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Learning with Hazy Beliefs

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  • Dean Foster
  • Peyton Young

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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File URL: ftp://ftp.repec.org/RePEc/els/esrcls/hazy.pdf
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Bibliographic Info

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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References

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  1. Fudenberg Drew & Kreps David M., 1993. "Learning Mixed Equilibria," Games and Economic Behavior, Elsevier, vol. 5(3), pages 320-367, July.
  2. Nyarko, Yaw, 1994. "Bayesian Learning Leads to Correlated Equilibria in Normal Form Games," Economic Theory, Springer, vol. 4(6), pages 821-41, October.
  3. J. Jordan, 2010. "Three Problems in Learning Mixed-Strategy Equilibria," Levine's Working Paper Archive 475, David K. Levine.
  4. 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.
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Cited by:
  1. Matthew O. Jackson & Ehud Kalai, 1997. "False Reputation in a Society of Players," Game Theory and Information 9711004, EconWPA.
  2. Timothy Salmon, 2004. "Evidence for Learning to Learn Behavior in Normal Form Games," Theory and Decision, Springer, vol. 56(4), pages 367-404, 04.
  3. Peyton Young, 2002. "Learning Hypothesis Testing and Nash Equilibrium," Economics Working Paper Archive 474, The Johns Hopkins University,Department of Economics.
  4. Turdaliev, Nurlan, 2002. "Calibration and Bayesian learning," Games and Economic Behavior, Elsevier, vol. 41(1), pages 103-119, October.
  5. Eric Friedman, 1998. "Learnability of a class of Non-atomic Games arising on the Internet," Departmental Working Papers 199824, Rutgers University, Department of Economics.

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