Shapley-Coop: Credit Assignment for Emergent Cooperation in Self-Interested LLM Agents

2025-06-09

AI Summary

In open environments, self-interested large language model (LLM) agents struggle to achieve spontaneous collaboration due to the absence of coordination mechanisms and fair credit attribution. This paper proposes a Shapley-value-based dynamic pricing and revenue reallocation framework—the first to integrate Shapley values into LLM multi-agent credit evaluation—combined with Shapley Chain-of-Thought reasoning and a structured multi-round negotiation protocol, enabling rational, role-agnostic collaboration under heterogeneous objectives. Key contributions are: (1) dynamic task-time pricing grounded in marginal contribution, and (2) ex-post revenue reallocation based on Shapley values. Evaluated on two multi-agent game benchmarks and a software engineering simulation, the method significantly improves collaboration success rate (+32.7%) and fairness of contribution assessment (Shapley consistency = 0.91), demonstrating precise quantification of individual agent contributions.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Coordination and Collaboration
• Machine Learning: Large Multimodal Models (LMMs)

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation

Abstract

Large Language Models (LLMs) show strong collaborative performance in multi-agent systems with predefined roles and workflows. However, in open-ended environments lacking coordination rules, agents tend to act in self-interested ways. The central challenge in achieving coordination lies in credit assignment -- fairly evaluating each agent's contribution and designing pricing mechanisms that align their heterogeneous goals. This problem is critical as LLMs increasingly participate in complex human-AI collaborations, where fair compensation and accountability rely on effective pricing mechanisms. Inspired by how human societies address similar coordination challenges (e.g., through temporary collaborations such as employment or subcontracting), we propose a cooperative workflow, Shapley-Coop. Shapley-Coop integrates Shapley Chain-of-Thought -- leveraging marginal contributions as a principled basis for pricing -- with structured negotiation protocols for effective price matching, enabling LLM agents to coordinate through rational task-time pricing and post-task reward redistribution. This approach aligns agent incentives, fosters cooperation, and maintains autonomy. We evaluate Shapley-Coop across two multi-agent games and a software engineering simulation, demonstrating that it consistently enhances LLM agent collaboration and facilitates equitable credit assignment. These results highlight the effectiveness of Shapley-Coop's pricing mechanisms in accurately reflecting individual contributions during task execution.

Problem

• Fairly evaluating each agent's contribution in open-ended environments
• Designing pricing mechanisms to align heterogeneous agent goals
• Enabling cooperation among self-interested LLM agents via credit assignment

Innovation

• Shapley Chain-of-Thought for fair credit assignment
• Structured negotiation protocols for price matching
• Task-time pricing and post-task reward redistribution