Calibrated Forecasting and Persuasion
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911674576928768 |
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| author | Jain, Atulya Perchet, Vianney |
| author_facet | Jain, Atulya Perchet, Vianney |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_15680 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Calibrated Forecasting and Persuasion Jain, Atulya Perchet, Vianney Theoretical Economics Computer Science and Game Theory 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. |
| title | Calibrated Forecasting and Persuasion |
| topic | Theoretical Economics Computer Science and Game Theory |
| url | https://arxiv.org/abs/2406.15680 |