We consider the problem of cost sharing in the presence of increasing returns to scale and potential strategic behavior on the part of consumers. We show that any smooth and strictly monotonic mechanism for which a Nash equilibrium exists for all profiles of convex and monotonic preferences must be dictatorial. However, we propose a cost sharing mechanism, the decreasing serial mechanism, for which an interesting domain restriction ensures existence of a noncooperative equilibrium for its cost sharing game. A characterization theorem of the mechanism based on the strategic properties of existence, uniqueness, and efficiency of its noncooperative equilibrium is provided.