Polynomial Time Algorithms for Determining Optimal Strategies

We study the multiobjective control of time-discrete systems with given starting and final states. The dynamics of the system is controled by p actors (players) which intend to minimize their integral-time costs of systemʹs passages by a certain trajectory. We seek for a Nash equilibrium which can be gained as an algorithmic solution of a noncooperative game. Sufficient conditions for the existence of Nash equilibria for the considered dynamic noncooperative games are given and polynomial-time algorithms for finding the optimal strategies are elaborated.