This paper aims at providing a critical overview of the main solution concepts adopted by the cooperative game theoretical approach in analysing the constitution of an international environmental agreement (IEA). The first part is mainly descriptive and focuses on the basic features of the ‘global warming game’ characterizing the differences of the cooperative and non‐cooperative approaches to deal with this theme. It then presents the most adopted cooperative solution concepts critically analysing their ratio. Furthermore, two alternative solutions, the Rawlsian Nucleolus and a ‘revisited’ Nash Bargaining solution are proposed, both based on the concept of Minimum Feasible Core. The second part is dedicated to a numerical exercise based on a standard emissions game in order to compare the mentioned concepts with particular focus on their redistributive properties and on their capability to minimize the potential losses caused by free riding. The Rawlsian Nucleolus is, among the considered solutions, the one with the highest redistributive properties, outperforming, on this regard, the Chander and Tulkens solution that still tends to prioritize polluted countries. The ability of avoiding losses from free riding is shown to be strongly correlated with the redistributive properties of solution concepts till the point that their ranking perfectly coincides.