Abstract: With the transition of energy systems toward decarbonization and cleaner energy integration, this study proposes a low-carbon economic optimal strategy for multi-integrated energy systems based on a dual-game framework, aiming to promote renewable energy accommodation, reduce carbon emissions, and mitigate multi-agent interest conflicts in multi-integrated energy systems. First, considering the multi-energy interaction characteristics and low-carbon requirements, a low-carbon operation framework for integrated multi-energy systems is constructed, incorporating a tiered reward-punishment carbon trading mechanism. Second, to address conflicts in energy demands and carbon quota allocation among multiple integrated energy systems, a dual-game optimization strategy combining Stackelberg-Nash bargaining is proposed. In terms of vertical coordination for carbon trading, the integrated energy system operator acts as the leader, guiding follower integrated multi-energy systems in optimizing carbon quota trading plans by setting time-of-use carbon prices. While in terms of horizontal collaboration for energy sharing, integrated multi-energy systems engage in electricity-heat sharing through Nash bargaining to maximize cooperative benefits. Finally, the model is solved using an adaptive differential evolution algorithm and the alternating direction method of multipliers. Case studies demonstrate that the proposed strategy significantly enhances the economic efficiency and low-carbon performance of integrated energy systems.