Evolutionary Game Analysis of Inter-provincial Diversified Ecological Compensation Collaborative Governance

The inter-provincial watershed diversified ecological compensation (DEC) collaborative governance mechanism is an important initiative to achieve long-term ecological compensation. However, it is difficult to effectively coordinate the promotion of environmental protection and livelihood improvement due to the different interests of local governments. Based on the interest demands among local governments, this study analyzes the operation mode of DEC mechanism, constructs an evolutionary game model of DEC collaborative governance among local governments, and conducts dynamic simulation analysis with Shaanxi and Henan provinces as examples. The results show that the upstream government quickly chooses to actively participate when the downstream government's willingness to promote is more significant than 0.4. Fund allocation ratios of 0.7, 0.2, and 0.1 for government, market, and social compensation better promote collaborative governance strategies. The low-level cost can drive the upstream and downstream governments to construct a DEC mechanism. In addition, the reward and punishment mechanism is more effective for the downstream government, and the benefit allocation ratio significantly impacts the upstream government. The greater the absorption capacity of the upstream government, the more it can drive to realize social benefits and collaboration. To promote the DEC mechanism through collaborative governance and provide new ideas for ecological protection and development of the Yellow River basin (YRB).


Introduction
In cross-basin water resource ecological protection, watershed ecological compensation mechanisms play a critical role in mitigating or solving ecological externalities as a strong incentive to balance the relationship between economic development and water quality protection in a watershed (Yu et al. 2020;Li et al. 2022). In China, ecological compensation based on government financial compensation has exposed the problem of marginal diminishing benefits of ecological and environmental management (Wang and Li 2015). While improving the technical level of water resource protection (Sepehri and Sarrafzadeh 2018), the government has begun to pay attention to diversified ecological compensation (DEC). For example, in the Xin'an River Basin, local governments promote the participation of compensation subjects in ecological compensation through multi-channel and diversified compensation fund allocation ratios based on the actual situation. However, the DEC mechanism faces a complex network of cooperation in the implementation process (Li and Peng 2021;Ren et al. 2021). In the Yellow River basin (YRB), due to different interest demands, local governments cannot coordinate industrial cooperation and talent exchange (Zhang 2022), and it is challenging to achieve collaborative governance in information communication and governance concepts. Therefore, the compensation mechanism stays at the agreement level.
Existing studies around DEC mainly focus on compensation funds Hao et al. 2021), compensation subjects (Zheng et al. 2019), compensation methods (Xue et al. 2020), and institutional guarantees (Liu et al. 2021a). Among them, the main focus around compensation methods is on the following two aspects. (1) In the evaluation of compensation methods, the study mainly used the synthetic control method, energy quantification method, and data envelopment analysis to systematically study the effectiveness and fairness of compensation methods from the perspectives of water pollution intensity (Hu et al. 2022), agricultural water rights trading (Lv et al. 2021), and compensation policy quantification (Dai et al. 2022).
(2) From the perspective of numerical models, a large number of studies have been conducted on the impact of ecological compensation methods on the compensation object around the dynamic distribution of compensation funds on stakeholders' demand (Lu et al. 2022), the impact of compensation methods on public green production behavior and livelihood assets (Yang and Zheng 2021;Liu et al. 2021b), and the motivation and change pattern of residents' ecological compensation willingness .
The above studies provide meaningful insights into implementing DEC methods, but there are still shortcomings. First, the existing studies only focus on the evaluation of benefits and their impacts, and the studies on how to implement the DEC method are limited and primarily case studies Sun et al. 2020), lacking the exploration of the implementation mechanism of DEC. Second, local governments have different interest demands, and previous studies have focused only on a single ecological compensation benefit, ignoring the differences in the interest demands of upstream and downstream governments, and have not considered the impact of DEC on the development of the endogenous capacity of upstream governments. The upstream government, whose right to development is restricted due to ecological protection, has an endogenous capacity mainly for social benefits, expecting to maximize social benefits based on resources, technology, and education provided by DEC methods, with active absorption as the path to improve the quality of life of the public (Peng 2020).
Around the mechanisms of social benefit enhancement, existing studies suggest that absorptive capacity can effectively enhance organizational performance and facilitate the conversion of inputs into benefits. The specific mechanism is to identify relevant information and opportunities by absorbing external information and knowledge (Emiliano de Souza et al. 2022). Second, through the relational network of members within the organization, the transfer of internal knowledge is realized to promote the integration and utilization of knowledge (Backmann et al. 2015), which in turn leads to the enhancement of benefits. In response to the dual objectives of environmental protection and livelihood improvement (Ju et al. 2022), absorptive capacity is applied to studying DEC. Thus, the absorptive capacity of upstream governments can be expressed as the ability to acquire external knowledge about social development, such as education, employment, and technology, from DEC methods and then apply them to social benefit enhancement.
To sum up, this study aims to fill the above gaps and promote stable cooperation between upstream and downstream governments. The contributions of this study are as follows: (1) A DEC operation mechanism is constructed from the core elements of the consultation mechanism.
(2) Based on the perspective of collaborative governance, this study constructs an evolutionary game model for the collaborative governance of DEC. This study provides a new idea for implementing an ecological compensation mechanism in the YRB from the micro mechanism level. (3) The absorptive capacity theory is introduced to analyze the influencing factors of establishing the DEC cooperative governance mechanism based on the demands of stakeholders. The systematic analysis accords with the goal of national ecological compensation in the new era and provides insights into the ecological compensation construction of the upper and lower reaches of the YRB. The rest of this study is structured as follows. Section 2 introduces the operation mechanism of DEC and constructs the evolutionary game model of collaborative governance. Section 3 carries out numerical simulations according to the actual situation of Shaanxi Province and Henan Province. Section 4 provides an analysis and discussion of the simulation results. Section 5 describes the main research conclusions of this study to promote the maximization of ecological compensation benefits.

