Individual participation and incentive coordination in watershed ecological compensation project: insights from China’s Xin’an River Basin pilot

The success or failure of executing the watershed ecological compensation (WEC) policy is primarily contingent on incentive designs. How do different contractual designs influence the actions of micro-individuals in WEC? How may individuals be enticed to engage in WEC project? Taking the first inter-provincial WEC-Xin’an River Basin (XRB) pilot in China as a case, this study investigates the impacts of government-oriented, market-oriented, and incentive-cooperation contracts on individuals’ behavior based on the framework of Stackelberg games. Subsequently, differences in efforts and profits of diverse individuals are compared and analyzed for each contract. The case-specific numerical example is then utilized to validate theoretical outcomes and to support subsequent key insights. First, the government-oriented contract exhibits effectiveness in bolstering the efforts and interests of micro-individuals, whereas it also places the government under tremendous financial strain. Second, the market-oriented contract formed by the output contribution rate assists in overcoming deficiencies of excurrent government-oriented contract. But it remains controversial if, in the absence of government inspection, investors that devote more cooperative-efforts are not rewarded with further dividends, ultimately diminishing their enthusiasm for the WEC-XRB project. Lastly, the incentive-cooperation contract reinforced by market dominance is advantageous for improving the efficacy of water resource management under the existing government-oriented policy relying on command-and-control instruments.


