How to Promote Quality and Equity of Early Childhood Education for Sustainable Development in Undeveloped Rural Areas of China: An Evolutionary Game Study

Round 1

Reviewer 1 Report

REVIEW REPORT

In relation to the main question addressed by the research, it would be convenient to clarify more specifically the objectives to be achieved, since it is addressed in a general way and it is not entirely clear what the final objectives are.
I consider the topic original and relevant to the field of work, being unusual in the educational field, with which it can provide new perspectives that provide broader knowledge on the subject.

Reflecting on the different educational models and strategies addressed in rural and urban contexts and establishing their possible relationships, allows knowing the state of the current situation, in order to be able to make decisions regarding how to best distribute the funds.

In this sense, there is talk of achieving a more sustainable education, but it would be necessary to provide a more adequate definition of the concept of sustainability in education and contextualize which aspects of it are related to the main question addressed by the research. This should also be qualified for primary and infant. A deeper theoretical justification should be made in this regard.

Likewise, it is necessary to specify more about what advantages and/or disadvantages a tripartite model of evolutionary game can offer. Similarly, talk more about what this evolutionary game consists of.

In addition, in the conclusions, it would also be interesting to contemplate a series of limitations and future lines of research, especially since it is a study that is being carried out for the first time in the educational field.

Finally, although the bibliography is adequate, it would be convenient to add more reference literature to previous similar works in the same or other areas that may have some kind of relationship with the present work. You should also consider looking for more up-to-date sources.

Author Response

Point 1：I consider the topic original and relevant to the field of work, being unusual in the educational field, with which it can provide new perspectives that provide broader knowledge on the subject.

Response 1: Thank you very much for your time involved in reviewing the manuscript and your very encouraging comments on the merits. We also appreciate your clear and detailed feedback and hope that the explanation has fully addressed all of your concerns.

 

Point 2: In relation to the main question addressed by the research, it would be convenient to clarify more specifically the objectives to be achieved, since it is addressed in a general way and it is not entirely clear what the final objectives are.

Response 2: I am very grateful to your comments for the manuscript. Our final objectives are to investigate the efficacy of policy portfolio of preferential input, regulation, supervision and quality evaluation to improve quality of rural ECE for equitable and sustainable development in disadvantaged areas. To achieve the objectives, we develop a tripartite evolutionary game model of ECE providers in undeveloped rural areas, local governments and central government, and correlates governments financial support with the regulation and supervision in ECE as strategy combination via reward-punishment mechanism. Through the evolution process of “change-adjustment-convergence” of behavioral decisions, each party seek optimization to achieve the ideal stable equilibrium state. The numerical simulation is used to verify the dynamic evolutionary process. The simulation results presented the governments’ subsidies and reward, regulation and supervision have a substantive effect on the improvement of quality and equity. So the governments should strengthen the regulation and supervision to rural ECE, formulate more reasonable reward and punishment mechanism, adjust and optimize the policies and measures to improve the efficiency of educational funding.

With regard to your suggestion of “to clarify more specifically the objectives to be achieved”, we have added the content at line 149-163 as follows:

There are high-quality resources scarcity in undeveloped rural areas, which hinders the equitable and sustainable development of ECE. Can the sustainable government support efficaciously enlarge and efficiently allocate the limited educational resources to promote the quality and equity? Can the governments’ regulation and supervision on ECE effectively improves the service quality? To explore the above issues, the study develops a tripartite evolutionary game model of ECE providers in undeveloped rural areas, local governments and central government, and correlates governments financial support with the regulation and supervision in ECE as strategy combination via reward-punishment mechanism. Through the analysis of three behavioral actors’ strategy choices in the dynamic process by employing evolutionary game theory, the aim of study is to investigate efficacy of the policy portfolio of preferential input, regulation, supervision and quality evaluation to improve quality of rural ECE for equitable and sustainable development in disadvantaged areas.

