Research on Community Sports Governance Based on the Participation of Multiple Subjects

The urban community is the basic cell of the public service system of national fitness and has long been a shortcoming. Therefore, the governance of public sports services in urban communities is the “key and difficult point” that constrains China’s national strategy of promoting national fitness and the goal of building a strong sports nation [1-2]. The traditional model of unilateral rough governance by the government has been difficult to adapt to the current development needs, and there is a need to change the traditional governance model and promote the modernization of the governance system and governance capacity of the public sports services in urban communities with the idea of intelligent governance for improvement [3-6]. Adhering to the underlying logic of combining “digital transformation” and “demand-oriented”, a technical structure of community sports service governance integrating “people, technology, and space” is constructed, so as to promote the modernization of community sports service governance in China [7-10].

Urban community sports public service governance as an important part of grassroots social governance, build urban community sports public service governance synergy, give full play to the power of multiple subjects of co-governance, is to meet the upgrade of community residents’ sports demand, to achieve the equalization of community sports public service effective path [11-14]. The construction of a new pattern of social governance in the new era cannot be separated from the joint participation of multiple subjects [15]. The implementation of the concerted participation of multiple subjects in the governance of public sports services is an important part of the construction of the innovative Chinese sports governance system, and its core issue is the realization of the structural relationship between multiple subjects such as the government, the market, the society and individuals and the governance of public sports services [16-18]. Among them, the construction of community sports service intelligent governance system with the help of digital technology can solve the problem of accurate supply of sports services that cannot be realized in traditional governance, thus improving the efficiency of governance [19-21]. Through the reshaping of the subject relationship, multiple subjects can realize reciprocal collaboration and form governance synergy under the support of equal status [22-23]. Through the construction of governance platform, it can realize the reconstruction of community space and provide new kinetic energy for the governance of community sports services [24-25].

Multi-subject collaborative governance in the field of sports is conducive to giving full play to the different characteristics of different subjects, alleviating the governance dilemma of the government “taking care of everything”, and devoting more resources to the key areas of sports [26-27]. To realize the organic cooperation of governance between different subjects, and finally build a new governance pattern.

With the development of community sports service governance in recent years, some scholars have proposed that the future governance of community sports services must be based on a governance platform as a hub, through information sharing, to realize the collaborative governance of multiple subjects. Zha, J. explored the effect of governance of community sports centers supported by advanced technological means, and the combination of technologies such as the Internet of Matters and big data, which can give full play to the advantages of information resources, and significantly improve community management efficiency in the supervision of sports facilities and governance of public sports services [28]. Gao, Y. et al. examined the networked governance model of sports services, taking multiple institutions such as government and universities as service objects, establishing a model of sports service supply structure, and realizing the synergistic participation of multiple subjects in the governance of community sports services through the construction of an information security mechanism and an information-sharing system, which provided valuable reference for the development of the networked management of sports business [29]. Wang, J. et al. constructed a public service platform based on the Internet communication system, utilizing Internet channels and media terminals to distribute content to information subjects, enabling information to be shared at the nodes with high efficiency, and facilitating the development of informationization of public sports services [30]. Qiao, J. Using big data analysis technology to study public sports service management data, on the basis of objective description and analysis, combining knowledge mapping and intelligent algorithms to optimize the public sports service management measures, and promote the forward development of public sports service [31]. Sharma, A. et al. showed that digital technology facilitates the enhancement of the dynamics of users’ participation in sports within the community, and that it is important for the development of community sports management through the creation of a community management application that attracts sports enthusiasts to communicate, organize, and participate in an information platform [32]. Yu, L. proposed an online-to-offline sports community that utilizes mobile internet technology to create an online platform for user communication, which subsequently evolves to an offline experience, and incorporates data analytics to detect, organize, and evaluate data generated by the sports community, which helps to enhance the effectiveness of sports activities in the community [33]. Hao, Y. et al. explored the feasibility of public sports service innovation strategies supported by cloud computing technology, and the edge computing-based public sports service innovation system gained high satisfaction in community sports governance [34]. Wang, C. et al. analyzed the dilemmas faced by community sports pension services, introduced social embeddedness theory and digital governance theory, and relied on modern information technology and infrastructure construction to realize the intelligent transformation of public sports services, which effectively improved the governance efficiency and service quality [35]. Liu, C. et al. studied community sports development measures based on IoT system, which utilized IoT technology to digitally manage public health services, and the health service system for the elderly established on this basis was effective in improving physical fitness of the elderly and community sports participation [36]. Abinesh, R. et al. created a sports mobile application for the university community that can provide comprehensive sports-related information to multiple subjects, which is conducive to enhancing user experience, promoting sports participation, etc., and effectively meets the needs of sports management in the university community environment [37]. This means that while material-level technology is important, supporting sports service governance through the application of material-level technology alone is not sufficient to support community sports governance, and realizing the innovation of multiple subjects’ synergy and bottom-up governance model is the key to community sports service governance.

