Technical Note—Fairness-Aware Online Price Discrimination with Nonparametric Demand Models

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 regulations and laws. This paper studies the problem of dynamic discriminatory pricing under a relative price fairness constraint in the pricing literature. We first establish a regret lower bound of $\mathrm{\Omega }(T^{4/5})$ under the price fairness constraint. Then, we propose an optimal dynamic pricing policy with a regret upper bound of $\tilde{O}(T^{4/5})$, which enforces the strict price fairness constraint. The separation between our $\tilde{\mathrm{\Theta }}(T^{4/5})$-type optimal regret and the usual $\sqrt{T}$-type optimal regret in the dynamic pricing literature illustrates the intrinsic difficulty from the information-theoretical perspective raised by the fairness constraint. Our technical tools to establish the lower-bound result enrich the lower-bound techniques in dynamic pricing literature and may provide insights for deriving lower bounds for other problems related to learning-constrained optimal prices.

Supplemental Material: All supplemental materials, including the code, data, and files required to reproduce the results, are available at https://doi.org/10.1287/opre.2022.0292.