IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2406.15680.html

Calibrated Forecasting and Persuasion

Author

Listed:
  • Atulya Jain
  • Vianney Perchet

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.

Suggested Citation

  • Atulya Jain & Vianney Perchet, 2024. "Calibrated Forecasting and Persuasion," Papers 2406.15680, arXiv.org, revised Mar 2026.
    • Handle: RePEc:arx:papers:2406.15680
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2406.15680
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Kuvalekar, Aditya & Lipnowski, Elliot & Ramos, João, 2022. "Goodwill in communication," Journal of Economic Theory, Elsevier, vol. 203(C).
    2. Andreas Kleiner & Benny Moldovanu & Philipp Strack, 2021. "Extreme Points and Majorization: Economic Applications," Econometrica, Econometric Society, vol. 89(4), pages 1557-1593, July.
    3. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, December.
    4. Kolotilin, Anton, 2018. "Optimal information disclosure: a linear programming approach," Theoretical Economics, Econometric Society, vol. 13(2), May.
    5. Andrey Bernstein & Shie Mannor & Nahum Shimkin, 2014. "Opportunistic Approachability and Generalized No-Regret Problems," Mathematics of Operations Research, INFORMS, vol. 39(4), pages 1057-1083, November.
    6. Dean P. Foster & Sergiu Hart, 2021. "Forecast Hedging and Calibration," Journal of Political Economy, University of Chicago Press, vol. 129(12), pages 3447-3490.
    7. Arieli, Itai & Babichenko, Yakov & Smorodinsky, Rann & Yamashita, Takuro, 2023. "Optimal persuasion via bi-pooling," Theoretical Economics, Econometric Society, vol. 18(1), January.
    8. Wojciech Olszewski & Marcin Pęski, 2011. "The Principal-Agent Approach to Testing Experts," American Economic Journal: Microeconomics, American Economic Association, vol. 3(2), pages 89-113, May.
    9. Shie Mannor & Gilles Stoltz, 2010. "A Geometric Proof of Calibration," Mathematics of Operations Research, INFORMS, vol. 35(4), pages 721-727, November.
    10. Crawford, Vincent P & Sobel, Joel, 1982. "Strategic Information Transmission," Econometrica, Econometric Society, vol. 50(6), pages 1431-1451, November.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kreutzkamp, Sophie & Lou, Yichuan, 2025. "Persuasion without ex-post commitment," Journal of Economic Theory, Elsevier, vol. 228(C).
    2. Semyon Malamud & Andreas Schrimpf, 2021. "Persuasion by Dimension Reduction," Swiss Finance Institute Research Paper Series 21-69, Swiss Finance Institute.
    3. Roberto Corrao & Yifan Dai, 2023. "The Bounds of Mediated Communication," Papers 2303.06244, arXiv.org, revised Nov 2023.
    4. Zeng, Yishu, 2023. "Derandomization of persuasion mechanisms," Journal of Economic Theory, Elsevier, vol. 212(C).
    5. Lily Ling Yang, 2024. "Information Design with Costly State Verifi cation," CRC TR 224 Discussion Paper Series crctr224_2024_502, University of Bonn and University of Mannheim, Germany.
    6. Qianjun Lyu & Wing Suen & Yimeng Zhang, 2023. "Coarse Information Design," Papers 2305.18020, arXiv.org, revised Jun 2025.
    7. Andreas Kleiner & Benny Moldovanu & Philipp Strack, 2026. "Extreme Points and Majorization," Cowles Foundation Discussion Papers 2492, Cowles Foundation for Research in Economics, Yale University.
    8. Oleg Muratov, 2023. "Entrepreneur–Investor Information Design," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 64(4), pages 1431-1467, November.
    9. Malamud, Semyon & Cieslak, Anna & Schrimpf, Paul, 2021. "Optimal Transport of Information," CEPR Discussion Papers 15859, C.E.P.R. Discussion Papers.
    10. Makoto Shimoji, 2022. "Bayesian persuasion in unlinked games," International Journal of Game Theory, Springer;Game Theory Society, vol. 51(3), pages 451-481, November.
    11. Gregorio Curello & Ludvig Sinander, 2022. "The comparative statics of persuasion," Papers 2204.07474, arXiv.org, revised Nov 2025.
    12. Dirk Bergemann & Stephen Morris, 2019. "Information Design: A Unified Perspective," Journal of Economic Literature, American Economic Association, vol. 57(1), pages 44-95, March.
    13. Frédéric Koessler & Françoise Forges, 2008. "Multistage Communication With And Without Verifiable Types," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 10(02), pages 145-164.
    14. Makoto Shimoji, 2016. "Rationalizable Persuasion," Discussion Papers 16/08, Department of Economics, University of York.
    15. Anton Kolotilin & Andriy Zapechelnyuk, 2025. "Persuasion Meets Delegation," Econometrica, Econometric Society, vol. 93(1), pages 195-228, January.
    16. Golosov, Mikhail & Skreta, Vasiliki & Tsyvinski, Aleh & Wilson, Andrea, 2014. "Dynamic strategic information transmission," Journal of Economic Theory, Elsevier, vol. 151(C), pages 304-341.
    17. Frank Yang & Kai Hao Yang, 2025. "Multidimensional Monotonicity and Economic Applications," Cowles Foundation Discussion Papers 2428, Cowles Foundation for Research in Economics, Yale University.
    18. Christoph Carnehl & Anton Sobolev & Konrad Stahl & André Stenzel, 2025. "Designing Vertical Differentiation with Information," CRC TR 224 Discussion Paper Series crctr224_2025_700v2, University of Bonn and University of Mannheim, Germany, revised Feb 2026.
    19. Maxim Ivanov, 2021. "Optimal monotone signals in Bayesian persuasion mechanisms," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(3), pages 955-1000, October.
    20. Yuval Heller & Christoph Kuzmics, 2019. "Renegotiation and Coordination with Private Values," Graz Economics Papers 2019-10, University of Graz, Department of Economics.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2406.15680. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.