Multi-Time Generalized Nash Equilibria with Dynamic Flow Applications

Shipra Singh, Aviv Gibali and Simeon Reich
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Shipra Singh: Department of Mathematics, The Technion—Israel Institute of Technology, Haifa 3200003, Israel
Aviv Gibali: Department of Mathematics, ORT Braude College, Karmiel 2161002, Israel
Simeon Reich: Department of Mathematics, The Technion—Israel Institute of Technology, Haifa 3200003, Israel

Mathematics, 2021, vol. 9, issue 14, 1-23

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.

Keywords: multi-time generalized Nash equilibrium problem; projected dynamical system; river basin pollution problem; traffic network equilibrium problem; variational inequality problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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