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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.