Statistics Papers

Document Type

Journal Article

Date of this Version

10-1999

Publication Source

Games and Economic Behavior

Volume

29

Issue

1-2

Start Page

73

Last Page

78

DOI

10.1006/game.1999.0719

Abstract

Over the past few years many proofs of the existence of calibration have been discovered. Each of the following provides a different algorithm and proof of convergence: D. Foster and R. Vohra (1991, Technical Report, University of Chicago), (1998, Biometrika85, 379–390), S. Hart (1995, personal communication), D. Fudenberg and D. Levine (1999, Games Econ. Behavior29, 104–130), and S. Hart and A. Mas-Colell (1997, Technical Report, Hebrew University). Does the literature really need one more? Probably not. But the algorithm proposed here has two virtues. First, it only randomizes between two forecasts that are very close to each other (either p or p + ϵ). In other words, the randomization only hides the last digit of the forecast. Second, it follows directly from Blackwell's approachability theorem, which shortens the proof substantially. Journal of Economic Literature Classification Numbers: C70, C73, C53.

Copyright/Permission Statement

© 1999. This manuscript version is made available under the CC-BY-NC-ND 4.0 license

Keywords

individual sequences, worst-case data, regret, learning

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Date Posted: 27 November 2017

This document has been peer reviewed.