Policies designed to control greenhouse gases imply domestic tradeoffs and international externalities, which lead to both domestic and international conflicts, influencing their feasibility and implementations. Our paper investigates two quantitative aspects within this debate. We intend to quantify the impact of: (a) the internalization of international externalities; and (b) the damage associated with a short-term view of climate policies. In this respect, we adopt the innovative (in this field) idea of model predictive control to formalize moving-horizon policy strategies and, thus, to build counterfactuals characterized by a different horizon for all policymakers.