Alvin Roth On Matching Markets, Economic Engineering, & How Economics Has Changed In Recent Decades

Alvin Roth is the Winner of the 2012 Nobel Memorial Prize in Economics.

He is the Craig and Susan McCaw Professor of Economics at Stanford University & the Gund Professor of Economics and Business Administration Emeritus at Harvard University. He was the President of the American Economic Association in 2017.

By Aiden Singh, April 24, 2025

Introduction

In 2012, Professor Alvin Roth was jointly awarded the Nobel Memorial Prize in Economic Sciences for ‘the theory of stable allocations and the practice of market design’.

Professor Roth’s early research focused on game theory and on economic experiments which tested game-theoretic ideas.

Of particular interest to Professor Roth were ‘matching markets’ - markets such as university admissions or medical residency allocation in which price adjustments alone don’t clear the market.

As a game theorist, Professor Roth demonstrated the difficultly of achieving outcomes in matching markets in which both parties to a transaction are satisfied. 

Among the obstacles to achieving such ‘stable matches’ in matching markets are situations in which annual markets ‘unravel’. Such a situation can arise when, for example, competition for the best doctors pressures residency programs to make offers to medical students earlier in their training (e.g. year 3 of medical school instead of year 4). The earlier offers mean that programs are proffering residencies to students with less information about how good of a doctor that student will ultimately become and students are faced with accepting or declining earlier offers without full information about which offers they may later receive if they wait.

Another obstacle to achieving ‘stable matches’ in matching markets is the ‘couples problem’. This situation arises when, for example, a married couple of newly-graduating doctors needs to find two medical residencies in the same geographical area, making the challenge of matching these graduates to residency programs more complicated.

Only fitting then that, having spent the early part of his academic career theoretically demonstrating how difficult the problem of achieving stable matches can be, Professor Roth would spend much of the rest of his career designing and redesigning matching markets in an to attempt to overcome the problems he had identified. As Professor Roth puts it, ‘In my role as a theorist, it had been enough to note that [matching] couples [to residency programs] therefore presented a hard problem. In my new role as a market designer, they would become my problem.’

Professor Roth was asked to help redesign the National Resident Matching Program which matches newly-graduating medical doctors in the United States with residency programs. The algorithm that he co-developed for the Program continues in use today.

More recently, Professor Roth has worked on facilitating exchanges of donor kidneys.

Professor Roth continues to be a proponent of ‘the economist as engineer’, arguing that economics can be used, not merely to theorize about how markets work, but also to help design and improve them.

In our conversation, we discussed the evolution of Professor Roth’s career from a theorist and experimenter to a practicing ‘economic engineer’. We also discussed his views on the role of economics and his thoughts on how the discipline has evolved over the years. 

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Game Theory

Aiden Singh: What initially drew you to game theory as an approach to understanding human interaction?

Alvin Roth: So in the early 1970s I was a graduate student in operations research PhD program at Stanford. And a lot of the point of view of operations research in those days was that you're interested in the operations of a single company and it's got some well-defined set of objectives, and you're trying to maximize something. So we had courses with names like inventory theory and reliability theory which were meant to think about how you should run your warehouses and how you should replace your equipment and maintain it.

And we had no regular course on game theory, but Michael Maschler visited from the Hebrew University in Jerusalem and gave a course on game theory and I thought: this is for me.

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Experimental Economics

Aiden Singh: In addition to your work on game theory, your early research also focused on experiments that say something about game theory. What sparked the interest in the experimental approach?

Alvin Roth: So I wrote a game theoretic dissertation without any experiments. And in 1974 I took a position as an assistant professor at the University of Illinois.

And in 1974 Keith Murnighan graduated with a PhD in social psychology.

He and I got along in many dimensions. And one of the things we decided to do was see whether the things I'd studied in my dissertation played out in laboratory conditions. Experiments allowed us to test which abstract models play out in the lab and which didn’t. And it gives you a way to see what ideas you might want to explore further.

Aiden Singh: You’ve said that the axiomatic theories of the sort developed by game theorists such as John Nash didn’t account for the results you found in your early experimental work. How so?

But one of the things you notice immediately in the lab is that if you remove the abstraction and put the dollar back into it - if people know that they're bargaining over a dollar - that affects things. 

Now, it’s easy to see how much of a dollar each person in the bargaining situation gets, but it’s hard to see what a person’s utility for getting a certain amount of money is.

