# Promoting the Low-Carbon Transition of Power Construction Projects under MRV: An Evolutionary Game Analysis

^{1}

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## Abstract

**:**

## 1. Introduction

- What are the factors that influence the behavioral strategies of each participant of PCPs under the MRV system, and what are the relationships among the participants as the evolutionary game system tends to stabilize?
- In the process of low-carbon transition of PCPs under the MRV system, how can we ensure that the core benefits are not damaged while promoting participants to actively fulfill their responsibilities of carbon-emission reduction?
- What is the low-carbon transition mechanism for PCPs under the MRV system, and what are its internal components?

- This paper reveals the roles of participants in PCPs under the MRV system, describing the interaction mechanism among the participants.
- The paper explores the changes in the behavioral strategies of each participant under different circumstances, confirming the influence of the main parameters.
- This paper proposes a low-carbon transition mechanism for PCPs under the MRV system, which provides scientific and reasonable suggestions for participants to avoid the emergence of rent-seeking behavior.

## 2. Literature Review

#### 2.1. The Low-Carbon Benefits of the MRV

#### 2.2. The Key Participants in PCPs under the MRV

#### 2.3. Evolutionary Game Theory

#### 2.4. Research Gap

- There is a research gap in the equilibrium state and corresponding conditions for MRV systems to realize the low-carbon benefits of PCPs, and the interactions among the behavioral strategies of key participants are unclear.
- Existing studies have focused more on exploring the factors influencing the behavioral strategies of key participants in PCPs from the perspective of MRV, while neglecting the influence of public participation on the evolution of the whole system.
- The use of evolutionary game theory to solve the problem of rent-seeking behavior can provide relevant suggestions for the participants. However, none of the existing studies have clearly indicated the implementation strength and scope of the relevant measures, and the effectiveness of the application cannot be guaranteed.

## 3. Tripartite Evolutionary Game Modeling

#### 3.1. Application of Evolutionary Game

#### 3.2. Model Assumptions

**Assumption 1.**

**Assumption 2.**

_{1}, α

_{2}) = (implementation of high-level carbon-emission monitoring and reporting programs, and implementation of low-level carbon-emission monitoring and reporting programs). The probability that the construction units will choose α

_{1}is x (0 ≤ x ≤ 1), and the probability to choose α

_{2}is (1 − x).

**Assumption 3.**

_{1}, β

_{2}) = (Standardized Verification, Irregularity Verification). The probability that carbon-emission third-party-verification agencies will choose β

_{1}is y (0 ≤ y ≤ 1), and the probability to choose β

_{2}is (1 − y).

**Assumption 4.**

_{1}, γ

_{2}) = (Strict Supervision, Permissive Supervision), and chooses γ

_{1}with probability z (0 ≤ z ≤ 1) and γ

_{2}with probability (1 − z).

#### 3.3. Model Establishment

#### 3.3.1. The Strategy Stability Analysis for Construction Units

_{x}= yz(I

_{t}− C

_{h}+ R

_{b}+ R

_{c}) + y(1 − z)(I

_{t}− C

_{h}+ R

_{b}) + (1 − y)z(I

_{t}− C

_{h}+ R

_{b}+ R

_{c}) + (1 − y)(1 − z)(I

_{t}− C

_{h}+ R

_{b}) = zR

_{p}+ I

_{t}− C

_{h}+ R

_{b}

_{1−x}= yz(−Cl − Cr − Lr − Pc) + y(1 − z)(−Cl − Cr) + (1 − y)z(It − Cl − Cr − Lr − Pc) + (1 − y)(1 − z)(It − Cl − Cr) = −yIt + z(−Lr − Pc) + It − Cl − Cr

**Inference 1.**

**Inference 2.**

#### 3.3.2. The Strategy Stability Analysis for Carbon-Emission Third-Party-Verification Agencies

**Inference 3.**

**Inference 4.**

#### 3.3.3. The Strategy Stability Analysis for the Power Grid Company

**Inference**

**5.**

**Inference**

**6.**

_{1}(0,0,0), e

_{2}(0,0,1), e

_{3}(0,1,0), e

_{4}(1,0,0), e

_{5}(0,1,1), e

_{6}(1,0,1), e

_{7}(1,1,0), e

_{8}(1,1,1), and some mixed strategy equilibrium points e*(x*,y*,z*), where x*, y*, z*∈ [0, 1]. Therefore, e

_{9}((C

_{r}− C

_{e})/C

_{r},(C

_{h}− C

_{l}− C

_{r}− R

_{b})/I

_{t},0),e

_{10}((−C

_{s}+ R

_{g}+ P

_{c}+ P

_{a}+ L

_{g})/(R

_{c}+ P

_{c}+ L

_{g}),0,(C

_{h}− C

_{l}− C

_{r}− R

_{b})/L

_{r}+ P

_{c}+ R

_{c}),e

_{11}(0,(R

_{g}+ P

_{c}+ P

_{a}+ L

_{g}− C

_{s})/(R

_{a}+ P

_{a}+ L

_{g}),(C

_{r}− C

_{e})/(L

_{c}+ P

_{a}+ R

_{a})),e

_{12}((C

_{r}− C

_{e}− L

_{c}− P

_{a}− R

_{a})/C

_{r},(C

_{h}− C

_{l}− C

_{r}− R

_{b}− L

_{r}− R

_{c}− P

_{c})/I

_{t},1).

