To solve the problems of environmental pollution and the conflict of interests of multi-market players in a regional integrated energy system, a multi-agent game collaborative optimization method for a regional integrated energy system considering a reward and punishment ladder carbon trading mechanism and dual incentive integrated demand response is proposed. First, to fully consider the low-carbon nature of the system, a reward and punishment ladder carbon trading mechanism is introduced to limit the carbon emissions of each stakeholder. Then an integrated demand response strategy based on price and carbon compensation is proposed on the user side. Secondly, considering the initiative and decision-making ability of the source, load and storage parties, a multi-agent low-carbon interaction mechanism based on carbon trading and game collaborative optimization is proposed, and the decision-making model of each stakeholder is constructed. Finally, an adaptive differential evolution algorithm combined with the Gurobi toolbox is used to solve the proposed model. The simulation results verify the effectiveness of the proposed model. In a low-carbon framework, each stakeholder can reasonably adjust its own strategies and take into account the economic and environmental benefits of the system. This work is supported by the National Natural Science Foundation of China (No. 51607105).