Herbert Eli "Herb" Scarf (July 25, 1930 – November 15, 2015) was an American mathematical economist and Sterling Professor of

Economics Economics () is the social science that studies the production, distribution, and consumption of goods and services. Economics focuses on the behaviour and interactions of economic agents and how economies work. Microeconomics anal ...

Yale University Yale University is a private research university in New Haven, Connecticut. Established in 1701 as the Collegiate School, it is the third-oldest institution of higher education in the United States and among the most prestigious in the w ...

Education and career

Scarf was born in Philadelphia, the son of Jewish emigrants from Ukraine and Russia, Lene (Elkman) and Louis Scarf. During his undergraduate work he finished in the top 10 of the 1950

William Lowell Putnam Mathematical Competition The William Lowell Putnam Mathematical Competition, often abbreviated to Putnam Competition, is an annual mathematics competition for undergraduate college students enrolled at institutions of higher learning in the United States and Canada (regar ...

, the major mathematics competition between universities across the United States and

Canada Canada is a country in North America. Its ten provinces and three territories extend from the Atlantic Ocean to the Pacific Ocean and northward into the Arctic Ocean, covering over , making it the world's second-largest country by to ...

. He received his PhD from Princeton in 1954, supervised by

Salomon Bochner Salomon Bochner (20 August 1899 – 2 May 1982) was an Austrian mathematician, known for work in mathematical analysis, probability theory and differential geometry. Life He was born into a Jewish family in Podgórze (near Kraków), then ...

Contributions

Among his notable works is a seminal paper in cooperative game in which he showed sufficiency for a

core (economics) In cooperative game theory, the core is the set of feasible allocations that cannot be improved upon by a subset (a ''coalition'') of the economy's agents. A coalition is said to ''improve upon'' or ''block'' a feasible allocation if the members ...

in general balanced games. Sufficiency and necessity had been previously shown by

Lloyd Shapley Lloyd Stowell Shapley (; June 2, 1923 – March 12, 2016) was an American mathematician and Nobel Prize-winning economist. He contributed to the fields of mathematical economics and especially game theory. Shapley is generally considered one of ...

for games where players were allowed to transfer utility between themselves freely. Necessity is shown to be lost in the generalization.

Recognition

Scarf received the 1973 Frederick W. Lanchester Award for his contribution ''The Computation of Economic Equilibria'' with the collaboration of Terje Hansen, which pioneered the use of numeric

algorithm In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing ...

s to solve

general equilibrium In economics, general equilibrium theory attempts to explain the behavior of supply, demand, and prices in a whole economy with several or many interacting markets, by seeking to prove that the interaction of demand and supply will result in an o ...

systems using

Applied general equilibrium In mathematical economics, applied general equilibrium (AGE) models were pioneered by Herbert Scarf at Yale University in 1967, in two papers, and a follow-up book with Terje Hansen in 1973, with the aim of empirically estimating the Arrow–Debr ...

models. He was a member of the

American Academy of Arts and Sciences The American Academy of Arts and Sciences (abbreviation: AAA&S) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, a ...

, the National Academy of Sciences, and the

American Philosophical Society The American Philosophical Society (APS), founded in 1743 in Philadelphia, is a scholarly organization that promotes knowledge in the sciences and humanities through research, professional meetings, publications, library resources, and communit ...

, and was elected to the 2002 class of

Fellow A fellow is a concept whose exact meaning depends on context. In learned or professional societies, it refers to a privileged member who is specially elected in recognition of their work and achievements. Within the context of higher education ...

s of the Institute for Operations Research and the Management Sciences.

References

External links

Personal web site

* 1930 births 2015 deaths Members of the United States National Academy of Sciences General equilibrium theorists 20th-century American economists 21st-century American economists 20th-century American mathematicians Yale University faculty Fellows of the Econometric Society Presidents of the Econometric Society Yale Sterling Professors John von Neumann Theory Prize winners Distinguished Fellows of the American Economic Association Fellows of the American Academy of Arts and Sciences Fellows of the Institute for Operations Research and the Management Sciences 21st-century American mathematicians Members of the American Philosophical Society {{US-mathematician-stub