Geodesic
Potential game in parallel transport network with symmetric externalities
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 15 (2023) no. 4, pp. 94-105

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The paper considers a model of a transport system with parallel channels and BPR delay functions with symmetric linear externalities. We consider the case where the impact of channel loads to the delay is pairwise symmetric. For this case, it is proved that the game of traffic allocation among channels is potential, and the price of anarchy is limited by the value $\frac{4}{3}$.
Keywords: Wardrop equilibrium, optimal profile, social costs, Price of Anarchy, externalities. 
@article{MGTA_2023_15_4_a4,
     author = {Julia V. Chirkova},
     title = {Potential game in parallel transport network with symmetric externalities},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {94--105},
     publisher = {mathdoc},
     volume = {15},
     number = {4},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2023_15_4_a4/}
}
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Julia V. Chirkova. Potential game in parallel transport network with symmetric externalities. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 15 (2023) no. 4, pp. 94-105. http://geodesic.mathdoc.fr/item/MGTA_2023_15_4_a4/