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

LLM-based multi-agent systems produce outputs through ordered interactions, yet contribution attribution lacks a unified semantic account of how agents generate, preserve, and transform task-relevant information. Existing methods typically rely on counterfactual valuation by removing agents or comparing system scores across agent subsets. These approaches require costly workflow reruns that may alter downstream context. They also leave much of the intermediate semantic information unused, limiting their ability to explain specific contributions within a realized trajectory. We propose Semantic Cooperative Games (SCG), a framework that represents a realized language interaction trajectory as a semantic generation hypergraph and derives an agent-level value function from its semantic support relations. We define the Semantic Shapley Value (SSV) and introduce SLIC, a single-trajectory algorithm that constructs the hypergraph, recovers minimal semantic supports, and applies Boolean absorption to compute SSV without rerunning agent subsets. Our theory provides an axiomatic foundation for SSV and guarantees that it reduces to the classical Shapley value whenever the latter is well-defined within our framework. In a three-agent medical question-answering workflow where the classical Shapley value is well-defined, SLIC reduces API calls by 85.7% relative to an exhaustive Shapley baseline, achieving a Kendall rank correlation of \(\tau_b = 0.814\) with the baseline attribution. In more general workflows involving multiple roles, SSV correlates strongly with score drops under moderate to strong perturbations, while revealing cases in which semantic contribution and failure impact diverge. SCG provides an interpretable paradigm for contribution attribution and lays the groundwork for systematic annotation of semantic actions and their contributions in Group-of-Thought workflows.