Research on the driving principle and guiding strategy of the public's collaborative supervision of the sharing economy in my country

Jing Su

Journal & Issue Details

Applied Mathematics and Nonlinear Sciences

Journal Details

Format: Journal
eISSN: 2444-8656
First Published: 01 Jan 2016
Publication timeframe: 2 times per year
Languages: English

The rapid development of the sharing economy not only has a huge impact on the economy, environment, society, government and other aspects but also further reshapes people's daily life, subverts the traditional business model and affects the existing system and mechanism by ‘destroying regulation.’ Therefore, the aspects of ‘whether’ and ‘how’ to effectively supervise and govern the sharing economy have become a global governance problem. In response to this problem, scholars from all over the world have put forward many regulatory ideas, and different regulatory models have been adopted in practice. For the regulation and governance of the sharing economy, many experts and practitioners around the world have proposed three main strategies [1,2]. First, stop and delay, i.e. to prevent and delay the development of sharing economy regulation through mandatory administrative measures to avoid possible negative problems. Policy regulations that adopt the strategy of blocking and delaying often use traditional policy norms to measure regulatory practices, which will inevitably hinder the healthy development of the new sharing economy. Therefore, many public policy scholars have criticised the government as ‘lazy government [3]. Second, modify or establish a new regulatory framework to accommodate regulation. Scholars such as Koopman believe that the public policies formulated by the government should be continuously improved so as to better co-ordinate with the development of the sharing economy market [4]. Peng Yue advocates reducing administrative intervention, adopting responsive regulation strategies, gradually solving various conflicts and problems caused by the sharing economy, as well as seeking a dynamic balance between supervision and regulation [5]. This strategy has been accepted by many experts, scholars and local governments. Third, to apply government threats: that is to say, the government does not adopt a clear attitude or measures but conducts supervision through relatively broad and flexible means such as acquiescence or intimidation, which is a vague regulatory strategy [6]. This strategy is often applied to the initial stage of the sharing economy, and the government adopts a wait-and-see attitude, neither prohibiting new forms of sharing economy nor allowing them to be legalised. Some scholars believe that although the threat strategy is suspected of inaction, it also has certain advantages. It can not only provide regulatory space for the development of new formats but also restrain them and prevent their barbaric development [7].

Research on industrial collaborative innovation mainly focusses on high-tech industries and resource-based industries [8]. Osborne et al. [9] used the composite system synergy degree model to analyse the collaborative innovation mechanism of my country's high-tech industries and put forward suggestions on the collaborative innovation of high-tech industries based on the experimental results. Alford J et al. [10] explored the mechanism of collaborative innovation in emerging industries based on the theory of synergy and found that collaborative innovation requires enterprises to play a leading role and, with the passage of time, the degree of innovation among collaborative subjects will gradually deepen. Rich R C et al. [11, 12] took the coal industry as the research object and used the synergy model to analyse the synergy degree of the innovation system of coal enterprises, in order to provide help for the co-ordinated development of the industry, academia and research in the coal industry. Ansell C et al. [13] proposed to develop a mobile application to enable the public to participate in the recycling of renewable resources to a greater extent. System tests and practical applications show that public participation can significantly improve the recycling rate of renewable resources. Victor P et al. [14] constructed a tripartite evolutionary game model for the collaborative innovation of government, industry, university and research, and they found that each participant was affected by each other's willingness to participate in different degrees; they used MatLab simulation analysis to find that there was sensitivity of each participant to different parameters. From the perspective of collaborative innovation, Brandsen A L et al. [15] constructed an evolutionary game model of the co-operative alliance of manufacturing enterprises and logistics enterprises and found the formation method and stable state of the two collaborative innovations through simulation analysis.

On the basis of the theory of collaborative governance, the theory of responsive regulation and the theory of co-production, this study draws on the existing research results to analyse how to encourage the public to participate in the collaborative regulatory governance of the sharing economy. The research mainly adopts a combination of field research and literature research, qualitative analysis and quantitative research, normative research and empirical research. Second, we use inductive and deductive methods, and in the third step, we apply game analysis. The supervision of new forms of sharing economy requires the co-operation of enterprises, government departments and the public.

Reflections on the collaborative supervision and governance of my country's sharing economy

First, multiple co-ordination and co-operative supervision and governance are the inevitable trends in the regulation of the sharing economy in the future. The sharing economy realises the separation of ownership and use rights and also makes the traditional government supervision model completely invalid. In the supervision of the sharing economy, the government's regulatory role must rely on the enterprise platform to regulate and guide users, which requires the enterprise to assume the responsibility for operation management services; users or the public can provide feedback information to the enterprise to co-operate with the management of the enterprise or to the government. Complaints and protests are used to supervise corporate violations. Therefore, the government, companies and the public have become the main stakeholders involved in sharing economic activities. The three interact, restrict each other and are indispensable to each other; they then build a multi-dimensional synergy with the media and social organisations, yielding the modern regulatory governance system.

Second, the current practice of collaborative supervision and governance in my country is still in its infancy. The supervision of the sharing economy involves multiple subjects, such as the government, enterprises and society. It has become the theoretical consensus of the whole society to build a multiple co-operative supervision and governance system. However, judging from the past practice of collaborative supervision and governance of the sharing economy in my country, due to the large influx of venture capital, the long-term goal of ‘making the city better’ of bicycle companies has succumbed to the pressure of capital, resulting in a pattern of collaborative supervision and governance exploration, thus resulting in a completely broken system. After the end of the ‘bike melee’, although the government and enterprises have started new explorations of co-operative supervision, they have not yet established a standardised and effective communication system and mechanism [16]. At the same time, it is always difficult for bicycle companies to find an effective profit model, and the value co-creation role of the public has always been seriously ignored, which has become an important obstacle to the construction of a collaborative supervision and governance system.

