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Learning with Hazy Beliefs


  • Dean Foster
  • Peyton Young


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.

Suggested Citation

  • Dean Foster & Peyton Young, "undated". "Learning with Hazy Beliefs," ELSE working papers 023, ESRC Centre on Economics Learning and Social Evolution.
  • Handle: RePEc:els:esrcls:023

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    References listed on IDEAS

    1. Fudenberg Drew & Kreps David M., 1993. "Learning Mixed Equilibria," Games and Economic Behavior, Elsevier, vol. 5(3), pages 320-367, July.
    2. J. Jordan, 2010. "Three Problems in Learning Mixed-Strategy Equilibria," Levine's Working Paper Archive 475, David K. Levine.
    3. 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.
    4. Nyarko, Yaw, 1994. "Bayesian Learning Leads to Correlated Equilibria in Normal Form Games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(6), pages 821-841, October.
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    Cited by:

    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.
    2. 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.
    3. Matthew O. Jackson & Ehud Kalai, 1997. "False Reputation in a Society of Players," Discussion Papers 1184R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    4. Timothy Salmon, 2004. "Evidence for Learning to Learn Behavior in Normal Form Games," Theory and Decision, Springer, vol. 56(4), pages 367-404, April.
    5. Turdaliev, Nurlan, 2002. "Calibration and Bayesian learning," Games and Economic Behavior, Elsevier, vol. 41(1), pages 103-119, October.

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