The purpose of this paper is to explain the operation mechanism of community sports supply by analyzing the game process when multiple subjects participate in community sports governance, in order to improve the efficiency and participation of each subject when they carry out community sports governance. The basic hypotheses are formulated around the regulator, supplier and demand side of community sports services, and the payoff matrix of the game is constructed. Replicated dynamic equations are solved for the game matrix and the tripartite payoff tree model to derive the game equilibrium points of the three governance subjects respectively. The Jacobian matrix is constructed, and the combination analysis of evolutionary stable governance strategies is carried out to analyze the changes in the returns of different participating subjects under the three scenarios. On this basis, simulation is carried out to analyze the evolutionary stable strategies of each governance subject under multiple scenarios, and the effects of different governance conditions on the evolutionary results are examined.

2

The game model of community sports governance with the participation of multiple actors

2.1

Basic assumptions

In order to facilitate the construction of the evolutionary game model of the core interests of community sports governance, combined with the actual situation of the current community sports governance, the following assumptions are made on the basis of the mutual constraints, mutual influence and limited rationality of each stakeholder subject:

Hypothesis 1: Choose the sports regulator, the community sports service supplier and the demand side as the game subjects. The strategy space of the regulator’s participation in governance is strict regulation and lax regulation, with g denoting the probability that the regulator chooses the strict regulation strategy, and 1-g denoting the probability that it chooses the lax regulation strategy, g ∈ [0,1]. The strategy space of the supply side’s participation in governance is active and passive participation, with r denoting the probability that a service provider such as a sports business actively participates in community sports governance, and 1-r denoting the probability that a sports provider negatively participates in community sports governance, r ∈ [0,1]. The demand side’s strategy space for participation in governance is participation and non-participation, with s denoting the probability that the demand side chooses to actively participate in governance, and 1-s denoting the probability that the demand side chooses not to participate in governance, s ∈ [0,1].

Hypothesis 2: When the regulator adopts a strict regulatory strategy, the cost to be invested is denoted as C₁, and the socio-economic benefits gained by adopting a strict regulatory strategy that leads to the enhancement of community sports governance are denoted as N. For the service provider who actively participates in the governance, an incentive-led reward will be given, denoted as W. For the service provider who negatively participates in the governance, a penalty will be imposed on him/her depending on the specific situation, denoted as F. When the regulator adopts a lax regulatory strategy, its inaction or ineffectiveness will likely increase the opportunity cost of community sport service governance, thus triggering a competitive effect, denoted as C₂.

Hypothesis 3: Sports enterprises are regarded as community sports service supplying entities that cooperate with each other, complement each other and evolve together. When the supply side chooses to actively participate in community sports governance affairs, let the cost it needs to invest is D₁, and the direct economic benefits it obtains are E₁, and the potential benefits such as residents’ trust and reputation enhancement are F. When the supply side chooses to negatively participate in community sports governance affairs, let the cost it needs to invest is D₂, and the direct economic benefits it obtains are E₂. At this time, in the case that the sports management department chooses to strictly supervise the service, the service provider will not be able to participate in the community sports governance. In this case, if the sports management department chooses to strictly supervise the situation, the service provider will suffer from the loss of residents’ image and social trust, which is recorded as G.

Hypothesis 4: When community residents choose to actively participate in community sports governance, they need to invest a certain amount of time cost, energy cost and economic cost, etc., which is recorded as L, and gain pleasure experience, sense of value and sense of acquisition, etc., which is M. The sports management department maintains the incentives such as issuing sports consumption vouchers, honorary awards, and beautiful gifts, etc., which is recorded as O. When the community residents choose to actively participate in community sports governance strategy, the community residents will get a better experience, which is recorded as E₂. When community residents choose to actively participate in the community sports governance strategy, they will obtain additional benefits such as better service experience and product quality as H₁. When community residents choose not to participate in the community sports governance strategy, they can also obtain certain potential benefits, which are recorded as H₂.

