As a kind of new market trading policy, Renewable Portfolio Standard (RPS) and Tradable Green Certification (TGC) can greatly promote the consumption of renewable energy. Considering the introduction of RPS and TGC, there is a coupling relationship between the wholesale electricity market and the green certificate market, and there are game behaviors among the power producers in the market. Based on the equilibrium strategy of the electricity market, a multi-oligarch non-cooperative game model under the coordination of two markets is established. In the wholesale electricity market, power suppliers participate in market competition in the form of the Cournot model. In the green certificate market, renewable firms compete in the form of a supply function model. For the game model, the Nash equilibrium is solved by a multi-swarm co-evolutionary algorithm, and the strategic behavior of power suppliers under the interaction of two markets is analyzed. The results of simulation show the validity of the model and the feasibility of the algorithm. This work is supported by Fundamental Research Funds for the Central Universities (No. 2018py11).