Geodesic
Power Level Management in Wireless and DSL Networks with Transmission Cost
Contributions to game theory and management, Tome 1 (2007), pp. 15-41

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We study power level management in optimization and game frameworks with assumption that there is a transmission cost. In the optimization framework there is a single decision-maker who assigns network resources and in the game framework players share the network resources according to Nash equilibrium. We study conditions for uniqueness of the Nash equilibrium. Besides we provide a closed form solution to the problems, which allows us to solve it in a finite number of operations, and we also consider a jamming plot of the game.
Keywords: Nash equilibrium, resource allocation, non-linear programming. 
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     author = {Eitan Altman and Konstantin Avrachenkov and Andrey Garnaev},
     title = {Power {Level} {Management} in {Wireless} and {DSL} {Networks} with {Transmission} {Cost}},
     journal = {Contributions to game theory and management},
     pages = {15--41},
     publisher = {mathdoc},
     volume = {1},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CGTM_2007_1_a2/}
}
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Eitan Altman; Konstantin Avrachenkov; Andrey Garnaev. Power Level Management in Wireless and DSL Networks with Transmission Cost. Contributions to game theory and management, Tome 1 (2007), pp. 15-41. http://geodesic.mathdoc.fr/item/CGTM_2007_1_a2/