2.2

Modeling

Combined with the content of the assumptions, induction combing the selection strategy, selection probability, and profit and loss variables of each stakeholder subject, we can derive the benefit matrix of the three-party evolutionary game of the sports regulator, the supply side of community sports services and the demand side, as shown in Table 1.

Table 1.

The income matrix of the evolutionary game

		Consumer	Regulator
		Consumer	Strict regulation g	Loose regulation 1 − g
Supplier	Active participation r	Participated s	N − C₁ − W − O	−C₂
			E₁ + W + F − D₁	E₁ + F − D₁
			M + O + H₁ − L	M + H_l − L
		Not participated 1 − s	N − C₁ − W	−C₂
			E₁ + W − D₁	E₁ − D₁
			H₂	H₂
	Negative participation 1 − r	Participated s	N + K − C₁ − O	−C₂
			E₂ − D₂ − G − K	E₂ − D₂ − G
			M + O − L	M − L
		Not participated 1 − s	N + K − C₁	−C₂
			E₂ − D₂ − K	E₂ − D₂
			H₂	H₂

2.3

Model construction and solution

According to the Evolutionary Game Matrix and Evolutionary Game Tripartite Benefit Tree Model [38], the average benefits as well as the expected benefits of community sport governance, government, and the demand side are calculated, and then the tripartite replication dynamic equation is constructed.

2.3.1

Replicating the dynamic equation of community sport governance and its equilibrium points

On this basis, the expected and average benefits under different responses are measured using the evolutionary response matrix and the tripartite benefit tree of evolutionary responses, respectively, and the replicated dynamic equations of evolutionary responses are established on this basis.

The expected gain of choosing the active participation path for community sports governance is Ey₁: (1) $\begin{array}{l} E y_{1} & = & x [z (R_{E} - C_{1} + P_{E}) \\ + (1 - z) ((R_{E} - C_{1})] \\ + (1 - x) [z (R_{E} - C_{1} + P_{E}) \\ + (1 - z) (R_{E} - C_{1})] \end{array}$

The expected benefit of choosing the negative participation governance path for community sport governance is Ey₂: (2) $\begin{array}{l} E y_{2} & = & x [z (R_{E} - C_{2} - F_{E} - N_{E}) \\ + (1 - z) (R_{E} - C_{2} - F_{E})] \\ + (1 - x) [z (R_{E} - C_{2} - N_{E}) \\ + (1 - z) (R_{E} - c_{2})] \end{array}$

The average benefit of community sport governance decision-making behavior is E_y: (3) $E y = y E y_{1} + (1 - y) E y_{2}$

According to the evolutionary game theory, the replication dynamic equation of community sport governance is: (4) $\begin{array}{l} F (y) & = & \frac{d y}{d t} = y (E y_{1} - E y) \\ = & y (1 - y) [z (N_{E} + P_{E}) + c_{2} - c_{1} + x F_{E}] \end{array}$

Let F(y) = 0, the solution of this equation may be the equilibrium point in the evolutionary game process. 1)

When $z = z_{0} = \frac{C_{1} - C_{2} - x F_{E}}{N_{E} + P_{E}}$ , F(y) ≡ 0, indicates that the combination of strategies chosen for community sports governance does not change over time.

2)

When $z \neq z_{0} = \frac{C_{1} - C_{2} - x F_{E}}{N_{E} + P_{E}}$ , y = 0, y = 1 is two possible equilibrium points, and by the stability theorem for dynamic equations, the point is an equilibrium point in the evolutionary game when $\frac{d F (y)}{d y} < 0$ .

The derivation for F(y) is obtained: (5) $\frac{d F (y)}{d y} = (1 - 2 y) [z (N_{E} + P_{E}) + c_{2} - c_{1} + x F_{E}]$

Case 1: When $0 < z < \frac{C_{1} - C_{2} - x F_{E}}{N_{E} + P_{E}}$ , $\frac{d}{F} (y) d y |_{y = 0} < 0, \frac{d F (y)}{d y} |_{y = 1} > 0$ , then y = 0 is the equilibrium point of the evolutionary game of community sport governance, then the community sport governance tends to choose the decision of “not participating in community sport governance”.

Case 2: When $\frac{C_{1} - C_{2} - x F_{E}}{N_{E} + P_{E}} < z < 1$ , $\frac{d}{F} (y) d y |_{y = 0} > 0, \frac{d F (y)}{d y} |_{y = 1} < 0$ , then y = 1 is the equilibrium point of the evolutionary game of community sports governance, then the community sports governance tends to choose the decision of “active participation in community sports governance”.

