Evolutionary Game Analysis on Behavioral Strategies of Multiple Stakeholders in Inclusive Green Growth

The for stakeholders to IGG are analyzed. The local government should play a leading role in promoting IGG, and the decrease of the economy in the assessment on local government Abstract: Inclusive green growth has been set as an important initiative to solve the severe problems of 28 environmental degradation and severe income inequality. It requires the joint participation of local 29 government, enterprise and public. However, these stakeholders are not enthusiasm enough as there 30 are divergences among their interest goals. Hence, this paper analyses how to balance the 31 stakeholders’ interest goals based on the central supervision and local regulation in environmental 32 protection and income inequity alleviation. Therefore, an evolutionary game model between central 33 and local government, and an evolutionary game model among local government and enterprise and 34 public are conducted. The conclusions are drawn as follows: (1) The local government should play 35 a leading role in promoting IGG, public monitoring cost will hinder both enterprise and public’s participation. Finally, some recommendations are put forward.


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As an important initiative to solve severe problems faced by China of environmental degradation 17 and severe income inequality, IGG needs coordination among stakeholders of central government, 18 local government, enterprise and public. 19 However, the divergence among stakeholders' interest goals hindered them to positively promote 20 IGG.

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To understand and balance their interest goals, evolutionary game models were established to 22 analyze and simulate the central supervision and local regulation. 23 The conditions for all stakeholders to positively promote IGG are analyzed. 24 The local government should play a leading role in promoting IGG, and the decrease of the economy 25 proportion in the assessment on local government will significantly promote its enthusiasm. 26 Abstract: 27 Inclusive green growth has been set as an important initiative to solve the severe problems of 28 environmental degradation and severe income inequality. It requires the joint participation of local 29 government, enterprise and public. However, these stakeholders are not enthusiasm enough as there 30 are divergences among their interest goals. Hence, this paper analyses how to balance the 31 stakeholders' interest goals based on the central supervision and local regulation in environmental 32 protection and income inequity alleviation. Therefore, an evolutionary game model between central 33 and local government, and an evolutionary game model among local government and enterprise and 34 public are conducted. The conclusions are drawn as follows: (1) The local government should play 35 a leading role in promoting IGG, and the decrease of the economy proportion in the assessment on 36 local government will significantly promote its enthusiasm; (2) When the penalty on enterprise 37 increase, both enterprise and the public will choose positive participate behavior faster; (3) The high 38

