The Evolution Game Analysis of Platform Ecological Collaborative Governance Considering Collaborative Cultural Context

Abstract

Designing a successful and efficient collaborative governance mechanism to promote the value co-creation of complementors has become critical to platform owners. Therefore, using an evolutionary game theory approach, we first constructed a conceptual model of collaborative governance, analyzing the conditions of collaborative governance of multiple subjects. This was based on the belief that the design of a collaborative governance mechanism needs to nurture collaborative culture and internalize it into the practice of platform governance. Secondly, this paper built a tripartite evolutionary game model of platform enterprises, complementary enterprises, and users, systematically illustrating the strategy evolution process of the three parties under incentive and penalty mechanisms, and simulated the influence of parameters, such as cost, culture, and cooperative willingness, on the evolutionary results. The results showed that: (1) A culture of trust and encouragement of innovation was more conducive to collaborative innovation; (2) Platform enterprises are more sensitive to joint cost investment, work culture environment, and benefit distribution; (3) Complementary enterprises and users have a solid ambition to respond to the impulses of digital technology. In particular, when the initial desire to collaborate is low, the evolutionary process of platform enterprises presents an asymmetric ‘U’ shape. To enable stakeholders of the platform to formally, prudently, and deeply participate in the ecological governance process, platform enterprises should fully use network resources and digital technology to build a platform for high-intensity interaction and communication between complementary enterprises and users, and improve their identification with the innovation culture.

1. Introduction

Since Amazon blocked a large number of Chinese seller accounts in early April 2021 for reasons such as soliciting false reviews from consumers and manipulating reviews through gift cards, this action has sparked thinking about the governance of the platform ecology among academics and businesses. On the one hand, Amazon’s change in platform rules reflects the battle between platform enterprises and complementary enterprises for dominance of the service system. The ‘parasitic economy’ of excessive dependence on the platform increases the operational risks of complementary enterprises, reduces their bargaining power and operational efficiency, and participants need to make trade-offs between value creation (complementary capabilities) and value capture (reducing dependence). Therefore, some complementary players are establishing independent stations to break away from their over-reliance on the platform. On the other hand, some scholars believe that Amazon’s ‘blocking’ method is to create a healthy competitive market environment to avoid falling into the vicious phenomenon of bad money driving out good money. It follows that the design and deployment of platform governance have a significant impact on the actions and decisions of platform participants.

The platform ecosystem is essentially a structural arrangement with a high degree of power asymmetry, and platform enterprises are always in a favorable position to govern the ecosystem. Without adequate checks and balances on their growing power, platform owners will carry out activities that benefit themselves at the expense of other stakeholders at any time [1]. O’Mahony and Rebecca [2] regard platforms as a dynamic architecture and examine the involvement of external participants in four governance models (centralized, platform-dominant, hybrid, and decentralized). It is recommended that external actors be considered when designing and managing the platform, and if the development and governance process of the platform can be collectively decided, external participants will increase their contributions. Peter M. Senge proposed that the frontline issue of management today is well-being (Peter Sage, Senior Professor at MIT Sloan School of Management, delivered a speech at the 10th anniversary celebration of Tsinghua Management Review on 20 November 2021. https://www.tsinghua.edu.cn/info/1180/89211.htm), that is, enterprises need to care about the well-being of stakeholders in a chaotic social context and create a good working environment to promote the development of collaborative networks, which in turn will encourage innovation and genuine cooperation. Therefore, expediting the high-quality development of platform ecology is of strategic significance that decentralizes the decision-making power of platform enterprises and forms a multi-agent collaborative governance mechanism in which platform enterprises lead, complement enterprises collaborate, and users participate to improve the competitiveness of the platform ecosystem.

This paper analyzes the conditions that need to be satisfied for the design of collaborative governance mechanisms, focusing on how platform leaders construct collaborative governance mechanisms with active participation of members, and examines how the behavioral interactions of key stakeholders of collaborative governance affect the platform system. In summary, this paper extends the study of platform governance in several aspects. First, different from the existing studies which focus on the social responsibility of the governance of platform enterprises, this paper returns platform governance to the products or services provided by the platform itself. To achieve sustainable development of the platform ecology, it is necessary to enhance the products or services. Secondly, this paper introduces collaborative governance into platform governance, and considers the multi-agent collaboration of platform enterprises, complementary enterprises, and users. The importance and dynamism of complementary enterprises and user values in platform governance under open and sharing economy backgrounds need to be further explored. In addition, based on the assumption of the limited rationality of participants, this paper considers the influence of the time-series changes of their strategy choices on the evolutionary process. We explore the trajectory of tripartite behavior and evolutionary stabilization strategies. Finally, the impact of negative involvement on complementary enterprises and users, and punishment of platform enterprises on other participants of the platform ecology is explained by introducing parameters such as the discount coefficient of innovation results transformation and the incentive effect coefficient.

2. Conceptual Model Construction

2.1. Collaborative Governance and Its Preconditions

As a proven governance approach that emerged along with the modernization of national governance [3], collaborative governance has gradually attracted attention in the application of public services such as rural governance and ecological environment governance. For instance, Huang et al. [4] took the effectiveness of public participation in social governance as an entry point, and constructed a game analysis model of the tripartite involvement of government, enterprises, and the public to explore reasons for the lack of effectiveness in public participation. It was demonstrated that the active involvement of the public does not always bring positive benefits; to ensure the effectiveness of public participation, government supervision, coordination, and guidance are essential. Jing et al. [5] analyzed the collaborative strategies of local governments in the cooperative management of regional air pollution and believed that direct and synergistic governance benefits would positively affect the harmonious governance relationship. The ecological compensation among local governments did not necessarily promote cooperative relationships. Only by strengthening supervision and increasing the probability of random inspections did ecological compensation play a facilitating role.

By reviewing the literature, we found that collaborative governance is rarely found in platform ecological governance. Scholars have focused their research on platform governance in information security, knowledge governance, and content governance. For example, Xu and Yuan [6] explored the management of illegal and unlawful information in cyberspace. Bai et al. [7] explained that knowledge sharing plays a mediating role in the relationship between knowledge governance, and value co-creation. Peng et al. [8] argued that content governance is vital for user-created platforms, and their results showed that factors such as the cost of punishment and intensity of governance significantly impacted the decision-making behavior of participants. In addition, researchers have paid particular attention to the social responsibility governance of platform enterprises [9,10,11], arguing that the booming platform economy has also led to various social problems. The access threshold and screening mechanism of the travel platform for drivers are not strictly controlled; the review mechanism of the food ordering platform for the “three no” merchants with no production date, no quality certificate, and no manufacturer exists in name only; and the content platform lacks control over users’ vulgar creations. For instance, Douyin Live, with its instant interactive technical features, is dedicated to helping creators in the fields of agriculture, e-commerce, and knowledge realize their value, and has created a large number of jobs. However, the rapid development of the platform has resulted in the frequent emergence of bad behaviors, such as vulgar speculation and loss of reward. Douyin Live has increased its governance efforts and built a collaborative governance mechanism that unites industry associations and cooperates with regulators to help with the continuous output of quality content to create a clean live ecology. In essence, due to the inadequate management of the irresponsible behavior of bilateral users, the supply or consumption behavior generated by bilateral users relying on the platform has adverse effects on the economy and society, forming a deep-rooted problem of a lack of social responsibility for platform enterprises [12].

