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
Recommended Citation
Foster, D. P. (1999). A Proof of Calibration Via Blackwell's Approachability Theorem. Games and Economic Behavior, 29 (1-2), 73-78. http://dx.doi.org/10.1006/game.1999.0719
Date Posted: 27 November 2017
This document has been peer reviewed.