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.

翻译：价格歧视——即为不同客户群体设定不同价格的策略——在在线零售中被广泛应用。尽管这有助于提升在线零售商的收益，但也可能引发严重的公平性问题，甚至违反相关法规法律。本文研究公平约束下的动态歧视性定价问题。具体而言，我们考虑一个长度为$T$的有限销售周期，针对一种单一产品面向两个客户群体。每个客户群体拥有未知的需求函数，需要通过学习获得。在每个销售周期，卖方为每个群体设定价格，并观察其购买行为。现有文献主要关注收益最大化，而确保不同客户群体间的公平性在动态定价文献中尚未被充分探索。本文采用Cohen等人（2022年）提出的公平概念。针对价格公平性，我们提出了一种在遗憾（regret）意义上最优的动态定价策略，该策略强制执行严格的价格公平约束。与在线学习中标准的$\sqrt{T}$型遗憾不同，我们证明在本问题中最优遗憾为$\tilde{O}(T^{4/5})$。我们进一步将算法扩展到更一般的公平概念，其中需求公平性作为特例。为处理这一一般类别，我们提出了一种软公平约束，并开发了一种实现$\tilde{O}(T^{4/5})$遗憾的动态定价策略。同时，我们证明所提出的算法技术可适应更一般的场景，如多客户群体之间的公平性。