We develop a two-player, two-period game of climate change. In the first period, players non-cooperatively choose their emission level, which yields a private benefit. Aggregate emissions then determines the extent of the environmental damage that is incurred in the second period. In the second period, depending on aggregate emissions, players can decide to undertake solar radiation management (SRM) at some cost. SRM is a means to reduce temperature, but at the same time it is perceived as a risky activity since it potentially involves a series of negative environmental impacts. This is captured by assuming that positive SRM induces a shift from a certain damage to a (larger) expected damage. Solving for the Nash equilibrium in SRM strategies allows us to identify a critical emission threshold that triggers (unilateral) SRM by the player that is the most vulnerable to climate change. Moving back to the first period, we then investigate how the potential deployment of SRM in the future affects current emissions. In particular, we wonder if the threat of SRM may act as a coordination device. For that purpose we compare two alternative scenarios. Either the players commit to meeting the threshold and face the resulting coupled constraint on aggregate emissions. Or they get rid of it and non-cooperatively choose their emissions knowing that this will trigger (unilateral) SRM. Solving for the Nash equilibrium corresponding to the latter situation and the coupled constraint Nash equilibrium for the former, we show that under some conditions players may individually find it optimal to refrain from emitting too much in order to avoid SRM. This conclusion holds true even in the worst scenario in which one player -- the one that won't undertake SRM -- bears alone the responsibility of meeting (or not) the constraint.