Evolutionary Game and Simulation Analysis of Collaborative Innovation Mechanisms of Industrial Internet Platform-Based Ecosystem

Abstract

Digital platforms are transforming almost every industry today. To gain insight into the innovation mechanism of the industrial Internet platform-based ecosystem, combining its nature of sustainability, this paper investigates strategic factors, such as the intensity of platform governance, the eco-efficiency of cooperation, and the input costs of complementors. A platform ecological system game model comprised of the industrial Internet platform enterprise, industry chain complementors, and innovation chain complementors is then established. The results of game playing and simulation highlight four important facts as revealed by a Chinese COSMOPlat case. First, there are four evolutionary paths for collaborative relations among innovation entities in an ecosystem. Second, platform enterprise may utilize various strategies in the several stages of ecosystem evolution. Third, complementors in the industrial chain and innovation chain have different degrees of dependence on platform enterprise and distinct incentive factors. Finally, investment of platform enterprise in data security drives the construction and upgrading of the ecosystem. In this context, collaborative innovation in platform ecosystems is associated with a self-evolving, self-growing, self-driven, and sustainable cooperation and win–win mechanism. This study provides new ideas for the governance of the industrial Internet platform-based ecosystem.

1. Introduction

In recent years, the new generation of information technology has been deeply integrated into the manufacturing industry, and many countries expect to seek a new impetus for economic development through transformation and upgrades to the manufacturing industry [1]. Relying on the interface rules and open architecture set by platform enterprise, the industrial Internet platform can realize the ubiquitous link of industrial data elements, attract external participants, and jointly provide products and services for users, thus playing a significant role in promoting the high-quality development of China’s industrial economy and realizing the transformation and upgrading of the manufacturing industry [2,3,4]. In this situation, the global market of the industrial Internet platform maintains an active and innovative development trend, and the driving forces of the industrial Internet platform for digital transformation of the manufacturing industry are gradually emerging. According to the global market research consulting firm Marketsandmarkets, it is expected that the infrastructure and industrial development of China and other emerging economies, such as India and South Africa, will continue to promote the growth of the industrial Internet market before 2025. In the fastest-growing Chinese market, digital platforms represented by COSMOPlat and INDICS have emerged, and an industrial Internet platform ecosystem has been preliminarily built, which is expected to give rise to the world’s largest industrial Internet market in the future. This market will serve as a functional link and carrier competing with other emerging economies [5,6].

However, not all innovative ecosystems built on the industrial Internet platform can sustain and profit from the competition. The dichotomy between competition and cooperation is particularly evident in the construction investment and market return of platform enterprise within the platform ecosystem and in the collaborative innovation behavior of participants. There are two main reasons for this dichotomy: Firstly, the industrial Internet platform ecosystem is dynamic and complex due to its heterogeneous members and diverse interaction behaviors, which make it more difficult for the platform enterprise to govern [7]. Secondly, the cooperation strategies of complementors will evolve with the continuous evolution of ecosystems built by platform enterprise [8,9], and the traditional static innovation mechanisms will inevitably result in unsustainable systems. Therefore, this paper focuses on the following questions: (1) What are the components of an industrial Internet platform ecosystem? (2) What mechanism should platform enterprise and complementors in an ecosystem use to innovate? (3) Further, in different stages of system evolution, what strategies should a platform enterprise and complementors implement to promote sustainable innovation and bring high returns to the whole ecosystem?

As far as the industrial Internet platform ecosystem is concerned, existing research mainly focuses on its connotation, value, architecture design, enabling path, and sustainability. Liu et al. [5] and Zuo et al. [1] analyzed the connotation and characteristics of industrial Internet platform ecosystems and believed that it was a complex system formed by the interaction between different participating groups and the external environment. Gawer et al. [10] classified platforms into different types and confirmed that within industry platforms, external innovators as innovative business ecosystems can develop their complementary products, technologies, or services. Tao et al. [11] analyzed the importance of industrial Internet platform ecosystems and proposed that the construction of industrial ecology coordinated by different participating groups is a fast channel to support the development of industrial enterprise. Wang et al. [12] proposed a collaborative architecture of an industrial Internet platform to manage the interaction between physical and network components. Kim [13] analyzed the enabling paths of industrial Internet platform ecosystems and found that platform enterprise could build a stable business ecosystem by analyzing quality management and income structure, thus providing value and benefits for all participants. Inoue et al. [14] and Calabrese et al. [15] analyzed the strategic and innovative behavior of industrial Internet platform ecosystems and argued that ecosystem sustainability is a major source of maintaining the competitiveness of a firm or organization.