Introduction
As a formidable vehicle for sustaining ecosystem services and addressing a variety of ecological challenges among ecological protection stakeholders (Fu et al. 2018;Guo et al. 2021;, the watershed ecological compensation (WEC) is gaining widespread recognition and application (Gao et al. 2019), and is becoming highly demanded across nations throughout Asia, particularly in China. It is estimated that in 2019, more than 300 ecological compensation projects are in place globally with the intention of promoting watershed services, biodiversity, carbon, and so forth (OECD 2019). WEC entails a linkage between the watershed ecological service providers who commit to apply security water resource management practices to safeguard water flow, and the watershed ecological service investors (beneficiary) who agree to pay the provider to perform these  (Vogl et al. 2017;Bösch et al. 2019;Ureta et al. 2022). The provision of WEC to individuals, whether providers or investors, typically does not occur spontaneously, but entails extensive individuals' inputs. In other words, it is the outcome of a combination of natural and anthropogenic forces (Hausknost et al. 2017;Wang et al. 2022). In general, individuals can engage in the coproduction of WEC projects in two distinct ways (Yonariza and Mahdi 2019). For instance, watershed managers, particularly governments, are driven by inherent political concerns (Chen et al. 2021a;Yi et al. 2022); watershed landholders nurture their soil to cultivate food and crops (Long et al. 2020). On the other side, governments or citizen can also benefit by providing WEC (often co-produced), such as preserving water security and exposure to high-quality water supplies for inhabitants Jiao et al. 2021).
Notably, individuals' dual role is observed when they act as beneficiaries or co-producers as described above. Different levels of contributions, combined with asymmetric information between WEC providers and users, make it challenging for individuals to form long-term, diverse, and stable cooperative partnerships (Ren et al. 2021). Concurrently, the expansion of WEC is squeezed and confined by the primary objectives, such as input costs and rewards, which may diminish the involved individuals' motivation to put forth and devote efforts (Blicharska et al. 2022;Jiang et al. 2022). While individuals could become conscious of the necessity of WEC projects, but specific expenditures will impede their capacity to continue participation (Ren et al. 2020;Gastineau et al. 2021). Consequently, it is crucial to determine how to motivate WEC individuals to collaborate and undertake essential efforts.
Several studies have risen interested in specialized WEC incentive contracts (Lazaridou et al. 2019;Li et al. 2021). Whether it is a vertical fiscal transfer payment or a horizontal compensation payment, the plurality of WEC projects relies primarily on the state's command-and-control mechanisms (Cao et al. 2021;Fang et al. 2021). As Salzman et al. (2018) pointed out, China's unique political and central authority enables it to enforce ecological compensation contracts with the magnitude and velocity that other western political systems are incapable of, thereby expeditiously reshaping national policies and ecosystem patterns. Yet, in such government-oriented contract, multiple watershed ecological service providers and investors are typically placed in unequal positions that might cause potential conflicts between them owing to the uneven distribution of benefits (Liu and Dou 2022;Lu et al. 2022).
Different from the government-oriented contract, current market-oriented WEC contract somehow does not forcibly inculcate individuals with watershed environmental protection ethics (Daigneault et al. 2021); alternatively, it employs incentives to motivate watershed ecological service providers and investors to engage in ecologically responsible behavior spontaneously . For example, individuals may directly interact in the compensation transaction and jointly negotiate the procedure and quantity of compensation based on the value or cost of watershed ecological services (Huber-Stearns et al. 2015;Zeng et al. 2021). While owing to the ambiguous definition of initial environmental property rights and the vast variety of individuals participating in the transaction process, problems such as compensation complexities and high transaction costs have come to the fore (Guan et al. 2016;Banerjee et al. 2017). Moreover, unlike the government-oriented contract, in which decisions are made based on the overall long-term social interests, individuals involved in the market-oriented contract rarely make strategic decision on their specific or local interests, resulting in periodic short-term behaviors in transactions that are prone to abuse the long-term social interests (Raes et al. 2016;Aguilar et al. 2018). Consequently, the solitary WEC contract driven by the government or the market possesses amount of redundancy.
How do different contractual designs influence the actions of micro-individuals in WEC? How may individuals be enticed to engage in the WEC project? These questions about the complex entanglement between individuals' behavior and WEC contracts are rarely addressed. To facilitate extensive observations, this study intends to prove the impact of three types of WEC contracts on the behavior of watershed ecological service providers and investors through the following arguments. First, taking the first inter-provincial WEC-Xin'an River Basin (XRB) pilot in China as a case, the Stackelberg games are applied to shape outcomes of diverse individuals under the government-oriented, marketoriented, and incentive-cooperation contracts. Subsequently, the optimal equilibrium solution based on the maximizing of social welfare is fruitful for investigating the effects of several critical game elements on outcome states. Finally, the impact of three contracts on the behavior of individuals is compared, and options to enhance individual participation in the WEC-XRB project are investigated. The game theoretical modeling effort is subsequently assessed with data such as the "XRB Water Environment Compensation Agreement" and XRB-related urban ecological environment bureaus, to contextualize the theoretical outcomes and provide practical recommendations for the WEC-XRB project.
In fulfilling this plan of attack, this study contributes the political and economic analysis research of existent WEC projects. First, this study expands a comprehension of individual conflicts caused by itself or external constraints, and then, the necessity of unilateral-efforts and cooperative-efforts in influencing WEC project outputs and market outcomes is underscored. Second, based on the three contracts of government-oriented, market-oriented, and incentive-cooperation, the game models incorporating the influence of different individuals' efforts are designed, and the behavior changes of these micro-individuals are compared and analyzed for each contract. Third, the XRB which involves a package of public mechanisms (including financial subsidies and project-oriented supports) serves as the case-based example to simulate and illustrate how the sustainable collaboration could be accomplished in the WEC contracts.

Study area
The XRB originates in Xiuning County, Huangshan City, and stretches from west to east across Anhui and Zhejiang provinces, as delineated in Fig. 1. The total length of the XRB's mainstream is 358.5 km, and the entire drainage area is 11,674 km 2 , making it the third-largest water system after the Yangtze and Huaihe rivers in Anhui Province. As one of most essential sources of drinking water for China's Anhui and Zhejiang Provinces, its administrative boundaries encompass Huangshan District, She County, Xiuning County, Yi County, and Jixi County of Xuancheng City in Anhui Province, and it empties into Qiandao Lake in Zhejiang Province, via Jiekou.
Huangshan City, located in the upstream of XRB, is distinguished for its tourism and intensive agriculture. Substantial quantities of residential waste discarded by tourists and residues of pesticides and organic fertilizers from the agricultural industry may cause water contamination. Specifically, as Huangshan attained the phase of industrialization and rapid urbanization, the overexploitation and unrestrained utilization of resources caused an imbalance between the demand and supply of ecological environment in the basin. As a consequence, the water quality of the Qiandao Lake in the lower reach of XRB degraded progressively, and the nutrient status of the lake's water quality, which was formerly at a medium nutrient level, grew to a eutrophic level. The downstream of XRB is densely inhabited and heavily industrialized. Clearly, to guarantee the safety of drinking water and industrial production in the downstream, it is critical to strengthen the protection of upstream water sources.
In response to this circumstance, the Ministry of Finance and the Ministry of Environmental Protection of China announced the "XRB Water Environment Compensation Project Implementation Plan" in September 2011, therefore launching the first trans-provincial WEC pilot. To ensure the smooth implementation of WEC pilot project and further improve the regional water environment, it is necessary to clarify the stakeholders of the project. Given the mobility of water sources, upstream of the XRB serves as the providers of watershed ecological services, while downstream are investors. This implies that watershed ecological service providers engaging in the WEC-XRB project have to forego the profits acquired under the original water source circumstances, i.e., the opportunity costs of lowering watershed pollutants; investors acquire freshwater by investing in the WEC-XRB project.

