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

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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Pré-publication, Document de travail
2018
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Soumis le : mardi 10 avril 2018 - 11:15:52
Dernière modification le : mercredi 25 avril 2018 - 10:45:37

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  • HAL Id : hal-01762547, version 1

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Paulin Jacquot, Cheng Wan. Routing Game on Parallel Networks: the Convergence of Atomic to Nonatomic. 2018. 〈hal-01762547〉

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