HIVE: A hypergraph-based game-theoretic interactive value decomposition engine for multi-lateral agents collaboration

Multi-lateral agents collaboration plays a crucial role in realizing collective intelligence. However, it remains constrained due to challenges such as capturing higher-order dependencies in dynamic interactions and imbalanced credit assignment. In this paper, we propose the Hypergraph-based game-theoretic Interactive Value decomposition Engine (HIVE). The engine employs the hypergraph-weighted Position value, a game-theoretic allocation rule, to decompose the joint state-action value function into three components: individual state-action values, a global coordination baseline, and a dynamic cooperation residual. To implement this theoretical decomposition in practice, we design three neural networks to approximate these corresponding components. We further prove that this game-theoretic allocation rule admits a marginal utility function, which guarantees payoff allocation efficiency. And this allocation rule satisfies invariance to hyperedge-redundant payoffs. We also establish the necessary and sufficient conditions for HIVE to satisfy the Individual-Global-Max (IGM) principle. Experimental results show that HIVE converges consistently to optimal joint actions in matrix games and achieves an average win rate of 87.25% across SMAC and its SMACv2 extension, outperforming state-of-the-art value decomposition methods. This demonstrates the effectiveness of HIVE in enabling balanced credit assignment and reliable coordination.