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

arXiv: https://arxiv.org/abs/2607.18255 · HTML: https://mlsanity.com/paper/2607.18255/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reinforcement learning for LLM agents, one of 16 directions in LLM agents and tool use.
- Builds on 19 of its 47 references that are in the map.
- First posted on arXiv 14 May 2026.

## Placed in

- LLM agents and tool use / [Reinforcement learning for LLM agents](https://mlsanity.com/agents/reinforcement-learning-for-llm-agents/)

## Builds on (most cited first, 19 of 19)

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- [MetaGPT: Meta Programming for A Multi-Agent Collaborative Framework](https://mlsanity.com/paper/2308.00352/) (2023)
- [CAMEL: Communicative Agents for "Mind" Exploration of Large Language Model Society](https://mlsanity.com/paper/2303.17760/) (2023)
- [ChatDev: Communicative Agents for Software Development](https://mlsanity.com/paper/2307.07924/) (2023)
- [Counterfactual Multi-Agent Policy Gradients](https://mlsanity.com/paper/1705.08926/) (2017)
- [AgentVerse: Facilitating Multi-Agent Collaboration and Exploring Emergent Behaviors](https://mlsanity.com/paper/2308.10848/) (2023)
- [AFlow: Automating Agentic Workflow Generation](https://mlsanity.com/paper/2410.10762/) (2024)
- [HealthBench: Evaluating Large Language Models Towards Improved Human Health](https://mlsanity.com/paper/2505.08775/) (2025)
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- [QMSum: A New Benchmark for Query-based Multi-domain Meeting Summarization](https://mlsanity.com/paper/2104.05938/) (2021)
- [LegalBench: A Collaboratively Built Benchmark for Measuring Legal Reasoning in Large Language Models](https://mlsanity.com/paper/2308.11462/) (2023)
- [MedAgents: Large Language Models as Collaborators for Zero-shot Medical Reasoning](https://mlsanity.com/paper/2311.10537/) (2023)
- [Which Agent Causes Task Failures and When? On Automated Failure Attribution of LLM Multi-Agent Systems](https://mlsanity.com/paper/2505.00212/) (2025)
- [Cut the Crap: An Economical Communication Pipeline for LLM-based Multi-Agent Systems](https://mlsanity.com/paper/2410.02506/) (2024)
- [Theory of Mind for Multi-Agent Collaboration via Large Language Models](https://mlsanity.com/paper/2310.10701/) (2023)
- [Understanding and Optimizing Agentic Workflows via Shapley value](https://mlsanity.com/paper/2502.00510/) (2025)
- [AgentMonitor: A Plug-and-Play Framework for Predictive and Secure Multi-Agent Systems](https://mlsanity.com/paper/2408.14972/) (2024)

## Abstract (arXiv)

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.