International climate negotiations occur against the backdrop of increasing collective risk: the likelihood of catastrophic economic loss due to climate change will continue to increase unless and until global mitigation efforts are sufficient to prevent it. We introduce a novel alternating-offers bargaining model that incorporates this characteristic feature of climate change. We test the model using an incentivized experiment. We manipulate two important distributional equity principles: capacity to pay for mitigation of climate change and vulnerability to its potentially catastrophic effects. Our results show that less vulnerable parties do not exploit the greater vulnerability of their bargaining partners. They are, rather, more generous. Conversely, parties with greater capacity are less generous in their offers. Both collective risk itself and its importance in light of the recent Intergovernmental Panel on Climate Change report make it all the more urgent to better understand this crucial strategic feature of climate change bargaining.