AUTHOR SPOTLIGHT

In Conversation with...

ALVIN E. ROTH

Improving the human condition may not be the first thing most people think of when they ponder game theory and complex algorithms. But Al Roth is not most people. Raised by parents who were schoolteachers in New York, Roth was bored in high school, to the point where he dropped out after his junior year. Undaunted by an unchallenging school system, Roth had enrolled in classes at Columbia University where he ultimately earned his undergraduate degree in operations research in the engineering school. Prodded by one of his professors (Cyrus Derman), he applied to and was accepted at Stanford University, where he went on to earn his doctorate in operations research. That was the first inkling of good things to come—Roth’s technical knowledge and understanding of market design would have served him well in jump-starting a brilliant career in private industry. Instead, he focused his energies on operations research and changing the world, because, as he said in a 2012 interview with Forbes [1], “I look around the world, and I see all kinds of interesting, important problems we ought to solve with the tools we have.” Roth went on to use his knowledge of complex markets to redesign, in 2003, the public school matching program within the New York City school system, thereby improving the lives of hundreds of thousands of students by providing them more academic options. His revolutionary design reduced the number of students who had to be matched to schools over which they had expressed no preference from 30,000 to 3,000 (out of about 80,000 new high school students each year).

Roth, who is the Craig and Susan McCaw Professor of Economics at Stanford as well as the Gund Professor of Economics and Business Administration Emeritus at Harvard University, has authored numerous papers in Mathematics of Operations Research (MOR). He also volunteers his time and expertise as an Advisory Editor for the journal. INFORMS caught up with Roth in the Fall of 2016. As shown in the interview below, Roth’s bent to do good “with the tools we have” is a common thread that spans his career.

INFORMS:  Your first published paper, “Subsolutions and the Supercore of Cooperative Games,” [2] based on your doctoral thesis, appeared in MOR in 1976. The paper was handled by Nobel winner and MOR Founding Area Editor Robert Aumann. Can you share with us how your first experience with the peer review process went?

ROTH:  I recall that experience vividly. Aumann, in his editor’s letter, told me to ignore the referees, but to revise the paper along the lines he would describe. One revision he wanted had to do with the proof of my main theorem, for which I had used Zorn’s Lemma. He advised me to try to construct a proof which instead used transfinite induction. I didn’t know what transfinite induction was, so I was very skeptical, but I grimly trudged to the math library and got a copy of Hausdorff’s book Set Theory [3] to repair this gap in my education. I still remember how my hopes lifted when I opened the book and saw that it had been translated from the German by…Aumann. It turned out that he knew what he was talking about, and the proof that appears in my published MOR paper uses transfinite induction.

INFORMS:  In college, why did you decide on an operations research (OR) major rather than, say, economics or mathematics?

ROTH:  I was drawn to OR because I wanted to make things work better.

INFORMS: Who was your mentor while completing your doctoral thesis? Can you provide any advice for young researchers seeking a mentor?

ROTH:  My dissertation supervisor was Bob Wilson, and he was a great advisor. My advice to young researchers is that they should choose mentors whose work they admire and who can advise them on work that they think they will enjoy doing.

INFORMS:  Whose work influenced your research most? Can you cite some specific papers that shaped your early research?

ROTH:   Bob Wilson’s approach to game theory and economics certainly had a profound influence on me. One paper [4] that influenced my work a lot is:

Gale D, Shapley LS (1962) College admissions and stability of marriage. Am. Math. Monthly. 1962:69(1):9–15.

INFORMS: You were instrumental in launching the economics field of market design, a confluence of game theory and experimental economics. Can you describe how market design improves outcomes and stakeholder satisfaction in matching programs?

ROTH:  Marketplaces are tools that people use to help us coordinate and compete and organize ourselves to mutual benefit. But to do that well, marketplaces have to attract people to participate (i.e. to make a thick market), they have to help participants deal with the congestion that can arise when the market is thick enough to have lots of transactions that can potentially be considered, and they have to make the market safe to participate in. The ‘magic of the market’ doesn’t happen by magic, so there are lots of markets that don’t work well, and that don’t produce the benefits that they could. Proposing new rules for existing marketplaces, or new marketplaces, can sometimes help that along. (Compare the traditional markets for taxis, organized around taxi licenses issued by municipalities and the recent rise of Uber, for example.) Of course, market conditions change, and the behavior of participants change, so markets have to be monitored and changed themselves when they stop doing what we want them to do.

INFORMS:  Your work in market design resulted in vast improvements to several algorithmic-based matching systems, the first being the National Resident Matching Program for medical students applying for residency programs at teaching hospitals. Your process reduced the chances of students “gaming the system” and offered married couples better placement options. What flaw(s) in the market (i.e., thickness, safety, or congestion) did your enhanced algorithm correct? And was there an “ah-ha” moment in your research that helped determine the solution?

ROTH:  When I first learned that new American doctors got their jobs through a centralized clearinghouse, I understood that there would be game-theoretic issues in understanding how it functioned, and that I could probably learn a lot by studying the medical match. As I looked into how the labor market for new doctors has evolved over time, I did indeed learn a lot, including about problems that the market was experiencing, such as how to effectively help doctors who were married to other doctors to find two jobs together.

INFORMS:  You then applied market design methodology to kidney exchange programs as well as public school–matching programs. What are some other real-world settings that market design has positively influenced?

