This paper reconsiders a widely used game of coalition formation in international environmental negotiations. Due to the mathematical problems of giving a full characterization of the solution, up to now most of the work on this subject rested on numerical simulations to derive results. In this paper we show for a general class of payoff functions that when the game is approximated by assuming a continuum of players, a solution can be found. Using this result as a "benchmark solution", we further show that gains from cooperation resulting in simulations are due to an "integer effect", i.e. coalition size being treated as a discrete variable.