Prof. Sophie Yu
University of Pennsylvania
Talk: Flexibility Allocation in Random Bipartite Matching Markets: Exact Matching Rates and Dominance Regimes
Abstract: We study how a fixed flexibility budget should be allocated across the two sides of a balanced bipartite matching market. On each side, agents are either regular or flexible, with flexible agents being more likely to connect with agents on the opposite side. In this model, we derive an exact variational formula for the size of a maximum matching for any flexibility allocation (the derivation uses the local weak convergence framework of Bordenave, Lelarge and Salez (2011) by extending it to multi-type trees). Using this formula, we analytically characterize when concentrating all flexibility on one side dominates splitting it across both sides, and vice versa. This complements and sharpens the dominance regimes characterized by Freund, Martin and Zhao (2026), now grounded in an exact characterization of the matching rate rather than approximate algorithmic bounds. The paper is available at https://arxiv.org/abs/2604.02295.Besides, we also study the flexibility allocation in the spatial setting where we show a more uniform allocations of flexibility among the supply side nodes always yield more matches on average. The paper is available at: https://arxiv.org/abs/2601.13426
Biography: Sophie H. Yu is an assistant professor at The Wharton School of the University of Pennsylvania. She was a postdoctoral scholar in Management Science and Engineering at Stanford University. She holds a Ph.D. in Decision Sciences from Duke University's Fuqua School of Business in 2023, an M.S. in Statistical and Economic Modeling from Duke University in 2017, and a B.S. in Economics from Renmin University of China in 2015. Her research focuses on matching, inference, and algorithm design in large-scale networks and stochastic systems. Her research has been recognized by the Thomas M. Cover Dissertation Award from IEEE Information Theory Society, the Fuqua School of Business Best Dissertation Award, and a finalist for the George Nicholson Student Paper Competition.
