Two theses on the likelihood of international co-operation for achieving international optimality in transboundary pollution problems are being confronted: a pessimistic one and an optimistic one. On the one hand a "Small Stable Coalitions" (SSC) thesis — based on the stability of coalitions literature and put forward in several papers by Barrett, Carraro and Siniscalco — holds the view that only small subsets of the countries involved in a transfrontier pollution problem can ever emerge as a group and sign a treaty among themselves; on the other hand a "Grand Stable Coalition" (GSC) thesis — inspired by classical co-operative game theory and proposed by Chander and Tulkens — presents the contents of a feasible treaty which the authors show to enjoy some "core property", that is, to be more beneficial not only for all countries taken individually, as compared to a no treaty situation, but also more beneficial for all subgroups of them, for any partial treaty they might sign among themselves. An explicit and computable cost sharing formula for joint pollution abatement is exhibited to support the second view, designed to be included in the relevant treaty. The two views are formally developed in Section III, after that a presentation is given in Section II of the common underlying economic model of international environmental externalities. Section IV then identifies and discusses several game theoretic differences and similarities between the two approaches, namely those bearing on the notion of "coalition", on the phenomenon of "free riding" in its relation with "threats" in games with externalities, on the uses of the concept of "characteristic function" in co-operative games (with a suggested extension, designed towards reconciling the two approaches), and finally on the role of transfers and "side payments" in the international pollution problem under consideration. The concluding section stresses the fact that essentially two, different notions of group stability lie at the root of these diverging views.