We examine the size of stable coalitions in a participation game that has been used to model international environmental agreements, cartel formation, R&D spillovers, and monetary policy. The literature to date has relied on parametric examples; based on these examples, a consensus has emerged that in this kind of game, the equilibrium coalition size is small, except possibly when the potential benefits of cooperation are also small. In this paper, we develop a non-parametric approach to the problem, and demonstrate that the conventional wisdom is not robust. In a general setting, we identify conditions under which the equilibrium coalition size can be large even when potential gains are large. Contrary to previously examined leading special cases, we show that reductions in marginal abatement costs in an international environmental game can increase equilibrium membership, and we provide a measure of the smallest reduction in costs needed to support a coalition of arbitrary size.