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Discrete optimal control problems on networks and dynamic games with \(p\) players. (English) Zbl 1080.91016
Summary: We consider a special class of discrete optimal control problems on networks. The dynamics of the system is described by a directed graph of passages. An additional integral-time cost criterion is given and the starting and final states of the system are fixed. The game-theoretical models for such a class of problems are formulated, and some theoretical results connected with the existence of the optimal solution in the sense of Nash are given. A polynomial-time algorithm for determining Nash equilibria is proposed. The results are applied to decision making systems and determining the optimal strategies in positional games on networks.
91A43 Games involving graphs
49K30 Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)
91A25 Dynamic games
93C55 Discrete-time control/observation systems
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