In September 2020, the European Parliament decided to include the CO2 emitted on the all intra-European and 50% of extra-European voyages in the European Union Emission Trading System (EU-ETS) starting from 2022, in order to reduce the CO2 emission. With the implementation of EU-ETS, the maritime supply chain will inevitably be significantly affected. Different carbon quota allocations in ETS have different impact on the CO2 emission reduction, which motivates us to investigate the effect of different carbon quota allocations on maritime CO2 emission reduction. Therefore, this paper considers two carbon quota allocations: the historical total quantity method and the historical intensity method, and develops a game model for each method. Then, the equilibrium solutions of each game model are analyzed. With the help of the system dynamics and the software Vensim, numerical experiments are conducted to verify the properties obtained in the analysis of the equilibrium solutions. The experimental results indicate that 1) Green technology (GT) can effectively reduce carbon emissions. Based on long-term simulation results, the GT investments will be gradually offset by profiting from carbon quota trading. 2) Profits may vary with price, but the Historical Intensity method consistently achieves better carbon reduction effects or relatively higher profits. 3) The marginal profits of companies with similar historical intensity baselines are almost the same. This gives an advantage to companies who implement green technologies earlier, as they can quickly gain returns from GT.