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A Primer on the Game Theory Behind the National Resident Matching Program for the Medical Educator and Student

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A Correction to this article was published on 08 May 2020

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Every year, medical students vie for American graduate training through the National Resident Matching Program (NRMP). Some students yet behave in ways that imply persistent misunderstandings about the matching algorithm. This paper explains the economic and mathematical literature underpinning it for a medical audience. The NRMP implements the Roth-Peranson algorithm, finding a stable match by having students propose to residency programs according to their preference ranking. This configuration favors students while disfavoring hospitals. Game-theoretic analysis shows us that students are unequivocally unable to “game the system” by misstating their preferences. Telling the truth is the optimal strategy.

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  • 08 May 2020

    In the original article, Table 2 inadvertently omitted the letter “F” in the bottom right column.


  1. A point of international concern: the same algorithm is used in other residency matches outside of the USA. Both the Canadian [2] and Japanese [3] residency matches use the Roth-Peranson algorithm (however, I do not profess this to be an exhaustive list). The properties and results of the algorithm described in this paper apply to those countries as well.

  2. For those readers interested in a more mathematical treatment of the algorithm and its results discussed in this paper, Roth and Sotomayor’s book “Two-sided matching” [6] is an exceptional resource. The book also discusses the history of the NRMP and the interesting interplay between game theory and the real world in the evolution of the NRMP over the decades.


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I would like to express my sincere gratitude to Dr. Anastasios Papanastasiou of the Department of Economics at McMaster University, for casually sending me Gale and Shapley’s foundational paper as a reading exercise. It ignited my interest in matching theory and inspired this paper.

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Correspondence to Muhammad Maaz.

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The original version of this article was revised: In the original article, Table 2 inadvertently omitted the letter “F” in the bottom right column. Article is updated and the corrected table is shown below.

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Maaz, M. A Primer on the Game Theory Behind the National Resident Matching Program for the Medical Educator and Student. Med.Sci.Educ. 30, 965–969 (2020).

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