Title: Switching Gradient: Learning to Compete with Price Match Guarantee
Date/Time: 05-12-2025 / 13:30-14:30
Place: EA409
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.
Short Bio: Sichen Guo is currently a fifth-year Ph.D. candidate in the School of Information Management and Engineering at Shanghai University of Finance and Economics. She is also a visiting scholar at University of Miami. Her research interests lie in designing learning algorithms and their applications to operations management problems, with a particular focus on inventory management and dynamic pricing. Her work has resulted in minor revision in Operations Research, major revision in M&SOM. She also serves as reviewer for Management Science, M&SOM, POMS and Naval Research Logistics.