The Fixer

• Author: Maureen Burke
• Position: an Assistant Editor on the staff of Finance & Development.

Alvin Roth still recalls his visceral reaction in 1995 when he got the call from Bob Beran of the National Resident Matching Program. The “Match”—a clearinghouse that annually pairs thousands of newly minted U.S. physicians with jobs—was looking for someone to direct its redesign.Â

“Why me?” Roth remembers thinking, with an uneasy feeling. He knew, of course, why Beran had sought him out. Roth had written a book on matching and studied many market failures that preclude demand and supply from working accurately, including in the medical labor market. His investigation of clearinghouses and optimal matchups—such as between brides and grooms or doctors and hospitals—had earned him prominence in his field.Â

But as a theorist, he had not needed to worry about the details of implementing a mechanism to ensure a stable match, as optimal pairing is called. It had been enough to identify problems in the process. If he agreed to redesign the Match, though, he would have to find solutions.Â

This project marked Roth’s first venture into the real-world practice of market design, for which he would win the Nobel Prize in economics with Lloyd Shapley in 2012.Â

Physician, heal thy market

Roth had studied the market for new doctors. He knew that in the 1940s, competition for scarce medical students compelled hospitals to offer residencies to students increasingly early in their schooling, sometimes more than a year before graduation.Â

Clearly broken, the system was revised a few years later when medical schools agreed not to release information about their students until a certain date—but then, new issues emerged. Students on the waiting list for their first-choice hospital balked at accepting offers for their second choice, holding out as long as possible. As a result, waiting lists remained static until the very end of the selection period, when decisions were often made in haste. And when an offer was ultimately rejected, it was often too late for the hospital to make offers to other desirable candidates.Â

The process of matching new doctors and hospitals had become a messy process that displeased both medical students and their potential employers. To better align the preferences of medical students and hospitals, the Match—which paired students with hospitals using rank-order preference lists from both sides—was introduced in the early 1950s.Â

But there were new problems. The number of female medical students had grown dramatically, and many couples who met in medical school requested residencies in the same city. The Match could not accommodate these requests, so many people simply circumvented it, which signaled a breakdown in the system.Â

Roth agreed to refine and modernize the program and, together with Elliott Peranson, developed the mathematical procedure, or algorithm, that is still used today to match up new doctors and employers. The algorithm has been adopted by over three dozen labor market clearinghouses.Â

Matching markets

Economists traditionally study markets where prices adjust so that supply equals demand. But Roth is a game theorist who specializes in “matching markets”—markets in which changes in price alone do not clear the market. Participants can’t just choose what they want, even if they can afford it; they also must be chosen. Think college admissions or the dating market.Â

A pioneer of a new branch of economics called market design, Roth uses the mathematical tools of game theory to fix systems whose market mechanism has failed. Market designers have a clear-cut task in markets without prices, because if price is not playing a signaling role, there has to be another mechanism for clearing the market. Economists like Roth help design these mechanisms.Â

Market designers try to understand “the rules and procedures that make various kinds of markets work well or badly,” Roth explained in a 2007 article in the Harvard Business Review. “Their aim is to know the workings and requirements of particular markets well enough to fix them when they’re broken or to build markets from scratch when they’re missing.”

Much of Roth’s work builds on theory initiated by Shapley. In awarding the Nobel, the Royal Swedish Academy of Sciences cited the pair for “the theory of stable allocations and the practice of market design.” Shapley is generally...