On Monday the 2012 Nobel Memorial Prize in Economic Science was awarded to Lloyd Shapley and Al Roth, for their work on market design and matching theory, which relate to how individuals and firms find and select one another in areas from school choice to jobs to organ donations to marriage itself.

Dr. Shapley, 89, a professor emeritus at UCLA, made early theoretical contributions to the topic in the 1950’s and 1960’s.

Al Roth, in the process of moving from Harvard to Stanford, working independently, put the theories to practical use in markets including assigning students to public schools in New  York, Boston, Chicago, and Denver, matching kidney donors and, importantly, matching new doctors to hospitals.

Why is the work so noteworthy?

Disclosure time: I consider Al a friend, and have corresponded with him in the past about his work and its applicability to other contexts including Law Land. In fact, after the Nobel announcement, I sent him a congratulatory email which I fully expected to be buried in an avalanche of similar emails, phone calls, and media requests, all from more exalted folks. Al responded to me in less than five minutes. That’s Al.

These markets have an unusual feature in common: There are no prices, which normally do the heavy lifting of resource allocation and matching up buyers and sellers. Absent prices, how do you design a market that can arrive at a stable and optimal outcome?

And is it possible to arrive at a stable outcome even when persons on either side of the market disagree about what qualities make for the right match?

Turns out that it is possible, and that systems can be designed that produce matches that:

  • are fair;
  • are “stable” in the strict sense that no one in any of the resulting matches would want, and be able, to break off and pair up with a counterparty in another match;
  • and that cannot be manipulated by sophisticated players to their advantage.

Here’s how it works in a nutshell, courtesy of the NYT’s story on the Nobel:

In older matching systems, a student would apply to his first-choice school, which was often popular. If the student did not get in, then the application would be sent on to the student’s second choice. But if that was also a popular choice, then that school’s program would have already filled up by the time his application was even considered, and the process would repeat itself with his third-choice school and so on.

Even if students were qualified to get into one of their top schools, they could be shut out because they did not rank their preferences strategically. This created an incentive to try to game the system by listing a less popular school as their first choice because that way they would at least have a chance of getting in somewhere.

Mr. Roth designed a system in which students had an incentive to tell the truth about where they wanted to go. A centralized office could then assign them to a school best suited for them, based both on their own preferences and the preferences of the schools they were applying to.

The school systems he helped create use a “deferred acceptance algorithm,” which was developed by Mr. Shapley’s theoretical work.

The system works by tentatively accepting students to their top-choice school. It holds off on the final assignment until it has gone through all the other applications to make sure there are not other students who have a higher claim to a spot at that given school (because of higher test scores, a sibling at the school or whatever other criteria the school prioritizes), even if those students happened to rank the school lower on their list of preferences.

“The idea is to level the playing field,” Mr. Pathak said. “You want to make sure that not only do sophisticated players not have to spend the time learning the strategies and different heuristics that will get them ahead, but also that unsophisticated players are not hurt by the fact that they are not aware of all this information.”

This same sort of system is used to match new medical school graduates to medical residency programs, which was once a messy process that led to a lot of unhappy candidates. Now all residency assignments are posted simultaneously. In the mid-1990s Mr. Roth redesigned the system to help match married couples who were jointly looking for jobs at hospitals.

Does it really work?

Let’s get specific.

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