We offer a simple analytic framework for modelling an asymmetric multi-country world that faces negative impacts of climate change. A two-player asymmetric game combines economic efficiency and environmental vulnerability in the North-South competitive system. Comparison of competitive (Nash equilibrium) and cooperative strategies sheds a new light on integration between international and domestic climate policies. Focusing on the economic and environmental inequalities, we analyse the range of strategies that ensure positive payoffs for both North and South. Modelling alternatives for adaptation, mitigation, and international transfer are discussed and analysed in this framework.