Diversified Ecological Compensation Operation Mode
The watershed ecosystem serves a variety of economic, social, and environmental service functions in a water-bonded, stakeholder-centered ecosystem (Jia et al. 2021;Zhao 1995). DEC can be divided into government compensation based on financial compensation, inkind compensation, policy compensation, technology compensation, and education compensation, market compensation based on the trading of water rights, emission rights, carbon sinks, ecological labeling, and off-site development, and social compensation based on participation-based compensation for NGOs and environmental liability insurance (Zhang and Xu 2011). Due to the divergent interests of local governments, upstream and downstream governments in the practice of DEC need to create consultation mechanisms through cooperation to reshape the compensation model by the actual situation and create an open DEC system.
Given that China's DEC method is at a preliminary stage, the central government, as the maker of ecological compensation policies, needs to actively build a consultation platform to integrate ecological compensation information resources effectively. The downstream government, as the implementer, needs to provide ecological compensation funds and support to the upstream government. As the organizer, the upstream government needs to create an ecologically sound environment and offer high-quality water to the downstream government (Tang et al. 2022). Second, based on the consultation, the upstream and downstream governments should use the platform as a channel to promote the consultation mechanism in accordance with the logic of supply and demand collaboration, rule collaboration, and benefit collaboration, dynamically assess the actual situation of ecological compensation, and continuously reshape the compensation model to maximize the sustainable interests of all parties with the ideal combination of government compensation, social compensation, and ecological compensation (Fig. 1).

Basic Assumptions
In this study, with a finite rational upstream government and a downstream government as the participating parties, environmental changes impact both parties' strategic choices. The game equilibrium is achieved through successive decisions, so the following hypotheses are formulated.
1. According to the difference of interest demands, the upstream government expects more economic and social benefits, and the downstream government expects better ecological benefits with the least financial compensation, and the sets of strategy choices are {active participation, negative participation} and {promote, no promote}, respectively. 2. Supply and Demands Collaboration. To solve the upstream development problem, the downstream government needs to pay t to the upstream government as guiding funds to promote upstream development and ecological protection. Based on the compensation types negotiated by both parties, the ratio of the amount allocated by the downstream government to the upstream government for the three compensation modes is 1 , 2 , 3 ( 1 + 2 + 3 = 1 ), respectively. However, when compensation funds are invested, there will be losses (Li et al. 2020), such as the cost of evaluation and demonstration for project assistance, the cost of defining property rights in market compensation, and the cost of publicity in social compensation, so the guidance funds effectively invested by the downstream government are 1 t 1 , 2 t 2 , 3 t 3 ( P = 1 t 1 + 2 t 2 + 3 t 3 ), respectively. 3. Rule Collaboration. When the upstream government actively participates in the strategy, the ecological protection cost is C 0 , and the guaranteed cost of multiple compensation agreements is C 1 . When the downstream government chooses to promote the strategy, it needs to pay the guaranteed cost of the agreement is C 2 . When the two sides collaborate in governance, the central government will give incentives A. When one side does not collaborate, it will be punished by the central government H. When the upstream government passively participates, the downstream government will receive subsidizes E. 4. Economic benefits Collaboration. Both sides collaborating in governance will generate economic benefits such as tax revenue and industrial restructuring is R 1 The economic benefits generated when the downstream is promoted, but the upstream is negatively involved is R 2 , and the economic benefits are shared according to the contribution i (i = 1, 2, 1 + 2 = 1). 5. Social benefits and ecological benefits Collaboration. For the convenience of calculation, assume that the absorptive capacity coefficient is I 1 when the upstream government actively participates. The absorptive capacity coefficient formed by the upstream government through free-riding when the downstream promotes is I 2 . The social benefits generated by the upstream government under different strategies can be expressed as I 1 P and I 2 P, and the ecological benefits added by the downstream government when the upstream government actively participates is W.

