Volume 18, Number 4, October-December 2012
|Page(s)||969 - 986|
|Published online||16 January 2012|
Nash equilibria for a model of traffic flow with several groups of drivers
Traffic flow is modeled by a conservation law describing the density of cars. It is assumed that each driver chooses his own departure time in order to minimize the sum of a departure and an arrival cost. There are N groups of drivers, The i-th group consists of κi drivers, sharing the same departure and arrival costs ϕi(t),ψi(t). For any given population sizes κ1,...,κn, we prove the existence of a Nash equilibrium solution, where no driver can lower his own total cost by choosing a different departure time. The possible non-uniqueness, and a characterization of this Nash equilibrium solution, are also discussed.
Mathematics Subject Classification: 35E15 / 49K20 / 91A12
Key words: Scalar conservation law / Hamilton-Jacobi equation / Nash equilibrium
© EDP Sciences, SMAI, 2012
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