Differential Game ε-Slater Saddle Point ε-Slater Maximin and Minimax Hyperbolic Dynamic System Hyperbolic Boundary-Value Problem Approximat 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.