But in the laboratory, if my prize was worth $20 and your prize was worth $5, you would pretty quickly send me a message that said my prize is worth more than yours, so it’s only fair that you should get more probability. 

And so we started studying phenomena like that which weren't captured at all in Nash's model.

Aiden Singh: So you’ve conducted game-theoretic research and experimental research. And you’ve found that the results of these two methodological approaches don’t always line up. Given that, how do you currently view the relationship between game theory and experimental economics?

Alvin Roth: They're complementary. Theoretical physics and experimental physics aren't competitors; they’re complements to each other. You try to think about what might be happening and then you use experiments as a way to gain evidence. And that's how it is with game theory and experiments also.

Aiden Singh: So if you were designing the curriculum for an economics degree today, I figure your ideal scenario would include economics majors being exposed to both methodological approaches?

Alvin Roth: I think that's right.

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Matching Markets

Aiden Singh: Much of your game-theoretic research focused on matching markets and demonstrating how difficult achieving ‘stable matches’ can be. 

Can you explain what ‘matching markets’ are, what constitutes a ’stable match’ and why such matches can be difficult to achieve?

Alvin Roth: So let's start by taking a step back and first thinking about what a commodity market is.

A commodity market is one in which prices do all the work. 

So, for example, if you want to buy 5,000 bushels of hard red winter wheat, you can do so on the Chicago Board of Trade. And you wouldn’t care who you buy it from and the seller wouldn’t care who they're selling it to. And the commodity is well-defined: there’s an agreed upon definition of what constitutes hard red winter wheat. And so you can make a whole market for this commodity. And what matters in this commodity market is the price. And the job of the market is to find prices at which market clears - that is, at which supply equals demand and transactions take place.

And economists have spent most of the last couple of centuries thinking about markets as if they were perhaps all commodity markets.

But when you try to hire someone or get hired, that's not a commodity market: unlike in the case of the commodity market for hard red winter wheat, in the labor market both sides care who they're dealing with. An employer makes job offers to particular individuals and job seekers look for offers from particular employers. And so there's a relationship being formed - a match between the employer and the job-seeker. In other words, it’s a matching market rather than a commodity market. 

And matches are not easily viewed as commodity markets. Of course, you can twist yourself around to try to say that matches are also commodity markets. You could point out that there are prices for labor because jobs pay wages.

And a ‘stable matching’ occurs when there isn’t some other job that an applicant would have preferred and that would have preferred to hire that applicant but the market didn't match. There may be other jobs the applicant would have preferred, but that other employer preferred to hire other people. And there may be other employers who would have preferred to hire an applicant other than the one they hired, but that applicant preferred the job they took. So that scenario is called a ‘stable matching’.

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Applying Game Theory To The Study of Matching Markets

Aiden Singh: Why is game theory, as a methodological approach, conducive to studying the problem of achieving stable matches?

Alvin Roth: Well, game theory is conducive to studying the rules that make markets function - the 'rules of the game’. It’s good for studying market design and the rules by which markets are designed.

So when economists were just thinking about competitive equilibrium, we’d say, ‘well, the market determines a clearing price that has certain properties and then we can deduce things about those properties’. 

But a lot of my initial work focused on markets that have centralized clearing houses because, in order to organize a centralized clearing house, you have to make the rules very clear.

So for example, in a market like the National Resident Matching Program - the market for newly-graduating doctors in the United States - both the employers and the employees submit rank-order lists. So they submit a first choice, a second choice, and a third choice. And then an algorithm produces the matching between the employees and the employers. And you can study the algorithm, which is a central part of the architecture of the market, and see what whether it produces stable matchings or not. So you can study the rules of the market and the consequences of those rules.

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Redesigning Markets

Aiden Singh: You spent the early part of your career studying matching markets - what’s required for the production of stable matches, how to make matching markets ‘thick’, and how they can unravel. 

And, having demonstrated theoretically the challenges to operating well-functioning matching markets, you were then tasked with attempting to overcome these problems in practice. You’ve mentioned the National Resident Matching Program. Can you share with our audience some of the other matching markets you’ve helped redesign?

Alvin Roth: Well, there's the medical labor market - the national resident matching program for new doctors. And there are similar clearing houses for many medical specialties. Some similar markets are also employed now in Britain and elsewhere. 

