Equity is usually interpreted in terms of the concept of justice, such that an equitable share of the atmospheric space is understood in terms of past emissions. This emphasizes the collective nature of sharing the burden of mitigation and the duty to act for those who have emitted the most. An alternative is considered: the aggregate costs and benefits to all Parties that could result from both increasing the level of collective ambition and implementing a climate regime that supports bold actions across all Parties. The regional impacts and carbon flow costs across differentiated scenarios are assessed and it is argued that the majority of developing-country Parties would be better off if a high ambition outcome to which all contributed, but some more than others. Moreover, those with middle or low emissions would have proportionally more to gain (or lose) relative to the level of ambition compared to those that have had higher emissions. The climate regime should be built on the principle of common but differentiated responsibility and respective capabilities (CBDR&RC), in which all act early even if some do much more; one that accounts for justice but does not forget hope.Policy relevanceDiffering interpretations of equity and the principles of the United Nations Framework Convention on Climate Change (UNFCCC) are discussed, with a focus on how these can enhance or hinder collective action. Whilst the climate change negotiations are usually taken as games in which one party gains and another loses, and interactions are dogged by continuous conflict, it is explored instead how negotiation responses can be framed in terms of cooperation. This would emphasize the gains that could be achieved by common but differentiated collective action, which could result in a collective avoidance of impacts. The possibilities that this shift of perspective could bring are explored by comparing costs under global cooperation (or lack of it). It is found that cooperation reduces the total costs for these regions. Thus, thinking in terms of cooperation focuses the options for negotiation on the means and interpretations of the UNFCCC principles that spur action and avoid climate impacts through collective action.