#### 3.4. Analysis of Evolutionarily Stable Strategy

_{11}= (2x − 1)[−yI

_{t}− z(L

_{r}+ P

_{c}+ R

_{c}) − C

_{l}− C

_{r}− R

_{b}+ C

_{h}], J

_{12}= x(1 − x)I

_{t},J

_{13}= x(1 − x)(L

_{r}+ P

_{c}+ R

_{c}), J

_{21}= y(1 − y)C

_{r}, J

_{22}= (2y − 1)[−xC

_{r}− z(R

_{a}+ L

_{c}+ P

_{a}) + C

_{r}− C

_{e}], J

_{23}= y(1 − y)(L

_{c}+ P

_{a}+ R

_{a}), J

_{31}= z(1 − z)(yL

_{g}− R

_{c}− P

_{c}− L

_{g}), J

_{32}= z(1 − z)(xL

_{g}− R

_{a}− P

_{a}− L

_{g}), J

_{33}= (2z − 1)[−xyL

_{g}+ x(R

_{c}+ P

_{c}+ L

_{g}) + y(R

_{a}+ P

_{a}+ L

_{g}) + C

_{s}− R

_{g}− P

_{c}− P

_{a}− L

_{g}]. The eigenvalues of equilibrium points of each strategy and ESS condition are found as shown in Table 2.

**Inference 7**

**.**When C

_{e}− C

_{r}+ L

_{c}+ P

_{a}+ R

_{a}< 0 and C

_{l}− C

_{h}+ C

_{r}+ L

_{r}+ P

_{c}+ R

_{b}+ R

_{c}< 0, there are two equilibrium points e

_{2}, e

_{7}. At this time, the power grid company’s rewards and punishments for construction units and carbon third-party-verification agencies are weak, and both are less affected by the public and the benefits of violation of the verification are higher. The evolution of the system tends to be (0, 0, 1), and (1, 1, 0).

**Inference 8.**

_{c}+ P

_{c}> C

_{h}− C

_{l}− C

_{r}− L

_{r}− R

_{b}> 0, R

_{a}+ P

_{a}> C

_{r}− C

_{e}− L

_{c}> 0, and P

_{a}− R

_{c}+ R

_{g}> C

_{s}, P

_{c}− R

_{a}+ R

_{g}> C

_{s}, the system exists as only one ESS of e

_{7}. At this time, the degree of effect of the power grid company on the rewards and punishments for construction units and carbon third-party-verification agencies is greater than the gains of both intentions to rent seeking, which can effectively avoid the emergence of the mixed strategy equilibrium points.

## 4. Numerical Simulations

#### 4.1. Dynamic Evolutionary Results

_{h}= 100, C

_{l}= 20, I

_{t}= 200, C

_{r}= 35, P

_{c}= 40, R

_{c}= 20, C

_{e}= 10, P

_{a}= 35, R

_{a}= 15, C

_{s}= 20, L

_{g}= 15, R

_{g}= 10, R

_{b}= 5, L

_{c}= 5, L

_{r}= 10, and (x, y, z)=(0.2,0.2,0.2). At this point, the initial values are set to satisfy the conditional requirements in Inference 8. The evolution of the system over time 100 times is shown in Figure 3a,b. It can be found that the system converges to (1,1,0). The three parties are grouped and given initial probabilities of 0.2, 0.5, 0.7, and all of them eventually reach the desired equilibrium state.

#### 4.2. Sensitivity Analysis of Reward Parameters for the Power Grid Company

_{c}= 0, 20, 40, R

_{a}= 0, 15, 30, and numerical simulations are performed. The simulation results of the system evolving 100 times are shown in Figure 4 and Figure 5. It can be found that in terms of the rewards of the power grid company to the construction units, with the increasing R

_{c}, it accelerates the evolution speed of the probability of the construction units to implement high-level carbon monitoring and reporting stabilized at 1, while the probability of the power grid company’s strict supervision decreases. Similarly, concerning the rewards to carbon third-party-verification agencies, as R

_{a}increases, the probability of strict supervision decreases, and the probability of standardized verification by carbon third-party-verification agencies increases. Based on the above analysis, construction units and carbon third-party-verification agencies will be encouraged to regulate behaviors if they receive high rewards. However, high rewards will increase the burden on the power grid company, and the costs of strict supervision will reduce the willingness to implement strict supervision. Therefore, it is important to clarify the relationship between the rewards provided by the power grid company and the costs of strict regulation.

