IDEAS home Printed from https://ideas.repec.org/p/oxf/wpaper/731.html
   My bibliography  Save this paper

Limits to Rational Learning

Author

Listed:
  • Yehuda Levy

Abstract

A long-standing open question raised in the seminal paper of Kalai and Lehrer (1993) is whether or not the play of a repeated game, in the rational learning model introduced there, must eventually resemble play of exact equilibria, and not just play of approximate equilibria as demonstrated there. This paper shows that play may remain distant - in fact, mutually singular - from the play of any equilibrium of the repeated game. We further show that the same inaccessibility holds in Bayesian games, where the play of a Bayesian equilibrium may continue to remain distant from the play of any equilibrium of the true game.

Suggested Citation

  • Yehuda Levy, 2014. "Limits to Rational Learning," Economics Series Working Papers 731, University of Oxford, Department of Economics.
    • Handle: RePEc:oxf:wpaper:731
    as

    Download full text from publisher

    File URL: https://ora.ox.ac.uk/objects/uuid:4155f14d-6684-495a-9001-a7afc604eda8
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Jordan, J. S., 1991. "Bayesian learning in normal form games," Games and Economic Behavior, Elsevier, vol. 3(1), pages 60-81, February.
    2. John H. Nachbar, 1997. "Prediction, Optimization, and Learning in Repeated Games," Econometrica, Econometric Society, vol. 65(2), pages 275-310, March.
    3. Dean Foster & H Peyton Young, 1999. "On the Impossibility of Predicting the Behavior of Rational Agents," Economics Working Paper Archive 423, The Johns Hopkins University,Department of Economics, revised Jun 2001.
    4. Kalai, Ehud & Lehrer, Ehud, 1995. "Subjective games and equilibria," Games and Economic Behavior, Elsevier, vol. 8(1), pages 123-163.
    5. Kalai, Ehud & Lehrer, Ehud, 1993. "Rational Learning Leads to Nash Equilibrium," Econometrica, Econometric Society, vol. 61(5), pages 1019-1045, September.
    6. Matthew O. Jackson & Ehud Kalai & Rann Smorodinsky, 1999. "Bayesian Representation of Stochastic Processes under Learning: de Finetti Revisited," Econometrica, Econometric Society, vol. 67(4), pages 875-894, July.
    7. Yaw Nyarko, 1998. "Bayesian learning and convergence to Nash equilibria without common priors," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(3), pages 643-655.
    8. Ronald Miller & Chris Sanchirico, "undated". "Almost Everybody Disagrees Almost All the Time: The Genericity of Weakly Merging Nowhere," Scholarship at Penn Law upenn_wps-1001, University of Pennsylvania Law School.
    9. Sandroni, Alvaro, 1998. "Necessary and Sufficient Conditions for Convergence to Nash Equilibrium: The Almost Absolute Continuity Hypothesis," Games and Economic Behavior, Elsevier, vol. 22(1), pages 121-147, January.
    10. Lehrer, Ehud & Smorodinsky, Rann, 1997. "Repeated Large Games with Incomplete Information," Games and Economic Behavior, Elsevier, vol. 18(1), pages 116-134, January.
    11. Gilli, Mario, 2001. "A General Approach to Rational Learning in Games," Bulletin of Economic Research, Wiley Blackwell, vol. 53(4), pages 275-303, October.
    12. Ehud Lehrer & Rann Smorodinsky, 1996. "Compatible Measures and Merging," Mathematics of Operations Research, INFORMS, vol. 21(3), pages 697-706, August.
    13. Thomas D. Jeitschko, 1998. "Learning in Sequential Auctions," Southern Economic Journal, John Wiley & Sons, vol. 65(1), pages 98-112, July.
    14. Miller, Ronald I. & Sanchirico, Chris William, 1999. "The Role of Absolute Continuity in "Merging of Opinions" and "Rational Learning"," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 170-190, October.
    15. Thomas Norman, 2012. "Almost-Rational Learning of Nash Equilibrium without Absolute Continuity," Economics Series Working Papers 602, University of Oxford, Department of Economics.
    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. Norman, Thomas W.L., 2022. "The possibility of Bayesian learning in repeated games," Games and Economic Behavior, Elsevier, vol. 136(C), pages 142-152.

