Herbert E. Scarf

July 25, 1930 – November 15, 2015

Brief Biography

Herbert Eli Scarf was a distinguished economist and John von Neumann Theory Prize recipient who is known for his seminal work in inventory theory and the computation of fixed points, a key requirement in determining economic equilibria. He designed a proof of the convergence of an economy to equilibrium (whether or not production entails large discrete choices) and also made valuable contributions to balanced game theory

Born in Philadelphia, Pennsylvania, Scarf attended nearby Temple University and received his bachelor’s degree at age twenty-one. He pursued graduate study at Princeton University under Salomon Bochner, and placed in the top ten Putnam Prize contestants  as a student. In 1953, he worked at Bell Labs and at Princeton studied alongside Ralph Gomory and Lloyd Shapley. Scarf wrote his dissertation on differential operators on manifolds and applications to stochastic processes and received a PhD in 1954. His first postdoctoral position was at the RAND Corporation where he familiarized himself with the works of George B. Dantzig and other burgeoning operations researchers. In 1957, Scarf accepted a professorial position at Stanford University.

At Stanford, Scarf was given the opportunity to work alongside such OR leaders as Kenneth J. Arrow and University of California Berkeley professor Gerard Debreu, both of whom Scarf considers mentors and close friends. In 1958, he published his first major article on differential games with Lloyd Shapley of RAND, in Albert Tucker and Philip Wolfe’s Contribution to the Theory of Games. Scarf’s major contributions to inventory policy began with his presentation of the optimality of (S,s) policies in the dynamic inventory problem at the First Stanford Symposium in 1959, building upon the work of Theodore Harris, Jacob Marschak, and Arrow. That year, Scarf had been a visiting associate professor at the Cowles Foundation for Research in Economics at Yale University. In 1963, after a year with Stanford’s Center for Advanced Study in the Behavioral Sciences, he accepted a full professorship at Yale.

Scarf remained at Yale ever since and was the Sterling Professor Emeritus of Economics at the time of his passing. He twice served as Director of the Cowles Foundation (1967-1971 and 1981-1984) and the Division of Social Sciences (1971-1972 and 1973 - 1974). Scarf kept a close relationship with the operations research community of the California Bay Area, visiting Berkley’s Mathematical Sciences Research Institute as Research Scholar in the late 1980s and as a visiting professor to Stanford in the late 1970s.

Starting in 1963, Scarf sought a constructive procedure for finding economic equilibria without appealing to the standard fixed point arguments.  Over the next ten years, he built upon the work of Carlton Lemke and Harold Kuhn. In 1973, Scarf and Terje Hansen, a Yale PhD whose dissertation was on the subject, published The Computation of Economic Equilibria and received that year’s Frederick W. Lanchester Prize. The book was lauded as the first comprehensive treatment of an idea “which permits the constructive computation of approximate fixed points of continuous mappings.” The publication continues to be celebrated as an elegant blend of theory, computational experimentation, and practical application.

In addition to receiving the Lanchester Prize in 1973 and the John von Neumann Theory Prize ten years later, Scarf received numerous honors for his contributions to economics and operations research. He was an elected fellow of the American Academy of Arts and Sciences, the Institute for Operations Research and the Management Sciences, and the Econometric Society, which he served as president of in 1983. Scarf was additionally a member of the National Academy of Sciences and a Distinguished Fellow of the American Economic Association. 

Other Biographies

Wikipedia Entry for Herbert Scarf

Arrow K. J. & Kehoe T. J. (1994) Distinguished Fellow: Herbert Scarf's Contributions to Economics. Journal of Economic Perspectives, 8(4):161-181. (link)

Yale University Department of Economics. People: Herbert E. Scarf. Accessed April 10, 2015. (link)

Yang Z. (2012)  Herbert Scarf: a Distinguished American Economist. Discussion Papers in Economics, No. 12/06,  University of York, York, UK. (link)

Yang Z., ed. (2013) Herbert Scarf's Contributions to Economics, Game Theory and Operations, Volume 1: Economics and Game Theory. Palgrave Macmilan: London.


Temple University, AB 1951

Princeton University, MA 1952

Princeton University, PhD 1954 (Mathematics Genealogy)


Academic Affiliations
Non-Academic Affiliations

Key Interests in OR/MS


Memoirs and Autobiographies


Scarf H. E. (1991) The origins of fixed point methods. Lenstra J. K., Rinnooy Kan A. H. G., & Schrijver A., eds. in History of Mathematical Programming, A Collection of Personal Reminiscences, 126-134. North-Holland: Amsterdam.

Scarf H. E. (2014) My Intellectual Trajectory. Accessed June 22, 2015. 


Digressions & Impressions. In Memoriam: Herbert E. Scarf (1930-2015) by M.A. Khan. Published November 23, 2015. Accessed December 11, 2015. (link)

Yale University Cowles Foundation for Research in Economic Research. IN MEMORY: Herbert E. Scarf (July 25, 1930 - November 15, 2015). Published November 17, 2015. Accessed November 18, 2015. (link)

Yale University News. In memoriam: Herbert Scarf, pioneering economist and inspiring teacher. Published December 1, 2015. Accessed December 11, 2015. (link)

Roberts, S. (2015) Herbert Scarf, an Economist’s Mathematician, Dies at 85. New York Times November 23, 2015, p. A18 (National Edition).  (link).

Awards and Honors

Econometric Society Fellow 1963

American Academy of Arts and Sciences Fellow 1971

Frederick W. Lanchester Prize 1973

National Academy of Sciences Member 1976

John von Neumann Theory Prize 1983

American Economic Association Distinguished Fellow 1991

Institute for Operations Research and the Management Sciences Fellow 2002

Professional Service

National Academy of Sciences Economic Sciences Section, Chairman 1991-1994

Econometric Society, President 1983

Selected Publications

Scarf  H. E. & Shapley L. (1958) On differential games with survival payoffs. Dresher D., Tucker A. W., & Wolfe P., eds. in Contribution to the Theory of Games, Volume III. Princeton University Press: Princeton, NJ.

Clark A. J. & Scarf H. E. (1960) Optimal policies for a multi-echelon inventory problem. Management Science, 6(4): 475-79.

Scarf H. E. (1960) The optimality of (S,s) policies in the dynamic inventory problems. Arrow K. J., Karlin S., Suppers P., eds. in Mathematical Methods in the Social Sciences, 196-202. Stanford University

Scarf H. E. (1967) The approximation of fixed points of a continuous mapping. SIAM Journal of Applied Mathematics, 15(5): 1328-1343.

Scarf H. E. (1967) The core of an N person game. Econometrica, 35(1):50-69.

Scarf H. E. (1971) On the existence of a cooperativw solution for a general class of N-person games. Journal of Economic Theory, 3(2): 169-181.

Hansen T. & Scarf H. E. (1973) The Computation of Economic Equilibria. Yale University Press: New Haven CT.

Scarf H. E. & Shoven J. B. (1984) Applied General Equilibrium Analysis. Cambridge University Press: Cambridge, UK.

Scarf H. E. (1994) The allocation of resources in the presence of indivisibilities. The Journal of Economic Perspectives, 8(4):111-128.

Scarf H. E. (2002) Inventory theory. Operations Research, 50(1): 186-191. (link)

Additional Resources

Sethi, R. (2010) Herbert Scarf's 1964 Lectures: An Eyewitness Account, blog post Nov. 17, 2010.  Accessed Nov 15, 2015.  (link)