There's also school choice, which turns out to be mathematically a first cousin to these medical labor markets. So in New York City, Boston, Denver, New Orleans and a bunch of other American cities, my colleagues and I have helped organize school choice where families submit rank order lists of where they'd like the kids to go and the schools have some rule for assigning priorities to kids. And we helped the students and the schools match. 

I'm doing some work on the market for new economists. That market is in a little bit of transition right now because, like a lot of labor markets, interviews moved to Zoom during Covid. It used to be that interviews were conducted at our national meetings the first weekend in January. And having the interviews all tethered to the meetings affected the timing of all the other things in the market. But now that everyone is doing Zoom interviews, it's no longer tethered to a particular time of year. As a result, we're seeing the market get a little more diffuse, which may cause some problems. So I'm trying to understand those markets.

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Redesigning The Matching Market For Medical Residency Programs

Aiden Singh: One area I’d like to focus on in particular is your work redesigning the National Resident Matching Program, which asked you to redesign the algorithm it used to match graduating medical doctors with residency programs. 

Can you share with us some of the difficulties the program was faced with when it decided to reach out to you?

Alvin Roth: Well, I’d been studying the topic. And I have a visceral memory of that phone call. I was in my office in the University of Pittsburgh and the director of the match in those days was a guy named Bob Baron. And he said they were having problems and asked if I would help them fix it.

And I realized that I really didn't know very much about it even though I'd been studying it. 

And part of the reason was that it was perfectly okay when I thought of myself as a game theorist to say, ‘here’s how the market for new doctors works, here are some of the problems they have, and here's an indication of why those are hard problems’. 

And a particular problem that I'll mention is that an increasing number of medical students were married to their classmates. So they were married couples looking for two jobs. And when I had game-theoritically studied stable matches for married couples looking for two jobs, instead of getting nice results that said a stable matching always exists, I got a result that said if some households are two career couples looking for two jobs, then a stable matching might not even exist.

And that was a perfectly fine ending to a paper that I had written years before in the Journal of Political Economy. But of course, it didn't help solve the problem. It just identified the problem. And as a theorist, I was doing my job when I identified the problem. 

But to take responsibility for the problem was going to be something new.

And the reason this problem came up was, when the market for residencies started to get organized in the 1950s, there were hardly any women graduating from American medical schools. And today a bit over 50% of medical students are women. So today quite a few couples go through the residency match. And it presents a real challenge to try to find stable matches to residency programs for those couples.

Aiden Singh: How ready did you feel to take on this task when it was given to you?

Alvin Roth: Well I didn't feel ready at all. But I could see that the correct answer to the question of ‘will you try to do this?’ was to say ‘yes’. 

Economics is about markets and marketplaces and how people coordinate with each other. And if I was going to be serious about this topic, I should undertake the task.

And that's been very rewarding for me. That was the moment at which I went from being a game theorist to being a market designer -  from being an economic theorist to being an economic engineer. 

Aiden Singh: The algorithm that you devised is still in use. Can you tell us about the algorithm you came up with and how it overcomes the challenges the Resident Matching Program was facing?

Alvin Roth: Sure. What I’ll do first is describe the very simple algorithm that Lloyd Shapley and David Gale talked about in their famous 1962 paper called College Admissions and the Stability of Marriage, which the Nobel Prize Committee cited Shapley for.

The marriage model they outlined is a matching model between men and women which you could think of as a mnemonic for everybody on each side wants to match with just one person on the other side. 

And then their college admissions model was was more like a labor market: each college wants to admit many students but each student wants to only attend one college. 

So they had two very closely related two-sided models. You can always tell who are the men and who are the women or who are the colleges and who are the students. 

And let me mention that that's an important point because we can think of a lot of markets as if they were two-sided because they're two-sided in any given realization. If you go on the New York Stock Exchange and you look at the trades, you'll find some people buying Microsoft stock and some people selling Microsoft stock. So there are buyers and sellers. But that's not a structural part of the model: at a given price, I might be a buyer, and at another price, I might be a seller. So you have to build that into your model. 

But in a labor market, it's not a terrible assumption to say that there are firms and workers, and you can tell who is who. 

It’s not a perfect assumption. For example, I work in the labor market for college professors and if the wage for college professors fell low enough, I might no longer be in the market. But it's hard to imagine the wage getting so low that I would enter the market on the other side and become a university. It's not impossible - but we're not missing a lot of the action if we ignore that possibility. 

And so by saying that there are firms and workers - universities and professors - you get a lot of extra structure that can help you get some results. 

So here's Gale & Shapley’s deferred acceptance algorithm.