In addition, there are also studies related to the strategic research of interaction behavior between platform enterprise and participating groups in an industrial Internet platform ecosystem. For example, Zhu et al. [16] and Sun et al. [17] reviewed the growth and evolution mechanism of platform enterprises and the relationship among manufacturing enterprise groups from the perspective of interactive empowerment, and they proposed a universal development model for industrial Internet platform enterprises. From the perspective of blockchain, Zhang et al. [18] proposed a consensus-based model of distributed collaboration among industrial Internet platform enterprises to overcome distrust and insecurity among participating enterprises. Menon et al. [19] studied the behaviors of platform enterprises and end users from the perspective of openness and provided strategies for end users to choose among different platforms for cooperation. From the perspective of value co-creation, Li et al. [20] used the evolutionary game method to analyze the influencing factors of cooperation between industrial Internet platform enterprises and SMEs, and they then proposed a system evolution equilibrium strategy.

According to the literature review, the existing research has a certain reference role for collaborative innovation. In terms of research content, scholars attach importance to the enabling role and sustainability of ecosystem innovation of industrial Internet platforms and have divided ecosystem members of industrial Internet platforms. However, most of the current research focuses too much on the construction of industrial Internet platform ecosystems, while research on the sustainable innovative interaction behavior strategies of various groups in a system is largely ignored. Further, although industrial Internet platform enterprises combining their complementors need to carry out collaborative innovation to improve the competitiveness of the ecosystem, existing studies have generally ignored the fact that complementors are also active players, and, consequently, in the process of collaborative innovation with platform enterprises, they will also evolve different strategic behaviors in line with the ecological strategic scenarios within the system [21,22,23,24]. Moreover, the complementors will not actively co-create and share with platform enterprises due to limited rationality and benefit maximization. This will only happen with the driver created by the internal dynamic mechanism of sustainable value logic and through the incentive and governance strategies implemented by platform enterprise. The sustainable goal of maintaining ecosystem competitiveness of industrial Internet platforms can be realized by improving the willingness of the complementors to collaborate on innovation.

Compared with the existing literature, the contributions of this study are as follows: (1) By using the thought of value creation and distribution contained in the competition and cooperation strategy [25], this paper reveals the strategic behaviors chosen by complementors under different ecological strategic situations, providing a new idea for addressing the problems of easy breakdown of collaborative innovation relationship and low innovation enthusiasm of complementors in an ecosystem. (2) Based on the sustainable innovation theory proposed by Calabrese et al. [15], this paper embeds sustainable value logic into a dynamic model of three-party evolutionary game among platform enterprises, industrial chain complementors, and innovation chain complementors, avoiding the traditional static innovation mechanism that aims at maximizing benefits for platform enterprise. (3) This paper creatively incorporates scientific research institutions, universities, and other supporting groups into the evolutionary game model. The findings of this study provide alternative method for the governance of industrial Internet platform enterprises and complementors.

2. Theoretical Framework and Hypothesis Development

2.1. Theoretical Framework

Tiwana [26] defined a platform ecosystem as “a system that is different from products and services, and a third type of business model developed by platform organizations”. It can be seen from the scenario with embedded industrial Internet that an industrial Internet platform is no longer a one-time trading platform. Instead, it provides a more personalized and customized sustainable ecosystem through continuous interaction with users [27,28]. In this paper, we consider industrial Internet platform ecosystem as an organic whole enabled by modular architecture platforms and supported by industrial Internet technology. The system consists of four core elements: platform enterprise, complementors in the industrial chain (hardware and software suppliers, service providers, and other groups), complementors in the innovation chain (universities, research institutes, and other groups), and the external environment [1,29,30]. It is essentially a new sustainable industrial organization form with continuous self-evolution, self-growth, and self-adaptation, aiming to support industrial transformation and upgrading [5,31].