 

Point 3: Reflecting on the different educational models and strategies addressed in rural and urban contexts and establishing their possible relationships, allows knowing the state of the current situation, in order to be able to make decisions regarding how to best distribute the funds.

In this sense, there is talk of achieving a more sustainable education, but it would be necessary to provide a more adequate definition of the concept of sustainability in education and contextualize which aspects of it are related to the main question addressed by the research. This should also be qualified for primary and infant. A deeper theoretical justification should be made in this regard. 

Response 3: Thanks for your valuable suggestion. We have added the following contents in the first paragraph:

Sustainability, as an interdisciplinary concept, has been considered as an integration of different dimensions of ecological, economic and social aspects [1]. Although there is no standardized definition of the sustainability in education, it can be understood as the long-term stable development of education to ensure all children have access to inclusive and equitable quality resources for building future and guaranteeing intergenerational justice [2]. It has been found that the quality of people's long lives and sustainable development benefit from high-quality ECE [3]. ECE is also fundamental to breaking the intergenerational transmission of poverty.

Point 4: Likewise, it is necessary to specify more about what advantages and/or disadvantages a tripartite model of evolutionary game can offer. Similarly, talk more about what this evolutionary game consists of.

Response 4: Thanks for your insightful suggestions. These are the advantages and disadvantages this tripartite model can offer as follows: A tripartite model of evolutionary game is applied to analyze the behavioral strategies of relevant parties with bonded rationality, limited information and conflict of interests. Through the evolution process of “change-adjustment-convergence” of behavioral decisions, each party seek optimization to achieve the ideal stable equilibrium state, which can predict the participants’ strategic behavior scientifically and reasonably. To model the evolution process dynamically and flexibly can more authentically reflect the diversity and complexity of reality. But the evolutionary game emphasizes the dynamic process of changing behaviors, and the numerical simulation is only used to verify the equilibrium solutions of tripartite game, which cause the limitation in analytical precision compared to the methodology of econometric models.

As suggested by you, we have added the following contents on page 4, page5:

Evolutionary game theory was first proposed in research of biological evolution process, based on Darwin’s theory [4]. Smith and Price (1973) have introduced the concept of evolutionary stable strategy (ESS) to describe a stable state of the game [5]. With deepening the research, Smith (1982) refined the concept of Nash equilibrium (Nash 1953) [6]. The relationship between evolutionary equilibrium and replicator dynamics was discovered by Taylor and Jonker (1978) [7]. The replicator dynamics is the dynamic adjustment mechanism of the evolutionary game [8], and can describe the evolutionary change over time to achieve the final stable equilibrium state [9]. Thus evolutionary game theory combines game theoretic analysis with dynamic evolution [10]. In evolutionary game theory, the basic assumption of agents’ bonded rationality is used instead of complete rationality, which expanded the classic game theory. As a dynamic system, the evolutionary game model is created involving relevant parties with bonded rationality, limited information and conflict of interests. And theoretically, the dynamic process of participants’ decision-making is described by constantly adjusting and optimizing their own strategy for ESS. To model the evolution process dynamically and flexibly can more authentically reflect the diversity and complexity of reality. Therefore, evolutionary game theory is a useful tool for discussing strategic interaction to create a stable solution among decision-making subjects [11].

2.2 Model Analysis

Replicator dynamics equations describes the evolution of each party’s strategy over time in the three-dimensional dynamic system. According to the above hypotheses and the pay-off matrix, the replicator dynamics equations of puhui kindergarten, local government and central government are established.

Also, we have revised the following content on page 13:

Under the reward-punishment mechanism, the central government’s reward incentive is great enough to urge local governments’ active support and strict regulation. And punishment measures by the central governments can alter local governments’ inactive strategy. With different variables interaction in the evolutionary system, each party chooses among alternative strategies whose payoff depends on the choices of others [11], and seek optimization till no party can improve its payoff by following strategies other than ESS [12]. There evolves to ideal equilibrium state in which there is win-win situation and mutual benefits are achieved. Ultimately, puhui kindergartens can improve the quality, local governments and central government can actively promote quality and equity by incorporating strictly regulation and supervision into sustainable policy support for rural ECE. The simulation results confirm that the governments have a dominant role in promoting quality and equity of ECE in China, consistent with the consensus of major countries and regions in the world [13].   

