Calibrated Forecasting and Persuasion
Abstract
We study a dynamic game where an expert sends probabilistic forecasts to a decision-maker. The decision-maker verifies these forecasts using a calibration test based on past data. How should the expert send forecasts to maximize her payoff while passing the test? For a stationary ergodic process, we characterize the optimal forecasting strategy by reducing the dynamic game to a static persuasion problem. The distributions of forecasts that can arise under calibration are precisely the mean-preserving contractions of the distribution of conditionals. We compare the payoffs attainable by an informed and uninformed expert, providing a benchmark for the value of information. Finally, we consider a regret-minimizing decision-maker and show that the expert can always guarantee at least the calibration benchmark and sometimes strictly more.
Cite
@article{arxiv.2406.15680,
title = {Calibrated Forecasting and Persuasion},
author = {Atulya Jain and Vianney Perchet},
journal= {arXiv preprint arXiv:2406.15680},
year = {2026}
}
Comments
The conference version of this work has been accepted to the Twenty-Fifth ACM Conference on Economics and Computation (EC'24)