Context-Based Dynamic Pricing with Separable Demand Models

72 Pages Posted: 27 Jun 2022 Last revised: 11 Oct 2023

See all articles by Jinzhi Bu

Jinzhi Bu

The Hong Kong Polytechnic University

David Simchi-Levi

Massachusetts Institute of Technology (MIT) - School of Engineering

Chonghuan Wang

Massachusetts Institute of Technology (MIT)

Date Written: June 18, 2022

Abstract

Motivated by the empirical evidence observed from the real-world dataset, this paper studies context-based dynamic pricing with separable demand models. Consider a seller selling a product over a finite horizon of $T$ periods and facing an unknown expected demand function that admits a separable structure $f(p)+g(x)$, where $p\in\mathbb{R}$ and $x\in\mathbb{R}^d$ denote the product's price and features respectively. The seller does not know the exact expression of $f(p)$ or $g(x)$, but can dynamically adjust prices in each period based on the observed features and demands to learn their forms. The seller's objective is to maximize the $T$-period expected revenue. We systematically characterize the statistical complexity of the online learning problem under three configurations of demand models with different structures of $f(p)$ and $g(x)$. For each model, we design an efficient online learning algorithm with a provable regret upper bound. We also show that the upper bound is generally unimprovable by proving a matching regret lower bound in certain parameter regimes. Our results reveal fundamental differences in the optimal regret rates when $f(p)$ and $g(x)$ are endowed with different structures. The numerical results demonstrate that our learning algorithms are more effective than benchmark algorithms for all the three models, and also show the effects of the parameters associated with $f(p)$ and $g(x)$ on the algorithm's empirical regret.

Keywords: Separable Demand, Dynamic Pricing, Contextual Information, Online Learning

Suggested Citation

Bu, Jinzhi and Simchi-Levi, David and Wang, Chonghuan, Context-Based Dynamic Pricing with Separable Demand Models (June 18, 2022). Available at SSRN: https://ssrn.com/abstract=4140550 or http://dx.doi.org/10.2139/ssrn.4140550

Jinzhi Bu

The Hong Kong Polytechnic University ( email )

Hong Kong
27667415 (Phone)

David Simchi-Levi

Massachusetts Institute of Technology (MIT) - School of Engineering ( email )

MA
United States

Chonghuan Wang (Contact Author)

Massachusetts Institute of Technology (MIT) ( email )

77 Massachusetts Avenue
50 Memorial Drive
Cambridge, MA 02139-4307
United States

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