ROTH:  Market design is an ancient human activity, and there’s almost nothing we do when we’re not alone that isn’t touched by some market. Maybe that’s not apparent because we often think of commodity markets when we think of markets, and commodity markets (which also require lots of design) are markets in which prices do all the work in deciding who gets what. But many markets are matching markets in which you can’t just choose what you want, even if you can afford it, but in which you also have to be chosen. For example, you can’t just attend Stanford, you have to be admitted; you can’t just work for Google, you have to be hired. So when you start to think about matching markets as well as commodity markets, you can see that some of the most important decisions in our lives are mediated by markets: where to study, where to work, who to marry (you can’t just choose your spouse, you also have to be chosen). I wrote a general interest book on all this, called Who Gets What—and Why [5]. I’ve devoted a lot of my own work to labor markets, school choice, and kidney exchange. But lots of modern market design involves the design of auctions (big ones for electromagnetic spectrum, and frequent ones for internet advertisements) and pricing.

INFORMS:  Can you define the term “repugnant transactions” and provide an example? How do game theory and market design propose to resolve a morally reprehensible option that also has an upside to society?

ROTH:  I became interested in forbidden transactions by studying kidney transplantation. There are about 100,000 people in the U.S. on the waiting list for a deceased-donor kidney, but we only manage to do about 11,000 deceased donor transplants a year, and in addition not quite 6,000 living donor transplants (which are possible because healthy people have two kidneys and can remain healthy with one). When economists see a long queue for a scarce good, they suspect that a higher price might elicit more supply. But it’s against the law just about everywhere in the world to pay for a kidney for transplantation (with the exception of the Islamic Republic of Iran, which has a legal market for living donor kidneys). That is, by law, the price of a kidney must be zero; it must be a gift.

So (along with helping organize kidney exchange, which helps achieve more transplants without involving payments) I’ve also been studying “repugnant transactions,” by which I mean transactions that some people want to engage in, and others don’t think they should be allowed to, even when the others can’t detect that the transaction has taken place unless someone tells them. There are lots of these (think about same-sex marriage, for example), and they can be different in different places, change over time (in both directions), and be very consequential (like the medieval ban on charging interest on loans).

INFORMS:  Shifting gears, in 2012 you and Lloyd Shapley won the Nobel Prize in Economic Science “for the theory of stable allocations and the practice of market design” [6]. Was your share of the 2012 Nobel Prize based in part on your 1982 MOR paper [7]?

ROTH:  Yes indeed, that paper is discussed by the Nobel Committee on pages 12 and 13 of their Scientific Background document [8].

INFORMS:  What motivated you to initiate this research?

ROTH: I heard that new medical doctors got their jobs through a centralized clearinghouse, and it seemed to me that there would be a lot of game-theoretic issues associated with such a marketplace.

INFORMS:  In awarding the prize to both you and Shapley, did the Nobel Committee articulate why the prize was shared? Did your work build on Shapley’s work?

ROTH:  Indeed. One of the first things I found when I looked into the organization of the medical match was that the 1950s match algorithm was different from but equivalent to the deferred acceptance algorithm proposed in Gale and Shapley’s famous [4] paper. The Nobel Prize press release [9] stated, “Even though these two researchers worked independently of one another, 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. This year's prize is awarded for an outstanding example of economic engineering.”

INFORMS: How has your life changed since winning the Nobel?

ROTH: I’ve become much busier and apparently much more photogenic as well.

INFORMS: What projects are you working on currently?

ROTH:  I’m still deeply involved in expanding kidney exchange, and in trying to understand repugnant transactions. I’m also starting to try to understand the issues involved in effective refugee resettlement, since that’s a matching market that isn’t working very well.

INFORMS: What is the best advice you can give to students entering the field of operations research?

ROTH:  Try to find important problems that you also enjoy working on. It’s not enough merely to work on important problems that are worth solving, you also have to enjoy the work you’re planning to do, because if you don’t enjoy it you are unlikely to be able to work as hard as you will need to.

INFORMS:  Tell us something that few people know about you.

ROTH:  The most unusual honorary degree I’ve received came not from a university but from a sport: I am an honorary 7th Dan black belt in Shotokan style karate, a martial art that I engaged in when I was in college.

References

1. Adams S (2012) What Al Roth did to win the Nobel Prize in Economics. Forbes (October 15), http://www.forbes.com/sites/susanadams/2012/10/15/what-al-roth-did-to-win-the-nobel-prize-in-economics/2/#5113fef7e445. 
2. Roth AE (1976) Subsolutions and the Supercore of Cooperative Games. Math. Oper. Res. 1(1):43–49.  
3. Hausdorff F (1957) Set Theory (New York, AMS Chelsea Publishing Co.). 
4. Gale D, Shapley LS (1962) College admissions and stability of marriage. Am. Math. Monthly. 1962:69(1):9–15.  
5. Roth AE (2015) Who Gets What—and Why: The New Economics of Matchmaking and Market Design. (Boston, MA, Houghton Mifflin Harcourt). 
6. Royal Swedish Academy of Sciences (2012) The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2012. Retrieved from http://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/2012/. 
7. Roth AE (1982) The economics of matching: Stability and incentives. Math. Oper. Res. 7(4):617–628. doi:10.1287/moor.7.4.617.  
8. Royal Swedish Academy of Sciences, Economic Sciences Prize Committee (2012) Scientific background on the Sveriges Riksbank Prize in Economic Sciences in memory of Alfred Nobel 2012. Retrieved from http://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/2012/advanced-economicsciences2012.pdf. 
9. Royal Swedish Academy of Sciences (2012) The prize in economic sciences 2012 - Press release. (October 15), http://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/2012/press.html.  

 

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