  We propose to smooth out the calibration score, which measures how good a
forecaster is, by combining nearby forecasts. While regular calibration can be
guaranteed only by randomized forecasting procedures, we show that smooth
calibration can be guaranteed by deterministic procedures. As a consequence, it
does not matter if the forecasts are leaked, i.e., made known in advance:
smooth calibration can nevertheless be guaranteed (while regular calibration
cannot). Moreover, our procedure has finite recall, is stationary, and all
forecasts lie on a finite grid. To construct the procedure, we deal also with
the related setups of online linear regression and weak calibration. Finally,
we show that smooth calibration yields uncoupled finite-memory dynamics in
n-person games "smooth calibrated learning" in which the players play
approximate Nash equilibria in almost all periods (by contrast, calibrated
learning, which uses regular calibration, yields only that the time-averages of
play are approximate correlated equilibria).
