This paper analyses stability of coalitions for greenhouse gas abatement under different sharing rules applied to the gains from cooperation. We use a 12-region model to examine internal and external stability of coalitions. We determine and compare stable coalitions under different surplus sharing rules; for example, grandfathering (sharing proportional to current emissions) and a number of equitable rules, i.e. sharing according to historical responsibilities for past emissions. Due to strong free-rider incentives we find only small stable coalitions for all sharing rules examined. We observe that stable coalitions consist of regions with low marginal abatement costs that are attractive partners in any coalition and regions receiving the highest shares of the surplus from cooperation under a particular sharing rule. We find that equitable rules may not be conducive to success: in fact, a grandfathering scheme leads to the most successful coalition in terms of global abatement and global welfare.