Third, the role of the public has not been valued and brought into play. In the process of supervision and governance of shared bicycles in my country, enterprises and the government have successively played the leading roles of collaborative governance at different stages, but the role of the public in collaborative governance has always been ignored; multiple collaborative co-operation is often simplified in practice as a government–enterprise dual regulatory model. In the interviews and questionnaires, we also found that due to the lack of guidance and assistance from the government or enterprises, most of the public can – at the most – consciously follow the shared bicycle code of conduct, and it is difficult to truly co-operate with enterprises or the government and participate in the supervision and maintenance of shared bicycles in action. Among them, 36.4% of the interviewees said that they basically did not participate in any supervision and maintenance activities of shared bicycles, 39.6% of the interviewees had actively participated in the supervision and maintenance of shared bicycles but did not enjoy the material rewards given by the company and 51.8% of the interviewees have actively participated in the supervision and maintenance of shared bicycles but have not been commended by the government or enterprises [17, 18]. This shows that neither the enterprise nor the government pays attention to the public's co-production role in the supervision of shared bicycles. On the one hand, bicycle companies regard the public as a pure consumer, blindly hoping to regulate user behaviour through new technologies and systems, ignoring the role of the public as a value co-creator or co-producer of the sharing economy. On the other hand, the government is accustomed to using traditional regulatory thinking and models to supervise bicycle companies on behalf of users and the public, which tends to ignore the real needs of the public. In the supervision and governance of the sharing economy, the government, enterprises and society are all stakeholders, which cannot be ignored. Losing the participation of the public will inevitably lead to a sharp increase in the maintenance and scheduling costs of enterprises, and reduce the government's supervision performance of enterprises. It is difficult to establish a collaborative supervision and governance system. Therefore, paying attention to the role of the public as co-producers in the sharing economy, creating corresponding platforms and channels, as well as guiding the public to participate in the co-construction, co-governance and sharing of the sharing economy have become inevitable requirements for the realisation of collaborative supervision and governance in the future.

Analysis of the tripartite game between the government, enterprises and the public in the supervision of the sharing economy

3.1

Basic assumptions of the model

The main difference between the gas generator set and the co-generation unit is that it will use the chemical substances after burning natural gas to generate electricity, improving the efficiency of the starting point [19]. There is a certain relationship between the natural gas flow used by the unit and the generated electric power during operation, which can be expressed as follows.

Assumption 1. Participating agents = {1, 2, 3}. There are three types of participants in the model, namely enterprises related to the sharing economy, local governments and the public. In each game, an individual is randomly selected from the three groups to play the game.

Hypothesis 1. The set of corporate strategies related to the sharing economy is S1 = {active participation, not active participation}. ‘Active participation’ means that sharing economy-related enterprises actively participate in the collaborative supervision of the sharing economy industry through a series of technical supervision means; ‘inactive participation’ means that sharing economy-related enterprises take speculative behaviours and do not follow market rules. The local government policy set is S2 = {supervision, no supervision}. ‘Supervision’ means that local governments issue relevant policies and management measures to encourage relevant economies to actively participate in supervision; ‘non-supervision’ means that the government does not take any action to intervene in the supervision of relevant economies. The public policy set is S3 = {active participation, not active participation}. ‘Active participation’ refers to the public's subjective publicity and protection of the relevant sharing economic system in various ways in daily life, apart from providing feedback to enterprises and governments, thus assisting sharing economy-related enterprises in supervision; ‘non-active participation’ refers to the public taking on speculative behaviours and disrupting the market order. Therefore, there are a total of eight game strategy combinations among enterprises, the government and the public related to the sharing economy.

Hypothesis 2. The probability of active participation of sharing economy-related enterprises is x, and the probability of non-active participation is 1−x. The probability of local government regulation is y, and the probability of non-regulation is 1−y. The probability of active participation of the public is z, and the probability of inactive participation is 1 − z. The values of x, y and z are all between zero and one.

Hypothesis 3. When the local government chooses the ‘supervision’ strategy, the positive social benefits (R1 or R2) generated by the active participation of the sharing economy-related enterprises and the public in collaborative supervision belong to the local government; when the sharing economy-related enterprises and the public do not actively participate in the collaborative supervision, the social benefit of the local government is zero, and the local government will not get social benefits if it chooses ‘no regulation.’ If sharing economy-related enterprises and the public choose to actively participate in the strategy of collaborative supervision and if the local government chooses the supervision strategy, the sharing economy-related enterprises and the public will receive government subsidies; if the local government chooses not to supervise, or if the sharing economy-related enterprises and the public do not actively participate in collaborative supervision, the enterprises and the public related to the sharing economy will not receive government subsidies. If the sharing economy-related enterprises and the public choose not to actively participate, there will be speculative behaviours such as wanton price hikes. If the local government chooses to ‘regulate,’ the sharing economy-related enterprises and the public will be punished; if the local government chooses to ‘not supervise,’ the sharing economy-relevant businesses and the public will not be penalised.

