Sustaining high inter-satellite link (ISL) throughput under intermittent solar harvesting is a fundamental challenge for LEO mega-constellations. Existing works impose static power ceilings that ignore real-time battery state and comprehensive onboard power budgets, causing eclipse-period energy crises. Learning-based approaches capture battery dynamics but lack equilibrium guarantees and do not scale beyond small constellations. We propose the \textbf{Hierarchical Battery-Aware Game (HBAG)} algorithm, a unified game-theoretic framework for ISL power allocation that operates identically across finite and mega-constellation regimes. For finite constellations, HBAG converges to a unique variational equilibrium; as constellation size grows, the same distributed update rule converges to the Mean Field Game (MFG) equilibrium without algorithm redesign. Comprehensive experiments on Starlink Shell~A ($M=172$, $θ=0.38$) show that HBAG achieves \textbf{100\% energy sustainability rate} (ESR) in all 10 independent runs, representing a \textbf{+87.4\%} gain over the traditional static-power baseline (SATFLOW-L, ESR\,=\,12.6\%). At the same time, HBAG reduces the flow violation ratio by \textbf{78.3\%} to 7.62\% (below the 10\% industry tolerance). HBAG further maintains ESR $\geq 93.4\%$ across eclipse fractions $θ\in [0,\,0.6]$ and scales linearly to 5{,}000 satellites with less than 75\,ms per-slot runtime, confirming deployment feasibility at full Starlink scale.

翻译：在间歇性太阳能收集条件下维持高星间链路（ISL）吞吐量是低轨巨型星座面临的根本性挑战。现有研究施加的静态功率上限忽略了实时电池状态及全面机载功率预算，导致地影期能量危机。基于学习方法虽能捕获电池动态，但缺乏均衡保证且无法扩展至大型星座。我们提出**分层电池感知博弈（HBAG）算法**，这是一个统一的博弈论框架，用于ISL功率分配，在有限星座和巨型星座场景下运行机制完全一致。对于有限星座，HBAG收敛至唯一变分均衡；当星座规模扩大时，同一分布式更新规则无需算法重设计即可收敛至平均场博弈（MFG）均衡。在星链Shell A（M=172，θ=0.38）上的全面实验表明：HBAG在全部10次独立运行中实现**100%能量可持续率（ESR）**，较传统静态功率基线（SATFLOW-L，ESR=12.6%）提升**+87.4%**；同时将流违反率降低**78.3%**至7.62%（低于10%行业容忍阈值）。在地影比例θ∈[0,0.6]范围内，HBAG仍保持ESR≥93.4%，并线性扩展至5000颗卫星，每时隙运行时延低于75毫秒，证实了在全量星链规模下的部署可行性。