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

differential game In game theory, differential games are dynamic games that unfold in continuous time, meaning players’ actions and outcomes evolve smoothly rather than in discrete steps, and for which the rate of change of each state variable—like position, spe ...

Biography

Isaacs was born on June 11, 1914, in New York City. He worked for the

RAND Corporation The RAND Corporation, doing business as RAND, is an American nonprofit global policy think tank, research institute, and public sector consulting firm. RAND engages in research and development (R&D) in several fields and industries. Since the ...

from 1948 until winter 1954/1955. His investigation stemmed from classic pursuit–evasion type

zero-sum Zero-sum game is a mathematical representation in game theory and economic theory of a situation that involves two competing entities, where the result is an advantage for one side and an equivalent loss for the other. In other words, player on ...

dynamic two-player games such as the Princess and monster game. In 1942, he married Rose Bicov, and they had two daughters. His work in

pure mathematics Pure mathematics is the study of mathematical concepts independently of any application outside mathematics. These concepts may originate in real-world concerns, and the results obtained may later turn out to be useful for practical applications ...

included working with monodiffric functions, fractional-order mappings,

graph theory In mathematics and computer science, graph theory is the study of ''graph (discrete mathematics), graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of ''Vertex (graph ...

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 is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

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

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

, he worked with

aerodynamics Aerodynamics () is the study of the motion of atmosphere of Earth, air, particularly when affected by a solid object, such as an airplane wing. It involves topics covered in the field of fluid dynamics and its subfield of gas dynamics, and is an ...

, elasticity,

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

, 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 research university in Cambridge, Massachusetts, United States. Established in 1861, MIT has played a significant role in the development of many areas of modern technology and sc ...

in 1936, and received his MA and PhD from

Columbia University Columbia University in the City of New York, commonly referred to as Columbia University, is a Private university, private Ivy League research university in New York City. Established in 1754 as King's College on the grounds of Trinity Churc ...

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 Poland, Polish-born United States, American mathematician, notable for developing, alongside Merrill M. Flood, Merrill Flood, the game theory, game theoretical model of cooperat ...

, 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 ( 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 The Johns Hopkins University (often abbreviated as Johns Hopkins, Hopkins, or JHU) is a private university, private research university in Baltimore, Maryland, United States. Founded in 1876 based on the European research institution model, J ...

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 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 and George Leitmann (2004) * Nikolay Krasovskii and

Wendell Fleming Wendell Helms Fleming (March 7, 1928 – February 18, 2023) was an American mathematician, specializing in geometrical analysis and stochastic differential equations. Fleming received his PhD in 1951 under Laurence Chisholm Young at the Unive ...

(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-Champaig ...

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)
Pierre Cardaliaguet
& Mabel Tidball (2022)
Joel Brown

Roland Malhamé
(2024)

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 American game theorists American control theorists 1981 deaths 20th-century American mathematicians

Biography

Selected work(s)

The Isaacs Award

See also

Notes

References