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Environmental degradation and severe income inequality have become main challenges due to the 44 rapid economic pattern in China. These challenges have brought enormous pressures to the society 45 and restricted the further growth of economy (Liu and Lin, 2019). Currently, the pollution emission 46 in China still seems to be increasing, and the income gap is widening (Dai and Li, 2021). China's 47 carbon emission kept increasing, and the income of the top 10% has accounted for 40% social wealth 48 in 2017 (Hanewald, Jia, and Liu, 2021). Therefore, there is an urgent need to achieve an effective 49 economic transformation to improve environmental quality and alleviate income inequality (Pan et 50 al., 2019; Sun, Ding, Yang, Yang, and Du, 2020a). 51 Inclusive green growth (IGG) provides a key theoretical guidance for this economic transformation. 52 As the pathway to achieve sustainable development (World Bank, 2012), IGG is viewed as an 53 economic growth which improves the welfare of current and future generation (Albagoury, 2016). 54 It includes economic growth, income equity, energy conservation and emission reduction (Sun,Ding,55 Yang, Yang, and Du, 2020b). Inclusive green growth has been set as an important goal for further 56 economic transition in China's 12 th Five-Year Plan. 57 To achieve IGG, Chinese central government has made great effort to promote the participation of 58 stakeholders including local government, enterprise and public: Environment protection and income 59 inequality reduction are incorporated in local government assessment system; Enterprises are 60 encouraged to develop industries promoting green and income inequality alleviation; Besides, the 61 public is encouraged to promote a green lifestyle and purchase green and income equality products. 62 It is noteworthy that, despite repeated central government pledges to promote IGG, there are still 63 unenthusiastic stakeholders unwilling to positively participate in IGG. For example, in 2018, 27 64 local governments were criticized by central government for inadequate environmental governance, 65 and 8 were criticized for inadequate poverty reduction; Less than 40% of listed companies disclosed 66 poverty reduction information, and only 24.5% of listed companies disclosed environmental 67 protection information in 2017; Due to the public's low willingness to buy green products, the sales 68 of green foods in 2019 decreased by 15% compared to 2014. Therefore, improving the enthusiasm 69 of the above stakeholders to participate has become the key to promote IGG. 70 However, there are divergence of interest goals hinders their positive participation. Firstly, there are 71 divergence of interest goals between the central and local government. In the central supervision on 72 local government, the central government aims at the economic output, environmental quality, and 73 income equality, and these are also the key indicators for central government to assess local 74 government. While the local governments may tend to maximize the economic output, and 75 improving environmental quality and income equality is usually ignored (Zhang, Xue, and Zhou, 76 2019). Therefore, how to balance their interest goals by adjusting the assessment for local 77 government plays an important role on promoting the positive participation of local government 78 (Sheng, Zhou, and Zhu, 2020). 79 Secondly, in the local regulation on enterprise and public, the local government regulates the 80 enterprise to transit into environmental protection and income inequity alleviation, and public to 81 develop a green and income inequity alleviation lifestyle, including purchasing green products. 82 However, as the enterprises may aim at improving their economic benefits, they tend to negatively 83 transit because of the transition may cause financial losses to them (Du, Feng, Lu, Kong, and Yang, 84 2020) (Song, Zhao, and Zeng, 2017). Besides, the public aims at maximizing utility, they may be 85 less motivated in environmental protection and income inequity alleviation if the lifestyle change 86 has brought them excessive financial burden (Cui, Wang, and Wang, 2020). Thus, to promote the 87 participation of enterprise and public, their interest goals should be balanced by local government's 88 regulation (Sun, Wan, Zhang, and Zhou, 2019). 89 As a consequence, the inconsistent interest goals among these stakeholders have become key 90 practice barriers that hinder their positive participation in IGG in China. Thus, this paper simulates 91 the supervision on local government and the regulation on enterprise and public based on the IGG 92 strategies, and analyzes how to promote these stakeholders to positively participate in IGG based 93 on their interest goals. The main contributions of this study are as follows: (1) Based on the 94 connotation of IGG, the central supervision and the local regulation are analyzed by evolutionary 95 game models of central and local government, local government and enterprise and public, then we 96 investigate the conditions for them to positively participate.
(2) With numerical simulations, the 97 dynamic evolutionary directions are discussed.

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The structure of this paper is as follows: Section 2 introduces the literature on IGG, central 99 supervision and local regulation, applications of evolutionary game theory and presents the main 100 contributions. Section 3 describes the model of evolutionary game in IGG and the basic assumptions 101 in details. Section 4 presents the simulation results and illustrates the influencing factors. Then based 102 on the results, the conclusions and limitations are given in Section 5. 103

Literature review 104
The previous studies related to this paper mainly demonstrated the connotation, influencing factors 105 of inclusive green growth and the application of evolutionary game theory. 106 2.1 Researches on inclusive green growth 107 2.1.1 Connotation of inclusive green growth 108 A large number of economic development models were proposed to address the ecological and 109 environmental problems faced by society. Based on the researches on green growth and inclusive 110 growth continues, inclusive green growth was proposed, though the definition and feature of 111 inclusive green growth still remain unsolved.

