Calibration and Bayesian learning. (Q1867026)

According to the author, in a repeated game of incomplete information, myopic players form beliefs on next-period play and choose strategies to maximize next-period payoffs, and their beliefs are treated as forecast of future plays. The forecast accuracy is assessed using calibration tests, which measure asymptotic accuracy of beliefs against some reliazations; the beliefs are calibrated if they pass all calibration tests. For a positive Lebesgue measure of payoff vectors, beliefs are not calibrated; but if a payoff vector and a calibration test are drawn from a suitable product measure, beliefs pass the calibration test almost surely.