A seven-region based integrated assessment model is established in this paper targeting to model the emission reduction game worldwide. Under the Paris Agreement, given the emission mitigation scheme by 2025/2030, 2050, and 2100 for each country (region) as gaming strategy, the Nash equilibrium, the uncertainties of the game and the influences from external mitigation mechanisms are evaluated in each strategy combinations. In the reference scenario, no country (region) would take emission reduction after 2030 for the sake of their own optimal social welfare improvement, leading the global temperature rising to 2.62℃ by 2100. The Nash equilibrium remains stable even when the climatic and economic parameters are disturbed. As an alternative, an external sanction on non-mitigation is applied; in this scenario, climate change mitigation propagates across countries (regions) according to various sanction levels, in which developed countries tend to adopt mitigation strategy earlier than developing countries as a response to the non-mitigation sanction. Meanwhile, under the Paris Agreement, simulation also reveals the emission reduction from 2030 to 2050 has become crucial for making the 2℃ threshold viable if no extra mitigations are implemented before 2030. An emission reduction target higher than the developed and developing countries cutting emission 80% and 50% on 1990 level by 2050 is required in this circumstance, otherwise the global temperature will overshoot 2℃ around 2040.