Equilibrium Points for Open Acyclic Relations

Abstract

A formulation of a fixed point theorem, which can be applied conveniently to non-cooperative games and cooperative games, is suggested in this note.Let N1, … , Nm be m non-empty, finite disjoint sets. For k = 1, … , m we denote by Sk the simplex the coordinates of whose points are indexed by the members of Nk; thus Sk is the collection of all real functions xk defined on Nk which satisfy:1.11.2