Non-Dominated Solutions in Cooperative Games: A Dual Space Approach

Abstract

The concept of Pareto equilibrium points in cooperative games is extended to a more general class of equilibrium points, the so called non-dominated points with respect to a rather general class of "domination" cones. The problem of determining both the non-dominated decisions and the resulting non-dominated points (or solutions) is faced using a dual space approach based on techniques of convex analysis. Using this approach, also the cases of unbounded solution set and of domination cones containing subspaces may be treated and a complete characterization of the non-dominated decisions and of the corresponding solutions may be given.