The Nobel Prize in Economic Science was awarded Monday to two American economists, Lloyd Shapley and Alvin E. Roth, "for the theory of stable allocations and the practice of market design." A big part of what Messrs. Shapley and Roth received the prize for was their research and writing on "matching theory." Their work, especially Mr. Shapley's, is often quite abstract, but it has important practical implications.
Mr. Shapley is an emeritus professor at UCLA and Mr. Roth, who will shortly move to Stanford University, is a professor at Harvard University and Harvard Business School. Until the 1990s, both men were primarily theoretical economists, but Mr. Roth gradually moved toward applied economics. He utilized his and Mr. Shapley's insights to "design" markets.
One important area in which Mr. Roth's work has been used is to facilitate a kind of market—essentially a barter market—for kidney transplants. It is reasonable to conclude, therefore, that the work by Mr. Roth, and the Shapley insights from which much of it derives, has saved lives.
Matching theory can be applied to many aspects of life in which matches need to be made—in marriages, for instance, or the job market, or student placement in colleges. In 1962, Mr. Shapley and co-author David Gale published a short but pathbreaking article titled "College Admissions and the Stability of Marriage" in a mathematical journal.
The article presented what is now called the "Gale-Shapley deferred choice algorithm." The key word is "deferred." They showed that if each "girl" (yes, people wrote differently then) rejects all but her favorite of the "boys" who propose, but leaves her favorite hanging to allow for someone even better to come along later—and if each boy who is rejected proceeds to his second choice—then letting this process play out yields stability.
What is stability? It means that there is no boy-girl pair who would both rather be married to each other than to the person they did marry.
Of course, letting that algorithm run is unrealistic. Many girls will accept the boy who is good enough rather than wait until a long sorting-out process is over. But other uses for matching theory make more sense. It turns out that doctors had been using the algorithm to allocate residents to hospitals even before the Gale-Shapley article came along.
What complicated the marriage allocation procedure was the widespread advent of the two-career couple, when it couldn't be assumed that working couples would automatically accept whatever the algorithm decreed for one of the spouses. As economist Alex Tabarrok cleverly put it, "matching in the marriage market was beginning to derail matching in the doctor-hospital market."
Alvin Roth was asked to solve the problem and he quickly became a "market designer." He and co-author Elliott Peranson designed a matching system to handle the relatively new two-career-couple problem. The system is used by many medical specialties in the U.S.
Once Mr. Roth confronted the medical market, it wasn't that big a step to thinking about an especially knotty problem doctors faced: matching live kidney donors and recipients. The fact that the federal government has made it illegal for people to sell their kidneys means that there is a shortage. Mr. Roth's "market design" solution led to the New England Program for Kidney Exchange, which allows husbands and wives with incompatible kidneys to "swap" a kidney with another incompatible pair.
Mr. Roth's solution has not ended that shortage because his solution is essentially one of barter. The only suppliers in the market are those who want kidneys for their loved ones. But his system gives a better match.
There is a more fundamental solution to the kidney shortage. Don't "design" a market; simply allow one. A ban on selling kidneys is essentially a price control of zero and, like other price controls, causes a shortage. There are thousands of "demanders." There are also thousands of potential suppliers who, at a price of zero, are not willing to give up a spare kidney. A straightforward solution is to allow the sale of organs.
Now that the Nobel Peace Prize has been given to such an amorphous entity as the European Union, perhaps next year the Nobel in economics should go to the free market, which would do more than all the market designers to get kidneys to desperate people.
Mr. Henderson, who served on President Reagan's Council of Economic Advisers, is a research fellow with the Hoover Institution and an economics professor at the Naval Postgraduate School.