2.3.2

The replication dynamic equation for strict government regulation and its equilibrium point

The expected return to the government’s choice of a strict regulatory path is E_x1: (6) $\begin{array}{l} E_{x 1} & = & y [z (E_{G} - W_{1} + P_{G} - S_{1} + R) \\ + (1 - z) (E_{G} - W_{1} + R)] \\ + (1 - y) [z (E_{G} - W_{1} + F_{E} + P_{G} - S_{1}) \\ + (1 - z) (E_{G} - W_{1} + F_{E}) \end{array}$

The government’s expected gain from choosing the deregulation path is E_x2: (7) $\begin{array}{l} E_{x 2} & = & y [z (E_{G} - W_{2} - N_{G} + R) \\ + (1 - z) (E_{G} - W_{2} + R)] \\ + (1 - y) [z (E_{G} - W_{2} - N_{G}) \\ + (1 - z) (E_{G} - W_{2})] \end{array}$

According to evolutionary game theory, the replication dynamic equation for strict government regulation is: (8) $\begin{array}{l} F (x) & = & \frac{d x}{d t} = x (E x_{1} - E x) \\ = & x (1 - x) [z (N_{G} - S_{1} + P_{G}) + W_{2} - W_{1} + y F_{E}] \end{array}$

Let F(x) = 0, the solution to this equation may be the equilibrium point in the evolutionary game process. 1)

When $z = z_{0} = \frac{W_{1} - W_{2} - y F_{E}}{N_{G} - S_{1} + P_{G}}$ , F(x) ≡ 0, means that the combination of strategies chosen by the government does not change over time.

2)

When $z \neq z_{0} = \frac{W_{1} - W_{2} - y F_{E}}{N_{G} - S_{1} + P_{G}}$ , x = 0, x = 1 is two possible equilibrium points, and by the stability theorem of the dynamic equations, it is known that the point is the equilibrium point of the evolutionary game when $\frac{d F (x)}{d x} < 0$ .

This leads to the derivation of F(x): (9) $\frac{d F (x)}{d x} = (1 - 2 x) [z (N_{G} - S_{1} + P_{G}) + W_{2} - W_{1} + y F_{E}]$

Case 1: When $0 < x < \frac{W_{1} - W_{2} - y F_{E}}{N_{G} - S_{1} + P_{G}}$ , $\frac{d}{F} (x) d x | x = 0 < 0, \frac{d F (x)}{d x} | x = 1 > 0$ , then x = 0 is the equilibrium point of the evolutionary game of community sports governance, then the government tends to choose the “deregulation” decision.

Case 2: When $\frac{W_{1} - W_{2} - y F_{E}}{N_{G} - S_{1} + P_{G}} < x < 1$ , $\frac{d}{F} (x) d x |_{x = 0} > 0, \frac{d F (x)}{d x} |_{x = 1} < 0$ , then x = 1 is the equilibrium point of the community sports governance evolution game, then the community sports governance tends to choose “strict supervision” decision.

2.3.3

Replicated dynamic equations for demand-side participation in collaborative governance and their equilibrium points

The expected benefit to the demand side of choosing to participate in the collaborative governance path is E_z1: (10) $\begin{array}{l} E_{z 1} & = & x [y (I_{1} + I_{2} + S_{1} - C_{L}) \\ + (1 - y) (I_{1} + I_{2} + S_{1} - C_{L} - N_{L})] \\ + (1 - x) [y (I_{1} + I_{2})] - C_{L}) \\ + (1 - y) (I_{2} - C_{L} - N_{L}) \end{array}$

The expected benefit of the demand side choosing not to participate in the collaborative governance path is E_z2: (11) $\begin{array}{l} E_{z 2} & = & x [y (I_{1} - N_{L}) + (1 - y) (I_{1} - N_{L}] \\ + (1 - x) [y (I_{1} - N_{L}) - N_{L} (1 - y)] \end{array}$

According to the evolutionary game theory [39], the replication dynamic equation for demand-side participation in collaborative governance is: (12) $\begin{array}{l} F (z) & = & \frac{d z}{d t} = z (E z 1 - E x) \\ = & z (1 - z) (y N_{L} + I_{2} - C_{L} + x S_{1}) \end{array}$

Let F(z) = 0, the solution to this equation may be the equilibrium point in the evolutionary game process. 1)

When $y = y_{o} = \frac{C_{L} - I_{2} - x S_{1}}{N_{L}}$ , F(z) ≡ 0, means that the combination of strategies chosen by the government does not change over time.

