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On the Impossibility of Predicting the Behavior of Rational Agents

  • Dean P. Foster
  • H. Peyton Young

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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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
Date of revision:
Handle: RePEc:wop:safiwp:01-08-039
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  1. Fudenberg, D. & Kreps, D.M., 1992. "Learning Mixed Equilibria," Working papers 92-13, Massachusetts Institute of Technology (MIT), Department of Economics.
  2. John H. Nachbar, 1995. "Prediction, Optimization, and Learning in Repeated Games," Game Theory and Information 9504001, EconWPA, revised 14 Feb 1996.
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  4. Kalai, Ehud & Lehrer, Ehud, 1991. "Rational Learning Leads to Nash Equilibrium," Working Papers 91-18, C.V. Starr Center for Applied Economics, New York University.
  5. Jordan J. S., 1995. "Bayesian Learning in Repeated Games," Games and Economic Behavior, Elsevier, vol. 9(1), pages 8-20, April.
  6. 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.
  7. Lehrer, Ehud & Smorodinsky, Rann, 1997. "Repeated Large Games with Incomplete Information," Games and Economic Behavior, Elsevier, vol. 18(1), pages 116-134, January.
  8. 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.
  9. John H. Nachbar, 2001. "Bayesian learning in repeated games of incomplete information," Social Choice and Welfare, Springer, vol. 18(2), pages 303-326.
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