The study of Pareto equilibria for multiobjective games by fixed point and Ky Fan minimax inequality methods

In this paper, we present two ways to study the existence of weight Nash-equilibria and Pareto equilibria for multiobjective games. One is the ‘fixed-point method’ which is well known; and the second is the application of ‘Ky Fan minimax inequality’, which is not often used in the study of optimization, game theory, and mathematical programming. As results, several existence theorems for weight Nash-equilibria and Pareto equilibria are established which improve and unify the corresponding results in the recently existing literature.