Prof Alvin E Roth has applied economic theory to tackle issues such as kidney transplantation backlogs and doctor pairing. For this and more, he won the Nobel Prize in Economic Sciences 2012. Here, we’ll delve into the work he’s published with MDPI and explore its impact in the real world.

Who is Alvin E Roth?

Alvin E Roth is an American economist who was a pioneer in market design, which is a field that develops systems to stabilise markets. It essentially involves economists working as engineers aiming to match supply with demand and prevent imbalances causing disruption.

Roth has degrees in operational research, a field of engineering that applies scientific principles to administration problems. Furthermore, he studied game theory, a field that applies mathematics to solve situations with multiple decision makers.

He took particular interest in Lloyd Shapley (whom he won the Nobel Prize jointly with) and David Gale’s deferred acceptance algorithm, which refrains from accepting anyone until it ensures that pairs in a freely traded system are efficiently matched up.

As of 2024, Roth is the Craig and Susan McCaw Professor of Economics at Stanford University and the Gund Professor of Economics and Business Administration at Harvard.

Winning the Nobel Prize in Economic Sciences

Simply, Roth uses the mathematical tools of game theory and economics to find solutions to broken systems, particularly those that revolve around pairings. The Nobel Prize committee awarded him “for the theory of stable allocations and the practice of market design”.

How to match different people most effectively is a key economic problem. Shapley theoretically studied these matching problems, developing the aforementioned deferred acceptance algorithm.

In the 1980s, Roth used Shapley’s theoretical results to explain how markets function in practice.

Putting theory to the test with Alvin E Roth

Roth has published various articles with MDPI’s journal Games. Here, we’ll focus on connecting his work with MDPI on theoretical economics to real-world problem solving applications.

By publishing such work in an Open Access format, Roth enables researchers from other fields to access the insights of his disciplines and build from them. From this, cooperation and innovation can flourish, which is necessary in the multifaceted field of economics.

First, we’ll introduce you to some of the key concepts in Roth’s work, then one of his MDPI papers, and conclude by showing you how it connects to the vital work that won him the Nobel Prize.

What is market design?

As mentioned, market design is a field that develops systems to stabilise markets.

A commodity market revolves around prices that help stabilise supply and demand. But not all markets revolve around prices.

In matching markets, you can’t just choose what you want; you must also be chosen. Roth compares this to a marriage, where both sides pick each other and agree to match. A common practical example is how a university accepts your application, but it also competes with other universities for you.

Stability, or stable matching, means all participants involved have preferable matches on both sides. Deferred acceptance, in this context, is an algorithm that focuses on making all necessary rejections and matches before accepting. This helps ensure that no one is accepted before a better pairing is found for them.

The organisations that typically perform these matchings are known as clearinghouses. Roth performed theoretical and laboratory experiments to test clearinghouses and their algorithms.

How labour markets unravel

Alvin E Roth’s article in Games explores unravelling matching markets, creating an experiment to test theories of why they occur. Moreover, the first author, Muriel Niederle, was Roth’s first PhD student at Harvard and has since become a well-known researcher on markets.

In a labour market, most work begins around the same time—after graduating from university or school. Offers can be made and contracts signed at any point before employment.

For a market to unravel, matching offers are made earlier and more dispersed in time, often over a year before employment is set to begin. Unravelling is sometimes a cause of market failure, especially when contracts are determined by critical information that is not yet available (like grades).

Market failure has consequences, such as when unravelling occurred in the market for gastroenterology fellows. The matching system broke down in 1996, due to revisions in the amount of time required for training and a reduction in the number of available positions. By 1999, there were only 5% of the participants applying than three years before.

This sudden shift in supply led to an even greater upward shift in demand for fellows, meaning there were fewer applicants than fellowship positions for the first time. This lasted for over a decade.

Why does unravelling occur?

The common theory is that unravelling occurs due to an imbalance in demand and supply. There is a need for applications, but not enough people are applying (there is a shortage of workers), so employers start making offers earlier and earlier in competition with others.

So, Roth presents a model and experiment in which the workers’ quality only becomes known later in the market to test this theory and see what other patterns emerge.

Testing theoretical assumptions

In the experiment, Roth varied the conditions of demand and supply, looking for stable matching.

