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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. [4] The first to study the formal theory of differential games was Rufus Isaacs, publishing a text-book treatment in 1965. [5] 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).
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.
In the continuous formulation of pursuit–evasion games, the environment is modeled geometrically, typically taking the form of the Euclidean plane or another manifold. Variants of the game may impose maneuverability constraints on the players, such as a limited range of speed or acceleration. Obstacles may also be used.
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 ...
Further, the technique of regularization was used by N.N. Krasovskii in the theory of differential games. Differential inclusions are also found at the foundation of non-smooth dynamical systems (NSDS) analysis, [4] which is used in the analog study of switching electrical circuits using idealized component equations (for example using ...