Geodesic
Cooperative strong equilibrium in a~vehicle routing game
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 5 (2013) no. 3, pp. 3-26

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In the paper game-theoretic approach is considered for the vehicle routing problem with many distributors. Any customer is characterized by demand and wholesale price. Under this scenario some customers could be unvisited by a distributor. Such a statement is called vehicle routing game, VRG, in coordinated strategies. A procedure for determining strong equilibrium in the VRG is proposed. Such solution is stable against deviations of any coalition. In the procedure the optimization problem is solved iteratively for every distributor. On each step a set of customers is reduced. Existence of two types of strong equilibrium is solved. Cooperative strong equilibrium is presented. All results are illustrated with numerical examples.
Keywords: combinatorial optimization, Nash equilibrium, strong equilibrium, cooperative strong equilibrium, transportation network, vehicle routing problem. 
@article{MGTA_2013_5_3_a0,
     author = {Nikolay A. Zenkevich and Andrey V. Zyatchin},
     title = {Cooperative strong equilibrium in a~vehicle routing game},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {3--26},
     publisher = {mathdoc},
     volume = {5},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2013_5_3_a0/}
}
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Nikolay A. Zenkevich; Andrey V. Zyatchin. Cooperative strong equilibrium in a~vehicle routing game. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 5 (2013) no. 3, pp. 3-26. http://geodesic.mathdoc.fr/item/MGTA_2013_5_3_a0/