Abstract. 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 bar- gaining set. Key words: TV games, vN-M stable sets, large cores, bargaining sets. 1. Introduction Along with the Shapley value, the core is the most popular solution concept for cooperative games and it has found many economic applications. A major attraction of the core is its uniqueness and its characterization through sets of inequalities, which makes it a relatively easy object to handle. On the other hand, a conceptually better solution concept is the so-called von Neumann-Morgenstern stable set, introduced by von Neumann and Morgenstern (1944). For many years stable sets were the standard solution concept for cooperative games and the subject of many investigations (see, e.g., the surveys of Lucas, 1992, and Owen, 1995). Int J Game Theory (2005) 33: 189–213 DOI: 10.1007/s001820400191 We thank Jean-Francois Mertens, Enrico Minelli, William Thomson, and two anonymous referees for helpful comments. We also thank seminar audiences at CORE, Cornell, Pescara, and Rochester. We gratefully acknowledge the financial support of the Ministero dell’Istruzione, dell’Universita´ e della Ricerca. Stable cores of large games Massimo Marinacci and Luigi Montrucchio Dipartimento di Statistica e Matematica Applicata and ICER, Universita` di Torino, Piazza Arbarello 8, 10122 Torino, Italy. E-mails: massimo.marinacci@unito.it and luigi.montrucchio@unito.it URL: http://web.econ.unito.it/gma. Revised: September 2004