ESAIM: Control, Optimisation and Calculus of Variations

Table of Contents - October 2012 - Volume 18, Issue 04  

Research Article

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

Alberto Bressana1 and Ke Hana1

a1 Department of Mathematics, Penn State University University Park, 16802 Pa, USA. bressan@math.psu.edu; kxh323@psu.edu

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.

(Received August 20 2011)

(Online publication January 16 2012)

Key Words:

  • Scalar conservation law;
  • Hamilton-Jacobi equation;
  • Nash equilibrium

Mathematics Subject Classification:

  • 35E15;
  • 49K20;
  • 91A12