This paper explores the strategic behavior of power generators under green certificate trading policies, considering both renewable and conventional energy generators. Using game theory, we construct a Nash equilibrium model that incorporates the unit price of green certificates, the required quantity of certificates, and the cap on the quantity. By applying the Karush-Kuhn-Tucker conditions, we reform this Nash equilibrium problem as a mixed complementarity system, which can be solved by MATLAB software. Furthermore, we conduct sensitivity analysis and numerical tests on a number of important parameters. The results reveal that, under certain conditions, the unit price of green certificates does not affect the number obtained by renewable energy generators or purchased by conventional energy generators. However, as the required number of certificates for conventional energy generators increases, both the quantity of certificates that renewable generators obtained and conventional generators purchased increase proportionally. Additionally, the outcomes of limiting the quantity of green certificates awarded to renewable energy generators align with government regulations on the purchase requirements for conventional energy generators. This research provides new insights for power generators in ensuring financial viability and optimizing operations under green certificate trading policies. By enhancing carbon emission reduction capacity, these findings may contribute to the effective management of the electrical supply chain.