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Isaacs was born on June 11, 1914, in New York City. [1] He worked for the RAND Corporation from 1948 until winter 1954/1955. His investigation stemmed from classic pursuit–evasion type zero-sum dynamic two-player games such as the Princess and monster game. In 1942, he married Rose Bicov, and they had two daughters.
The problem was proposed by Rufus Isaacs in a 1951 report [2] for the RAND Corporation, and in the book Differential Games. [3] The homicidal chauffeur problem is a classic example of a differential game played in continuous time in a continuous state space.
In the study of competition, differential games have been employed since a 1925 article by Charles F. Roos. [7] The first to study the formal theory of differential games was Rufus Isaacs, publishing a text-book treatment in 1965. [8] One of the first games analyzed was the 'homicidal chauffeur game'.
Princess and monster games can be played on a pre-selected graph. It can be demonstrated that for any finite graph an optimal mixed search strategy exists that results in a finite payoff. This game has been solved by Steve Alpern and independently by Mikhail Zelikin only for the very simple graph consisting of a single loop (a circle).
It has been found that the viscosity solution is the natural solution concept to use in many applications of PDE's, including for example first order equations arising in dynamic programming (the Hamilton–Jacobi–Bellman equation), differential games (the Hamilton–Jacobi–Isaacs equation) or front evolution problems, [1] [2] as well as ...
A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. [21] [22] [23] Differential equations play a prominent role in engineering, physics, economics, biology, and other disciplines.
Isaacs was a former non-executive director at sports betting firm DraftKings, which in 2021 walked away from its $22 billion buyout bid for Entain to focus on its core U.S. market.
Lawrence Craig Evans (born November 1, 1949) is an American mathematician and Professor of Mathematics at the University of California, Berkeley.. His research is in the field of nonlinear partial differential equations, primarily elliptic equations.