We identify the core as an appealing stability concept of cooperative game theory, but argue that the non-cooperative approach has conceptual advantages in the context of economic problems with externalities. Therefore, we derive a non-cooperative foundation of core-stability for positive externality NTU-games. First, in the spirit of Hart/Kurz (1983), we develop a game that we call -game and show that strong Nash equilibria coalition structures in this game are identical to α- and β-core stable coalition structures. Second, as a by-product of the definition of the -game, we develop an extension called an game. Finally, we compare equilibria in theH- and I-game with those in the Δ- and Ѓ-game of Hart and Kurz (1983).