2)

When $y \neq y_{o} = \frac{C_{L} - I_{2} - x S_{1}}{N_{L}}$ , z = 0, z = 1 is two possible equilibrium points, and by the stability theorem of the dynamic equations, it is known that the point is the equilibrium point of the evolutionary game when $\frac{d F (z)}{d z} < 0$ .

This leads to the derivation of F(z): (13) $\frac{d F (z)}{d z} = (1 - 2 z) (y N_{L} + I_{2} - C_{L} + x S_{1})$

Scenario 1: When $0 < y < \frac{C_{L} - I_{2} - x S_{1}}{N_{L}}$ , $\frac{d}{F} (z) d z |_{z = 0} < 0, \frac{d F (z)}{d z} |_{z = 1} > 0$ , then z = 0 is the equilibrium point of the demand-side evolutionary game, then the community sport governance tends to choose the decision “not to participate in collaborative governance”.

Scenario 2: When $\frac{C_{L} - I_{2} - x S_{1}}{N_{L}} < y < 1$ , $\frac{d}{F} (z) d z |_{z = 0} > 0, \frac{d F (z)}{d z} |_{z = 1} < 0$ , then z = 1 is the equilibrium point of the demand-side evolution game, then the community sport governance tends to choose “participate in collaborative governance” decision.

2.4

Portfolio Analysis of Evolutionary Stabilization Strategies

Based on the above replicated dynamic equations of the sports regulator, the community sports service supplier and the demand side, let F(g) = 0, F(r) = 0 and F(s) = 0, respectively, we get 9 sets of eligible pure strategy equilibrium points, and the Jacobian matrix of the three-party evolutionary game system is [40]: (14) $[\begin{array}{l} \frac{\partial F (g)}{\partial g} & \frac{\partial F (g)}{\partial r} & \frac{\partial F (g)}{\partial s} \\ \frac{\partial F (r)}{\partial g} & \frac{\partial F (r)}{\partial r} & \frac{\partial F (r)}{\partial s} \\ \frac{\partial F (s)}{\partial g} & \frac{\partial F (s)}{\partial r} & \frac{\partial F (s)}{\partial s} \end{array}]$

The possible equilibrium states of the three-party game subjects are as follows:

Scenario 1: When N < C₁ − C₂ + W and E₁ − D₁ < E₂ − D₂ are satisfied, i.e., the economic benefits gained by the sports regulator by adopting the strategy of strict regulation are less than the costs it pays, and the economic benefits gained by the community sports service supplier by choosing the strategy of active participation are less than the economic benefits gained in the passive participation, (0, 1, 0) is the point of evolutionary stability. At this point, there is lax regulation by the sports regulator, active participation by the community sports service supply side and non-participation by the demand side. In this state, the active participation of sports enterprises and other community sports service suppliers in governance and the provision of quality service experience for community residents are the results expected to be seen by the higher-level sports administration, but the non-participation of community residents may lead to the imbalance of supply and demand for community sports services, the failure of supervision of the government’s purchasing of community sports services, and the failure of evaluating the agency behavior of the sports administration’s purchasing of commissioned sports social organizations, which is not conducive to the sustainable development of community sports governance.

Scenario 2: When N < C₁ − C₂ + O + W is satisfied, i.e., the economic benefits gained by the sport regulator from adopting a strict regulatory strategy are less than the various types of costs it pays, (0, 1, 1) is the stable point of the game’s evolution. At this point, the sports regulator laxly regulates, the community sports service supplier actively participates and the demand side participates. Although this state is a more idealized state, sports enterprises and other service suppliers cooperate and complement each other to hold community games, carry out scientific and technological guidance and provide physical fitness monitoring and other diversified sports services, and community residents and other service demanders take the initiative to express their own demand for sports services and feedback information, which can promote the community sports services to achieve the right match between supply and demand in the short term. However, sports enterprises, as limited rational economic beings, in the absence of effective supervision by sports regulators, will over time jeopardize the universality and public nature of community sports services, which is not conducive to the healthy development of community sports governance. Accordingly, in order to avoid the emergence of illegal and illicit behaviors of sports enterprises in the process of community sports governance, it is indispensable for sports regulators to pay a certain amount of supervision costs for their strong supervision and effective prevention.

