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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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