Long-tail imbalance is endemic to multi-label learning: a few head labels dominate the gradient signal, while the many rare labels that matter in practice are silently ignored. We tackle this problem by casting the task as a cooperative potential game. In our Curiosity-Driven Game-Theoretic Multi-Label Learning (CD-GTMLL) framework, the label space is split among several cooperating players that share a global accuracy payoff yet earn additional curiosity rewards that rise with label rarity and inter-player disagreement. These curiosity bonuses inject gradient on under-represented tags without hand-tuned class weights. We prove that gradient best-response updates ascend a differentiable potential and converge to tail-aware stationary points that tighten a lower bound on the expected Rare-F1. Extensive experiments on conventional benchmarks and three extreme-scale datasets show consistent state-of-the-art gains, delivering up to +4.3% Rare-F1 and +1.6% P@3 over the strongest baselines, while ablations reveal emergent division of labour and faster consensus on rare classes. CD-GTMLL thus offers a principled, scalable route to long-tail robustness in multi-label prediction.

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