Calibrated Forecasting and Persuasion

TL;DR

This paper analyzes how an expert can optimally send probabilistic forecasts to persuade a decision-maker while passing calibration tests, using a static persuasion framework for stationary processes.

Contribution

It characterizes the optimal forecasting strategies under calibration constraints and compares the value of information for informed versus uninformed experts.

Findings

Optimal strategies reduce to static persuasion problems.

Calibration constraints limit the set of feasible forecast distributions.

Experts can guarantee at least the calibration benchmark, sometimes more.

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.