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The speed of rational learning

Author

Listed:
  • Alvaro Sandroni

    (J. L. Kellogg Graduate School of Management, MEDS Department, Northwestern University 2001 Sheridan Road, Evanston, IL 60208, USA)

  • Rann Smorodinsky

    (J. L. Kellogg Graduate School of Management, MEDS Department, Northwestern University 2001 Sheridan Road, Evanston, IL 60208, USA)

Abstract

A central result in the rational learning literature is that if the true measure is absolutely continuous with respect to the beliefs then, given enough data, the updated beliefs merge with the true distribution. In this paper, we show that, under absolute continuity, weak merging occurs fast (at the rate $1/\sqrt t$) with density one. Moreover, if weak merging occurs fast enough (at the rate 1/t) then absolute continuity holds. These rates are sharp. We also show that, under some conditions, if weak merging occurs at the rate $1/\sqrt {t}$ then absolute continuity holds.

Suggested Citation

  • Alvaro Sandroni & Rann Smorodinsky, 1999. "The speed of rational learning," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(2), pages 199-210.
    • Handle: RePEc:spr:jogath:v:28:y:1999:i:2:p:199-210
    Note: Received: August 1997/Revised version: November 1998
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    Citations

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    Cited by:

    1. Colin, Stewart, 2011. "Nonmanipulable Bayesian testing," Journal of Economic Theory, Elsevier, vol. 146(5), pages 2029-2041, September.
    2. Conlon, John R., 2003. "Hope springs eternal: learning and the stability of cooperation in short horizon repeated games," Journal of Economic Theory, Elsevier, vol. 112(1), pages 35-65, September.
    3. Mario Gilli, 2002. "Rational Learning in Imperfect Monitoring Games," Working Papers 46, University of Milano-Bicocca, Department of Economics, revised Mar 2002.
    4. Gossner, Olivier & Tomala, Tristan, 2008. "Entropy bounds on Bayesian learning," Journal of Mathematical Economics, Elsevier, vol. 44(1), pages 24-32, January.

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