Personalized Pricing with Group Fairness Constraint

Xin Chen, Zexing Xu, Zishuo Zhao, Yuan Zhou

Abstract:

In the big data era, personalized pricing has become a popular strategy that sets different prices for the same product according to individual customers' features. Despite its popularity among companies, this practice is controversial due to the concerns over fairness that can be potentially caused by price discrimination. In this paper, we consider the problem of single-product personalized pricing for different groups under fairness constraints.
Specifically, we define group fairness constraints under different distance metrics in the personalized pricing context. We then establish a stochastic formulation that maximizes the revenue. Under the discrete price setting, we reformulate this problem as a linear program and obtain the optimal pricing policy efficiently. To bridge the gap between the discrete and continuous price setting, theoretically, we prove a general $\mathcal{O}(\frac{1}{l})$ gap between the optimal revenue with continuous and discrete price set of size $l$. Under some mild conditions, we improve this bound to $\mathcal{O}(\frac{1}{l^2})$.
Empirically, we demonstrate the benefits of our approach over several baseline approaches on both synthetic data and real-world data. Our results also provide managerial insights into setting a proper fairness degree as well as an appropriate size of discrete price set.