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Patterns, Types, and Bayesian Learning

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  • Matthew O. Jackson
  • Ehud Kalai
  • Rann Smorodinsky

Abstract

Consider a probability distribution governing the evolution of a descrete-time stochastic process. Such a distribution may be represented as a convex combination of more elementary probability measures, with the interpretation of a two-stage Bayesian procedure. In the first stage, one of the measures is randomly selected according to the weights of the convex combinations (i.e., their prior probabilities), and in the second stage the selected measure governs the evolution of the stochastic process. Generally, however, the original distribution has infinitely many different insights about the process depending on the representation with which they start. This paper identifies one endogenous representation which is natural in the sense that its component measures are precisely the learnable probabilistic patterns.

Suggested Citation

  • Matthew O. Jackson & Ehud Kalai & Rann Smorodinsky, 1997. "Patterns, Types, and Bayesian Learning," Discussion Papers 1177, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  • Handle: RePEc:nwu:cmsems:1177
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    References listed on IDEAS

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    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.
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    3. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, January.
    4. Spiegel, Mark M., 1995. "Threshold effects in international lending," Journal of Development Economics, Elsevier, vol. 46(2), pages 341-356, April.
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    6. Harsanyi, John C, 1995. "Games with Incomplete Information," American Economic Review, American Economic Association, pages 291-303.
    7. Ehud Kalai & Ehud Lehrer, 1992. "Weak and Strong Merging of Opinions," Discussion Papers 983, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    8. Lehrer, Ehud & Smorodinsky, Rann, 1997. "Repeated Large Games with Incomplete Information," Games and Economic Behavior, Elsevier, vol. 18(1), pages 116-134, January.
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    11. Kalai, Ehud & Lehrer, Ehud, 1993. "Rational Learning Leads to Nash Equilibrium," Econometrica, Econometric Society, pages 1019-1045.
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    15. Yaw Nyarko, 1998. "Bayesian learning and convergence to Nash equilibria without common priors," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 643-655.
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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

    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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