Generalizations of the Nash equilibrium theorem on generalized convex spaces (Q2747944)

This article presents some generalizations of the classical von Neumann-Sion minimax theorem, the Fan-Ma intersection theorem, the Fan-Ma type analytic alternative, and the Nash-Ma equilibrium theorem in \(G\)-convex spaces without any linear structure (a \(G\)-convex space \((X,D,\Gamma)\) is a triple in which \(X\) is a topological space, \(D\) a nonempty set such that, for each \(A= \{a_0,a_1,\dots, a_n\}\subseteq D\), \(n= 1,2,\dots\), there exists a subset \(\Gamma(A)\) of \(X\) and a continuous function \(\phi_A:\Delta_n\to \Gamma(A)\) for which \(J\subseteq \{0,1,\dots, n\}\) implies \(\phi_A(\Delta_J)\subseteq \Gamma(\{a_j: j\in J\})\); here \(\Delta_n\) is an \(n\)-simplex).