Model specification
Refer to Kretschmer and Puranam (2008) for the statement of the cooperative output function of individuals with diverse technical advances, i.e., both the individual output contribution and the synergistic output effect of cooperative behavior are considered. Accordingly, this study envisages that in the WEC-XRB project, the watershed ecological service investors and providers would simultaneously perform two kinds of pollution control efforts, including their individual antipollution efforts and the collaborative efforts. It should be noted that in this study, both watershed ecological service investors and providers contribute to the same WEC project. To this end, the output function ( Y r ) of the two actors is identical, and can be expressed as follows: where e r represents the unilateral-efforts of the watershed ecological service providers and investors; and the two actors' cooperative-efforts are denoted by c r . The influence coefficients of unilateral-efforts and cooperative-efforts on total outputs are denoted by and , respectively; and is the influence coefficient of bilateral cooperation on the total output, and meets 0 < , , < 1.
To benefit from the WEC-XRB project, the watershed ecological service providers need to exert more effort to conserve the watershed ecosystem, and the investors also need to put forth greater effort to run the project (Pfaff et al. 2019). These efforts substantially increased the expenditures of ecological service providers and investors in watersheds, while the marginal output of efforts will drop when watershed ecological service providers and investors enhance their efforts to reduce watershed contamination. When the effort prices remain fixed, two actors' falling marginal production increases their marginal pollution control costs (Jiang et al. 2019). Consequently, it is assumed that the costs of watershed ecological service investors and providers caused by pollution control are as follows: where E r represents the water pollution treatment cost function satisfying the law of rising marginal costs; and such pollution control cost ( E r ) of two actors in the WEC-XRB project is an increasing function of its unilateral-efforts and cooperative-efforts ( e r , c r ), that is,  Additionally, 0 < k r < 1 is the cost coefficient associated with water pollution control, and covers the escalating (1) Y r = e r + c 3−r + e r c 3−r , ∀r = 1, 2, expenses (funds, labor, and physical assets, etc.) that actors must incur to fix up each extra unit. According to the WEC-XRB standard, the investors initiate the cooperative input and income sharing plan based on the providers' requirements (Brownson and Fowler 2020). The two local actors would determine their respective effort strategies based on thorough information and strive to maximize the anticipated welfare of their respective decisionmaking systems. Accordingly, a typical Stackelberg game model is established between two actors, which is influenced by the unilateral and cooperative pollution control efforts of both sides of the game. This model supports watershed in determining its ideal strategy under competitors' strategies and makes pollution control investment alternatives. To this end, the welfare functions of watershed ecological service investors and providers may thus be described as follow: This study investigates the influence of three contracts on micro-individuals' behavior and the overall profitability of the WEC-XRB project in the subsections that follow, where superscripts G, M, and I represent the governmentoriented, market-oriented, and incentive-cooperation contracts, respectively. The decision schematic of watershed ecological service investors and providers in the WEC-XRB project is depicted in Fig. 2.

