Fairness-aware Online Price Discrimination with Nonparametric Demand Models

73 Pages Posted: 2 Nov 2021 Last revised: 29 Aug 2023

See all articles by Xi Chen

Xi Chen

New York University (NYU) - Leonard N. Stern School of Business

Jiameng Lyu

Tsinghua University - Yau Mathematical Sciences Center

Xuan Zhang

University of Illinois at Urbana-Champaign

Yuan Zhou

Tsinghua University - Yau Mathematical Sciences Center; Tsinghua University - Department of Mathematical Sciences

Date Written: October 31, 2021

Abstract

Price discrimination, which refers to the strategy of setting different prices for different customer groups, has been widely used in online retailing. Although it helps boost the collected revenue for online retailers, it might create serious concerns about fairness, which even violates the regulation and laws. This paper studies the problem of dynamic discriminatory pricing under fairness constraints. In particular, we consider a finite selling horizon of length T for a single product with two groups of customers. Each group of customers has its unknown demand function that needs to be learned. For each selling period, the seller determines the price for each group and observes their purchase behavior. While existing literature mainly focuses on maximizing revenue, ensuring fairness among different customers has not been fully explored in the dynamic pricing literature. This work adopts the fairness notion from Cohen et al. (2022). For price fairness, we propose an optimal dynamic pricing policy regarding regret, which enforces the strict price fairness constraint. In contrast to the standard sqrt(T)-type regret in online learning, we show that the optimal regret in our case is \tilde{O}(T^{4/5}). We further extend our algorithm to a more general notion of fairness, which includes demand fairness as a special case. To handle this general class, we propose a soft fairness constraint and develop a dynamic pricing policy that achieves \tilde{O}(T^{4/5}) regret. We also demonstrate that our algorithmic techniques can be adapted to more general scenarios such as fairness among multiple groups of customers.

Keywords: Dynamic pricing, Demand Learning, Fairness, Nonparametric Demands

JEL Classification: C44

Suggested Citation

Chen, Xi and Lyu, Jiameng and Zhang, Xuan and Zhou, Yuan, Fairness-aware Online Price Discrimination with Nonparametric Demand Models (October 31, 2021). Available at SSRN: https://ssrn.com/abstract=3953575 or http://dx.doi.org/10.2139/ssrn.3953575

Xi Chen (Contact Author)

New York University (NYU) - Leonard N. Stern School of Business ( email )

44 West 4th Street
Suite 9-160
New York, NY NY 10012
United States

Jiameng Lyu

Tsinghua University - Yau Mathematical Sciences Center ( email )

Beijing
China

Xuan Zhang

University of Illinois at Urbana-Champaign ( email )

Yuan Zhou

Tsinghua University - Yau Mathematical Sciences Center ( email )

Beijing
China

Tsinghua University - Department of Mathematical Sciences ( email )

Beijing, 100084
China

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