#### 4.3. Sensitivity Analysis of Punishment Parameters for the Power Grid Company

_{a}= 0, 20, 40 and P

_{c}= 0, 40, 80, and the system evolves 100 times as shown in Figure 6 and Figure 7. When the power grid company makes no punishments, the probability that the construction units implementing low-level carbon monitoring and reporting programs and irregular verification by carbon-emission third-party-verification agencies increase slightly. As P

_{c}keeps increasing, the evolution of construction units stabilizing to implement high-level carbon monitoring and reporting programs accelerates, and the probability of strict supervision by the power grid company increases. The probability of standardizing verification increases as P

_{a}continues to increase. In addition, before the probability of standardizing verification evolution stabilizes at 1, the probability of strict supervision by the power grid company increases. Therefore, increasing the punishments for the construction units and carbon third-party-verification agencies can promote the probability of strict supervision by the power grid company, and effectively promote the advancement of the MRV system.

#### 4.4. Sensitivity Analysis of Other Parameters

_{s}= 10, 20, 30, R

_{g}= 5, 10, 15, C

_{r}= 15, 35, 55, and C

_{h}= 80, 100, 120, respectively, and the simulation results of the system evolving 100 times are shown in Figure 8, Figure 9, Figure 10 and Figure 11. From Figure 8 and Figure 9, it can be seen that the increase in the costs of strict supervision by the power grid company accelerates the evolution of the probability of construction units implementing high-level carbon monitoring and reporting programs to stabilize at 1, which means that the probability of strict supervision by the power grid company decreases. In contrast, the higher the degree of public recognition, the higher the probability of strict supervision. The public recognition of the power grid company invariably enhances its credibility. Therefore, promoting public participation in the development of PCPs under the MRV system can enhance the power grid company’s willingness to adhere to strict supervision.

_{r}increases, the probability of construction units implementing high-level carbon monitoring and reporting programs increases, while the probability of carbon-emission third-party-verification agencies standardizing verification decreases. In addition, as the system evolves to the equilibrium point, the willingness of the construction units implementing high-level carbon monitoring and reporting programs decreases as C

_{h}increases. Although the high-level carbon monitoring and reporting programs provide the guarantee for construction units through verification, the introduction of advanced carbon-monitoring equipment and technology puts cost pressure on the construction units. Therefore, it is important to balance the costs of implementing high-level carbon monitoring and reporting programs in combination with other parameters to promote the fulfillment of the carbon-monitoring tasks.

## 5. Discussion

#### 5.1. MRV Joint Rewards and Punishments Mechanism

#### 5.2. Input Costs Control Mechanism

#### 5.3. Low Carbon Technology Introduction Mechanism

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A

_{l}+ C

_{r}+ R

_{b}− C

_{h}) + z(L

_{r}+ R

_{c}+ P

_{c})]/(−I

_{t}), J(y) = 0. At this point, d(F(x))/dx ≡ 0, and the stable state cannot be determined. When y < [(C

_{l}+ C

_{r}+ R

_{b}− C

_{h}) + z(L

_{r}+ R

_{c}+ P

_{c})]/(−I

_{t}), then J(y) > 0, d(F(x))/dx|

_{x}

_{= 0}< 0, and x = 0 is the equilibrium point. Conversely, x = 1 is the equilibrium point. Therefore, this paper assumes that the probability of the construction units implementing low- or high-level carbon monitoring and reporting programs is denoted as V

_{1−x}and V

_{x}, respectively, as follows:

**Proof 1.**

_{x}with respect to the different variables shows that if the result is greater than 0, the variable increases and so does V

_{x}, which means that the probability of the construction units implementing high-level carbon monitoring and reporting programs increases. It can be found that ∂(V

_{x})/∂(I

_{t}) > 0, ∂(V

_{x})/∂(R

_{b}) > 0, ∂(V

_{x})/∂(C

_{l}) > 0, ∂(V

_{x})/∂(C

_{r}) > 0, ∂(V

_{x})/∂(L

_{r}) > 0, ∂(V

_{x})/∂(R

_{c}) > 0, ∂(V

_{x})/∂(P

_{c}) > 0, ∂(V

_{x})/∂(C

_{h}) < 0. As I

_{t}, R

_{b}, C

_{l}, C

_{r}, L

_{r}, R

_{c}, P

_{c}increase, V

_{x}increases. Conversely, as C

_{h}increases, V

_{x}decreases. □

**Proof 2.**

_{l}+ C

_{r}+ R

_{b}− C

_{h}) + z(L

_{r}+ R

_{c}+ P

_{c})]/(−I

_{t}) or z < (yI

_{t}+ C

_{l}+ C

_{r}+ R

_{b}− C

_{h})/(−L

_{r}− P

_{c}− R

_{c}), x = 0 is the equilibrium point. Therefore, as y and z continue to increase until y > [(C

_{l}+ C

_{r}+ R

_{b}− C

_{h}) + z(L

_{r}+ R

_{c}+ P

_{c})]/(−I

_{t}) or z > (yI

_{t}+ C

_{l}+ C

_{r}+ R

_{b}− C

_{h})/(−L

_{r}− P

_{c}− R

_{c}), the stable strategy of the construction units grows from x = 0 to x = 1. □

