Generic stability and essential components of generalized KKM points and applications
The authors present generic essentialness and essential components for generalized KKM points (see e.g. [\textit{P. Q. Khanh, N. H. Quan} and \textit{J.-C. Yao}, Nonlinear Anal., Theory Methods Appl. 71, No. 3--4, A, 1227--1234 (2009; Zbl 1176.47041)]) and apply them to solutions of variational inclusions and maximal elements. The definitions of a generalized KKM mapping with respect to a multivalued mapping \(T\) (\(T\)-KKM mapping in short) and \(T\)-KKM points are proposed. The authors prove generic stability: the set of essential points of a KKM-point map is a dense residual subset of a Hausdorff metric space of \(T\)-KKM maps. The existence of essential components of sets of \(T\)-KKM points is considered. From applications to solutions of variational inclusions the existence of essential components of Nash equilibria and Pareto efficient points is derived.
scientific article; zbMATH DE number 5886728
scientific article