Scenario 3: When C₁ − C₂ + O + W < N is satisfied, i.e., the economic benefits gained by the sports regulator by adopting the strategy of strict regulation are greater than the various types of costs it pays, (1, 1, 1) is the stable point of the game’s evolution. In this state, strict regulation by the sports regulator, active participation of community sports service suppliers and demand-side participation is a very ideal state, where the higher-level sports regulator is able to give high priority to the community sports governance, and to provide relevant welfare policies such as financial subsidies, tax exemptions and material support. The supply side, such as sports enterprises, can provide community sports services and related products of high quality and better quality. Community residents are able to exert their subjective initiative and actively express their own demands, realizing the appropriate matching of supply and demand for community sports services.

3

Simulation analysis of community sport governance game models

3.1

Simulation of game models in different contexts

3.1.1

Lax government regulation, active corporate governance and lack of participation by community residents in oversight

Using Matlab2020a software to assign values to the parameters, assuming that C₁=25, C₂=20, C₃=15, E₁=7, E₂=8, E₃=10, H₁=2, H₂=5, H₃=7, H₄=9, L₁=12, L₂=10, L₃=7, and its replicated dynamic equation system evolves 50 times over time, the simulation paths and the results are shown in Figure 1. At this time, the equilibrium point (0, 1, 0) is the evolutionary stable strategy for social forces to participate in community sports governance.

From Figure 1, the scenario is in a stable state when L₁-C₁<0. At this time, the government may choose loose regulation because the higher level government does not pay enough attention to this problem, the public does not know enough about the implementation of the policy and lack of awareness of supervision, so that the government’s loose regulation will suffer less accountability from the higher level government and the loss of social reputation, and is less than the cost of strict regulation, so the government chooses to loose regulation. In the process of collaborative governance, the probability of strict regulation by government departments (X) will gradually decrease to 0 and remain stable, which means that the government departments will evolve from strict regulation to lax regulation according to the benefits in the evolutionary game. When C₂-E₂-H₂-L₃<0, the scenario is in a stable state. At this time, the loss of social reputation brought about by the enterprise’s negative governance is greater than the difference between the cost of positive governance and the social reputation gained by the enterprise and the rewards given by the government in the evaluation of excellence and awards, and the overall benefit of choosing negative governance is damaged, so the enterprise chooses positive governance. The probability of positive governance (Y) will gradually increase to reach 1 and remain stable, indicating that the enterprise will evolve from negative governance to positive governance in the evolutionary game according to the revenue situation. When H₄-C₃<0, the scenario is in a stable state. At this point, the feedback and compensation received from the government department when the demand-side monitoring finds problems is less than the cost of participating in the monitoring, resulting in the demand-side will choose not to participate in the monitoring. The probability of demand-side monitoring (Z) will gradually decrease to 0 and remain stable, indicating that the demand-side will evolve from participation to non-participation depending on the benefits. This indicates that the higher level government should attach great importance to the implementation of the policy and the management of the problem, urge the local government departments to carry out strict supervision, advocate the participation of all walks of life in supervision, enhance the public’s awareness of supervision, and the government departments should give timely feedback and effective compensation when the demand side participates in the supervision, so as to promote the participation of the demand side in the supervision.

3.1.2

Strict government regulation, active corporate governance and lack of community participation in oversight

The simulation paths and results of replicating the system of dynamic equations evolving over time 50 times are shown in Figure 2. The equilibrium point (1, 1, 0) at this time is the evolutionary stable strategy for social forces to participate in community sports governance.

From Figure 2, the scenario is in a steady state when C₁-L₁<0. At this time, the cost paid by the government department to strictly regulate is smaller, and is smaller than the accountability of the higher government and the loss of social reputation suffered by the government department to loosely regulate, then the government department chooses to strictly regulate. In the process of collaborative governance, the probability of strict regulation by the government department (X) will gradually increase and eventually reach 1 and remain stable, indicating that in the evolutionary game, the government department will evolve from lax regulation to strict regulation according to the benefits. When C₂-E₂-H₂-H₃-L₃<0, the scenario is in a stable state. In the case of strict government regulation, the enterprise’s negative governance will be penalized and accountable by the relevant departments, and will affect the enterprise’s social reputation, and the sum of the two will lead to a larger loss of the enterprise’s gains from negative governance, so the enterprise chooses to govern positively. The probability of positive corporate governance (Y) will gradually increase and eventually reach 1 and remain stable, indicating that the enterprise will evolve from negative governance to positive governance in the evolutionary game according to the revenue situation. When H₄-C₃<0, the scenario is in a stable state. At this time, community residents may choose not to participate in supervision due to the reason that the supervision mechanism is not smooth and the feedback effect is not good, resulting in the community residents to participate in the supervision of the cost is larger and greater than the participation in the supervision of the discovery of the problem of the government departments of the feedback and compensation, leading to community residents to choose not to participate in the supervision. The probability of community residents’ participation in supervision (Z) will gradually decrease and eventually fall to 0 and remain stable, indicating that in the evolutionary game community residents will evolve from participating in supervision to not participating in supervision according to the benefits. This shows that the establishment of a smooth monitoring and feedback mechanism to reduce the cost of community residents’ participation in monitoring can promote better participation in governance and improve the effect of collaborative governance. The degree of punishment and accountability for the problems of negative corporate governance in the strict supervision of government departments directly affects the choice of corporate governance strategies, and the strict supervision of government departments effectively promotes the positive governance of enterprises.