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The United Nations Economic and Social Commission for Asia and the Pacific (UNESCAP) 113 explained the connotation of green growth, believing that "green growth is an environmental 114 sustainable economic process adopted to promote low-carbon development and benefit all members Distelkamp, 2012) defined green growth as an environmental policy strategy that aims at an absolute 118 decoupling between economic growth and resource consumption. (Reilly, 2012) argued that green 119 growth should cover economic growth, reducing environmental impact and job creations. 120 With continuous attention to issues as poverty and equity, inclusive growth has gradually attracted 121 attention. The World Bank suggested that an inclusive system should be established to provide a 122 wide range of opportunities, without separating growth from equity policies. World Bank (World 123 Bank, 2006) analyzed the issue of inclusive growth in Andhra Pradesh, and pointed out that inclusive 124 growth mainly includes agricultural growth, job creation, poverty reduction, and the alleviation of 125 social and regional inequality. (Dev S M, 2007) summarized inclusive growth into three concepts: 126 sustainable and responsible business, social progress and human well-being, and excellent 127 governance. 128 As shown in the above, though both based on the sustainability of economic growth, green growth 129 focuses more on resources and environment, while inclusive growth focuses more on social fairness. 130 The economy is suggested to be rapid, green and inclusive, and support the poverty for survival and 131 development. (Coughlan S, Lehmann F, and Lehmann J P, 2009) argued that there exists the balance 132 between social benefits and environmental costs, as well as the welfare among generations. (Dhingra 133 R M, 2015) concluded that inclusive green growth is an economic mode with equal opportunities, 134 which is conducive to the access to opportunities, capabilities and security. 135 2.1.2 The implement paths of inclusive green growth 136 The existing researches on inclusive green growth promotion mostly focus on influencing factors.

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(Ojha, Pohit, and Ghosh, 2020) employed a recursively dynamic India-specific CGE model, 138 analyzed how to get the balance among greening, growth and inclusiveness. programs, and found that adopting the rewarding strategy is more efficient than penalizing strategy 161 and combination strategy of penalizing and rewarding. 162 2.2.2 The local government regulation on enterprise and public 163 The existing research mainly focus on how to promote the efficiency of local government regulation.

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(Yao, Zhang, and Guo, 2020) built a two-tier stochastic frontier analysis model to evaluate the 165 impact of local government and enterprises on actual carbon dioxide emissions reduction, and the 166 results showed that the local governments have a greater influence in carbon dioxide reduction than 167 enterprises, therefore it is of great importance to enhance the participation of enterprises. found that the elimination of unqualified small enterprises has improved the profitability of heavily 172 polluting enterprises. However, there are also literatures analyzed the impact of government 173 regulation on enterprises' productivity, and the results proved that the "win-win" goal between 174 economic output and environmental quality has not been achieved under severe sanctions (Cai and 175 Ye, 2020; Tang, Liu, and Wu, 2020). 176 There are also literatures emphasized the importance of public's participation on government 177 regulation. (Wang, Chu, and Gu, 2021) utilized a spatial durbin model is used to investigate the 178 impact of public attention on wastewater treatment, and the results show that public attention will 179 help improve wastewater treatment by promoting government to enact laws and regulations. applied an evolutionary game model focusing on the consumers and enterprises' strategies in energy 187 transition, and found that the government incentives may not promote consumer's participation, and 188 the enterprises will choose to transit only when the consumers' participation will bring market 189 prospects and a good social reputation. and the results showed that the brand benefits and the economic benefits from consumers' green 208 product consumption are the main factors affecting the GTI system. 209 2.4 Summary 210 In summary, the importance of local government, enterprise and public's participation to central 211 supervision and local regulation was emphasized in the literature, while there are few research gaps: 212 Firstly, the existing research about IGG has studied the characteristic of IGG and its driving factors, 213 while few studies analyzed how to promote the stakeholders' participation in IGG. Secondly, in the 214 existing research about central supervision and local regulation, most of the literatures focused on 215 the regulation on environmental protection, and ignored the regulation on income inequity 216 alleviation. Besides, the impact of local regulation on enterprises' participation remains unclear. 217 Thirdly, the role of public is mainly set as consumer, few studies considered its role as a monitor. 218 Thus, to analyze the central supervision and local regulation in environmental protection and income 219 inequity alleviation, this paper constructs a central and local and a local government and enterprise 220 and public evolutionary game model, to explore how to promote these stakeholders to positively 221 participate in IGG. 222

