The Person and Contribution
Written by Shmuel Zamir in Memoriam for Michael B. Maschler (Discussion Paper #493, November 2008).
Professor Michael B. Maschler, a prominent and distinguished member of the game theory community, a leader and architect of the theory of games as it is known today, passed away on July 20, 2008, at the age of 81. His prolific scientific activity extended over 56 years, from the first paper he published at the age of 25 to the last two books he coauthored, published in the months after his death.
Born in Jerusalem on July 22, 1927, he got his Ph.D. from the Department of Mathematics at the Hebrew University in 1956; upon submission of his thesis on the theory of functions of complex variables, he joined the department as an instructor. His meeting with Robert J. Aumann, a newly recruited young lecturer in the department, was a turning point in his career as he was “converted” to game theory and became one of the small group of people who developed and shaped game theory in the early Sixties. This was the beginning of the remarkable Aumann–Maschler collaboration, which extended over many decades and had a great impact on the foundations of game theory. Both men were research associates in the Econometric Research Program at Princeton University in the years 1961–1963, where much of the “action” in game theory took place. A few years later, in 1967–1968, both were members of a group of specialists who advised the U.S. Arms Control and Disarmament Agency (ACDA) in Washington, D.C., to which the theory of games with incomplete information owes its origin.
Michael Maschler’s greatest impact is on cooperative game theory. He originated the bargaining set for cooperative games (in collaboration with R. J. Aumann) and then its conceptual derivative, the kernel (in collaboration with M. Davis and B. Peleg), which in turn inspired D. Schmeidler to introduce the next conceptual derivative, the nucleolus. The extensive studies of these concepts and their wide variety of applications constitute one of the three major approaches to cooperative game theory, the others being the core and the Shapley value. Maschler’s numerous studies, in collaboration with B. Peleg, G. Owen, L. Shapley, M. Potters, S. H. Tijs, and others, explore the relationships between all these concepts as well as the Nash bargaining solution. His work on the Nash bargaining problem led Maschler to introduce, in collaboration with M. Perles, the subtle and original superadditive solution, which was further investigated by several authors. In studying the cooperative game solution concepts, Maschler developed the notions of consistency and reduced game due to Sobolev, and studied their role, relevance, and applications to various solution concepts (see, e.g., his work with G. Owen on the consistent Shapley value and his work with J. A. M. Potters and S. H. Tijs on the general nucleolus). A beautiful piece of work making original use of cooperative game theory—and, specifically, the notion of consistency—is Maschler’s joint work with R. J. Aumann on a bankruptcy problem from the Talmud, in which they relate an ancient problem and its ancient solution to a modern game-theoretic solution concept, namely, the nucleolus. Another contribution of Maschler was in applying cooperative game theory to network games, which he did in collaboration with D. Granot, A. van den Nouweland, S. H. Tijs, and H. Reijnierse. Still within his contributions to cooperative game theory and its applications, Maschler recently got interested in the dynamics of voting systems, a line of research that he developed in collaboration with S. Barberà, D. Granot, and J. Shalev.
One of the most important events in the mid-Sixties was the development of the theory of games with incomplete information, and Maschler was part of it. This happened while he was a member of a group of specialists (including R. J. Aumann, G. Debreu, J. Harsanyi, H. Kuhn, H. Scarf, R. Selten, and R. Stearns) that was formed to advise the U.S. Arms Control and Disarmament Agency in Washington, D. C., during the negotiation between the U.S. and the Soviet Union over an arms reduction agreement (the SALT agreement). The pioneering works of Aumann and Maschler on repeated games with incomplete information became a starting point and a cornerstone of a rich and still growing field of research and, because they largely inspired the breakthrough result of Mertens and Neyman, had a major impact on the related field of stochastic games as well. A testimony to the importance of the seminal work of Aumann and Maschler on repeated games with incomplete information is the fact that these works, written in 1967–1968, and for almost three decades available only as classified ACDA reports, were published, due to their growing relevance, in 1995 as an MIT Press book which won the Lanchester Prize Citation for that year. The Aumann and Maschler work on repeated games with incomplete information was a central element in the Nobel Prize Committee announcement that awarded the 2005 Nobel Prize in Economics to Robert J. Aumann.
A by-product of Maschler’s involvement in several consulting projects, such as the ACDA, the U.S. Air Force office of Scientific Research, and the Office of Naval Research, was his important contribution to the theory of inspection games. His two papers published in those years are basic references in any work in this field.
An important aspect of Maschler’s professional contribution was his extraordinary talent as an educator. He was an excellent teacher at all levels. His game theory lecture notes were published at the Hebrew University (1970), at the IMSSS at Stanford University (1973), and at the Institute for Advanced Studies in Vienna (1978). But his role as an educator started much earlier, as I can personally attest: Maschler was my high school mathematics teacher, a most challenging and effective one. In this capacity, he became one of the first “experimental game theorists,” as he ran experiments in class on the formation of coalitions in games with an empty core. The results of these experiments were published in 1962, long before experimental economics and game theory became so widespread.
For years he was an active and central figure in the Israeli education system. He chaired curriculum committees for mathematics in elementary, middle, and high schools. He delivered a lecture on mathematics curriculum for humanistic studies at the International Congress of Mathematicians in Stockholm (1962) and on the exponential and logarithmic functions in the new high school curriculum at the Israel Mathematical Union Conference in Tel Aviv (1987). Maschler authored many textbooks that were widely used all over the country. Here again I happened to have a privileged look, as I was involved in the instruction and supervision of the schoolteachers using his textbooks. Michael Maschler supervised Ein-Ya Gura in a rather unique Ph.D. project involving teaching selected topics in game theory to middle school students. The project was successful and they both coauthored a book in Hebrew on the subject. The english version of this book was published by Cambridge University Press in 2008. A textbook on game theory for undergraduate and graduate level students in Hebrew, on which Michael was working on with Eilon Solan and me, was published two months after he passed away. The English version of the book is forthcoming by Cambridge University Press.
Let me conclude by saying a few words about the pleasant personality of Michael Maschler. He was most supportive, encouraging, and truly interested in others’ work. His friendly and sincere attitude to everyone around him, independently of their age, grade, or status, was rather remarkable. He became a friend who was fun and a pleasure to be with, to anyone whom he worked or interacted with. He was a valuable and much-beloved member of the game theory community, who will sorely miss him.