The National Residency Matching Program is a process almost all medical residents go through. Since 1952 the program has strived to match graduating medical students to residency training programs. Medical students are offered interviews at a number of residency programs. The medical students then rank all the residency programs they interviewed at in terms of preference, while the residency programs do the same for all the medical students they interviewed.
The algorithm the NRMP then uses to match medical students with residency programs isn’t terribly complicated to understand, but I’m sure the math behind it and proving its efficiency were.
Now two American economists whose work centered on such matching algorithms and game theory have won the 2012 Noble Prize for Economics. As the NRMP website itself describes the contributions of Lloyd Shapley and Alvin Roth,
Shapley and his colleague, David Gale, developed the “stable marriage” algorithm in which men and women rank each other as potential mates and a series of offer rounds produces a best match. The Gale-Shapley algorithm is the basis of the matching algorithm used by the NRMP, and Roth worked with NRMP to adapt it so that it proposes matches on the basis of the applicant rather than the program rank order lists.
While others built off Dr. Shapley’s work for the debut in 1952, Dr. Roth worked directly with the NRMP in the 1990s to tweak the match, especially as it related to match married couples.
For the fourth year medical students going through interviews for residency right now and the match, just remember however frustrating the process is it was complicated enough to warrant a Noble Prize. So, some respect.