Estimation of High-Dimensional Contextual Pricing Models with Nonparametric Price Confounders

Personalized or contextual pricing is widespread practice in a number of revenue management problems. A pricing algorithm or platform utilizes a user's personal data to make the most profitable pricing decisions that could vary among individuals. In this paper, we study the question of estimating a demand regression model with high-dimensional data, incorporating an unknown, non-parametric pricing function that acts as a confounding term to the demand model because of the involvement of personal data in algorithm's pricing decisions. We propose a high-dimensional instrumental variable regression method which uses properly cen- tered contextual vectors as approximate instruments in a Lasso formulation to mitigate the bias from price confounders. We further propose a de-biased approach based one two-level partition of the price interval from dynamic programming, and show that the de-biased approach typically results in smaller estimation errors. Finally, we corroborate our methodological and theoretical results with numerical studies and propose some questions for future research.