Two-Stage and Three-Party Transboundary Watershed Management Based on Valuation Adjustment Mechanism (VAM) Agreement

Abstract

The severe water shortage and pollution problems have become the bottleneck restricting the sustainable development of the economy and society. River basin ecological compensation is an important way to solve transboundary water pollution. To increase the cooperation willingness between governments and enterprises, and clarify the operation mechanism, this paper built a two-stage river basin ecological compensation mechanism in horizontal and vertical directions under VAM agreement. The results show that the externalization of environmental protection costs by the free-riding behavior of governments is the fundamental reason for the failure of the autonomous evolutionary game. The VAM agreement can reduce the uncertainty of upstream and downstream governments in environmental protection expenditure through contract pricing based on water quality, significantly improve free-riding behavior, and make the strategy of maximizing social benefits possible. After signing the VAM agreement, the upstream governments and enterprises become the main players in the second stage of the game, and the game results directly affect the final ownership of the downstream water quality and the ownership of the gambling amount. When the upstream government and enterprises adopt different strategies, by adjusting "environmental protection funds and fines", "sewage treatment costs", "upstream government governance costs" and "gambling amount", the negative side's strategic choices can be improved. However, when both sides adopt negative strategies, the adjustment of a single variable cannot achieve the optimal stability strategy of maximizing social benefits, and a more comprehensive strategy combination is needed. The research results are expected to provide a reference for the government to formulate environmental policies and promote coordinated basin governance.

Appendix

Tables 10 and 11

Table 10 Variable value

Table 11 Model parameters and meanings

It should be noted that ${f}_{1}<{f}_{2}$, ${R}_{1}>{R}_{2}$, ${R}_{3}>{R}_{5}$ and ${R}_{6}>{R}_{4}$.

Condition 2:

• 1. When ${Q}_{0}+{Q}_{2}-({\alpha }_{1}-{\alpha }_{2}){C}_{1}<0$ and $\gamma (S+F+I)-({\beta }_{1}-{\beta }_{2}){C}_{2}<0$.

Table 12

Table 12 Analysis of partial stability

• 2. When ${Q}_{0}+{Q}_{2}-({\alpha }_{1}-{\alpha }_{2}){C}_{1}<0$ and $\gamma (S+F+I)-({\beta }_{1}-{\beta }_{2}){C}_{2}<0$.

Table 13

Table 13 Analysis of partial stability

• 3. When ${Q}_{1}+{Q}_{0}+\gamma I-({\alpha }_{1}-{\alpha }_{2}){C}_{1}<0$ and $({\beta }_{1}-{\beta }_{2}){C}_{2}-\gamma (S+F+I)<0$.

Table 14

Table 14 Analysis of partial stability

• 4. When $({\alpha }_{1}-{\alpha }_{2}){C}_{1}-{Q}_{1}-{Q}_{0}-\gamma I<0$ and $({\beta }_{1}-{\beta }_{2}){C}_{2}-\gamma (S+F)<0$.

Table 15

Table 15 Analysis of partial stability

Condition 3

• 1. When $-({\alpha }_{1}-{\alpha }_{2}){C}_{1}<0$ and $\gamma (S+F+I)-({\beta }_{1}-{\beta }_{2}){C}_{2}<0$.

Table 16

Table 16 Analysis of partial stability

When $({\alpha }_{1}-{\alpha }_{2}){C}_{1}<0$ and $\gamma (S+F)-({\beta }_{1}-{\beta }_{2}){C}_{2}<0$.

According to the parameter design, $({\alpha }_{1}-{\alpha }_{2}){C}_{1}>0$ always holds. Therefore, this situation is not discussed.

• 2. When $\gamma I+{Q}_{1}-{Q}_{3}-({\alpha }_{1}-{\alpha }_{2}){C}_{1}<0$ and $({\beta }_{1}-{\beta }_{2}){C}_{2}-\gamma (S+F+I)<0$.

Table 17

Table 17 Analysis of partial stability

• 3. When ${Q}_{3}+({\alpha }_{1}-{\alpha }_{2}){C}_{1}-{Q}_{1}-\gamma I<0$ and $({\beta }_{1}-{\beta }_{2}){C}_{2}-\gamma (S+F)<0$.

Table 18

Table 18 Analysis of partial stability

Condition 4

• 1. When $-({\alpha }_{1}-{\alpha }_{2}){C}_{1}<0$ and $\gamma (S+F+I)-({\beta }_{1}-{\beta }_{2}){C}_{2}<0$.

