We study a dynamic game of climate policy design in terms of emissions and solar radiation management (SRM) involving two heterogeneous regions or countries. Countries emit greenhouse gasses (GHGs), and can block incoming radiation by unilateral SRM activities, thus reducing global temperature. Heterogeneity is modelled in terms of the social cost of SRM, the environmental damages due to global warming, the productivity of emissions in terms of generating private benefits, the rate of impatience, and the private cost of geoengineering. We determine the impact of asymmetry on mitigation and SRM activities, concentration of GHGs, and global temperature, and we examine whether a trade-off actually emerges between mitigation and SRM. Our results could provide some insights into a currently emerging debate regarding mitigation and SRM methods to control climate change, especially since asymmetries seem to play an important role in affecting incentives for cooperation or unilateral actions.