The Competition for Partners in Matching Markets

Yash Kanoria (), Seungki Min () and Pengyu Qian ()
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Yash Kanoria: Decision, Risk and Operations Division, Columbia Business School, Columbia University, New York, New York 10027
Seungki Min: Department of Industrial and Systems Engineering, Korea Advanced Institute of Science and Technology, Daejeon 34141, Republic of Korea
Pengyu Qian: Operations and Technology Management Department, Questrom School of Business, Boston University, Boston, Massachusetts 02215

Management Science, 2025, vol. 71, issue 6, 5230-5250

Abstract: We study the competition for partners in two-sided matching markets with heterogeneous agent preferences, with a focus on how the equilibrium outcomes depend on the connectivity in the market. We model random partially connected markets, with each agent having an average degree d in a random (undirected) graph and a uniformly random preference ranking over their neighbors in the graph. We formally characterize stable matchings in large random markets with small imbalance and find a threshold in the connectivity d at log 2 n (where n is the number of agents on one side of the market), which separates a “weak competition” regime, where agents on both sides of the market do equally well, from a “strong competition” regime, where agents on the short (long) side of the market enjoy a significant advantage (disadvantage). Numerical simulations confirm and sharpen our theoretical predictions, and demonstrate robustness to our assumptions. We leverage our characterizations in two ways: First, we derive prescriptive insights into how to design the connectivity of the market to trade off optimally between the average agent welfare achieved and the number of agents who remain unmatched in the market. For most market primitives, we find that the optimal connectivity should lie in the weak competition regime or at the threshold between the regimes. Second, our analysis uncovers a new conceptual principle governing whether the short-side enjoys a significant advantage in a given matching market, which can moreover be applied as a diagnostic tool given only basic summary statistics for the market. Counterfactual analyses using data on centralized high school admissions in a major U.S. city suggests that both our design insights and our diagnostic principle have practical value.

Keywords: matching markets; stable matching; competition; market design; diagnosis from summary statistics (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormnsc:v:71:y:2025:i:6:p:5230-5250

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