Abstract
This study establishes a market sharing mechanism for watershed ecological compensation between an upstream and downstream government based on the game-theoretical approach. It is found that, in this transboundary market sharing mechanism, the upstream government is encouraged to make more effort to protect the watershed ecosystem. As a result, a market-sharing compensation mechanism can bring Pareto improvements to all stakeholders. Furthermore, the influences of several key factors on the performance of the market sharing mechanism are investigated, which provides theoretical guidance for establishing and implementing such a mechanism in practice.
HIGHLIGHTS
Resolves compensation and allocation problems between upstream and downstream.
Makes full use of the ecological benefits from the watershed.
Proposes a market sharing ecological mechanism based on a cooperation game.
Analyzes the influencing factors of the market sharing mechanism.
It is conditional on the market sharing mechanism being beneficial.
INTRODUCTION
In recent years, watershed ecological compensation has been paid more and more attention by government and academia (Zhang et al. 2010; Chen et al. 2021). The Chinese government has implemented numerous ecological compensation programs to alleviate watershed pollution and to resolve the balance between ecological protection and economic development (Adhikari & Agrawal 2013; Wu & Jin 2020; Zheng et al. 2021). However, China's implementation of ecological compensation is still in the exploratory stage. Ecological compensation is mainly based on transfer payments from the central government or between local governments (Zhang et al. 2017), resulting in many problems, such as insufficient funding sources, high transaction cost, imperfect operation mechanism, the lack of effective coordination between provinces, and so on (Li et al. 2021). Therefore, it is necessary to explore more effective ecological compensation mechanisms to resolve the above problems.
The approach of introducing an effective market mechanism into ecological compensation has gradually become the consensus of government and the whole society (Schomers & Matzdorf 2013; Yu et al. 2020; Zou & Mao 2022). In 2012, Anhui and Zhejiang provinces signed the first cross-provincial ecological compensation agreement in China (Li et al. 2020). The agreement illustrates that if water quality at the provincial boundary reaches the standard level, the Anhui province will obtain compensation funds from Zhejiang Province and Central government. Otherwise, Anhui Province and the Central government provide funds to Zhejiang Province (Cheng et al. 2020). From 2012 to 2014, the central and local governments invested jointly in Xin'an River ecological compensation. From 2015 to 2017, the government began to establish point-to-point targeted ecological compensation. After 2019, the government proposed to explore a market-oriented ecological compensation mechanism in Xin'an River Basin.
However, there are still several theoretical problems left to be resolved. For example, how can the rights and interests of different stakeholders in cross-provincial watershed ecological compensation be protected? What are the key factors affecting the effective operation of the market sharing mechanism?
To address these issues, a market sharing ecological compensation model is proposed in this study. For simplicity of analysis, the mechanism is established between an upstream government and a downstream government, and it can be modeled through a game-theoretical approach. Game theory is a mathematical theory and method to study cooperation or competition interactions among multiple players. It considers the predicted behavior and actual behavior of players in the game, and explores their optimization strategies (Myerson 1991). Game theory has been widely used to study watershed ecological compensation in the literature. Li et al. (2017) applied a game theory approach to study the significance of building ecological corridors for watersheds and analyzed the role of the stakeholders. Gao et al. (2019) formulated an evolution game theory to study the ecological compensation interactions between upstream governments, downstream governments and central government. Ren et al. (2021) investigated the game strategies in government-led watershed ecological compensation in the Xin'an River Basin. In addition to the above literature, there are a stream of other researches on watershed ecological compensation using game theory. However, as far as we know, market sharing ecological compensation has not previously been studied from a game theorectial approach. This is the gap we intend to fill in this study.
In the game model formulated in this study, the upstream government and the downstream government, as two players, make their decisions on watershed ecological protection efforts, so as to maximize their own payoffs. There are two sources of payoffs: one is the implicit payoff, the other is the payoff from the market. The improvement of watershed ecological service brought by protection efforts can bring implicit payoff to governments; this is widely assumed in the literature (Deng et al. 2019; Ding et al. 2022), and is in line with practice. In fact, the improvement of the ecological environment can improve the reputation of a city, attract more tourism and investment, and thus increase the government's tax and other revenues. Compared with implicit payoff, we focus more on the market payoff, which is ignored in the existing literature. We assume that the downstream government has established a watershed ecosystem service market, as the Zhejiang government in the downstream region of the study area has done, and sells watershed services to users in the market. As a result, the downstream government will get a payoff from the market, while the upstream government do not.
