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On the Impossibility of Predicting the Behavior of Rational Agents

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  • Dean 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 players?strategy should be optimal given his or her prediction of the opponents?strategies We demonstrate that there is an inherent tension between rationality and prediction when players are uncertain about their opponents?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 player�s 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 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.
    • Handle: RePEc:jhu:papers:423
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    Cited by:

    1. Young, H. Peyton, 2002. "On the limits to rational learning," European Economic Review, Elsevier, vol. 46(4-5), pages 791-799, May.
    2. Burkhard C. Schipper, 2022. "Strategic Teaching and Learning in Games," American Economic Journal: Microeconomics, American Economic Association, vol. 14(3), pages 321-352, August.
    3. Norman, Thomas W.L., 2022. "The possibility of Bayesian learning in repeated games," Games and Economic Behavior, Elsevier, vol. 136(C), pages 142-152.
    4. Chernov, G. & Susin, I., 2019. "Models of learning in games: An overview," Journal of the New Economic Association, New Economic Association, vol. 44(4), pages 77-125.
    5. Burkhard Schipper, 2015. "Strategic teaching and learning in games," Working Papers 151, University of California, Davis, Department of Economics.
    6. Norman, Thomas W.L., 2015. "Learning, hypothesis testing, and rational-expectations equilibrium," Games and Economic Behavior, Elsevier, vol. 90(C), pages 93-105.
    7. Sami Al-Suwailem, 2012. "Complexity and Endogenous Instability," ASSRU Discussion Papers 1203, ASSRU - Algorithmic Social Science Research Unit.
    8. Al-Suwailem, Sami, 2014. "Complexity and endogenous instability," Research in International Business and Finance, Elsevier, vol. 30(C), pages 393-410.
    9. 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.
    10. Levy, Yehuda John, 2015. "Limits to rational learning," Journal of Economic Theory, Elsevier, vol. 160(C), pages 1-23.
    11. Thomas Norman, 2012. "Almost-Rational Learning of Nash Equilibrium without Absolute Continuity," Economics Series Working Papers 602, University of Oxford, Department of Economics.
    12. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    13. 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.
    14. H. Peyton Young, 2007. "The Possible and the Impossible in Multi-Agent Learning," Economics Series Working Papers 304, University of Oxford, Department of Economics.
    15. 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.
    16. Georges, Christophre, 2006. "Learning with misspecification in an artificial currency market," Journal of Economic Behavior & Organization, Elsevier, vol. 60(1), pages 70-84, May.
    17. Dean P Foster & Peyton Young, 2006. "Regret Testing Leads to Nash Equilibrium," Levine's Working Paper Archive 784828000000000676, David K. Levine.
    18. Babichenko, Yakov, 2012. "Completely uncoupled dynamics and Nash equilibria," Games and Economic Behavior, Elsevier, vol. 76(1), pages 1-14.
    19. Thomas Norman, 2012. "Learning Within Rational-Expectations Equilibrium," Economics Series Working Papers 591, University of Oxford, Department of Economics.
    20. Anke Gerber, "undated". "Learning in and about Games," IEW - Working Papers 234, Institute for Empirical Research in Economics - University of Zurich.

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