A formal write-up of the simple proof (1995) of the existence of calibrated forecasts by the minimax theorem, which moreover shows that $N^3$ periods suffice to guarantee a calibration error of at most $1/N$.
A formal write-up of the simple proof (1995) of the existence of calibrated forecasts by the minimax theorem, which moreover shows that $N^3$ periods suffice to guarantee a calibration error of at most $1/N$.