Existence of simple Berge equilibrium for non-cooperative games under uncertainty

Under the assumption that the domain of the undetermined parameters can vary is known, the existence of simple Berge equilibrium for non-cooperative games is investigated.Based on the concept of simple Berge equilibrium and NS-equilibrium introduced by Zhukovskii for non-cooperative games,the notions of Pareto simple Berge equilibrium(PSBE) and Weak Pareto simple Berge equilibrium(WPSBE) are defined,and theorems of existence of the equilibrium are also provided by means of the Ky Fan inequality.Finally,a numeric example is raised to illustrate the proposed method's feasibility.