In order to study the conditions for a world self-enforcing agreement on climate change, we model cooperative and non-cooperative world climate strategies with an integrated version of the world 15-region techno-economic MARKAL model in which abatement costs and climate related damages are both included. Assuming interregional transfers to share the global gain of cooperation, our work adopts the point of view of dynamic partial equilibrium computation coupled with cooperative game-theoretic principles. The results illustrate how the climatic and economic gap between cooperation and non-cooperation, the willingness of regions to cooperate, and the amount of sidepayments, depend on the level and distribution of climate damages, the abatement costs, and the emission levels in the reference case. The internal (in)stability of farsighted coalitions without transfers (non-cooperation) is also analyzed. The current project appears to be the first one of the sort using a world, large and detailed technology explicit model such as MARKAL.