Government-oriented contract
In the government-oriented contract, national government plays a leading role in the formulation of WEC-XRB project. In specific, under the support of national administrative rights, the government compensates actors in pollution treatment projects through various approaches, such as financial subsidies, direct investment, special funds, preferential policies, technical support, and education assistance (Liu and Mao 2020;Li et al. 2020Li et al. , 2022a. To incentivize watershed ecological service investors and providers to engage more in water pollution prevention, individuals may well be compensated based on their actual output by national governments. To this effect, it is assumed that the national government allocates incomes equitably to both actors involved in the WEC-XRB project, i.e., the entire benefits of green cooperation are shared between watershed ecological service investors and providers. In this process, the income distribution coefficients of watershed ecological service investors and providers are denoted as s 1 ands 2 , and s 1 , s 2 > 1 is satisfied. Under this contract, the objective welfare functions of two actors in such government-oriented contract are as described in the following: The Stackelberg equilibrium can be obtained by using the backward induction approach proposed by Stackelberg (1934). Under the government-oriented contract, the Hessian matrix of watershed ecological service providers' welfare c a n b e d e r i v e d f r o m E q .
onstrating that this matrix is negative semi-definite with the respect to both e 2 and c 2 . Hence, let the first partial derivatives of the right parts of Eq. (6) with respect to e 2 and c 2 be zero. Consequently, the following equations can be formed: Max G 2 e 2 , c 2 = s 2 e 2 + c 1 + e 2 c 1 + e 1 + c 2 + e 1 c 2 − 1 2 k 2 e 2 2 + c 2 2 .
(7) e G 2 = After inserting Eq. (7) into Eq. (5), the welfare equation becomes: Taking the first partial derivatives of the right-hand side of Eq. (8) with respect to e 1 and c 1 be zero, respectively, the optimal unilateral-efforts and cooperative-efforts of watershed ecological service investors and providers can be calculated as follows: Substituting Eq. (9) into Eq. (7) yields the optimal unilateral-efforts and cooperative-efforts of watershed ecological service providers under the government-oriented contract: The maximum welfares of two local actors may be achieved by substituting the equilibrium solutions { e G r * , c G r * } of watershed ecological service investors and providers into Eqs. (5) and (6):

Market-oriented contract
In the market-oriented contract, as the supply and demand actors of the WEC-XRB project, the watershed ecological service providers and investors establish direct contact and collaboratively negotiate water pollution management measures (Zeng et al. 2021), hence influencing the implementation outcome of the whole WEC-XRB project. Per the preceding description, the watershed ecological investors are situated the downstream of XRB, with a superior economic statue than the providers. In addition, as the dominant actor in the Stackelberg game, watershed ecological investors are keener to remediate water contamination to ensure their own survival and growth, resulting in a higher effect on the production of WEC-XRB project. Ultimately, the output of the WEC project differs markedly between the watershed ecological service investors and providers. Hereafter, it is assumed that the output contribution rate of the watershed ecological service investors ( b 1 ) is greater than that of pro- The output function of WEC-XRB project can subsequently be restated as Y = bY 1 + (1 − b)Y 2 , and the objective welfare functions of two actors in such marketoriented contract may thus be analyzed per the following: Under the market-oriented contract, the Hessian matrix of watershed ecological service providers' welfare can be inferred from Eq. (14) as for H = k 2 2 > 0 , revealing that this matrix is negative semidefinite with the respect to both e 2 and c 2 . Hence, let the first partial derivatives of the right parts of Eq. (14) with respect to e 2 and c 2 be zero. Hereafter, the following equations can be obtained below: After substituting Eq. (15) into Eq. (13), the welfare equation is given: Max M 2 e 2 , c 2 = (1 − b) e 2 + c 1 + e 2 c 1 + b e 1 + c 2 + e 1 c 2 − 1 2 k 2 e 2 2 + c 2 2 .
(15) e M 2 = ( The optimal unilateral-efforts and cooperative-efforts of watershed ecological service investors can be obtained by letting the first partial derivatives of the right part of Eq. (16) with respect to e 1 and c 1 be zero, respectively: When Eq. (17) 13) and (14):

Incentive-cooperation contract
The incentive-cooperation contract unties government regulation with marketization behavior, which is regarded as a selective and adaptive performance of market mechanism in China's economic and political context (Jiang et al. 2019). In this process, the government's technical intervention has become the core of marketization, which legalizes government interference perpetually (Chen et al. 2021b). Combining the preceding two contracts, the objective welfare functions of watershed ecological service investors and providers in the incentive-cooperation contract may thus be expressed as: Max I 1 (e 1 , c 1 ) = s 1 b e 1 + c 2 + e 1 c 2 + (1 − b) e 2 + c 1 + e 2 c 1 − for H = k 2 2 > 0 , proving that this matrix is negative semidefinite with the respect to both e 2 and c 2 . Hence, let the first partial derivatives of the right parts of Eq. (22) with respect to e 2 and c 2 be zero. Hereafter, the following equations can be obtained below: After substituting Eq. (23) into Eq. (21), the profit equation can be written as: Letting the first partial derivatives of the right part of Eq. (24) with respect to e 1 and c 1 be zero, respectively, the optimal unilateral-efforts and cooperative-efforts of watershed ecological service investors can be obtained as follows: (23) e I 2 = providers under the incentive-cooperation contract into Eqs. (21) and (22) yields the maximum profits of the two local actors:

