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

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.