Is the world cooperative or non-cooperative? Researchers using Game Theory to model International Environmental Agreements (IEAs) have addressed this very question from multiple perspectives. This current study aims to add to the discussion by expanding the modelling, focusing on some innovative features of the modelling, such as replacing one IEA with two simultaneous IEAs, substituting symmetric countries with asymmetric ones, comparing myopic stability with farsighted stability. It considers the cooperative and non-cooperative nature of countries that intend to build an IEA and to do this utilises not only tools from non-cooperative game theory such as the myopic stability and Nash equilibrium, but also tools from cooperative game theory, such as the farsighted stability, Shapley Value and Nash Bargaining solution. The integrated assessment model FUND developed by Richard Tol provides the cost-benefit function for pollution abatement in the game theory model used.