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.
Keywords: scalar conservation law, Hamilton-Jacobi equation, Nash equilibrium
@article{COCV_2012__18_4_969_0,
author = {Bressan, Alberto and Han, Ke},
title = {Nash equilibria for a model of traffic flow with several groups of drivers},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {969--986},
year = {2012},
publisher = {EDP Sciences},
volume = {18},
number = {4},
doi = {10.1051/cocv/2011198},
mrnumber = {3019468},
zbl = {1262.35199},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2011198/}
}
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 SP - 969 EP - 986 VL - 18 IS - 4 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2011198/ DO - 10.1051/cocv/2011198 LA - en ID - COCV_2012__18_4_969_0 ER -
%0 Journal Article %A Bressan, Alberto %A Han, Ke %T Nash equilibria for a model of traffic flow with several groups of drivers %J ESAIM: Control, Optimisation and Calculus of Variations %D 2012 %P 969-986 %V 18 %N 4 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/cocv/2011198/ %R 10.1051/cocv/2011198 %G en %F COCV_2012__18_4_969_0
Bressan, Alberto; Han, Ke. Nash equilibria for a model of traffic flow with several groups of drivers. ESAIM: Control, Optimisation and Calculus of Variations, Tome 18 (2012) no. 4, pp. 969-986. doi: 10.1051/cocv/2011198
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