# Harold W. Kuhn

### From Wikimization

## Vita

Dr. Harold W. Kuhn, Professor Emeritus of Mathematical Economics at Princeton University, was a member of two separate departments of instruction --- Mathematics and Economics. His fields of research include linear and nonlinear programming, theory of games, combinatorial problems, and the application of mathematical techniques to economics.

I was born in Santa Monica, California, on July 29, 1925. I married Estelle Henkin in 1949. We have three sons, six grandsons, and a granddaughter. I am a veteran of service with the U.S. Army from 1944-46. I trained in Japanese in the Army Language Program at Yale University.

After graduating with a B.S. degree in 1947 from the California Institute of Technology, I enrolled in Princeton's Graduate School where I received an M.A. in 1948 and Ph.D. in 1950. I was the Henry B. Fine Instructor in the Mathematics Department for academic year 1949-50.

During the academic year 1950-51, I studied in Paris as a Fulbright Research Scholar. I was a Lecturer in Mathematics at Princeton during the following year. In 1952, I began a seven-year association with Bryn Mawr College, attaining the rank of Associate Professor.

Following a year's study at the London School of Economics as a National Science Foundation Senior Postdoctoral Fellow (1958-59), I returned to Princeton as Associate Professor of Mathematical Economics. I was promoted to the rank of Professor in 1963. Since that time, I have spent leaves of absence at the University of Rome as a National Science Foundation Senior Postdoctoral Fellow (1965-66) and at the London School of Economics as a National Science Foundation Science Faculty Fellow (1971-72).

I have been a consultant to various government organizations and to several corporations, and was senior consultant and member of the Board of Directors for Mathematica Inc. a Princeton-based research firm (not Wolfram) from 1961 to 1983 when it was acquired by Martin-Marietta. In this capacity, I directed a number of projects, including safety and reliability of nuclear weapons for the Atomic Energy Commission, inspection systems and the methodology of utility theory for the Arms Control and Disarmament Agency, and aggregation for traffic assignment models for the Department of Transportation.

A former President (1954-55) of the Society for Industrial and Applied Mathematics, I am a member of the American Mathematical Society, the Mathematical Association of America, and a Fellow of the Econometric Society. I am a former Executive Secretary (1957-1960) of the Division of Mathematics of the National Research Council - National Academy of Sciences. I served for several years as a member. I was elected to the Council of the Association of American University Professors for the period 1959-62.

As a member of the Princeton University Advisory Committee on Policy (1967-71), I wrote the position paper "Students and the University" which led to broad changes in participation by students in governance of the University. During this period, I also served on the Committee on Structure of the University, the Council of Princeton University Community, and was the first Chair of its Committee on Rights and Rules.

As an economist, I have taught undergraduate courses in price theory and managerial economics, and graduate courses in micro-economics, trade theory, and mathematical economics which was cross-listed in the graduate program for the Department of Mathematics where I also taught an undergraduate course in linear and nonlinear programming.

Among my publications, specially noteworthy is my work on nonlinear programming (jointly with A. W. Tucker, 1950), extensive games (1950), the Hungarian Method for the Assignment Problem (1955), an algorithm for Nash equilibria of bimatrix games (1959), extensions of Sperner's Lemma (1960), approximations of fixed points by simplicial subdivisions (1968), and an algorithm for the zeros of polynomials (1974). I also edited the first two volumes of Contributions to the Theory of Games and Linear Inequalities and Related Systems in the series Annals of Mathematics Studies with Dr. Albert W. Tucker of Princeton's Department of Mathematics. As co-director of NATO International Summer Schools with Dr. G. P. Szego, I edited proceedings on Mathematical Systems Theory and Economics (Springer-Verlag) and Differential Games (North-Holland). I also edited the Proceedings of the Princeton Symposium on Mathematical Programming; this was the sixth in a distinguished series of international symposia, held at Princeton in 1967. In 1980, I was awarded the John von Neumann Theory Prize of the Operations Research Society of America (jointly with David Gale and A. W. Tucker). In 1982, I received a Guggenheim Fellowship. In 1992, I was elected as a Fellow of the American Academy of Arts and Sciences, and I received an honorary life membership to the Hungarian Operations Research Society. In 2000, I received a Founders Award in recognition of "fundamental contributions to mathematical programming during its formative years" at the 17th International Symposium of the Mathematical Programming Society. In 2002, I received a Fellows Award from the Institute for Operations Research and Management Sciences (INFORMS).

My recent activities have been centered on game theory. In June 1987, I directed a NATO Advanced Study Institute on "Games with Incomplete Information and Bounded Rationality" held in Capri, Italy. In 1991, in a return to a problem I first studied in 1953, a complete set of facets was found for the asymmetric 6-city traveling salesman problem; this was joint work with Hale Trotter. At the Nobel Awards ceremonies in Stockholm in 1994, I chaired a seminar on the work of John Nash in Game Theory. A transcript was published in Les Prix Nobel 1994 published by the Nobel Foundation. This seminar has been republished by the Journal of Economic Theory and the Duke Mathematical Journal in 1996. A volume of basic papers in game theory that I edited, entitled Classics in Game Theory, was published by the Princeton University Press in 1997. In 2002, I coedited The Essential John Nash with Sylvia Nasar; also published by the Princeton University Press. The Press has also published my "Lectures on Game Theory" in March 2003. The Society for Industrial and Applied Mathematics is preparing a DVD with accompanying transcript and notes for a series of lectures that I recorded at the Audiovisual Centre of London University in the spring of 1972 entitled Foundations of Mathematical Programming.

On November 14, 2000, I was awarded an Honorary Doctoral Degree in Economics by the University of Bergamo, Italy. The Lectio Magistralis, entitled "Al Posto Giusto Nel Momento Giusto," has been translated and is published as "Being in the Right Place at the Right Time" in the 50th Anniversary Issue of the journal Operations Research (50, Jan/Feb 2002, pp.132-4).

In 2004, the scientific journal Naval Research Logistics established an annual "best paper" award. In creating that award, the publishers and editors of the journal sought the paper best representing the journal since its founding in 1954; they selected my paper "The Hungarian Method for the Assignment Problem.” According to the journal's citation, "This pioneering paper set a style for both the content and exposition of many other algorithms in combinatorial optimization and also directly inspired the primal-dual algorithm for more general linear optimization problems."

Professor Kuhn retired in July 1995 becoming Professor of Mathematical Economics Emeritus at Princeton University. Since 2005 he has resided in New York City. In May 2009 Professor Kuhn was elected to the Inaugural Group of Fellows of the Society for Industrial and Applied Mathematics (SIAM) for seminal contributions to game theory and to linear and nonlinear programming, and for leadership of SIAM in its early years.

## External Links

57 Years of Close Encounters with George

Presented at the George B. Dantzig Memorial Paper Cluster, INFORMS Annual Meeting, Washington DC, October 14, 2008