Proxy-Aided Demand Learning with an Application to Various Pricing Problems

Tao Shen, Yifan Cui

Abstract: In data-driven demand learning, understanding customer willingness to pay presents a significant challenge because of the complex interplay between various influencing factors. This paper addresses the multifaceted relationship between key demand drivers (e.g., price) and demand outcomes (e.g., sales) and underscores the difficulties in identifying causal effects under endogeneity. To mitigate confounding bias, we introduce proxy variables into the demand learning process. Inspired by the proximal causal inference framework, we categorize proxies into outcome and treatment types, enabling the identification and estimation of demand outcomes, particularly expected potential sales at specific price points, through the use of a bridge function. The paper further explores practical applications of the proposed demand learning process in data-driven pricing problems, focusing typically on challenges in static and contextual pricing and then extending to broader decision-making problems. Thereafter, the regret bounds of these applications are also established. In addition, simulations and real data analysis demonstrate that our proposed method effectively addresses demand learning challenges and outperforms existing methodologies. Funding: This work was supported by the National Key Research and Development Program of China [Grant 2024YFA1015600] and the National Natural Science Foundation of China [Grants 12471266 and U23A2064]. 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.2025.1793.

External IDs:doi:10.1287/opre.2025.1793