## 2 Materials and Methods
### Proposed Method
#### 2.3.4 Implementations
In addition, by employing GNNs to fuse information across multiple agents, our model endows each agent with a more comprehensive view of the environment during the execution phase, resulting in significantly enhanced decision-making quality. Experimental results in the SMAC environment demonstrate that QMIX-GNN outperforms existing methods, particularly in complex scenarios where collaboration and coordination are critical. Ablation studies further validate the contributions of our proposed information infusion and heterogeneous information processing modules. While the current work is based on the SMAC framework, which inherently influences the design of our infusion mechanism, our findings can provide valuable insights into methods for improving scalability and performance in heterogeneous environments. Future work may focus on refining the information fusion mechanism to adaptively adjust to varying task complexities and exploring privacy-aware fusion strategies to broaden the applicability of our method in scenarios with decentralized or communication-constrained agents. We believe that these enhancements will further bridge the gap between theoretical advancements and real-world applications, offering a promising direction for future research into multi-agent reinforcement learning. Overall, our proposed QMIX-GNN model not only addresses key limitations in existing CTDE approaches but also establishes a robust foundation for developing more effective and scalable MARL systems in heterogeneous environments. **Author Contributions:** Conceptualization, T.Z. and B.Z. ; methodology, T.Z. and B.Z. ; software, B.Z. and T.C. ; validation, T.Z., B.Z. and T.C. ; formal analysis, B.Z. ; investigation, T.Z. ; resources, T.Z. ; data curation, B.Z. ; writing--original draft preparation, B.Z. ; writing--review and editing, T.Z. and B.Z. ; visualization, B.Z. and T.C. ; supervision, T.Z. ; project administration, T.Z. ; funding acquisition, T.Z. All authors have read and agreed to the published version of the manuscript. **Funding:** This research was funded by the Chengdu Key Research and Development Support Program \"Jie Bang Gua Shuai\" Project under grant number 2023-JB00-00012-GX. **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** All experiments are conducted on the StarCraft Multi-Agent Challenge platform ([[https://github.com/oxwhirl/smac](https://github.com/oxwhirl/smac)]([https://github.com/oxwhirl/smac](https://github.com/oxwhirl/smac)), accessed on 10 June 2023). **Acknowledgments:** We would like to express our sincere gratitude to everyone who contributed to the development of this paper for their valuable support and insightful feedback. **Conflicts of Interest:** The authors declare no conflicts of interest. ## Abbreviations

The following abbreviations are used in this manuscript: \begin{tabular}{l l} MARL & Multi-Agent Reinforcement Learning \\ GNN & Graph Neural Network \\ GAT & Graph Attention Network \\ GRU & Gated Recurrent Unit \\ RNN & Recurrent Neural Network \\ \end{tabular} 

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