From the perspective of multi-stakeholders, considering the rent-seeking phenomenon existing in the inspection and acceptance of low-carbon renovation under the government’s reward and punishment mechanism, this paper constructs a tripartite evolutionary game model of the government, third-party testing institutions, and high-carbon emission enterprises, analyzes the stability of the evolutionary strategies of all parties involved, and tests the influence of the reward and punishment mechanism, rent-seeking cost, and the cost difference between high carbon and low carbon on the choice of tripartite strategies through simulation. Finally, the stability of the equilibrium point in the tripartite game system is verified. The results show that 1 the government’s increase in the reward and punishment mechanism will promote the low-carbon renovation of high-carbon emission enterprises and the refusal to rent-seeking behavior choices, but the increase in incentives will weaken the government’s supervision; 2 the reward and punishment mechanism set by the government must meet the condition that the sum of the strength of the reward and punishment mechanism for each party is greater than its speculative income, so as to ensure the quality of low-carbon renovation of high-carbon emission enterprises; 3 the greater the rent-seeking cost paid by high-carbon emission enterprises, the more conducive it is to avoiding the unqualified low-carbon renovation of high-carbon emission enterprises; and 4 under the premise of certain sales revenue, the greater the cost difference between low-carbon production and high-carbon production, the lower the willingness of enterprises to low-carbon renovation. Therefore, reducing the production cost difference is an effective way to promote the low-carbon renovation of high-carbon emission enterprises.

When the government decides to use the public-private partnership (PPP) in projects, such as infrastructure construction, selecting a private-sector partner that meets the project's needs is one of the key factors for successful implementation, but this is ignored in existing research. On this basis, this paper proposes a GRA-VIKOR method based on the combined weight of the improved CRITIC-entropy weight method (EWM). The traditional CRITIC method is improved by combining it with EWM. The combined weights are measured, which reduces the limitations of the single weight. Considering the inherent correlation of evaluation indicators, the VIKOR method is combined with the grey relational analysis (GRA), which makes the results of the selection assessment more reasonable. This paper carries out a case study of the first inland navigation PPP project in China. Through preliminary tracking studies, it tests the effectiveness of the proposed method, the superiority of which is demonstrated by comparing the evaluation results with those of the traditional GRA methods, VIKOR, and TOPSIS.