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

Published online by Cambridge University Press:  16 January 2012

Alberto Bressan  and
Ke Han
Alberto Bressan
Affiliation:
Department of Mathematics, Penn State University University Park, 16802 Pa, USA. bressan@math.psu.edu; kxh323@psu.edu
Ke Han
Affiliation:
Department of Mathematics, Penn State University University Park, 16802 Pa, USA. bressan@math.psu.edu; kxh323@psu.edu
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Abstract

Traffic flow is modeled by a conservation law describing the density of cars. It isassumed that each driver chooses his own departure time in order to minimize the sum of adeparture and an arrival cost. There are N groups of drivers, Thei-th group consists of κidrivers, sharing the same departure and arrival costsϕi(t),ψi(t).For any given population sizesκ1,...,κn,we prove the existence of a Nash equilibrium solution, where no driver can lower his owntotal cost by choosing a different departure time. The possible non-uniqueness, and acharacterization of this Nash equilibrium solution, are also discussed.

Keywords

Scalar conservation lawHamilton-Jacobi equationNash equilibrium
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 18 , Issue 4 , October 2012 , pp. 969 - 986
Copyright
© EDP Sciences, SMAI, 2012

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