Table 19

Table 19 The equilibrium point analysis of evolutionary stability strategy

When $({\alpha }_{1}-{\alpha }_{2}){C}_{1}<0$ and $\gamma (S+F)-({\beta }_{1}-{\beta }_{2}){C}_{2}<0$.

According to the parameter design, $({\alpha }_{1}-{\alpha }_{2}){C}_{1}>0$ always holds. Therefore, this situation is not discussed.

• 2. When $\gamma I+{Q}_{1}+{Q}_{0}-({\alpha }_{1}-{\alpha }_{2}){C}_{1}<0$ and $({\beta }_{1}-{\beta }_{2}){C}_{2}-\gamma (S+F+I)<0$.

Table 20

Table 20 The equilibrium point analysis of evolutionary stability strategy

• 3. When $({\alpha }_{1}-{\alpha }_{2}){C}_{1}-{Q}_{0}-{Q}_{1}-\gamma I<0$ and $({\beta }_{1}-{\beta }_{2}){C}_{2}-\gamma (S+F)<0$.

Table 21

Table 21 The equilibrium point analysis of evolutionary stability strategy

1.1 Numerical Simulation

This paper is committed to promoting the evolution of the game behavior between the upstream government and polluting enterprises to an "ideal" strategy combination, that is, the equilibrium state in which the upstream government chooses the "strong governance" strategy and the polluting enterprise chooses the "complete sewage treatment" strategy (x = 1, y = 1). In order to better explore the strategic evolution tendency of the upstream government department and the polluting enterprise, the variables in the non-ideal state under different constraints of Condition 1–4 will be adjusted respectively, and the influence of parameter values on the evolution results will be analyzed. According to the operability in the actual situation and the characteristics of constraints in different situations, this paper selects the environmental funds, the environmental fines, the incentive funds, the gambling amount, the governance cost and the cost of sewage treatment as the adjustment variables.

• 1. When the evolution result is (1, 0)

In this case, the upstream government adopts the "strong governance" strategy, and the polluting enterprise chooses the "partial sewage treatment" strategy. Based on the original parameter value, assuming that other variables remain unchanged, the initial values of $x$ and $y$ are set to 0.5 respectively, with S (the environmental funds), F (the environmental fines) and C2 (the cost of sewage treatment) as variables, assign values to them respectively, and conduct several simulation experiments. The results are shown in the figures below.

As can be seen from Fig. 9a-b, with the continuous rise of S, the polluting enterprise gradually transforms from the "partial sewage treatment" strategy to the "complete sewage treatment" strategy, and the whole system begins to evolve from "invalid" evolution equilibrium point (1, 0) to "ideal" equilibrium point (1, 1). The reason may be that with the continuous improvement of the environmental funds, the comprehensive income of the polluting enterprise choosing the "strong governance" strategy is greater than their cost expenditure. Although such funds cannot be used for other purposes, they can only be withdrawn and deducted according to particular purposes, limiting the possibility of using these funds as daily operating expenses but reducing sewage treatment's economic burden. In order to comply with the requirements of local environmental regulations and avoid being punished by the environmental protection department, the upstream enterprise is willing to accept government funding to treat the sewage generated by the enterprise and finally achieve the "ideal" equilibrium point of the system through the efforts of both parties.

As can be seen from Fig. 9c-d with the continuous increase of the environmental fines, the whole system also begins to evolve from the invalid evolution equilibrium point (1, 0) to the ideal equilibrium point (1, 1). The reason may be that with the strengthening of the punishment of the upstream government on the polluting enterprise, the comprehensive income of the polluting enterprise choosing the "strong governance" strategy is greater than its expenditure, and the polluting enterprise cannot risk discharging the sewage directly into the river. If the upstream government finds that the enterprise pollutes the river during its supervision, the daily production and operation of the whole enterprise will be greatly affected. On the one hand, high fines will cause huge financial pressure to the enterprise; On the other hand, the environmental protection department is bound to inspect the pollutant discharge enterprise in accordance with relevant laws and regulations, and order the pollutant discharge enterprise to stop production for rectification, resulting in the shutdown of the whole enterprise.

