Dynamic game model for preventing and controlling atmospheric pollution

Abstract

The invention belongs to the technical field of environmental protection, and provides a dynamic game model for air pollution prevention and control. Comprising a social economic model, an environmental model and an environmental economic endogenous model; the environment model comprises a pollutant discharge capacity function and a pollutant concentration function; the environmental economy endogenous model comprises a pollutant loss function, a health loss coefficient function and a pollutant emission reduction cost function; and the social economic model comprises an objective function, an economic total output function, a dominable output function and a consumption function.

Description

Technical Field

[0001] The invention belongs to the technical field of environmental protection, and in particular relates to a dynamic game model for air pollution prevention and control. Background Art

[0002] The heterogeneity of economic development and pollution levels in different regions requires that my country cannot adopt a "one-size-fits-all" approach when designing emission reduction paths, and should fully consider the differences in economic development levels and environmental governance capabilities in various regions. At present, most of the research on regional bargaining for pollutant emission reduction is qualitative research, which uses schematic diagrams to show the choices of both parties in the game. Although this kind of research can objectively show the game process, it cannot provide quantitative information to policymakers. There are obvious differences in the economic development level and pollutant emission levels in different regions. The establishment of a coordinated emission reduction mechanism requires the use of comprehensive and systematic methods and models, which not only consider the overall economic development level and environmental characteristics, but also the development differences and characteristics of various regions. Summary of the invention

[0003] The technical problem to be solved by the present invention is to provide a dynamic game model for air pollution prevention and control, develop a regional environmental economic system dynamic game model (REEG model), incorporate a dynamic game mechanism into the environmental economic system model, solve the Nash equilibrium under dynamic conditions, and obtain the game strategy for pollution reduction in various regions.

[0004] To achieve the above object, the present invention provides the following technical solutions:

[0005] A dynamic game model for air pollution prevention and control, including: a social economic model, an environmental model and an endogenous environmental economic model;

[0006] Environmental model, including pollutant emission function and pollutant concentration function; used to control the pollutant emission rate x in the tth year of the ith region i (t), based on the pollutant emission function and the pollutant concentration function, calculate the pollutant concentration M in the ith region in the tth year i (t);

[0007] The environmental economic endogenous model includes a pollutant loss function, a health loss coefficient function, and a pollutant reduction cost function; on the one hand, it is used to i (t), based on the health loss coefficient function and the pollutant concentration function, calculate the effective labor force L′ after deducting the pollutant loss from the pollutant concentration in the ith region in the tth year i (t); On the other hand, for i (t), based on the pollutant reduction cost function, calculate the pollutant reduction cost D of the ith region in the tth year i (t);

[0008] The socio-economic model includes an objective function, a total economic output function, a disposable output function, and a consumption function; on the one hand, it is used to calculate the economic output function according to the D i (t) and L′ i (t), based on the total economic output function and the disposable output function, calculate the disposable output Y i (t); according to the Y i (t) and the investment I in the i-th region in year t i (t), calculate the consumption C of the ith region in year t based on the consumption function i (t), on the other hand, for use according to the C i (t) and the population L of the ith region in year t i (t), calculate the objective function and obtain the pollutant emission control rate x corresponding to the maximum value of the objective function i (t) and the ratio of investment to disposable output I i (t) / Y i (t).

[0009] Furthermore, in the socio-economic model of the present invention,

[0010] The objective function is:

[0011]

[0012] The total economic production function is:

[0013] Q i (t) = A i (t)K i (t) γ L′ i (t) 1-γ (2)

[0014] The disposable output function is:

[0015] Y i (t) = [1-D i (t)]Q i (t) (3)

[0016] The consumption function is:

[0017] C i (t) = Y i (t)-I i (t) (4)

[0018] Among them, Q i (t) is the total economic output of the ith region in the tth year, A i (t) is the technological progress of the ith region in the tth year, K i(t) is the capital stock of the ith region in the tth year, γ is the capital share parameter, and 1-γ is the labor share parameter.

[0019] Furthermore, the socio-economic model of the present invention also includes the constraint relationship of capital stock in adjacent years:

[0020] K l · (t) = I i (t)-δ K K i (t) (5)

[0021] Among them, K i (t) represents the capital stock of the ith region in year t, δ K is the depreciation rate of capital stock, K l · (t) represents the capital stock of the ith region in year t+1.