The formulation of model and method 223
This research employs evolutionary game model to analyze the interest conflicts among 224 stakeholders. The evolutionary game theory was first applied to the analysis of game behavior 225 among animals (Smith, 1974 The stakeholders' game strategies are as follows: 231 The central government, supervises and assesses the local government from the economic output, The local government is also an important regulator in inclusive green growth, its strategies 240 including positive regulation (PR) and negative regulation (NR). Positive regulation means that the 241 local government strictly promotes the inclusive green behavior of the enterprise and public, 242 severely cracks down on the enterprise's negative behaviors, therefore it may promote enterprises 243 and the public to implement inclusive green behaviors. The economic output may be hindered when 244 promoting the environmental quality and income inequity reduction. Negative regulation means that 245 the government does not supervise any behavior of enterprise. If the probability of local government 246 choosing positive regulate is x, then 1-x is the probability of choosing negative regulate. 247 The enterprise is another important stakeholder in inclusive green growth, has two kinds of game 248 strategies, which are positive implementation (PI) and negative implementation (NI). Positive 249 implementation represents that enterprise produces green, income inequity alleviation products and 250 increase social security expenditure. Positive implementation may significantly improve the 251 environmental quality and reduce the income gap. Although positive implementation behavior 252 promotes the environmental protection and income inequity reduction, it also brings cost burden to 253 the enterprises. Negative implementation represents that enterprise produces regular products and 254 the public gets less social security. Hence, subsidies for positive implementation are needed to 255 compensate enterprises. If the probability of the enterprise choosing positive implement is y, then 256 1-y is the probability of choosing negative implement. 257 The public's behavioral strategies support the development of inclusive green growth. Public can 258 choose participation behavior (PB) and non-participation behavior (NB). The positive participation 259 behavior indicates that the public monitors the inclusive green effort of enterprise and local 260 government, and also buys green and income inequity alleviation products. The non-participation 261 behavior indicates the public buys regular products without monitoring. If the probability of the 262 public choosing participation behavior is z, then 1-z is the probability of choosing non-participation 263 behavior.

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The interactions among the stakeholders are shown in Fig 1.  (2) The parameters related to enterprise 283 The regulation cost and benefit of enterprise's positive implementation is denoted by CE and BE, 284 such as insurance paid to employees and the public franchise, thus, the public gets benefit as EP. 285 The local government and enterprise loss a social reputation N when enterprise chooses negative 286 strategy. RE is the improvement of the enterprise's credibility when the public positively participates. 287 The penalty for negative behavior of enterprise is denoted by FE. The price and sales volume of 288 products under enterprise' inclusive behavior and traditional behavior are expressed as Pi, Qi, PN 289 and QN.

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(3) The parameters related to public 291 As the implementer and monitor of inclusive green behavior, the public pays participation cost CP 292 and monitor cost CS. 293 Based on the above assumptions, under different choices of behavioral strategies, the payoff matrix 294 is shown as in Table 1 and Table 2. 295 296 Table 1 The  3.3 Stability analysis of central government and local government model 302 As shown in Table 1, the expected revenues of the governments choosing positive and negative 303 strategies can be calculated respectively. 304 The expected revenues of the central government choosing positive strategy E11 and positive 305 strategy E12: 306 The expected revenues of the local government choosing positive strategy E21 and positive strategy 309 E22: 310 Then the replicator dynamic equation of the governments' strategies as follows: 313 Let F(w)=0, F(x)=0, we can obtain 4 pure strategy solutions, which are (0,0), (0,1),(1,0) and (1,1).

