To address the challenges of source-load uncertainty

multi-agent benefit distribution imbalance

and slow convergence in the collaborative optimization of multi-integrated energy systems (MIES) and distribution networks (DN)

a distributed optimal scheduling strategy based on hybrid game theory and improved analytical target cascading (ATC) method is proposed. First

interval numbers are used to characterize the fluctuation characteristics of distributed generation and loads

establishing a robust multi-agent game model. Second

the double-layer DN-MIES collaborative framework is constructed. By integrating the Nash bargaining model

a dynamic electricity price trading mechanism is established to achieve multi-agent benefit balance and market incentive compatibility among multiple agents. Furthermore

a maximum variation analysis based ATC (MVA-ATC) algorithm is designed to simultaneously handle uncertainty and computation efficiency during the distributed optimization process. Simulation results show that the proposed method significantly improves system economy

ensures fair benefit distribution among agents

and reduces computational complexity. The work provides both theoretical support and a technical pathway for collaborative optimization of multi-energy subjects in new power systems.