The speed of rational learning

Alvaro Sandroni () and Rann Smorodinsky ()
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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

International Journal of Game Theory, 1999, vol. 28, issue 2, 199-210

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.

Keywords: Rational; learning; ·; merging; ·; speed; of; convergence (search for similar items in EconPapers)
Date: 1999-05-17
Note: Received: August 1997/Revised version: November 1998
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Citations: View citations in EconPapers (4)

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