General theory of equilibrium in models with complementarities

Abstract

We provide a new and general theory of order nearest comparative statics for subsets of equilibria in models with complementarities used widely in economics and other disciplines. Order nearest equilibria are motivated naturally in the theory of monotone comparative statics of equilibrium, but their existence does not follow from results based on weak set order or strong set order, in general. We provide such results and develop the general theory using weak monotonicity of selections from best response correspondences and two new set comparison relations: Star complete relation and star lattice relation. We do not require any continuity properties. Our results hold for standard models with complementarities prevalent in the literature and allow for new cases.