Stability of weighted Nash equilibrium for multiobjective population games

This paper studies the existence and stability of weighted Nash equilibria for multiobjective population games. By constructing a Nash s mapping, the existence of weighted Nash equilibria is established. Furthermore, via the generic continuity method, each weighted Nash equilibrium is shown to be stable for most of multiobjective population games when weight combinations and payoff functions are simultaneously perturbed. Besides, this leads to the stability of Nash equilibria for classical population games with the perturbed payoff functions. These results play cornerstone role in the research concerning multiobjective population games.