Results
The preceding sections outline three contracts and determine the optimal strategies of watershed ecological service investors and providers. Hereafter, this study compares the three contracts to offer intriguing insights into how the conditions affect the watershed ecological service investors and providers' pollution control efforts.
To sum up, only when k 1 k 2 > 2s 1 s 2 2 can preceding outcomes be determined directly. However, how the output contribution rate (b) and income distribution coefficients s 1 , s 2 affect the optimal unilateral-efforts and cooperative-efforts cannot be directly inferred, which needs further analysis in the subsequent numerical example.

Numerical illustration
To evaluate the validity and universality of the preceding model assumptions, this study integrates multiple values of exogenous variables with the reality of WEC-XRB pilot. Then, a numerical illustration serves to depict the input-output gap between watershed ecological service investors and providers, as well as the effect of output contribution rate and income distribution coefficients on the two actors' pollution control efforts under the government-oriented, marketoriented, and incentive-cooperation contracts.
As reported by the Huangshan City Ecological Environment Bureau, Huangshan City accumulated about 2 billion yuan in engineering investment to maintain the water quality and safety of XRB in 2020, accounting for 36% of the total investment of 33 livelihood projects (5.492 billion yuan). Accordingly, in this study, the watershed ecological service investors and providers' unilateral-efforts in pollution control can be regarded as a part of cost inputs of both sides in specific practice. Referring to the aforementioned input ratio, it is assumed that the influence coefficient of both actors' unilateral-efforts on the total output ( ) is 0.36, and that the influence coefficient of cooperative-efforts on the total output ( ) is denoted as 0.3, and the influence coefficient of bilateral cooperation on the output ( ) is then 0.06.
In accordance with the "XRB Water Environment Compensation Agreement," the federal government would contribute 3 hundred million yuan to the WEC-XRB project.
Correspondingly, it is anticipated that the investment will be distributed equally between watershed ecological service investors and providers in the WEC-XRB project. Then, the income distribution coefficients of two actors ( s 1 and s 2 ) can be fixed to 1.5, respectively. Moreover, regarding the investors as the WEC-XRB project's promoter, it is assumed that the cost coefficient of investors ( k 1 ) is 0.5 with reference to Jiang et al. (2021), while the cost coefficient of providers ( k 2 ) is set to 0.3; the output contribution rate of investors ( b ) is recorded as 0.6. The numerical specification is revealed in Table 1.
As illustrated in Fig. 3, the optimal profits and cost inputs (by one hundred million yuan for unit) of watershed ecological service investors and providers in the WEC-XRB project can be calculated initially. Notably, the government-oriented contract yields the greatest optimal profits for both actors, at 3.0541 and 3.1967; however, it also corresponds to the maximum cost inputs at 1.5775 and 1.435, followed by the incentive-cooperation and market-oriented contracts. Moreover, horizontal comparisons of both actors reveal that, under market-oriented and incentivecooperation contracts, the optimal profits of the watershed ecological investors are greater than those of the providers, which are 0.2661 and 0.287, respectively. Nevertheless, under the marketoriented and incentive-cooperation contracts, the cost inputs of watershed ecological investors are 0.0903 and 0.2477, which are less than that of providers. In contrast, the government-oriented contract yields opposite results to those outlined above.
Interestingly, though the optimal total profit under the government-oriented contract in the WEC-XRB pilot project is far higher than the other two contracts, the input-output ratio (the total cost inputs/the optimal total profits), which measures the economic effectiveness of the investment project, exhibits a poor side. For example, through calculation-via the data in the Fig. 3, the input-output ratio under the government-oriented contract is 48.2%, and the ratio under the market-oriented contract towards 37.5%, while it raises to 89.8% under the incentive-cooperation contract. Evidently, the input-output ratio under the incentive-cooperation contract is the highest among three contracts, indicating that it is economically feasible.

