Inaugural lecture Jean-Jacques Herings: A game theoretic perspective on competition and cooperation

Published: 19th June 2023 Last updated: 19th June 2023

Two of the biggest success stories in the application of game theory – allocating students to schools and auctioning spectrum licenses – are based on the same fundamental principles, as Professor of Quantitative Microeconomics Jean-Jacques Herings will show in his inaugural address on Friday, June 23, 2023. He will connect competition and cooperation to cases where both lead to the same, favorable outcomes.

Jean-Jacques Herings’ work shows that school choice problems and assignment problems such as those concerning spectrum licenses can both be regarded as specific cases of a general model he has developed. He has designed a procedure that generalizes both the deferred acceptance algorithm, which can help resolve school choice problems, and the simultaneous multi-round auction, which is used to deal with assignment problems. Both methods are used separately in practice.

Matching problems

In his address, titled Competition and Cooperation, Herings will elaborate on these two types of matching problems in detail (see text box below).

School choice problems and assignment problems explained

School choice problems

The purpose of admission procedures in school choice is to match a given number of students as well as possible with a given number of schools. The matching procedure takes into account the schools students prefer as well as the priorities schools assign to students, for example students whose siblings attend the same school or who live close to school. Another factor is the maximum number of students a school has the capacity to admit.

Good matching is stable matching. What this means is that it rules out the possibility of matching a school that is below capacity with a student who has a stronger preference for that school than the student who has actually been allocated to it. It also rules out the possibility of matching a school that is at capacity with a student who has a stronger preference for that school than the student who has actually been allocated to it, while the school assigns a higher priority to that student than to one of the students who it has admitted. And finally it rules out the possibility of any student being allocated to a school that is unacceptable to them.

The deferred acceptance algorithm is a method to find a stable matching in school choice problems, and it has the additional advantage of students having an interest in reporting their real preferences. This algorithm has become the global default in allocating students to schools.

Assignment problems

The purpose of assignment problems, the second type of matching Herings will discuss, is to match a given number of objects as well as possible with potential buyers at prices to be determined later. One major practical application of such procedures is allocating the use of radio spectrum frequencies to companies in the telecommunications industry.

Here too, good matching is stable matching. What this means is that it rules out the possibility of matching an object with a buyer who not only has a stronger preference for the object than the buyer to whom the object has actually been allocated but who is also prepared to pay a higher price than the buyer to whom the object has actually been allocated.

The simultaneous multi-round auction is a method for finding a stable matching in an assignment problem. It was first used in the US in 1994 in auctioning parts of the radio spectrum, and many other countries have since begun to use it.

Stable matching prevents a school and a student or a seller and a buyer from making a match that is more beneficial to them through cooperation. For allocation problems, it is possible to achieve stable matching by organizing a competitive market. For school choice problems, such an approach was long considered impossible.

Fundamental principles

Herings shows that both school choice problems and assignment problems can be regarded as specific cases of a general model he has developed. He has also designed a procedure that generalizes both the deferred acceptance algorithm and the simultaneous multi-round auction. And he shows that procedures for dealing with both allocation problems and choice-of-school problems can be based on a competitive market mechanism.