## 3 Beam Allocation Algorithm Based on MAPPO and Stackelberg Game
### Beam Allocation Algorithm Based on MAPPO
The simulation results show that under conditions where all weights are 1 and the number of transceiving antennas is 64, the proposed IMSBA algorithm increases V2V total energy efficiency by 92.5% and the probability of target vehicle sensing position RMSE being less than 0.2m by 43.6% compared to the ISSBA algorithm, effectively solving the beam allocation problem in scenarios with coexisting I2V and V2V communications. ## 6 Limitations and Future Work

Although the IMSBA scheme performs well in simulations, it still has several limitations. First, the Stackelberg game relies on the perfect CSI assumption, which is difficult to guarantee in practice and may affect the performance. Second, MAPPO faces training efficiency and stability challenges when the multi-intelligence scale is expanded. In addition, the target vehicle switching mechanism relies on high-quality sensing information, which may trigger misjudgment under a low SINR. Finally, the simulation adopts idealized modeling and lacks real-road and channel environment verification. Future work will focus on algorithm scalability, computational simplification, and practical deployment evaluation. Conceptualization, J.L., Y.Z., and D.W.; methodology. J.L., Y.Z., and D.W.; software, J.L., Y.Z., and D.W.; validation, Y.Z. ; formal analysis, J.L., Y.Z., and D.W.; writing--original draft preparation, J.L., Y.Z., and D.W.; writing--review and editing, J.L., Y.Z., and D.W.; visualization, J.L. ; supervision, Y.Z. ; project administration, D.W.; funding acquisition, D.W. All authors have read and agreed to the published version of the manuscript. This work was supported in part by Natural Science Foundation of Xiamen, China (Grant number 3502Z20227177) and National Natural Science Foundation of China (Grant number 62171392 and 62271427). Not applicable. The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author. The authors declare no conflicts of interest. ## References

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