Stable cores of large games

We give general conditions, based on the largeness of the core, under which cores of exact TU games are their unique von Neumann-Morgenstern stable sets. We show that this condition is satisfied by convex games and by nonatomic exact market games. In this way, we extend and unify earlier results existing in literature. Under some additional conditions we also prove the equivalence between the core and the Mas-Colell bargaining set.