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Multi-Time Generalized Nash Equilibria with Dynamic Flow Applications

Author

Listed:
  • Shipra Singh

    (Department of Mathematics, The Technion—Israel Institute of Technology, Haifa 3200003, Israel
    These authors contributed equally to this work.)

  • Aviv Gibali

    (Department of Mathematics, ORT Braude College, Karmiel 2161002, Israel
    The Center for Mathematics and Scientific Computation, University of Haifa, Haifa 3498838, Israel
    These authors contributed equally to this work.)

  • Simeon Reich

    (Department of Mathematics, The Technion—Israel Institute of Technology, Haifa 3200003, Israel
    These authors contributed equally to this work.)

Abstract

We propose a multi-time generalized Nash equilibrium problem and prove its equivalence with a multi-time quasi-variational inequality problem. Then, we establish the existence of equilibria. Furthermore, we demonstrate that our multi-time generalized Nash equilibrium problem can be applied to solving traffic network problems, the aim of which is to minimize the traffic cost of each route and to solving a river basin pollution problem. Moreover, we also study the proposed multi-time generalized Nash equilibrium problem as a projected dynamical system and numerically illustrate our theoretical results.

Suggested Citation

  • Shipra Singh & Aviv Gibali & Simeon Reich, 2021. "Multi-Time Generalized Nash Equilibria with Dynamic Flow Applications," Mathematics, MDPI, vol. 9(14), pages 1-23, July.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:14:p:1658-:d:594103
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    References listed on IDEAS

    as
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