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Patterns, Types, and Bayesian Learning

Listed author(s):
  • Matthew O. Jackson

    (California Institute of Technology)

  • Ehud Kalai

    (Northwestern University)

  • Rann Smorodinsky

    (Technion)

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.

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Paper provided by EconWPA in its series Game Theory and Information with number 9711002.

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Length: 27 pages
Date of creation: 25 Nov 1997
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
Contact details of provider: Web page: http://econwpa.repec.org

References listed on IDEAS
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  1. 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.
  2. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, January.
  3. Sonsino, Doron, 1997. "Learning to Learn, Pattern Recognition, and Nash Equilibrium," Games and Economic Behavior, Elsevier, vol. 18(2), pages 286-331, February.
  4. Harsanyi, John C, 1995. "Games with Incomplete Information," American Economic Review, American Economic Association, vol. 85(3), pages 291-303, June.
  5. Kalai, Ehud & Lehrer, Ehud, 1994. "Weak and strong merging of opinions," Journal of Mathematical Economics, Elsevier, vol. 23(1), pages 73-86, January.
  6. Fudenberg, Drew & Levine, David K., 1999. "Conditional Universal Consistency," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 104-130, October.
  7. Kalai, Ehud & Lehrer, Ehud, 1993. "Rational Learning Leads to Nash Equilibrium," Econometrica, Econometric Society, vol. 61(5), pages 1019-1045, September.
  8. Rothschild, Michael, 1974. "A two-armed bandit theory of market pricing," Journal of Economic Theory, Elsevier, vol. 9(2), pages 185-202, October.
  9. P. Frevert, 1971. "Note," Review of Economic Studies, Oxford University Press, vol. 38(2), pages 269-270.
  10. 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.
  11. Jackson, Matthew O. & Kalai, Ehud, 1997. "Social Learning in Recurring Games," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 102-134, October.
  12. Lehrer, Ehud & Smorodinsky, Rann, 1997. "Repeated Large Games with Incomplete Information," Games and Economic Behavior, Elsevier, vol. 18(1), pages 116-134, January.
  13. Dov Samet, 1996. "Common Priors and Markov Chains," Game Theory and Information 9610008, EconWPA.
  14. Stinchcombe, Maxwell B., 1990. "Bayesian information topologies," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 233-253.
  15. Dov Samet, 1996. "Looking Backwards, Looking Inwards: Priors and Introspection," Game Theory and Information 9610007, EconWPA.
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