Multi-label classification (MLC) faces persistent challenges from label imbalance, spurious correlations, and distribution shifts, especially in rare label prediction. We propose the Causal Cooperative Game (CCG) framework, which models MLC as a multi-player cooperative process. CCG integrates explicit causal discovery via Neural Structural Equation Models, a counterfactual curiosity reward to guide robust feature learning, and a causal invariance loss to ensure generalization across environments, along with targeted rare label enhancement. Extensive experiments on benchmark datasets demonstrate that CCG significantly improves rare label prediction and overall robustness compared to strong baselines. Ablation and qualitative analyses further validate the effectiveness and interpretability of each component. Our work highlights the promise of combining causal inference and cooperative game theory for more robust and interpretable multi-label learning.