Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/450

 Title: A Differential Game Described by a Hyperbolic System Authors: Souroujon, Diko Keywords: Differential Gameε-Slater Saddle Pointε-Slater Maximin and MinimaxHyperbolic Dynamic SystemHyperbolic Boundary-Value ProblemApproximat Model (scheme) Issue Date: 1999 Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences Citation: Serdica Mathematical Journal, Vol. 25, No 4, (1999), 259p-282p 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 strategies, program ε-Slater maximins and minimaxes for each ε ∈ R^N > 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 program 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. URI: http://hdl.handle.net/10525/450 ISSN: 1310-6600 Appears in Collections: Volume 25 Number 4

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