## Appendix B

_{r}+ C

_{f}]/(−L

_{c}− P

_{a}− R

_{a}), G(z) = 0, d(F(y))/dy ≡ 0, then the stable state cannot be determined. When z < [(x − 1)C

_{r}+ C

_{f}]/(−L

_{c}− P

_{a}− R

_{a}), G(z) > 0, d(F(y))/dy|

_{y}

_{= 0}< 0, then y = 0 is the equilibrium point. Conversely, y = 1 is the equilibrium point. Therefore, this paper assumes that the probability of the carbon-emission third-party-verification agencies implementing violation or standardized verification is denoted as V

_{1−y}and V

_{y}, respectively:

**Proof 3.**

_{y}, it can be found that ∂(V

_{y})/∂(C

_{r}) > 0, ∂(V

_{y})/∂(R

_{a}) > 0, ∂(V

_{y})/∂(P

_{a}) > 0, ∂(V

_{y})/∂(L

_{c}) > 0, ∂(V

_{y})/∂(C

_{e}) < 0. With increasing C

_{r}, R

_{a}, P

_{a}, L

_{c}, V

_{y}increases. Conversely, as C

_{e}increases, V

_{y}decreases. □

**Proof 4.**

_{r}+ C

_{e}]/(−L

_{c}− P

_{a}− R

_{a}) or x < [C

_{e}− C

_{r}+ x(L

_{c}+ P

_{a}+ R

_{a})]/(−C

_{r}), y = 0 is the equilibrium point. Therefore, as z and x continue to increase until z > [(x − 1)C

_{r}+ C

_{e}]/(−L

_{c}− P

_{a}− R

_{a}) or x > [C

_{e}− C

_{r}+ x(L

_{c}+ P

_{a}+ R

_{a})]/(−C

_{r}), the stable strategy of the carbon-emission third-party-verification agencies grows from y = 0 to y = 1. □

## Appendix C

_{a}+ P

_{a}+ L

_{g}) − C

_{s}+ R

_{g}+ P

_{c}+ P

_{a}+ L

_{g}]/(−yL

_{g}+ R

_{c}+ P

_{c}+ L

_{g}), H(x) = 0, d(F(z))/dz ≡ 0, then the stable state cannot be determined. When x < [−y(R

_{a}+ P

_{a}+ L

_{g}) − C

_{s}+ R

_{g}+ P

_{c}+ P

_{a}+ L

_{g}]/(−yL

_{g}+ R

_{c}+ P

_{c}+ L

_{g}), H(x) < 0, d(F(z))/dz|

_{z}

_{=1}< 0, then z = 1 is the equilibrium point. Conversely, z = 0 is the equilibrium point. Therefore, this paper assumes that the probability of the power grid company implementing strict or permissive supervision is denoted as V

_{z}and V

_{1−z}, respectively:

**Proof 5.**

_{z}, it can be found that ∂(V

_{z})/∂(R

_{g}) > 0, ∂(V

_{z})/∂(L

_{g}) > 0, ∂(V

_{z})/∂(P

_{a}) > 0, ∂(V

_{z})/∂(P

_{c}) > 0, ∂(V

_{z})/∂(R

_{a}) < 0, ∂(V

_{z})/∂(R

_{c}) < 0, ∂(V

_{z})/∂(C

_{s}) < 0. This means that as R

_{g}, L

_{g}, P

_{a}, P

_{c}increase, V

_{z}increases. Conversely, as R

_{a}, R

_{c}, C

_{s}increase, V

_{z}decreases. □

**Proof 6.**

_{a}+ P

_{a}+ L

_{g}) − C

_{s}+ R

_{g}+ P

_{c}+ P

_{a}+ L

_{g}]/(−yL

_{g}+ R

_{c}+ P

_{c}+ L

_{g}) or y < [−x(R

_{c}+ P

_{c}+ L

_{g}) − C

_{s}+ R

_{g}+ P

_{c}+ P

_{a}+ L

_{g}]/(R

_{a}+ P

_{a}+ L

_{g}− xL

_{g}), z = 1 is the equilibrium point. Therefore, as x and y continue to increase until x > [−y(R

_{a}+ P

_{a}+ L

_{g}) − C

_{s}+ R

_{g}+ P

_{c}+ P

_{a}+ L

_{g}]/(−yL

_{g}+ R

_{c}+ P

_{c}+ L

_{g}) or y > [−x(R

_{c}+ P

_{c}+ L

_{g}) − C

_{s}+ R

_{g}+ P

_{c}+ P

_{a}+ L

_{g}]/(R

_{a}+ P

_{a}+ L

_{g}− xL

_{g}), the stable strategy of the power grid company decreases from z = 1 to z = 0. □

