Pervasive edge computing allows peer devices to establish independent communication connections,which enables users to process massive computing tasks with low delay.However,distributed devices cannot obtain the global system status of the network in real time,thus the fairness of resource utilization cannot be guaranteed.To solve this problem,a resource allocation scheme for pervasive edge computing based on Generative Adversarial Network (GAN) is proposed.In this scheme,a multi-objective optimization problem is established for minimizing the time delay and energy consumption,which is then transformed into a maximum reward problem according to the random game theory.And then a computation offloading algorithm based on multi-agent imitation learning is proposed,which combines multi-agent Generative Adversarial Imitation Learning (GAIL) and Markov Decision Process (MDP) to approximate the performance of experts,and realizes online execution of the algorithm.Finally,combined with Non-dominated Sorting Genetic Algorithm Ⅱ (NSGA-Ⅱ),the time delay and energy consumption are jointly optimized.Simulation results show that,compared with other edge computing resource allocation schemes,the proposed solution shortened the time delay by 30.8% and reduced the energy consumption by 34.3%.