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Nash Equilibria in Traffic Networks with Multiple Populations and Origins–Destinations

Author

Listed:
  • Rinaldo M. Colombo

    (University of Brescia)

  • Luca Giuzzi

    (University of Brescia)

  • Francesca Marcellini

    (University of Brescia)

Abstract

Different populations of vehicles travel along a network. Each population has its origin, destination and travel costs — which may well be unbounded. Under the only requirement of the continuity of the travel costs, we prove the existence of a Nash equilibrium for all populations. Conditions for its uniqueness are also provided. A few cases are treated in detail to show specific situations of interest.

Suggested Citation

  • Rinaldo M. Colombo & Luca Giuzzi & Francesca Marcellini, 2025. "Nash Equilibria in Traffic Networks with Multiple Populations and Origins–Destinations," Journal of Optimization Theory and Applications, Springer, vol. 206(2), pages 1-26, August.
    • Handle: RePEc:spr:joptap:v:206:y:2025:i:2:d:10.1007_s10957-025-02706-4
    DOI: 10.1007/s10957-025-02706-4
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    References listed on IDEAS

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    1. Rinaldo M. Colombo & Helge Holden, 2016. "On the Braess Paradox with Nonlinear Dynamics and Control Theory," Journal of Optimization Theory and Applications, Springer, vol. 168(1), pages 216-230, January.
    2. Anna Nagurney & David Parkes & Patrizia Daniele, 2007. "The Internet, evolutionary variational inequalities, and the time-dependent Braess paradox," Computational Management Science, Springer, vol. 4(4), pages 355-375, October.
    3. Hubert Asienkiewicz & Łukasz Balbus, 2019. "Existence of Nash equilibria in stochastic games of resource extraction with risk-sensitive players," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 502-518, October.
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