Existence of equilibrium solutions for multi-objective population games with fuzzy parameters

This paper investigates the existence of equilibrium solutions for multi-objective population games with payoff functions involving fuzzy parameters. This paper first puts forward the concepts of α-Pareto-Nash-Slater equilibria and weakly α-Pareto-Nash-Slater equilibria for such games. Furthermore, the existence of α-Pareto-Nash-Slater equilibria is proved by Fan-Glicksberg fixed point theorem and that of weakly α-Pareto-Nash-Slater equilibria is shown by vector-valued Ky Fan inequality. Finally, their feasibility is illustrated by some examples.