For stationary ergodic processes the set of calibration-passing forecast distributions equals the mean-preserving contractions of the conditional distribution, allowing the dynamic game to be solved via static persuasion.
Furthermore, we can characterize the set of outcomes that result from calibrated strategies and solve for the optimal forecasting strategy
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Calibrated Forecasting and Persuasion
For stationary ergodic processes the set of calibration-passing forecast distributions equals the mean-preserving contractions of the conditional distribution, allowing the dynamic game to be solved via static persuasion.