Multilayered Decision Problems
Résumé
If we generalize the Kyoto game which was presented at Lamsade-Dimacs workshop in 2004, we obtain a decision problem which can be described by a multilayered structure. This structure represents a hidden multiobjective control problem of a time-discrete systems with given starting and final states. The dynamics of the system are controlled by p actors (players). Each of the players intends to minimize his own integral-time cost of the system's passages using a certain admissible trajectory. At each stage (level) decisions are made by the players. Nash Equilibria conditions can derived and algorithms for solving dynamic games in positional form are described. The existence theorem for Nash equilibria is related with the introduction of an auxiliary dynamic c-game. We present the decision problem in that c-game which is defined on a special layered structure. The algorithmic principle which exploits this special structure for the decision processes will be described. New complexity results are presented and first numerical results are discussed.
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