Selling Quality-Differentiated Products in a Markovian Market with Unknown Transition Probabilities.

How to Price a Product Line When Customer Preferences Change over Time Quality-differentiated products can help sellers increase their profits through market segmentation. However, in many business applications, such as online search and consumer lending, customer preferences evolve over time, making it difficult for sellers to use market segmentation. In their study "Selling Quality-Differentiated Products in a Markovian Market with Unknown Transition Probabilities," Keskin and Li analyze dynamic pricing of a vertically differentiated product line when customer preferences for quality can shift over time. Keskin and Li show that data-driven learning is essential when operating in a changing market with unknown customer heterogeneity. Keskin and Li also develop a bounded learning policy that implements near-optimal data-driven learning in a Markov-modulated demand environment. In this paper, we study a firm's dynamic pricing problem in the presence of unknown and time-varying heterogeneity in customers' preferences for quality. The firm offers a standard product as well as a premium product to deal with this heterogeneity. First, we consider a benchmark case in which the transition structure of customer heterogeneity is known. In this case, we analyze the firm's optimal pricing policy and characterize its key structural properties. Thereafter, we investigate the case of unknown market transition structure and design a simple and practically implementable policy, called the bounded learning policy, which is a combination of two policies that perform poorly in isolation. Measuring performance by regret (i.e., the revenue loss relative to a clairvoyant who knows the underlying changes in the market), we prove that our bounded learning policy achieves the fastest possible convergence rate of regret in terms of the frequency of market shifts. Thus, our policy performs well without relying on precise knowledge of the market transition structure. Supplemental Material: The e-companion is available at https://doi.org/10.1287/opre.2022.0316. [ABSTRACT FROM AUTHOR]