  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.
