# Fairness-aware Online Price Discrimination with Nonparametric Demand Models

42 Pages Posted: 2 Nov 2021 Last revised: 17 Nov 2021

See all articles by Xi Chen

## Xi Chen

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

## Xuan Zhang

University of Illinois at Urbana-Champaign

## Yuan Zhou

Tsinghua University - Yau Mathematical Sciences Center

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 concern in fairness, which even violates the regulation and law. 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. In this work, we adopt the fairness notion from (Cohen et al. 2021a). For price fairness, we propose an optimal dynamic pricing policy in terms of 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 $\tilde{\Theta}(T^{4/5})$. 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 the dynamic pricing policy that achieves $\tilde{O}(T^{4/5})$ regret.

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

JEL Classification: C44

Suggested Citation

Chen, Xi 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