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

TL;DR

<3-5 sentence high-level summary> The paper tackles the challenge of efficiently offloading agentic AI tasks in Internet of Agents (IoA) by modeling a two-tier incentive mechanism that couples a Stackelberg game among Wireless Agents (WAs), Mobile Agents (MAs), and Fixed Agents (FAs) with a Double Dutch Auction (DDA) between FAs and Aerial Agents (AAs). It introduces a diffusion-based DRL algorithm to solve the complex DDA resource market and demonstrates through numerical results that this approach yields superior social welfare and faster convergence than traditional DRL methods. The framework captures energy, latency, and pricing interactions across four agent types in a vehicular-edge setting, enabling scalable, overload-protective computation offloading. The work advances practical resource allocation for embodied AI in IoA and provides a blueprint for integrating hierarchical games with market-based auctions using diffusion-informed learning. The findings indicate that diffusion-based guidance can effectively balance cost, performance, and interaction overhead in dynamic multi-agent environments.

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 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.

Figures (8)

• Figure 1: The outline of the proposed hybrid framework. The first layer establishes a Stackelberg game to model the interactions among WAs, MAs, and FAs. Subsequently, the second layer conceptualizes the dynamics between FAs and AAs through a DDA. The framework concludes with the application of algorithms to determine the corresponding strategic solutions.
• Figure 2: The two-tier agentic AI task offloading system model. The left side illustrates the IoA framework in a vehicular context, while the right side details the formulation of the two-tier task offloading system.
• Figure 3: Illustration of the Algorithm \ref{['Linear-Search']} for solving $p_i$ of a MA by fixing the prices $p_j=6.0$ of FA $j$. (a) Total latency comprises WA-MA transmission and local computing of MA. (b) Total latency comprises WA-FA transmission and local computing of FA. (c) Total latency comprises WA-FA transmission, FA-AA transmission, and local computing of AA.
• Figure 4: Illustration of the Algorithm \ref{['Stackelberg_algorithm']} for solving $o_{n,i}$, $p_i$ and $p_j$ of WA, MA and FA, respectively. (a) Total latency comprises WA-MA transmission and local computing of MA. (b) Total latency comprises WA-FA transmission and local computing of FA. (c) Total latency comprises WA-FA transmission, FA-AA transmission, and local computing of AA.
• Figure 5: Test reward comparison of the proposed diffusion-based DRL algorithm with other algorithms, i.e., PPO, greedy, and random algorithms.

Theorems & Definitions (2)

• Theorem 1
• proof