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Information Design with Unknown Prior

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  • Ce Li
  • Tao Lin

Abstract

Information designers, such as online platforms, often do not know the beliefs of their receivers. We design learning algorithms so that the information designer can learn the receivers' prior belief from their actions through repeated interactions. Our learning algorithms achieve no regret relative to the optimality for the known prior at a fast speed, achieving a tight regret bound $\Theta(\log T)$ in general and a tight regret bound $\Theta(\log \log T)$ in the important special case of binary actions.

Suggested Citation

  • Ce Li & Tao Lin, 2024. "Information Design with Unknown Prior," Papers 2410.05533, arXiv.org, revised Sep 2025.
    • Handle: RePEc:arx:papers:2410.05533
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    References listed on IDEAS

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    1. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
    2. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, December.
    3. Paul R. Milgrom, 1981. "Good News and Bad News: Representation Theorems and Applications," Bell Journal of Economics, The RAND Corporation, vol. 12(2), pages 380-391, Autumn.
    4. Kolotilin, Anton, 2015. "Experimental design to persuade," Games and Economic Behavior, Elsevier, vol. 90(C), pages 215-226.
    5. Guru Guruganesh & Yoav Kolumbus & Jon Schneider & Inbal Talgam-Cohen & Emmanouil-Vasileios Vlatakis-Gkaragkounis & Joshua R. Wang & S. Matthew Weinberg, 2024. "Contracting with a Learning Agent," Papers 2401.16198, arXiv.org.
    6. Arieli, Itai & Babichenko, Yakov, 2019. "Private Bayesian persuasion," Journal of Economic Theory, Elsevier, vol. 182(C), pages 185-217.
    7. Piotr Dworczak & Alessandro Pavan, 2022. "Preparing for the Worst but Hoping for the Best: Robust (Bayesian) Persuasion," Econometrica, Econometric Society, vol. 90(5), pages 2017-2051, September.
    8. Michael Spence, 1973. "Job Market Signaling," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 87(3), pages 355-374.
    9. Tao Lin & Yiling Chen, 2024. "Generalized Principal-Agent Problem with a Learning Agent," Papers 2402.09721, arXiv.org, revised Oct 2025.
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