[0022] Furthermore, in the environmental economic endogenous model of the present invention,

[0023] Pollutant emission function:

[0024] E i (t) = [1-x i (t)]σ i (t)Q i (t), 0≤x i (t)≤1 (6)

[0025] Pollutant concentration function:

[0026]

[0027] Among them, σ i (t) is the emission intensity of pollutants, S i is the effective area of ​​region i, β ij is the pollutant transfer coefficient between regions.

[0028] Furthermore, the environmental economic endogenous model of the present invention also includes the constraint relationship of pollutant emission intensity in adjacent years:

[0029]

[0030] Among them, g i (t) represents the natural intensity decline rate of the pollutant, σ i (t) represents the pollutant emission intensity of the ith region in the tth year, σ l · (t) represents the pollutant emission intensity of the ith region in year t+1.

[0031] Furthermore, in the environmental economic endogenous model of the present invention,

[0032] Pollutant loss function:

[0033] L′ i (t) = [1-λ i (t)]L i (t) (9)

[0034] Health loss coefficient function:

[0035] λ i (t) = a λ M i (t) 2 +b λ M i (t) (10)

[0036] Pollutant reduction cost function:

[0037] D i (t) = a D x i (t) 2 +b D x i (t) (11)

[0038] Among them, λ i (t) is the health loss coefficient of the ith region in the tth year; a λ and b λ is the health loss parameter; a D and b D is the emission reduction cost parameter.

[0039] Beneficial effects:

[0040] Taking into full consideration the different pollution characteristics and economic development levels of various regions, the inter-regional game is incorporated into the modeling of the environmental economic system, a dynamic game model is constructed, the Nash equilibrium is solved (i.e., the pollutant emission control rate is solved based on the objective function), and the emission reduction effects and differences of regional cooperation and non-cooperative games are quantitatively explored, and the optimal path for pollution reduction in various regions, i.e., the emission control rate, is specifically described. This dynamic game model for air pollution control breaks through the bottleneck of the current environmental economic complex system model that ignores the feedback relationship between the environment and the economic system, constructs a dynamic game model that couples the environmental system and the economic system, internalizes environmental health impacts, cross-regional transmission of pollutants, and regional heterogeneity into the socio-economic model, describes the feedback relationship between the economic model and the environmental model, and provides a systematic and scientific theoretical system for regional environmental governance research. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0042] Figure 1 It is a framework diagram of the dynamic game model of the regional environmental economic system. DETAILED DESCRIPTION

[0043] The embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0044] It should be noted that the following embodiments and features in the embodiments may be combined with each other in the absence of conflict; and, based on the embodiments in the present disclosure, all other embodiments obtained by ordinary technicians in the field without making any creative work are within the scope of protection of the present disclosure.

[0045] It should be noted that various aspects of the embodiments within the scope of the appended claims are described below. It should be apparent that the aspects described herein may be embodied in a wide variety of forms, and any specific structure and / or function described herein is merely illustrative. Based on the present disclosure, it should be understood by those skilled in the art that an aspect described herein may be implemented independently of any other aspect, and two or more of these aspects may be combined in various ways. For example, any number of aspects described herein may be used to implement the device and / or practice the method. In addition, other structures and / or functionalities other than one or more of the aspects described herein may be used to implement this device and / or practice this method.

[0046] like Figure 1 As shown, an embodiment of the present application is a dynamic game model for air pollution prevention and control, including three interacting sub-models: a socio-economic model, an environmental model, and an endogenous environmental economic model: a pollutant transport model (i.e., the inter-regional pollutant transfer coefficient in the pollutant concentration function), which describes the path of mapping air pollutant emissions to pollutant concentrations, as well as the regional transfer of pollutants; a model that describes the evolution of pollutants over time (i.e., the pollutant emissions and pollutant concentration functions), which depends on the path of air pollutant concentrations; an economic model that describes how the economy and society are affected by pollutants over time (i.e., the pollutant loss function and the pollutant reduction cost function), and describes how economic activities lead to pollutant emissions. The framework diagram is as follows Figure 1As shown in the figure, economic activities in various regions generate pollutants and discharge them into the environmental system. Pollutants diffuse and transfer across regions and have heterogeneous impacts on people's health, which in turn leads to labor (population) losses. At the same time, pollutant emission reduction in various regions incurs economic costs, and pollution losses and emission reduction costs jointly affect their respective economic systems.