 

Point 5: In addition, in the conclusions, it would also be interesting to contemplate a series of limitations and future lines of research, especially since it is a study that is being carried out for the first time in the educational field.

Response 5: Thanks for your valuable suggestions. We have added the following contents in the last paragraph: This study has some limitations that should be addressed. First, the governments’ corruption and seeking behavior could influence their strategy options. Also, the development of regional economy has direct and indirect impact on local governments’ fiscal budget, the continuance and stability of financial investment to ECE. Thus, these influencing factors, which was neglected here, could be considered into analytical framework in future research. Secondly, the numerical simulation is only used to verify the equilibrium solutions of tripartite game, which limits the analytical precision in companion with the methodology of econometric models. In future work, the field experiment could be designed and conducted in some undeveloped rural areas of China. Through field investigation and econometric analysis, the real data would be collected, and the simulation results would be checked.

 

Point 5: Finally, although the bibliography is adequate, it would be convenient to add more reference literature to previous similar works in the same or other areas that may have some kind of relationship with the present work. You should also consider looking for more up-to-date sources. 

Response 6: Thank you for pointing this out. We have added the following contents on page 3:

There are both qualitative and quantitative analyses of existing literature on the quality, equity and development of ECE in rural China. Some studies demonstrated that insufficiency of consistent investment, the poor conditions of kindergartens, lack of teaching staff and high mobility led to low quality and impeded sustainable development of rural ECE [14] [15]. Some studied the allocation efficiency of ECE resources [16], and it is suggested to adjust the way of financial incentive while increasing the investment in ECE [17]. As shown by some research [18], the lack of government supervision resulted in a serious waste of ECE resources, so it is necessary to strengthen regulation and supervision for the improvement of ECE quality[19][20]. Some literature proposed policy recommendations on the promotion of quality and equity, the development of ECE [21] [22]. In precious literature, it was not discussed further and examine whether these policy recommendations are efficacious or not. As all levels of governments, kindergartens, families with children pursue different benefits in the development process of ECE, this process can be regarded as the process of “change-adjustment-convergence” of behavioral decisions in multi-agent game [23] [24]. Thus the policy effect can be studied and predicted through analyzing the behavioral strategies’ interaction in the dynamic process by using evolutionary game theory. Existing literature rarely employs evolutionary games to study issues in the education field, there is one research that analyzed the factors affecting different stakeholders’ choice of strategies, and built an evolutionary game model among local governments, providers of preschool education and families with children who needed ECE [25]. This study explores high-quality, equity and sustainable development of ECE in application to evolutionary game theory and MATLAB numerical simulation for the first time.

 