The sustainable innovation theory is derived from the concept of “diversity of ecological innovation” proposed by Carrillo-Hermosilla et al. [32] in 2010, who believed that ecological innovation can be an effective measure for the sustainable development of the platform innovation ecosystem. Subsequently, Calabrese et al. [15] defined sustainable innovation as an innovative behavior that improves sustainability performance in terms of ecology, society, and economy, and their research focus on the level of industrial organization is the continuous interaction with complementors in the governance process of sustainable innovation [33]. Based on the above theories, this paper constructs a sustainable innovation mechanism of an industrial Internet platform-based ecosystem starting from a platform enterprise governance mechanism, as shown in Figure 1. According to this innovation mechanism, the interactive behavior patterns of various innovation entities in a system are dominated by platform enterprise that integrate and coordinate heterogeneous resources. For the industrial chain complementor, a platform enterprise builds the industrial Internet platform, realizes intelligent production, and drives industrial transformation and upgrading. For the innovation chain complementor, platform enterprises provide an open platform architecture and interface to achieve innovation empowerment and platform upgrading.

2.2. Hypothesis Development

In the context of a platform ecosystem sustainable innovation mechanism built on governance mechanisms of platform enterprise, how does the innovation behavior of complementors evolve in response to the behavioral strategies of platform enterprise, and what factors influence their collaborative innovation activities? The objective of this study is two-fold: (1) To identify what actions complementors typically take to respond to changes in the strategies of platform enterprise and to maintain their unique competitiveness. (2) To provide an overall picture of what factors influence the collaborative innovation behavior of complementors and platform enterprise and to suggest countermeasures for ensuring the sustainability of platform ecosystems.

Analysis of the game strategies of complementors and platform enterprise: The industrial Internet platform ecosystem selected for this paper is built by a smart manufacturing enterprise and, thus, the platform enterprise has the core dominant power, acting as a decision maker in the process of collaborative innovation with complementors and implementing incentives or governance strategies to sustain collaborative innovation with complementors. For complementors, collaborative innovation is the only way to achieve prosperity, as rapid economic development and technological iteration increase the demand for and risk of innovation. However, not all complementors can build the platform ecosystem, and many firms have joined existing platform ecosystems to reap the dividends of rapid ecological expansion [34]. Complementors seek competitive advantages through the sharing of supporting resources and technology and reasonable benefit distribution in the industrial Internet platform. In this way, their competition and cooperation properties evolve synergistically, guiding, transforming, linking, and relying on each other, and eventually forming a dichotomous relationship between competition and cooperation [35]. Therefore, the game strategy of complementors is a combination of competition and cooperation.

Analysis of the key factors of complementors and platform enterprise: In a realistic scenario where the development of industrial Internet is still in its infancy, complementors need to enter the ecosystem because they cannot afford the high cost of platform construction, but they may miss out on ecological technological dividends due to large platform access cost and concerns about the security of their corporate data. In such cases, a platform enterprise may choose to provide value-added services for complementors at the beginning of the platform ecosystem to reduce their platform access cost. On the other hand, small- and medium-sized complementors admitted by the platforms can suffer from a lack of independent innovation ability due to overreliance on the platforms. To address this situation, platform enterprise usually signs a phased collaborative innovation contract with the complementors, the purpose of which is to urge the complementors to innovate more actively. In this paper, we deconstructed the structural relationship of the ecosystem and the operational mechanism of the interaction behavior of innovation subjects. On this basis, we identified the impact of factors, such as input costs and data security, on platform enterprise and complementors, and we analyzed how platform enterprise and complementors create overall competitiveness through dynamic and stable collaborative innovation mechanisms, which is particularly vital for their sustainable development.

3. Materials and Methods

3.1. Model Variables and Assumptions

In the evolutionary game model constructed in this paper, there are three groups of participants, namely platform enterprise, industry chain complementor, and innovation chain complementor, each group playing different roles in the ecosystem and having unique innovation resources. They have a competitive and cooperative relationship with each other, and changes in key factors will affect their respective strategic choices. Based on the above analysis, this paper proposes the following five hypotheses from a sustainable perspective, combining the “cost–benefit” model and evolutionary game theory:

Premise 1: Participants in a game process include a platform enterprise, an industrial chain complementor, and an innovation chain complementor, and all game players are rationally bound.