## Appendix D

**Proof 7.**

_{e}− C

_{r}+ L

_{c}+ P

_{a}+ R

_{a}< 0, C

_{l}− C

_{h}+ C

_{r}+ L

_{r}+ P

_{c}+ R

_{b}+ R

_{c}< 0, condition a is satisfied, e

_{12}is unstable, and the eigenvalues of e

_{2}, e

_{7}are negative, so they are ESS. Condition b is also satisfied, e

_{9}is unstable. If conditions c and d cannot be satisfied, then e

_{10}and e

_{11}are meaningless. □

**Proof 8.**

_{c}+ P

_{c}> C

_{h}− C

_{l}− C

_{r}− L

_{r}− R

_{b}> 0, R

_{a}+ P

_{a}> C

_{r}− C

_{e}− L

_{c}> 0, condition a is not satisfied, so e

_{2}, e

_{12}is meaningless. Condition b is satisfied, so e

_{9}is unstable. When additional conditions P

_{a}− R

_{c}+ R

_{g}> C

_{s}, P

_{c}− R

_{a}+ R

_{g}> C

_{s}, conditions c and d are satisfied, so e

_{10}and e

_{11}are meaningless. □

## References

- Goh, T.; Ang, B.W.; Su, B.; Wang, H. Drivers of Stagnating Global Carbon Intensity of Electricity and the Way Forward. Energy Policy
**2018**, 113, 149–156. [Google Scholar] [CrossRef] - Liang, K.; Li, W.J.; Wen, J.H.; Ai, W.K.; Wang, J.B. Research Characteristics and Trends of Power Sector Carbon Emissions: A Bibliometric Analysis from Various Perspectives. Environ. Sci. Pollut. Res.
**2023**, 30, 4485–4501. [Google Scholar] [CrossRef] - Wang, Y.; Su, X.L.; Qi, L.; Shang, P.P.; Xu, Y.H. Feasibility of Peaking Carbon Emissions of the Power Sector in China’s Eight Regions: Decomposition, Decoupling, and Prediction Analysis. Environ. Sci. Pollut. Res.
**2019**, 26, 29212–29233. [Google Scholar] [CrossRef] [PubMed] - Guo, H.Y.; Davidson, M.R.; Chen, Q.X.; Zhang, D.; Jiang, N.; Xia, Q.; Kang, C.Q.; Zhang, X.L. Power Market Reform in China: Motivations, Progress, and Recommendations. Energy Policy
**2020**, 145, 111717. [Google Scholar] [CrossRef] - Tao, Y.; Wen, Z.G.; Xu, L.N.; Zhang, X.; Tan, Q.L.; Li, H.F.; Evans, S. Technology Options: Can Chinese Power Industry Reach the Co2 Emission Peak before 2030? Resour. Conserv. Recycl.
**2019**, 147, 85–94. [Google Scholar] [CrossRef] - Jin, J.L.; Zhou, P.; Li, C.Y.; Guo, X.J.; Zhang, M.M. Low-Carbon Power Dispatch with Wind Power Based on Carbon Trading Mechanism. Energy
**2019**, 170, 250–260. [Google Scholar] [CrossRef] - Qiu, T.Z.; Wang, L.C.; Lu, Y.B.; Zhang, M.; Qin, W.M.; Wang, S.Q.; Wang, L.Z. Potential Assessment of Photovoltaic Power Generation in China. Renew. Sust. Energy Rev.
**2022**, 154, 111900. [Google Scholar] [CrossRef] - Luo, Z.B.; Wang, X.B.; Wen, H.; Pei, A. Hydrogen Production from Offshore Wind Power in South China. Int. J. Hydrogen Energy
**2022**, 47, 24558–24568. [Google Scholar] [CrossRef] - Cai, Y.; Wang, L.; Wang, W.W.; Liu, D.; Zhao, F.Y. Solar Energy Harvesting Potential of a Photovoltaic-Thermoelectric Cooling and Power Generation System: Bidirectional Modeling and Performance Optimization. J. Clean Prod.
**2020**, 254, 120150. [Google Scholar] [CrossRef] - Wilberforce, T.; Olabi, A.G.; Sayed, E.T.; Elsaid, K.; Abdelkareem, M.A. Progress in Carbon Capture Technologies. Sci. Total Environ.
**2021**, 761, 143203. [Google Scholar] [CrossRef] - Reznicek, E.P.; Braun, R.J. Reversible Solid Oxide Cell Systems for Integration with Natural Gas Pipeline and Carbon Capture Infrastructure for Grid Energy Management. Appl. Energy
**2020**, 259, 114118. [Google Scholar] [CrossRef] - Cui, X.Y.; Zhao, T.; Wang, J. Allocation of Carbon Emission Quotas in China’s Provincial Power Sector Based on Entropy Method and Zsg-Dea. J. Clean Prod.
**2021**, 284, 124683. [Google Scholar] [CrossRef] - Yang, X.Y.; Guo, X.P.; Li, Y.; Yang, K. Heterogeneous Impacts of Multi-Energy Power Generation on Carbon Emissions: Evidence from China’s Provincial Data. Environ. Sci. Pollut. Res.
**2023**, 30, 35334–35351. [Google Scholar] [CrossRef] [PubMed] - Lin, B.Q.; Jia, Z.J. Why Do We Suggest Small Sectoral Coverage in China’s Carbon Trading Market? J. Clean Prod.
**2020**, 257, 120557. [Google Scholar] [CrossRef] - Stolz, B.; Held, M.; Georges, G.; Boulouchos, K. The CO
_{2}Reduction Potential of Shore-Side Electricity in Europe. Appl. Energy**2021**, 285, 116425. [Google Scholar] [CrossRef] - Lin, B.Q.; Jia, Z.J. What Will China’s Carbon Emission Trading Market Affect with Only Electricity Sector Involvement? A Cge Based Study. Energy Econ.
**2019**, 78, 301–311. [Google Scholar] [CrossRef] - Hu, Y.J.; Li, X.Y.; Tang, B.J. Assessing the Operational Performance and Maturity of the Carbon Trading Pilot Program: The Case Study of Beijing’s Carbon Market. J. Clean Prod.
**2017**, 161, 1263–1274. [Google Scholar] [CrossRef] - Tang, R.H.; Guo, W.; Oudenes, M.; Li, P.; Wang, J.; Tang, J.; Wang, L.; Wang, H.J. Key Challenges for the Establishment of the Monitoring, Reporting and Verification (Mrv) System in China’s National Carbon Emissions Trading Market. Clim. Policy
**2018**, 18, 106–121. [Google Scholar] [CrossRef] - Ochieng, R.M.; Visseren-Hamakers, I.J.; Arts, B.; Brockhaus, M.; Herold, M. Institutional Effectiveness of Redd Plus Mrv: Countries Progress in Implementing Technical Guidelines and Good Governance Requirements. Environ. Sci. Policy
**2016**, 61, 42–52. [Google Scholar] [CrossRef] - Hare, W.; Stockwell, C.; Flachsland, C.; Oberthur, S. The Architecture of the Global Climate Regime: A Top-Down Perspective. Clim. Policy
**2010**, 10, 600–614. [Google Scholar] [CrossRef] - Smith, P.; Soussana, J.F.; Angers, D.; Schipper, L.; Chenu, C.; Rasse, D.P.; Batjes, N.H.; van Egmond, F.; McNeill, S.; Kuhnert, M.; et al. How to Measure, Report and Verify Soil Carbon Change to Realize the Potential of Soil Carbon Sequestration for Atmospheric Greenhouse Gas Removal. Glob. Chang. Biol.