Effects of output contribution rate on both actors' unilateral-efforts
Based on the given data, when comparing the effect of output contribution rate ( b ) on both actors' unilateral-efforts in the WEC-XRB project, it can be found that under the market-oriented and incentive-cooperation contracts, the variation of unilateral-efforts between watershed ecological service investors and providers reveals an opposite trend, as shown in Fig. 4. More in specific, when the increase of output contribution rate ( b ) rises, it is apparent that the watershed ecological service investors' unilateralefforts ( e M 1 and e I 1 ) exhibit an upward trend, while providers' unilateral-efforts ( e M 2 and e I 2 ) manifest a downward trend. Furthermore, since the government-oriented contract is unaffected by market forces, b has no effect on the unilateral-efforts of both actors accordingly, and obviously, the unilateral-efforts under the government-oriented contract are the highest among three contracts. It is worth noting that only when 0.5 < b<0.55, the providers' unilateral-efforts are superior to those of investors; otherwise, the investors' unilateral-efforts under various contracts are constantly stronger than those of providers. Besides that, when b>0.55, the difference between watershed ecological service investors and providers' unilateral-efforts will become progressively large; in other words, the effect of the output contribution rate on the watershed ecological service investors is vastly higher than that on providers.

Effects of output contribution rate on both actors' cooperative-efforts
The variation trend of output contribution rate (b) on both actors' cooperative-efforts in the WEC-XRB project can be depicted in Fig. 5. In contrast to Fig. 4, a rise of output contribution rate is triggering the growth of the watershed ecological service providers' cooperative-efforts ( c M 2 and c I 2 ), while those of investors ( c M 1 and c I 1 ) are dropping. In addition, there is a disparity between two actors' involvement to cooperative-efforts, and this disparity widens as the output contribution rate rises. In other words, the output contribution rate influences the cooperative-efforts of the watershed ecological service providers more than those of investors.

Effects of income distribution coefficient on both actors' unilateral-efforts
By holding the remaining parameters constant, the differences between the two actors' optimal unilateral-efforts with varied income distribution coefficients ( s 1 and s 2 ) in the WEC-XRB project are illustrated in Fig. 6. Consequently, the calculation outcomes of Eqs. (29-32) can be obtained initially as the income distribution coefficients increase, i.e., e G . In specific, if the watershed ecological service providers' income distribution coefficient ( s 2 ) is fixed at 1.5, watershed ecological service investors and providers' unilateral-efforts under the government-oriented and market-oriented contracts ( e G 1 * , e G 2 * , e I 1 * , and e I 2 * ) will grow as the investors' income distribution coefficient ( s 1 ) increases. Similarly, if the income distribution coefficient ( s 1 ) of investors is equally maintained at this value, the growth in s 2 corresponds to the same trend of both actors' unilateral-efforts. This observation implies that the growth of income distribution coefficients has a beneficial impact on both actors' unilateral-efforts. A more interesting thing is that when such income distribution coefficients expand to a certain extent, the income distribution coefficient of watershed ecological service investors will have a stronger impact on themselves, as well as the income distribution coefficient of watershed ecological service providers.

Effects of income distribution coefficient on both actors' cooperative-efforts
Similarly, the difference between the two actors' optimal cooperative-efforts with varied income distribution coefficients ( s 1 and s 2 ) in the WEC-XRB project can be depicted in Fig. 7. Evidently, as the income distribution coefficients grow, it becomes glaringly obvious that the cooperativeefforts of both actors under the government-oriented contract are greater than those under the incentive-cooperation and market-oriented contracts. This corresponds to the results of Eqs. (33-36), i.e., e G 1 * > e I 1 * > e M 1 * and e G 2 * > e I 2 * > e M 2 * are proven. It is worth noting that the difference between the watershed ecological service investors and providers' cooperative-efforts is initially smaller. But, when the income distribution coefficient reaches a certain value, the difference of watershed ecological service investors' cooperative-efforts will always be larger than that of providers. Moreover, a comparison with Fig. 6 reveals that the increment in the The influence coefficient of unilateral-efforts on total outputs 0.36 The influence coefficient of cooperative-efforts on total outputs 0.3 The influence coefficient of bilateral cooperation on total outputs 0.06 k 1 The cost coefficient of investors 0.5 k 2 The cost coefficient of providers 0.3 b The output contribution rate of investors 0.6 s 1 The income distribution coefficient of investors 1.5 s 2 The income distribution coefficient of providers 1.5 income distribution coefficients has a minor effect on both actors' cooperative-efforts than on the unilateral-efforts.