Premise 2: Platform enterprise (P) will adopt different strategies to carry out collaborative innovation with the complementors. Its strategy set is (incentive and governance) and the probability of the two strategies is x (0 ≤ x ≤ 1) and 1 − x, respectively. Similarly, the industrial chain complementor (D) and innovation chain complementor (G) can also choose different strategies according to their own needs, and their strategy set is (cooperation and competition). Their corresponding strategy probabilities are y (0 ≤ y ≤ 1) and 1 − y, and z (0 ≤ z ≤ 1) and 1 − z, respectively.

Premise 3: The ecosystem construction cost of a platform enterprise is denoted as K, and the cost of implementing platform governance to maintain sustainable development of the system is denoted as L (K > L). The total input cost of the information infrastructure required by the industrial chain complementor to access the industrial Internet platform is denoted as C. When the innovation chain complementor and platform enterprise jointly develop key generic technologies, they need to invest certain technology and human resources, and the total cost is denoted as M. Platform enterprise provides value-added services (such as service market promotion and platform connection technical support) to encourage the industry chain complementor to access the platform and maintain a strategic relationship with continuous innovation collaboratives, which will reduce the total input cost C of the industry chain complementor. The reduced part is denoted as S, and the cost of the industry chain complementor is, therefore, C-S.

Premise 4: The traditional revenue from the normal operation of platform enterprise is recorded as R₁. The traditional earnings of the industrial chain complementor and the innovation chain complementor before they enter the ecosystem are denoted as R₂ and R₃, respectively. When platform enterprise, industrial chain complementor, and innovation chain complementor jointly carry out sustained collaborative innovation by focusing on user scenarios, the platform enterprise will obtain ecological benefits, which are denoted as E₁, and the total ecological benefits of the two complementors are denoted as E₂. Assuming the user value-added sharing coefficient of the industrial chain complementor is t (0 ≤ t ≤ 1), its ecological benefits will be tE₂. Assuming the user value-added sharing coefficient of the innovation chain complementor is 1 − t, its ecological benefits will be (1 − t) E₂. When one of the complementors withdraws from the ecological competition strategy, the platform will still receive ecological benefits, which are recorded as E₃ (E₃ < E₁), and meanwhile, the cooperative complementor will also obtain ecological benefits, which are recorded as E₄ and E₅ for the two complementors, respectively.

Premise 5: The realistic situational constraints on continuous collaborative innovation among platform enterprise, industrial chain complementor, and innovation chain complementor come from two aspects: First, after the complementors join the industrial Internet platform, due to concerns about their network and data security, they may take certain measures that prevent platform enterprise from expanding the ecosystem and maintaining active users, and the data security costs, thus incurred, are denoted as H. Second, governance is required after access to the platform. To encourage and urge continuous innovation of the complementors, platform enterprise may sign a cooperation contract with complementors during the cooperation period. Speculative behaviors or similar negative behaviors of the complementors will reduce the value-added services provided by the platform, and the loss of such speculative behaviors is recorded as F₁ and F₂ for the two complementors, respectively.

3.2. Model Building

Based on the above assumptions, a payoff matrix is obtained for the competitive and cooperation strategy game model of the industrial Internet platform ecosystem, as shown in

Table 1. The payoff matrix of a tripartite game between a platform enterprise, an industrial chain complementor, and an innovation chain complementor.

Innovation Chain Complementor			Platform Enterprise
			Incentive x	Governance 1 − x
Industrial chain complementor	cooperation y	cooperation z	R1 + E1 − K, R2 + tE2 − (C − S), R3 + (1 − t) E2 − M	R1 + E1 − K, R2 + tE2 − C, R3 + (1 − t) E2 − M
		competition 1 − z	R1 + E3 − K − H, R2 + E4 − (C − S), R3	R1 + E3 + F2 − L, R2 + E4 − C, R3 − F2
	competition 1 − y	cooperation z	R1 + E3 − K − H, R2, R3 + E5 − M	R1 + E3 + F1 − L, R2 − F1, R3 + E5 − M
		competition 1 − z	R1 − K, R2, R3	R1, R2, R3

.

