Studies that demonstrate that climate change is human induced are becoming more and more prevalent. Even though most world leaders are aware of this urgency and know that we must work at mitigating it quickly, little has been accomplished in terms of widespread participation in an International Environmental Agreement (IEA). The purpose of this paper is to create a link between studies on the use of border tax adjustments (BTAs) and coalition formation. The main contribution is that the punishment will be based on relative emissions between signatories and defectors. It is a structure that is more likely be accepted by the World Trade Organization (WTO) since it may be seen as fair due to the fact that if signatories and defectors emit the same amount of pollution then there will be no punishment. The main results indicate that this form of punishment may lead to small, partial, or full cooperation, depending on the parameter values. Additionally, at any equilibrium level, the signatories have a punishment structure that induces defectors to reduce their emissions by the same amount. In the end, this punishment may be seen as a credible threat because at equilibrium no punishment is imposed, yet if we remove the possibility of punishment it breaks down to a situation wherein no large coalitions are feasible.