Hierarchical Battery-Aware Game Algorithm for ISL Power Allocation in LEO Mega-Constellations

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 ($M=172$, $\theta=0.38$) 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 $\theta \in [0,\,0.6]$ and scales linearly to 5{,}000 satellites with less than 75\,ms per-slot runtime, confirming deployment feasibility at full Starlink scale.