Residency Program Matching as a Two-Sided Matching Market
In medical education, residency is a three- to six-year training program that medical students must complete at a postgraduate hospital. Until the 1940s, the market suffered from a Prisoner’s Dilemma problem in which competition by hospitals for residents resulted in a race to fill residency positions earlier and earlier in a medical student’s career. This process resulted in unstable transaction dates and made it impossible for the market to clear, so a new centralized market system was introduced. In this matching method, known as the National Residency Matching Program (NRMP), medical students submit applications to specific residency programs. After applicant interviews are complete, the process enters a “Match” phase that is based on the principal of two-sided matching markets. Residency positions are assigned by a centralized computerized system that assigns individuals to residency programs based on rank order lists (ROLs) from both residency programs and applicants. There are many more applicants than residency positions so it is not possible to produce perfect matching in the market (applicants represent a constricted set); however, it is possible for both applicants and residency positions to remain unmatched if they are undesirable.
Centralized matching algorithms are only successful if they produce “stable” matchings. Matching between residents and programs is stable if and only if there are no applicant-program pairs such that the applicant prefers that program to his or her current match, and the program prefers the applicant to one of its current matches. For a simple two-sided matching market without outside variations, at least one stable matching can always be found no matter what ROLs are submitted. Each set of stable matchings always contains a “program-optimal” and an “applicant-optimal” stable matching, with optimal matching based on which side holds power over proposing offers. In each stable matching, the same applicants are unmatched and the same positions are unfilled. Lastly, when the “applicant-offering” algorithm is used, no applicant can possibly improve his match by submitting a ROL different from his or her true preferences.
Despite the advantages of a centralized system of matching markets, a problem arose in that there were multiple stable matchings, and students and hospitals disagreed about what stable matching was best for them. In the original “program-offering” NRMP algorithm, hospitals made offers to the highest-ranked students who held the best of the offers they had so far received. However, in a market with no other complexities, there is a systematic advantage to the side that makes the offers. This system drove students to lie about their choices, since it was not in their best interest to state their true preferences on their ROL. Students became less willing to participate in the match in an orderly way and attempted to “cheat” the system, encouraging misrepresentation and mutual distrust. In addition, residency programs attempted to exploit this situation by employing unfair post-interview recruitment practices to try and solicit commitments from applicants to rank a particular program at the top of their ROL. In response, the algorithm was changed in 1996 from “program-offering” to “applicant-offering,” although an analysis conducted by Harvard economist Alvin Roth showed that, empirically, it makes no difference which side proposes (only one resident in a thousand would end up at a different place). Even with the revisions, however, the matching system deviates from what might be expected in a free labor market. There are still many opportunities for the system to improve in the future, for example by allowing for price competition and instituting measures to make truthful ranking a dominant strategy for both applicants and residency programs.
References:
http://kuznets.fas.harvard.edu/~aroth/papers/1996_JAMA_NMRPasLaborMarket.html
http://www.siam.org/pdf/news/305.pdf
http://jama.ama-assn.org.proxy.library.cornell.edu/content/278/9/729.full.pdf
For a detailed analysis of residency program matching and game theory, read Alvin Roth’s paper: “The Evolution of the Labor Market for Medical Interns and Residents: A Case Study in Game Theory.” (1984). Journal of Political Economy; 92(6): 991-1016.