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Patterns, Types, and Bayesian Learning

Author

Listed:
  • Matthew O. Jackson

    (California Institute of Technology)

  • Ehud Kalai

    (Northwestern University)

  • Rann Smorodinsky

    (Technion)

Abstract

Bayesian Statisticians, decision theorists, and game theorists often use Bayesian representations to describe the probability distribution governing the evolution of a stochastic process. Generally, however, one given distribution has infinitely many different Bayesian representations. This paper identifies natural, endogenous representations whose component distributions are learnable and follow patterns. Any given distribution that satisfies an asymptotic mixing condition has a unique, up to an equivalence class, natural Bayesian representation which can be obtained by conditioning on the tail-field of the process. This result follows a parallel to de Finetti's theorem, but with exchangeability weakened to asymptotic mixing which admits many more applications.

Suggested Citation

  • Matthew O. Jackson & Ehud Kalai & Rann Smorodinsky, 1997. "Patterns, Types, and Bayesian Learning," Game Theory and Information 9711002, EconWPA.
  • Handle: RePEc:wpa:wuwpga:9711002
    Note: Type of Document - postscript; prepared on gateway e 3100; to print on postscript; pages: 27 ; figures: none. comments welcome
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    References listed on IDEAS

    as
    1. Jackson, Matthew O. & Kalai, Ehud, 1997. "Social Learning in Recurring Games," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 102-134, October.
    2. Nabil Al-Najjar, 1996. "Aggregation and the Law of Large Numbers in Economies with a Continuum of Agents," Discussion Papers 1160, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, March.
    4. Kalai, Ehud & Lehrer, Ehud, 1993. "Rational Learning Leads to Nash Equilibrium," Econometrica, Econometric Society, vol. 61(5), pages 1019-1045, September.
    5. Sonsino, Doron, 1997. "Learning to Learn, Pattern Recognition, and Nash Equilibrium," Games and Economic Behavior, Elsevier, vol. 18(2), pages 286-331, February.
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    8. Lehrer, Ehud & Smorodinsky, Rann, 1997. "Repeated Large Games with Incomplete Information," Games and Economic Behavior, Elsevier, vol. 18(1), pages 116-134, January.
    9. Dov Samet, 1996. "Common Priors and Markov Chains," Game Theory and Information 9610008, EconWPA.
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    14. Yaw Nyarko, 1998. "Bayesian learning and convergence to Nash equilibria without common priors," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(3), pages 643-655.
    15. Dov Samet, 1996. "Looking Backwards, Looking Inwards: Priors and Introspection," Game Theory and Information 9610007, EconWPA.
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    Cited by:

    1. Nyarko, Y., 1998. "The Truth is in the Eye of the Beholder: or Equilibrium in Beliefs and Rational Learning in Games," Working Papers 98-12, C.V. Starr Center for Applied Economics, New York University.

    More about this item

    Keywords

    patterns; asymptotic mixing; types; Bayesian learning; stochastic processes;

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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