Hybrid Stackelberg Game and Diffusion-based Auction for Two-tier Agentic AI Task Offloading in Internet of Agents

The Internet of Agents (IoA) is rapidly gaining prominence as a foundational architecture for interconnected intelligent systems, designed to facilitate seamless discovery, communication, and collaborative reasoning among a vast network of Artificial Intelligence (AI) agents. Powered by Large Language and Vision-Language Models, IoA enables the development of interactive, rational agents capable of complex cooperation, moving far beyond traditional isolated models. IoA involves physical entities, i.e., Wireless Agents (WAs) with limited onboard resources, which need to offload their compute-intensive agentic AI services to nearby servers. Such servers can be Mobile Agents (MAs), e.g., vehicle agents, or Fixed Agents (FAs), e.g., end-side units agents. Given their fixed geographical locations and stable connectivity, FAs can serve as reliable communication gateways and task aggregation points. This stability allows them to effectively coordinate with and offload to an Aerial Agent (AA) tier, which has an advantage not affordable for highly mobile MAs with dynamic connectivity limitations. As such, we propose a two-tier optimization approach. The first tier employs a multi-leader multi-follower Stackelberg game. In the game, MAs and FAs act as the leaders who set resource prices. WAs are the followers to determine task offloading ratios. However, when FAs become overloaded, they can further offload tasks to available aerial resources. Therefore, the second tier introduces a Double Dutch Auction model where overloaded FAs act as the buyers to request resources, and AAs serve as the sellers for resource provision. We then develop a diffusion-based Deep Reinforcement Learning algorithm to solve the model. Numerical results demonstrate the superiority of our proposed scheme in facilitating task offloading.