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

Alberto Bressan, Ke Han
2012 E S A I M: Control, Optimisation and Calculus of Variations  
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 κ i drivers, sharing the same departure and arrival costs ϕ i (t), ψ i (t). For any given population sizes κ 1 , . . . , κ n , we prove the existence of a Nash equilibrium solution, where no driver can lower his own total cost by
more » ... g a different departure time. The possible nonuniqueness, and a characterization of this Nash equilibrium solution, are also discussed.
doi:10.1051/cocv/2011198 fatcat:rtefr4gyybd55ojsj6244uw3sy