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

Large Language Models (LLMs) are increasingly deployed as autonomous agents in multi-agent systems, and promising coordination has been demonstrated in handling complex tasks under predefined roles and scripted workflows. However, significant challenges remain in open-ended environments, where agents are inherently self-interested and explicit coordination guidelines are absent. In such scenarios, misaligned incentives frequently lead to social dilemmas and inefficient collective outcomes. Inspired by how human societies tackle similar coordination challenges--through temporary collaborations like employment or subcontracting--a cooperative workflow \textbf{Shapley-Coop} is proposed. This workflow enables self-interested Large Language Model (LLM) agents to engage in emergent collaboration by using a fair credit allocation mechanism to ensure each agent's contributions are appropriately recognized and rewarded. Shapley-Coop introduces structured negotiation protocols and Shapley-inspired reasoning to estimate agents' marginal contributions, thereby enabling effective task-time coordination and equitable post-task outcome redistribution. This results in effective coordination that fosters collaboration while preserving agent autonomy, through a rational pricing mechanism that encourages cooperative behavior. Evaluated in two multi-agent games and a software engineering simulation, Shapley-Coop consistently enhances LLM agent collaboration and facilitates equitable outcome redistribution, accurately reflecting individual contributions during the task execution process.