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

2026-05-14

arXiv.org

AI Summary

This study addresses the challenges of high computational cost, large variance, and the neglect of semantic states in contribution attribution within LLM-based multi-agent systems by proposing the SCG framework. This framework models language flows as semantic hypergraphs and introduces a Boolean absorption mechanism combined with cooperative game theory to define the Semantic Shapley Value. Furthermore, it designs the SLIC algorithm to achieve efficient single-trajectory attribution, accurately capturing intermediate semantic contributions without requiring counterfactual re-execution. Evaluations on medical benchmarks demonstrate that this approach reduces computational costs by 93.3% while maintaining highly consistent results, effectively revealing the discrepancies between semantic contributions and fault impacts.

Abstract

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.

Problem

• Contribution Attribution
• Multi-Agent Systems
• Large Language Models
• Semantic Cooperative Games
• Counterfactual Valuation

Innovation

• Semantic Cooperative Games
• Semantic Shapley Value
• Contribution Attribution
• Multi-Agent Systems
• Hypergraph