The objective of this paper is to study in which way the strategies to combat climate change, as prescribed in the UN SDG number 13, are influenced by ambiguity aversion. Countries can tailor the UN SDGs to their priorities and situations, but the urgency in their planned actions to combat climate change and its impact is affected by the form of uncertainty surrounding their decisions. Following a Choquet-Brownian process to model ambiguity aversion on the dynamics of environmental damage, we study an international pollution control problem where countries may behave cooperatively or non-cooperatively. We show that carbon emissions decrease, as perceived ambiguity increases, in keeping with the precautionary principle, and such decrease is lower if countries behave non-cooperatively. We also examine the interrelation between the precautionary principle and the effects of a declining social discount rate and increase in population, and find that optimal policies induce more precaution. Our results have important implications for national strategies and actions to combat climate change.