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Enhance performance in manufacturing carbon emission (MCE) reduction has become a widespread consensus and a necessary part, which cannot be achieved without the joint participation of manufacturing enterprises and supervisory departments. Accordingly, how to coordinate the interests of both sides and design a reasonable incentive-compatible mechanism becomes an urgent task at present. Considering the two subsidy funding channels of peer funds and government finance, this study applies the evolutionary game model to analyze feasible schemes for designing incentive-compatible mechanism of MCE supervision, discusses and simulates the realistic scenarios and influencing factors of incentive-compatible mechanism under the non-subsidized and subsidized schemes. The results show that MCE supervision is in an incentive-incompatible state under the non-subsidized incentive scheme, while in a constrained incentive-compatible state under the subsidized incentive scheme. With the increase of peer funds and penalty coefficient or the decrease of subsidy coefficient, the period of MCE supervision to reach an incentive-compatible state becomes shorter. However, a lower peer fund and penalty coefficient or a higher subsidy coefficient will contribute to a state of incentive-incompatible or a periodic cycle state of "incentive-compatible → incentive-incompatible →incentive-compatible→..." in the MCE supervision. [ABSTRACT FROM AUTHOR]