Carbon leakage and competitiveness concerns are some of the main reasons why an international environmental agreement is lacking to fight climate change. Many studies discussed the adoption of a border tax adjustment (BTA) to allow countries that would like to implement a carbon tax to level the playing field with imports. The big drawback from these studies is that the other country is not allowed to react by adopting itself a carbon tax to avoid being punished with the BTA. The model proposed in this paper looks at the optimization of two different governments and their respective firms. A BTA parameter is modeled between 0 and 1 representing the possible value of the BTA depending on both countries environmental policy allowing countries to have different carbon policies. The result that a BTA parameter of 0.5 yields the highest total welfare could increase its acceptance within the WTO.