Model Construction
The probability of the upstream government participating actively is x, and the probability of negatively participating is 1-x. The probability of the downstream government choosing to promote is y, and the probability of not promoting is 1-y. The payoff matrix is shown in Table 1. The parameters of the evolutionary game and their meanings are shown in Table 2. The upstream government's expected return is F 11 or F 12 when it chooses the "active participation" or "negative participation" strategy, and the overall average expected return is F 1 , then we have.
From the above, the replication dynamic equation for the upstream government can be obtained as: The downstream government's expected return is N 11 or N 12 when it chooses the "promote" or "no promote" strategy, and the overall average expected return is N 1 , then we have.
From the above, the replication dynamic equation for the downstream government can be obtained as: Meaning of parameters x Probability of active participation of upstream government (0 ≤ x ≤ 1) y Probability of downstream government promotion (0 ≤ y ≤ 1) C 0 , C 1 Upstream government ecological protection and agreement protection cost I 1 , I 2 Absorptive capacity coefficient when the upstream government actively and negatively participate t Downstream government expenditure of ecological compensation guide funds 1 , 2 , 3 Three types of compensation model fund allocation ratio t 1 , t 2 , t 3 Three types of compensation models actually guide funds P = 1 t 1 + 2 t 2 + 3 t 3 Actual ecological compensation guide funds C 2 Downstream government agreement guarantee cost W Increased ecological benefits for downstream governments when the upstream government actively participate E Subsidies from the central government to the downstream government when the upstream government negatively participate R 1 , R 2 Economic benefits with and without collaboration 1 , 2 The proportion of economic benefits allocated to the upstream government and the downstream government A Rewards is given by the central government when both parties collaborate H Penalties is given by the central government when a party cooperates negatively

System Stability Analysis
By associating the replicated dynamic equations of the upstream and downstream governments and making F(x) = 0, F(y) = 0 , the five local equilibrium points of the upstream and downstream government evolutionary game system are E 1 (0, 0), E 2 (0, 1), . According to the stability judgment criterion of the Jacobi matrix (Friedman 1991), the stability analysis of the local equilibrium point of the system, the Jacobi matrix J is shown as follows. where, The corresponding trace is: The corresponding determinant is: The equilibrium points gradually converge to the local steady state of the system when and only when the five local equilibrium points of the system satisfy Det(J) > 0 , Tr(J) < 0 , which is an evolutionary stability strategy (ESS). The stability of the equilibrium points of the system in each case is shown in Table 3.
It can be seen from Table 3 that the stability of the system is affected by many parameters, and the situation of the system depends on the different values of each parameter.
1. When C 2 − 2 R 2 − E > 0 , the stabilization strategy of upstream and downstream governments will be constant (0,0). When the cost of promoting for the downstream government is greater than the economic benefits and government incentives reaped, the downstream government will choose not to promote, and the upstream government will choose to participate negatively. 2. When C 2 − 2 R 2 − E < 0 and 1 (R 1 − R 2 ) + B(I 1 − I 2 ) + A + H − C 0 − C 1 < 0 , (0,1) is a stabilization strategy. Downstream governments choose to promote when the cost to the downstream government is less than the sum of the economic benefits and incentives allocated. However, upstream governments choose to participate negatively when active participation's benefits are less than negative participation's.

When
(1,1) is a stable strategy. Upstream governments will choose to actively participate when the benefits of cooperation are higher than the benefits of non-cooperation. At the same time, downstream governments will choose to promote their strategy as long as the difference between the cost of advancement and the penalty is lower than the sum of the economic benefits reaped and the government's incentives.
In summary, considering the policy-driven and realistic situation of DEC in the YRB, the collaborative governance strategy is an effective way to ensure the maximum effectiveness of ecological compensation in the YRB. Therefore, to make it the only evolutionary stabilization strategy, the constraints need to satisfy the following conditions.