And the reason why it’s a ‘deferred acceptance’, is because it tells you a process by which people make acceptance decisions, but the acceptance decisions will only come at the end: they’ll be deferred until a college or a firm (as the case might be) sees that no more applications are coming in.

And I'm going to tell you this as if people were taking sequential actions, but the way to understand it is as the operations of an algorithm.

The actions people are going to take are as follows. People applying to a school are going to list their first choice, their second choice, their third choice, and their fourth choice. And people admitting students are going to list the students in order of preference or priority. So that's the actions that the two sides - the students and the schools - will take. 

And then the algorithm is going to operate on those as follows. 

Every applicant applies to his or her first choice. And every school orders the applications according to its preferences or priorities. And, if the school is up to capacity already, it rejects all the others. But it doesn't accept the ones it hasn't rejected yet. It's going to defer acceptance until the end. 

And what happens next is that the people who were rejected, they now apply to their next choice. And the schools that get new applications don't care about when they got them; they just care where the applicants are in the school’s preference list, and they order them. And some of the new applicants may bump some of the older applicants. And every applicant who's below the preference threshold for the capacity of school is rejected.

And that keeps going: every applicant who's rejected applies to their highest-ranked school that hasn't rejected them yet and every school holds on to its highest-ranked applicants that it's gotten so far - regardless of when it's gotten them - and rejects the rest. 

And the algorithm only stops when there are no more applications - when each applicant has either had his/her application held by a school or has run to the bottom of his list and has no more places he or she wants to apply to. 

And then the algorithm stops.

Now every school accepts the applicants whose applications it's holding at the end. (In other words, the acceptances have been deferred until this point.) 

And this algorithm produces a stable matching.

And the way to see that is the following.

Suppose I am an applicant and at the end of this process, I am matched to my second choice school. I would prefer to go to my first choice school and, if my first choice school would also prefer to have me rather than some other student it accepted, then the algorithm will be unstable. But how did I get matched to my second choice school? Well, first, I applied to my first choice school and they rejected me when they could fill all their places with people they like better than me. So I may prefer to go to them, but they don't prefer to have me. So we're not a ‘blocking pair’ - a pair that would be happier together causing the match to be unstable. We don't produce an instability. So that's the proof.

So we use algorithms like that in New York City schools and in other school districts around the country. And it produces a stable matching. 

Now when you think about applications for residency programs, some of the applicants are couples.

And one of the important innovations is that you can't just ask each member of the couple what they would like. You have to ask the couple what's your first choice, what's your second choice, and so on. I call it the ‘iron law of marriage’ which says that you can't be happier than your spouse. 

So spouses who are applicants for residency have to create a rank order list of pairs of positions. So my wife and I might say, our preferred first two positions are these two jobs in Boston and our second preference is these two jobs in New York and our third preference is these two jobs in Denver, and so on.

So now we go through the deferred acceptance algorithm, and my wife and I apply to our first choice, say, two jobs in Boston. And if the two jobs like us, they hold our applications and they reject some other people.

But now suppose some third person gets rejected somewhere else, maybe San Francisco. And that person’s next choice is the job that's holding my application. And suppose the job that’s holding my application prefers that person over me. So they reject me. 

Well now the algorithm has to give me and my wife, as a couple, a chance to apply to our next choice - and our next choice is two entirely different jobs in a different city. 

So the algorithm now has to withdraw my wife from the place that's holding her application. 

But in order to hold her application, they had to reject other people's applications. And since they're not going to hire my wife - she’s going to some other city with me - they would now prefer to hire them. So there are potential blocking pairs. In other words, the proof I gave you earlier that produced a stable matching in the simple case with no couples is now going to fail. There will be people who prefer the residency program that rejected them in favor of my wife and the residency program would now prefer to hire them rather than whoever they hired after my wife’s application was withdrawn because she’ll be going to another city as part of a couple. 

So the algorithm that produces stable matchings when there are no couples no longer produces stable matchings when there are couples. And so the deferred acceptance algorithm leaves you with a bunch of instabilities that you have to fix. 

And years ago, I'd written a paper with John Vande Vate in Econometrica that gave an indication of how you might fix one error at a time - one blocking pair at a time. 

And that's what we now use in the National Resident Matching Program. 

And because stable matchings might not always exist, you can create examples where things might not converge to a stable matching. But it turns out those circumstances are extraordinarily rare, so that's not a practical problem.