3.1.3

Lax government regulation, active corporate governance, and participation of community residents in monitoring

The simulation paths and results of replicating the system of dynamic equations evolving over time 50 times are shown in Figure 3. The equilibrium point (0, 1, 1) at this time is the evolutionary stable strategy of the collaborative governance system of social forces involved in corporate sports governance.

The probability (X) of strict regulation by government departments in the process of collaborative governance will gradually decrease and eventually fall to 0 and remain stable, indicating that the government departments will evolve from strict regulation to lax regulation in the evolutionary game according to the benefits. When L₁-C₁<0, the scenario is in a stable state. At this time, it may be due to the government regulation involves more departments, the synergistic effect between the departments is not good, resulting in the government strict regulation of the cost is larger, and greater than the government lax regulation by the accountability of the higher level of government and the loss of social reputation, then the government departments choose to lax regulation. When C₂-E₂-H₁-H₂-L₃<0, the scenario is in a stable state. Community residents participate in supervision when the negative governance of the enterprise after the problems caused by the interests of community residents, the community residents will demand compensation from the enterprise, and the impact on the social reputation of the enterprise to bring losses, so the enterprise will choose positive governance. The probability of positive governance (Y) will gradually increase to reach 1 and remain stable, indicating that the enterprise will evolve from negative governance to positive governance according to the benefits in the evolutionary game. When C₃-H₄<0, the scenario is in a stable state. At this time, community residents participate in monitoring the discovery of problems when the government compensation received is greater than the cost paid, then community residents choose to participate in monitoring. The probability of community residents’ participation in monitoring (Z) will gradually increase and eventually reach 1 and remain stable, indicating that community residents will evolve from non-participation to participation in monitoring according to the benefits in the evolutionary game. This indicates that improving the coordination and collaboration between government departments can effectively help the government reduce the cost of supervision, which is conducive to the efficiency of government participation in collaborative governance. The active participation of community residents in supervision can effectively safeguard their own interests and urge enterprises to actively manage the problem of social forces participating in corporate sports governance.

3.2

Impact of different governance conditions on evolutionary outcomes

3.2.1

Impact of penalty levels on governance evolution outcomes

In order to analyze the impact of changes in the penalty amount F and M on the evolutionary game process and results of different subjects’ strategic choices, keeping other parameters unchanged, assigned F=10, 20, 40, M=30, 40, 60, respectively, the strategy evolution process and results of the subject of the tripartite game are shown in Figure 4.

With the gradual increase in the amount of punishment by the regulator, the evolution of the strategy choice of sports service enterprises stabilized in the active participation of the convergence speed will be more and more rapid, the time is getting longer and longer, and ultimately stabilized at 1. At this time, the regulator will gradually relax the supervision, cost savings, strategy stabilized in the loose supervision, community residents due to the lack of effective incentives to ultimately choose not to participate. However, in this case, if the regulator is in a state of relaxed supervision for a long period of time, it will not be conducive to the performance of supervision and management duties by the regulator itself, and it will easily lead to the problems of mismatch between supply and demand and insufficient supply, which will create speculative space for the sports service enterprises. In turn, sports service enterprises will consider their own interests, and their strategic choices will gradually tend to negative participation over time, which also indirectly indicates that, if we want to maintain a good environment for the governance of the supply of community sports public services in the long term, and to guarantee the quality of community sports products and services, the regulator will not be able to solve the root causes of the problem by increasing the amount of penalties, and it must pay a certain amount of supervision costs to carry out strong supervision and effective prevention.