If there is no market sharing compensation in the game, the downstream government has two souces of payoffs, while the upstream government only gets a implicit payoff. In order to encourage the upstream government to take more efforts to protect the watershed ecological ecosystem, the downstream government intends to shares a certain rate of market payoffs to the upstream government. This is the market sharing compensation mechanism, which will be discussed in this study. We will explore the key factors for establishing an effective ecological market sharing compensation mechanism, and investigate the influences of these factors on the revenues of stakeholders, as well as the social welfare.
The contribution of this paper is that a market-sharing ecological compensation has been established based on game theory. The established model can well protect the rights and interests of different stakeholders in cross-provincial watershed ecological compensation. As far as we know, this is the first game-theoretical model that introduces market mechanisms into watershed ecological compensation. Though the model seems less complicated, it is expected to be the prelude to the theoretical research of market sharing ecological compensation.
MATERIALS AND METHODS
Study area
The Location of Xin'an River Basin.
It is worth noting that the values used for the variables in the simulations are hypothetical. The model has not been applied using true values from the study area, because we are focusing on introducing a theoretical method in this study.
The market sharing compensation model
Market sharing mechanism for watershed ecological compensation.
Key factors, players and strategies
The market sharing mechanism aims to resolve the compensation and allocation problems between upstream and downstream governments. Before the implementation of a watershed ecological compensation project, the players negotiate and determine their strategies respectively, and finally reach a contract. Specifically, the downstream government decides whether to compensate the upstream government and, if so, it needs to determine the market sharing rate offered to the upstream government. In response to the downstream government's decision, the upstream government decides how much effort to make to protect the watershed ecology.
Key factors
We extracted several key factors that influence the performance of a market sharing ecological compensation mechanism from the literature (Fu et al. 2018; Wunder et al. 2018; Xu & Han 2019; Gastineau et al. 2021; Liu & Yan 2022). The key factors are presented as follows:
: Protection efforts taken by the upstream and downstream governments, respectively. They include building ecosystem protection infrastructures, improving and monitoring the water quality in the watershed, and so on.
: Unit protection costs of the upstream and downstream governments, respectively. These occur when the government takes efforts to protect the ecosystem, and will increase as protection effort increases.
: Watershed ecological service level. This is closely affected by the protection efforts taken by the upstream and downstream governments. The more effort undertaken, the higher the ecological service level will be. Watershed ecological service level is always measured by the proportional levels of pollutant, nitrogen oxide or others in the watershed. In this study, we use a 1–5 point score to score the watershed service level; the higher the score, the better the watershed service level.
: Impact coefficients of watershed ecological service level on the local government's implicit payoff. We assume that 
.
: The unit price for watershed ecological service. The price is determined by the downstream government before establishing the ecological service market. Throughout the following context, the price p is assumed to be fixed.
: Demand for watershed ecological service. In the market sharing mechanism, the watershed ecological service is transacted in the ecological service market. The demand is positively correlated to the ecological service level L.
: Market sharing coefficient offered by the downstream government to the upstream government. The market sharing coefficient should be negotiated by both players before the implementation of the contract.
Stakeholder payoffs
are the cost coefficients of the upstream and downstream governments, respectively. An assumption of the effort–cost relationship follows (Xin & Sun 2017; Chen et al. 2019): the ecosystem protection effort will improve the watershed ecological service level, which is assumed to satisfy the following equality:
is the initial watershed ecological service level, and 
are the impact coefficients of the efforts of the upstream and downstream governments, respectively on the improvement of watershed ecological service level.
is the initial demand of ecological service, and r is the sensitive coefficient of watershed ecological service level.With these assumptions, we can analyze the payoffs of the governments under different strategies in the market sharing mechanism.
Scenario without compensation
are an equilibrium, it will satisfy the following two conditions:
Scenario with market sharing compensation
are an equilibrium, it will satisfy the following two conditions:
RESULTS AND DISCUSSION
Equilibrium decisions
with respect to 
, we can obtain the optimal protection effort for the upstream government as follows:
, by taking the first-order derivatives of 
and 
with respect to 
and 
respectively, the optimal protection efforts are:
By comparing the equilibrium results of efforts in the above two scenarios, we observe that: 
and 
. From the above equalities, we discover that compared with the effort taken in the mechanism without market sharing compensation, the upstream government makes more effort to protect the ecological system in the market sharing mechanism. By contrast, the downstream government takes less effort to protect the ecological system in the market sharing mechanism than that in the mechanism without market sharing.
and market sharing rate 
, so as to maximize its own payoff. Figure 3 shows that the payoff function of the downstream government is jointly concave in 
and 
, thus it has a unique optimal solution. Since the relationship between optimal effort and optimal market sharing rate has been determined, the problem left is to determine the optimal market sharing rate for the downstream government's payoff. 
