Carbon Emission Efficiency Network: Evolutionary Game and Sensitivity Analysis between Differentiated Efficiency Groups and Local Governments

Round 1

Reviewer 1 Report

This study explores the choice of a tripartite evolutionary game between high and low efficiency groups and local governments under different strategy combinations in a carbon efficiency emission network in the context of China’s “double carbon”, which is an interesting question with a more standardized approach and some useful results. However, some minor modifications are required and the following are my comments：

1. In 3.2 Model Derivation, it is suggested to elaborate the basis of parameter setting in more detail
2. The policy implications in the “5 Policy Implications” section are common-sense. It is suggested that the main conclusions and policy implications in section 6 be placed in one section, with the main conclusions discussed first, and then specific and insightful policy recommendations based on the main conclusions.
3. It is proposed to summarize the main work and contributions of this paper in Section 6, and to explain the limitations of this study and future research prospects.

Author Response

Dear Reviewers:

         Thank you for your letter and for the reviewer’s comments concerning our manuscript entitled Carbon Emission Efficiency Network: Evolutionary Game and Sensitivity Analysis Between Differentiated Efficiency Groups and Local Governments (ID: 1581074). We have studied comments carefully and have made correction. Revised portion are marked by highlight in the paper. The main corrections in the paper and the responds to the reviewer’s comments are as follows:

1. In 3.2 Model Derivation, it is suggested to elaborate the basis of parameter setting in more detail

Responses: It is very important to explain the basis of parameter setting in detail for the objectivity of our research. In the process of setting the parameters, we consider the interaction between the behaviors of different participants. There is a correlation between efficiency spillover and green transformation among groups, and there is a correlation between efficiency spillover and non-supervision with local government groups, which are expressed by parameters. Please see the highlights on Page 7 of the paper.

2. The policy implications in the “5 Policy Implications” section are common-sense. It is suggested that the main conclusions and policy implications in section 6 be placed in one section, with the main conclusions discussed first, and then specific and insightful policy recommendations based on the main conclusions.

Responses: We rediscovered the key information in the conclusion, and put forward targeted policy suggestions accordingly. Please see the highlights on Page 16 of the paper.

3. It is proposed to summarize the main work and contributions of this paper in Section 6, and to explain the limitations of this study and future research prospects.

Responses: We described the work done by the research, and finally added the assumption and arrangement for future research. Please see the highlights on Page 16 of the paper.

Reviewer 2 Report

It is an interesting attempt to simulate the evolution mechanism of the carbon emission efficiency network. The hypotheses and conclusions formulated by the authors seem logical and the work is well contextualized in previous studies. However, there are doubts about the reliability of the sensitivity study results in relation to reality; in fact, the authors suggest some options to implement the system.  But still, I consider it is a valuable step in this relevant topic.

Author Response

Dear Reviewers:

         Thank you for your letter and for the reviewer’s comments concerning our manuscript entitled Carbon Emission Efficiency Network: Evolutionary Game and Sensitivity Analysis Between Differentiated Efficiency Groups and Local Governments (ID: 1581074). Your suggestions are of great significance to guide our next research, and will be an important direction for improvement in the simulation of evolutionary systems.

Reviewer 3 Report

This study attempts to discuss the conditions needed for different players and trilateral interconnected systems to implement balanced and stable strategies via a trilateral evolutionary game model. The topic is interesting, authors present good scientific background, the methodology is suitable and results are interesting for the readers. Also, this article is a good work for theoretical discussion and simulation.

I have some suggestions for this paper to be more suitable for this journal as follows:

First, Fig. 1 is not clear for readers. I strongly suggest that the authors show a new and high-quality figure for readers.

Second, the authors are good at modeling and mathematical simulations. I am curious about the reasons of simulation initial values. For instance, in line 466-468, the values of M, N, Q, H, S, C, P, R, and L are given the sources from many experiments in MATLAB 2021a environment. The setting of parameter is very important to the simulation results. I suggest that the authors need to briefly explain the experiments in the appendix section.

Third, in the last section, I suggest that it would be clear to have a table or map with different results compared between the experimental results of different scenarios of this paper to highlight the advantage of this study.

Author Response

Dear Reviewers:

         Thank you for your letter and for the reviewer’s comments concerning our manuscript entitled Carbon Emission Efficiency Network: Evolutionary Game and Sensitivity Analysis Between Differentiated Efficiency Groups and Local Governments (ID: 1581074). We have studied comments carefully and have made correction. Revised portion are marked by highlight in the paper. The main corrections in the paper and the responds to the reviewer’s comments are as follows:

1. 1 is not clear for readers. I strongly suggest that the authors show a new and high-quality figure for readers.

Responses: We redraw image 1 and provide a high-resolution image in this paper.. Please see the highlights on Page 6 of the paper.

• The authors are good at modeling and mathematical simulations. I am curious about the reasons of simulation initial values. For instance, in line 466-468, the values of M, N, Q, H, S, C, P, R, and L are given the sources from many experiments in MATLAB 2021a environment. The setting of parameter is very important to the simulation results. I suggest that the authors need to briefly explain the experiments in the appendix section..

Responses: Generally speaking, the simulation initial value is very important to the simulation results of the system, and we are also very careful when choosing the initial value. In many simulation experiments, we found some rules and explained them. The analysis results in Table 3 show that there is only one stable equilibrium point (1,1,0) in the whole evolutionary system, and other equilibrium points can not be realized under the initial assumption. During the simulation experiment, we changed the variable values many times to make them meet the eigenvalue conditions except (1,1,0) in Table 3. At this time, the variable values may be unrealistic, even some variable values are negative, but the results show that the evolution trajectory has the same changing trend as expected in Table 3. Therefore, we think that these simulation values are available as long as the conditions in Table 3 can be met and the variable values accord with the actual situation. The initial values given in this paper are selected on the basis of maximizing the difference of evolution trajectories, with the purpose of more clearly comparing the sensitivity of the evolution trajectories of the system to different variable values. At the same time, we also submitted the simulation file while submitting the modified file, so readers can reproduce the results according to the simulation file, or have a deeper discussion. Please see Appendix A highlighted on page 17 of the paper.

• In the last section, I suggest that it would be clear to have a table or map with different results compared between the experimental results of different scenarios of this paper to highlight the advantage of this study.

Responses: At the end of the article, we added Appendix B, which aims to compare the sensitivity of trilateral evolutionary game system to different influencing factors, and at the same time, it is also helpful for readers to restore the research results or make deeper research through the codes and files we provide. Please see the highlights on Page 17 and 18 of the paper.