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.
Econometrica 89, 4 (2021), 1557–1593
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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.