Managing edge resources is one of key issues in edge computing. Recent works of resource allocation in edge computing focus on service caching and request scheduling on edge nodes by distributing tasks over cloud and edge nodes, so as to achieve high-quality services and low latency. Unfortunately, most schemes do not pay enough attention on service providers which also have their own resources. To serve users, service providers cooperate with edge nodes and are sometimes independent of the edge operators with their own objectives. To deal with the cooperation and conflict among users, service providers and edge nodes, we propose a cyclic selection model to depict the resource allocation among users, edge nodes and service providers where they cooperate for completing user requests and compete for their own interest. Such resource allocation problem can be formulated as a non-linear integer programming which is very difficult to solve. Thus, we propose a three-sided cyclic game (3CG) involving users, edge nodes, and service providers who make their decisions: users select preferred services, service providers select cost-effective edge nodes, edge nodes select high-value users. 3CG is proved to have pure-strategy Nash equilibriums and an approximation ratio. We develop central and distributed approximate algorithms for resource allocation. The evaluation results of 3CG show the effectiveness and efficiency of the proposed algorithms.