[0047] Socioeconomic Model

[0048] The prototype of the social economic module is the standard Solow economic growth model, which maximizes social welfare by balancing investment and consumption. The social welfare function of the REEG model is the sum of the discounted per capita consumption utility weighted by population. Formula (1) is the mathematical expression of the objective function.

[0049]

[0050] Among them, t represents time, i represents region, and u i (t) is the consumption utility of the ith region in the tth year, L i (t) is the population (labor force) of the ith region in the tth year. The population (labor force) is an exogenous variable and it is assumed that the population (labor force) is not affected by pollution. i (t) is the consumption function of the ith region in the tth year, ρ is the discount rate. t0 represents the initial time, and ρ0 represents the initial discount rate.

[0051] In terms of setting the production function, this model uses the Cobb-Douglas production function to represent the economic output of each region, as shown in formula (2). Considering the two input factors of capital and labor, the total output is a function of capital and effective labor.

[0052] Q i (t) = A i (t)K i (t) γ L′ i (t) 1-γ (2)

[0053] Among them, Q i (t) is the total economic output of the ith region in year t; A i (t) is the technological progress of the ith region in the tth year, which is assumed to be an exogenous variable; K i (t) is the capital stock of the ith region in the tth year; L′ i (t) is the effective labor force in the ith region in the tth year after deducting the pollution loss; γ is the capital share parameter, and 1-y is the labor share parameter.

[0054] Unlike the Solow model, economic output needs to deduct the input of pollutant emission reduction and pollutant losses, because in the short term, economic growth and environmental pollution are in a trade-off relationship. Environmental governance requires costs, and environmental pollution also brings losses. In the short term, environmental pollution will affect economic growth. Therefore, the economic output function after deducting the cost of pollutant emission reduction and pollutant losses is shown in formula (3).

[0055] Y i (t) = [1-D i (t)]Q i (t) (3)

[0056] Among them, Y i (t) represents the disposable output of the ith region in year t (minus the cost of emission reduction); D i (t) represents the emission reduction cost function of the ith region in the tth year.

[0057] The main destination of net output is simplified to consumption and investment, without considering government expenditure, international and inter-regional trade, as shown in formula (4).

[0058] C i (t) = Y i (t)-I i (t) (4)

[0059] Among them, I i (t) represents the investment in the ith region in year t.

[0060] Investment will lead to an increase in capital stock. The total capital stock of the production sector in the current period is equal to the sum of the capital stock of the previous period after depreciation and the investment of the previous period, as shown in formula (5).

[0061] K l · (t) = I i (t)-δ K K i (t) (5)

[0062] Among them, K i (t) represents the capital stock of the ith region in year t, δ K is the depreciation rate of the capital stock.

[0063] Environmental Model

[0064] The environmental module includes the emission and concentration of atmospheric pollutants, as well as the transfer of pollutants between regions. As shown in formula (6), economic activities generate pollutant emissions, and pollutant emissions can be reduced through emission reduction policies.

[0065] E i (t) = [1-x i(t)]σ i (t)Q i (t), 0≤x i (t)≤1 (6)

[0066] Among them, E i (t) represents the pollutant emissions of the ith region in the tth year. Pollutant emissions are generated due to the use of fossil fuels in economic and production activities. This model assumes that the pollutant emissions of the region are generated by production activities and takes into account the emission control rate set by the region to control air pollution. i (t) is the pollutant emission control rate of the ith region in the tth year, and the emission control rate of each region is limited to between 0 and 1. i (t) represents the total economic output of the ith region in the tth year, σ i (t) is the emission intensity of pollutants.

[0067] According to historical experience, my country's annual atmospheric pollutant emissions have a downward trend. Assuming that the pollutant emission intensity σ i (t) is a natural decline, which may be attributed to the use of clean energy and the improvement of energy efficiency, and has no direct relationship with emission reduction efforts, as shown in formula (7). i (t) represents the natural intensity decrease rate of the pollutant.

[0068]

[0069] The pollutant concentration is shown in formula (8), and due to various natural environmental factors such as geographical location, regional area, wind speed and direction, the pollutant concentration will transfer between regions. i (t) represents the pollutant concentration in the ith region in the tth year, S i is the effective area of ​​region i, β ij is the pollutant transfer coefficient between regions.

[0070]

[0071] Endogenous model of environmental economy

[0072] The economic module and the environmental module are mainly connected through the health loss of pollutants and the cost function of emission reduction. The connection between the economic module and the environmental module is that economic activities produce pollutant emissions; the role of the environmental module to the economic module includes two parts, one is the loss of health and labor caused by pollutants, and the other is the cost of emission reduction.

