Abstract:  Under the assumption that the domain of the undetermined parameters is known, the existence of strong Berge equilibrium for non-cooperative games and generalized non-cooperative games are investigated. Based on the concept of strong Berge equilibrium and NS-equilibrium for non-cooperative games under uncertainty, the notions of strong Berge equilibrium for non-cooperative games and generalized non-cooperative games under uncertainty are defined. Further, the existence of the equilibrium for non-cooperative games and generalized non-cooperative games are proved by using Fan-Glicksberg fixed point theorem. Finally, a numeric example illustrates the feasibility of the proposed method.

Key words: non-cooperative games, generalized non-cooperative games, uncertainty, strong Berge equilibrium, existence