Assumption 2. According to the above parameter settings in the model, the income matrix of the sharing economy-related enterprises, local governments and the public under eight strategies can be calculated as shown in Table 1.

Table 1

The benefit matrix of sharing economy-related enterprises, local governments and the public under eight strategies

A	Business benefit
F	Corporate punishment
P	Probability of violation
U	Government budget
H	Government cost
B	Cost of government remediation
Q	Government oversight probability
T	Business loss
D	Government losses
I	Social regulation probability

Assumption 3. Define the model parameters and their meanings (Table 2). All parameters are positive values. The following S1 and S2 represent the gains from speculative behaviours of sharing economy-related companies and the public, and W represents the gains from the sharing economy-related companies’ active participation in collaborative management. C1 is the cost of the active participation of enterprises related to the sharing economy, C2 is the cost of the public's active participation, C3 is the cost of local government supervision, C4 is the cost of the public's active participation in the collaborative management for sharing economy-related enterprises, R1 and R2 represent sharing of the social benefits obtained by economic-related enterprises or the public actively participating in the collaborative management of the government and the social benefits obtained by both parties actively participating in the collaborative management of the government. G1 and G2 respectively indicate that when the local government is supervised, the sharing economy-related enterprises and the public actively participate in the collaborative management. P1 and P2 represent the punishment for the speculative behaviours of sharing economy-related enterprises and the public when the local governments are supervised, respectively, and L1 and L2 represent the reputation benefits gained from the active participation of sharing economy and local government-related enterprises in collaborative management.

Table 2

Definition of model parameters and their meanings

Strategy mix	Renewable resource companies’ benefit	Public benefit

Active participation, supervision, active participation	C₄ − C₁ + G₁ + W +L₁	−C₃ + R₂ + L₂	−C₂ + G₂
Active participation, supervision, passive participation		−C₃ + R₁ + L₂	S₂ −P₂
Active participation, no regulation, active participation	C₄ − C₁ +W + L₁	0	−C₂
Active participation, no supervision, passive participation	−C₁ +W + L₁	0	S₂
Passive participation, supervision, active participation	S₁ − P₁	−C₃ + R₁ + L₂	−C₂ + G₂
Passive participation, regulation, passive participation	S₁ − P₁	−C₃ + L₂	S₂ − P₂
Passive participation, no supervision, active participation	S₁	0	−C₂
Passive participation, no regulation, passive participation	S₁	0	0

In order to explore the important role of public participation in co-operative supervision and to better build a multi-disciplinary co-operative supervision governance system, this study continues to add the public as a subject to the game model [20]. In this case, the extended form of the tripartite game between government departments, enterprises and the public is shown in Figure 1:

Three-party game model under public participation

3.2

Construction of evolutionary game model

3.2.1

Expected benefits of enterprises related to the sharing economy

Assuming that the expected revenue of sharing economy-related companies choosing the ‘active participation’ strategy is U₁₁, the expected revenue of sharing economy-related companies choosing the ‘inactive participation’ strategy is U₁₂ and the average expected revenue is U₁, then we have the following relations: (1) $\begin{array}{l} U_{11} & = yz (C_{4} - C_{1} + G_{1} + W + L_{1}) + y (1 - z) (- C_{1} + G_{1} + W + L_{1}) + (1 - y) z (C_{4} - C_{1} + W + L_{1}) \\ + (1 - y) (1 - z) (- C_{1} + W + L_{1}) = G_{1} y + C_{4} z + W - C_{1} + L_{1} \end{array}$ \matrix{{{U_{11}}} \hfill & {= yz\left({{C_4} - {C_1} + {G_1} + W + {L_1}} \right) + y(1 - z)\left({- {C_1} + {G_1} + W + {L_1}} \right) + (1 - y)z\left({{C_4} - {C_1} + W + {L_1}} \right)} \hfill \cr {} \hfill & {+ (1 - y)(1 - z)\left({- {C_1} + W + {L_1}} \right) = {G_1}y + {C_4}z + W - {C_1} + {L_1}} \hfill \cr} (2) $U_{12} = yz (S_{1} - P_{1}) + y (1 - z) (S_{1} - P_{1}) + (1 - y) z S_{1} + (1 - y) (1 - z) S_{1} = S_{1} - P_{1} y$ {U_{12}} = yz\left({{S_1} - {P_1}} \right) + y(1 - z)\left({{S_1} - {P_1}} \right) + (1 - y)z{S_1} + (1 - y)(1 - z){S_1} = {S_1} - {P_1}y (3) $U_{1} = x U_{11} + (1 - x) U_{12} = x (G_{1} y + C_{4} z + W - C_{1} + L_{1}) + (1 - x) (S_{1} - P_{1} y)$ {U_1} = x{U_{11}} + (1 - x){U_{12}} = x\left({{G_1}y + {C_4}z + W - {C_1} + {L_1}} \right) + (1 - x)\left({{S_1} - {P_1}y} \right)

