Learning Fair Demand Models

2026-06-04

AI Summary

This study addresses the risk of discriminatory outcomes in data-driven pricing arising from group disparities in demand models. It investigates mechanisms for incorporating fairness constraints within a two-stage pricing pipeline—comprising demand estimation and price optimization—and systematically compares enforcing group parity or Rawlsian fairness at either the price or demand level. Theoretical analysis reveals that directly imposing fairness on training loss can yield suboptimal outcomes. To address this, the authors propose a novel strategy that applies price fairness during estimation and demand fairness during optimization, deriving conditions under which social welfare is maximized. Empirical evaluations using linear and nonlinear demand models, along with real-world vaccine pricing data, demonstrate that when market structures are similar, price fairness in the estimation stage benefits consumers more, whereas demand fairness in the optimization stage performs better; under Rawlsian fairness, both strategies are equivalent and effective.

Abstract

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.

Problem

• fair pricing
• demand modeling
• algorithmic fairness
• price discrimination
• social welfare

Innovation

• fair pricing
• demand estimation
• price optimization
• Rawlsian fairness
• algorithmic fairness