Rufus Philip Isaacs (June 11, 1914 – January 18, 1981) was a game theorist especially prominent in the 1950s and 1960s with his work on differential games.

Biography

Isaacs was born on 11 June 1914 in

New York City New York, often called New York City or NYC, is the most populous city in the United States. With a 2020 population of 8,804,190 distributed over , New York City is also the most densely populated major city in the Un ...

. He worked for the RAND Corporation from 1948 until winter 1954/1955. His investigation stemmed from classic

pursuit–evasion Pursuit–evasion (variants of which are referred to as cops and robbers and graph searching) 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 ...

type

zero-sum Zero-sum game is a mathematical representation in game theory and economic theory of a situation which involves two sides, where the result is an advantage for one side and an equivalent loss for the other. In other words, player one's gain is e ...

dynamic two-player games such as the

Princess and monster game In game theory, a princess and monster game is a pursuit–evasion game played by two players in a region. Formal Definition In his book ''Differential Games'' (1965), Rufus Isaacs defined the game as: This game remained a well-known open ...

. In 1942, he married Rose Bicov, and they had two daughters. His work in pure mathematics included working with monodiffric functions, fractional-order mappings,

graph theory In mathematics, graph theory is the study of ''graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are conn ...

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. Functions of each type are infinitely differentiable, but complex ...

s, and

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mat ...

. In graph theory he constructed the first two infinite families of snarks. In

applied mathematics Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathemati ...

, he worked with

aerodynamics Aerodynamics, from grc, ἀήρ ''aero'' (air) + grc, δυναμική (dynamics), is the study of the motion of air, particularly when affected by a solid object, such as an airplane wing. It involves topics covered in the field of fluid dy ...

, elasticity,

optimization Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfi ...

, and differential games, which he is most known for. He received his bachelor's degree from

MIT The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the m ...

in 1936, and received his MA and PhD from

Columbia University Columbia University (also known as Columbia, and officially as Columbia University in the City of New York) is a private research university in New York City. Established in 1754 as King's College on the grounds of Trinity Church in Manhatt ...

in 1942 and 1943 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 Melvin Dresher (born Dreszer; March 13, 1911 – June 4, 1992) 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 ...

, Wendell H. Fleming, Irving L. Glicksberg, Oliver A. Gross, Samuel Karlin, John W. Milnor, John F. Nash, and Lloyd S. Shapley. His work has significant influence on mathematical optimization including fundamental concepts such as

dynamic programming Dynamic programming is both a mathematical optimization method and a computer programming method. The method was developed by Richard Bellman in the 1950s and has found applications in numerous fields, from aerospace engineering to economics. ...

( Richard E. Bellman) and the Pontryagin maximum principle (Breitner 2005) which are widely used in economics and many other fields. Isaacs was a professor of Mathematical Sciences and Electrical Engineering at the

Johns Hopkins University Johns Hopkins University (Johns Hopkins, Hopkins, or JHU) is a private research university in Baltimore, Maryland. Founded in 1876, Johns Hopkins is the oldest research university in the United States and in the western hemisphere. It consi ...

between 1967 and his retirement in 1977.

Selected work(s)

*Isaacs, Rufus. ''Differential Games'', John Wiley and Sons, 1965.

The Isaacs Award

The executive board of the

International Society of Dynamic Games The International Society of Dynamic Games (ISDG) is an international non-profit, professional organization for the advancement of the theory of dynamic games. History The ISDG was founded on August 9, 1990 in Helsinki, Finland, at the site of ...

decided in 2003 to establish a prize to recognize the "outstanding contribution to the theory and applications of dynamic games" of two scholars at each of its symposium, starting in 2004. The prize was named after Isaacs. The recipients of this prize are: *

Yu-Chi Ho Yu-Chi "Larry" Ho (; born March 1, 1934) is a Chinese-American mathematician, control theorist, and a professor at the School of Engineering and Applied Sciences, Harvard University. He is the co-author of ''Applied Optimal Control'', and an i ...

and

George Leitmann George Leitmann (born May 24, 1925) is an Austrian-born American engineering scientist and educator. Early life and education Leitmann was born on May 24, 1925, to a fully assimilated Jewish family in Vienna, Austria. His paternal grandfather wa ...

(2004) * Nikolay Krasovskii and

Wendell Fleming Wendell Helms Fleming (born March 7, 1928) is an American mathematician, specializing in geometrical analysis and stochastic differential equations. Fleming received in 1951 his PhD under Laurence Chisholm Young at the University of Wisconsin� ...

(2006) * and Alain Haurie (2008) *

Tamer Başar Mustafa Tamer Başar (born January 19, 1946) is a control and game theorist who is the ''Swanlund Endowed Chair'' and Center for Advanced Study Professor of Electrical and Computer Engineering at the University of Illinois at Urbana-Champaign, ...

and (2010) * Steffen Jørgensen and Karl Sigmund (2012) * Eitan Altman and Leon Petrosyan (2014) * Martino Bardi and Ross Cressman (2016) * Andrzej Nowak and Georges Zaccour (2018)

Notes

References

*Yu, P. L. "An appreciation of professor Rufus Isaacs" Journal of Optimization Theory and Applications, Springer Netherlands. Volume 27, Number 1 / January, 1979 *Breitner, M. H. "The Genesis of Differential Games in Light of Isaacs' Contributions". Journal of Optimization Theory and Applications, Springer Netherlands. Volume 124, Number 3 / March, 2005 {{DEFAULTSORT:Isaacs, Rufus 1914 births Massachusetts Institute of Technology School of Science alumni Columbia University alumni University of Notre Dame faculty Game theorists Control theorists 1981 deaths 20th-century American mathematicians

Biography

Selected work(s)

The Isaacs Award

See also

Notes

References