Rufus Isaacs (game theorist)
Encyclopedia
Rufus Philip Isaacs was a game theorist especially prominent in the 1950s and 1960s with his work on differential game
s.
type zero-sum
dynamic two player games such as the Princess and monster game
. In 1942, He married Rose Barcov, and they had two daughters.
His work in pure mathematics
included working with monodiffric functions, fractional order mappings, graph theory
, analytic function
s, and number theory
. In graph theory he constructed the first two infinite families of snarks
. In applied mathematics
, he worked with aerodynamics
, elasticity
, optimization
, and differential games, which he is most known for. He received his bachelors from MIT in 1936, and received his MA and PhD from Columbia University
in 1942 and 1942 respectively. His first post after the war ended was at Notre Dame
, but he left in 1947 due to salary issues. While at RAND, much of his work was classified, and thus remained unknown until the publication of his classic text on differential games a decade after leaving RAND. His career after RAND was spent largely in the defense and avionics industries. While at RAND, he worked with researchers including Richard E. Bellman, Leonard D. Berkovitz, David H. Blackwell, John M. Danskin, Melvin Dresher
, Wendell H. Fleming, Irving L. Glicksberg, Oliver A. Gross, Samuel Karlin
, John W. Milnor, John F. Nash, and Lloyd S. Shapley. His work has influenced such fundamental economic concepts as dynamic programming
(Richard E. Bellman) and the Pontryagin maximum principle (Breitner 2005).
Differential game
In game theory, differential games are a group of problems related to the modeling and analysis of conflict in the context of a dynamical system. The problem usually consists of two actors, a pursuer and an evader, with conflicting goals...
s.
Biography
He worked for the RAND Corporation from 1948 until winter 1954/1955. His investigation stemmed from classic pursuit-evasionPursuit-evasion
Pursuit-evasion is a family of problems in mathematics and computer science in which one group attempts to track down members of another group in an environment. Early work on problems of this type modeled the environment geometrically...
type zero-sum
Zero-sum
In game theory and economic theory, a zero-sum game is a mathematical representation of a situation in which a participant's gain of utility is exactly balanced by the losses of the utility of other participant. If the total gains of the participants are added up, and the total losses are...
dynamic two player games such as the Princess and monster game
Princess and monster game
In game theory, the princess and monster game is a pursuit-evasion game played by two players in a region. The game was devised by Rufus Isaacs and published in his book Differential Games as follows. "The monster searches for the princess, the time required being the payoff. They are both in a...
. In 1942, He married Rose Barcov, and they had two daughters.
His work in pure mathematics
Pure mathematics
Broadly speaking, pure mathematics is mathematics which studies entirely abstract concepts. From the eighteenth century onwards, this was a recognized category of mathematical activity, sometimes characterized as speculative mathematics, and at variance with the trend towards meeting the needs of...
included working with monodiffric functions, fractional order mappings, graph theory
Graph theory
In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of...
, analytic function
Analytic function
In mathematics, an analytic function is a function that is locally given by a convergent power series. There exist both real analytic functions and complex analytic functions, categories that are similar in some ways, but different in others...
s, and number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
. In graph theory he constructed the first two infinite families of snarks
Snark (graph theory)
In the mathematical field of graph theory, a snark is a connected, bridgeless cubic graph with chromatic index equal to 4. In other words, it is a graph in which every vertex has three neighbors, and the edges cannot be colored by only three colors without two edges of the same color meeting at a...
. In applied mathematics
Applied mathematics
Applied mathematics is a branch of mathematics that concerns itself with mathematical methods that are typically used in science, engineering, business, and industry. Thus, "applied mathematics" is a mathematical science with specialized knowledge...
, he worked with aerodynamics
Aerodynamics
Aerodynamics is a branch of dynamics concerned with studying the motion of air, particularly when it interacts with a moving object. Aerodynamics is a subfield of fluid dynamics and gas dynamics, with much theory shared between them. Aerodynamics is often used synonymously with gas dynamics, with...
, elasticity
Elasticity (physics)
In physics, elasticity is the physical property of a material that returns to its original shape after the stress that made it deform or distort is removed. The relative amount of deformation is called the strain....
, optimization
Optimization (mathematics)
In mathematics, computational science, or management science, mathematical optimization refers to the selection of a best element from some set of available alternatives....
, and differential games, which he is most known for. He received his bachelors from MIT in 1936, and received his MA and PhD from Columbia University
Columbia University
Columbia University in the City of New York is a private, Ivy League university in Manhattan, New York City. Columbia is the oldest institution of higher learning in the state of New York, the fifth oldest in the United States, and one of the country's nine Colonial Colleges founded before the...
in 1942 and 1942 respectively. His first post after the war ended was at Notre Dame
University of Notre Dame
The University of Notre Dame du Lac is a Catholic research university located in Notre Dame, an unincorporated community north of the city of South Bend, in St. Joseph County, Indiana, United States...
, but he left in 1947 due to salary issues. While at RAND, much of his work was classified, and thus remained unknown until the publication of his classic text on differential games a decade after leaving RAND. His career after RAND was spent largely in the defense and avionics industries. While at RAND, he worked with researchers including Richard E. Bellman, Leonard D. Berkovitz, David H. Blackwell, John M. Danskin, Melvin Dresher
Melvin Dresher
Melvin Dresher was a Polish-born American mathematician, notable for developing, with Merrill Flood, the game theoretical model of cooperation and conflict known as the Prisoner's Dilemma while at RAND in 1950 .Dresher came to the United States in 1923...
, Wendell H. Fleming, Irving L. Glicksberg, Oliver A. Gross, Samuel Karlin
Samuel Karlin
Samuel Karlin was an American mathematician at Stanford University in the late 20th century.Karlin was born in Yanova, Poland and immigrated to Chicago as a child...
, John W. Milnor, John F. Nash, and Lloyd S. Shapley. His work has influenced such fundamental economic concepts as dynamic programming
Dynamic programming
In mathematics and computer science, dynamic programming is a method for solving complex problems by breaking them down into simpler subproblems. It is applicable to problems exhibiting the properties of overlapping subproblems which are only slightly smaller and optimal substructure...
(Richard E. Bellman) and the Pontryagin maximum principle (Breitner 2005).