Payoff surface of downstream government on the effort and market sharing rate.
into the downstream government's payoff function 
, then consider the first-order condition 
. Solving this equation, the unique equilibrium 
for the governments in the scenario with market sharing compensation can be obtained based on the following formula:
Simulation analysis and discussion
To further investigate the influences of specified factors on the payoffs of governments under different ecological protection cooperation mechanisms, simulation experiments were conducted to analyze the sensitivities of the cost coefficients, the implicit payoff impact coefficients, ecological service level improvement coefficients, and demand improvement coefficients. The initial values of these parameters are specified in Table 1.
 | 0.5 ($ 10,000 per effort square) |
 | 0.6 ($ 10,000 per effort square) |
 | 1 (score improvements per effort) |
 | 0.6 (score improvements per effort) |
 | 1.5 ($ 10,000 per effort) |
 | 2 ($ 10,000 per effort) |
 | 1.5 (ton per score) |
 | 0 (ton) |
 | 1 (score) |
 | 3 ($ 10,000 per ton) |
| | 0.5 ($ 10,000 per effort square) |
| | 0.6 ($ 10,000 per effort square) |
| | 1 (score improvements per effort) |
| | 0.6 (score improvements per effort) |
| | 1.5 ($ 10,000 per effort) |
| | 2 ($ 10,000 per effort) |
| | 1.5 (ton per score) |
| | 0 (ton) |
| | 1 (score) |
| | 3 ($ 10,000 per ton) |
and 
. The results are shown in Figure 4(a) and 4(b), where 
varies from 
to 
and 
varies from 
to 
. 
The effect of cost coefficients on the payoffs of governments: (a) sensitivity analysis of 
, and (b) sensitivity analysis of 
.
The effect of cost coefficients on the payoffs of governments: (a) sensitivity analysis of , and (b) sensitivity analysis of .
From Figure 4(a), with the increase of the upstream government's cost coefficient 
, the upstream and downstream payoffs all decrease, no matter if the market sharing compensation is applied or not. Moreover, the Pareto improvements of both governments are also decreasing with the increase of 
. When 
increases to 0.89, the market sharing compensation brings no improvement payoff to either governments. Hence, it is not beneficial to the payoffs of either government to adopt the market sharing compensation if the cost coefficient 
is too large.
Figure 4(b) shows that the payoffs of the downstream government decrease with the increase of cost coefficient 
in both scenarios, but the Pareto improvement increases as 
increases. Meanwhile, with the increase of 
, the payoff of the upstream government decreases in the scenario without compensation while increasing in the scenario of market sharing compensation. The Pareto improvement of the upstream government also increases as 
increases. Another point that can be seen from Figure 4(b) is that, if 
is smaller than 
, the market sharing compensation brings fewer payoffs to both of the governments than that under the mechanism without compensation. Thus, it is optimal to abandon the market sharing compensation if the cost coefficient 
is too small.
and 
. In Figure 5(a), the social welfare coefficient 
varies from 
to 
, while all the other parameters are fixed as specified in Table 1. Similarly, in Figure 5(b), all the parameters are fixed except 
, which varies also from 
to 
. 
The effect of social welfare coefficients on government payoffs: (a) sensitivity analysis of 
, and (b) sensitivity analysis of 
.
The effect of social welfare coefficients on government payoffs: (a) sensitivity analysis of , and (b) sensitivity analysis of .
From Figure 5(a), the payoffs of the downstream government increase with the increase of the coefficient 
in both scenarios, but the Pareto improvement decreases as 
increases. However, the payoff of the upstream government increases with the increase of 
under the mechanism without compensation while it decreases under the market sharing compensation scenario. As for the downstream government, the Pareto improvement of the upstream government is also decreasing as 
increases. The figure infers that the market sharing compensation fails to be beneficial to the payoffs of both governments if 
. That is, the smaller 
, the greater Pareto improvement brought by the market sharing mechanism.
