Faces of Rationalizability," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 7(1), pages 1-39, May.
    16. Borgers, Tilman, 1993. "Pure Strategy Dominance," Econometrica, Econometric Society, vol. 61(2), pages 423-430, March.
    17. Mamoru Kaneko, 2005. "Game Theory and Mutual Misunderstanding," Studies in Economic Theory, Springer, number 978-3-540-26812-3, September.
    18. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2002. "Strong Belief and Forward Induction Reasoning," Journal of Economic Theory, Elsevier, vol. 106(2), pages 356-391, October.
    19. Apt Krzysztof R., 2004. "Uniform Proofs of Order Independence for Various Strategy Elimination Procedures," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 4(1), pages 1-48, September.
    20. Samuelson, Larry, 1992. "Dominated strategies and common knowledge," Games and Economic Behavior, Elsevier, vol. 4(2), pages 284-313, April.
    Full references (including those not matched with items on IDEAS)

    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. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2019. "Comprehensive rationalizability," Games and Economic Behavior, Elsevier, vol. 116(C), pages 185-202.
    3. Barelli, Paulo & Galanis, Spyros, 2013. "Admissibility and event-rationality," Games and Economic Behavior, Elsevier, vol. 77(1), pages 21-40.
    4. Xiao Luo & Ben Wang, 2022. "An epistemic characterization of MACA," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(4), pages 995-1024, June.
    5. Burkhard Schipper & Martin Meier & Aviad Heifetz, 2017. "Comprehensive Rationalizability," Working Papers 174, University of California, Davis, Department of Economics.
    6. Adam Brandenburger & Amanda Friedenberg, 2014. "Self-Admissible Sets," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 8, pages 213-249, World Scientific Publishing Co. Pte. Ltd..
    7. Manili, Julien, 2024. "Order independence for rationalizability," Games and Economic Behavior, Elsevier, vol. 143(C), pages 152-160.
    8. Geir B. Asheim & Andrés Perea, 2019. "Algorithms for cautious reasoning in games," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(4), pages 1241-1275, December.
    9. Asheim, Geir B. & Brunnschweiler, Thomas, 2023. "Epistemic foundation of the backward induction paradox," Games and Economic Behavior, Elsevier, vol. 141(C), pages 503-514.
    10. Chen, Yi-Chun & Long, Ngo Van & Luo, Xiao, 2007. "Iterated strict dominance in general games," Games and Economic Behavior, Elsevier, vol. 61(2), pages 299-315, November.
    11. Shuige Liu, 2018. "Characterizing Permissibility, Proper Rationalizability, and Iterated Admissibility by Incomplete Information," Papers 1811.01933, arXiv.org.
    12. Catonini, Emiliano & De Vito, Nicodemo, 2020. "Weak belief and permissibility," Games and Economic Behavior, Elsevier, vol. 120(C), pages 154-179.
    13. Asheim, G.B. & Dufwenberg, M., 1996. "Admissibility and Common Knowledge," Discussion Paper 1996-16, Tilburg University, Center for Economic Research.
    14. Asheim, Geir B. & Dufwenberg, Martin, 2003. "Admissibility and common belief," Games and Economic Behavior, Elsevier, vol. 42(2), pages 208-234, February.
    15. Joseph Y. Halpern & Yoram Moses, 2017. "Characterizing solution concepts in terms of common knowledge of rationality," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(2), pages 457-473, May.
    16. Balkenborg, Dieter & Hofbauer, Josef & Kuzmics, Christoph, 2016. "Refined best reply correspondence and dynamics," Center for Mathematical Economics Working Papers 451, Center for Mathematical Economics, Bielefeld University.
    17. Ziegler, Gabriel & Zuazo-Garin, Peio, 2020. "Strategic cautiousness as an expression of robustness to ambiguity," Games and Economic Behavior, Elsevier, vol. 119(C), pages 197-215.
    18. Dieter Balkenborg & Josef Hofbauer & Christoph Kuzmics, 2015. "The refined best-response correspondence in normal form games," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(1), pages 165-193, February.
    19. Yi-Chun Chen & Xiao Luo & Chen Qu, 2016. "Rationalizability in general situations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(1), pages 147-167, January.
    20. V. K. Oikonomou & J. Jost, 2020. "Periodic Strategies II: Generalizations and Extensions," Papers 2005.12832, arXiv.org.

    More about this item

    Keywords

    Rationalizability; Modal logic; Necessitation;
    All these keywords.

    JEL classification:

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

    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:eee:gamebe:v:110:y:2018:i:c:p:248-257. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622836 .

    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.