EXISTENCE OF NONCOOPERATIVE EQUILIBRIA IN SOCIAL-SYSTEMS

Social systems, their non-cooperative equilibria, and the auxiliary no tion of a feasibility-choice system are defined. Using a fixed point t heorem of Prakash and Sertel (Semigroup Forum, 1974, 9, 117-138) in to pological semivector spaces, equilibrium existence results are establi shed for feasibility-choice systems, and then applied to obtain an exi stence theorem for non-cooperative equilibria in social systems with a rbitrarily many individuals, each choosing behaviors according to a cl osed and upper semiconvex complete preorder from feasible regions lyin g in a locally convex Hausdorff topological vector space. One's feasib le region and preference depend continuously on one's own and others' behaviors and feasible regions, thus permitting rich externalities Als o, sets of optimal solutions are shown to be upper semicontinuous in f easible sets, and an appendix reviews hyperspaces and topological semi vector spaces.