An auction mechanism is an effective resource allocation method that can increase the revenue of resource providers in the field of edge computing. Existing auction mechanism designs mostly aim to maximize social welfare when allocating resources, but these schemes lead to low revenue. In contrast, clinching auctions have achieved good results in spectrum allocation and advertising due to their high revenue. Therefore, a clinching auction mechanism is a promising tool for allocating edge computing resources. However, clinching auctions have the drawback that they can only allocate homogeneous finitely divisible goods, meaning that they cannot be directly applied for resource allocation in edge computing. This article presents two new auction mechanisms that improve on the clinching auction. Specifically, based on the principle of increasing global prices and local competition, two mechanisms are designed, one from the perspective of resource providers (MDCAM‐ECS) and the other from the perspective of users (MDCAM‐User), to solve the problem of edge computing resource allocation and pricing with deployment constraints and user budget constraints. The mechanisms proposed in this article have the properties of individual rationality, truthfulness, and computational efficiency. In the experiments, in terms of social welfare and revenue, our algorithms can achieve a 20% improvement over existing algorithms, such as fixed‐price, Vickery–Clarke–Groves (VCG), and monotonic critical‐price mechanisms. Additionally, in most experiments, our algorithm can ensure resource utilization greater than 80%.