From discrete to continuous Wardrop equilibria

Jean-Bernard Baillon; Guillaume Carlier

doi:10.3934/nhm.2012.7.219

Article Contents

2012, Volume 7, Issue 2: 219-241. Doi: 10.3934/nhm.2012.7.219

This issue Previous Article Iterative strategies for solving linearized discrete mean field games systems Next Article Explicit solutions of some linear-quadratic mean field games

From discrete to continuous Wardrop equilibria

Jean-Bernard Baillon^1, and
Guillaume Carlier^2,

1.
Laboratoire Marin Mersenne, Université Paris I, 90 rue de Tolbiac, 75013, Paris
2.
CEREMADE, UMR CNRS 7534, Université Paris-Dauphine, Pl. de Lattre de Tassigny, 75775 Paris Cedex 16

Received: November 2011

Revised: March 2012

Published: June 2012

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Abstract

The notion of Wardrop equilibrium in congested networks has been very popular in congested traffic modelling since its introduction in the early 50's, it is also well-known that Wardrop equilibria may be obtained by some convex minimization problem. In this paper, in the framework of $\Gamma$-convergence theory, we analyze what happens when a cartesian network becomes very dense. The continuous model we obtain this way is very similar to the continuous model of optimal transport with congestion of Carlier, Jimenez and Santambrogio [6] except that it keeps track of the anisotropy of the network.

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Mathematics Subject Classification: Primary: 90C46, 90C35; Secondary: 49N15.

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References

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