Geodesic
Cooperative solutions in communication games
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 4 (2012), pp. 37-45

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The computational algorithm for finding the shortest trajectory connecting some set of initial vertices with some set of terminal vertices is proposed. The trajectory may consist of paths having common edges. The cost of passing through a common edge enters the total cost of trantistion only once. The additional condition that the paths of the players need to contain predefined vertices is introduced. The algorithm built is used to compute the value of a characteristic function of corresponding cooperative game, this lets effectively compute different optimal solutions of cooperative theory. The computational experiment with 26 vertices is held in the research, and the Shapley value for the case with three players is computed.
Keywords: networks, cooperative games, Shapley value, characteristic function.
Mots-clés : Bellman equation 
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     author = {M. I. Karpov and L. A. Petrosyan},
     title = {Cooperative solutions in communication games},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
     pages = {37--45},
     publisher = {mathdoc},
     number = {4},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSPUI_2012_4_a3/}
}
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M. I. Karpov; L. A. Petrosyan. Cooperative solutions in communication games. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 4 (2012), pp. 37-45. http://geodesic.mathdoc.fr/item/VSPUI_2012_4_a3/