3.3. Model Analysis

3.3.1. Construction of a Return Expectation Function of the Industrial Internet Platform-Based Ecosystem

The expected return of platform enterprise after choosing incentive or governance strategy and the average expected return ($U_{11},U_{12},\overline{U_1}$) are given below, respectively:

$$\begin{array}{c}{U}_{11}=yz\left(R_1+E_1-K\right)+y(1-z)\left(R_1+E_3-K-H\right)\\ +(1-y)z\left(R_1+E_3-K-H\right)\\ +(1-y)(1-z)\left(R_1-K\right)\\ U_{12}=yz\left(R_1+E_1-L\right)+y(1-z)\left(R_1+E_3-L\right)\\ \hspace{1em} +(1-y)z\left(R_1+E_3-L\right)+(1-y)(1-z)R_1\\ \overline{U_1}=x{U}_{11}+(1-x)U_{12}\end{array}$$

The expected return of the industrial chain complementor after choosing cooperation or competition strategy and the average expected return ($U_{21},U_{22},\overline{U_2}$) are given below, respectively:

$$\begin{array}{c}{U}_{21}=xz\left[R_2+t{E}_2-(C-S)\right]+x(1-z)\left[R_2+E_4-(C-S)\right]\\ \hspace{1em} +(1-x)z\left[R_2+t{E}_2-C\right]+(1-x)(1-z)\left(R_2+E_4-C\right)\\ U_{22}=xz{R}_2+x(1-z)R_2+(1-x)z\left(R_2-F_1\right)+(1-x)(1-z)R_2\\ \overline{U_2}=y{U}_{21}+(1-y)U_{22}\end{array}$$

The expected return of the innovation chain complementor after choosing cooperation or competition strategy and the average expected return complementors ($U_{31},U_{32},\overline{U_3}$) are given below, respectively:

$$\begin{array}{c}{U}_{31}=xy\left[R_3+(1-t)E_2-M\right]+(1-x)y\left[R_3+(1-t)E_2-M\right]\\ +x(1-y)\left[R_3+E_5-M\right]+(1-x)(1-y)\left[R_3+E_5-M\right]\\ U_{32}=xy{R}_3+(1-x)y\left(R_3-F_2\right)+x(1-y)R_3+(1-x)(1-y)R_3\\ \overline{U_3}=z{U}_{31}+(1-z)U_{32}\end{array}$$

3.3.2. The Solution of the Replicator Dynamic Equation of Industrial Internet Platform-Based Ecosystem using Evolutionary Stability Strategy

According to the above analysis, the replicator dynamic equation for the strategy selection of platform enterprise can be written as follows:

$$\begin{array}{c}F\left(x\right)=dx/dt=x(1-x)\left(U_{11}-U_{12}\right)\hfill \\ =x(1-x)[-yz(L-2H)-y(H-L)-z(H-L)-K]\hfill \end{array}$$

(1)

The replicator dynamic equation for strategy selection of the industrial chain complementor is as follows:

$$\begin{array}{cc}& F\left(y\right)=dy/dt=y(1-y)\left(U_{21}-U_{22}\right)\hfill \\ & =y(1-y)\left[z\left(F_1-E_4+t{E}_2\right)+xS-xz{F}_1+E_4-C\right]\hfill \end{array}$$

(2)

The replicator dynamic equation for strategy selection of the innovation chain complementor is as follows:

$$\begin{array}{c}F\left(z\right)=dz/dt=z(1-z)\left(U_{21}-U_{22}\right)\hfill \\ =z(1-z)\left[-y\left(E_5-E_2-F_2+t{E}_2\right)-xy{F}_2-M+E_5\right]\hfill \end{array}$$

(3)

Formulas (1)–(3) are combined to obtain the replication system of platform enterprise, industrial chain complementor, and innovation chain complementor:

$$\left\{\begin{array}{c}F\left(x\right)=x(1-x)[-yz(L-2H)-y(H-L)-z(H-L)-K]\\ F\left(y\right)=y(1-y)\left[z\left(F_1-E_4+t{E}_2\right)+xS-xz{F}_1+E_4-C\right]\\ F\left(z\right)=z(1-z)\left[-y\left(E_5-E_2-F_2+t{E}_2\right)-xy{F}_2-M+E_5\right]\end{array}\right.$$

(4)

