Differential Games

a branch of the mathematical theory of control, dealing with the control of an object in conflict situations. In differential games the possibilities of the players are described by differential equations containing control vectors, manipulated by the players. In choosing his control, each player can use only current information on the behavior of other players. There are two categories of differential games: those for two players and those for many players. The most thoroughly studied games are the differential games of pursuit, in which there are two players—the pursuer and the pursued. The goal of the pursuer is to guide a vector z(t) to a given set M in the shortest possible time. The goal of the pursued is to delay the moment of arrival of the vector z(t) in M. Fundamental results in the study of differen-tail games were obtained during the 1960’s in the USSR by L. S. Pontriagin, N. N. Krasovskii, E. F. Mishchenko, and B. N. Pshenichnyi and in the USA by R. Isaacs, L. Berkovitz, and W. Fleming.