Geodesic
Atomic Routing Game with Capacity Constraints
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 10 (2018) no. 1, pp. 65-82

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A model of an atomic routing game is considered. A network in this model has capacity constraints. Players in this game choose routes from some sources to one sink. The cost of passing each arc is determined by an increasing and convex function that depends on the number of players. Algorithms for finding the Nash equilibrium and social optimum are developed. These algorithms have a polynomial time complexity. The model can be used for transport networks with limited traffic flows.
Keywords: network games, routing games, network flows, Nash equilibrium, algorithm for finding equilibrium. 
@article{MGTA_2018_10_1_a3,
     author = {Darya A. Paltseva and Andrey P. Parfyonov},
     title = {Atomic {Routing} {Game} with {Capacity} {Constraints}},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {65--82},
     publisher = {mathdoc},
     volume = {10},
     number = {1},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2018_10_1_a3/}
}
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Darya A. Paltseva; Andrey P. Parfyonov. Atomic Routing Game with Capacity Constraints. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 10 (2018) no. 1, pp. 65-82. http://geodesic.mathdoc.fr/item/MGTA_2018_10_1_a3/