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Designing New Markets

Aiden Singh: More recently, you’ve moved beyond redesigning existing matching markets to working on designing entirely new markets. 

In particular, you’ve helped develop kidney exchanges for those in need of donor kidneys.

You’ve described markets in which people pay for organ donations as ‘repugnant markets’. Why might they labelled as such?

Alvin Roth: I use the term repugnant transactions to talk about transactions that some people would like to engage in and other people think they shouldn't be allowed to for moral or ethical reasons.

In the U.S., the National Organ Transplant Act of 1984 says you can't pay donors for their kidneys.

And one consequence of that is that there aren't enough kidneys for transplant. In the United States alone, we have about a 130,000 people each year who are newly diagnosed with kidney failure. And transplant would be the treatment of choice. But we do fewer than 30,000 transplants a year. So that means every year, there are 100,000 people who could potentially use a transplant but are going to die without one. So we have a big shortage and a long waiting list.

There are more than 500,000 Americans on dialysis right now, and somewhat over 90,000 of them are registered at some hospital on the waiting list for an organ. But remember, we do fewer than 30,000 transplants a year. So there would be more people on the waiting list if they had more prospect of getting a transplant. 

And when economists see long lines for something, we can detect that prices aren't being allowed to help increase supply. And that's exactly the case here: the National Organ Transplant Act says that you can't pay for a kidney. 

So the question that my colleagues and I started to to think about was: if we can't pay for kidneys, can we still increase the number of transplants?

I should take a step back and say that transplants can come from dead donors.

But kidneys are unusual because they can also come from living donors: healthy living people have two kidneys and can remain healthy with one. So if someone has kidney disease, someone who loves them enough can save their life by giving them a kidney. 

But remember, kidneys have to be well-matched to the recipient. So someone might love me enough to give me a kidney but is not be actually able to do so because their kidney isn't a immunological match for my physiology.

And so kidney exchange saves a lot of lives, but not enough.

So the idea of ‘repugnance’ in this context is that paying for kidneys is a morally-contested controversial market.

And I'm spending a good deal of my time studying other related areas as well. 

So in the United States, for instance, it's legal to pay, and we do pay, donors of blood plasma. 

And blood plasma has become increasingly important in medical care - it’s on the World Health Organization's list of essential pharmaceuticals.

But many countries don't allow plasma donors to be paid, and those countries almost uniformly fail to generate enough plasma from unpaid donors in their country to fill the medical needs of their patients. 

But, by and large, there isn't a terrible worldwide shortage, at least not in the developed world, because those countries buy plasma from the United States. We're the Saudi Arabia of blood plasma. We export tens of billions of dollars of plasma products each year. So, it might be time to rethink questions of how generous we can be to kidney donors as well because there's a terrible shortage of kidney transplants.

Aiden Singh: You helped form the New England Program for Kidney Exchange. What were the challenges faced in setting up such an exchange?

Alvin Roth: The first thing was we had to convince doctors that it was worthwhile listening to economists. It turns out doctors don't automatically think of economists as fellow members of the helping professions. And that's been true generally for lots of things.

Certainly in my career, very few medical people have come to me and said, ‘We can use your help’. 

Although, as we talked about I got a call from the residency matching program. 

But kidneys was a bit of a tough sell. That was one of the things we had to convince our medical colleagues in Massachusetts of. 

But lately, it's become a standard part of care. So that's become less difficult to talk about. 

Aiden Singh: And you briefly alluded to the idea of chains, when you were explaining the market for kidney donations. What are ‘long non-simultaneous chains’?

Alvin Roth: So when we started, the way I explained exchange was I have a donor who can't give to me but might be able to give to you, and you have a donor who can't give to you but might be able to give to me, and we can exchange as a pair. 

But that's hard to scale up because it's logistically difficult - we do exchanges like that simultaneously and that's part of what makes it logistically difficult. Four operations are needed: two nephrectomies taking the kidney from the donor and two transplants. And we do them at the same time to make sure that both parties get a transplant - to make sure that nothing intervenes between one transplant and another that leaves some pair having donated a kidney but not having gotten one. 

But we have a couple of hundred non-directed donors a year in the United States. Non-directed donors are people who want to give a kidney but don't have a particular recipient in mind. So they're exceptional altruists of a certain kind, but not so vanishingly rare that they aren't important. They’re very important in kidney exchange because they allow us to organize chains of transplant in which every pair gets a kidney before they give one because, being non-directed donors, the chain doesn't have to loop back to them: they don't have a particular patient who has to get a kidney in response to their donation.

