Task scheduling on edge computing servers is an important issue that affects user experience. Existing scheduling methods require centralized control to achieve the best overall performance. However, it is impractical to force all users to act according to centralized control. We propose a distributed edge computing server task scheduling model based on game theory. Our method comprehensively considers the link quality from the mobile device to the server and the server's computing resource allocation when selecting edge computing servers, and achieves a balance between link quality and computing resources. Once the Nash equilibrium is reached, our model can provide different QoS for users of different priorities. Acceleration methods are proposed to achieve the Nash equilibrium faster. The simulation results show that the proposed model can provide differentiated services while optimizing the scheduling of computing resources, and ensure that the algorithm achieves an approximate Nash equilibrium in polynomial time.