[0073] This model affects the loss of air pollution on the supply of labor. Pollution affects health and thus causes a reduction in labor supply. The function of pollutant loss is shown in formula (9).

[0074] L′i (t) = [1-λ i (t)]L i (t) (9)

[0075] Among them, L′ i (t) represents the effective labor force in the ith region in year t after deducting the pollution loss, λ i (t) is the health loss coefficient of the ith region in the tth year.

[0076] The health loss parameter is fitted by a quadratic function. The specific formula is shown in (10). The health loss is a nonlinear function of the pollutant concentration. i (t) represents the pollutant concentration in the ith region in the tth year, a λ and b λ is the health loss parameter. When there is no pollution, the health loss of pollution is zero. Therefore, the form of the health impact of pollution is a quadratic function without a constant term.

[0077] λ i (t) = a λ M i (t) 2 +b λ M i (t) (10)

[0078] Emission reduction efforts require investment costs, and the emission reduction cost function is marginally increasing. Due to the limitations of factors such as technology level, compared with the early stage of emission reduction, achieving higher emission reduction targets requires higher costs than in the early stage. This model also measures the emission reduction cost function through a quadratic function fit, as shown in formula (11). The emission reduction cost is a nonlinear function of the emission control rate. Among them, D i (t) represents the pollutant emission reduction cost of the ith region in the tth year, x i (t) represents the emission control rate of the ith region in the tth year, a D and b D is the emission reduction cost parameter. When no emission reduction is carried out, the emission reduction cost is zero, so the emission reduction cost is in the form of a quadratic function without a constant term.

[0079] D i (t) = a D x i (t) 2 +b D x i (t) (11)

[0080] The embodiment of the present application constructs a dynamic game model to solve the Nash equilibrium, and quantitatively explores the emission reduction effects and differences between regional cooperation and non-cooperative games, specifically describing the optimal path for pollution reduction in each region. Each region does not cooperate with each other and pursues the maximization of its own social welfare.

[0081] The following uses Beijing, Tianjin, Hebei, Shanxi and Inner Mongolia as examples to elaborate on the cross-regional transmission path of air pollution:

[0082] According to the pollutant transmission path, the concentration equations of different regions are slightly different. i = 1-5 represent Beijing, Tianjin, Hebei, Shanxi and Inner Mongolia respectively. Taking Beijing as an example (Formula 12), when i = 1, it represents the pollutant transmission path in Beijing. In addition to being converted from local emissions, the pollutant concentration in Beijing is also affected by pollutants from Hebei and Shanxi.

[0083] M1(t)=β 11 [E1(t) / S1]+β 13 [E3(t) / S3]+β 14 [E4(t) / S4] (12)

[0084] When i=2, it represents the pollutant transmission path in Tianjin. In addition to being converted from local emissions, the pollutant concentration in Tianjin is also affected by pollutants from Hebei and Shanxi. In addition, the model considers the emission outlet of pollutants. Since Tianjin has a part of the coastline, pollutants will decay naturally along the coastline. The natural decay rate δ M2 It is expressed by the ratio of Tianjin coastline to the national coastline.

[0085] M2(t)=(1-δ M2 ){β 22 [E2(t) / S2]+β 23 [E3(t) / S3]+β 24 [E4(t) / S4]} (13)

[0086] When i = 3, it represents the pollutant transmission path in Hebei. The pollutant concentration in Hebei is converted from local emissions and is only affected by pollutants in Shanxi. Similarly, the model considers the emission outlet of pollutants. Since Hebei has a part of the coastline, pollutants will decay naturally along the coastline, and the natural decay rate δ M3 It is expressed by the ratio of Hebei's coastline to the national coastline.

[0087] M3(t)=(1-δ M3 ){β 33 [E3(t) / S3]+β 34 [E4(t) / S4]} (14)

[0088] The pollutant concentration in Shanxi only considers emissions in this region and is not affected by other regions, as shown in Formula 15:

[0089] M4(t)=β 44 [E4(t) / S4] (15)

[0090] Finally, the pollutant transmission in Inner Mongolia is the same as that in Beijing. When i=5, it indicates the pollutant transmission path in Inner Mongolia. In addition to being converted from local emissions, the pollutant concentration is also affected by pollutants from Hebei and Shanxi. In addition, when selecting the effective area, Inner Mongolia only considers some densely populated areas.

