Coincidence theorems for families of multimaps and their applications to equilibrium problems
Let \(\{X_i\}_{i\in I}\), \(\{Y_j\}_{j\in J}\) be two families of convex sets each in a Hausdorff locally convex topological vector space and \(\{H_j:X=\prod_{i\in I} X_i\multimap Y_j\}_{j\in J}\), \(\{T_i:Y=\prod_{j\in J} Y_j\multimap X_i\}_{i\in I}\) be two families of multimaps. The paper is primarily concerned with the study of the existence of some coincidence points for the multimaps \(H=\prod_{j\in J}H_j\) and \(T=\prod_{i\in I}T_i\). Using some selection theorems and fixed point theorems the authors establish, under various conditions, several coincidence theorems for \(H\) and \(T\). In the last part of the paper the authors study the equilibrium problem with \(m\) families of players and \(2m\) families of constraints on strategy sets. Applying the coincidence theorems obtained in the first part the authors establish various existence theorems of equilibria of this problem and existence theorems of equilibria of abstract economics with two families of players.
scientific article; zbMATH DE number 1883749