A Section Theorem in Topological Ordered Spaces and its Applications to the Existence of Pareto Equilibria for Multi-objective Games

Section theorem has become an important role in social economy and mathematics field. The solutions of several problems, for example, optimization problem, fixed point problem, non-cooperative game problem, complementarity problem, and variational inequality problem, can be formulated as special cases of section theorem. So it is necessary to study section problem. In the setting of topological ordered spaces, the main purpose of this paper is to prove a section theorem, and next, as its applications, a weighted Nash equilibrium existence theorem and a Pareto equilibrium existence theorem for multi-objective games are obtained in topological ordered spaces. Our results improve and unify the corresponding results in the recently existing literatures.