Many countries signed the Paris Agreement (2015) to reduce greenhouse gas emissions. However, the national commitments do not include international shipping. In a separate agreement, countries are negotiating specific targets to reduce emissions from international shipping by 20 to 30% in 2030 and by 70 to 80% in 2040, compared to emission levels in 2008. These targets exist, but sufficient global emission reduction policies are not yet in place. The updated greenhouse gas strategy stipulates a limitation on the greenhouse gas intensity of fuels, complemented by an economic instrument. Since the IMO does not possess legislative power over member states, the policy instruments it stipulates are more likely to be adopted if they are self-enforcing, ensuring that countries are better off with the policy measures than without. In this paper, we analyze three policy scenarios. The first best scenario uses the world social cost of carbon as a basis. Since full global cooperation is unrealistic due to unenforceable international agreements, this scenario serves as a benchmark. The second type of scenario is the non-cooperative scenario, where each country sets its own carbon tax based on its national climate damage. The third type of scenario is the bilateral cooperation scenario, where a pair of countries agrees on a common carbon policy.