3.2.2

Expected benefits of local governments

Assuming that the expected return of the local government choosing the ‘regulatory’ strategy is U₂₁, the expected return of the local government choosing the ‘non-regulation’ strategy is U₂₂ and the average expected return is U₂, then we get the following: (4) $\begin{array}{l} U_{21} & = xz (- C_{3} + R_{2} + L_{2}) + x (1 - z) (- C_{3} + R_{1} + L_{2}) + (1 - x) z (- C_{3} + R_{1} + L_{2}) \\ + (1 - x) (1 - z) (- C_{3} + L_{2}) = (R_{2} - 2 R_{1}) xz + R_{1} (x + z) - C_{3} + L_{2} \end{array}$ \matrix{{{U_{21}}} \hfill & {= xz\left({- {C_3} + {R_2} + {L_2}} \right) + x(1 - z)\left({- {C_3} + {R_1} + {L_2}} \right) + (1 - x)z\left({- {C_3} + {R_1} + {L_2}} \right)} \hfill \cr {} \hfill & {+ (1 - x)(1 - z)\left({- {C_3} + {L_2}} \right) = \left({{R_2} - 2{R_1}} \right)xz + {R_1}(x + z) - {C_3} + {L_2}} \hfill \cr} (5) $U_{22} = 0$ {U_{22}} = 0 (6) $U_{2} = y U_{21} + (1 - y) U_{22} = (R_{2} - 2 R_{1}) xyz + R_{1} (x + z) y - C_{3} y + L_{2} y$ {U_2} = y{U_{21}} + (1 - y)\quad {U_{22}} = \left({{R_2} - 2{R_1}} \right)xyz + {R_1}(x + z)y - {C_3}y + {L_2}y

3.2.3

Expected benefits of the public

Assuming that the expected benefit of the public choosing the ‘active participation’ strategy is U₃₁, the expected benefit of the public choosing the ‘inactive participation’ strategy is U₃₂ and the average expected benefit is U₃, we get the following expressions: (7) $U_{31} = xy (G_{2} - C_{2}) + x (1 - y) (- C_{2}) + (1 - x) y (G_{2} - C_{2}) + (1 - x) (1 - y) (- C_{2}) = G_{2} y - C_{2}$ {U_{31}} = xy\left({{G_2} - {C_2}} \right) + x(1 - y)\left({- {C_2}} \right) + (1 - x)y\left({{G_2} - {C_2}} \right) + (1 - x)(1 - y)\left({- {C_2}} \right) = {G_2}y - {C_2} (8) $U_{32} = xy (S_{2} - P_{2}) + x (1 - y) (S_{2}) + (1 - x) y (S_{2} - P_{2}) + (1 - x) (1 - y) (S_{2}) = - P_{2} y + S_{2}$ {U_{32}} = xy\left({{S_2} - {P_2}} \right) + x(1 - y)\left({{S_2}} \right) + (1 - x)y\left({{S_2} - {P_2}} \right) + (1 - x)(1 - y)\left({{S_2}} \right) = - {P_2}y + {S_2} (9) $U_{3} = z U_{31} + (1 - z) U_{32} = z (G_{2} y - C_{2}) + (1 - z) (- P_{2} y + S_{2})$ {U_3} = z{U_{31}} + (1 - z){U_{32}} = z\left({{G_2}y - {C_2}} \right) + (1 - z)\left({- {P_2}y + {S_2}} \right)

Based on the above assumptions and calculations of the model, a replication dynamic analysis is carried out on the proportion of the government adopting the ‘regulatory’ strategy and the proportion of the sharing economy-related enterprises and the public adopting the ‘active participation’ strategy.

The replication dynamic equation of sharing economy-related enterprises is as follows: (10) $F (x) = \frac{dx}{dt} = x (U_{11} - U_{1}) = x (1 - x) (G_{1} y + C_{4} z + W - C_{1} + L_{1} - S_{1} + P_{1} y)$ F(x) = {{dx} \over {dt}} = x\left({{U_{11}} - {U_1}} \right) = x(1 - x)\left({{G_1}y + {C_4}z + W - {C_1} + {L_1} - {S_1} + {P_1}y} \right)

The replication dynamic equation of the local government is as follows: (11) $F (y) = \frac{dy}{dt} = y (U_{21} - U_{2}) = y (1 - y) [(R_{2} - 2 R_{1}) xz + R_{1} (x + z) - C_{3} + L_{2}]$ F(y) = {{dy} \over {dt}} = y\left({{U_{21}} - {U_2}} \right) = y(1 - y)\left[{\left({{R_2} - 2{R_1}} \right)xz + {R_1}(x + z) - {C_3} + {L_2}} \right]

The replication dynamic equation of the public is as follows: $F (z) = \frac{dz}{dt} = z (U_{31} - U_{3}) = z (1 - z) (G_{2} y - C_{2} + P_{2} y - S_{2})$ F(z) = {{dz} \over {dt}} = z\left({{U_{31}} - {U_3}} \right) = z(1 - z)\left({{G_2}y - {C_2} + {P_2}y - {S_2}} \right)

In Eq. (6), EB,i, Φ_EB,i and P_EB,i represent the output thermal power, conversion efficiency, electrical power consumed and the number of electric boilers, respectively.