**2020**, 26, 219–241. [Google Scholar] [CrossRef] - Panagakos, G.; Pessoa, T.D.; Dessypris, N.; Barfod, M.B.; Psaraftis, H.N. Monitoring the Carbon Footprint of Dry Bulk Shipping in the Eu: An Early Assessment of the Mrv Regulation. Sustainability
**2019**, 11, 5133. [Google Scholar] [CrossRef] - Perosa, B.; Newton, P.; da Silva, R.F.B. A Monitoring, Reporting and Verification System for Low Carbon Agriculture: A Case Study from Brazil. Environ. Sci. Policy
**2023**, 140, 286–296. [Google Scholar] [CrossRef] - Vargas, R.; Alcaraz-Segura, D.; Birdsey, R.; Brunsell, N.A.; Cruz-Gaistardo, C.O.; de Jong, B.; Etchevers, J.; Guevara, M.; Hayes, D.J.; Johnson, K.; et al. Enhancing Interoperability to Facilitate Implementation of Redd Plus: Case Study of Mexico. Carbon Manag.
**2017**, 8, 57–65. [Google Scholar] [CrossRef] - Olczak, M.; Piebalgs, A.; Balcombe, P. Methane Regulation in the Eu: Stakeholder Perspectives on Mrv and Emissions Reductions. Environ. Sci. Policy
**2022**, 137, 314–322. [Google Scholar] [CrossRef] - Gao, L.; Zhao, Z.Y. The Evolutionary Game of Stakeholders’ Coordination Mechanism of New Energy Power Construction Ppp Project: A China Case. Sustainability
**2020**, 12, 1045. [Google Scholar] [CrossRef] - Poulsen, R.T.; Ponte, S.; van Leeuwen, J.; Rehmatulla, N. The Potential and Limits of Environmental Disclosure Regulation: A Global Value Chain Perspective Applied to Tanker Shipping. Glob. Environ. Polit.
**2021**, 21, 99–120. [Google Scholar] [CrossRef] - Weng, X.J.; Yuan, C.H.; Hu, Q.H.; Xu, Y.H. Evolutionary Game and Simulation Analysis on Quality Supervision of Low-Carbon Renovation of High-Carbon Emission Enterprises under the Reward and Punishment Mechanism. Front. Environ. Sci.
**2023**, 11, 1126275. [Google Scholar] [CrossRef] - Eissa, R.; Eid, M.S.; Elbeltagi, E. Current Applications of Game Theory in Construction Engineering and Management Research: A Social Network Analysis Approach. J. Constr. Eng. Manage.
**2021**, 147, 04021066. [Google Scholar] [CrossRef] - Wang, G.; Chao, Y.C.; Cao, Y.; Jiang, T.L.; Han, W.; Chen, Z.S. A Comprehensive Review of Research Works Based on Evolutionary Game Theory for Sustainable Energy Development. Energy Rep.
**2022**, 8, 114–136. [Google Scholar] [CrossRef] - Tian, H.L.; Zhao, L.; Guo, S. Comprehensive Benefit Evaluation of Power Grid Investment Considering Renewable Energy Development from the Perspective of Sustainability. Sustainability
**2023**, 15, 8299. [Google Scholar] [CrossRef] - Wang, H.Y.; Gao, L.; Jia, Y. The Predicament of Clean Energy Technology Promotion in China in the Carbon Neutrality Context: Lessons from China’s Environmental Regulation Policies from the Perspective of the Evolutionary Game Theory. Energy Rep.
**2022**, 8, 4706–4723. [Google Scholar] - Jiang, K.; You, D.M.; Merrill, R.; Li, Z.D. Implementation of a Multi-Agent Environmental Regulation Strategy under Chinese Fiscal Decentralization: An Evolutionary Game Theoretical Approach. J. Clean Prod.
**2019**, 214, 902–915. [Google Scholar] [CrossRef] - Xu, S.T.; Zhou, Z.F.; Liu, K. Multi-Evolutionary Game Research on Heavy Metal Pollution Control in Soil: Based on a Third-Party Perspective. Sustainability
**2020**, 12, 5306. [Google Scholar] [CrossRef] - Li, K.; Dong, F. Government Strategy for Banning Gasoline Vehicles: Evidence from Tripartite Evolutionary Game. Energy
**2022**, 254, 124158. [Google Scholar] [CrossRef] - Hsueh, L. Do Businesses That Disclose Climate Change Information Emit Less Carbon? Evidence from S&P 500 Firms. Clim. Chang. Econ.
**2022**, 13, 2250003. [Google Scholar] - Liu, D.N.; Zhang, X.; Gao, C.C.; Yang, M.; Li, Q.; Li, M. Cost Management System of Electric Power Engineering Project Based on Project Management Theory. J. Intell. Fuzzy Syst.
**2018**, 34, 975–984. [Google Scholar] [CrossRef] - Wang, H.X.; Huang, Z.; Zhang, X.; Huang, X.; Zhang, X.W.; Liu, B. Intelligent Power Grid Monitoring and Management Strategy Using 3d Model Visual Computation with Deep Learning. Energy Rep.
**2022**, 8, 3636–3648. [Google Scholar] [CrossRef] - Zhou, S.L.; He, H.J.; Zhang, L.P.; Zhao, W.; Wang, F. A Data-Driven Method to Monitor Carbon Dioxide Emissions of Coal-Fired Power Plants. Energies
**2023**, 16, 1646. [Google Scholar] [CrossRef] - Li, J.Y.; Li, S.S.; Wu, F. Research on Carbon Emission Reduction Benefit of Wind Power Project Based on Life Cycle Assessment Theory. Renew. Energy
**2020**, 155, 456–468. [Google Scholar] [CrossRef] - Lyapunov, A.M. The General Problem of the Stability of Motion. Int. J. Control
**1992**, 55, 531–773. [Google Scholar] [CrossRef] - Dubrau, A.; Hendren, L. Taming Matlab. ACM SIGPLAN Not.
**2012**, 47, 503–522. [Google Scholar] [CrossRef]

