INTERVIEW WITH JEAN-FRANÇOIS MERTENS (1946–2012)

Extract

Every game theorist knows of Mertens and Zamir (1985)'s universal beliefs space, which gives deep foundations to Harsanyi's model of Bayesian games, and Kohlberg and Mertens (1986)'s strategic stability, which is the first stone of a complete, axiomatic theory of selection among Nash equilibria. Some French mathematicians refer to the “Mertens–Zamir operator” when using techniques that Mertens and Zamir (1971) introduced to solve a class of repeated games with incomplete information. Readers of Macroeconomic Dynamics may instead have seen Mertens and Rubinchik's 2012 article “Intergenerational Equity and the Discount Rate for Policy Analysis.”

The previous examples give just a slight idea of the scope of Jean-François Mertens's contributions, which also deal with general equilibrium, stochastic games, nonatomic cooperative games, and the strategic foundations of microeconomic theory. In his 2005 MD interview, Robert Aumann says, “A [. . .] person at CORE who has had a tremendous influence on game theory [. . .] is Jean-François Mertens. Mertens has done some of the deepest work in the discipline, some of it in collaboration with Israelis like my students Kohlberg, Neyman, and Zamir; he established a Belgian school of mathematical game theory that is marked by its beauty, depth, and sophistication.” The short interview that follows will definitely not account for the variety and the relevance of Jean-François's research achievements, but is typical of the way in which he talked about his work.

Jean-François asked me to interview him for MD during the spring of 2010. We discussed by e-mail the topics that would be covered and on July 6, 2010, I came to Louvain-la-Neuve with a tape recorder. After lunch, Jean-François suggested that we have coffee on a terrace near the golf course and there, he patiently answered my questions, sometimes in French, sometimes in English, for about two hours. We planned to go on for at least another round but kept postponing the project. . . . When I saw Jean-François for the last time, in February 2012, I gave him the transcript of the July 2010 interview, but he hardly commented on it. He rather told me about an ongoing research article, “A Random Partitions Approach to the Value,” to be presented (by Abraham Neyman) as a “von Neumann lecture” at the World Congress of Game Theory in Istanbul in July 2012. At the same time, he was also completing, with Anna Rubinchik, the revision of a companion paper to the MD article referred to previously (“Equilibria in an Overlapping Generations Model with Transfer Policies and Exogenous Growth,” forthcoming in Economic Theory).

Even if Jean-François did not proofread the transcript that follows, I cannot keep this material for myself. I am confident that those who have known Jean-François will take the interview, even incomplete, as an opportunity to remember his enthusiasm and his patience when he was talking about research. He would often start by identifying holes in obvious or well-known solutions to basic problems, and after a few audacious but illuminating shortcuts, would describe the most surprising achievements in everyday words. I hope that the interview will give an idea of Jean-François's approach to those who did not know him.

Quite naturally, because MD was the planned outlet of the interview, we started by talking about the paper on the discount rate for policy analysis, which was already mentioned in the preceding. Jean-François made a number of informal comments, which usefully complement the MD article. He also explained how this paper led him and his coauthor to undertake a thorough analysis of overlapping generations economies in continuous time. This made a perfect transition to Jean-François's views on general equilibrium theory, his own work in this area, and his early career.

The next step would be Jean-François's meeting with Bob Aumann, who introduced him to game theory. Jean-François pursued Aumann and Maschler's seminal work on infinitely repeated games with incomplete information, mostly with Shmuel Zamir. He went on with the existence of a value in stochastic games, another model of infinitely long games, which was introduced by Shapley in 1953. This research was undertaken with Abraham Neyman at the Institute of Advanced Studies in Jerusalem in 1980. Soon after, Mertens and Zamir started to review and complete all available results on repeated games in order to prepare a reference book on this topic. The material kept growing. Sylvain Sorin joined the team in the nineties and a draft appeared as a 1994 CORE discussion paper. However, in 2010, the book was still unpublished. . . the interview ends up with Jean-François's feelings about the project.

As shown by the list of publications at the end, many important contributions of Jean-François Mertens to game theory and microeconomics are not even mentioned in the interview. During his stay at the Institute of Advanced Studies in Jerusalem in 1980, Jean-François not only worked with Abraham Neyman on stochastic games, but also had his first discussions with Elon Kohlberg on refinements of Nash equilibria. These would be followed by many others, at CORE and Harvard, until the famous Econometrica paper appeared in 1986. For the next 15 years or so, Jean-François further developed the theory of strategic stability, by himself and with his students.

During the same period, Jean-François was also making progress on a completely different problem, the extension of the Shapley value to nonatomic cooperative games. Aumann and Shapley (1974) had made the first steps by proposing a value for smooth games. Jean-François proposed a complete answer to the problem in the eighties and, as already pointed out above, kept working on related topics until the very end.

Even without entering into details, a description of Jean-François's more recent contributions would be beyond the scope of this short introduction. As the interview makes clear, Jean-François became more and more interested in the foundations of microeconomic theory. A typical example is his “limit price mechanism,” which can be loosely described as a double auction with several goods or as an extension of Shapley and Shubik's strategic market games. Another example is “relative utilitarianism,” which, as Jean-François explains in the interview, plays a crucial role in the determination of an appropriate social discount rate for the evaluation of long-term economic policies. Let us listen to him.