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This paper analyses in a systematic way the effect of benefit and cost parameter heterogeneity on the stability and effectiveness of International Environmental Agreements. Compared to existing literature, we consider a more general form of heterogeneity, different functional forms and alternative collective decision making processes in coalitions with and without transfers. Using systematic numerical simulations and novel visualization techniques, we show that transfers are crucial to overcome heterogeneity both in terms of stability and effectiveness. Without, or with limited transfers heterogeneous coalitions are often unstable and ineffective. More research on less than ideal transfer schemes and collective decision making rules is necessary to bridge the gap between theoretical models and the reality of international negotiations on transboundary pollution problems. (C) 2019 Elsevier B.V. All rights reserved.