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

Alberto Bressan; Ke Han

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

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

Abstract

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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.

How to cite

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Bressan, 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 -

References

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