He found that for unravelling to occur, there needs to be a comparable amount of supply and demand, contrary to the common theory. For it to happen, firms must be willing to make early offers and workers must be willing to accept them.

The unravelling occurs because the competition between and for elite firms is fierce, but the quality of workers may not be reliably revealed until after a lot of hiring has been completed. And, even in markets with more applicants than positions, there may be a shortage of the most highly qualified applicants.

So, unravelling occurs, not because of a shortage of workers, but because elite firms start making offers earlier and earlier when competing for high-quality applicants, whose quality can only be determined later.

Roth’s article has increased our understanding of which markets unravel, what role supply and demand plays, and how this can ripple through an entire market. This provides clearinghouses with the knowledge needed to put systems in place to prevent unravelling, which can lead to important job positions not being filled, and ensure stability.

Furthermore, the article inspired impactful research that expands on its theories, such as one exploring the timing of unravelling and how strategically timing policies can influence it.

But what is the value of such theoretical work?

Real-world applications of market design

Roth has applied such theoretical findings to solve real-world problems. Let’s explore three examples of Roth updating inefficient clearinghouse systems.

Medical school

In the 1950s, there were almost no female medical students. Now, the number is closer to 50% and there are romantic couples. The 1950s medical match system, which places medical school graduates into residency jobs across the USA, struggled to accommodate for couples.

Furthermore, as demand increased, competition for good students and good jobs caused positions to be offered earlier and earlier. This caused various issues, like jobs being offered before students even graduated and students being rushed into decisions: issues essentially reflecting a market unravelling.

In response, Roth and Elliot Peranson redesigned the mathematical algorithm so that it dealt more gracefully with married couples and other situations in which individuals may need two positions. Also, they redesigned other features that made substitutions more beneficial to both sides.

This system is still in place and is known as the National Residency Matching Program.

New York schools

In most areas, children choose between a limited selection of schools in their local area. However, in big cities, children face a staggering number of choices for schools. For example, in New York, 80,000 eighth-grade students can choose between 700 different high school programs. Finding the right match is especially meaningful for children living in neighbourhoods with low-ranking schools.

When Roth analysed the New York school matching system, a third of the students didn’t participate. The system was dysfunctional and highly congested, with schools having their own screening mechanisms that further complicated the process.

Roth and his team weaved this convoluted system into one transparent clearinghouse that required students list up to 12 choices in order of preference. Then, a deferred acceptance clearinghouse matched them accordingly. This solved the congestion and made the process much less confusing. As a result, participation jumped from 66 to 83%.

Roth also developed a similar system for Boston.

Kidney donors

Roth taught in Pittsburgh, where one of the pioneering kidney transplant centres was. He used kidney donors as an example in his teaching of game theory, as a good that could be traded between pairs to obtain better matches.

After the revolutionary first transplants, demand exceeded what the system could manage. The waiting list for kidneys was 85,000 in the USA, and 4000 people died per year due to organ shortages. People would volunteer as donors, but due to blood types not matching, the organs could not be exchanged.

Designing a new patient‒donor matching system

So, Roth and his team collaborated with several kidney exchange networks.

Together, they designed an algorithm for incompatible patient‒donor pairs to match with other incompatible pairs. The system made pairs that meant a patient and donor with incompatible blood types could match with another pair that have incompatible blood types, so that between them two new patient‒donor pairs would emerge that were compatible. Moreover, they included non-paired and diseased donors into the algorithm too.

Roth intuited that it wasn’t a question of demand being greater than supply. Rather, there were enough kidneys, and we just weren’t mobilising them well enough. Roth and his team’s work has helped thousands of patients with incompatible donors receive transplants of life-saving compatible kidneys.

Saving lives using economics with Alvin E Roth

Roth explains how

I’ve always been interested in using mathematics to make the world work better.

His work explores economic theory and applies the findings to solving real-world problems, some of which have helped saved thousands of lives. For this and more, he received the Nobel Prize in Economic Sciences 2012. And we are very grateful to feature his work in our journal Games.

Games is a scholarly, peer reviewed, Open Access journal of strategic interaction, game theory and decision-making published bimonthly online by MDPI. The journal is indexed within Scopus, ESCI, MathSciNet, and other databases.

If you’re interested in submitting, it will have a section for you. See the journal homepage if you are considering submitting your work.