Herbert Scarf
Encyclopedia
Herbert Eli "Herb" Scarf (born July 25, 1930 in Philadelphia, PA) is an American
mathematical economist
and Sterling Professor
of Economics
at Yale University
. He is a member of the American Academy of Arts and Sciences
. During his undergraduate work he finished in the top 10 of the 1950 William Lowell Putnam Mathematical Competition
, the major mathematics competition between universities across the United States and Canada
. He received his PhD from Princeton in 1954.
Among his notable works is a seminal paper in cooperative game
in which he showed sufficiency for a core (economics)
in general balanced games. Sufficiency and necessity had been previously shown by Lloyd Shapley
for games where players were allowed to transfer utility between themselves freely. Necessity is shown to be lost in the generalization.
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
s to solve general equilibrium
systems using Applied general equilibrium
models.
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
mathematical economist
Mathematical economics
Mathematical economics is the application of mathematical methods to represent economic theories and analyze problems posed in economics. It allows formulation and derivation of key relationships in a theory with clarity, generality, rigor, and simplicity...
and Sterling Professor
Sterling Professor
A Sterling Professorship is the highest academic rank at Yale University, awarded to a tenured faculty member considered one of the best in his or her field...
of Economics
Economics
Economics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...
at Yale University
Yale University
Yale University is a private, Ivy League university located in New Haven, Connecticut, United States. Founded in 1701 in the Colony of Connecticut, the university is the third-oldest institution of higher education in the United States...
. He is a member of the American Academy of Arts and Sciences
American Academy of Arts and Sciences
The American Academy of Arts and Sciences is an independent policy research center that conducts multidisciplinary studies of complex and emerging problems. The Academy’s elected members are leaders in the academic disciplines, the arts, business, and public affairs.James Bowdoin, John Adams, and...
. During his undergraduate work he finished in the top 10 of the 1950 William Lowell Putnam Mathematical Competition
William Lowell Putnam Mathematical Competition
The William Lowell Putnam Mathematical Competition, often abbreviated to the Putnam Competition, is an annual mathematics competition for undergraduate college students of the United States and Canada, awarding scholarships and cash prizes ranging from $250 to $2,500 for the top students and $5,000...
, the major mathematics competition between universities across the United States and Canada
Canada
Canada is a North American country consisting of ten provinces and three territories. Located in the northern part of the continent, it extends from the Atlantic Ocean in the east to the Pacific Ocean in the west, and northward into the Arctic Ocean...
. He received his PhD from Princeton in 1954.
Among his notable works is a seminal paper in cooperative game
Cooperative game
In game theory, a cooperative game is a game where groups of players may enforce cooperative behaviour, hence the game is a competition between coalitions of players, rather than between individual players...
in which he showed sufficiency for a core (economics)
Core (economics)
The core is the set of feasible allocations that cannot be improved upon by a subset of the economy's consumers. A coalition is said to improve upon or block a feasible allocation if the members of that coalition are better off under another feasible allocation that is identical to the first...
in general balanced games. Sufficiency and necessity had been previously shown by Lloyd Shapley
Lloyd Shapley
Lloyd Stowell Shapley is a distinguished American mathematician and economist. He is a Professor Emeritus at University of California, Los Angeles, affiliated with departments of Mathematics and Economics...
for games where players were allowed to transfer utility between themselves freely. Necessity is shown to be lost in the generalization.
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
Algorithm
In mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...
s to solve general equilibrium
General equilibrium
General equilibrium theory is a branch of theoretical economics. It seeks to explain the behavior of supply, demand and prices in a whole economy with several or many interacting markets, by seeking to prove that a set of prices exists that will result in an overall equilibrium, hence general...
systems using Applied general equilibrium
Applied general equilibrium
In mathematical economics, applied general equilibrium 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–Debreu general equilibrium model with empirical data, to provide...
models.