A Differential Game Described by a Hyperbolic System
Diko Souroujon, Asen L. Dontchev · Bulgarian Digital Mathematics Library (BulDML) at IMI-BAS (Institute of Mathematics and Informatics) · 1999
Abstract. An antagonistic differential game of hyperbolic type with a separable linear vector pay-off function is considered. The main result is the description of all ε-Slater saddle points consisting of program strate-gies, program ε-Slater maximins and minimaxes for each ε ∈ RN> for this game. To this purpose, the considered differential game is reduced to find the optimal program strategies of two multicriterial problems of hyperbolic type. The application of approximation enables us to relate these problems to a problem of optimal program control, described by a system of ordinary differential equations, with a scalar pay-off function. It is found that the result of this problem is not changed, if the players use positional or pro-gram strategies. For the considered differential game, it is interesting that the ε-Slater saddle points are not equivalent and there exist two ε-Slater saddle points for which the values of all components of the vector pay-off function at one of them are greater than the respective components of the other ε-saddle point. Introduction. The present paper is a continuation of the results of [11] and [12], related to the antagonistic multicriterial differential games, described by a hyperbolic dynamic system.