References

1. Soini, ; Dessein, J..Culture-sustainability relation: Towards a conceptual framework. Sustainability 2016, 8.
2. Vogt, ; Weber,C.. Current challenges to the concept of sustainability, Global Sustainability. 2019.
3. Samuelsson, I.P..Why We Should Begin Early with ESD: The Role of Early Childhood Education. International Journal of Early Childhood. 2011.
4. Smith, J. M. Evolution and the theory of games. Gambridge University Press. 1982.
5. Smith, J.M.; Price. G. R..The logic of animal conflict. 1973, 246,, 15-18.
6. Nash,J..Two-person cooperative games. Econometrica. 1953, 21,128–140.
7. McNamara, M.; Weissing, F. J.. Evolutionary Game Theory.Springer. 2010.
8. Weibull, W..Evolutionary Game Theory. MIT Press.Cambridge. 1996.
9. Tuyls, ;Parsons, S..What evolutionary game theory tells us about multiagent learning. Artificial Intelligence. 2007, 7, 406–416. 
10. Samuelson, L.(2002). Evolution and Game Theory, Journal of Economic Perspectives, 16(2), 47-66.
11. Parsapour-Moghaddam, P.;Abed-Elmdoust, A.; Kerachian, R..A Heuristic Evolutionary Game Theoretic Methodology for Conjunctive Use of Surface and Groundwater Resources. Water Resources Management. 2015, 29, 5 –18.
12. Friedman, D.. On economic applications of evolutionary game theory, Journal of Evolutionary Economics.1998, 8,15–43.
13. Wang,M.; Wei, J.D.. Statistically Based Assessment and Decision-Making in Preschool Education. Mathematical Problems in Engineering. 2022.
14. Li, L.; Yang, L.J.. Bottlenecks and Rescue: Basic Quality Assurance of Preschool Education in Poor Rural Areas in the Midwest of China. Academic Exploration. 2019, 5, 150-156.
15. Gong,X.; Li. Z.Y..Predicament and Breakthrough Strategy of Preschool Education Development in Poor Rural Areas — Based on Investigation of 41 Rural Kindergartens. Reform of Administration 2019, 6, 28-34.
16. Li, J.J;H Z.. Current Situation of Resource Allocation Efficiency of Preschool Education in China and Its Countermeasures, Journal of Schooling Studies. 2020, 17, 47-58.
17. Qiu,Z.H.; Zhang, L.; Hu, X.N.. Achievements，Problems and Countermeasures of Constructing Pubic Service System for Preschool Education in Rural Areas —Based on Investigation of N City in Central Region. Educational Research. 2016, 6, 58-63.
18. Cui,S.Q.; Yuan, L.S.; Tian, Z.L..On the Role of the Government in the Development of Preschool Education—based on the analysis of economic theory and practical experience. Studies in Preschool Education. 2011,5, 3-8.
19. Li,K.Q.; Zheng, Z..A County-level Evaluation Model of Preschool Resource Allocation. Studies in Early Childhood Education. 2014, 10, 23-29.
20. Wang, J.; Xie, Y.C.. The High-quality of Rural Preschool Education: Connotation, Logic and Long-term Mechanism.Journal of Northeast Normal University(Philosophy and Social Sciences). 2022, 2., 29-37.
21. Zhou, Y.; Yang, R.H.. An Analysis of The System Factors of Influencing Preschool Education Equality And Balanced Development Between Urban And Rural Areas —taking Guangdong province as a case study. Studies in Preschool Education. 2010, 5, 12-19.
22. Huang, J.; Xiong, C.C..Quality Preschool Education in China: Development Connotation and Realization Approach. Educational Sciences.2021, 3,33-47
23. Friedman, .Evolutionary games in economics. Econometrica.1991. 59, 3, 637-66.
24. Weibull., J. Evolutionary Game theory. MIT Press.1997.
25. Xu,L.; Wang,J.,X; Li,X.,P. The Multi-evolutionary Game Model of Inclusive Preschool Education from the Perspective of Government Procurement of Public Service. Operations. Research and Management Science. 2018, 27, 85-93.

 

Author Response File: Author Response.pdf

Reviewer 2 Report

Dear Authors and Dear Editor,

The paper, entitled as "How to Promote Quality and Equity of Early Childhood Education for Sustainable Development in Undeveloped Rural Areas of China: An Evolutionary Game Study" is an interesting paper in terms of its focus on the role of education and its relation to economic development in rural and urban areas. Authors define a three player evolutionary game theoretic approach to investigate the relationships. Though the paper is interesting, it has many problems that should be attended. I regret to inform you that though I liked focus of the paper, I have concerns that the problem stated in the title is not as effectively analyzed in this paper. The following points should be attended by the authors to improve the paper. 

