Calibrated Forecasting and Persuasion

Atulya Jain and Vianney Perchet

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Abstract: 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.

Date: 2024-06
New Economics Papers: this item is included in nep-gth, nep-mic and nep-upt
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