The Structure of Admissible Points with Respect to Cone Dominance,
MASSACHUSETTS INST OF TECH CAMBRIDGE OPERATIONS RESEARCH CENTER
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The set of admissible pareto-optimal points of a closed convex set X is studied 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, a representation theorem of Arrow, Barankin and Blackwell is extending 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, and 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, local properties of admissible points are considered in terms of Kuhn-Tucker type characterizations. Necessary and sufficient conditions are specified for an element of X to be a Kuhn-Tucker point, conditions which, in addition, provide local characterizations of strictly admissible points.
- Theoretical Mathematics