Abstract
Worldwide cooperation is necessary to mitigate the effects of climate change. Many previous investigations employed the so-called collective risk dilemma, where the risk of losing everything whenever a target is not met was fixed from the outset, rendering predictions dependent on snapshot values assumed for this parameter, whose importance was found to be paramount. Here, we couple risk with the overall success of mitigation, investigating the co-evolution of risk and cooperation in a world where countries are partitioned in two different wealth classes, allowing us to further assess the impact of wealth inequality and homophily on the co-evolutionary dynamics. We show that the stochastic dynamics is dominated by a global attractor, typically located in a region of low risk, where most developed countries cooperate most of the time while developing countries cooperate to a lesser extent. This scenario assumes no homophily which, when moderate, can contribute to increase overall cooperation, more so when combined with the presence of a small fraction of developing countries that opt for an unconditional cooperative behavior.