A hierarchical framework and Bayesian game model for multi-load aggregator strategic interaction under incomplete information

High renewable penetration intensifies power fluctuations in distribution networks, making load aggregators (LAs) essential providers of flexibility. However, in practice, multiple LAs operate within the same area, with their decisions coupled through dynamic interactions in power flows and profits. Commercial privacy further creates information barriers, forcing LAs to decide under incomplete information and uncertain outcomes. To address these challenges, this paper investigates the modeling of multi-LA strategic interactions. A hierarchical information-decision-execution framework is formulated, in which a Bayesian game model is used to describe the physical and economic interdependencies among LAs, with equilibrium solutions defining the optimal strategies. Furthermore, a Productive Mixed-Attention Transformer (PMA-Transformer) is developed to enable the DSO to accurately estimate each LA's regulation capacity and resource composition, providing reliable type estimates for dynamic prior construction in the game. Finally, a constraint-aware vSoC balancing and priority-based allocation strategy (CSB-PAS) is proposed for node-level power allocation, improving computational efficiency while respecting user comfort and device constraints. Simulation results show that the proposed approach effectively meets the regulation target and enhances voltage quality. Compared with the complete information game approach, it also improves the total utility by 5.06%.