The convergence of generative large language models (LLMs), edge networks, and multi-agent systems represents a groundbreaking synergy that holds immense promise for future wireless generations, harnessing the power of collective intelligence and paving the way for self-governed networks where intelligent decision-making happens right at the edge. This article puts the stepping-stone for incorporating multi-agent generative artificial intelligence (AI) in wireless networks, and sets the scene for realizing on-device LLMs, where multi-agent LLMs are collaboratively planning and solving tasks to achieve a number of network goals. We further investigate the profound limitations of cloud-based LLMs, and explore multi-agent LLMs from a game theoretic perspective, where agents collaboratively solve tasks in competitive environments. Moreover, we establish the underpinnings for the architecture design of wireless multi-agent generative AI systems at the network level and the agent level, and we identify the wireless technologies that are envisioned to play a key role in enabling on-device LLM. To demonstrate the promising potentials of wireless multi-agent generative AI networks, we highlight the benefits that can be achieved when implementing wireless generative agents in intent-based networking, and we provide a case study to showcase how on-device LLMs can contribute to solving network intents in a collaborative fashion. We finally shed lights on potential challenges and sketch a research roadmap towards realizing the vision of wireless collective intelligence.
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