Semantic Cooperative Games for Contribution Attribution in LLM-Based Multi-Agent Systems

Contribution attribution has become a central problem in LLM-based multi-agent systems, where final outputs are produced through multiple agents, message exchanges, and ordered workflow dependencies. Existing attribution methods often rely on counterfactual valuation, such as removing agents or comparing score changes across altered agent subsets. In language-mediated workflows, these methods require repeated model calls, introduce high variance, and do not explicitly capture the intermediate semantic states through which agents produce, preserve, and transform task-relevant information. We propose Semantic Cooperative Games (SCG), a framework that represents a realized language flow as a semantic generation hypergraph and induces an agent-level semantic value function on this structure. We define the Semantic Shapley Value (SSV) to allocate contribution over semantic support logic, and introduce SLIC, a single-trajectory algorithm that constructs the semantic hypergraph, recovers minimal semantic supports, applies Boolean absorption, and computes SSV without rerunning agent subsets. We prove that SSV reduces to the classical Shapley value under standard set-based, fully observable, and no-order-dependence conditions. On a medical benchmark satisfying these conditions, SLIC reduces computation cost by 93.3% while remaining highly consistent with a Monte Carlo Shapley baseline. In more general multi-role workflows, SSV aligns with perturbation-induced score-drop profiles and exposes cases where semantic contribution and failure impact diverge. Overall, SLIC provides a fast, counterfactual-free, and interpretable attribution method for complex LLM-based multi-agent systems.