And so you can have non-simultaneous chains because the harm of a link breaking is much less than if some pair had already given a kidney and then didn't get one. This is everybody gets a kidney first, and then if the chain breaks, that's disappointing, but the pair that was expecting a transplant at that point still has a kidney. Their the donor still has a kidney. They can still take part in subsequent kidney exchanges. 

So a big percentage - at some time it was more than half, and it may still be - of the more than 1,000 kidney exchange transplants that take place each year in the United States are parts of chains.

And one reason is that chains can be long. There have been chains with 60 people in the picture, although most chains are shorter than that. 

But another reason is that some patients are very hard to match: it’s very hard to find a kidney that's good for them. Those are patients that have lots of antibodies to human proteins. And so, even if there's a blood-type compatible kidney, they probably can't take it because they have so many antibodies. And for them, finding a kidney is like finding a needle in a haystack. Supposing you and I both represent highly-sensitized hard to match pairs, it's very unlikely that my pair can give to your pair because you guys are highly-sensitized: you can only take very hard to find kidneys. And even if we could give you a kidney, the chance that you could give one back to us is very small because there's only a very small chance we can take any kidney. 

But supposing now we're in a big dataset - a big room full of hard to match pairs. The chance that my pair can give a kidney to someone in the room is not so bad because, even if a highly-sensitized person only has a one in a hundred chance of being able to take a kidney, if there are 500 people in the room, the chance that my pair can give a kidney to someone in the room is not so small. And they can't give a kidney back to us for the same reason: we can only take one in a hundred. But the chance that they can give a kidney to someone else in the room is not so small, and that they can give it to someone else, and that they can give it to someone else. And that's how long chains form. 

So not only do long chains facilitate a bunch of transplants because they're long - each link in the chain is a transplant - but they allow us to reach hard to reach pairs that couldn't have been reached in simple two-way or three-way exchanges. So that's why chains are important.

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Economic Engineering

Aiden Singh: Zooming out from specific markets and towards your philosophy of and approach to economics, you’ve advocated for the idea of economist as engineer. Can you tell us what economics as a discipline looks like under this vision? How does it differ from economics as a discipline today?

Alvin Roth: The answer to the first question is: I don't know what that's going to look like as a discipline. 

But one way that economics looks as a discipline today is, when you read a paper in an economics journal, most of its references are often to other papers in economics journals. 

But when you're studying something like kidney transplants, you have to learn about the detailed rules of kidney transplantation. So some of my papers on kidney exchange have been in economics journals, but many of them are in medical journals. And the reason is that the people we're trying to to help take care of their patients are transplant surgeons. And they're not interested in theorems about stability. They're interested in reports about surgeries that have been done. And that's who my colleagues and I have to talk to if we want to be persuasive to kidney surgeons.

So one possibility for literatures is that it will spread out into application areas. When Archimedes was a physicist and an engineer, if there were journals in those days, presumably, he would have published papers about bridges in physics journals because bridges depend on physics. But, of course, today, people who want to build bridges still depend on physics, but they publish in journals of civil engineering - and not just journals of civil engineering, but journals of civil engineering that have a lot of papers on bridges. 

So it's possible that market designers will to have to go out and talk to the people whose markets they're trying to help design in non-economics journals.

So I don't know what the future disciplinary boundaries are going to be.

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The Changing Scope of Economics

Aiden Singh: You’ve told the story of how, in the early 1980s, you submitted for publication an article on matching markets which was rejected by the Journal of Political Economy.

At the time, the editor of the journal, George Stigler, who shortly thereafter won the Nobel Prize in Economics, declined to accept the paper for publication because he was of the view that a clearinghouse is not a marketplace if it doesn’t use price/wage adjustments to clear the market. 

In other words, for Professor Stigler, matching markets weren’t really an appropriate topic for consideration by economists. 

And you therefore ultimately published that paper in the Journal of Mathematics of Operations Research. 

But by 2012, you had won the Nobel Prize in Economics for your work on matching markets.

What are your thoughts on how economics has developed over the last few decades in terms of the scope of the topics economists conduct research on?

Alvin Roth: Matching markets have become a much more central topic in economics. 

Professor Stigler, who won the Nobel Prize himself thirty years before I did, was at the University of Chicago which was known for developing price theory. In a certain sense, they were showing how flexible price theory was and how you could think of almost all markets as if they were commodity markets that could be cleared by price alone. 

