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On the Impossibility of Predicting the Behavior of Rational Agents

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  • 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.

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Bibliographic Info

Paper provided by Santa Fe Institute in its series Working Papers with number 01-08-039.

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Date of creation: Aug 2001
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Handle: RePEc:wop:safiwp:01-08-039

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Keywords: Rationality; learning; prediction; equilibrium;

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References

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  1. Kalai, Ehud & Lehrer, Ehud, 1993. "Rational Learning Leads to Nash Equilibrium," Econometrica, Econometric Society, vol. 61(5), pages 1019-45, September.
  2. Jordan J. S., 1995. "Bayesian Learning in Repeated Games," Games and Economic Behavior, Elsevier, vol. 9(1), pages 8-20, April.
  3. Fudenberg, D. & Kreps, D.M., 1992. "Learning Mixed Equilibria," Working papers 92-13, Massachusetts Institute of Technology (MIT), Department of Economics.
  4. Ronald Miller & Chris Sanchirico, . "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.
  5. Lehrer, Ehud & Smorodinsky, Rann, 1997. "Repeated Large Games with Incomplete Information," Games and Economic Behavior, Elsevier, vol. 18(1), pages 116-134, January.
  6. 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.
  7. John Nachbar, 2010. "Prediction, Optimization and Learning in Repeated Games," Levine's Working Paper Archive 576, David K. Levine.
  8. John H. Nachbar, 2001. "Bayesian learning in repeated games of incomplete information," Social Choice and Welfare, Springer, vol. 18(2), pages 303-326.
  9. Jordan, J. S., 1991. "Bayesian learning in normal form games," Games and Economic Behavior, Elsevier, vol. 3(1), pages 60-81, February.
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Citations

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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. H. Peyton Young, 2007. "The Possible and the Impossible in Multi-Agent Learning," Economics Series Working Papers 304, University of Oxford, Department of Economics.
  3. Babichenko, Yakov, 2012. "Completely uncoupled dynamics and Nash equilibria," Games and Economic Behavior, Elsevier, vol. 76(1), pages 1-14.
  4. Georges, Christophre, 2006. "Learning with misspecification in an artificial currency market," Journal of Economic Behavior & Organization, Elsevier, vol. 60(1), pages 70-84, May.
  5. 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.
  6. Yakov Babichenko, 2010. "Completely Uncoupled Dynamics and Nash Equilibria," Discussion Paper Series dp529, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  7. Al-Suwailem, Sami, 2014. "Complexity and endogenous instability," Research in International Business and Finance, Elsevier, vol. 30(C), pages 393-410.
  8. 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.
  9. Dean P Foster & Peyton Young, 2006. "Regret Testing Leads to Nash Equilibrium," Levine's Working Paper Archive 784828000000000676, David K. Levine.

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