As can be seen from Fig. 9e-f with the continuous reduction of the cost of sewage treatment, the whole system also began to evolve from the invalid evolution equilibrium point (1, 0) to the ideal equilibrium point (1, 1). The possible reason is that the cost of enterprise emission reduction is the key influencing factor in deciding whether an enterprise chooses the "complete sewage treatment" strategy. Under certain government subsidies, the lower the cost of sewage treatment, the less the relative expenditure of enterprises. However, the cost of sewage treatment cannot be achieved overnight. Only through long-term technological innovation, efficient resource allocation and perfect supporting measures can it be gradually reduced. In addition, the government's support for enterprises in this process is also essential. It should help enterprises realize green transformation through technology subsidies, preferential policies, environmental protection publicity and other aspects.

Fig. 9

Variable adjustment when the evolution result is (1, 0)

• 2. When the evolution result is (0, 1)

In this case, the upstream government adopts the "weak governance" strategy, and the polluting enterprise chooses the "complete sewage treatment" strategy. On the basis of the original parameter value, assuming that other variables remain unchanged, the initial values of $x$ and $y$ are set to 0.5 respectively, with C1 (the governance cost) and Q1 (the gambling amount) as variables, they are assigned values respectively, and several simulation experiments are carried out. The results are as follows.

As can be seen from Fig. 10a-d, with the continuous rise of the gambling amount, the upstream government gradually changed from the "weak governance" strategy to the "strong governance" strategy, and the whole system began to evolve from the invalid evolution equilibrium point (0,1) to the ideal equilibrium point (1,1). The possible reason is that in the process of increasing the gambling amount of the "strong governance, complete sewage treatment" strategy, its attraction to the upstream government is also gradually increasing (the gambling amount of "weak governance, complete sewage treatment" strategy is less than Q1). In order to obtain high-level basin compensation to cover the governance costs and obtain a certain amount of fiscal revenue, the upstream government will adopt more stringent standards and governance measures. At this time, the upstream government department and enterprise will work together to promote the improvement and restoration of the ecological environment in the basin and jointly promote sustainable development in the basin.

As can be seen from figures Fig. 10e-h, with the continuous reduction of the governance cost, the upstream government gradually changed from the "weak governance" strategy to the "strong governance" strategy, and the whole system began to evolve from the invalid evolution equilibrium point (0, 1) to the ideal equilibrium point (1, 1). The possible reason is that the governance cost is the key factor in determining what strategy the upstream government adopts. On the premise of constant subsidies to the enterprise, the lower the governance cost of the upstream government, the less the relative expenditure. The government's river basin governance contains many aspects, including the formulation of local environmental regulations, the supervision and management of enterprises, and the restoration of river basin water bodies, etc., so the government's cost reduction measures should also give reasonable consideration to these aspects.

• 3. When the evolution result is (0, 0)

At this time, the upstream government adopts the "weak governance" strategy, and the polluting enterprise chooses the "partial sewage treatment" strategy. On the basis of the original parameter value, assuming that other variables remain unchanged, the initial values of $x$ and $y$ are set to 0.5, F (the environmental fines), S (the environmental funs), I (the incentive funds), Q (the gambling amount), C1 (the governance cost) and C2 (the cost of sewage treatment) are used as adjustment variables to assign values respectively, and several simulation experiments are carried out. The results are as follows.

According to the variable adjustment, we find that the system cannot directly convert from the worst evolution result (0, 0) to the best evolution result (1, 1) by adjusting the above different variables separately in Condition1-3. The possible reason is that adjusting a single variable can only mobilize the enthusiasm of the upstream government or the polluting enterprise. If we want to muster the willingness of both parties, we may need to adjust multiple variables.

Fig. 10

Variable adjustment when the evolution result is (0, 1)

Condition 4 is slightly different from the above situation. In this case, whether the upstream government and the polluting enterprises adopt the strategy of "strong governance, partial sewage treatment" or "weak governance, complete sewage treatment", they can not meet the minimum water quality requirements. The upstream government must pay the downstream government the ecological "gambling" amount. However, according to the variable adjustment results, we can see that the whole system can evolve toward the ideal equilibrium point (1, 1) by increasing F (the environmental fines) or reducing S (the environmental funds) and C2 (the cost of sewage treatment). The possible reason is that compared with Condition 1–3, the current situation has a higher target water quality standard and a higher demand for water treatment. Therefore, its variable adjustment result is a little bit different.

Currently, the Chinese government vigorously advocates the concept of sustainable development. For cost reasons, local governments may ignore river basin governance in the short term. Still, in the long run, local governments will intervene in river basin pollution to meet the needs of people and social development. Therefore, the evolution strategy of (0, 0) can only appear in the short term under the current policy practice, so we will not analyze and interpret this strategy too much.