Optimal paths in network games with p players
Proceedings of the 5th Twente workshop on on Graphs and combinatorial optimization
Graph theory: An algorithmic approach (Computer science and applied mathematics)
Graph theory: An algorithmic approach (Computer science and applied mathematics)
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In this paper we study a special class of multiobjective discrete control problems on dynamic networks. We assume that the dynamics of the system is controlled by p actors (players) and each of them intend to minimize his own integral-time cost by a certain trajectory. Applying Nash and Pareto optimality principles we study multiobjective control problems on dynamic networks where the dynamics is described by a directed graph. Polynomial-time algorithms for determining the optimal strategies of the players in the considered multiobjective control problems are proposed exploiting the special structure of the underlying graph. Properties of time-expanded networks are characterized. A constructive scheme which consists of several algorithms is presented.