Geodesic
Discrete optimal control problems on networks and dynamic games with p players
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2004), pp. 67-88.

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We consider a pecial 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. 
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Dmitrii Lozovanu; Stefan Pickl. Discrete optimal control problems on networks and dynamic games with $\mathbf p$ players. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2004), pp. 67-88. https://geodesic-test.mathdoc.fr/item/BASM_2004_2_a7/

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