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Multiobjective Control of Time-Discrete Systems and Dynamic Games on Networks

In: Pareto Optimality, Game Theory And Equilibria

Author

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  • Dmitrii Lozovanu

    (Moldovan Academy of Sciences)

Abstract

We consider time-discrete systems with a finite set of states. The starting and the final states of the dynamical system are fixed. We assume that the dynamics of the system is controlled by pactors (players), and each of them intends to optimize his own integral-time cost of the system's passages by a certain trajectory. Applying Nash and Pareto optimality principles for such a model, we obtain multiobjective control problems, solutions of which correspond with solutions of noncooperative and cooperative dynamic games, respectively. Necessary and sufficient conditions for the existence of Nash equilibrium and Pareto optimum in considered game control models are derived. Such conditions for stationary and nonstationary cases of the dynamic games are formulated. In the following, we extend dynamic programming technique for determining Nash equilibrium and Pareto optimum for dynamic games in positional form, especially for dynamic games on networks. Ef- ficient polynomial-time algorithms are elaborated for finding optimal strategies of players in dynamic games on networks. These algorithms are applied for studying and solving cyclic games. In addition, computational complexity of the proposed algorithms for the considered class of dynamic problems is discussed. Some extensions and generalizations of obtained results are suggested.

Suggested Citation

  • Dmitrii Lozovanu, 2008. "Multiobjective Control of Time-Discrete Systems and Dynamic Games on Networks," Springer Optimization and Its Applications, in: Altannar Chinchuluun & Panos M. Pardalos & Athanasios Migdalas & Leonidas Pitsoulis (ed.), Pareto Optimality, Game Theory And Equilibria, pages 665-757, Springer.
    • Handle: RePEc:spr:spochp:978-0-387-77247-9_26
    DOI: 10.1007/978-0-387-77247-9_26
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