Geodesic
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

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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.

DOI : 10.1051/cocv/2011198
Classification : 35E15, 49K20, 91A12
Keywords: scalar conservation law, Hamilton-Jacobi equation, Nash equilibrium 
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     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},
     publisher = {EDP-Sciences},
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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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