On the stability of the solution for multiobjective generalized games with the payoffs perturbed

This paper studies the stability of weakly Pareto–Nash and Pareto–Nash equilibrium for multiobjective generalized games with the payoff perturbed. Using a simple characterization of the weakly Pareto–Nash solution, we obtain a generic continuous result concerning weakly Pareto–Nash solution mapping. Examples are given to show that Pareto–Nash equilibrium mapping is neither upper semicontinuous nor lower semicontinuous. Through seeking the sub-mapping, we prove that most multiobjective generalized games have at least one essential Pareto–Nash solution.