1. In the Abstract, the first sentence should be revised. It does not state what paper focuses at and for which country. Further, the first sentence should state the importance of the paper.
2. The abstract is too general, method is not clearly stated, general sentences are given. Policy recommendations are made in abstract but they are not specific. More direct and specific writing in abstract shold be preferred as the end of the abstract approaches.
3. Some references are after the sentences and after the dots. Example: line 28, Ref. [1]; line 32, Ref. [2]. References should be within the sentence, not afterwards. Check this in the whole article because they are many. Also, I suggest revising some sentences as: According to [1],.... or, As stated by [2],...
4. Some sentences should be revised since they are not very academically clear. Example: "The development of ECE is heavily dependent on the local economy, so its develop-51 ment level is in alignment with the local economic situation." Do you mean there is a positive association between the level of economic development and ECE? State that way, the word, economic situation is not academically correct from an economics perspective.
5. Line 54 and 55 necessitates a reference.
6. Same for line 66-67. You are making a statement about the ECE policy in China. From which source?
7. At line 147, what is puhui? It is all throughout the text and if checked, definition is not made in the first place it was used. This is so central for the paper but no explanation is made about it. Puhui is in 48 different place in the paper. The first place is at line 105. You should explain it. You should state the importance of it.  
8. "...This paper uses evolutionary game theory to analyze the effect of the increasing sub sidies..." Which game theory? Which model? Stating game theory is too general. Which game theoretic literature is used or referenced? These are not clear. The methodology raises serious concerns.
9. No equation numbers are given.
10. The objective functions are not clear.
11. The game theoretic approach follows simulation analysis. However, in my opinion, such a methodology is not enough and it should be supported with real data and econometric models in the methodology to derive conclusions and to check if the results are in line with those obtained from the simulation.
12. In conclusion, I suggest no references within. These should be in the discussion section.
13. For a paper that focuses on the role of education and on the relation between sustainability, economic development and human capital, the paper should also be based on economic development literature on human capital and economic development. The paper fails to possess these and I suggest augmenting the paper with this respect in the intro, in the literature and in the discussion sections.

I regret to inform that at this point, my decision is reject however the paper also has potential. As a result, though my decision is towards reject, if corrections are made carefully, a second round evaluation could also be possible. Therefore, I will select major revision.

 

Author Response

Point 1: In the Abstract, the first sentence should be revised. It does not state what paper focuses at and for which country. Further, the first sentence should state the importance of the paper.  

Response 1: I am very grateful to your comments for the manuscript. As suggested by you, we have revised the first and second sentence as follows:

To promote the sustainable development of early childhood education(ECE) in undeveloped rural areas of China, it is vital to guarantee high-quality equity for all children from disadvantaged backgrounds. Focus on investigating the efficacy of China governments’ policy support to promote the quality and equity, the study constructs a tripartite evolutionary game model of ECE providers in undeveloped rural areas, local governments and central government, and correlates the governments’ financial investment with the regulation and supervision in ECE as strategy combination via reward-punishment mechanism.

Point 2: The abstract is too general, method is not clearly stated, general sentences are given. Policy recommendations are made in abstract but they are not specific. More direct and specific writing in abstract should be preferred as the end of the abstract approaches.

Response 2: Many thanks for your valuable suggestion. We have revised the abstract as follows:

To promote the sustainable development of early childhood education(ECE) in undeveloped rural areas of China, it is vital to guarantee high-quality equity for all children from disadvantaged backgrounds. Focusing on analyzing the efficacy of China governments’ policy support to promote the quality and equity, the study constructs a tripartite evolutionary game model of ECE providers in undeveloped rural areas, local governments and central government, and correlates the governments’ financial investment with the regulation and supervision in ECE as strategy combination via reward-punishment mechanism. Through the evolution process of “change-adjustment-convergence” of behavioral decisions, each party seek optimization to achieve the ideal stable equilibrium state. The numerical simulation is used to verify the dynamic evolutionary process. The simulation results presented the governments’ subsidies and reward, regulation and supervision have a substantive effect on the improvement of quality and equity. So the governments should strengthen the regulation and supervision to rural ECE, formulate more reasonable reward and punishment mechanism, adjust and optimize the policies and measures to improve the efficiency of educational funding. This study can provide reference value for the optimization of relevant policies and the practical operation of new policy making.

