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

1 Hybrid Stackelberg Game and Diffusion-based Auction for Two-tier Agentic AI Task Offloading in Internet of Agents Yue Zhong, Yongju Tong, Jiawen Kang*, Minghui Dai, Hong-Ning Dai, Zhou Su, Dusit Niyato, Fellow, IEEE Abstract—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 connec- tivity 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. Index Terms—Internet of Agents, Two-tier agentic AI task offloading, Stackelberg game, Double Dutch auction, Diffusion- based DRL algorithm. I. Introduction As a new networking paradigm, Internet of Agents (IoA) has emerged as the core framework for next-generation in- Yue Zhong, Yongju Tong, and Jiawen Kang are with the School of Automation, Guangdong University of Technology, Guangzhou 510006, China (e-mail: 2112404106@mail2.gdut.edu.cn; tongyongju1@mails.gdut.edu.cn; kavinkang@gdut.edu.cn). Minghui Dai is with the School of Computer Science and Technology, Donghua University, Shanghai 201620, China (e-mail: minghuidai@dhu.edu.cn). Hong-Ning Dai is with the Department of Computer Sci- ence, Hong Kong Baptist University, Hong Kong, China (e-mail: hndai@ieee.org). Zhou Su is with the School of Cyber Science and Engineering, Xi’an Jiaotong University, Xi’an 710049, China (e-mail: zhousu@ieee.org). Dusit Niyato is with the School of Computer Science and Engineer- ing, Nanyang Technological University, Singapore 639798 (e-mail: dniyato@ntu.edu.sg). (*Corresponding author: Jiawen Kang) telligent networks [1]. This agent-centric model is designed to support the seamless interconnection, autonomous discovery, and collaborative reasoning of countless het- erogeneous physical and virtual agents. The proliferation and sophistication of these agents are driven by a recent advent in the field of Artificial Intelligence (AI), i.e., the transition from disembodied models to Embodied AI (EAI) [2]. Unlike their predecessors, which are isolated and task-specific, EAI gives rise to embodied agents, i.e., intelligent entities that can autonomously perceive their surroundings, process information, and interact with physical objects [3]. The integration of these interactive and rational embodied agents into the IoA architecture is a critical step toward Artificial General Intelligence (AGI), enabling them to operate and cooperate seamlessly with humans and other agents in complex and dynamic environments [4]. As a key component of the IoA physical domain, Wire- less Agents (WAs) are designed for autonomous operation and interaction within dynamic environments. Their core functions and tasks are inherently compute-intensive, as they need to continuously process vast streams of sensor data to perceive their surroundings and execute precise physical actions. In this context, autonomous vehicles can act as WAs to perform advanced agentic AI tasks. For instance, these agents formulate on-the-fly strategies in congested traffic (e.g., determining right-of-way at a busy junction) or utilize local models for environmental under- standing (e.g., forecasting pedestrian behavior from vi- sual data) that are profoundly demanding computational tasks [5]. The strict constraints on heat dissipation and physical space for high-performance onboard hardware (e.g., GPUs) of the vehicles create a critical performance bottlene

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