Calibrated Forecasting and Persuasion
Provides a theoretical framework for optimal strategic forecasting under calibration constraints, relevant to experts and decision-makers in settings like weather prediction or economic forecasting.
This paper characterizes optimal forecasting strategies for an expert who must pass a calibration test while maximizing payoff in a dynamic game with a decision-maker. It shows that the set of achievable forecast distributions under calibration are mean-preserving contractions of the distribution of conditionals, and compares payoffs for informed vs. uninformed experts.
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.