Existence of non-cooperative equilibria in social systems

Social systems, their non-cooperative equilibria, and the auxiliary notion of a feasibility-choice system are defined. Using a fixed point theorem of Prakash and Sertel (Semigroup Forum, 1974, 9, 117-138) in topological semivector spaces, equilibrium existence results are established for feasibility-choice systems, and then applied to obtain an existence theorem for non-cooperative equilibria in social systems with arbitrarily many individuals, each choosing behaviors according to a closed and upper semiconvex complete preorder from feasible regions lying in a locally convex Hausdorff topological vector space. One's feasible region and preference depend continuously on one's own and others' behaviors and feasible regions, thus permitting rich externalities Also, sets of optimal solutions are shown to be upper semicontinuous in feasible sets, and an appendix reviews hyperspaces and topological semivector spaces.