# Nash equilibria for a model of traffic flow with several groups of drivers

ESAIM: Control, Optimisation and Calculus of Variations (2012)

- Volume: 18, Issue: 4, page 969-986
- ISSN: 1292-8119

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topBressan, Alberto, and Han, Ke. "Nash equilibria for a model of traffic flow with several groups of drivers." ESAIM: Control, Optimisation and Calculus of Variations 18.4 (2012): 969-986. <http://eudml.org/doc/272910>.

@article{Bressan2012,

abstract = {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.},

author = {Bressan, Alberto, Han, Ke},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {scalar conservation law; Hamilton-Jacobi equation; Nash equilibrium; non-uniqueness},

language = {eng},

number = {4},

pages = {969-986},

publisher = {EDP-Sciences},

title = {Nash equilibria for a model of traffic flow with several groups of drivers},

url = {http://eudml.org/doc/272910},

volume = {18},

year = {2012},

}

TY - JOUR

AU - Bressan, Alberto

AU - Han, Ke

TI - Nash equilibria for a model of traffic flow with several groups of drivers

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2012

PB - EDP-Sciences

VL - 18

IS - 4

SP - 969

EP - 986

AB - 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.

LA - eng

KW - scalar conservation law; Hamilton-Jacobi equation; Nash equilibrium; non-uniqueness

UR - http://eudml.org/doc/272910

ER -

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