**Figure 2.**Decision tree of the power grid company, construction unit, and carbon third-party-verification agency. Source: own creations.

**Figure 12.**The low-carbon transition mechanism for PCPs under the MRV system. Source: own creations.

Parameters | Descriptions | References |
---|---|---|

I_{t} | Income obtained by the construction units through carbon verification. | [28,36,37,38] |

I_{v} | Income from verification by carbon-emission third-party-verification agencies. | |

C_{h} | Costs for construction units to implement high-level carbon-monitoring programs. | |

C_{l} | Costs for construction units to implement low-level carbon-monitoring programs. | |

C_{r} | Costs of applying for rent seeking by construction units to pass carbon verification. | |

C_{e} | Extra costs incurred by carbon-emission third-party-verification agencies in the event of profit-driven violations in verification. | |

C_{S} | Costs of inputs when strictly supervised by the power grid company. | |

C_{m} | Costs of environmental governance required by the power grid company’s negligent supervision, leading to substandard construction units passing verification. | |

R_{b} | Construction units implement high-level carbon-emission monitoring and reporting programs, which are supported by the public and add value to the brand. | [17,39,40] |

R_{e} | Construction units deliver environmental benefits to the power grid company. | |

R_{a} | The power grid company rewards carbon-emission third-party-verification agencies for the standardized verification. | |

R_{c} | The power grid company rewards construction units for implementing high-level carbon-emission monitoring and reporting programs. | |

R_{g} | The power grid company receives a credibility boost from strict supervision. | |

P_{c} | The power grid company punishes construction units for failing carbon verification. | [26,31,36] |

