In this paper, some further results on the stability of Ky Fan's points are proposed by introducing a type of stronger perturbation of section mappings defined by a semi-metric called the maximum Hausdorff semi-metric, and the existence of the essential components of the set of Ky Fan's points to this perturbation is proved. As an application, the existence of the essential component of the Nash equilibrium is presented using the proposed method, and strong robustness to payoff function perturbation is achieved.
Keywords: Ky Fan’s points; Nash equilibrium; essential component; maximum Hausdorff semi-metric; section mappings.