Realistic Background and Parameter Setting
In 2022, the document "Yellow River Basin Ecological and Environmental Protection Plan" provides an essential basis and action guide for ecological and environmental protection work in the YRB from the national level. Collaborative governance by local governments has become a significant trend, so this study simulates and analyzes the {active participation and promotion} situation with Matlab.
In the YRB, around the sudden water pollution events in inter-provincial watersheds, Henan Province has signed a joint prevention and control agreement with Shaanxi Province and is further supporting the orderly establishment of an inter-provincial DEC mechanism by guiding funds. It is crucial to explore how to achieve ecological and environmental management and coordinated regional development in Henan Province and Shaanxi Province through DEC mechanisms. Therefore, through the research of Henan Provincial Water Resources Department and literature analysis Fan et al. 2021), the numerical analysis parameters are set as follows:t 1 = 2.8 , Table 3 Evolutionary stability analysis of system equilibrium points

Analysis of the Influence of Initial Values on The Evolutionary Results
From Fig. 2a, it is clear that the system stabilizes in the equilibrium strategy regardless of how the initial probability varies within the interval. From Fig. 2b, it is shown that the higher the initial willingness of the upstream government, the faster the downstream government tends to stabilize. As seen in Fig. 2c, the higher the initial willingness of the downstream government, the faster the upstream government tends to stabilize. From the above figures, it can be seen that the upstream government quickly tends to stabilize when the initial willingness of the downstream government is higher than 0.4, and the initial willingness of the downstream government has a non-negligible influence on the strategy choice of the upstream government.

Dynamic Impact Analysis of the Proportion of Funds Allocated by Different Compensation Methods
To analyze the influence of the allocation ratio of government, market, and social compensation methods on the strategic choice of upstream governments, the allocation ratio mix of funds is adjusted. As seen in Fig. 3, the ratio of 0.7, 0.2, and 0.1 can encourage the upstream government to choose the active participation strategy more quickly. As shown by the above figure, when Henan province invests funds to guide the development of the Shaanxi provincial government at the present stage, the government compensation mode can better promote Shaanxi Province to get more economical and social benefits at a lower cost.

Analysis of the Dynamic Impact of Agreement Guarantee Costs
Under the constraints, the agreement guarantee cost is set to 0.5, 1, and 2. Figure 4 shows that the lower the cost, the faster the upstream and downstream government tend to stabilize. At the same time, the time for upstream governments to reach stability is 1.3, 1.6, and 1.7, respectively, and the time for downstream governments to reach stability is about 1. From the above data, it is clear that compared with downstream governments, upstream governments' strategy choice is directly affected by the change in the agreement guarantee cost. The higher the cost, the longer the time for upstream governments to choose an active participation strategy.

Analysis of the Dynamic Impact of Benefit Distribution
As can be seen from the simulation results in Fig. 5, the benefit distribution proportion of 0.5 and 0.5 is not the result of fast and stable upstream and downstream governments. For upstream governments, the higher the proportion of benefit distribution, the faster they choose the active participation strategy. For the downstream government, when the benefit distribution of the downstream government is high, the stabilization rate is faster. By   Fig. 3 Influence of different compensation distribution proportions on upstream governments comparing the upstream and downstream governments, we can see that the upstream government is more sensitive to the distribution proportion.

Analysis of the Dynamic Impact of the Absorption Capacity Coefficient
The simulation results in Fig. 6 show that the absorptive capacity coefficient is positively proportional to the convergence probability when the upstream government actively participates. The change of the absorptive capacity coefficient is inversely proportional to the convergence rate of the probability of stabilization when negatively participating. This result further confirms the conclusion of the previous analysis that the greater the absorptive capacity when actively participating, the greater the social benefits and the greater the willingness to collaborate in governance. The absorptive capacity at the time of negative participation represents the upstream government's ability to piggyback on the resources  Figure 7 shows that the higher the reward from the central government, the faster the rate of stabilization. The higher the reward or penalty, the faster the rate of choosing collaborative governance. Among them, under the same reward, the impact of reward change on the downstream government is more significant than that of the downstream government. Under the same punishment, the central government's punishment significantly impacts the downstream government. The results further indicate that downstream governments are more sensitive to the incentive and constraint mechanism. The central government should give better play to the incentive and constraint mechanism to promote collaborative governance.

