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Patterns, Types, and Bayesian Learning

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Author Info
Matthew O. Jackson
Ehud Kalai
Rann Smorodinsky

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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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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Lehrer, Ehud & Smorodinsky, Rann, 1997. "Repeated Large Games with Incomplete Information," Games and Economic Behavior, Elsevier, vol. 18(1), pages 116-134, January. [Downloadable!] (restricted)
  2. Kalai, Ehud & Lehrer, Ehud, 1993. "Rational Learning Leads to Nash Equilibrium," Econometrica, Econometric Society, vol. 61(5), pages 1019-45, September. [Downloadable!] (restricted)
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  3. Dov Samet, 1996. "Common Priors and Markov Chains," Game Theory and Information 9610008, EconWPA. [Downloadable!]
  4. Sonsino, Doron, 1997. "Learning to Learn, Pattern Recognition, and Nash Equilibrium," Games and Economic Behavior, Elsevier, vol. 18(2), pages 286-331, February. [Downloadable!] (restricted)
  5. Harsanyi, John C, 1995. "Games with Incomplete Information," American Economic Review, American Economic Association, vol. 85(3), pages 291-303, June.
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  6. Kalai, Ehud & Lehrer, Ehud, 1994. "Weak and strong merging of opinions," Journal of Mathematical Economics, Elsevier, vol. 23(1), pages 73-86, January. [Downloadable!] (restricted)
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  7. 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. [Downloadable!]
  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. [Downloadable!]
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  9. Rothschild, Michael, 1974. "A two-armed bandit theory of market pricing," Journal of Economic Theory, Elsevier, vol. 9(2), pages 185-202, October. [Downloadable!] (restricted)
  10. Drew Fudenberg & David K. Levine, 1997. "Conditional Universal Consistency," Levine's Working Paper Archive 471, David K. Levine. [Downloadable!]
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  11. Stinchcombe, Maxwell B., 1990. "Bayesian information topologies," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 233-253. [Downloadable!] (restricted)
  12. Dov Samet, 1996. "Looking Backwards, Looking Inwards: Priors and Introspection," Game Theory and Information 9610007, EconWPA. [Downloadable!]
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  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. [Downloadable!]
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