Multi-Time Generalized Nash Equilibria with Dynamic Flow Applications

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.