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{(w, x)|0≤w≤1;0≤x≤1}. 317 To further investigate the dynamic equilibrium point of the system, stability analysis of four 318 equilibrium points is made. When x= According to the above analysis, when the supervision cost reduces and penalty for local 329 governments increases, the central government is encouraged to positive supervise. By enhancing 330 the importance of inclusive and green degree in the assessment and increasing the penalty, x can 331 move toward 1. 332 Thus, the Jacobian matrix J1 is obtained from the first partial derivative of the replicator dynamic 333 equations. 334 As shown in Table 3 if the central government lacks enough penalty on negative local government, and emphasis on 341 economy output in assessment, the governments would both choose the strategy of "negative 342 supervision". 343 There is second equilibrium point (0, 1) when RL*(γg+γi) >LL*γe+CL. As can been seen that increase 344 the proportion of inclusiveness and green degree in assessment, central government will choose 345 negative strategy while local government will positive regulate.

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If CC-FL<0, CL-FL+LL*γe-RL*(γg+γi)>0, there is the last equilibrium point (1, 0). In this equilibrium 347 point, the penalty on local government gives central government an incentive to positively supervise, 348 but cannot promote the local government to positively regulate. 349 350 Table 3 Equilibrium Points between the governments 351 Equilibrium Points det J1 and tr J1 Condition The (1 z)(1 x)(P Q N) The expected revenues of public choosing participate behavior and non-participate behavior 364 strategies, denoted by E51, E52: 365 Thus, the replicator dynamic equation of the government, enterprise and public can be set as follows: 368 , there are F'(z)| z=1 >0 and F'(z)| z=0 <0 , so z=0 is the evolution 387 equilibrium point, and the public's strategic choice is not to participate. 388 From the above analysis, as the penalty on enterprise decreases and subsidies to the public increase, 389 when the enterprise begins to positive implement and the public starts to choose non-participate 390 behavior, the government will choose negative regulate. The increasing penalties and product 391 revenue under inclusive green effort will promote enterprise to positive implement. Meanwhile, the 392 increase of government subsidies and traditional product price and the decrease of product price 393 under inclusive green effort will promote public to participate. 394 Let F(x)=0, F(y)=0, F(z)=0, we can obtain 8 pure strategy solutions of the three dimensional 395 dynamic system, which are (0, 0, 0), (0, 1, 0), (0, 0, 1), (0, 1, 1), (1, 0, 0), (1, 0, 1), (1, 1, 0), (1, 1, 396 1), respectively. These eight equilibrium points constitute the boundary of the solutions of the 397 tripartite evolutionary game, which is {(x, y, z)|0≤x≤1;0≤y≤1;0≤z≤1}. In addition, there 398 exists a mixed strategy solution (x * , y * , z * ).

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To summarize this section, the stability of all the equilibrium points in three-dimensional dynamic 400 system are analyzed, and their stability are judged by Lyapunov's method. The system realizes ESS 401 requests all the eigenvalues of Jacobian matrix have negative real parts . 402 After calculation, mixed strategy can be proved not an ESS because that its eigenvalues 404 simultaneous have negative real parts cannot be guaranteed. Thus, the eight equilibrium points (pure 405 strategy solutions) are taken into Jacobian matrix, and the eigenvalues of each equilibrium point are 406 obtained sequentially, only (0, 0, 1) and (1, 1, 0) are instability points, then the conditions of possible 407 equilibrium points are judged as shown in Table 4. 408 409 Table 4 The Limited by length, we cannot analyze all the local stabilities of each equilibrium point. According 412 to the characteristics of regional development, this paper selects ESS in the typical stage of inclusive 413 green growth as can be seen in Table 5. 414 415 Table 5 The three stages of inclusive green growth the traditional product revenue is between the benefits of enterprise and public's positive behaviors. 420 Therefore, the central government positively strengthens the supervision over the local government, 421 while the local government, enterprise and public choose negative participate behaviors. Thus, this 422 stage corresponds to the ESS (1, 0) and (0, 0, 0). As can be seen from the Table 3, Table 4, in the 423 initial stage of IGG, four inequalities should be met to realize optimal ESS (1, 0) and (0, 0, 0). 424 In the middle stage of IGG, the benefits of local government's positive regulation are higher than 425 the cost of its positive regulation, and the product revenue under inclusive green effort is between 426 the enterprise's negative implementation cost and public's positive participation benefits. Therefore, 427 as the proportion of environmental protection and income inequity reduction in the assessment 428 increase, and the product revenue under inclusive green effort decreases, the local government, 429 enterprise and public will begin to choose positive behaviors. This stage corresponds to the ESS (0, 430 1) and (1, 1, 1). 431 As in the mature stage, the penalty on local government is lower than central government's positive 432 supervision cost, and the subsidies to the public are between the cost of public's positive 433 participation and local government's positive regulation. In this stage, the governments will slowly 434 withdraw from IGG, and the enterprise and public will take the initiative to implement positive 435 behavior without governments' supervision, resulting in the ESS (0, 0) and (0, 1, 1). 436

