Nash-regularized heterogeneous graph transformer networks for strategic task offloading in 6G edge computing

The rapid urbanization and digital transformation of modern cities demand intelligent infrastructure capable of supporting massive IoT deployments and real-time decision-making across diverse smart city applications. The evolution toward sixth-generation (6G) wireless networks introduces unprecedented challenges for task offloading due to ultra-low latency, massive connectivity, and heterogeneous device requirements in urban environments. Traditional methods face limitations in scalability, adaptability, and multi-agent coordination needed for city-scale deployments. To address these gaps, we propose the Heterogeneous Graph Transformer Deep Q-Network with Nash Equilibrium Integration (HGT-DQN-NEI), a novel framework that synergistically combines graph neural networks, transformer architectures, reinforcement learning, and game-theoretic principles for intelligent multi-agent task offloading. The heterogeneous graph transformer effectively models complex 6G topologies, while the Deep Transformer Q-Network enhances decision making under partial observability. A distributed Nash equilibrium mechanism ensures stable coordination among agents with provable convergence guarantees. Extensive experiments validate the proposed approach across diverse scenarios, including urban, highway, industrial, and rural deployments. Results demonstrate a 23.4% reduction in task completion latency, 31.7% improvement in energy efficiency, and 18.9% enhancement in resource utilization compared to state-of-the-art baselines. The framework achieves stable convergence within approximately 30–50 episodes and scales efficiently to networks with over 1000 heterogeneous agents, while maintaining sub-millisecond decision times essential for smart city applications.