The option to tackle climate change by means of Solar Radiation Management (SRM) is mostly thought to reduce efforts of mitigating greenhouse gas emissions. Here we hypothesize that (i) a unilateral threat to employ SRM can induce players to commit to strategies with increased mitigation effort compared to what would be observed at the Nash equilibrium in emission strategies only and (ii) there exists a way to share the burden imposed by commitment to avoid SRM that Pareto dominates an alternative that would involve too high current emission levels then followed by future SRM deployment. To study these hypotheses we develop a two-region, two-stage, two-period game where regions choose mitigation and SRM. While SRM targets regional climate preferences, in line with current scientific evidence its deployment leads to uncertain damages on the other region. We first develop the general theory and then study a more specific linear-quadratic application. Finally we calibrate the model to real-world data and find that hypothesis (ii) holds for plausible values.