Calibration and Bayesian learning

In a repeated game of incomplete information, myopic players form beliefs on next-period play and choose strategies to maximize next-period payoffs. Beliefs are treated as forecast of future plays. Forecast accuracy is assessed using calibration tests, which measure asymptotic accuracy of beliefs against some realizations. Beliefs are calibrated if they pass all calibration tests. For a positive Lebesgue measure of payoff vectors, beliefs are not calibrated. But, if payoff vector and calibration test are drawn from a suitable product measure, beliefs pass the calibration test almost surely. JEL classification numbers: C10, C70, C72 *Turdaliev, Federal Reserve Bank of Minneapolis and University of Minnesota. The support of the NSF is gratefully acknowledged. I am grateful to Professor James Jordan for bringing my attention to the problem, his advice, and encouragement. I am grateful to Professor Edward Green for many conversations and very helpful suggestions. I also thank participants of the Spring 1999 Midwest Economic Theory Meeting and the Tenth International Conference on Game Theory at SUNY Stony Brook for helpful comments. The views expressed herein are those of the author and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System.