The preceding research has laid the groundwork for comprehending collaborative governance and platform governance. Unfortunately, they tend to solely focus on the social responsibility governance of platform enterprises, whereas the high-quality development of platform ecosystems is more dependent on the innovation of participants. More importantly, most academics have ignored the conditions for collaborative governance. Ansell and Alison [13] designed a collaborative governance model consisting of initial conditions, institutional design, leadership, and the collaborative process. Among them, initial conditions stipulate the power-resource-knowledge asymmetries of the participants, which constitute the resources or liabilities in the collaborative process. Institutional design construes the ground rules for cooperation, and leadership provides the necessary mediation and facilitation for the collaborative process, which is a critical ingredient in building trust, exploring mutual interests, and mobilizing members to move cooperation forward. Ulbrich et al. [14] identified six success factors for developing teamwork capabilities in networked organizations: partners with complementary capabilities to meet task requirements; open and transparent communication; high commitment; similarity of authority and hierarchy within the firm; negotiation and agreement on rules for cooperation; and a reasonable expectation of success. Therefore, it is necessary to analyze the critical elements of the cooperative governance of the platform before designing the collaborative governance mechanism.

2.2. Collaborative Culture

Every organization shapes its culture in undetected ways. As part of organizational action, culture creates a specific logic for what the organization is attempting to achieve and shapes actors’ preferences and behaviors [15]. Collaborative culture, as a core dimension of organizational culture, reflects the organization’s responsibility, recognition, and commitment to a common goal or vision. Scholarly research on collaborative culture has concentrated on four dimensions so far:

(1)

The mediating role of collaborative culture in the relationship between leader style and knowledge sharing. For example, Yang [16] contends that effective knowledge sharing is enhanced when the leader serves as a mentor or facilitator. On the one hand, managers as mentors can help their subordinates improve their working ability, while as facilitators, leaders are more concerned with team harmony and committed to involving employees in the organizational growth process. Leadership and organizational culture, according to Lei et al. [17], are key factors influencing employee knowledge sharing. They argue that ethical leaders focus on two-way communication and interactive fairness in the organization, and have greater motivation to shape an organizational culture of integrity and trustworthy cooperation, which promotes tacit or explicit knowledge dissemination among employees.

(2)

Collaborative culture influences team innovation through knowledge sharing or knowledge management. According to Barczak et al. [18], teams with higher emotional intelligence are better able to capture their members’ cooperative needs and promote a collaborative culture through team trust, thereby increasing team creativity. When members of an organization seek or provide support to one another to achieve work goals, it strengthens the process of mutual trust and collaboration among members [19]. This perspective helps to comprehend the process through which individual perceptions evolve into a synergistic culture, so identifying the signals of cooperation from organizational members is particularly crucial for creating a synergistic culture. As a collaborative culture is founded on mutual respect, care, and support, it is the starting point for developing collective power that can mobilize all members to use organizational resources for a variety of exploratory activities [20]. This includes promoting organizational learning [21] and stimulating knowledge acquisition, knowledge sharing, and knowledge application behaviors among employees, which in turn can lead to incremental innovation and radical innovation [22,23], or product innovation and process innovation [20].

(3)

The role of collaborative culture in inter-organizational project collaboration. Firms are frequently constrained by resources and methodological knowledge. Inter-organizational collaboration can integrate internal and external expertise in an area to increase a firm’s capacity for innovation [24]. Hernandez et al. [25] discovered that inter-organizational collaborative innovation initiatives have an impact on firm performance, and that an innovative collaborative culture can improve employees’ attitudes toward their jobs. Villena et al. [26] investigated factors that affect technical knowledge creation by project teams in the architecture, engineering, and construction (AEC) industry. Corporate culture, the support provided by senior management, and knowledge management all had an impact on the technical competence of engineering projects. As a result, creating an ambiance where team members feel comfortable is an effective way to encourage increased contributions from project teams.

(4)

Collaborative culture in supply chain cooperation. Kumar et al. [27] emphasized that close relationships and collaborative culture are essential for supply chain collaboration. The latter can promote the development of cohesive synergistic networks among supply chain participants and strengthen the partnership among participants, which in turn promotes cooperative activities. On the other hand, Yu et al. [28] concentrated on how dynamic trust was formed among suppliers, customers, and regulators in a green new product development (green NPD) process and argued that trust measures should be adopted for different collaborators based on the national culture of China.

According to the above-mentioned literature, collaborative culture plays a hidden but critical role in knowledge management, innovation activities, and project collaboration in organizations, which regulate actor behavior. As a result, we argue that in a collaborative governance mechanism built by platform enterprises, complementary enterprises, and users, managers must cultivate a collaborative culture that guides participants to fulfill their responsibilities and commit to a common vision as a model for individual perceived goals.

2.3. Conceptual Model

Regarding the collaborative conditions of platform participants, collaborative management often falls into synergistic dilemmas due to insufficient capacity of members, ambiguous role positioning and governance functions, or even an imbalance of power, knowledge, and resources among stakeholders. Invalid collaborative governance occurs when the process is manipulated by powerful actors, such that important stakeholders who spend time and energy are not able to participate in a meaningful way. Therefore, the differences among interested parties and the issues of equality, distribution of responsibilities, and powers among actors caused by such differences need to be clarified. At the same time, the roles of platform enterprises, complementary enterprises, and users determine the complementarity among the three types of participants. Successful cooperative governance of a platform requires a consensus on enriching the types of complementary products or services, improving the quality of products or services, and integrating the capabilities and knowledge of participants for value co-creation, thus enhancing the competitiveness of the platform and forming a virtuous and organic platform ecology. A cooperative relationship with stakeholders and mutually reinforcing advantages is based on equal trust, resource balance, and clear boundaries of responsibilities, which constitute the constraints for the collaborative governance of platform participants. Moreover, fostering a culture of cooperation based on interpersonal relationships is extremely important for constructing collaborative networks [29]. It is undeniable that trust and identification with certain values can steer practical collaboration in business relationships and deepen collective recognition. The organic cycle of the business ecosystem needs to achieve symbiosis and coexistence based on cooperative culture, such as an open and transparent communication mechanism, encouraging innovation and diversity. It can provide a centripetal force for the principal part, and a platform ecosystem can only coexist for a long time under the nourishment of culture. When designing collaborative governance mechanisms, it is important to clarify synergetic conditions among participants and gradually internalize the culture into governance practices to genuinely bring out the effects of collaborative governance.

This paper constructs a conceptual model of the collaborative governance mechanism for platform participants, including a management center formed by platform enterprises, an innovation production center established by complementary enterprises, and a knowledge information center composed of ordinary users and head users. The three parties reach a cooperative contract, which stipulates that the complementary enterprise and users both bear the responsibility of governance (empowering the complementary enterprise and the user), and the platform enterprises pay specific compensation to both groups. The management center sets the incentive subsidies or penalty amounts for complementary enterprises and users. Complementary enterprises mainly focus on enriching the types of complementary products and improving the quality of products, whereas the cooperation between the platform and complementary enterprises forms a ‘supply chain collaboration’. The head users not only contribute their knowledge and ideas, but also act as product designers and decision-makers to promote new product development, and enhance innovation ability. The collaboration between complementary enterprises and users forms an ‘innovation collaboration chain’, and the cooperation between platform enterprises and users forms the ‘network collaboration chain’. The collaborative governance mechanism of the platform ecosystem is shown in Figure 1.

3. Research Design

3.1. Research Method

This paper uses evolutionary game theory to deduce the impact of the strategic choices of platform firms, complementary firms, and users on the performance of collaborative governance. Evolutionary game theory is an approach derived from biological evolution that combines game-theoretic analysis with an examination of dynamic evolutionary processes. It rejects the assumption of perfect rationality in favor of the belief that people usually achieve game equilibrium through trial and error. The approach has been widely applied in the management field, particularly in public governance fields such as supply chain management and environmental protection, thanks to groundbreaking research by Smith and Price [30] and Taylor and Jonker [31]. For instance, Ji et al. [32] used evolutionary game theory to analyze the relationship between suppliers and manufacturers in green procurement behavior in supply chain management. They then built a replicated dynamic system to verify the hypothesis that the recycling ability of suppliers directly determines the greenness of the supply chain. Mahmoudi and Rasti-Barzoki [33] used the evolutionary game approach to observe the carbon emissions performance of producers and markets in the context of different government strategies, and found that governments play a crucial role in addressing greenhouse gas emissions and that imposing tariffs could significantly mitigate environmental degradation. Based on the assumption that participants have limited rationality, Wu et al. [34] formulated a collaborative innovation game model with government oversight, university leadership, and enterprise participation. They discovered that enterprises were more sensitive to the severity of penalties and distribution of benefits; the authors suggested that the government should create a diversified promotion strategy with distinct preferential policies for enterprises and universities.

