This study discusses how to facilitate the barrier-free circulation of energy big data among multiple entities and how to balance the energy big data ecosystem under government supervision using dynamic game theory. First, we define the related concepts and summarize the recent studies and developments of energy big data. Second, evolutionary game theory is applied to examine the interaction mechanism of complex behaviors between power grid enterprises and third-party enterprises in the energy big data ecosystem, with and without the supervision of government. Finally, a sensitivity analysis is conducted on the main factors affecting co-opetition, such as the initial participation willingness, distribution of benefits, free-riding behavior, government funding, and punitive liquidated damages. The results show that both government supervision measures and the participants’ own will have an impact on the stable evolution of the energy big data ecosystem in the dynamic evolution process, and the effect of parameter changes on the evolution is more significant under the state of no government supervision. In addition, the effectiveness of the developed model in this work is verified by simulated analysis. The present model can provide an important reference for overall planning and efficient operation of the energy big data ecosystem.