Discussion
This study focuses on the influence of different WEC contracts on micro-individuals' behavior and the entire WEC-XRB project profitability via determining and comparing optimum equilibrium strategies, as well as simulating the repercussions. It is suggested that watershed ecological service investors and providers may choose their maximum effort based on the incentive structures of different WEC contracts. First, the government-oriented contract generates profits by incentivizing participants to minimize water pollution emissions, as opposed to depriving one side's incomes (Meng et al. 2019;Sun et al. 2020), and is thus an efficient mechanism. Currently, the vast majority of China's WEC projects utilize this vertical compensation structure (Zhai et al. 2021). As the results of this study show, the government-oriented contract is a productive agreement since it enhances the unilateral-and cooperative-efforts efforts of both watershed ecological service investors and providers, and simultaneously increases the profits of both entities. The explanation for this actuality is that the intention of the government-oriented horizontal incentive contract is to counterbalance local economy caused by environmental development constraints in the affected community, and maintain the sustainable provision of public services when local authority revenues are severely impacted (To and Dressler 2019).
Nevertheless, as the majority of procurement expenditures emanate from the national treasury, the national government has been experiencing tremendous financial strain (Li et al. 2022b). As demonstrated by the preceding case analysis, under the government-oriented contract, the profit margins of watershed ecological service investors and providers are the greatest of all assessment contracts, but the cost inputs also constitute the largest. Owing to the complexity in measuring and monetizing the value of ecological environmental services and asymmetric information (Pan et al. 2017), governments struggle to comprehend the opportunity cost of each service, leading to the excessive payment costs. Simultaneously, regardless of the fact that several individuals (e.g., farmers, land owners, wetland managers, or industries in the basin) share the benefits of watershed pollution control, only the government offers substantial financial assistance, resulting in high operating and maintenance expenditures (Shen et al. 2021).
Second, the market-oriented contract constructed by the output contribution rate aids in overcoming the deficiencies of excurrent government-oriented contract that relies heavily on command-and-control mechanisms. The findings indicate Fig. 3 The optimal profits and cost inputs of two actors that an increase in the output contribution rate releases not only beneficial effect on the improvement of watershed ecological service investors' unilateral-efforts and watershed ecological service providers' cooperative-efforts, but also a detrimental effect on the progression of providers' unilateralefforts and investors' cooperative-efforts. Consequently, as the watershed ecological service investors increase their investment in water pollution remediation, in this circumstance, the providers reap more benefits without extra efforts. In the absence of government oversight, the investors that commit more cooperative-efforts will not get further dividends, thereby diminishing their incentive to collaborate. As Van Hecken et al. (2015) argued, the social-political context is overlooked by market-oriented incentives as traditional solutions to ecological challenges. To this end, empowering the watershed ecological service investors with both more decision-making authority and incentives can be seen as leading to possibly better outcomes in the WEC project.
Lastly, the kind of government-oriented or market-oriented contracts is rarely advantageous for the augmentation of interactants' antipollution efforts, and both face certain restrictions. Henceforth, the incentive-cooperation is becoming a fair and effective contract, as it can not only incentivize watershed ecological service investors and providers to deal with water resources protection, but also safeguard the equality of all individuals' status in the decision-making process. Increasingly, it is acknowledged that the pursuit of equality is crucial to gather the wide support and legitimacy required to attain ecological ambitions, despite the reality that it regularly drives environmental degradation (Droste et al. 2018). As can be observed from the preceding findings, establishing alternative income distribution coefficients will have remarkable effects on respective pollution control efforts when implementing incentive strategies. Consequently, in accordance with the premise of maximizing the Fig. 4 The optimal unilateral-efforts with output contribution rate Fig. 5 The optimal cooperative-efforts with output contribution rate interests of all stakeholders, the national government ought to conduct a thorough evaluation of the relevant factors, and thus formulate the incentive criteria that are practicable ).

