Leveraging Reviews: Learning to Price with Buyer and Seller Uncertainty

Abstract

Customers can access hundreds of reviews for a single product in online marketplaces. Buyers often use reviews from other customers that share their type---such as height for clothing or skin type for skincare products---to estimate their values, which they may not know a priori. 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 that 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. In this work, we study this pricing problem in an online setting where the seller interacts with a set of buyers of finitely many types, one by one, over a series of T rounds. At each round, the seller first sets a price. Then, a buyer arrives and examines the reviews of the previous buyers with the same type, which reveal those buyers' ex-post values. Based on the reviews, the buyer decides to purchase if they have good reason to believe their ex-ante utility is positive. Crucially, the seller does not know the buyer's type when setting the price, nor even the distribution over types. We provide a no-regret algorithm that the seller can use to obtain high revenue. When there are d types, after T rounds, our algorithm achieves a problem-independent Õ ( T 2/3 d 1/3 ) regret bound. However, when the smallest probability q min that any given type appears is large, specifically when q min ∈ Ω( d −2/3 T −1/3 ), the same algorithm achieves a [EQUATION] regret bound. We complement these upper bounds with matching lower bounds in both regimes, showing that our algorithm is minimax optimal up to lower-order terms. This is a summary of work that won the Exemplary AI Track Paper Award at EC'24.