Dynamic Contextual Pricing with Doubly Non-Parametric Random Utility Models

TL;DR

This paper develops doubly nonparametric random utility models for dynamic pricing, providing theoretical guarantees and improved estimation techniques to optimize pricing strategies in digital markets.

Contribution

It introduces novel population equations and establishes uniform convergence rates for nonparametric demand estimation in dynamic pricing, advancing the theoretical framework and practical application.

Findings

Minimax optimal learning rates for utility and noise estimation

New regret bounds highlighting the impact of model complexity and noise smoothness

Enhanced nonparametric methods for real-time demand estimation

Abstract

In the evolving landscape of digital commerce, adaptive dynamic pricing strategies are essential for gaining a competitive edge. This paper introduces novel {\em doubly nonparametric random utility models} that eschew traditional parametric assumptions used in estimating consumer demand's mean utility function and noise distribution. Existing nonparametric methods like multi-scale {\em Distributional Nearest Neighbors (DNN and TDNN)}, initially designed for offline regression, face challenges in dynamic online pricing due to design limitations, such as the indirect observability of utility-related variables and the absence of uniform convergence guarantees. We address these challenges with innovative population equations that facilitate nonparametric estimation within decision-making frameworks and establish new analytical results on the uniform convergence rates of DNN and TDNN, enhancing their applicability in dynamic environments. Our theoretical analysis confirms that the statistical learning rates for the mean utility function and noise distribution are minimax optimal. We also derive a regret bound that illustrates the critical interaction between model dimensionality and noise distribution smoothness, deepening our understanding of dynamic pricing under varied market conditions. These contributions offer substantial theoretical insights and practical tools for implementing effective, data-driven pricing strategies, advancing the theoretical framework of pricing models and providing robust methodologies for navigating the complexities of modern markets.