According to the theorem proposed by Friedman [36], the evolutionary stability strategy (ESS) of a replicator dynamic equation system can be obtained from the local stability analysis of the Jacobian matrix of the system. Let F(x) = 0, F(y) = 0, F(z) = 0, and the equilibrium points of the system are $E_1(0,0,0)$, $E_2(1,0,0)$, $E_3(0,1,0)$, $E_4(0,0,1)$, $E_5(1,1,0)$, $E_6(1,0,1)$, $E_7(0,1,1)$, and $E_8(1,1,1)$, $E_1$ to $E_8$ are pure strategy Nash equilibrium solutions of the evolutionary game. The Jacobian matrix of the three-party evolutionary game system is:

$$J=\left[\begin{array}{ccc}{J}_1& J_2& J_3\\ J_4& J_5& J_6\\ J_7& J_8& J_9\end{array}\right]=\left[\begin{array}{ccc}\frac{dF\left(x\right)}{dx}& \frac{dF\left(x\right)}{dy}& \frac{dF\left(x\right)}{dz}\\ \frac{dF\left(y\right)}{dx}& \frac{dF\left(y\right)}{dy}& \frac{dF\left(y\right)}{dz}\\ \frac{dF\left(z\right)}{dx}& \frac{dF\left(z\right)}{dy}& \frac{dF\left(z\right)}{dz}\end{array}\right]$$

(5)

where

$$=\left[\begin{array}{ccc}(1-2x)[-yz(\mathrm{L}-2H)& x(1-x)[-z(\mathrm{L}-2H)& x(1-x)[-y(\mathrm{L}-2H)\\ -y(H-L)-z(H-L)-K]& -(H-L)-K]& -(H-L)-K]\\ y(1-y)\left(S-z{F}_1\right)& (1-2y)\left[z\left(F_1-E_4+t{E}_2\right)\right.\left.+x\mathrm{S}-xz{F}_1+E_4-C\right]& y(1-y)\left(-x{F}_1+F_1-E_4+t{E}_2\right)\\ z(1-z)\left(-y{F}_2\right)& z(1-z)\left(-x{F}_2-E_5+E_2+F_2-t{E}_2\right)& (1-2z)\left[-y\left(E_5-E_2-F_2+t{E}_2\right)\right.\left.-xy{F}_2-M+E_5\right]\end{array}\right]$$

3.3.3. Stability Analysis of Equilibrium Points in the Evolutionary Game System

The Jacobian eigenvalues corresponding to the above equilibrium points are shown in

Table 2. The eigenvalues of the Jacobian matrix.

Equilibrium Point	Eigenvalue λ1	Eigenvalue λ2	Eigenvalue λ3
E1 (0,0,0)	−K	E4 − C	E5 − M
E2 (1,0,0)	K	E4 − (C − S)	E5 − M
E3 (0,1,0)	L − (K + H)	C − E4	(1 − t) E2 + F2 − M
E4 (0,0,1)	L − (K + H)	F1 + tE2 − C	M − E5
E5 (1,1,0)	(H + K) − L	−[E4 − (C − S)]	(1 − t) E2 − M
E6 (1,0,1)	(H + K) − L	tE2 − (C − S)	M − E5
E7 (0,1,1)	L − K	−(F1 + tE2 − C)	−[(1 − t) E2 + F2 − M]
E8 (1,1,1)	K − L	−[tE2 − (C − S)]	−[(1 − t) E2 − M]

.

To facilitate the analysis of Jacobian matrix eigenvalue symbols corresponding to different equilibrium points, without losing generality, we suppose that $E_4-\left(C-S\right)>0$; ${tE}_2-\left(C-S\right)>0$. If platform enterprise implements the incentive strategy, the ecological benefit of the industry chain complementor is greater than its cost; that is, when x = 0, the industry chain complementor will choose to cooperate with platform enterprise. Therefore, equilibrium points $E_2(\mathrm{1,0},0)$ and $E_6\left(\mathrm{1,0},1\right)$ are not considered anymore, as shown in

Table 3. Local stability of the equilibrium points (Cases 1, 2, and 3).