 

Point 3: Some references are after the sentences and after the dots. Example: line 28, Ref. [1]; line 32, Ref. [2]. References should be within the sentence, not afterwards. Check this in the whole article because they are many. Also, I suggest revising some sentences as: According to [1],.... or, As stated by [2],...

Response 2: Thanks for your so detailed suggestion. We have revised it directly in the revised paper. Also, with regard to your suggestion of “some sentences as: According to [1],....”, we have revised the sentences at line102-108 as flows :

According to the statistics from the Department of Education of China [1], the national gross enrollment rate of ECE rose from 62.3 percent in 2011 to 88.1 percent in 2021, and has reached 85.2%; about 80 percent of new kindergartens nationwide were concentrated in central and western regions and about 60 percent were distributed in rural areas, where there was the fastest development of ECE; in 2021, the coverage of puhui kindergartens in rural areas reached 90.6%, and the enrollment rate in poverty-stricken areas increased significantly.

 

Point 4: Some sentences should be revised since they are not very academically clear. Example: "The development of ECE is heavily dependent on the local economy, so its development -51 level is in alignment with the local economic situation." Do you mean there is a positive association between the level of economic development and ECE? State that way, the word, economic situation is not academically correct from an economics perspective.

Response 4: Thank you for pointing this out. As suggested by you, we have revised these sentences at line 61-64 as follows:

The government's financial input capacity, which is closely related to the regional economic development, has a direct effect on the quantity and quality of educational resource supply [2]. Generally, the level of educational development is consistent with the level of economic development in the region.

 

Point 5: Line 54 and 55 necessitates a reference.
Response 5: Thank you for pointing this out. With regard to your suggestion, we have added the reference:

The remarkable gap of economic development rooted in urban-rural dual structure between urban and rural areas [3].

 

Point 6: Same for line 66-67. You are making a statement about the ECE policy in China. From which source?

Response 6: Thank you for pointing this out. As suggested by you, the specific modifications at line 74-81 are as follows:

On the other hand, taxes were divided into central taxes, local taxes, and shared taxes between central and local governments according to “Decision of The State Council on implementing the Tax Assignment System” in 1990s [4]. By increasing central government’s tax sharing, the finance capacity of the central government had been strengthened while the finance capacity of local governments had been weakened [5]. However, local governments need take the main responsibility for public investment in education [6], which resulted in the mismatch between local governments’ responsibility and capacity of financial input in education.

 

Point 7: At line 147, what is puhui? It is all throughout the text and if checked, definition is not made in the first place it was used. This is so central for the paper but no explanation is made about it. Puhui is in 48 different place in the paper. The first place is at line 105. You should explain it. You should state the importance of it.

Response 2: Thanks for your valuable suggestion. We have revised the content in the first paragraph (line 39-43) as follows:

In China, it is the vital goal to universalize puhui ECE, which refers to deliver affordable, accessible, and accountable ECE services for all needy families [7]. Puhui (普惠) is a two-character word in Chinese: as stated by Cambridge Dictionary[8], pu (普) means “universally” and “generally” involving or relating to most or all people; hui (惠) means “beneficial”, “favorable”, and “kind” and refers to something good, helpful and affordable.

