  How should an expert send forecasts to maximize her utility subject to
passing a calibration test? We consider a dynamic game where an expert sends
probabilistic forecasts to a decision maker. The decision maker uses a
calibration test based on past outcomes to verify the expert's forecasts. We
characterize the optimal forecasting strategy by reducing the dynamic game to a
static persuasion problem. A distribution of forecasts is implementable by a
calibrated strategy if and only if it is a mean-preserving contraction of the
distribution of conditionals (honest forecasts). We characterize the value of
information by comparing what an informed and uninformed expert can attain.
Moreover, we consider a decision maker who uses regret minimization, instead of
the calibration test, to take actions. We show that the expert can achieve the
same payoff against a regret minimizer as under the calibration test, and in
some instances, she can achieve strictly more.
