# A Differential Game Described by a Hyperbolic System

Serdica Mathematical Journal (1999)

- Volume: 25, Issue: 4, page 259-282
- ISSN: 1310-6600

## Access Full Article

top## Abstract

top## How to cite

topSouroujon, 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 -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.