From Confounding to Learning: Dynamic Service Fee Pricing on Third-Party Platforms

We study a dynamic assortment problem on a two-sided service platform with incomplete information and heterogeneous customers in a discrete-time setting. In each period, a customer arrives seeking service, and the platform chooses an assortment of sellers to display. The customer then proposes a transaction to at most one seller in the assortment according to a multinomial logit choice model. After a fixed number of periods, sellers review the proposals they have received and each chooses at most one customer according to another multinomial logit choice model, after which the cycle repeats. A key challenge is that the platform does not know the choice-model parameters of either customers or sellers in advance. To our knowledge, this is the first study of a dynamic assortment problem in which both sides' choice parameters are unknown. We develop a data-driven algorithm that learns these parameters while optimizing the platform's objective over time. We evaluate performance using regret, which measures revenue loss relative to a clairvoyant benchmark that knows all parameters and customer arrivals in advance. We show that the algorithm's worst-case regret grows polylogarithmically over time, and we derive a matching lower bound, establishing its rate optimality.

We study contextual dynamic pricing with linear valuations and bounded-support agnostic noise, whose induced demand curve may be non-Lipschitz with arbitrary jumps and atoms. Such discontinuities break the cross-context interpolation arguments used by smooth-demand pricing algorithms, while the best previous method achieved only $\tilde O(T^{3/4})$ regret. We propose Conservative-Markdown Redirect-UCB Pricing, a polynomial-time algorithm that combines randomized parameter estimation, conservative residual-grid probing, and confidence-based one-step redirection. Our algorithm achieves $\tilde O(T^{2/3})$ optimal regret, matching the known lower bounds of Kleinberg and Leighton (2003) up to logarithmic factors and improving over the previous upper bound of Xu and Wang (2022). Under stochastic well-conditioned contexts, this closes the long-existing open regret gap in linear-valuation contextual pricing under agnostic non-Lipschitz noise distribution.

Data-driven pricing is increasingly prevalent in sectors such as airlines, lending, insurance, and retail. By learning demand models from customer features and setting prices accordingly, these systems may generate discriminatory outcomes that raise fairness concerns. This leads to fundamental questions - how and where should systems incorporate fairness considerations in the pricing pipeline, and how does it ultimately affect societal outcomes? To answer these, we study a stylized model where a seller has a two-stage decision pipeline comprising linear demand model estimation followed by price optimization. The seller considers fairness notions in training loss, price, and demand, under both parity-wise and Rawlsian perspectives. We show that equalizing training loss across consumer groups leads to multiple solutions, which in turn can result in undesirable outcomes despite being a standard approach in fair machine learning. Focusing instead on fairness applied directly to prices or demand, we compare two strategies that enforce fairness in either the demand estimation stage or the price optimization stage. For parity-wise fairness, we characterize when each strategy yields higher social welfare under small fairness levels. We show that when market sizes and prices in the dataset are similar, imposing price fairness in the estimation stage is more beneficial to consumers, whereas imposing demand fairness in the optimization stage yields better consumer outcomes. For Rawlsian fairness, the two strategies coincide exactly. Lastly, we extend our model to alternate demand functions and conduct a case study using real-world vaccine pricing data.