Jean-Jacques Herings: “You can optimize pretty much everything with mathematics”

Jean-Jacques Herings describes himself as an abstract thinker. As a schoolboy he reached the finals of the National Chemistry Olympiad, but doing experiments with test tubes, Bunsen burners and pipettes was not where his real enthusiasm lay. He would much rather be racking his brains to reduce complex phenomena to their essence using mathematical tools. “I’d always enjoyed mathematics, and I chose to study econometrics in Tilburg because it was a challenging program that combined two studies: economics and mathematics.” It certainly was a tough program: only half the students successfully graduated, Jean-Jacques recalls. But the small group that remained appreciated and stimulated one another. “And in the evenings we would go together into town to play billiards or cards. It was a tight-knit group.”

The link with Tilburg

Jean-Jacques also did his doctoral research at Tilburg. In 1988 the Center for Economic Research was founded (CentER), and this gave research at the university a strong quality boost. “As a student you don’t really realize that such excellent researchers are walking around – as a doctoral student you think it’s normal. Only after I had gathered a lot of comparison material did I realize how much my diplomas were worth. Tilburg leads economics research in the Netherlands, and the program here is one of the best in Europe.” Later on Jean-Jacques was a guest researcher at a variety of universities abroad, including Paris, Yale and Hong Kong, and a professor at Maastricht University, but the link with Tilburg always remained.

The distribution of scarce goods

Jean-Jacques’ working field is rather abstract. He could have gone into physics, he says. There, too, mathematical instruments are used to better understand complex phenomena – in that case in the material world. It is no accident that Nobel Prize winner Jan Tinbergen trained as a physicist. But as an econometrist Jean-Jacques concentrates on core questions in economics. “At the highest level of abstraction it’s all about scarcity. There is limited capital, there are limited resources and a limited workforce. How do you make sure that scarce goods are distributed so that everyone’s welfare is ideally served?’’

Fish auction, art auction

An auction, for example, can be a good way of ensuring that goods end up in the right place – whether those goods are artworks, fish, radio frequencies, emission rights, or wind turbine parks. But there are many different kinds of auctions. A good auction is designed to best meet its objectives. A fish auction has to reach a fair price quickly, to avoid spoilage. An auction of radio frequencies for internet services has to provide a good playing field, with enough competitive bidders, so that these bidders are also stimulated to deliver good quality. And the rules of engagement have to make sense. For instance, bidders must have access to adequate information in order to reliably assess the value of these radio frequencies, and they have to be able to combine the most suitable frequencies. Auction theory uses mathematical models to predict how sellers and bidders take strategic decisions and thereby influence one another, and it attempts to predict the outcome of the auction. On the basis of these predictions, auction theoreticians can then advise on how best to design an auction in order to attain a given goal.

A pioneer in seeing connections

Matching theory is another field in which mathematical models are used to link suppliers and ‘demanders’ as effectively as possible. “I’m proudest of the article I wrote in which I was the first to combine two currents in matching theory, currents which until then had been strictly divided,” says Jean-Jacques. This concerned theories on matching with and without money. An example of matching with money is the house market, where a house-owner and a buyer get together in order to negotiate a price. However, in other matching processes money should actually play no role; for example, the distribution of donor organs among the patients who need them, or the distribution of student places in popular schools and study programs. “Thoe two currents in matching theory had developed separately for decades, and each had its own literature – each even had its own Nobel Prize winner. Four years ago I was the first to see how these two currents could be combined to form a single whole. Actually that process is common to much of my work, the fact that I often see links that others haven’t seen before. And I’m proud of that.”

The distribution of donor kidneys

For theoretical economists like Jean-Jacques it is often hard to demonstrate what their work means to society. But precisely because it is so abstract, his work has applications in the most widely differing areas. “That’s the great thing about mathematics; if you analyze and simplify a phenomenon to the deepest possible level, the model can then be applied in any number of ways.” For instance, Jean-Jacques has been in personal contact with someone who was the first to apply matching theory to allocating donor kidneys to those patients who would benefit the most. “A person like that reads my articles, gains new insights into how they can deal with a certain problem, and then applies them in practice.” At conferences, too, theoreticians and practitioners regularly gather to exchange the newest developments.

Asylum-seekers and rivers

The distribution of asylum-seekers across a country is yet another unexpected application of matching theory. Asylum-seekers often possess specific kinds of expertise. “You could take this into consideration when determining where these people should be invited to settle: develop a model to map their expertise and needs, and then have them go where their expertise is needed.” Another example is water management. “I wrote an article about situations in which parties can only collaborate indirectly. One such application is a river that passes through three countries. Country C depends on country A, where the river has its source – but country B lies in between. How much water can each country use, how do you arrange the mutual relationships, and how do upstream countries compensate downstream countries for the water they take out of the river?”

It takes a while sometimes, but the insights, models and algorithms we develop ultimately make their way into society

Optimizing everything

Jean-Jacques is also very enthusiastic about Tilburg University’s Zero Hunger Lab. He is not currently involved with it, but he can well imagine how mathematical techniques can help to calculate, for example, how food or water can best be transported from A to B in order to relieve hunger and poverty. “You can optimize pretty much everything with mathematics. It takes a while sometimes,” Jean-Jacques admits, “but the insights, models and algorithms we develop ultimately make their way into society. They provide ideas, in all sorts of different fields, about the best way to tackle a problem.”

Universal values, Catholic roots

Back to Tilburg: why did Jean-Jacques decide to make the professorial move here, since he now has to commute further from Cadier en Keer in Limburg, where he lives? It was mainly the level of ambition in the faculty, he answers. “I’m a very ambitious person, too; I always want to reach as high as possible and get as much as possible out of something. And I find the campus very inspiring. The fact that everyone you meet here is in the same field, working together to create something worthwhile. That creates a sense of calm. And finally, the values that are held highest here: friendliness between colleagues, and the four Cs – Connected, Curious, Caring and Courageous – that this university takes so seriously. They’re universal values, but they’re also clearly rooted in the Catholic faith. I’m a Catholic too, and I think that plays a role, that it’s one of the reasons I have always felt at home here.”

Three objectives

For Jean-Jacques, a new period in his career began in March. What would he like to achieve as professor? “I think it’s important that the people in my group can work together in an enjoyable way as colleagues, that they can get the best out of themselves, and that they can generate new and ground-breaking insights. Those are my three objectives. They’re what I try to achieve in my own work, and I want to encourage those aims in my own group and among my students. So that they can take part in a program of the highest possible quality, just as I did.”

Date of publication: 13 June 2022