A support function approach to the characterization of optimal gain vectors in cooperative games

A dual space approach is proposed to the characterization of solutions in cooperative games, which are "non-dominated" with respect to a rather general class of "domination structures" (closed convex cones). To this aim, a general theory is proposed of correspondences between sets of Rn and their transformed in Rn+1*, as well as between their respective boundaries, and various properties of these correspondences are derived. It is shown how these results may be applied to get a complete geometrical characterization of the "non-dominated solutions", which may be computationally obtained by using the sub-differential of the support function of the original set. Further extensions are given, for example to the computation of "non-dominated decisions".