A Dynamic Matching Mechanism for College Admissions: Theory and Experiment

Abstract

Market design provides managerial insights into the success and failure of various market institutions in allocating scarce resources. We investigate a dynamic matching mechanism used in real-world college admissions, where students share a common priority ranking. Theoretically, we prove that efficient and stable matching occurs with an arbitrarily high probability, assuming sufficient revision opportunities and rationality. This predicts that the dynamic mechanism is less stable than the deferred acceptance mechanism and less efficient than the Boston mechanism. We confirm this prediction in a low-complexity laboratory setting. However, in a high-complexity setting, the dynamic mechanism matches the stability of the deferred acceptance and the efficiency of the Boston mechanism, as both underperform in this setting. This finding indicates that the dynamic mechanism is more resilient to increased complexity. We attribute this resilience to its belief-independent characterization of rationalizable strategies. Beyond college admissions, the dynamic mechanism has potential applications in housing assignments, job allocations, and ascending auctions. This paper was accepted by Axel Ockenfels, decision analysis. Funding: B. Gong gratefully acknowledges financial support from National Science Foundation of China [Grant 72373041], Major Project of Shanghai Education Commission’s Research and Innovation Program [Grant 2023ZKZD05-79]; Fundamental Research Funds for the Central Universities [Grant 2022QKT004]. Y. Liang is particularly thankful for the Barbour Scholarship’s financial support during her doctoral studies at the University of Michigan while working on this paper. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2022.00871 .