After a detailed examination of the previously mentioned literature, we found that a replicator dynamic and evolutionary stable strategy were the most fundamental concepts of evolutionary game theory. A replicator dynamic characterizes the steady state of an evolutionary game, whereas an evolutionary stable strategy depicts the dynamic convergence of participants to this steady state, that is, the dynamic process in which participant interactions affect their payoffs. As a result, we contend that the process of participant strategy selection in a collaborative platform governance system is consistent with the core features of evolutionary game theory, in which participants, as finite rational individuals, continuously modify and improve (learn and imitate) their behavior to improve the collaborative governance system. At the same time, the actors’ strategy selection is essentially a dynamic process that governs the operation rule of the game system.

3.2. Model Assumpptions

Based on evolutionary game theory, this paper explores the interactions among incentive subsidies of platform enterprises, innovation collaboration of complementary enterprises, and user willingness for knowledge sharing, as well as the effects of factors such as culture and benefit distribution on the participants. Based on this, the following primary hypotheses are given:

Hypothesis 1 (H1). 

The platform ecosystem is a complex system consisting of platform enterprises, complementary enterprises, manufacturers of complementary products, raw material suppliers, and their users. In order to simplify the complex game process, this paper only considers the coordination among platform enterprises, complementary enterprises, and users, which are closely related to the platform ecosystem. We assume that the three parties reach a collaborative contract to share governance responsibilities. As the dominant player in governance, platform enterprises will adopt two governance strategies of incentive and punishment for complementary enterprises and users. The strategy set of complementary enterprises is {innovation collaboration, negative collaboration}, and the user’s strategy set is {knowledge collaboration, passive collaboration}.

Hypothesis 2 (H2). 

We assume that the direct benefits of the platform, complementary enterprises, and users in the ecology are $W_1$, $W_2$ and $W_3$, respectively. When the three parties cooperate in governance, the costs to be paid are $C_1$, $C_2$ and $C_3$, respectively. In addition, assuming that the synergistic cultural atmosphere of the platform ecosystem is $d$, which determines the degree of cooperation among the platform members, this, in turn, affects the synergistic benefits $R$. The three actors will obtain synergistic benefits $W_i+{\alpha }_{i}dR$, respectively, where ${\alpha }_i$ denotes the coefficient of synergistic benefits distribution. If users cooperate negatively, the success rate of converting new complementary products and services will decrease, leading to a significant discount in the collaborative benefits of the platform and complementary enterprises. The discount rate is $a$. At this time, the collaboration gains created by the platform and complementary enterprises are $\left(1-a\right)dR$, and the coefficients of benefits distribution between them are ${\beta }_1$ and ${\beta }_2$, where ${\beta }_1+{\beta }_2=1$. When platform firms adopt a penalty strategy, the synergistic benefits created by the complementary firms and users are $dE$, at which time the income distribution of the two are ${\beta }_{2}dE$ and ${\beta }_{3}dE$, where ${\beta }_2+{\beta }_3=1$. It is stipulated that when two parties actively govern and one party is passive, this will bring potential loss $L_i$.

Hypothesis 2a (H2a). 

Under the incentive strategy, platform enterprises will implement a corresponding incentive and subsidy policies for the complementors who actively participate in innovation governance. At the same time, platform enterprises will monitor whether complementary enterprises and users have effectively fulfilled the responsibility of collaborative management. According to the contract, the platform will judge whether to compensate the complementary enterprises and users. The incentive subsidy $M$ paid by the platform to the complementary enterprises of innovation collaboration is mainly used for commission reduction and brand promotion cost reduction. At this time, the complementary enterprises will also subsidize $S$ to the users of knowledge collaboration. When complementary firms collaborate negatively, the incentive subsidy $M$ of platform firms is primarily used to directly subsidize the users of knowledge collaboration. The difference in the subsidy effect caused by problems such as user information asymmetry is denoted by $k$ as the effective coefficient of the direct subsidy.

Hypothesis 2b (H2b). 

Under the penalty strategy, the platform will impose a fine $F$ on the complementary firms that are negatively innovating. If core users are not highly motivated to be involved in platform governance, the platform will fine the complementary enterprises $F$, and the complementary enterprises will fine the users $G$. In addition, if both complementary firms and users collaborate negatively, there is a loss of direct gains to the platform stakeholders, with a loss factor noted as $c$.

Hypothesis 3 (H3). 

In the platform ecology, complementary firms, as the core of providing products and services, do not generate synergistic benefits when they negatively innovate. When users negatively synergize, the conversion success rate of new products and services will be prone to decline, leading to a significant discount in synergistic gains for the platform and complementary enterprises, with a discount rate $a$. Assuming that users actively participate in innovating products and services, complementary firms have a strong spirit of adventure and exploration to innovate, and when complementary firms subsidize users, this will increase the market success rate of the product, which in turn enables complementary firms to gain additional revenue $E$, including reputation brought by user trust.

The above parameters and descriptions are shown in

Table 1. Related parameters and meanings.

Parameters	Meaning
$W_1$, $W_2$, $W_3$	Represent the direct benefits of the platform, complementary enterprises, and users in the platform ecosystem, $W_i>0$.
$C_1$, $C_2$, $C_3$	Represent collaborative costs among the platform, complementary enterprises, and users, $C_i>0$.
$R$	Collaborative benefits are obtained when platform, complementary enterprises, and users collaborate in governance, $R>0$.
$k$	Indicates the effectiveness factor of direct subsidies to users by platform enterprises when incentivizing, $k\in \left[0,1\right]$.
$M$	Subsidy under incentive strategy of platform enterprises, $M>0$.
$E$	Collaborative profits created by both complementary firms and users under the penalty strategy, $R>E>0$.
$L_1$	Potential losses from platform enterprise penalty strategies when complementary enterprises or users collaborate, $L_1>0$.
$L_2$	Potential losses of complementary firms when users collaborate in knowledge and complementary firms negatively collaborate, $L_2>0$.
$L_3$	Potential losses from negative user collaboration when the platform and complementary firms cooperate, $L_3>0$.
$S$	User subsidy for knowledge collaboration by complementary enterprises under incentive strategy of platform enterprises, $M>S>0$.
$F$	Penalties of complementary enterprises imposed by platform when complementary enterprises or users negatively collaborate, $F>0$.
$G$	Penalties for users by complementary enterprises in case of negative collaboration, $0<G<F$.
$a$	The coefficient of loss of collaborative profits of platform ecology when complementary firms innovate, but users negatively synergize, $a\in \left[0,1\right]$.
$b$	The direct revenue increase factor when the platform and user cooperate, $b\in \left[0,1\right]$.
$c$	Direct profit loss coefficient of the platform caused by negative coordination between complementary enterprises and users under penalty strategy of platform enterprises, $c\in \left[0,1\right]$.
$d$	The degree of identification of participants with a synergistic culture, $d\in \left[0,1\right]$.
${\alpha }_1,{\alpha }_2,{\alpha }_3$	Denote the three-party collaborative income distribution coefficients, ${\alpha }_1+{\alpha }_2+{\alpha }_3=1$.
${\beta }_1,{\beta }_2,{\beta }_3$	The two-party profit distribution coefficient when the platform cooperates with the complementary firms,${\beta }_1+{\beta }_2=1$, and when the complementary firms cooperate with the users,${\beta }_2+{\beta }_3=1$.
$x,y,z$	The probability of collaboration among the platform, complementary enterprises, and users, $x,y,z\in \left[0,1\right]$.

