Via Forbes

Alvin Roth sees plenty of ways economics can make a difference in people’s lives. In contrast with the authors of bestselling books like Freakonomics, who are fascinated by obscure but intriguing questions like how to detect cheating by sumo wrestlers, Roth relishes real-world challenges. “Some say economics has all kinds of good tools and techniques, but it has an absence of interesting problems,” notes Roth, 58, who holds a joint appointment in the Harvard economics department and the business school. “I look around the world, and I see all kinds of interesting, important problems we ought to solve with the tools we have.”

In particular Roth uses the mathematical tools of game theory to find fixes for big, broken systems. Over the last 20 years he has pioneered a branch of economics known as market design. Among Roth’s accomplishments: designing networks for kidney donations and creating elegant systems that enable huge urban school districts to optimally place multitudes of students among hundreds of schools.

“He’s unusual, because he’s highly respected as a theorist, but he’s also working directly in the field,” observes Eric Maskin, an economist at the Institute for Advanced Study in Princeton, N.J. and corecipient of the 2007 Nobel Prize in economics for theoretical work on market design. “Al has managed to find ways to adapt the theory in very clever and ingenious ways.”

The most daunting real-world problem Roth has solved so far: New York City’s high school match, which he tackled in 2003. While many American kids simply attend their neighborhood high school, eighth graders in big cities like New York face a staggering number of choices. In theory, at least, each of the city’s 80,000 eighth graders has the option of going to any one of 700 high school programs. The right match can be especially meaningful for kids who live in impoverished neighborhoods with lousy schools.

Before Roth got involved, the matching system was so screwed up that a third of the city’s eighth graders didn’t even participate. “It was like a crowded, crazy bazaar somewhere in the Middle East,” recalls Neil Dorosin, a former New York Department of Education official.

Roth, aided by a Harvard graduate student and a young economist at Columbia, redesigned the system using a version of what’s known as a deferred-acceptance algorithm. Roth has used modified forms of this same algorithm to design matching systems for Boston’s public school system and for placing medical school graduates with residency programs.

The algorithm is most easily explained in the context of matching multiple men and women who want to marry. First, each man proposes to his first-choice woman. Women who get numerous proposals reject their least preferred suitors, but don’t make a firm commitment just yet. The rejected guys make new offers, in order of their preferences, perhaps resulting in new rejections, until none of the guys is rejected or no rejected guy wants to propose to anyone else. At that point the women accept their most preferred suitor. For the men who don’t get matches in the first round because they didn’t list enough choices, there is another round where the men are offered a list of still-single women and they make another set of choices. Sometimes a third round is needed.

Applied to the high school scenario, the men are the equivalent of students and the women are the schools. In New York it gets more complicated, because many schools have their own screening mechanisms. Roth and his team were able to weave all that complexity into one transparent, reliable system where students list up to 12 choices in order of preference. Since Roth revamped things the participation rate jumped from 66% to 93%.

It’s too bad that the system did not exist when Roth went to high school in the late 1960s in Queens, N.Y. He attended nearby Van Buren High School, where he dropped out in his junior year. Sheepish when asked to explain why–Roth’s parents were both high school teachers, adding to the irony–he concedes that his decision came down to boredom. “I think I was understimulated,” he says.

Roth had been taking weekend engineering classes at Columbia University, and a professor there suggested he apply to college. He was admitted and earned a degree in engineering and then a doctorate from Stanford, in a branch of engineering called operations research, which uses mathematics to organize systems with lots of moving parts. “I’ve always been interested in using mathematics to make the world work better,” says Roth.

Roth’s specialty within operations research: game theory, which analyzes situations in which the outcome depends on the actions of multiple people. By the 1980s game theory was considered a strain of economics.

Roth arrived at Harvard in 1998 after stints at the University of Illinois at Urbana-Champaign and the University of Pittsburgh. Though he’d published a book in 1990 that was much studied by game theorists, all of Roth’s work was academic until 1995, when he tackled the medical school match, a mechanism that places medical school grads into 25,000 residency jobs across the country.

As women flocked to med school and more students married, the old system, designed by doctors back in the 1950s, struggled to accommodate couples who wanted residencies in the same place. Graduates were starting to make arrangements directly with hospitals. Roth’s revamp took effect in 1998. It worked so well he has since helped redesign the matching system for specialties like gastroenterology.

Roth makes the redesigning of complex markets look easy. Warm and animated, he favors jeans, open-necked shirts and Merrell hiking shoes. Leaning over a cup of Turkish coffee at a cafe across the Charles River from his messy journal-strewn corner office, he bends over backward to give credit to his younger protégés, students and coauthors. “Market design is a team sport,” he insists.

“He uses very rigorous game theory,” attests MIT economics professor Parag Pathak, the former student of Roth’s who worked on the New York City match project. “He’s always conveyed to his students that we should try to connect what we’re doing to empirical facts.”

A set of dismaying facts led Roth to design a system for matching incompatible kidney donor pairs and lone altruistic donors with other donors and recipients. The waiting list for donor kidneys stretches to 85,000 in the U.S., and 4,000 patients die each year as a result of the organ shortage. In 2003 Roth started work on a system that would allow people who want to donate kidneys to loved ones but can’t because their blood types don’t match, to exchange organs with other incompatible donor pairs. At this point the numbers of kidneys transplanted using Roth’s system is small, fewer than 1,000 in 2009. But the potential is promising. “Al’s work on kidney matching is one of the few great modern advances in transplant policy,” says the American Enterprise Institute’s Sally Satel.

Practical work like this impresses Roth’s colleagues. “Al is amazing,” says Duke professor and behavioral economist Dan Ariely. “I would say I’m his biggest fan, but there are too many people who claim that title.”