    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. Mario Gilli, 2002. "Rational Learning in Imperfect Monitoring Games," Working Papers 46, University of Milano-Bicocca, Department of Economics, revised Mar 2002.
    2. Norman, Thomas W.L., 2022. "The possibility of Bayesian learning in repeated games," Games and Economic Behavior, Elsevier, vol. 136(C), pages 142-152.
    3. Young, H. Peyton, 2002. "On the limits to rational learning," European Economic Review, Elsevier, vol. 46(4-5), pages 791-799, May.
    4. Dean Foster & H Peyton Young, 1999. "On the Impossibility of Predicting the Behavior of Rational Agents," Economics Working Paper Archive 423, The Johns Hopkins University,Department of Economics, revised Jun 2001.
    5. John H. Nachbar, 2005. "Beliefs in Repeated Games," Econometrica, Econometric Society, vol. 73(2), pages 459-480, March.
    6. Anke Gerber, "undated". "Learning in and about Games," IEW - Working Papers 234, Institute for Empirical Research in Economics - University of Zurich.
    7. Thomas Norman, 2012. "Almost-Rational Learning of Nash Equilibrium without Absolute Continuity," Economics Series Working Papers 602, University of Oxford, Department of Economics.
    8. Yoo, Seung Han, 2014. "Learning a population distribution," Journal of Economic Dynamics and Control, Elsevier, vol. 48(C), pages 188-201.
    9. Lehrer, Ehud & Smorodinsky, Rann, 2000. "Relative entropy in sequential decision problems1," Journal of Mathematical Economics, Elsevier, vol. 33(4), pages 425-439, May.
    10. Matthew O. Jackson & Ehud Kalai, 1997. "False Reputation in a Society of Players," Discussion Papers 1184R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    11. Burkhard C. Schipper, 2022. "Strategic Teaching and Learning in Games," American Economic Journal: Microeconomics, American Economic Association, vol. 14(3), pages 321-352, August.
    12. Foster, Dean P. & Young, H. Peyton, 2003. "Learning, hypothesis testing, and Nash equilibrium," Games and Economic Behavior, Elsevier, vol. 45(1), pages 73-96, October.
    13. Burkhard Schipper, 2015. "Strategic teaching and learning in games," Working Papers 151, University of California, Davis, Department of Economics.
    14. Sandroni, Alvaro & Smorodinsky, Rann, 2004. "Belief-based equilibrium," Games and Economic Behavior, Elsevier, vol. 47(1), pages 157-171, April.
    15. Jindani, Sam, 2022. "Learning efficient equilibria in repeated games," Journal of Economic Theory, Elsevier, vol. 205(C).
    16. Turdaliev, Nurlan, 2002. "Calibration and Bayesian learning," Games and Economic Behavior, Elsevier, vol. 41(1), pages 103-119, October.
    17. Miller, Ronald I. & Sanchirico, Chris William, 1999. "The Role of Absolute Continuity in "Merging of Opinions" and "Rational Learning"," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 170-190, October.
    18. Nyarko, Y., 1998. "The Truth is in the Eye of the Beholder: or Equilibrium in Beliefs and Rational Learning in Games," Working Papers 98-12, C.V. Starr Center for Applied Economics, New York University.
    19. Sandroni, Alvaro, 1998. "Necessary and Sufficient Conditions for Convergence to Nash Equilibrium: The Almost Absolute Continuity Hypothesis," Games and Economic Behavior, Elsevier, vol. 22(1), pages 121-147, January.
    20. Matthew Jackson & Ehud Kalai, 1995. "Recurring Bullies," Discussion Papers 1151, Northwestern University, Center for Mathematical Studies in Economics and Management Science.

    More about this item

    Keywords

    Rational Learning; Repeated Games; Nash Equilibrium;
    All these keywords.

    JEL classification:

    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary 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:oxf:wpaper:731. 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: Anne Pouliquen (email available below). General contact details of provider: https://edirc.repec.org/data/sfeixuk.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.