A Differential Game Described by a Hyperbolic System

Souroujon, Diko. "A Differential Game Described by a Hyperbolic System." Serdica Mathematical Journal 25.4 (1999): 259-282. <http://eudml.org/doc/11518>.

@article{Souroujon1999,
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.},
author = {Souroujon, Diko},
journal = {Serdica Mathematical Journal},
keywords = {Differential Game; ε-Slater Saddle Point; ε-Slater Maximin and Minimax; Hyperbolic Dynamic System; Hyperbolic Boundary-Value Problem; Approximat Model (scheme); differential game; hyperbolic boundary-value problem; -Slater saddle point},
language = {eng},
number = {4},
pages = {259-282},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {A Differential Game Described by a Hyperbolic System},
url = {http://eudml.org/doc/11518},
volume = {25},
year = {1999},
}

TY - JOUR
AU - Souroujon, Diko
TI - A Differential Game Described by a Hyperbolic System
JO - Serdica Mathematical Journal
PY - 1999
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 25
IS - 4
SP - 259
EP - 282
AB - 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.
LA - eng
KW - Differential Game; ε-Slater Saddle Point; ε-Slater Maximin and Minimax; Hyperbolic Dynamic System; Hyperbolic Boundary-Value Problem; Approximat Model (scheme); differential game; hyperbolic boundary-value problem; -Slater saddle point
UR - http://eudml.org/doc/11518
ER -