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Matching Markets in Residency Programs

The concepts associated with graph theory, networks, and game theory can seem a bit abstract when they’re just laid out as variables and numbers in a textbook, but they have a vast array of applications to the real world—and not just in traditional sectors like economics. We can see applications of game theory and market concepts in areas from pop culture to science to the arts. This article in particular discusses how Dr. Lloyd Shapely and Dr. Alvin Roth were able to apply the principles of matching markets to residency programs for medical school graduates. Each year, when seniors graduate from medical school, they are matched with residency programs across the country by the national board. The two researchers developed an algorithm to make this pairing process more efficient and to ensure that everyone is as pleased with the outcome as possible.

The algorithm allows residency students and residency programs to respectively rank each other and places residents in their highest ranked choice that also wants them and has an empty space. This algorithm uses concepts we learned of matching markets, perfect matching, and constricted sets. In the traditional residence-matching program, there was no method to the madness, and constricted sets would often result, wherein residency programs would have n amount of spots open and n+1 or more amount of residents vying for the spot, meaning some residents wouldn’t get paired up. The researchers’ algorithm results in perfect matching, wherein each node in one set (the residents) can be paired with a node in the other set (the residency programs). Thus, game theory and market principles allowed for more efficient matching in this case, and more people are happier overall with the results.



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September 2018