“Switching Gradient:
Learning to Compete with Price Match Guarantee “
by Sichen Guo
Shanghai University
Place: MA-330
Abstract
Price Match Guarantee (PMG) has become a widespread strategy among retailers to attract and retain customers by promising to match lower prices. However, how sellers should dynamically set prices under PMG, especially without full knowledge of price competition remains unclear. We model an online price competition in a duopoly market with asymmetric PMG adoption. Customers request a refund when the price difference exceeds their hassle threshold, thereby distorting both sellers’ revenue functions. Each seller observes only their own realized demand and must learn to optimize on the fly without knowing the demand model or the other’s information. The setting poses unique challenges, including discontinuous and non-convex revenue functions due to PMG, and biased, incomplete feedback due to online competition.
To address these, we propose a novel switching gradient algorithm, where the PMG provider alternates between real and artificial gradients based on a diagnostic function, while the other seller ignores PMG distortions in gradient estimation. Our algorithm achieves dynamic regret at order $\mathcal{O}(\log T \sqrt{T})$ and last-iterate convergence to the static Nash equilibrium at order $\mathcal{O}(\log T / \sqrt{T})$. We introduce a new analytical framework to rigorously quantify the regret and convergence rates even under asymmetric knowledge and heterogeneous step sizes. For retailers adopting PMG or other pricing mechanisms that introduce discontinuities in revenue, our framework offers a practical way to adapt classical gradient-based learning algorithms to accommodate structural complexities. For sellers competing against PMG adopters, our findings indicate that conventional pricing policy may remain effective, even without adjusting to the new environment, and the burden of adaptation lies primarily on the PMG provider. Furthermore, we demonstrate that improved outcomes and higher prices may not be achieved without additional information sharing, highlighting the Price of Non-Cooperation.
Bio
Sichen Guo is a Ph.D. candidate in Management Science and Engineering at the Shanghai University of Finance and Economics and a visiting doctoral researcher at the University of Miami’s Herbert Business School. Her research focuses on dynamic programming, stochastic optimization, data-driven methods, and online algorithms, with applications in inventory management, revenue management, and human–AI collaboration.
Her current work includes projects on multiproduct inventory systems, robust allocation policies for distribution networks, and pricing games with price-matching guarantees. Several of his papers are under major revision at leading journals such as Operations Research and Manufacturing & Service Operations Management. He is also a contributing author to a recent book on modern inventory management.
