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Information Design with Unknown Prior

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  • Tao Lin
  • Ce Li

Abstract

Classical information design models (e.g., Bayesian persuasion and cheap talk) require players to have perfect knowledge of the prior distribution of the state of the world. Our paper studies repeated persuasion problems in which the information designer does not know the prior. The information designer learns to design signaling schemes from repeated interactions with the receiver. We design learning algorithms for the information designer to achieve no regret compared to using the optimal signaling scheme with known prior, under two models of the receiver's decision-making. (1) The first model assumes that the receiver knows the prior and can perform posterior update and best respond to signals. In this model, we design a learning algorithm for the information designer with $O(\log T)$ regret in the general case, and another algorithm with $\Theta(\log \log T)$ regret in the case where the receiver has only two actions. (2) The second model assumes that the receiver does not know the prior and employs a no-regret learning algorithm to take actions. We show that the information designer can achieve regret $O(\sqrt{\mathrm{rReg}(T) T})$, where $\mathrm{rReg}(T)=o(T)$ is an upper bound on the receiver's learning regret. Our work thus provides a learning foundation for the problem of information design with unknown prior.

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

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    1. Kolotilin, Anton, 2015. "Experimental design to persuade," Games and Economic Behavior, Elsevier, vol. 90(C), pages 215-226.
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    7. Michael Spence, 1973. "Job Market Signaling," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 87(3), pages 355-374.
    8. Tao Lin & Yiling Chen, 2024. "Generalized Principal-Agent Problem with a Learning Agent," Papers 2402.09721, arXiv.org, revised Oct 2024.
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