.

3.3. Constructing Payment Matrix

In this model, platform enterprises, complementary enterprises, and users voluntarily make strategic choices, and the probabilities of the three parties positively collaborating are $x$, $y$ and $z$, respectively. The chances of negative synergy are $1-x$, $1-y$ and $1-z$, respectively. According to the above assumptions, the tripartite game payment matrix is shown in

Table 2. Tripartite evolutionary game payoff matrix.

		The Users	Platform Enterprises
			Motivation (x)	Punishment (1 − x)
Comple-mentary Enterprises	Collaborat-ive Innovation $\left(y\right)$	Knowledge Contribution $\left(z\right)$	$W_1-C_1+{\alpha }_{1}dR-M$	$W_1-L_1$
			$W_2-C_2+{\alpha }_{2}dR+M-S$	$W_2-C_2+{\beta }_{2}dE$
			$W_3-C_3+{\alpha }_{3}dR+S$	$W_3-C_3+{\beta }_{3}dE$
		Negative Sharing $(1-z)$	$W_1+{\beta }_1\left(1-a\right)dR-C_1$	$W_1+F$
			$W_2+{\beta }_2\left(1-a\right)dR-C_2$	$W_2-C_2-F+G$
			$W_3-L_3$	$W_3-L_3-G$
	Negative Innovation $(1-y)$	Knowledge Contribution $\left(z\right)$	$\left(1+b\right)W_1-C_1-M$	$W_1+F$
			$W_2-L_2$	$W_2-L_2-F$
			$\left(1+b\right)W_3-C_3+kM$	$W_3-C_3$
		Negative Sharing $(1-z)$	$W_1-C_1$	$\left(1-c\right)W_1+F$
			$W_2$	$\left(1-c\right)W_2-F+G$
			$W_3$	$\left(1-c\right)W_3-G$

.

4. Analysis of the Evolutionary Model

4.1. Establishment and Analysis of Replication Dynamic Equations

4.1.1. Replication Dynamic Equation of Platform Enterprises

The replication dynamic equation is a widely used learning dynamic equation that shows that the growth rate of participants choosing a strategy is not only proportional to the number of people who choose the strategy in that period, but also to the difference between the returns of that strategy and the average returns [35]. According to Table 2, the expected profit of the incentive strategy for platform firms is $U_X$, the expected benefit of the penalty strategy is $U_{1-X}$, and the average return is ${\overline{U}}_x$, as follows:

$$\begin{array}{l}{U}_X=yz\left(W_1-C_1+{\alpha }_{1}dR-M\right)+y(1-z)\left[W_1+{\beta }_1\left(1-a\right)dR-C_1\right]+(1-y)z\left[\left(1+b\right)W_1-C_1-M\right]\\ +(1-y)(1-z)\left[W_1-C_1\right]\end{array}$$

(1)

$$U_{1-X}=yz\left[W_1-L_1\right]+y(1-z)\left[W_1+F\right]+(1-y)z\left[W_1+F\right]+(1-y)(1-z)\left[\left(1-c\right)W_1+F\right]$$

(2)

$${\overline{U}}_X=x{U}_X+\left(1-x\right)U_{1-X}$$

(3)

The replication dynamic equation of the platform enterprises is

$$\begin{array}{l}F\left(x\right)=\frac{dx}{dt}=x\left(U_X-{\overline{U}}_x\right)\\ =x\left(1-x\right)\{yz[{\alpha }_{1}dR-{\beta }_1\left(1-a\right)dR+L_1+\left(c-b\right)W_1\left]+y\right[{\beta }_1\left(1-a\right)dR-c{W}_1]\\ +z[\left(b-c\right)W_1-M+F]+c{W}_1-C_1-F\}.\end{array}$$

(1)

$F\left(x\right)=0$, when $z=z_0=\frac{-c{W}_1+C_1+F-y\left[{\beta }_1\left(1-a\right)dR-c{W}_1\right]}{\left(b-c\right)W_1-M+F+y\left[{\alpha }_{1}dR-{\beta }_1\left(1-a\right)dR+L_1+\left(c-b\right)W_1\right]}$. Regardless of what the value of $z$ is, the strategic choices of platform firms tend to be stable.

(2)

If $z\ne z_0$, let $F\left(x\right)=0$. Then, two stable points can be obtained: $x=0$, $x=1$. Find the partial derivative of $F\left(x\right)$ with respect to $x$:

$$\begin{gathered} \frac{d\left[F\left(x\right)\right]}{dx}=\left(1-2x\right)\left\{yz\left[{\alpha }_{1}dR-{\beta }_1\left(1-a\right)dR+L_1+\left(c-b\right)W_1\left]+y\right[{\beta }_1\left(1-a\right)dR- \\ c{W}_1\left]+z\right[\left(b-c\right)W_1-M+F\right]+c{W}_1-C_1-F\right\} \end{gathered}$$

If $0<z<z_0$, $\frac{d\left[F\left(x\right)\right]}{dx}<0$ when $x=0$, and $\frac{d\left[F\left(x\right)\right]}{dx}>0$ when $x=1$. Then, $x=0$ is the steady point. Similarly, if $z_0<z<1$, $x=1$ is the steady point.

4.1.2. Replication Dynamic Equation of Complementary Enterprises

The expected return for complementary firms choosing positive innovation is $U_Y$, the expected return for choosing ‘negative innovation’ is $U_{1-Y}$, and the average return is ${\overline{U}}_Y$, as follows:

$$\begin{gathered} U_Y=zx\left[W_2-C_2+{\alpha }_{2}dR+M-S\right]+z\left(1-x\right)\left[W_2-C_2+{\beta }_{2}dE\right]+\left(1-z\right)x\left[W_2+{\beta }_2\left(1-a\right)dR-C_2\right] \\ +\left(1-z\right)\left(1-x\right)\left[W_2-C_2-F+G\right] \end{gathered}$$

(4)

$$U_{1-Y}=zx\left[W_2-L_2\right]+z\left(1-x\right)\left[W_2-L_2-F\right]+\left(1-z\right)x\left[W_2\right]+\left(1-z\right)\left(1-x\right)\left[\left(1-c\right)W_2-F+G\right]$$

(5)

$${\overline{U}}_Y=y{U}_Y+\left(1-y\right)U_{1-Y}$$

(6)

Then, the replication dynamic equation of the complementary enterprises is

$$\begin{gathered} F\left(y\right)=\frac{dy}{dt}=y\left(U_Y-{\overline{U}}_Y\right)=y\left(1-y\right)\{xz\left[{\alpha }_{2}dR-{\beta }_2\left(1-a\right)dR-{\beta }_{2}dE+c{W}_2+ \\ M-S-F\left]+x\right[{\beta }_2\left(1-a\right)dR-c{W}_2\right]+z\left(L_2+F+{\beta }_{2}dE-c{W}_2\right)+c{W}_2-C_2\} \end{gathered}$$

(1) $F\left(y\right)=0$, when $x=x_0=\frac{-z\left(L_2+F+{\beta }_{2}dE-c{W}_2\right)-c{W}_2+C_2}{{\beta }_2\left(1-a\right)dR-c{W}_2+z\left[{\alpha }_{2}dR-{\beta }_2\left(1-a\right)dR-{\beta }_{2}dE+c{W}_2+M-S-F\right]}$. This indicates that the percentage of complementary firms’ efforts to innovate is a stable strategy that does not change over time, no matter what the portion is.

(2) If $x\ne x_0$, let $F\left(y\right)=0$. Then, two stable points can be obtained: $y=0$, $y=1$.

