Multi-access edge computing (MEC) is a cutting-edge technology integral to 5G and future mobile networks. However, the computational capabilities of edge servers may sometimes be insufficient to meet service delay requirements. As a result, computation tasks need to be offloaded to other MEC servers for processing. In this paper, we introduce a novel offloading solution based on Stackelberg game, i.e., Game-based Offloading (GBO), to maximize the processed computation tasks while ensuring the service delay requirements. To tackle the problem, we use the block coordinate descent method to find the optimal solution within given delay constraints. Simulation results demonstrate that under various experimental circumstances, the proposed GBO method significantly outperforms baseline methods, such as the non-offloading and the ODO [9] methods in terms of the probability of successfully processed tasks.