Stability of solutions for Ky Fanʹs section theorem with some applications Original Research Article

In this paper, we prove that “most of” problems in Ky Fanʹs section theorem (in the sense of Baire category) are essential and that for any problem in Ky Fanʹs section theorem, there exists at least one essential component of its solution set. As applications, we deduce both the existence of essential components of the set of Ky Fanʹs points based on Ky Fanʹs minimax inequality theorem and the existence of essential components of the set of Nash equilibrium points for general n-person non-cooperative games with non-concave payoffs.