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Network models of discrete optimal control and dynamic games with \(p\) players. (English. Russian original) Zbl 1046.49017
Discrete Math. Appl. 11, No. 6, 625-642 (2001); translation from Diskretn. Mat. 13, No. 4, 126-143 (2001).
Summary: We consider network models of a problem of discrete optimal control with fixed ends formulated as a game with \(p\) players. We investigate the problem of existence of optimal strategies of the players in the sense of Nash in the network dynamic model of the game with \(p\) players and obtain results which allow us to construct polynomial algorithms for solving the problem.

MSC:
49K30 Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)
91A25 Dynamic games
05C20 Directed graphs (digraphs), tournaments
90B10 Deterministic network models in operations research
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