Equilibria for abstract economies with convex or acyclic valued correspondences

Abstract Using collectively fixed point theorems, we establish new equilibrium results for abstract economies where the constraint and preference correspondences are Kakutani or acyclic maps. First we present a variety of new collectively fixed point theorems based on a generalized Schauder type theorem. This then enables us to establish new equilibrium results for abstract economies where, in particular, we obtain new general results for acyclic valued constraint and preference correspondences.