Engineering the climate via Solar Radiation Management (SRM) is increasingly considered as a component of future climate policies. We study the strategic incentives for countries to choose the level of SRM at different times in the future, accounting for the regionally uneven effect of SRM on climate variables, heterogeneous preferences of countries for the state of the global climate, and climate change adjusted GDP growth rates. We find that even though some countries would have significant gains from realizing their individually preferred level of SRM, the economic incentives for many countries are not sufficient to consider unilateral SRM implementation to be beneficial. In contrast, several countries have strong incentives to join coalitions to prevent that too much SRM is applied. The likely scenario is that a coalition will set a level of SRM close to the global efficient level.