Find the partial derivative of $F\left(y\right)$ with respect to $y$:

$$\begin{gathered} \frac{d\left[F\left(y\right)\right]}{dy}=\left(1-2y\right)\left\{xz\left[{\alpha }_{2}dR-{\beta }_2\left(1-a\right)dR-{\beta }_{2}dE+c{W}_2+M-S-F\left]+ \\ x\right[{\beta }_2\left(1-a\right)dR-c{W}_2\right]+z\left(L_2+F+{\beta }_{2}dE-c{W}_2\right)+c{W}_2-C_2\right\} \end{gathered}$$

If $0<x<x_0$, ${\left.\frac{d\left[F\left(y\right)\right]}{dy}\right|}_{y=0}<0$ and ${\left.\frac{d\left[F\left(y\right)\right]}{dy}\right|}_{y=1}>0$, then $y=0$ is the steady point. If $x_0<x<1$, ${\left.\frac{d\left[F\left(y\right)\right]}{dy}\right|}_{y=0}>0$ and ${\left.\frac{d\left[F\left(y\right)\right]}{dy}\right|}_{y=1}<0$, then $y=1$ is the steady point.

4.1.3. Replication Dynamic Equation of the Users

The expected profit for users choosing knowledge contribution is $U_Z$, the expected return for choosing ‘passive sharing’ is $U_{1-Z},$ and the average benefit is ${\overline{U}}_Z$, as follows:

$$\begin{gathered} U_Z=yx\left[W_3-C_3+{\alpha }_{3}dR+S\right]+y\left(1-x\right)\left[W_3-C_3+{\beta }_{3}dE\right]+\left(1-y\right)x\left[\left(1+b\right)W_3-C_3+kM\right] \\ +\left(1-y\right)\left(1-x\right)\left[W_3-C_3\right] \end{gathered}$$

(7)

$$U_{1-Z}=yx\left[W_3-L_3\right]+y\left(1-x\right)\left[W_3-L_3-G\right]+\left(1-y\right)x\left[W_3\right]+\left(1-y\right)\left(1-x\right)\left[\left(1-c\right)W_3-G\right]$$

(8)

$${\overline{U}}_Z=z{U}_Z+\left(1-z\right)U_{1-Z}$$

(9)

Then, the replication dynamic equation of the users is

$$\begin{gathered} F\left(z\right)=\frac{dz}{dt}=Z\left(U_Z-{\overline{U}}_Z\right)=z\left(1-z\right)\{xy[S+{\alpha }_{3}dR-{\beta }_{3}dE+\left(c-b\right)W_3-kM]+ \\ x\left[\left(b-c\right)W_3+kM-G\right]+y\left(L_3+{\beta }_{3}dE-c{W}_3\right)+c{W}_3+G-C_3\} \end{gathered}$$

(1)

$F\left(z\right)=0$, when $y=y_0=\frac{C_3-c{W}_3-G-x\left[\left(b-c\right)W_3+kM-G\right]}{x\left[S+{\alpha }_{3}dR-{\beta }_{3}dE+\left(c-b\right)W_3-kM\right]+L_3+{\beta }_{3}dE-c{W}_3}$. It shows that no matter what proportion of users actively contribute knowledge, the final behavior is a stable strategy.

(2)

If $y\ne y_0$, let $F\left(z\right)=0$. Two stable points can be obtained: $z=0$, $z=1$. Find the partial derivative of $F\left(z\right)$ with respect to $z$:

$$\begin{gathered} \frac{d\left[F\left(z\right)\right]}{dz}=\left(1-2z\right)\{xy[S+{\alpha }_{3}dR-{\beta }_{3}dE+\left(c-b\right)W_3-kM]+x\left[\left(b-c\right)W_3+kM-G\right] \\ +y\left(L_3+{\beta }_{3}dE-c{W}_3\right)+c{W}_3+G-C_3\} \end{gathered}$$

If $0<y<y_0$, ${\left.\frac{d\left[F\left(z\right)\right]}{dz}\right|}_{z=0}<0$ and ${\left.\frac{d\left[F\left(z\right)\right]}{dz}\right|}_{z=1}>0$, then $z=0$ is the steady point. If $y_0<y<1$, ${\left.\frac{d\left[F\left(z\right)\right]}{dz}\right|}_{z=0}>0$ and ${\left.\frac{d\left[F\left(z\right)\right]}{dz}\right|}_{z=1}<0$, then $z=1$ is the steady point. When the probability of innovation by complementary enterprises is greater than $y_0$, users will be more willing to contribute knowledge.

4.2. Equilibrium Solution Analysis of the Three-Party Evolutionary System

4.2.1. Solving the Stabilization Strategy

Combining the replication dynamic equations of platform enterprises, complementary enterprises, and users, the replication dynamic system of the platform is obtained as:

$$\{\begin{array}{c}F\left(x\right)=\frac{dx}{dt}=x\left(U_X-{\overline{U}}_x\right)=x\left(1-x\right)\{yz\left[{\alpha }_{1}dR-{\beta }_1\left(1-a\right)dR+L_1+\left(c-b\right)W_1\right]+ \\ y\left[{\beta }_1\left(1-a\right)dR-c{W}_1\left]+z\right[\left(b-c\right)W_1-M+F\right]+c{W}_1-C_1-F\}\\ F\left(y\right)=\frac{dy}{dt}=y\left(U_Y-{\overline{U}}_Y\right)=y\left(1-y\right)\{xz[{\alpha }_{2}dR-{\beta }_2\left(1-a\right)dR-{\beta }_{2}dE+c{W}_2+M-\\ S-F\left[+x\right]{\beta }_2\left(1-a\right)dR-c{W}_2]+z\left(L_2+F+{\beta }_{2}dE-c{W}_2\right)+c{W}_2-C_2\}\\ F\left(z\right)=\frac{dz}{dt}=z\left(U_Z-{\overline{U}}_Z\right)=z\left(1-z\right)\{xy[S+{\alpha }_{3}dR-{\beta }_{3}dE+\left(c-b\right)W_3-kM]\\ +x\left[\left(b-c\right)W_3+kM-G\right]+y\left(L_3+{\beta }_{3}dE-c{W}_3\right)+c{W}_3+G-C_3\}\end{array}$$

(10)

Let the right-hand side of Equation (1) be equal to 0, and we have 8 equilibrium points:$E_1\left(0,0,0\right)$, $E_2\left(0,0,1\right)$, $E_3\left(0,1,0\right)$, $E_4\left(0,1,1\right)$, $E_5\left(1,0,0\right)$, $E_6\left(1,0,1\right)$, $E_7\left(1,1,0\right)$, and $E_8\left(1,1,1\right)$.

4.2.2. Stability Analysis of Equilibrium Points

In an evolutionary game model, under the assumption of bounded rationality, the players’ behavior will change over time, thereby changing the evolutionary equilibrium point and eventually reaching a stable point. That is, the equilibrium point obtained by the replication dynamic equation is not necessarily a sound strategy for system evolution, and the stability of the equilibrium point needs to be further analyzed by means of stability theory. When the eigenvalues of the Jacobian matrix are all negative, the equilibrium point is the evolutionarily stable strategy [36]. Therefore, we solve Equation (10) for the partial derivatives with respect to $x$, $y$ and $z$, which form the Jacobian matrix, as follows:

