IDEAS home Printed from https://ideas.repec.org/p/wop/safiwp/01-08-039.html
   My bibliography  Save this paper

On the Impossibility of Predicting the Behavior of Rational Agents

Author

Listed:
  • Dean P. Foster
  • H. Peyton Young

Abstract

A foundational assumption in economics is that people are rational -- they choose optimal plans of action given their predictions about future states of the world. In games of strategy this means that each playersÕ strategy should be optimal given his or her prediction of the opponentsÕ strategies. We demonstrate that there is an inherent tension between rationality and prediction when players are uncertain about their opponentsÕ payoff functions. Specifically, there are games in which it is impossible for perfectly rational players to learn to predict the future behavior of their opponents (even approximately) no matter what learning rule they use. The reason is that, in trying to predict the next-period behavior of an opponent, a rational player must take an action this period that the opponent can observe. This observation may cause the opponent to alter his next-period behavior, thus invalidating the first playerÕs prediction. The resulting feedback loop has the property that, in almost every time period, someone predicts that his opponent has a non-negligible probability of choosing one action, when in fact the opponent is certain to choose a different action. We conclude that there are strategic situations where it is impossible in principle for perfectly rational agents to learn to predict the future behavior of other perfectly rational agents, based solely on their observed actions.

Suggested Citation

  • Dean P. Foster & H. Peyton Young, 2001. "On the Impossibility of Predicting the Behavior of Rational Agents," Working Papers 01-08-039, Santa Fe Institute.
  • Handle: RePEc:wop:safiwp:01-08-039
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Fudenberg Drew & Kreps David M., 1993. "Learning Mixed Equilibria," Games and Economic Behavior, Elsevier, vol. 5(3), pages 320-367, July.
    2. John H. Nachbar, 1997. "Prediction, Optimization, and Learning in Repeated Games," Econometrica, Econometric Society, vol. 65(2), pages 275-310, March.
    3. Jordan, J. S., 1991. "Bayesian learning in normal form games," Games and Economic Behavior, Elsevier, vol. 3(1), pages 60-81, February.
    4. Kalai, Ehud & Lehrer, Ehud, 1993. "Rational Learning Leads to Nash Equilibrium," Econometrica, Econometric Society, vol. 61(5), pages 1019-1045, September.
    5. Jordan J. S., 1995. "Bayesian Learning in Repeated Games," Games and Economic Behavior, Elsevier, vol. 9(1), pages 8-20, April.
    6. John H. Nachbar, 2001. "Bayesian learning in repeated games of incomplete information," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(2), pages 303-326.
    7. 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.
    8. Lehrer, Ehud & Smorodinsky, Rann, 1997. "Repeated Large Games with Incomplete Information," Games and Economic Behavior, Elsevier, vol. 18(1), pages 116-134, January.
    9. Monderer, Dov & Shapley, Lloyd S., 1996. "Fictitious Play Property for Games with Identical Interests," Journal of Economic Theory, Elsevier, vol. 68(1), pages 258-265, January.
    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. Al-Suwailem, Sami, 2014. "Complexity and endogenous instability," Research in International Business and Finance, Elsevier, vol. 30(C), pages 393-410.
    2. Yakov Babichenko, 2010. "Completely Uncoupled Dynamics and Nash Equilibria," Discussion Paper Series dp529, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    3. Levy, Yehuda John, 2015. "Limits to rational learning," Journal of Economic Theory, Elsevier, vol. 160(C), pages 1-23.
    4. 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.
    5. Babichenko, Yakov, 2012. "Completely uncoupled dynamics and Nash equilibria," Games and Economic Behavior, Elsevier, vol. 76(1), pages 1-14.
    6. Young, H. Peyton, 2002. "On the limits to rational learning," European Economic Review, Elsevier, vol. 46(4-5), pages 791-799, May.
    7. Norman, Thomas W.L., 2015. "Learning, hypothesis testing, and rational-expectations equilibrium," Games and Economic Behavior, Elsevier, vol. 90(C), pages 93-105.
    8. Georges, Christophre, 2006. "Learning with misspecification in an artificial currency market," Journal of Economic Behavior & Organization, Elsevier, vol. 60(1), pages 70-84, May.
    9. H. Peyton Young, 2007. "The Possible and the Impossible in Multi-Agent Learning," Economics Series Working Papers 304, University of Oxford, Department of Economics.
    10. Joshua M. Epstein & Ross A. Hammond, 2001. "Non-Explanatory Equilibria: An Extremely Simple Game With (Mostly) Unattainable Fixed Points," Working Papers 01-08-043, Santa Fe Institute.
    11. Dean P Foster & Peyton Young, 2006. "Regret Testing Leads to Nash Equilibrium," Levine's Working Paper Archive 784828000000000676, David K. Levine.

    More about this item

    Keywords

    Rationality; learning; prediction; equilibrium;

    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:wop:safiwp:01-08-039. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Thomas Krichel). General contact details of provider: http://edirc.repec.org/data/epstfus.html .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.