Numerical simulation 437
In China, the central government is appealing the stakeholders to positively participate to promote 438 the economy booming, improve environmental quality and reduce income inequality. In order to 439 intuitively describe the dynamic evolution of stakeholders in the inclusive green growth, numerical 440 simulations are introduced to the above optimal evolutionary stability strategy in the typical stages.

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On the basis of the situation in China, the Sections 4.1, 4.2 analyze the strategic behaviors of the 442 stakeholders, and clarify the impact of parameters on their strategic behaviors. To clarify the impact of variables on stakeholders' strategic behaviors, we introduce the numerical 445 simulation to analyze the dynamic process for the evolutionary systems. We set the strategy 446 probabilities of all stakeholders as 0.5. Then take the initial stage as an example, the parameters are 447 set as follows: CC=5, RL=20, FL=20, LL=15, CL=30, γi=0. The ESS of each stage in IGG is as shown in the Fig 2.1 and Fig 2.2. In the initial stage, the local 451 government, and enterprise reach the equilibrium point fast, while the central government slowly 452 chooses the positive supervise behavior. In the middle stage, the governments and enterprise reach 453 the equilibrium point early, though the public chooses the positive participate behavior in the last. 454 As can be seen, in the mature stage, the central government and public take a longer time to choose 455 negative supervision and positive participate behavior. 456 Therefore, the local government reaches the equilibrium at the quickest speed in both models, and 457 the evolutionary speed of public is slowest. Hence, the local government should play a leading role 458 in promoting IGG. 459 460 In order to further analyze the impacts of main parameters' changes on the strategic behaviors of 468 the stakeholders, sensitivity analysis is performed through numerical simulations. Thus, as shown 469 in Fig 3.1 and Fig 3.2, the numerical simulations for the penalty on local government FL, economy 470 proportion in assessment γe, product price under inclusive green effort Pi, penalty on enterprise FE, 471 public's monitoring cost CS, respectively. 472 473 15, and 20, and γe are set as 0.3, 0.6, and 0.9. The decrease of FL will result in a dual decreases of 477 both x and w, while x decreases faster. This indicates that as the penalty on local government 478 decreases, the central government and local government's enthusiasm will both be reduced, and 479 local government is more sensitive to this decrease. Besides, when γe decreases, w quickly stabilizes 480 at 1, and x takes a longer time to reach 0. Thus, the decrease of the economic proportion in the 481 assessment will significantly promote central and local governments' willingness to participate, and 482 it has a greater impact on local government. In conclusion, the penalty on local government and the 483 economy proportion in assessment both have a positive impact on promoting central and local 484 government to participate in IGG, and local government is more sensitive to the changes of these 485 parameters.