 

Point 8: "...This paper uses evolutionary game theory to analyze the effect of the increasing sub sidies..." Which game theory? Which model? Stating game theory is too general. Which game theoretic literature is used or referenced? These are not clear. The methodology raises serious concerns.
Response 8: Thank you for your concerns about the methodology. The explanation are as follows: Based on Darwin’s theory, evolutionary game theory is applied to analyze the behavioral strategies of relevant parties with bonded rationality, limited information and conflict of interests through the dynamic evolutionary process. This paper constructs a three-party payoff matrix of puhui kindergarten, local government and central government, which are presented in the game payoff matrix (Table 1). According to the hypotheses and the pay-off matrix, we establish the replicator dynamics equations of puhui kindergarten, local government and central government. Replicator dynamics equations can describe the evolution of each party’ strategy over time. By using the evolutionary game theory and replicator dynamics equations, we analyze the dynamic evolution process of each party’s decision behavior to achieve the ideal stable equilibrium.

To state this more clearly, we have added the content in the methodology section (line 83-201) as follows:

Evolutionary game theory was first proposed in research of biological evolution process, based on Darwin’s theory [9]. Smith and Price (1973) have introduced the concept of evolutionary stable strategy (ESS) to describe a stable state of the game [10]. With deepening the research, Smith (1982) refined the concept of Nash equilibrium (Nash 1953) [11]. The relationship between evolutionary equilibrium and replicator dynamics was discovered by Taylor and Jonker (1978) [12]. The replicator dynamics is the dynamic adjustment mechanism of the evolutionary game [13], and can describe the evolutionary change over time to achieve the final stable equilibrium state [14]. Thus evolutionary game theory combines game theoretic analysis with dynamic evolution [15]. In evolutionary game theory, the basic assumption of agents’ bonded rationality is used instead of complete rationality, which expanded the classic game theory. As a dynamic system, the evolutionary game model is created involving relevant parties with bonded rationality, limited information and conflict of interests. And theoretically, the dynamic process of participants’ decision-making is described by constantly adjusting and optimizing their own strategy for ESS. To model the evolution process dynamically and flexibly can more authentically reflect the diversity and complexity of reality. Therefore, evolutionary game theory is a useful tool for discussing strategic interaction to create a stable solution among decision-making subjects [16].

Also, we have revised the following content at line 231, and line 264-266:

2.1 Model Construction

Based on the above model hypotheses, this paper constructs a three-party payoff matrix of puhui kindergarten, local government and central government, as shown in Table 1.

 

Point 9:  No equation numbers are given.

Response 9: Thanks for your so detailed suggestion. We have revised it directly on page 6-8.

 

Point 10: The objective functions are not clear.

Response 10: Thank you for pointing this out. Replicator dynamics equations are the objective functions. To make it clearly, we have revised the following contents at line 89-91, and line 270–273:

The replicator dynamics is the dynamic adjustment mechanism of the evolutionary game [13], and can describe the evolutionary change over time to achieve the final stable equilibrium state [14].

2.2 Model Analysis

Replicator dynamics equations describes the evolution of each party’s strategy over time in the three-dimensional dynamic system. According to the above hypotheses and the pay-off matrix, the replicator dynamics equations of puhui kindergarten, local government and central government are established.

 

Point 11: The game theoretic approach follows simulation analysis. However, in my opinion, such a methodology is not enough and it should be supported with real data and econometric models in the methodology to derive conclusions and to check if the results are in line with those obtained from the simulation.
Response 11: Thanks for your insightful suggestions. You pointed out an interesting research topic for our future work. Existing literature with both qualitative and quantitative analyses proposed policy recommendations on the promotion of quality and equity for the development of ECE [17] [18], some suggested to adjust the way of financial incentive while increasing the investment [19], some proposed to strengthen regulation and supervision [20] [21]. However, these studies cannot discuss further and examine whether these policy recommendations are efficacious or not. As all levels of governments, kindergartens, families with children pursue different benefits in the development process of ECE, this process can be regarded as the process of “change-adjustment-convergence” of behavioral decisions in multi-agent game [22] [23]. Thus the policy effect can be studied theoretically and predicted through analyzing the behavioral strategies’ interaction in the dynamic process by using evolutionary game theory. And the numerical simulation can verify the evolutionary process. To use the method of evolutionary game model and numerical simulation, the paper investigates whether the sustainable policy support of governments can efficaciously promote the quality and equity. Of course, the methodology has the limitation in analytical precision, in companion with econometric model supported by real data. 

