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Working paper 791
Itai Arieli, Yakov Babichenko, Dima Shaiderman, Xianwen Shi, "Persuading while Learning", 2025-01-16
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Abstract: We propose a dynamic persuasion model of product adoption, where an impatient, long-lived sender commits to a dynamic disclosure policy to persuade a sequence of short-lived receivers to adopt a new product. The sender privately observes a sequence of signals, one per period, about the product quality, and therefore the sequence of her posteriors forms a discrete-time martingale. The disclosure policy specifies ex ante how the sender's information will be revealed to the receivers in each period. We introduce a new concept called ``Blackwell-preserving kernels'' and show that if the sender's belief martingale possesses these kernels, the family of optimal strategies for the sender takes an interval form; namely, in every period, the set of martingale realizations in which adoption occurs is an interval. Utilizing this, we prove that if the sender is sufficiently impatient, then under a random walk martingale, the optimal policy is fully transparent up to the moment of adoption; namely, the sender reveals all the information she privately holds in every period.

Keywords: Dynamic Information Design, Bayesian Persuasion, Learning

JEL Classification: D83; D82