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The sensitivity analysis in local government and enterprise and public model is as can be seen in 487 Fig 3.2. As for product price of from enterprises' inclusive green effort, the values of Pi are set as 4, 488 5 and 6. FE are set as 26, 29, 32, and CS are set as 20, 25 and 30. When Pi increases, y takes a longer 489 time to reach equilibrium point 0, while z reaches faster and its equilibrium point has changed from 490 1 to 0. The increase of FE shortens time for y and z to reach equilibrium point, and x gradually 491 stabilized at 1. As CS increases, it can be found that y finally stabilizes at 0. In summary, the results 492 show that the increasing product price under inclusive green effort will promote the enterprise's 493 enthusiasm for positively implement in IGG, but also hinders the public's participation willingness. 494 The increase of penalty on enterprise will promote both enterprise and public to positively 495 participate, while the increase of public monitoring cost hinders them both. Meanwhile, all these 496 three parameters have little impact on local government's strategies. The achievement of IGG has a great significance for China's further sustainable development. In 503 order to improve IGG degree and enhance the stakeholders' enthusiasm to participate, this paper 504 established an evolutionary game model between central and local government and a model among 505 local government and enterprise and public, and analyzed how to promote the stakeholders' 506 participations under central supervision and local regulation in IGG. Numerical simulations were 507 conducted to investigate the impacts of relevant parameters on the stakeholders' strategic behaviors. 508 These findings can help policy-makers in China to improve their guide planning, and the model may 509 also be replicated in other developing countries to obtain IGG by promoting economic growth, 510 environmental protection and income inequity reduction. After analysis, the following conclusions 511 are drawn: 512 (1) In the initial stage, the proportion of economic output in the assessment, should be reduced to 513 promote the local government to positively regulate, and the product revenue under enterprises' 514 positive inclusive green effort and the cost for the public to participate should be reduced to promote 515 enterprise and public to positively participate in IGG. What's more, the product revenue under 516 inclusive green effort should be kept between the cost of enterprise's positive implementation and 517 the benefits of the public's positive participation. 518 In the middle stage, the subsidies for the public should be kept between the cost of public and local 519 government to transit to the mature stage. 520 In the mature stage, the governments gradually relax the supervision and regulation, the enterprise 521 and the public become the main force for IGG.

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(2) Among the stakeholders, the local government reaches equilibrium at a fastest speed, and the 523 public is the latest to reach equilibrium point, therefore local government should play a leading role. 524 In the central and local game model, increasing the penalty on local government and decreasing 525 economic proportion in assessment have a greater impact on promoting local government's 526 regulation. In the local and enterprise and public game model, when the product price under 527 enterprises' inclusive green effort increases, the enthusiasm of enterprise increases, while the 528 enthusiasm of deceases. The increase of penalty on enterprise will improve the enterprise and 529 public's willingness to participate, though the increase of public's monitoring cost will reduce the 530 enterprise and public's willingness. 531 5.2 Policy implications 532 Based on the above analysis suggested, some implications are put forward as follows: 533 As the major driving force in the initial stage, central government should further improve the 534 assessment on local government. It is crucial to strictly refine the local government's accountability 535 in environmental protection and income inequity reduction, and enhance the local government's 536 political benefits for environmental protection and income inequity reduction. Besides, fiscal 537 policies should be rational formulated to reduce local government's regulate cost, such as financial 538 subsidies and special funds for income inequity reduction and environmental protection. Meanwhile, 539 subsidies for technological innovation and inclusive green production should be set to promote 540 enterprises' enthusiasm. 541 Strictly supervision and official certification should be conducted to the enterprises' behavior on 542 environmental protection and income inequity reduction, to enhance their technological innovation 543 and social reputation. 544 The public should be particularly encouraged to participate in IGG. Public supervision platform, 545 subsidy mechanism and policy advocacy should be conducted via the Internet and public media, in 546 order to reduce their monitoring cost and public awareness on IGG. 547 In this paper, model analysis and numerical simulation were used to investigate IGG, the strategies