P_{a} | The power grid company punishes carbon-emission third-party-verification agencies. | |

L_{r} | Construction units’ failure to meet carbon reduction leads to reputational damage. | |

L_{g} | The grid company is being punished by higher regulators for loose supervision. | |

L_{c} | Disclosure of irregularities in carbon-emission third-party-verification agencies leads to loss of credibility. |

Equilibrium Points | Eigenvalues | State | Conditions | |
---|---|---|---|---|

λ_{1} λ_{2} λ_{3} | ||||

e_{1}(0, 0, 0) | C_{e} − C_{r}, C_{l} + C_{r} + R_{b} − C_{h}, L_{g} + P_{a} + P_{c} + R_{g} + C_{s} | (−,−,+) | \ | Unstable |

e_{2}(0, 0, 1) | C_{e} + L_{c} + P_{a} + R_{a} − C_{r}, C_{s} − L_{g} − P_{a} − P_{c} − R_{g}, C_{l} + C_{r} + L_{r} + P_{c} + R_{b} + R_{c} − C_{h} | (−,−,−) | a | ESS |

e_{3}(0, 1, 0) | C_{r} − C_{e}, P_{c} + R_{g} − C_{s} − R_{a}, C_{l} + C_{r} + I_{t} + R_{b} − C_{h} | (+,×,+) | \ | Unstable |

e_{4}(1, 0, 0) | C_{e}, P_{a} + R_{g} − C_{s} − R_{c}, C_{h} − C_{l} − C_{r} − R_{b} | (+,×,+) | \ | Unstable |

e_{5}(0, 1, 1) | C_{s} + R_{a} − R_{g} − P_{c}, C_{r} − C_{e} − L_{c} − P_{a} − R_{a}, C_{l} + C_{r} + I_{t} + L_{r} + P_{c} + R_{b} + R_{c} − C_{h} | (×,+,+) | \ | Unstable |

e_{6}(1, 0, 1) | C_{s} + R_{c} − R_{g} − P_{a}, C_{e} + L_{c} + P_{a} + R_{a}, C_{h} − C_{l} − C_{r} − L_{r} − P_{c} − R_{b} − R_{c} | (×,+,+) | \ | Unstable |

e_{7}(1, 1, 0) | −C_{e}, R_{g} − R_{a} − R_{c} − C_{s}, C_{h} − C_{l} − C_{r} − I_{t} − R_{b} | (−,−,−) | \ | ESS |

e_{8}(1, 1, 1) | −C_{e} − L_{c} − P_{a} − R_{a}, C_{s} + R_{a} + R_{c} − R_{g}, C_{h} − C_{l} − C_{r} − I_{t} − L_{r} − P_{c} − R_{b} − R_{c} | (×,+,+) | \ | Unstable |

e_{9}(x_{1}, y_{1}, 0) | λ_{1} = −λ_{3}, λ_{2} = c_{1} | (+,×,−) | b | Unstable |

e_{10}(x_{2}, 0, z_{2}) | λ_{1} = −λ_{2}, λ_{3} = c_{2} | (+,−,×) | c | Unstable |

e_{11}(0, y_{3}, z_{3}) | λ_{1} =c_{3}, λ_{2} = −λ_{3} | (×,+,−) | d | Unstable |

e_{12}(x_{4}, y_{4}, 1) | λ_{1} =c_{4}, λ_{2} = −λ_{3} | (×,+,−) | a | Unstable |

_{r}> C

_{e}+ L

_{c}+ P

_{a}+ R

_{a}, C

_{h}> C

_{l}+ C

_{r}+ R

_{b}+ L

_{r}+ P

_{c}+ R

_{c}; b: C

_{h}> C

_{l}+ C

_{r}+ R

_{b}; c: C

_{h}< C

_{l}+ C

_{r}+ R

_{b}+ L

_{r}+ P

_{c}+ R

_{c}; and d: C

_{r}< C

_{e}+ L

_{c}+ P

_{a}+ R

_{a}. Source: own creations.

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## Share and Cite

**MDPI and ACS Style**

Li, L.; Zhu, R.; Song, K.; Zhang, O.; Jiang, X.
Promoting the Low-Carbon Transition of Power Construction Projects under MRV: An Evolutionary Game Analysis. *Buildings* **2023**, *13*, 2874.
https://doi.org/10.3390/buildings13112874

**AMA Style**

Li L, Zhu R, Song K, Zhang O, Jiang X.
Promoting the Low-Carbon Transition of Power Construction Projects under MRV: An Evolutionary Game Analysis. *Buildings*. 2023; 13(11):2874.
https://doi.org/10.3390/buildings13112874

**Chicago/Turabian Style**

Li, Lihong, Rui Zhu, Kun Song, Ou Zhang, and Xue Jiang.
2023. "Promoting the Low-Carbon Transition of Power Construction Projects under MRV: An Evolutionary Game Analysis" *Buildings* 13, no. 11: 2874.
https://doi.org/10.3390/buildings13112874