An Approximation Theorem and Generic Uniqueness of Weakly Pareto-Nash Equilibrium for Multiobjective Population Games

We mainly study an approximation theorem and generic uniqueness of weakly Pareto-Nash equilibrium (PNE) for multiobjective population games. First, we define the concept of approximate weakly PNE of multiobjective population games. Then, an approximation theorem is proved under very mild conditions. Furthermore, we prove the generic uniqueness of weakly PNE for multiobjective population games by establishing a function space. Finally, we obtain the generic uniqueness of weakly PNE for multiobjective population games in the case of function perturbation. The above results are new and improve the related results of the recent literature.