Analysis of the Influence of Supply and Demand Collaboration on Collaborative Governance
Around the collaborative governance of DEC, the effective combination of local government's willingness and compensation mode should be used to promote the collaboration of supply and demand. From the simulation results in Figs. 2 and 3, the DEC mechanism should focus on the downstream government and the government compensation mode.
In the ecological protection of the YRB, Shaanxi Province, which is dominated by heavy industry, has significant ecological benefits. However, the input cost and benefit are not coordinated, and the opportunity cost of regional economic development is high. First of all, as a beneficiary of the ecological environment, Henan Province should take DEC mechanism as the core while carrying out government financial subsidies to take into account (a) Influence of absorptive capacity on upstream government when actively promoting (b) Influence of absorptive capacity on upstream government when negatively promoting Fig. 6 Impact of absorptive capacity on upstream government the dual contradiction of the shortage of upstream ecological protection funds and the limited development, and stimulate the initiative of the upstream stakeholders in ecological protection. Second, in the previous studies on DEC, the research conclusion only explained that the DEC mechanism should be promoted, and how to implement the mechanism was not further explored. From the perspective of the allocation ratio of compensation model funds, this study found that from the perspective of the watershed ecological protection and governance cycle, the goal in the short term is to achieve high-quality ecology first Fedra 2015). Therefore, government compensation based on fund compensation and project compensation can achieve benefits faster.

Analysis of the Impact of Rule Collaboration on Collaborative Governance
In DEC practices, the appropriate setting of agreement protection costs and reward and punishment mechanisms can promote rule collaboration in an orderly manner. First, under the low-level cost scenario, Henan and Shaanxi provinces are more willing to collaborate in governance (Liu et al. 2021c). As the compensation object, Shaanxi Province has a high opportunity cost due to ecological protection, and it is necessary to reasonably optimize the agreement guarantee cost of the upstream government according to the regional development differences. Second, existing studies on central government rewards and punishments argue that the central government should play the role of a reward and punishment mechanism to promote upstream and downstream governments (Sheng and Webber 2017), and this study further explains the sensitivity of downstream governments to the reward and punishment mechanism. The central government can take advantage of the significant influence of the reward and punishment mechanism on the downstream government to play the role of incentive and constraint mechanism with the downstream government as the core.

Analysis of the Impact of Benefit Collaboration on Collaborative Governance
Ecological protection and high-quality development of the YRB cannot be achieved without the benefits generated by DEC. From the economic benefit distribution ratio perspective, when the distribution ratio is biased upstream, it is more likely that Shaanxi Province can afford to promote ecological protection and management while maintaining regional economic development. Regarding social benefits, Shaanxi Province, as the compensation object, is in a vulnerable position, and its perception of social benefits will impact its ecological protection behavior (Yuan et al. 2022). In terms of its demand for green industrial transformation, Shaanxi Province, through its absorptive capacity, can use financial compensation to prioritize support for green industries, use the technical and educational payment to enhance residents' technical and developmental abilities, etc. The multi-dimensional capacity is used to improve the green innovation cooperation capacity and further promote local social development and people's well-being. While promoting Shaanxi Province to alleviate the shortage of ecological compensation funds further promotes improving social benefits.

Limitations
Given the DEC mechanism, this study only considers the upstream and downstream governments to describe the reality of ecological compensation better. More interest subjects can be considered in the subsequent research to build an evolutionary game model of local governments and enterprises and the public. Second, based on evolutionary game theory, this study only considers the influencing factors at the current stage. In future research, it is necessary to combine the ecological environment governance cycle, further explore the combination optimization of DEC methods, and dynamically adjust the optimal combination of compensation methods and influencing factors.

Conclusion
Based on the difference of interest demands, this study considers the absorptive capacity of upstream governments, analyzes the cooperative governance mechanism and model of DEC, and provides a new research perspective and insight into the implementation mechanism of DEC for upstream and downstream governments of the YRB. The study showed that: 1. For supply and demand collaboration, when the initial willingness of the downstream government is greater than 0.4, the upstream government will quickly choose the active participation strategy. In addition, when the fund allocation ratio of government compensation, market compensation, and social compensation is 0.7, 0.2, and 0.1, the local government's interests can be maximized, and collaborative governance can be realized faster.
2. For rule cooperation, when the agreement guarantee cost is low, upstream and downstream governments are more likely to choose cooperative governance strategies faster. At the level of equal reward and punishment, the downstream government is more sensitive to the reward and punishment mechanism than the upstream government. 3. For revenue collaboration, compared with the stability of the downstream government, when the proportion of economic benefit distribution is biased towards the upstream government, collaborative governance can be better promoted. The greater its absorption capacity, the greater the social benefits generated, and the more it can promote the long-term mechanism of ecological compensation.