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

50 Pages Posted: 10 Feb 2020 Last revised: 30 Aug 2021

See all articles by N. Bora Keskin

N. Bora Keskin

Duke University - Fuqua School of Business

Meng Li

University of Houston - Department of Decision & Information Sciences

Date Written: August 28, 2021

Abstract

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.

Keywords: quality-differentiation, pricing, Markov-modulated demand, exploration-exploitation, regret

Suggested Citation

Keskin, N. Bora and Li, Meng, Selling Quality-Differentiated Products in a Markovian Market with Unknown Transition Probabilities (August 28, 2021). Available at SSRN: https://ssrn.com/abstract=3526568 or http://dx.doi.org/10.2139/ssrn.3526568

N. Bora Keskin (Contact Author)

Duke University - Fuqua School of Business ( email )

100 Fuqua Drive
Durham, NC 27708-0120
United States

HOME PAGE: http://faculty.fuqua.duke.edu/~nk145/

Meng Li

University of Houston - Department of Decision & Information Sciences ( email )

United States

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