3.2.4

Gas boiler model

Gas boilers are different from electric boilers. Electric boilers use electricity as the main energy source, while gas boilers use natural gas as the main energy source. The operating principle is as follows: after natural gas is input to the gas boiler, the boiler will burn the natural gas. When the water temperature reaches the standard value, it will form hot water or steam, and the gas boiler will send this hot water and steam to the outside. Gas boilers not only have higher heating efficiency than electric boilers (the conversion rate even reaches 99% [21]) but also can reduce pollutant emissions, so they are more suitable than electric boilers. The relationship between the amount of natural gas consumed by the gas boiler per unit time and the output thermal power is as follows: (12) $F_{GB, i} = \frac{Φ_{GB, i}}{GHV \times η_{GB, i}}, \forall i = 1, 2, \dots, N_{gb}$ {F_{GB,i}} = {{{\Phi _{GB,i}}} \over {GHV \times {\eta _{GB,i}}}},\quad \forall i = 1,2, \ldots,{N_{gb}}

Network model of subsystems of integrated energy system

4.1

Network model of power subsystem

There are two kinds of co-ordinates in the non-linear power flow equation of the power system (the rectangular co-ordinates and the polar co-ordinates), but the active power P_i and reactive power Q_i will be calculated using the polar co-ordinates. The calculation formula is as follows: (13) $P_{i} = V_{i} \sum_{j = 1}^{Ne} V_{j} (G_{ij} cos θ_{ij} + B_{ij} sin θ_{ij}), \forall i = 1, 2, N_{e}$ {P_i} = {V_i}\sum\limits_{j = 1}^{Ne} {V_j}({G_{ij}}\cos {\theta _{ij}} + {B_{ij}}\sin {\theta _{ij}}),\forall i = 1,2,{N_e} (14) $Q_{i} = V_{i} \sum_{j = 1}^{Ne} V_{j} (G_{ij} sin θ_{ij} - B_{ij} cos θ_{ij}), \forall = 1, 2, N_{e}$ {Q_i} = {V_i}\sum\limits_{j = 1}^{Ne} {V_j}({G_{ij}}\sin {\theta _{ij}} - {B_{ij}}\cos {\theta _{ij}}),\forall = 1,2,{N_e}

In Eq. (14), V_i, θ_ij, G_ij, B_ij, and Ne represent the voltage amplitude, voltage phase angle difference, real part of node derivative element, imaginary part of point derivative element and the number of power system nodes, respectively.

4.2

Network model of natural gas subsystem

Gas pipelines, compressors, gas sources and gas loads together form a natural gas system [22]. Gas sources are classified into gas fields and shale gas. Gas pipelines are responsible for natural gas transportation. Long-distance gas pipelines are usually buried underground. The compressor exists to make up for the pressure loss of natural gas during the transmission process, and it plays the role of boosting or reducing pressure at different positions. The network model of natural gas mainly considers the pipeline flow model and the compressor model, and the pipeline flow F_mn can be expressed as follows: (15) $F_{mn} = K_{r} s_{mn} \sqrt{s_{mn} (π_{m}^{2} - π_{n}^{2})}, \forall r = 1, 2, \dots, N_{p}$ {F_{mn}} = {K_r}{s_{mn}}\sqrt {{s_{mn}}(\pi _m^2 - \pi _n^2)},\forall r = 1,2, \ldots,{N_p} (16) $S_{mn} = {\begin{matrix} + 1, & π_{m} - π_{n} \geq 0 \\ - 1, & π_{m} - π_{n} 0 \end{matrix}$ {S_{mn}} = \left\{{\matrix{{+ 1,} & {{\pi _m} - {\pi _n} \ge 0} \cr {- 1,} & {{\pi _m} - {\pi _n}0} \cr}} \right.

In the formula, m and n are the head node and end node of the gas pipeline, respectively; π_m and π_n are the pressures of the nodes m and n, respectively; S_mn represents the gas flow direction; K_r is the pipeline coefficient of the gas pipeline r. This paper considers all the pipeline coefficients of the gas pipelines as constants; N_p is the number of natural gas pipelines [23]. The electric power H_r and flow rate τ_r consumed by the gas compressor are calculated as follows: (17) $H_{r} = B_{r} C_{r} [{(\frac{π_{n}}{π_{m}})}^{Z_{r} (ε - 1 \ ε)} - 1], \forall r = 1, 2, \dots, N_{r}$ {H_r} = {B_r}{C_r}\left[{{{\left({{{{\pi _n}} \over {{\pi _m}}}} \right)}^{{Z_r}(\varepsilon - 1\backslash \varepsilon)}} - 1} \right],\quad \forall r = 1,2, \ldots,{N_r} (18) $τ_{r} = a_{c, r} + β_{c . r} H_{r} + y_{c, r} H_{r}^{2}, \forall r = 1, 2, \dots, N_{r}$ {\tau _r} = {a_{c,r}} + {\beta _{c.r}}{H_r} + {y_{c,r}}H_r^2,\quad \forall r = 1,2, \ldots,{N_r}

In the expressions, H_r is the electric power consumed by the rth compressor branch, the unit is megawatt (MW); C_r is the flow through the rth compressor branch, the unit is million standard cubic feet of gas per day (MMCFD) [24]; B_r is the compressor of the rth compressor branch coefficient; Z_r is the inlet gas compression factor of the rth compressor branch; ɛ is the adiabatic coefficient; α_c,r, β_c,r and γ_c,r are the compressor consumption coefficients; N_r is the number of compressors.

The calculation formula of the flow of the injected gas F_m at the node m of the natural gas system is as follows: (19) $F_{m} = \sum_{r = 1}^{N_{p}} B_{mr} L_{r} + \sum_{r = 1}^{N_{r}} E_{mr} C_{r} + \sum_{r = 1}^{N_{r}} T_{mr} τ_{r} \forall m = 1, 2, \dots, N_{m}$ {F_m} = \sum\limits_{r = 1}^{{N_p}} {B_{mr}}{L_r} + \sum\limits_{r = 1}^{{N_r}} {E_{mr}}{C_r} + \sum\limits_{r = 1}^{{N_r}} {T_{mr}}{\tau _r}\forall m = 1,2, \ldots,{N_m}

In the formula, B_mr, E_mr and T_mr are the node–pipeline correlation matrix B, the node–compressor correlation matrix E and the node–compressor inlet node correlation matrix T of the mth row and the rth column element; N_m is the total number of natural gas system nodes.