[0091] M5(t)=β 55 [E5(t) / S5]+β 53 [E3(t) / S3]+β 54 [E4(t) / S4] (16)

[0092] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed by the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims

1. A dynamic game model for air pollution prevention and control, characterized in that: include: Socioeconomic models, environmental models, and endogenous environmental-economic models; Environmental model, including pollutant emission function and pollutant concentration function; The environmental economic endogenous model includes pollutant loss function, health loss coefficient function and pollutant reduction cost function; The socioeconomic model includes the objective function, the total economic output function, the disposable output function, and the consumption function.

2. The dynamic game model for air pollution prevention and control according to claim 1 is characterized in that: include: Socioeconomic models, environmental models, and endogenous environmental-economic models; Environmental model, including pollutant emission function and pollutant concentration function; used to control the pollutant emission rate x in the tth year of the ith region i (t), based on the pollutant emission function and the pollutant concentration function, calculate the pollutant concentration M in the ith region in the tth year i (t); The environmental economic endogenous model includes a pollutant loss function, a health loss coefficient function, and a pollutant reduction cost function; on the one hand, it is used to i (t), based on the health loss coefficient function and the pollutant concentration function, calculate the effective labor force L′ after deducting the pollutant loss from the pollutant concentration in the ith region in the tth year i (t); On the other hand, for i (t), based on the pollutant reduction cost function, calculate the pollutant reduction cost D of the ith region in the tth year i (t); The socio-economic model includes an objective function, a total economic output function, a disposable output function, and a consumption function; on the one hand, it is used to calculate the economic output function according to the D i (t) and L′ i (t), based on the total economic output function and the disposable output function, calculate the disposable output Y i (t); according to the Y i (t) and the investment I in the i-th region in year t i (t), calculate the consumption C of the ith region in year t based on the consumption function i (t), on the other hand, for use according to the C i (t) and the population L of the ith region in year t i (t), calculate the objective function and obtain the pollutant emission control rate x corresponding to the maximum value of the objective function i (t) and the ratio of investment to disposable output I i (t) / Y i (t).

3. The dynamic game model for air pollution prevention and control according to claim 2 is characterized in that: In the socioeconomic model, The objective function is: The total economic production function is: Q i (t)=A i (t)K i (t) γ L′ i (t) 1-γ (2) The disposable output function is: Y i (t)=[1-D i (t)]Q i (t) (3) The consumption function is: C i (t)=Y i (t)-I i (t) (4) Among them, Q i (t) is the total economic output of the ith region in the tth year, A i (t) is the technological progress of the ith region in the tth year, K i (t) is the capital stock of the ith region in the tth year, γ is the capital share parameter, and 1-γ is the labor share parameter.

4. The dynamic game model for air pollution prevention and control according to claim 3 is characterized in that: The socio-economic model also includes constraints on capital stocks in adjacent years: Among them, K i (t) represents the capital stock of the ith region in year t, δ K is the depreciation rate of the capital stock, represents the capital stock of the ith region in year t+1.

5. The dynamic game model for air pollution prevention and control according to claim 3 is characterized in that: In the endogenous environmental economic model, Pollutant emission function: E i (t)=[1-x i (t)]σ i (t)Q i (t),0≤x i (t)≤1 (6) Pollutant concentration function: Among them, σ i (t) is the emission intensity of pollutants, S i is the effective area of ​​region i, β ij is the pollutant transfer coefficient between regions.

6. The dynamic game model for air pollution prevention and control according to claim 5 is characterized in that: In the endogenous environmental economic model, The environmental economic endogenous model also includes the constraint relationship between pollutant emission intensities in adjacent years: Among them, g i (t) represents the natural intensity decline rate of the pollutant, σ i (t) represents the pollutant emission intensity of the ith region in the tth year, It represents the pollutant emission intensity of the ith region in the t+1th year.

7. The dynamic game model for air pollution prevention and control according to claim 5 is characterized in that: The endogenous environmental economic model Pollutant loss function: L′ i (t)=[1-λ i (t)]L i (t) (9) Health loss coefficient function: λ i (t)=a λ M i (t) 2 +b λ M i (t) (10) Pollutant reduction cost function: D i (t)=a D x i (t) 2 +b D x i (t) (11) Among them, λ i (t) is the health loss coefficient of the ith region in the tth year; a λ and b λ is the health loss parameter; a D and b D is the emission reduction cost parameter.

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