Leveraging Reviews: Learning to Price with Buyer and Seller Uncertainty

In online marketplaces, buyers often use reviews from other customers that share their type—such as height for clothing and skin type for skincare products—to estimate their values. Customers with few relevant reviews may hesitate to purchase except at a low price, so for the seller, there is a tension between setting high prices and ensuring there are enough reviews so buyers can confidently estimate their values. Simultaneously, sellers may use reviews to gauge the demand for items they wish to sell. We study this pricing problem in an online setting in which the seller interacts with a set of buyers of finitely many types, one by one. At each round, the seller sets a price. A buyer arrives and examines the reviews of previous buyers of the same type. Based on the reviews, the buyer decides to purchase if the buyer believes the buyer’s ex ante utility is positive. The seller does not know the buyer’s type when setting the price or the distribution over types. We provide a no-regret algorithm that the seller can use to obtain high revenue with matching lower bounds.

Funding: This work was supported by the Alfred P. Sloan Foundation, Amazon Research Awards, the National Science Foundation Division of Computing and Communication Foundations [Grants CCF-2145898, CCF-2338226, IIS-2441796], the Office of Naval Research [Grant N00014-24-1-2159], Schmidt Futures (Schmidt Sciences AI2050 fellowship), and the C3.ai Digital Transformation Institute.

Supplemental Material: All supplemental materials, including the code, data, and files required to reproduce the results, are available at https://doi.org/10.1287/opre.2023.0447.