Date of this Version
Games and Economic Behavior
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.
© 1999. This manuscript version is made available under the CC-BY-NC-ND 4.0 license
individual sequences, worst-case data, regret, learning
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.