Pervasive edge computing allows peer devices to establish independent communication connections, which can help users process massive computing tasks with low delay. However, distributed devices cannot obtain the global system status of the network in real time, and cannot guarantee the fairness of resource utilization. To solve this problem, a resource allocation scheme for pervasive edge computing based on generative adversary network (GAN) is proposed. In this scheme, firstly, a multi-objective optimization problem is established based on minimizing the time delay and energy consumption, then the optimization problem is transformed into the maximum reward problem according to the random game theory, and then a computation offloading algorithm based on multi-agent imitation learning is proposed. The algorithm combines multi-agent generation against imitation learning (GAIL) and Markov strategy (MDP) to approximate the performance of experts, and realizes the online execution of the algorithm. Finally, combined with non-dominated sorting genetic algorithm II (NSGA-II) multi-objective optimization algorithm, the time delay and energy consumption are jointly optimized. Simulation results show that, compared with other edge computing resource allocation schemes, the time delay of the proposed solution is shortened by 30.8% and the energy consumption is reduced by 34.3%.