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

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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.

Original languageEnglish (US)
Pages (from-to)969-986
Number of pages18
JournalESAIM - Control, Optimisation and Calculus of Variations
Volume18
Issue number4
DOIs
StatePublished - Oct 2012

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Control and Optimization
  • Computational Mathematics

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