The global carbon emission mitigation schemes would mainly determine the trends of global climate change and the global economic growth. Although many mitigation schemes were proposed by scholars and institutions, seldom of the schemes seem to satisfy countries all around the world. It is quite urgent to find a solution to mitigate climate change, which should also be acceptable by the world. Therefore, a global carbon mitigation scheme is proposed and simulated in this paper by employing game theory and using the integrated assessment model, EMRICES. Game theory is used to analysis the free-riding behaviors for setting the mitigation scheme. The mitigation scheme firstly grantees that the increase of global temperature is no more than 2°C till 2100. Secondly, every country participating in the scheme would benefit from the scheme comparing with the situation when there is no carbon reduction request, which is called Pareto improvement principle. Accumulated welfare is used as the index and it is a function of consumptions. Thirdly, the fairness of mitigation scheme is taken into consideration as well in the scheme according to the common but differentiated responsibilities principle. The Pareto improvement principle and the common but differentiated responsibilities principle may be incompatible sometimes. If developed countries interest is adequately safeguarded, developing countries would usually bear more carbon reduction. Thus, when searching for the mitigation scheme, the two principles both as objectives are given different priorities. The Pareto improvement principle is given the primary priority. As for the common but differentiated responsibilities principle, we try to minimize the developed countries accumulated welfares improvement and maximize the developing countries. The scheme was searched as following: China should reduce 20% carbon emissions of 2005s level by 2050; USA should reduce 63% carbon emissions of 1990s level by 2050; Japan should reduce 85% carbon emissions of 1990s levels by 2050; EU should reduce 85% carbon emissions of 1990s levels by 2050; high developed countries should reduce 50% carbon emissions of 2005s levels by 2050; middle developed countries should reduce 20% carbon emissions of 2005s levels by 2050; developed countries should reduce 82% carbon emissions of 1990s levels by 2050. All the countries should keep the carbon emission level no more than 2050s after 2050. As the result shows, the global temperature increases by 1.996°C in 2100. The global temperature increment can be controlled within 2°C. All the countries or regions accumulated welfares are improved and developing countries obviously improve more than developed countries. In a word, we find a scheme that satisfies the three requirements. Finally, sensitive analysis is conducted for the important parameters. The results show that the variation of discount rate will not change the no-cooperation Nash equilibrium but it does affect the Pareto improvement solution. The higher the discount rate is, the harder would be to achieve the Pareto improvement. Developing countries discount rates are generally higher than developed countries due to the different economic consumptions growth rate among the countries. Thus, this factor should be considered as well in global climate negotiations for fairness.