And so when he got my paper, which didn't have price clearing in it, his reaction was that it wasn't really economics. He wrote me a nice letter saying something like, ‘Your paper is very interesting, and I can see you worked very hard on it and got interesting results, but the only economics is in the title’

But not too long after that, the journal, with him no longer as editor, published my first paper on the medical match. So once it was put in the context of here's a labor market of doctors and hospitals trying to hire them, then it became more apparent that it was indeed economics - it’s a market.

And today we talk about matching markets all the time.

Many markets are not commodity markets and shouldn't be modelled as commodity markets because you can learn more about them by modelling them in a way that has more connection to how they work.

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The Nobel

Aiden Singh: I’ll close by asking two questions I posed to your doctoral advisor and fellow Nobel Laureate Professor Robert Wilson during my conversation with him.

Who is someone who has not won a Nobel Prize yet that you think deserves one?

Alvin Roth: Let me first say that there are lots of people who would be great candidates.

That being the case, one of the ways to look at it is to consider the things that didn't used to be important but are becoming important in economics.

And one of them is the study of networks. And so a favorite pair of candidates of mine are our Stanford colleagues, a sociologist and an economist. So Mark Granovetter, who's a sociologist who wrote a paper years ago about the strength of weak ties and about how people get jobs through connections - but not through their closest connections, but through their more distant connections. And, my colleague in the economics department, Matthew Jackson. I think that would be a great pair to show how network analysis migrated from sociology to economics, where it's blossomed. That's one that I would feel very cheerful about if it were to happen.

But lots of people could and should get the Nobel Prize. The Nobel Prize Committee has a limit - they can only give a maximum three prizes a year. If I were on the Committee, I would work hard to give three at a time.

Aiden Singh: If you were an newly-minted economist looking to make a name for yourself today, what areas of research might you be focusing on? 

Alvin Roth: Well, I think market design still has a lot of promise. I think it's a big part of the future of game theory.

Another area would be the intersection of economics and computer science. When I talk to you about market design, I'm talking about designing the rules of the market. But we're rapidly nearing and passing the point at which we can also talk about designing the agents in the market. For example, there's already lots of algorithmic trading in financial markets and there's going to be more and more. 

You're going to have agents that can do what a human secretary used to do a few years ago - things like booking travel, making sure to use the frequent flyer miles, and so on. There's no reason to think that we won't be seeing that fairly soon.

And that's going to change markets. It'll change advertising. To advertise to an AI is going to be different than to advertise to a human being. But you'll need to advertise them. You'll need to let them know what flights you're offering if you're an airline, for example.

And just in general, of course, computers already play a big role in the economy. So I think it's going to be important for economists to be literate in computer science - just as it's becoming important for computer scientists to be literate in economics.

There's an annual conference called EC, which stands for Economics & Computation, run by computer scientists and and economists. This year it’ll be held here at Stanford. And years ago, it was called EC and it stood for electronic commerce - a much more limited set of subjects. So you can already see that the connection between computer science and economics is growing and I think that's going to continue.

Aiden Singh: Bonus question: if a young economist were to take you up on this suggestion, how do you think the matching market for newly-graduating economists might treat that person?

Alvin Roth: That's a good question. 

So market design has already done pretty well and I have students at a lot of fine places. So the labor market has been good for them. 

The intersection of computer science and economics is a little tougher because what we need to be doing - and we're seeing only a very little of it so far - is we need to sometimes be hiring computer scientists into economics departments in order to give us the rounded story we need and vice-versa.

And hiring people across disciplines is tough. 

But my professional history gives a ray of hope because I came of age professionally when economics departments had to start hiring game theorists. And game theorists mostly didn't have economics degrees right at the beginning. I didn’t - I had a degree in operations research. A lot of game theorists had degrees in mathematics. Nevertheless, game theory entered economics. 

If a candidate doesn't have an economics degree one thing that could be asked is 'but what would he or she teach’? And the answer has to be, well, they’d teach the parts of computer science that intersect with economics and that economists should know about.

So it's a little bit of a bump in the road, but I think we're starting to make it there. We're starting to see it. And I hope that it will continue and that someone who studies the intersection of market design and economics will can find a home in economics, regardless of whether their degree is in economics or computer science. In other words, based on what they do rather than what their degree is in. 

But that's still a little bit of a challenge.

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