3.2.2

Impact of Incentive Gains on Governance Evolution Outcomes

In order to analyze the influence of the changes of reward returns N and E on the process and results of the evolutionary game of strategy selection of different subjects, they are assigned N = 5, 7, 9, and E = 7, 8, 10, respectively, while keeping other parameters unchanged. The strategy evolution process and results of the three-party game subjects are shown in Figure 5.

With the gradual increase of the reward benefits N and E of the regulator for the active participation of sports service enterprises in governance, sports service enterprises choose to actively participate in and supply high-quality sports products and services for a longer and faster time, and eventually evolve and stabilize at 1. The probability of active participation by community residents and strict supervision by the regulator will gradually decrease, and ultimately evolve and stabilize at 0. In this case, the regulator, through the Increasing the amount of incentive power can effectively mobilize sports service enterprises to participate in the governance initiative, enriching the community sports product categories and service categories, but it is difficult to realize the precise supply of community sports public services, docking community residents’ diversified and personalized sports service needs. At the same time, in the long run, it will also increase the financial pressure and workload of the supervisory departments, forcing them to be reluctant to spend a lot of energy into the governance process, and the strategy gradually tends to be lax supervision, which indirectly provides opportunities for the sports service industry to seek huge profits, and is not conducive to enhancing the quality of governance of the community sports public service supply.

3.2.3

Impact of incentivizing residents on governance evolution outcomes

Certain material, spiritual and economic incentives help mobilize community residents to participate in governance. In order to analyze the influence of the change of regulatory incentive amount H on the process and results of different subjects’ evolutionary game, under the premise of keeping the other parameters unchanged, respectively assigned H = 2, 5, 9. The dynamic evolution process of the strategy of the subjects of the tripartite game and the results are shown in Fig. 6.

With the gradual increase of regulatory incentive H, the time for community residents to choose active participation in governance strategy will be gradually shortened, and the speed of stabilizing strategy selection will be gradually accelerated and eventually stabilized at 1. The probability of regulators’ choosing strict supervision and active participation will tend to 0, and the probability of sports service enterprises’ passive participation in governance will gradually decrease due to the strong urging of community residents. In this case, the regulator can stimulate community residents to participate in governance through a variety of incentives, although it can effectively prevent sports service enterprises from overstepping and misbehaving, cultivate the self-governance ability of community residents, and enhance the relationship between the government and the people, but due to the lack of communication with the sports service provider, it is easy to produce problems such as deviation of demand and supply, asymmetry of information, and irrational resource allocation, which is detrimental to improving the quality and level of the community sports public service supply. This is not conducive to improving the quality and level of public service provision in the community.

4

Conclusion

This study constructs a game model of community sports governance and analyzes the equilibrium of interests of multiple governance subjects under multiple combinations of evolutionary stabilization strategies. The simulation results show that when the reputation loss of the regulator is less than the cost of regulation, the probability of strict regulation will gradually decrease to zero and remain stable. When the reputation loss of the sports service provider is greater than the “governance cost-governance benefit”, the probability of active governance tends to be 1. When the cost of community residents’ participation in monitoring is greater than the government’s compensation and incentives, the probability of community residents’ monitoring gradually decreases to 0 and remains stable. In addition, the amount of punishment by the regulator experiences a process of rising and then falling. Reward benefits, material and spiritual incentives and other factors all have a positive effect on community residents’ participation in community sports governance. Accordingly, this paper argues that to improve the efficiency and motivation of community sports governance, a balance of incentives and disincentives should be realized, and governance and supervision should be carried out moderately.

Sprache:: Englisch

Zeitrahmen der Veröffentlichung:: 1 Hefte pro Jahr
Fachgebiete der Zeitschrift:: Biologie, Biologie, andere, Mathematik, Angewandte Mathematik, Mathematik, Allgemeines, Physik, Physik, andere

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Research on Community Sports Governance Based on the Participation of Multiple Subjects

Weifu Qin

Online veröffentlicht: 29. Sept. 2025

Eingereicht: 11. Jan. 2025

Akzeptiert: 08. Mai 2025

DOI: https://doi.org/10.2478/amns-2025-1087

SchlüsselwörterGame model, Revenue tree model, Jacobian matrix, Community sports governance, Multiple subjects

© 2025 Weifu Qin, published by Sciendo.

This work is licensed under the Creative Commons Attribution 4.0 International License.

Schlüsselwörter
Game model, Revenue tree model, Jacobian matrix, Community sports governance, Multiple subjects