International climate negotiations occur against the backdrop of increasing collective risk: as long as collective mitigation efforts continue to fail, the likelihood of climate change-induced catastrophic economic loss will continue to increase. Nonetheless, no existing climate bargaining model includes this characteristic feature. We introduce a novel bargaining game that incorporates collective risk, and investigate its effects in an incentivized experiment by manipulating two important distributional equity principles related to climate change: the capacity to pay for its mitigation and vulnerability to its negative effects. Contrary to previous research, our results show that the less vulnerable parties do not exploit the greater vulnerability of their bargaining partners, rather they are more generous. Conversely, parties with greater capacity are less generous in their offers. Both collective risk itself and its consequences in light of the recent IPCC report make it all the more urgent to better understand this crucial strategic feature of climate change bargaining.