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Meanwhile, Reinforcement Learning (RL) is widely recognized for enhancing agent intelligence, but limited work has studied fine-tuning LaMAS with foundational RL techniques. Directly applying conventional Multi-Agent Reinforcement Learning (MARL) to LaMAS also introduces major challenges due to the unique mechanisms of LaMAS. To address these challenges, this article presents a comprehensive study of LLM-based MARL and proposes Multi-Agent Reinforcement Fine-Tuning (MARFT). We introduce Flex-MG, a new Markov Game formulation aligned with real-world LaMAS optimization, together with a universal algorithmic framework tailored to LaMAS. 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