The construction of China's electricity market is still in the primary stage. The trading behavior of market participants is not standardized, and there are many violations. In order to maintain the stable and efficient operation of the electricity market, scientific and effective supervision and incentive mechanisms are urgently needed. Starting from the actual needs of supervision, a three-party game model of regulatory agencies, power generation companies and power users has been established. The evolutionary and stable strategies of this system can be analyzed under the static and dynamic premium and penalty mechanisms respectively. The simulation results show that the evolution and stability of the system could not be achieved under the static premium and penalty mechanism. In contrast, the stable balance of the system could be achieved under the dynamic mechanism. By adjusting the relevant parameters, an ideal stable state can be achieved, and effective supervision can be realized. Finally, relevant policy recommendations are given based on the results of the evolutionary game and simulation analysis.