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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

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Bibliographic Info

Paper provided by The Johns Hopkins University,Department of Economics in its series Economics Working Paper Archive with number 423.

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Date of creation: Feb 1999
Date of revision: Jun 2001
Handle: RePEc:jhu:papers:423

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References

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  1. John H. Nachbar, 1997. "Prediction, Optimization, and Learning in Repeated Games," Econometrica, Econometric Society, vol. 65(2), pages 275-310, March.
  2. Drew Fudenberg & David Kreps, 2010. "Learning Mixed Equilibria," Levine's Working Paper Archive 415, David K. Levine.
  3. Ehud Kalai & Ehud Lehrer, 1990. "Rational Learning Leads to Nash Equilibrium," Discussion Papers 895, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  4. John H. Nachbar, 2001. "Bayesian learning in repeated games of incomplete information," Social Choice and Welfare, Springer, vol. 18(2), pages 303-326.
  5. Jordan, J. S., 1991. "Bayesian learning in normal form games," Games and Economic Behavior, Elsevier, vol. 3(1), pages 60-81, February.
  6. Lehrer, Ehud & Smorodinsky, Rann, 1997. "Repeated Large Games with Incomplete Information," Games and Economic Behavior, Elsevier, vol. 18(1), pages 116-134, January.
  7. 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.
  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.
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Cited by:
  1. Yakov Babichenko, 2010. "Completely Uncoupled Dynamics and Nash Equilibria," Discussion Paper Series dp529, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  2. Young, H. Peyton, 2002. "On the limits to rational learning," European Economic Review, Elsevier, vol. 46(4-5), pages 791-799, May.
  3. Peyton Young, 2002. "Learning Hypothesis Testing and Nash Equilibrium," Economics Working Paper Archive 474, The Johns Hopkins University,Department of Economics.
  4. Dean P Foster & Peyton Young, 2006. "Regret Testing Leads to Nash Equilibrium," Levine's Working Paper Archive 784828000000000676, David K. Levine.
  5. 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.
  6. Georges, Christophre, 2006. "Learning with misspecification in an artificial currency market," Journal of Economic Behavior & Organization, Elsevier, vol. 60(1), pages 70-84, May.
  7. Al-Suwailem, Sami, 2014. "Complexity and endogenous instability," Research in International Business and Finance, Elsevier, vol. 30(C), pages 393-410.
  8. H. Peyton Young, 2007. "The Possible and the Impossible in Multi-Agent Learning," Economics Series Working Papers 304, University of Oxford, Department of Economics.
  9. Babichenko, Yakov, 2012. "Completely uncoupled dynamics and Nash equilibria," Games and Economic Behavior, Elsevier, vol. 76(1), pages 1-14.

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