$$\begin{gathered} J=\left[\begin{array}{ccc}\left(1-2x\right)\{yz[{\alpha }_{1}dR+L_1- \\ {\beta }_1\left(1-a\right)dR+\left(c-b\right)W_1] \\ +y\left[{\beta }_1\right(1-a)dR-c{W}_1] \\ +z[\left(b-c\right)W_1-M+F] \\ +c{W}_1-C_1-F\}& x\left(1-x\right)\{z[{\alpha }_{1}dR+L_1- \\ {\beta }_1\left(1-a\right)dR+\left(c-b\right)W_1] \\ {\beta }_1\left(1-a\right)dR-c{W}_1\}& x\left(1-x\right)\{y[{\alpha }_{1}dR+L_1- \\ {\beta }_1\left(1-a\right)dR+\left(c-b\right)W_1] \\ +\left(b-c\right)W_1-M+F\}\\ y\left(1-y\right)[z({\alpha }_{2}dR-{\beta }_{2}dE \\ -{\beta }_2\left(1-a\right)dR+c{W}_2 \\ +M-S-F)+ \\ \left(1-a\right)d{\alpha }_2{R}_2-c{W}_2]& \left(1-2y\right)\{xz[{\alpha }_{2}dR-{\beta }_{2}dE- \\ {\beta }_2\left(1-a\right)dR+c{W}_2+M- \\ S-F\left]+x\right[{\beta }_2\left(1-a\right)dR \\ -c{W}_2]+z(L_2+F+{\beta }_{2}dE \\ -c{W}_2)+c{W}_2-C_2\}& y\left(1-y\right)[x({\alpha }_{2}dR-{\beta }_{2}dE \\ -{\beta }_2\left(1-a\right)dR+c{W}_2 \\ +M-S-F)+L_2 \\ +F+{\beta }_{2}dE-c{W}_2]\\ z\left(1-z\right)\{y[S+{\alpha }_{3}dR- \\ {\beta }_{3}dE+\left(c-b\right)W_3-kM \\ kM]+\left(b-c\right)W_3 \\ +kM-G\}& z\left(1-z\right)\left\{x\right[S+{\alpha }_{3}dR- \\ {\beta }_{3}dE+\left(c-b\right)W_3-kM \\ kM]+L_3+{\beta }_{3}dE-c{W}_3& \left(1-2z\right)\left\{xy\right[S+{\alpha }_{3}dR- \\ {\beta }_{3}dE+\left(c-b\right)W_3-kM] \\ +x\left[\left(b-c\right)W_3+kM-G\right] \\ +y(L_3+{\beta }_{3}dE-c{W}_3) \\ +c{W}_3+G-C_3\}\end{array}\right] \end{gathered}$$

When the equilibrium point is $E_1\left(0,0,0\right)$, that is, $x=0,y=0,z=0$, the corresponding Jacobian matrix is: $J=\left[\begin{array}{ccc}c{W}_1-C_1-F& 0& 0\\ 0& c{W}_2-C_2& 0\\ 0& 0& c{W}_3+G-C_3\end{array}\right]$; the eigenvalues are ($c{W}_1-C_1-F$), ($c{W}_2-C_2$) and ($c{W}_3+G-C_3$). Similarly, the eigenvalues corresponding to the eight equilibrium points in the Jacobian matrix are obtained, as shown in

Table 3. Eigenvalues of Jacobian matrix of platform ecological collaborative governance system.

Equilibrium Points	$\mathbf{Eigenvalue} {\mathit{\lambda }}_1$	$\mathbf{Eigenvalue} {\mathit{\lambda }}_2$	$\mathbf{Eigenvalue} {\mathit{\lambda }}_3$
$E_1\left(0,0,0\right)$	$c{W}_1-C_1-F$	$c{W}_2-C_2$	$c{W}_3+G-C_3$
$E_2\left(0,0,1\right)$	$b{W}_1-C_1-M$	$L_2+F+{\beta }_{2}dE-C_2$	$-\left(c{W}_3+G-C_3\right)$
$E_3\left(0,1,0\right)$	${\beta }_1\left(1-a\right)dR-C_1-F$	$-\left(c{W}_2-C_2\right)$	$L_3+{\beta }_{3}dE+G-C_3$
$E_4\left(0,1,1\right)$	$L_1+{\alpha }_{1}dR-C_1-M$	$-\left[L_2+F+{\beta }_{2}dE-C_2\right]$	$-\left(L_3+{\beta }_{3}dE+G-C_3\right)$
$E_5\left(1,0,0\right)$	$-\left(c{W}_1-C_1-F\right)$	${\beta }_2\left(1-a\right)dR-C_2$	$b{W}_3+kM-C_3$
$E_6\left(1,0,1\right)$	$-\left(b{W}_1-C_1-M\right)$	${\alpha }_{2}dR+M-S-C_2+L_2$	$-\left(b{W}_3+kM-C_3\right)$
$E_7\left(1,1,0\right)$	$-\left[{\beta }_1\left(1-a\right)dR-C_1-F\right]$	$-\left[{\beta }_2\left(1-a\right)dR-C_2\right]$	${\alpha }_{3}dR+S-C_3+L_3$
$E_8\left(1,1,1\right)$	$-\left(L_1+{\alpha }_{1}dR-C_1-M\right)$	$-\left[{\alpha }_{2}dR+M-S+L_2-C_2\right]$	$-\left({\alpha }_{3}dR+S-C_3+L_3\right)$

.

To facilitate the analysis of the signs of the eigenvalues corresponding to different equilibrium points, it was assumed that the benefits of cooperation among the three platform subjects were greater than the benefits of negative synergy. Then, ${\alpha }_{1}dR-C_1-M>0$, ${\alpha }_{2}dR-C_2+M-S>0$, and ${\alpha }_{3}dR-C_3+S>0$. Under this condition, the evolution and stability strategy of platform collaborative governance is discussed for two situations:

Case 1: When the benefits gained from the cooperation of any two parties are greater than the benefits of negative innovation, that is, ${\beta }_{2}dE-C_2>0$, ${\beta }_{3}dE-C_3>0$, ${\beta }_1\left(1-a\right)d{R}_1-C_1>0$, ${\beta }_2\left(1-a\right)d{R}_2-C_2>0$, $b{W}_1-C_1-M>0$, and $b{W}_3+kM-C_3>0$, it can be determined that the eigenvalues corresponding to $E_8\left(1,1,1\right)$ are all non-positive. When $c{W}_1-C_1-F<0$, $c{W}_2-C_2<0$, and $c{W}_3+G-C_3<0$, the equilibrium point of system evolution is $E_1\left(0,0,0\right)$, and the rest of the equilibrium points are non-stable points.

Case 2: When only two parties choose to work together, the benefits obtained are less than the usual benefits of platform ecological participants, that is,${\beta }_{2}dE-C_2<0$, ${\beta }_{3}dE-C_3<0$, ${\beta }_1\left(1-a\right)d{R}_1-C_1<0$, ${\beta }_2\left(1-a\right)d{R}_2-C_2<0$, $b{W}_1-C_1-M<0$, and $b{W}_3+kM-C_3<0$. It can be determined that the eigenvalues corresponding to $E_8\left(1,1,1\right)$ are non-positive at this point and are the stability points of the replicated dynamical system. $E_6\left(1,0,1\right)$ and $E_7\left(1,1,0\right)$ are the saddle points, whereas the stability of $E_1\left(0,0,0\right)$, $E_2\left(0,0,1\right)$, $E_3\left(0,1,0\right)$, and $E_5\left(1,0,0\right)$ need further discussion, and their corresponding stability conditions are shown in

Table 4. Equilibrium point and stability.

Equilibrium Point	Case 1		Case 2
	Symbol of Eigenvalue	Conditions of Stability	Symbol of Eigenvalue	Conditions of Stability
$E_1\left(0,0,0\right)$	($\pm$,$\pm$,$\pm$)	$c{W}_1-C_1-F<0$ $c{W}_2-C_2<0$ $c{W}_3+G-C_3<0$	($\pm$,$\pm$,$\pm$)	$c{W}_1-C_1-F<0$ $c{W}_2-C_2<0$ $c{W}_3+G-C_3<0$
$E_2\left(0,0,1\right)$	($+$,$+$,$\pm$)	Unstable point	($-$,$\pm$,$\pm$)	${\beta }_{2}dE-C_2+L_2+F<0$ $c{W}_3+G-C_3>0$
$E_3\left(0,1,0\right)$	($\pm$,$\pm$,$+$)	Unstable point	($-$,$\pm$,$\pm$)	$c{W}_2-C_2>0$ $L_3+{\beta }_{3}dE-C_3+G<0$
$E_4\left(0,1,1\right)$	($+$,$-$,$-$)	Unstable point	($+$,$\pm$,$\pm$)	Unstable point
$E_5\left(1,0,0\right)$	($\pm$,$+$,$-$)	Unstable point	($\pm$,$-$,$-$)	$c{W}_1-C_1-F>0$
$E_6\left(1,0,1\right)$	($-$,$+$,$-$)	Unstable point	($+$,$+$,$+$)	Saddle point
$E_7\left(1,1,0\right)$	$(\pm$,$-$,$+$)	Unstable point	($+$,$+$,$+$)	Saddle point
$E_8\left(1,1,1\right)$	($-$,$-$,$-$)	ESS	($-$,$-$,$-$)	ESS

.