According to Figure 5(b), the payoffs of the downstream government increase with the increase of the coefficient 
in both scenarios. A similar phenomenon occurs for the downstream government. It can also be seen from the figure that, the Pareto improvements of upstream and downstream governments all increase with the increase of 
. However, when 
, the market sharing compensation fails to be beneficial.
and 
are presented in Figure 6. In Figure 6(a), all the parameters are fixed except 
, which varies from 
to 
. Similarly, in Figure 6(b), 
varies from 
to 
, while all the other parameters are fixed. 
The effect of ecological service level improvement coefficients on the payoffs of governments (a) sensitivity analysis of 
, and (b) sensitivity analysis of 
.
The effect of ecological service level improvement coefficients on the payoffs of governments (a) sensitivity analysis of , and (b) sensitivity analysis of .
Figure 6(a) shows that, both the payoffs of upstream and downstream governments increase with the increase of the parameter 
. Moreover, the Pareto improvements of both governments also increase as 
increases. If 
, it is not beneficial to the payoffs of both governments to implement the market sharing mechanism.
Figure 6(b) shows the results for sensitivity analysis of 
, which is different from that of 
. Although the payoffs of the downstream government are increasing in 
, the Pareto improvement is decreasing. On the other hand, the payoff of the upstream government is increasing in 
under the mechanism with no market sharing compensation, while it is decreasing under the market sharing mechanism. The Pareto improvement of the upstream government is also decreasing in 
. As 
increases to 
, the Pareto improvement vanishes and then the market sharing mechanism will not be beneficial as 
further increases. Hence, the market sharing compensation should be implemented only in the case where 
is not too large.
to 
. 
The effect of demand improvement coefficient on the payoffs of governments.
It can be seen from Figure 7 that, both the payoffs of upstream and downstream governments increase with the increase of demand improvement coefficient r and the Pareto improvements also increase. However, when 
, the market sharing mechanism is not beneficial to the payoffs of both the upstream and downstream governments. Hence, only when r is not too small, can it be ensured that the market sharing mechanism is beneficial to the payoffs of both governments.
The value of the parameter r is related to several factors, such as market size, or the purpose of purchasing watershed ecological services. If customers buy water resources for industrial production, then their watershed service level requirements will not be high. In that case, the improvement of watershed ecological level can not bring much more demand, that is, the value of r is relatively small. Therefore, the government will have less motivation to put more effort into improving the ecological service level, because more effort will lead to more cost without bringing more payoffs. Under this scenario, the market sharing mechanism will not be benificial to the payoffs of both governments.
Future applications
It is worth noting that there are some key points outside the scope of this study, and the model discussed in this study could be the grounds for very interesting papers in future research. We briefly discuss some possible future topics as follows:
A limitation of the model discussed in this study is that only two players are considered in the game. However, in practice, the successful operation of a watershed ecological market requires the cooperation of multiple parties, such as governments, enterprises and residents. Therefore, it is desirable to extend our model to a cooperative game with multiple players.
The users’ willingness to pay for watershed ecological service is crucial for the establishment and successful implementation of a market sharing compensation mechanism. Hence, governments should cultivate a more efficient ecological service market to improve the willingness of enterprises and residents to pay for ecological system services. How to encourage the willingness to pay for watershed ecological service is an interesting and important topic for further research.
The ecological service price p is assumed to be a constant in this study. However, the market has always been divided into several segments in reality, and ecological service prices are different in different market segments. In addition, the prices can also be determined dynamically, which could bring more payoffs to ecological service providers. How to find the optimal dynamic pricing policy is a topic worthy of further research.
CONCLUSION
Ecological compensation plays an important role in balancing ecosystem protection and economic development. In this study, a market sharing mechanism was proposed for watershed ecological compensation, under which upstream and downstream governments cooperate together to protect an ecosystem and share benefits from the ecosystem service market. Compared to existing studies, the market-sharing compensation mechanism presented here is essential to inform transboundary watershed management and encourage the sustainable development of an ecosystem. In practice, it is better to introduce computer vision and other machine learning methods to improve the efficiency of any market-sharing mechanism (An et al. 2022; Zhou et al. 2022). We find that the more effort taken by the upstream government, the higher the value of the watershed ecosystem will be, and then more demand and market profits will be obtained. Thus, in a market sharing compensation mechanism, the upstream government should make more effort to protect the watershed ecosystem.
DATA AVAILABILITY STATEMENT
All relevant data are included in the paper or its Supplementary Information.
CONFLICT OF INTEREST
The authors declare there is no conflict of interest.
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