This paper explores the application of large language models (LLMs) in designing strategic mechanisms -- including auctions, contracts, and games -- for specific purposes in communication networks. Traditionally, strategic mechanism design in telecommunications has relied on human expertise to craft solutions based on game theory, auction theory, and contract theory. However, the evolving landscape of telecom networks, characterized by increasing abstraction, emerging use cases, and novel value creation opportunities, calls for more adaptive and efficient approaches. We propose leveraging LLMs to automate or semi-automate the process of strategic mechanism design, from intent specification to final formulation. This paradigm shift introduces both semi-automated and fully-automated design pipelines, raising crucial questions about faithfulness to intents, incentive compatibility, algorithmic stability, and the balance between human oversight and artificial intelligence (AI) autonomy. The paper discusses potential frameworks, such as retrieval-augmented generation (RAG)-based systems, to implement LLM-driven mechanism design in communication networks contexts. We examine key challenges, including LLM limitations in capturing domain-specific constraints, ensuring strategy proofness, and integrating with evolving telecom standards. By providing an in-depth analysis of the synergies and tensions between LLMs and strategic mechanism design within the IoT ecosystem, this work aims to stimulate discussion on the future of AI-driven information economic mechanisms in telecommunications and their potential to address complex, dynamic network management scenarios.