Fairness-aware Contextual Dynamic Pricing with Strategic Buyers

TL;DR

This work tackles fairness-aware contextual dynamic pricing when buyersull group status is private and can be strategically manipulated. It proposes a two-phase exploration-exploitation policy that enforces a price fairness constraint $|p_{0t}-p_{1t}|\le\delta$ while accounting for buyersairness learning via an offline regression oracle, achieving a regret bound of $O(\sqrt{T}+H(T))$ where $H(T)$ captures fairness-perception learning, and a corollary to $O(\sqrt{T})$ when learning is fast; a matching $\Omega(\sqrt{T})$ lower bound shows rate-optimality. Theoretical results are complemented by simulations and a real HMDA-based analysis showing persistent price discrimination by race and quantified regret reductions (e.g., 35.06%) under the proposed policy. The approach integrates contextual demand modeling, KKT-based fair pricing, and buyer-learning dynamics to deter manipulation and improve long-term profitability. Overall, the paper advances fairness-aware decision-making in dynamic pricing with strategic, partially-informed buyers and provides practical guidance for regulatory-compliant pricing in sensitive domains.

Abstract

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.

Figures (7)

• Figure 1: Fairness-aware contextual dynamic pricing process with strategic buyers. The seller can only observe the buyer's revealed group status $G_t'$, which may differ from the true group status $G_t$.
• Figure 2: Regret plots for the two policies. The two subplots show the regrets of two different scenarios: decision tree regression and neural network. The red and blue lines represent the mean regret of our pricing policy and the benchmark pricing policy without buyers' fairness learning, respectively, over 20 independent runs. The light gray areas around these lines depict the standard errors of the estimates.
• Figure 3: Regret plots for our policy. The two subplots show the regrets of the policy at different values of $d$ and $q$. The remaining caption is the same as Figure \ref{['fig6']}.
• Figure 4: Regret plots for the two policies. The three subplots show the regrets of three different scenarios, $B\in\{3, 4, 5\}$. The remaining caption is the same as Figure \ref{['fig6']}.
• Figure 5: Regret plots for the two policies. The two subplots show the regrets of three different scenarios, $c_\delta\in\{1, 2, 3\}$. The remaining caption is the same as Figure \ref{['fig6']}.

Theorems & Definitions (6)

• proof
• proof
• proof
• proof
• proof
• proof