This paper addresses the multi-user computation offloading problem in mobile-edge cloud computing, a paradigm that provides cloud computing capabilities at the edge of pervasive radio access networks. The authors show that finding a centralized optimal solution is NP-hard due to the multi-channel wireless interference environment, and thus adopt a game-theoretic approach for distributed computation offloading. They formulate the problem as a multi-user computation offloading game and analyze its structural properties, proving that it admits a Nash equilibrium and possesses the finite improvement property. A distributed computation offloading algorithm is designed to achieve this equilibrium, with an upper bound on convergence time derived. The efficiency ratio of the Nash equilibrium solution is quantified in terms of the number of beneficial cloud computing users and system-wide computation overhead. Numerical results demonstrate that the proposed algorithm achieves superior performance and scales well as the number of users increases.This paper addresses the multi-user computation offloading problem in mobile-edge cloud computing, a paradigm that provides cloud computing capabilities at the edge of pervasive radio access networks. The authors show that finding a centralized optimal solution is NP-hard due to the multi-channel wireless interference environment, and thus adopt a game-theoretic approach for distributed computation offloading. They formulate the problem as a multi-user computation offloading game and analyze its structural properties, proving that it admits a Nash equilibrium and possesses the finite improvement property. A distributed computation offloading algorithm is designed to achieve this equilibrium, with an upper bound on convergence time derived. The efficiency ratio of the Nash equilibrium solution is quantified in terms of the number of beneficial cloud computing users and system-wide computation overhead. Numerical results demonstrate that the proposed algorithm achieves superior performance and scales well as the number of users increases.