This paper deals with the design of equilibrium solutions with coupled constraints in dynamic games of greenhouse gas (GHG) emission abatement. Self-enforcing International Environmental Agreements (IEA) among different groups of countries call for Nash equilibrium solutions when the abatement strategies of the countries are defined. In this paper we study the effect of having another party, like e.g. the United Nations, which would impose to all players a coupled constraint on the total emissions allowed over the 21^st century, or on the concentration of carbon reached at the end of the century. We show, using different formulations of environmental game, that the normalized equilibria obtained under a coupled constraint on emissions or concentration are close to Pareto optimality. This gives a clue on the way the post-Kyoto negotiations could yield an agreement which could be close to efficiency.