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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.

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Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1177.

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Date of creation: Jan 1997
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Handle: RePEc:nwu:cmsems:1177

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  1. Rothschild, Michael, 1974. "A two-armed bandit theory of market pricing," Journal of Economic Theory, Elsevier, vol. 9(2), pages 185-202, October.
  2. Ehud Kalai & Ehud Lehrer, 1990. "Rational Learning Leads to Nash Equilibrium," Discussion Papers 895, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  3. Fudenberg, Drew & Levine, David K., 1999. "Conditional Universal Consistency," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 104-130, October.
  4. 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.
  5. 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.
  6. Harsanyi, John C., 1994. "Games with Incomplete Information," Nobel Prize in Economics documents 1994-1, Nobel Prize Committee.
  7. Yaw Nyarko, 1998. "Bayesian learning and convergence to Nash equilibria without common priors," Economic Theory, Springer, vol. 11(3), pages 643-655.
  8. Matthew Jackson & Ehud Kalai, 1995. "Social Learning in Recurring Games," Discussion Papers 1138, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  9. Lehrer, Ehud & Smorodinsky, Rann, 1997. "Repeated Large Games with Incomplete Information," Games and Economic Behavior, Elsevier, vol. 18(1), pages 116-134, January.
  10. Stinchcombe, Maxwell B., 1990. "Bayesian information topologies," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 233-253.
  11. Dov Samet, 1996. "Looking Backwards, Looking Inwards: Priors and Introspection," Game Theory and Information 9610007, EconWPA.
  12. Sonsino, Doron, 1997. "Learning to Learn, Pattern Recognition, and Nash Equilibrium," Games and Economic Behavior, Elsevier, vol. 18(2), pages 286-331, February.
  13. Dov Samet, 1996. "Common Priors and Markov Chains," Game Theory and Information 9610008, EconWPA.
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