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The threat of climate catastrophes has been shown to radically change optimal climate policy and prospects for international climate agreements. We characterize the strategic behavior in emissions mitigation and agreement participation with a potential climate catastrophe happening at a temperature threshold. Players are heterogeneous in a conceptual and two numerical models. We confirm that thresholds can induce large, stable coalitions. The relationship between the location of the threshold and the potential for cooperation is non-linear, with the highest potential for cooperation at intermediate temperature thresholds located between 2.5 and 3 degrees of global warming. We find that some regions such as Europe, the USA and China are often pivotal to keeping the threshold because the rest of the world abandons ambitious mitigation and the threshold is crossed without their participation. As a result, their incentives to cooperate can be amplified at the threshold. This behavior critically depends on the characteristics of the threshold as well as the numerical model structure. Conversely, non-pivotal regions are more likely to free-ride as the threshold inverts the strategic response of the remaining coalition. Moreover, we find that our results depend on which equilibrium concepts is applied to analyze coalition formation as well as the introduction of uncertainty about the threshold.
