We model climate change as a dynamic game and prove existence of a unique subgame-perfect Nash equilibrium (SPNE) that is also Markov perfect. We interpret this unique SPNE as the business-as-usual (BAU) equilibrium and show that if the countries are not sufficiently symmetric then the familiar trigger strategy equilibria may not be Pareto improvements over the BAU equilibrium and may even lack efficiency properties. We then motivate and introduce a subgame-perfect cooperative agreement as an improvement over the BAU equilibrium in the sense that every country or coalition of countries is better off in every subgame, irrespective of the extent of heterogeneity of the countries. We characterize subgame-perfect cooperative agreements and identify sufficient conditions for their existence. We show that (direct or indirect) transfers between countries to balance the costs and benefits of controlling climate change are a necessity and not a matter of approach.