The time consistency of the optimality principles in non-zero sum differential games

Abstract

The investigation of optimality principles in non-zero sum differential games and multicriterial control problems leads to the important conclusion that the optimality principles taken from the corresponding static (simultaneous game) theory are usually dynamic unstable (time inconsistent), thus they could not be used without special regularization attempts. In general the optimality principle may be considered as a point to set mapping corresponding to any differential game or multicriterial control problem. In a zero-sum differential game and multicriterial problem an "optimal" trajectory

generated by a given optimality principle has to provide the dynamic or strong dynamic stability of the optimality principle used when the process develops along the

. That's why from our point of view the consideration of the dynamic stability principles relatively to the given trajectories is important (see [1], [2], [6], [7]).