5. Simulation Analysis and Results

5.1. Parameters Setting

To intuitively demonstrate the dynamic evolutionary path and steady state of the platform collaborative governance system under different constraints, this paper adopted numerical simulation to analyze the influence of different strategies of platform enterprises, complementary enterprises, and users on the system. Then, for the two ideal evolutionary stable states, Case 1 and Case 2, we compared and analyzed the systems’ tendency to stabilize, by changing the values of the main parameters. According to the primary assumptions and stability conditions of the model, with reference to the principle of equation balance [35], the initial parameters of the system were assigned as follows: $W_1$ = 80, $W_2$ = 40, $W_3$ = 15, $R$ = 100,$C_1$ = 20, $C_2$ = 15, $C_3$ = 10, $k$ = 0.5, $M$ = 8, $L_1$ = 15, $L_2$ = 10,$L_3$ = 5, $E=$ 60,$S$ = 5, $F$ = 10, $G$ = 5, $a=b=c$ = 0.2, $d$ = 0.5, ${\alpha }_1$= 0.4, ${\alpha }_2=0.35$,${\alpha }_3=0.25$, and ${\beta }_3={\beta }_3={\beta }_3=0.5$.

5.2. Simulation Analysis

5.2.1. The Impact of Collaborative Costs

Figure 2 presents the impact of the change in governance costs on the players’ strategy choices. The critical value of ${\mathit{C}}_{\mathbf{1}}$ was in the $\left(27,28\right)$ interval when the governance cost of the complementary firms was 15 and that of the users was 10. When ${\mathit{C}}_{\mathbf{1}}$ was lower than the critical value, $\mathit{x}$ converged to 1. That is, the platform firms eventually chose the subsidy strategy, and the smaller ${\mathit{C}}_{\mathbf{1}}$ was than the critical value, the faster $\mathit{x}$ converged to 1. When ${\mathit{C}}_{\mathbf{1}}$ was greater than the critical value, $\mathit{x}$ converged to 0. The platform eventually chose the penalty strategy, and the larger ${\mathit{C}}_{\mathbf{1}}$ was than the critical value, the faster $\mathit{x}$ converged to 0.

When the management cost of the platform was 20 and the cooperating cost of users was 10, the critical value of ${\mathit{C}}_{\mathbf{2}}$ was in the interval of $\left(29,30\right)$. When ${\mathit{C}}_{\mathbf{2}}$ was less than the critical value, the initial willingness of complementary enterprises to actively participate in governance tended to decline. Then, with the enhancement of the cooperation of other members, they eventually started actively innovating. The complementary enterprises and their dynamic process of strategy change showed an asymmetrical U-shaped curve. When ${\mathit{C}}_{\mathbf{2}}$ was larger than the critical value, the rate of negative innovation of complementary firms accelerated and converged to 0.

When the governance cost of the platform was 20 and the innovation cost of complementary firms was 15, the critical value of ${\mathit{C}}_{\mathbf{3}}$ was in the range of $\left(18,19\right)$. When ${\mathit{C}}_{\mathbf{3}}$ was less than the critical value, users’ willingness to collaborate in knowledge first showed a slight downward trend, and then quickly converged to 1 with the increase in other members’ willingness to participate. Compared with the platform and complementary enterprises, users were highly motivated to contribute knowledge and were the first to converge on 1. When ${\mathit{C}}_{\mathbf{3}}$ was greater than the critical value, the speed of user passive collaboration was accelerated. The simulation results showed that platform enterprises were the most sensitive to the input of collaboration cost, followed by complementary enterprises and users. If the cooperative cost is controlled within an affordable range of the three parties, this could promote collaborative governance of the platform.

5.2.2. The Effect of Participant Strategy Selection Probabilities

Assuming that other parameters remain unchanged, Figure 3 represents the effect of changes in the incentive strategy of platform enterprises, under the condition that the probability of complementary enterprises and users actively participating in governance is 0.5. The difference in the probability of platform firm subsidies hardly impacts the willingness of complementary firms and users to actively participate. When $x=0$, the platform enterprises prefer to adopt a punitive approach to governance, and complementary enterprises and users will eventually choose to actively innovate, due to the loss caused by the inadequate performance of responsibilities.

Taking $y=0.3$, $y=0.5$, and $y=0.8$ to represent the low, medium, and high initial willingness of complementary firms to participate in innovation, when the initial desire of complementary firms to join is low, the choice of platform firms undergoes a U-shaped change, as shown in Figure 4. As the initial willingness of complementary enterprises to participate gradually becomes stronger, the U-shaped change process of platform enterprises is no longer apparent and the speed of convergence to 1 is accelerated. With $z=0.2$, $z=0.5$, and $z=0.8$, the initial willingness of users to participate in innovation is low, medium, and high. When users do not have a strong desire to participate in governance, the platform enterprises will punish them. As the willingness of users and complementary enterprises to participate increases, the platform enterprises gradually reduce the intensity of punishment, and the U-shaped characteristic of the evolutionary path is no longer prominent. The evolutionary results show that the willingness of complementary enterprises and users to participate in governance largely influences the incentive or punishment strategy of the platform enterprises. When the desire of the two in cooperative management is too low, the platform enterprises tend to resort to the punishment strategy until both parties have a strong sense of participation.

5.2.3. The Effect of Platform Subsidy $\mathit{M}$ and Utility $\mathit{k}$ of Direct Subsidy to Users

Figure 5 expresses the evolutionary impact of the three subsidy combinations on the collaborative governance system: low-subsidy, low-effect ($k=0.3$, $M=4$ and $S=2$) and high-subsidy, high-effect ($k=0.6$, $M=14$, $S=6$; $k=0.6$, $M=15$, $S=6$), respectively. The system stabilizes to $\left(1,1,1\right)$ in the low-subsidy-low-effect scenario, indicating that even if the subsidy received by complementary enterprises and users is low, it will not affect the aspiration of the two to actively participate in the end. In contrast, in the high-subsidy-high-effect scenario, when the subsidy cost borne by the platform firms increases from 14 to 15, the platform firms evolve from an incentive subsidy strategy to a penalty strategy, and the system grows steadily from $\left(1,1,1\right)$ to $\left(0,1,1\right)$, indicating that when a platform company pays excessively high incentive subsidies, it will affect its desire to incentivize.

5.2.4. The Effect of Fines Charged by Platform Firms

Figure 6 portrays the platform’s penalty effect on the evolutionary stabilization strategy of the tripartite system. When the fines charged by the platform firms to the complementary firms who passively innovate change from 15 to 30, it speeds up the active participation of complementary firms and users in management, while reducing the initial ambition of platform enterprises to adopt punitive strategies. As the deterrent effect of high fines by platform firms makes complementary firms and users show a strong desire to collaborate, platform firms also gradually adopt incentive strategies.

5.2.5. The Effect of Platform Ecological Collaborative Culture

Figure 7 presents the influence of the cultural atmosphere of cooperative governance on the platform collaborative governance system. With $d=0.3$, $d=0.4$, and $d=0.7$ indicating different cultural contexts of the governance system, it is found that the system stabilizes at $\left(0,1,1\right)$, when the participants have a low cultural identity for innovation cooperation. As the cultural identity of members to the innovation team increases from 0.3 to 0.4, the system evolution tends to move toward $\left(1,1,1\right)$. This indicates that the strategy of platform firms is more sensitive to the cultivation and transmission of innovation culture. Stakeholders in collaborative governance need to cultivate mutual trust and culture that encourages innovation, to promote the platform ecology and create more excellent innovation benefits.

