How to “Win” the National Resident Matching Program
Source: Fixing the “Match”: How to Play the Game: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3399603/
Perhaps one of the most stressful events in a medical student’s academic career is The Match, or more specifically, the National Resident Matching Program. This is the data-driven algorithm that matches students from all over the country into specific specialties using an intricate algorithm, the research behind which won the 2012 Nobel Prize in Economic Sciences. The algorithm is set up as a game with two players – the applying medical student, and the prospective residency programs for that student. The basic algorithm is run as such – The student proposes to his/her top-ranked program, asking for a residency; the program accepts the proposal if it has an open spot, retaining the right to reject it later if a better suitor arrives. If the proposal is rejected, the student can propose to the next program on their list. If they are accepted to their next program, logic takes that another student will need to propose to another program. The two economists, David Gayle and Lloyd Shapley, researched this algorithm (and won the Nobel Prize for it) and determined that the algorithm is optimal for the proposer. This indicates that the students are guaranteed their optimal program. In their research, the students should use a true-preference strategy which means that they should use a ranking system for their programs of interest strictly based on their own preferences. This is the student’s best response such that regardless of what other students or programs do, no other strategy can produce a better outcome for a specific student. If the student and the program use their best responses – that is, to simply list their own personal preferences – a Nash Equilibrium will be established such that there will be mutual best responses between the two.
As we define this as a game, and it has been proven that this game airs in favor of the students, then why is it that some students are unable to match into any program? This is because not everyone realizes how the game is played. Advisors will tell applicants to consider all of the factors that go into matching into a specific program, which, in effect, overcomplicates the decision on the part of the student. This can result in a student listing a “backup” program at a higher rank than their preferences. This results in them deviating from their best response, in effect causing them to “lose” the game because they could have had a better outcome had they listed their preferred programs first. Furthermore, some programs do not follow the true preference strategy in a very similar way to that of the applicants. Program directors regularly use a strategy in which they give candidates who preferred their program a higher rank than the true strength of the applicant. This is similar to the deviation from the best response of the applicant described earlier. They are effectively giving a position to a “backup” student by not adhering to their own preferences. Both of these factors destroy the Nash Equilibrium which permit the use of mutual best responses by both the programs and the students.
This then begs the question on the part of the programs; why would they follow this strategy? Two different theories have been proposed. There is the theory that the programs prefer students who prefer them because the program directors believe that they will be more interested as residents; although there has been no such research to backup this claim. Another theory is that programs deviate from their optimal strategy simply because they do not like the uncertainty provided by the Match itself. Therefore, they are willing to trade an optimal result for greater certainty. The same holds true for the students as well. The route of the deviation from the optimal strategies on both sides is the fear of the uncertainty provided by the Match. This leads us back to the original statement about how best to “play the game” and that is for both students and programs alike to list their preferred matches simply based on personal preference, as this is the ideal strategy for all players involved. All that is needed is for all players to act selfishly, as is suggested in the defining assumptions of the original game theory model.