MONOGRAPH A Primer on the Game Theory Behind the National Resident Matching Program for the Medical Educator and Student Muhammad Maaz 1,2 # International Association of Medical Science Educators 2020, corrected publication 2020 Abstract 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. Keywords Residency . Match . Postgraduate education . NRMP Introduction Every year, medical students wishing to practice in the USA apply to be matched to graduate training through the National Residency Matching Program (NRMP). Much has been writ- ten in the medical literature about what is colloquially termed the “The Match,” from analyses of matching statistics to cor- relates of matching success. Despite the considerable interest in The Match, the mechanisms of the algorithm and its impli- cations yet remain somewhat a mystery to medical students. Despite educational resources devoted to The Match during medical school, recent empirical evidence by Rees-Jones sug- gests that medical students participating in the NRMP still engage in behavior that reflects a misunderstanding of how the algorithm works [1]. Rees-Jones also presents experimen- tal evidence that shows that people behave better in such sys- tems when they are taught the underlying theory of how the algorithm works [1], which is the aim of this paper. A solid understanding of the theory behind the algorithm will be of use to both medical educators and students in preparing for The Match. The algorithm used by The Match was developed by, and has been extensively studied by, researchers in a field called matching theory, inhabited by economists, mathemati- cians, and computer scientists. Though the matching theory literature is quite extensive and established in answering com- mon concerns about The Match, these questions still abound in medical circles. This is quite possibly due to the language barrier: research in matching theory is communicated in eso- teric mathematical symbolisms and formal logic, leading to a disconnect between what is known in matching theory and what is known by those in the medical field. In this paper, I aim to cross that divide by elucidating the underlying matching theory and game theory for a non-economist/non- mathematician audience in the hopes of clearing up the con- fusion surrounding The Match. How Does the NRMP Matching Algorithm Work? The NRMP 1 uses an algorithm called the Roth-Peranson al- gorithm [4], a modification [4] of the deferred acceptance (DA) algorithm developed in 1962 by Gale and Shapley [5], 1 A point of international concern: the same algorithm is used in other resi- dency 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. * Muhammad Maaz maazm@mcmaster.ca 1 Faculty of Health Sciences, McMaster University, Hamilton, Ontario, Canada 2 Department of Economics, McMaster University, Hamilton, Ontario, Canada https://doi.org/10.1007/s40670-020-00955-8 Published online: 17 April 2020 Medical Science Educator (2020) 30:965–969