Conclusion
The intention of WEC is to utilize incentives to alter the relative value of water treatment costs and benefits, hence altering individuals' rational decision and minimizing watershed contamination. To this end, using the first interprovincial WEC-XRB pilot in China as a case, this study proposes Stackelberg game models to shape outcomes of diverse individuals under the government-oriented, marketoriented, and incentive-cooperation contracts. The optimal equilibrium solution based on the maximization of social welfare is beneficial for examining the effects of pivotal game elements on outcome states. These may include both individuals' unilateral-efforts on watershed mitigation and cooperative-efforts throughout the project duration. Finally, the impact of three contracts on the behavior of individuals is compared, and options to enhance individual participation in WEC projects are investigated. The game theoretical modeling effort is subsequently assessed by the numerical illustration within a case-based example to contextualize the theoretical outcomes and provide practical recommendations for WEC projects. This study adds to the understanding of individual participation and incentive coordination in WEC project, and yields several insights. First, the government-oriented contract exhibits effectiveness in bolstering the efforts and interests of micro-individuals, whereas it also places the government under tremendous financial strain. Second, the market-oriented contract constructed by the output contribution rate is committed to overcoming the flaws of Fig. 6 The difference between optimal unilateral-efforts with income distribution coefficients Fig. 7 The difference between optimal cooperative-efforts with income distribution coefficients government-oriented contract. While questions remain in the absence of government inspection, investors that devote more cooperative-efforts are not rewarded with further dividends, ultimately diminishing their incentive to collaborate on WEC projects. Lastly, the incentive-cooperation structure reinforced by market dominance is advantageous for improving the efficacy of water pollution mitigation under the existing government-oriented system relying on command-andcontrol instruments. Some clear and straightforward policy implications are consequently outlined based on the aforementioned observations. First, it is forced to add marketization instruments into WEC projects. The organic blending of market-based instruments and government-oriented WEC contracts may motivate individuals to maximize their profits via negotiations, hence maximizing the overall return of WEC projects. In particular, the WEC market-based instruments exemplified by water rights trading merit wider application, which is favorable to optimizing regional water resource distribution and attaining water conservation and water environment preservation objectives. Second, empowering investors and suppliers of watershed ecological services with extra incentives could be conducive to enhancing WEC project outcomes. In the market-oriented WEC contract that disregards the social-political context, decision-making authority should be decentralized to investors with a higher economic development level, thus stimulating the involvement of providers. Furthermore, consider increasing the subsidy coefficient of WEC projects, which in turn incentivize investors and providers to strengthen their pollution control efforts, generating a sustainable virtuous cycle for both sides of the watershed. Third, the national government ought to provide a thorough evaluation on pertinent elements, such as losses of input and opportunity cost of watershed ecological protectors, profits of watershed ecological beneficiaries, and restoration costs of watershed ecological devastation. Additionally, by evaluating the extent of economic growth in specific regions, the compensation criteria that are practicable to the advancement of WEC projects should indeed be devised.
This study retains several limitations that call for further research. Besides income distribution coefficients, the expansion of this study might explore the incorporation of the cost-sharing coefficient into existing models and its adaptation to the execution of WEC projects, thereby preserving a balance between cost inputs and outputs for individual engaged. Practically, participation in the execution of WEC projects is not restricted to single watershed ecological service providers and investors; particular social capitals, major enterprises, and the public at large may also be involved. The integration of these extra stakeholders poses fascinating challenges for future game analytics and research.
Author contribution Ke Jiang: conceptualization, investigation and supervision, writing-original draft, writing-review and editing; Die Wang: formal analysis, data curation, writing-review and editing; Yusheng Wang: methodology, validation, writing-review and editing.
Funding This work was financially supported by the Humanities and Social Science Foundation of Ministry of Education of China (no. 20YJC790050); the Social Science Foundation of Jiangsu Province (no. 22EYC019); the National Social Science Foundation of China (no. 22CJY059); and the Foundation from China Scholarship Council (no. 202109045008).
Data availability Supplementary data to this study will be provided upon request.

Declarations
Ethics approval Not applicable.

Competing interests
The authors declare no competing interests.