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Learning with Hazy Beliefs

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Author Info
Dean Foster
Peyton Young

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Abstract

Players are rational if they always choose best replies given their beliefs. They are good predictors if the difference between their beliefs and the distribution of the others' actual strategies goes to zero over time. Learning is deterministic if beliefs are fully determined by the initial conditions and the observed data. (Bayesian updating is a particular example). If players are rational, good predictors, and learn deterministically, there are many games for which neither beliefs nor actions converge to a Nash equilibrium. We introduce an alternative approach to learning called prospecting in which players are rational and good predictors, but beliefs have a small random component. In any finite game, and from any initial conditions, prospecting players learn to play arbitrarily close to Nash equilibrium with probability one.

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Paper provided by ESRC Centre on Economics Learning and Social Evolution in its series ELSE working papers with number 023.

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Handle: RePEc:els:esrcls:023

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  1. Foster, Dean P. & Vohra, Rakesh V., 1997. "Calibrated Learning and Correlated Equilibrium," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 40-55, October. [Downloadable!] (restricted)
  2. Fudenberg Drew & Kreps David M., 1993. "Learning Mixed Equilibria," Games and Economic Behavior, Elsevier, vol. 5(3), pages 320-367, July. [Downloadable!] (restricted)
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  3. Nyarko, Yaw, 1994. "Bayesian Learning Leads to Correlated Equilibria in Normal Form Games," Economic Theory, Springer, vol. 4(6), pages 821-41, October.
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Eric Friedman, 1998. "Learnability of a class of Non-atomic Games arising on the Internet," Departmental Working Papers 199824, Rutgers University, Department of Economics. [Downloadable!]
  2. Matthew O. Jackson & Ehud Kalai, 1997. "False Reputation in a Society of Players," Game Theory and Information 9711004, EconWPA. [Downloadable!]
    Other versions:
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This page was last updated on 2009-11-25.

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