STRUCTURE OF ADMISSIBLE POINTS WITH RESPECT TO CONE DOMINANCE

We study the set of admissible (Pareto-optimal) points of a closed, convex set X when preferences are described by a convex, but not necessarily closed, cone. Assuming that the preference cone is strictly supported and making mild assumptions about the recession directions of X, we extend a representation theorem of Arrow, Barankin, and Blackwell by showing that all admissible points are either limit points of certain strictly admissible alternatives or translations of such limit points by rays in the closure of the preference cone. We also show that the set of strictly admissible points is connected, as is the full set of admissible points. Relaxing the convexity assumption imposed upon X, we also consider local properties of admissible points in terms of Kuhn-Tucker type characterizations. We specify necessary and sufficient conditions for an element of X to be a Kuhn-Tucker point, conditions which, in addition, provide local characterizations of strictly admissible points. © 1979 Plenum Publishing Corporation.