5.2.6. The Effect of Collaborative Benefit Distribution

Figure 8 illustrates the benefit allocation coefficient effect on the three actors’ strategic evolution. The results show that platform firms are more sensitive to the income distribution coefficient. When the benefit allocation forms a way of earning more for more work, which is dominated by platform firms, $\mathit{x}$ converges to 1 the fastest. When the average income distribution is the mainstay, the initial ambition of platform enterprises to adopt incentive strategies shows a downward trend. When the losses brought by the platform enterprises’ choice of penalty strategies are higher than the costs, the desire of complementary enterprises and users to participate rises to a particular value. At this point, the willingness of platform enterprises to adopt incentive strategies starts to increase and eventually goes to 1. When the revenue distribution forms a democratic and equal distribution with complementary enterprises and users as the mainstay, it will accelerate the speed of active participation of complementary enterprises and users compared with the averaging revenue distribution, but the change is relatively weak.

Figure 9 shows the effect of the benefit distribution coefficient on the system evolution when only two parties cooperate. Figure 9a presents the impact of the income distribution coefficient between the platform and complementary firms when the users are not enthusiastic about contributing knowledge. Figure 9b depicts the influence of the revenue distribution coefficients between platform firms and users when the complementary firms passively innovate. The evolutionary results indicate that the averaged revenue distribution cannot promote the active participation of platform members in governance. In summary, it can be seen from Figure 8 and Figure 9 that when there is a significant difference in the collaborative investment involved in governance, more work and a greater payoff distribution is better at promoting cooperation among members.

5.3. Results and Discussion

Through a simulation analysis, this paper considered the impact of six groups of parameter changes on the collaborative governance of the platform: the cost of cooperative governance, probability of participants choosing different strategies, subsidy amount and subsidy effect under the incentive strategy of platform enterprises, fines under the punishment strategy of platform enterprises, collaborative culture, and distribution of collaborative benefits.

A discussion of the impact of changes in each parameter on platform participants’ returns is as follows: (1) The cost of cooperation influences the strategy choice of collaboration among platform ecosystem subjects. Platform enterprises, as the dominant player in collaborative governance, are more sensitive to the input of the cost of cooperation. If the collaborative cost that the participants of collaborative governance need to bear is higher than the benefit obtained, it will increase the ambition of the three parties to negatively collaborate. Therefore, as a ‘community of destiny’, on the one hand, the participants should reasonably plan for the cost of cooperative inputs and formulate cost-sharing contracts. On the other hand, platform enterprises should use the advantages of digital technology and network resources to promote the networked collaboration of participants, minimize the cost of cooperation, and promote a win-win situation for all parties. (2) The willingness of platform enterprises, complementary enterprises, and users to collaborate have different effects on the evolutionary system. When platform firms punitively engage in collaborative governance, it does not affect the eventual evolution of complementary firms to actively collaborate. When complementary firms and users have low desire to collaborate, platform firms tend to adopt a punishment strategy. With an increase in opportunity cost implied by the punishment strategy, the cheerful cooperative willingness of complementary enterprises and users will be enhanced, and platform enterprises will gradually adopt a subsidy strategy. (3) The simulation results of the three incentive–subsidy combinations show that a lower subsidy can also motivate complementary firms and users to actively collaborate. When the subsidy provided by the platform enterprise to the complementary enterprises is too high, the platform enterprise will give up the incentive due to the high cost and choose the punishment, even if it produces a good subsidy effect on users. Therefore, on the one hand, platform enterprises should focus on setting reasonable subsidy thresholds and pay attention to spiritual incentives for complementary enterprises and users. On the other hand, they should improve the effectiveness of user subsidies, creating open and transparent communication with users and reducing information asymmetry between the two sides. (4) As shown in Figure 6, the strategic choice of platform enterprises shows a U-shaped transformation process of ‘decrease-increase‘ of incentive willingness in the process of cooperative governance. In the early stage of evolution, the punishment strategy of platform enterprises seems to be more effective. As the amount of fines increase, it accelerates complementary enterprises and users choosing the innovation coordination strategy. With the increasing willingness of both parties to actively participate in governance, platform enterprises eventually change from the punishment strategy to adopt the subsidy policy, and the three parties will finally reach the equilibrium state of $\left(1,1,1\right)$. (5) The cultural atmosphere is more sensitive to the members than other factors affecting the cooperative governance strategies of platform participants. When the cultural atmosphere of the system is more substantial, the ambition of the participants to actively collaborate will be stronger. Therefore, platform companies should strive to cultivate a collaborative culture that encourages innovation. (6) Due to different role positions and division of labor among members, the collaborative investment will have some differences. Compared with the average income distribution method, more work and more pay are more likely to accelerate participants’ eventual choice for active collaboration.

6. Conclusions and Implications for Future Research

6.1. Conclusions

The purpose of this paper is to examine how platform enterprises can build an effective collaborative governance structure and motivate other important stakeholders in the ecosystem to actively participate in governance to promote the organic cycle of the platform. By introducing evolutionary game theory and collaborative governance theory to explain the impact of participant interactions on the development of the platform, this paper constructs a conceptual model of collaborative governance among platform enterprises, complementary enterprises, and users. It also explores the influence of parameters, such as governance costs, willingness to cooperate, subsidy and punishment, and benefit distribution ratios on the decision-making behavior of collaborative members. The simulation results showed that collaborative culture is a critical link in designing a collaborative governance mechanism. Successful collaborative governance is more likely to emerge in an organizational environment with a high commitment to the values, mission, and vision of the platform. Meanwhile, in a collaborative governance structure with a strong centripetal force, complementary firms and users seem to have a strong willingness to cooperate and innovate, regardless of the strategies adopted by the platform firms. Therefore, platform enterprises, as organizers and leaders of collaborative governance, should actively bear governance responsibilities and encourage complementary enterprises and users to actively participate in the process to achieve greater value creation.

6.2. Implications for Practice

Collaborative governance of the platform requires the joint participation of platform enterprises, complementary enterprises, and users. According to the above research findings, this paper presents practical implications for platform enterprises. (1) Build a collaborative governance platform for participants. The enthusiasm of complementary enterprises and users to participate in governance does not change with the choice of incentive subsidies or punishment strategies of platform enterprises. ‘Collaboration’ is a high-quality cooperation for common goals, so it is important to emphasize cultural characteristics such as trust and identity. Platform companies should build a real-time interactive and sharing platform for three-party collaboration. Whether they can provide technical support and an interactive culture for other members is crucial in determining whether the collaborative governance system can effectively operate. (2) Focus on the innovation of complementary enterprises and knowledge contribution behavior of users. In the era of value co-creation, the interaction between enterprises and users becomes a key source of value creation. Complementary enterprises and users should be aware of their essential roles in the collaborative governance system and take more initiative. At the same time, due to the difference in synergy costs invested by the three parties, the level of effort of all parties should be comprehensively considered. A reasonable cost-sharing mechanism and benefit distribution mechanism should be formulated to reduce the difficulty of cooperation for stakeholders to participate in management.

6.3. Future Work

This paper constructs a collaborative governance model of platform participants in different cultural contexts. Although this model provides platform members with guidance that is different from the social responsibility governance perspective, there are still some limitations in terms of theory and methodology. Subsequent studies should conduct an in-depth analysis of the mechanisms of mutual influence among parameters and the reasonable allocation mechanism of the cost. At the same time, further investigation is needed to obtain actual data of collaborative governance system parameters to represent the natural characteristics of the enterprises and users for empirical analysis and to develop effective cooperative incentive.