Routing Game on Parallel Networks: the Convergence of Atomic to Nonatomic

Paulin Jacquot 1, 2, 3 Cheng Wan 4, 5
1 TROPICAL - TROPICAL
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
5 DYOGENE - Dynamics of Geometric Networks
DI-ENS - Département d'informatique de l'École normale supérieure, CNRS - Centre National de la Recherche Scientifique : UMR 8548, Inria de Paris
Abstract : We consider an instance of a nonatomic routing game. We assume that the network is parallel, that is, constituted of only two nodes, an origin and a destination. We consider infinitesimal players that have a symmetric network cost, but are heterogeneous through their set of feasible strategies and their individual utilities. We show that if an atomic routing game instance is correctly defined to approximate the nonatomic instance, then an atomic Nash Equilibrium will approximate the nonatomic Wardrop Equilibrium. We give explicit bounds on the distance between the equilibria according to the parameters of the atomic instance. This approximation gives a method to compute the Wardrop equilibrium at an arbitrary precision.
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Paulin Jacquot, Cheng Wan. Routing Game on Parallel Networks: the Convergence of Atomic to Nonatomic. CDC 2018 - IEEE 57th Conference on Decision and Control, IEEE, Dec 2018, Miami, United States. ⟨hal-01762547⟩

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