“The combination of Shapley’s basic theory and Roth’s empirical investigations, experiments and practical design has generated a flourishing field of research and improved the performance of many markets,” the Nobel committee said in its announcement awarding what is formally known as the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel.
Shapley, a professor emeritus at UCLA, developed a theory of “matching methods, for how to best to match people up in large groups of, for example, men and women considering marriage. The goal is to ensure that the system is “stable,” that both partners feel that they have gotten the most attractive possible match; otherwise, they might separate in search of something better.
Shapley and colleague David Gale developed a process for ensuring that those matches are as stable as possible. In the process, known as the “Gale-Shapley algorithm,” there are a series of rounds in which men and women rank potential mates, and matches are made until everyone finds a spouse and the system is stable.
That work was purely theoretical — no marriages were arranged through the algorithm. But years later, Roth, now a visiting professor at Stanford University, developed ways to apply Shapley’s work to practical uses. The earliest and most widespread was in the system used to match new medical residents with hospitals that wish to employ them.
Roth first recognized that the National Resident Matching Program, which attempts to ensure that new doctors and the hospitals looking to hire them can get as good a match as possible, closely matched the Gale-Shapley algorithm. After all, an employer and employee trying to find the best match are in many ways similar to a hypothetical husband and wife looking to match up.
Roth then helped the resident matching program adapt its process to deal with couples who wished to ensure that they be hired by hospitals in the same city and to make the process less prone to manipulation by participants trying to game the system.
New York City schools faced similar problems in their old system for matching students with schools; students listed their preferred schools, but the system was prone to manipulation when less-qualified students could improve their odds of getting into a school by ranking it higher than they really viewed it.
Roth helped the schools revamp the system, using the lessons from the resident matching program and the theoretical work by Shapley. The result, according to materials from the Nobel committee, was a 90 percent drop in the number of students who were assigned to a school for which they had expressed no preference.
The field of “matching” has life-and-death consequences as well. Research is underway on applying the Gale-Shapley algorithm to the challenge of matching up kidney donors and those who need a transplant. This is a field with particular complications, as many willing to give a kidney to a loved one are not a match, so multi-direction trades can be useful — but that requires a complexity far beyond the original Shapley work in the 1960s or Roth’s efforts to put it to work in the 1980s.
“Some say economics has all kinds of good tools and techniques, but it has an absence of interesting problems,” Roth, 58, told Forbes magazine in 2010. “I look around the world, and I see all kinds of interesting, important problems we ought to solve with the tools we have.”