At time x < (C₃ − L₂ − R₁z)/(R₂z − 2R₁z + R₁), $F^{'} (y_{1}^{*}) < 0$ {F^{'}}\left({y_1^*} \right) < 0 and $F^{'} (y_{2}^{*}) > 0$ {F^{'}}\left({y_2^*} \right) > 0 , $y_{1}^{*} = 0$ y_1^* = 0 in order to stabilise the strategy, i.e. the local government adopts the non-regulatory strategy as the only global evolutionary stabilisation strategy.

At time x > (C₃ − L₂ − R₁z)/(R₂z − 2R₁z + R₁), $F^{'} (y_{1}^{*}) > 0$ {F^{'}}\left({y_1^*} \right) > 0 and $F^{'} (y_{2}^{*}) < 0$ {F^{'}}\left({y_2^*} \right) < 0 , $y_{2}^{*} = 1$ y_2^* = 1 in order to stabilise the strategy, i.e. the local government adopts the supervision strategy as the only global evolutionary stability strategy.

4.3

The public

According to the public replication dynamic expression in Eq. (17) constructed above, the game strategies adopted by the public are as follows:

At time y = (C₂ + S₂)/(G₂ + P₂), F(z) ≡ 0 This shows that no matter which strategy the public chooses, it is a stable strategy and will not change over time.

At time y ≠ (C₂ + S₂)/(G₂ + P₂), $z_{1}^{*} = 0$ z_1^* = 0 and $z_{2}^{*} = 1$ z_2^* = 1 . Two stabilisation strategies make F(z) = 0. F(z) derivation is available: (20) $F^{'} (z) = \frac{\partial (dz / dt)}{\partial z} = (1 - 2 z) (G_{2} y - C_{2} + P_{2} y - S_{2})$ {F^{'}}(z) = {{\partial (dz/dt)} \over {\partial z}} = (1 - 2z)\left({{G_2}y - {C_2} + {P_2}y - {S_2}} \right)

At time y < (C₂ + S₂)/(G₂ + P₂), $F^{'} (z_{1}^{*}) < 0$ {F^{'}}\left({z_1^*} \right) < 0 , $F^{'} (z_{2}^{*}) > 0$ {F^{'}}\left({z_2^*} \right) > 0 and $z_{1}^{*} = 0$ z_1^* = 0 . It is a stable strategy, i.e. the public adopts the strategy of inactive participation as the global unique evolutionary stable strategy.

At time y > (C₂ + S₂)/(G₂ + P₂), $F^{'} (z_{1}^{*}) > 0$ {F^{'}}\left({z_1^*} \right) > 0 , $F^{'} (z_{2}^{*}) < 0$ {F^{'}}\left({z_2^*} \right) < 0 and $z_{2}^{*} = 1$ z_2^* = 1 . It is a stable strategy, i.e. the public adopts an active participation strategy as the global unique evolutionary stable strategy.

From the above analysis, it can be seen that adjusting the relevant parameters makes the tripartite game between enterprises, local governments and the public in the sharing economy evolve to a relatively ideal stable state. Take (active participation, supervision, active participation) as an example: when the value of x is infinitely close to 1.0, indicating that enterprises related to the sharing economy tend to adopt active participation strategies, by reducing C1, reducing S1, increasing P1 and increasing G1, sharing economy-related enterprises can be prompted to take active participation strategies.

At time x > (C₃ − L₂ − R₁z)/(R₂z − 2R₁z + R₁), the value of y is close to 1.0, indicating that local governments tend to adopt regulatory strategies. It can reduce C3, increase L2, improve the reputation of the local government and prompt the local government to adopt a regulatory strategy.

At time y > (C₂ + S₂)/(G₂ + P₂), the value of z is close to 1.0, indicating that the public tends to take an active participation strategy. It can reduce C2, curb S2, increase P1, increase G1 and encourage the public to take an active participation strategy.

4.4

Game equilibrium analysis

4.4.1

Replicating dynamic system builds

Combining the above formulas, the replication dynamic system of sharing economy-related enterprises, local governments and the public is obtained as follows: (21) ${\begin{matrix} F (x) = x (1 - x) (G_{1} y + C_{4} z + W - C_{1} + L_{1} - S_{1} + P_{1} y) \\ F (y) = y (1 - y) [(R_{2} - 2 R_{1}) xz + R_{1} (x + z) - C_{3} + L_{2}] \\ F (z) = z (1 - z) (G_{2} y - C_{2} + P_{2} y - S_{2}) \end{matrix}$ \left\{{\matrix{{F(x) = x(1 - x)\left({{G_1}y + {C_4}z + W - {C_1} + {L_1} - {S_1} + {P_1}y} \right)} \cr {F(y) = y(1 - y)\left[{\left({{R_2} - 2{R_1}} \right)xz + {R_1}(x + z) - {C_3} + {L_2}} \right]} \cr {F(z) = z(1 - z)\left({{G_2}y - {C_2} + {P_2}y - {S_2}} \right)} \cr}} \right.

