We study under which conditions the core of a game involved in a convex decomposition of another game turns out to be a stable set of the decomposed game. Some applications and numerical examples, including the remarkable Lucas five player game with a unique stable set different from the core,...

We extend Rochfords (1983) notion of symmetrically pairwise-bargained equilibrium to assignment games with more than two sides. A symmetrically multilateral-bargained (SMB) allocation is a core allocation such that any agent is in equilibrium with respect to a negotiation process among all...