However, the high-quality ECE is still scare resource, which causes inequity and hinders the sustainable development of ECE in undeveloped rural areas of China, although the gap between urban and rural areas in enrollment opportunity of ECE has been remarkably narrowed with preferential policy and financial investment. At present, the issues of low-quality and inequity in rural ECE haven't been solved yet, so it is impossible to observe whether the sustainable support policy can improve the ECE quality, and collect real data to examine the simulation results. In future work, based on the study, we could design and conduct a field experiment in some undeveloped rural areas of China where the sustainable policy support could be implemented well. Through field investigation and econometric analysis, the real data would be collected, and the study results would be checked. We have added this as the prospect for future research in the revised paper.

   

Point 12: In conclusion, I suggest no references within. These should be in the discussion section.

Response 12: Thanks for your suggestion. We have revised the following content in the discussion section (line 555-567):

Under the reward-punishment mechanism, the central government’s reward incentive is great enough to urge local governments’ active support and strict regulation. And punishment measures by the central governments can alter local governments’ inactive strategy. With different variables interaction in the evolutionary system, each party chooses among alternative strategies whose payoff depends on the choices of others [16], and seek optimization till no party can improve its payoff by following strategies other than ESS [24]. There evolves to ideal equilibrium state in which there is win-win situation and mutual benefits are achieved. Ultimately, puhui kindergartens can improve the quality, local governments and central government can actively promote quality and equity by incorporating strictly regulation and supervision into sustainable policy support for rural ECE. The simulation results confirm that the governments have a dominant role in promoting quality and equity of ECE in China, consistent with the consensus of major countries and regions in the world [25].

 

Point 13: For a paper that focuses on the role of education and on the relation between sustainability, economic development and human capital, the paper should also be based on economic development literature on human capital and economic development. The paper fails to possess these and I suggest augmenting the paper with this respect in the intro, in the literature and in the discussion sections.
Response 13: Thank you for pointing this out. We apologize if the focus of the paper is not clearly stated. We hope that it is now clear that the study focuses on discussing the efficacy of ECE policy portfolio of preferential input, regulation, supervision and quality evaluation to improve quality and equity in undeveloped rural areas by adding the following sentences at line 146- 155:

There are high-quality resources scarcity in undeveloped rural areas, which hinders the equitable and sustainable development of ECE. Can the sustainable government support efficaciously enlarge and efficiently allocate the limited educational resources to promote the quality and equity? Can the governments’ regulation and supervision on ECE effectively improves the service quality? To explore the above issues, the study develops a tripartite evolutionary game model of ECE providers in undeveloped rural areas, local governments and central government, and correlates governments financial support with the regulation and supervision in ECE as strategy combination via reward-punishment mechanism.

Additionally, with regard to your suggestion of “augment literature in human capital and economic development in the intro, the discussion section”, we added the following contents at line 61-63, and line 543-546:

The government's financial input capacity, which is closely related to the regional economic development, has a direct effect on the quantity and quality of educational resource supply [26].

Meanwhile，teachers’ professional abilities are the key factor affecting the process quality of ECE [27]. The results showed that local governments’ input in human resources can effectively improve the quality of rural ECE, which provide strong support the research recommendations on the localization of rural teachers’ training [28].

Also, the relation between sustainability, economic development and education can be considered as future prospect of research, we added the following content in the last paragraph:

The development of regional economy has direct and indirect impact on local governments’ fiscal budget, the sustainability and stability of financial investment to ECE. Thus, these influencing factors, could be considered into analytical framework in future research.

 

References:

1. Ministry of Education of the People’s Republic of China website, Available online:

http://www.moe.gov.cn/fbh/live/2022/54405/mtbd/202204/t20220426_622063.html

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Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Dear Authors, I went over the paper and your response letter. I see that each critique is well addressed. Thank you. Congrats.