The Jacobian matrix of the system can be obtained as follows: (22) $\begin{array}{l} J & = [\begin{matrix} \frac{\partial F (x)}{\partial x} & \frac{\partial F (x)}{\partial y} & \frac{\partial F (x)}{\partial z} \\ \frac{\partial F (y)}{\partial x} & \frac{\partial F (y)}{\partial y} & \frac{\partial F (y)}{\partial z} \\ \frac{\partial F (z)}{\partial x} & \frac{\partial F (z)}{\partial y} & \frac{\partial F (z)}{\partial z} \end{matrix}] \\ = 0.95! [\begin{matrix} [(1 - 2 x) (G_{1} y + C_{4} z + W - C_{1} + L_{1} - S_{1} + P_{1} y) & x (1 - x) (G_{1} + P_{1}) & C_{4} x (1 - x) \\ y (1 - y) [(R_{2} - 2 R_{1}) z + R_{1}] & (1 - 2 y) [(R_{2} - 2 R_{1}) xz + R_{1} (x + z) - C_{3} + L_{2}] & y (1 - y) [(R_{2} - 2 R_{1}) x + R_{1}] \\ 0 & z (1 - z) (G_{2} + P_{2}) & (1 - 2 z) (G_{2} y - C_{2} + P_{2} y - S_{2}) \end{matrix}] \end{array}$ \matrix{J \hfill & {= \left[{\matrix{{{{\partial F(x)} \over {\partial x}}} & {{{\partial F(x)} \over {\partial y}}} & {{{\partial F(x)} \over {\partial z}}} \cr {{{\partial F(y)} \over {\partial x}}} & {{{\partial F(y)} \over {\partial y}}} & {{{\partial F(y)} \over {\partial z}}} \cr {{{\partial F(z)} \over {\partial x}}} & {{{\partial F(z)} \over {\partial y}}} & {{{\partial F(z)} \over {\partial z}}} \cr}} \right]} \hfill \cr {} \hfill & {= 0.95!\left[{\matrix{{\left[{(1 - 2x)\left({{G_1}y + {C_4}z + W - {C_1} + {L_1} - {S_1} + {P_1}y} \right)} \right.} & {x(1 - x)\left({{G_1} + {P_1}} \right)} & {{C_4}x(1 - x)} \cr {y(1 - y)\left[{\left({{R_2} - 2{R_1}} \right)z + {R_1}} \right]} & {(1 - 2y)\quad \left[{\left({{R_2} - 2{R_1}} \right)xz + {R_1}(x + z) - {C_3} + {L_2}} \right]} & {y(1 - y)\left[{\left({{R_2} - 2{R_1}} \right)x + {R_1}} \right]} \cr 0 & {z(1 - z)\left({{G_2} + {P_2}} \right)} & {(1 - 2z)\left({{G_2}y - {C_2} + {P_2}y - {S_2}} \right)} \cr}} \right]} \hfill \cr}

According to the system solution, the local equilibrium points are (0, 0, 0), (0, 0, 1), (0, 1, 0), (1, 0, 0), (1, 0, 1), (1), 1, 0), (0, 1, 1) and (1, 1, 1). In evolutionary game theory, the equilibrium point where all the eigenvalues of the Jacobian matrix are non-periodic is the evolutionary stable point of the system.

4.4.2

Stability analysis of equilibrium point

The Jacobian matrix of the system at the equilibrium point (1, 1, 1) is as follows: (23) $J_{(1, 1, 1)} = [\begin{matrix} - (G_{1} + C_{4} + W - C_{1} + L_{1} - S_{1} + P_{1}) & 0 & 0 \\ 0 & C_{3} - R_{2} - L_{2} & 0 \\ 0 & 0 & - (G_{2} - C_{2} + P_{2} - S_{2}) \end{matrix}]$ {J_{(1,1,1)}} = \left[{\matrix{{- \left({{G_1} + {C_4} + W - {C_1} + {L_1} - {S_1} + {P_1}} \right)} & 0 & 0 \cr 0 & {{C_3} - {R_2} - {L_2}} & 0 \cr 0 & 0 & {- \left({{G_2} - {C_2} + {P_2} - {S_2}} \right)} \cr}} \right]

From the above formula, the eigenvalues of the Jacobian matrix are the following: (24) $λ_{1} = - (G_{1} + C_{4} + W - C_{1} + L_{1} - S_{1} + P_{1})$ {\lambda _1} = - \left({{G_1} + {C_4} + W - {C_1} + {L_1} - {S_1} + {P_1}} \right) (25) $λ_{2} = C_{3} - R_{2} - L_{2}, λ_{3} = - (G_{2} - C_{2} + P_{2} - S_{2})$ {\lambda _2} = {C_3} - {R_2} - {L_2},{\lambda _3} = - \left({{G_2} - {C_2} + {P_2} - {S_2}} \right)

When the local government chooses the supervision strategy, and the sharing economy-related enterprises and the public choose the active participation strategy, the equilibrium point (1, 1, 1) of the system is the equilibrium point of evolution and stability, and λ 1, λ 2 and λ 3 must all be less than zero.

