Contextual pricing strategies are prevalent in online retailing, where the seller adjusts prices based on products' attributes and buyers' characteristics. Although such strategies can enhance seller's profits, they raise concerns about fairness when significant price disparities emerge among specific groups, such as gender or race. These disparities can lead to adverse perceptions of fairness among buyers and may even violate the law and regulation. In contrast, price differences can incentivize disadvantaged buyers to strategically manipulate their group identity to obtain a lower price. In this paper, we investigate contextual dynamic pricing with fairness constraints, taking into account buyers' strategic behaviors when their group status is private and unobservable from the seller. We propose a dynamic pricing policy that simultaneously achieves price fairness and discourages strategic behaviors. Our policy achieves an upper bound of $O(\sqrt{T}+H(T))$ regret over $T$ time horizons, where the term $H(T)$ arises from buyers' assessment of the fairness of the pricing policy based on their learned price difference. When buyers are able to learn the fairness of the price policy, this upper bound reduces to $O(\sqrt{T})$. We also prove an $Ω(\sqrt{T})$ regret lower bound of any pricing policy under our problem setting. We support our findings with extensive experimental evidence, showcasing our policy's effectiveness. In our real data analysis, we observe the existence of price discrimination against race in the loan application even after accounting for other contextual information. Our proposed pricing policy demonstrates a significant improvement, achieving 35.06% reduction in regret compared to the benchmark policy.

翻译：上下文定价策略在在线零售中普遍存在，即卖家根据产品属性和买家特征调整价格。尽管此类策略能够提升卖家利润，但当特定群体（如性别或种族）间出现显著价格差异时，会引发公平性担忧。这些差异可能导致买家产生负面的公平感知，甚至可能违反法律法规。另一方面，价格差异可能激励处于不利地位的买家策略性地操纵其群体身份以获取更低价格。本文研究了具有公平性约束的上下文动态定价问题，同时考虑了买家在其群体状态对卖家不可观测时的策略性行为。我们提出了一种动态定价策略，该策略在实现价格公平的同时抑制策略性行为。我们的策略在T个时间周期内实现了$O(\sqrt{T}+H(T))$的遗憾上界，其中$H(T)$项源于买家基于学习到的价格差异对定价策略公平性的评估。当买家能够学习定价策略的公平性时，该上界可降至$O(\sqrt{T})$。我们还证明了在本问题设定下，任何定价策略均具有$Ω(\sqrt{T})$的遗憾下界。我们通过大量实验证据支持了研究结论，展示了所提策略的有效性。在真实数据分析中，我们观察到即使在控制其他上下文信息后，贷款申请中仍存在针对种族的定价歧视。我们提出的定价策略表现出显著改进，与基准策略相比实现了35.06%的遗憾降低。