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In the context of global warming and energy scarcity, regional integrated energy system (RIES) can effectively improve energy utilization efficiency and reduce carbon emissions. However, this leads to the increased complexity of the market transactions. To this end, based on the mixed game strategy, a multi-agent low-carbon optimal dispatch model of RIES is proposed in this paper. Firstly, to fully consider the low-carbon objective of the system, a reward and punishment ladder carbon trading mechanism and a ladder integrated demand response (IDR) model are developed. Then, the decision models of the energy management operator (EMO), multiple energy hub agents (EHAs) and the user load aggregator (ULA) are constructed respectively with the goal of economy, and carbon emission flows are introduced as constraints. The interactive trading process of various stakeholders is simulated by a mixed game with master-slave game nested bidding strategy. Finally, the economics and carbon emissions of the system in different scenarios are analyzed by examples, and the effectiveness of the proposed model is verified. Numerical simulation results show that the proposed method not only has good economic and low-carbon environmental protection benefits, but also ensures the interests of various stakeholders. • A multi-agent energy trading mechanism is proposed to realize low-carbon operation. • A ladder integrated demand respond model considering carbon compensation is developed. • A multi-agent optimization strategy based on mixed game is proposed. [ABSTRACT FROM AUTHOR]