In the development process of an evolutionary game event, many influencing factors affect the strategic choices of enterprises, local governments and the public in the sharing economy. The change of a certain influencing factor will lead to changes in the strategic choice of at least one participant and the enterprise. The behaviour strategies of the government and the public are related, which will lead to continuous adjustment of the strategic choices of the corporate entity, government and the public. From the direction of maximising the interests of all game subjects, we can analyse the strategy (1, 1, 1). It is a situation that is beneficial to all three types of participants. Due to the needs of the development of circular economy, my country has strictly restricted the import of solid waste, and industries related to the sharing economy want to make up for the gap in supply and stabilise the price of upstream raw materials, and they urgently need to actively conduct technical supervision. The supervision of industrial operation management with the help of a new generation of Internet technology is one of the development trends. At the same time, in order to provide public recognition, local governments will actively participate in collaborative supervision by increasing financial subsidies to enterprises related to the sharing economy. Many cities across the country have begun to establish a sharing economic system. Therefore, the equilibrium point (1, 1, 1) is the most ideal development state, and its corresponding evolutionary game strategy is (active participation, supervision, active participation).

Numerical simulation analysis

Through the above analysis, we can see that under the condition of bounded rationality, the most suitable strategy choice for the evolutionary game enterprise, government and the public is (active participation, supervision, active participation).

G1=2, 4; G2=2, 4, i.e. the evolution of the equilibrium strategy of the corporate, government and the public after the government subsidies change is shown in Figure 2.

In general, the government's subsidy policy has a significant impact on the evolution of the public's strategy, and the local government's subsidy intensity is proportional to the speed at which sharing economy-related enterprises and the public converge to actively participate in the collaborative supervision strategy. Different initial probabilities also have a clear impact on the convergence speed of government, enterprises and the public. When the local government subsidy is large, although the initial probability of public participation in collaborative management is low, it will eventually tend to actively participate in collaborative management.

R1=1, 2; R2=2, 4. That is, after the social benefits of local governments change, the evolution of the equilibrium strategy is shown in Figure 3.

It can be seen from Figure 3 that changes in the social benefits of local governments have a significant impact on the strategic evolution of the corporate, government and the public, and they are positively correlated.

From the overall analysis of the data, it can be found that the choice of strategies between government, enterprises and the public is interactive and has a certain correlation mechanism.

Evolution curve of social benefit impact

However, because the actual economic strength and membership size of each participant are different, when a parameter change causes a change in the strategy choice of one of the participants, the evolutionary stable strategy will only be closer to (1, 1, 1), and the public will not respond to the parameter change. The sensitivity is higher, and different initial probabilities will affect the convergence speed of the participants and are positively correlated.

Conclusion

First of all, the strategic choices between the game subjects in the game model will affect each other, and the three-party relationship is developed in co-ordination, i.e. the evolutionary stable strategy is (active participation, supervision, active participation).

To encourage and attract the public to actively participate in collaborative supervision, the government can spread the relevant policies of the sharing economy through multiple channels, so that the public can better participate in the sharing economy system. Companies should also vigorously promote their own sharing economy platforms to encourage public participation. Therefore, local governments should take the lead, be led by enterprises, and the public should co-operate and assist local governments and enterprises to participate in the co-ordinated supervision of the sharing economy.

Figures & Tables

The benefit matrix of sharing economy-related enterprises, local governments and the public under eight strategies

A	Business benefit
F	Corporate punishment
P	Probability of violation
U	Government budget
H	Government cost
B	Cost of government remediation
Q	Government oversight probability
T	Business loss
D	Government losses
I	Social regulation probability

Definition of model parameters and their meanings

Strategy mix	Renewable resource companies’ benefit	Public benefit

Active participation, supervision, active participation	C₄ − C₁ + G₁ + W +L₁	−C₃ + R₂ + L₂	−C₂ + G₂
Active participation, supervision, passive participation		−C₃ + R₁ + L₂	S₂ −P₂
Active participation, no regulation, active participation	C₄ − C₁ +W + L₁	0	−C₂
Active participation, no supervision, passive participation	−C₁ +W + L₁	0	S₂
Passive participation, supervision, active participation	S₁ − P₁	−C₃ + R₁ + L₂	−C₂ + G₂
Passive participation, regulation, passive participation	S₁ − P₁	−C₃ + L₂	S₂ − P₂
Passive participation, no supervision, active participation	S₁	0	−C₂
Passive participation, no regulation, passive participation	S₁	0	0

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Applied Mathematics and Nonlinear Sciences

Research on the driving principle and guiding strategy of the public's collaborative supervision of the sharing economy in my country

Jing Su
Jing Su

Published Online: 14 Nov 2022

Volume & Issue: AHEAD OF PRINT

Page range: -

Received: 08 May 2022

Accepted: 08 Jul 2022

Journal & Issue Details

Applied Mathematics and Nonlinear Sciences

PDF Preview

Article

Fig. 1

Fig. 2

Fig. 3

Figures & Tables

Fig. 1

Fig. 2

Fig. 3

The benefit matrix of sharing economy-related enterprises, local governments and the public under eight strategies

Definition of model parameters and their meanings

References

Recent Articles

Applied Mathematics and Nonlinear Sciences

Research on the driving principle and guiding strategy of the public's collaborative supervision of the sharing economy in my country

Jing SuJing Su

Published Online: 14 Nov 2022

Volume & Issue: AHEAD OF PRINT

Page range: -

Received: 08 May 2022

Accepted: 08 Jul 2022

Journal & Issue Details

Applied Mathematics and Nonlinear Sciences

PDF Preview

Article

Fig. 1

Fig. 2

Fig. 3

Figures & Tables

Fig. 1

Fig. 2

Fig. 3

The benefit matrix of sharing economy-related enterprises, local governments and the public under eight strategies

Definition of model parameters and their meanings

References

Recent Articles

Jing Su
Jing Su