Mobile edge computing and ultra-dense network technologies have obvious advantages in improving the computing power of mobile devices and enhancing network capacity. However, under the scenario of convergence between the two, how to effectively reduce the co-channel interference among base stations and reduce the delay and energy consumption of task transmission is an important research topic. Therefore, this study designs a distributed wireless resource management algorithm based on multi-base station game equilibrium. The wireless resource management problem among small base stations is transformed into a game one to propose a reward-driven strategy selection algorithm. The base stations continuously update the selection probability of their strategies by iterations, which finally optimizes the sub-channel allocation and transmission power regulation. Simulation results show that the proposed algorithm has advantages in improving channel utilization and reducing latency and energy consumption for task transmission.