On the cores of cooperative games and the stability of the Weber set

In this paper conditions are given guaranteeing that the Core equals the D-core (the set of unDominated imputations). Under these conditions, we prove the non-emptiness of the intersection of the Weber set with the imputation set. This intersection has a special stability property: it is externally stable. As a consequence we can give a new characterization for the convexity of a cooperative game in terms of its stability (von Neumann–Morgenstern solutions) using the Weber set.