Equilibrium Point	Case 1				Case 2				Case 3
	λ1	λ2	λ3	Stability	λ1	λ2	λ3	Stability	λ1	λ2	λ3	Stability
E1 (0,0,0)	−	−	−	ESS	−	+	+,−	Instability point	−	+,−	+	Instability point
E3 (0,1,0)	−	+	+	Instability point	−	−	−	ESS	−	+,−	+,−	Instability point
E4 (0,0,1)	−	+	+	Instability point	−	+,−	+,−	Instability point	−	−	−	ESS
E5 (1,1,0)	+	−	+,−	Instability point	+	−	−	Instability point	+	−	+,−	Instability point
E7 (0,1,1)	−	−	−	ESS	−	+,−	+	Instability point	−	+	+,−	Instability point
E8 (1,1,1)	+	−	+,−	Instability point	+	−	+	Instability point	+	−	+,−	Instability point

. The stability strategy of an evolutionary game with eigenvalues of different equilibrium points is discussed by case as follows:

(1)

Case 1. When $E_4-C<0$ and $E_5-M<0$ or ${tE}_2+F_1-C>0$ and $({1-t)E}_2+F_2-M>0$, the eigenvalues corresponding to the equilibrium points $E_1(0,0,0)$ and $E_7(0,1,1)$ are all negative; that is, the strategy combinations (governance, competition, competition) and (governance, cooperation, cooperation) are stable points under this situation. In (governance, competition, competition) strategy combination, the ecological benefits obtained by the complementors through cooperation are less than their cost, so they will stop cooperating with platform enterprise and choose the competition strategy. In (governance, cooperation, cooperation) strategy combination, the ecological benefits obtained by the complementors through cooperation are greater than their cost, and they will continue to cooperate with platform enterprise and choose cooperation strategy.

(2)

Case 2. When $E_4-C>0$ and $({1-t)E}_2+F_2-M<0$, the eigenvalues corresponding to the equilibrium point $E_3(0,1,0)$ are all negative; that is, the strategy combination (governance, cooperation, competition) is the stable point in this situation. In (governance, cooperation, and competition) strategy combination, the ecological benefits obtained by the industrial chain complementor through cooperation are greater than the cost, while the ecological benefits obtained by the innovation chain complementor through cooperation complementors are less than the cost. Therefore, the industrial chain complementor will choose the cooperation strategy, while the innovation chain complementor will stop the cooperation and choose the competition strategy.

(3)

Case 3. When ${tE}_2+F_1-C<0$ and $E_5-M>0$, the eigenvalues corresponding to the equilibrium point $E_4(0,0,1)$ are all negative; that is, the strategy combination (governance, competition, cooperation) is the stable point in this situation. Similarly, in (governance, competition, and cooperation) strategy combination, when the ecological benefits obtained by the complementors are less than their cost, they will choose competitive strategy.

In summary, there are four evolutionary paths for the collaborative relation among innovation entities in the ecosystem, namely (governance, competition, competition), (governance, cooperation, cooperation), (governance, cooperation, competition), and (governance, competition, cooperation). In all four paths, platform enterprise chooses governance strategy, indicating that the sustainable interactive operation between platform enterprise and complementors in the ecosystem is carried out through the platform governance mechanism. The fact that cooperation and competition are both optional strategies for the complementors shows that the interaction behavior and the value creation mechanism between platform enterprise and the complementors are dynamic. Therefore, given the different paths derived from the different assumptions given in the above three cases, the key factors affecting the collaborative relation between platform enterprise and complementors are mainly cost and benefit, and related parameters include the input cost of platform enterprise and complementors and ecological benefits of the complementors. To find out more clearly how the above key factors affect the creation of value of platform enterprise and complementors, sensitivity analysis of key factors will be carried out based on the ideal collaborative state $E_7(0,1,1)$ for the innovation subjects in the ecosystem, that is, the simulated strategy combination of governance, cooperation, and cooperation.

4. Analysis of Case Simulation of the Ecosystem of COSMOPlat

4.1. Case Selection and Simulation Parameter Assignment

COSMOPlat, a subsidiary of Haier, is a digital platform that provides industrial internet services, including industrial Internet platform operation, industrial intelligence research, intelligent control, intelligent equipment, and automation. COSMOPlat was founded in 2017 and is based in Shanghai, China. By 2021, the COSMOPlat ecosystem had more than 700,000 registered customers and more than 6000 trading customers, with an overall trading volume of RMB 21 billion. Further, 30 million devices have been connected to the platform, and it now hosts more than 10,000 industrial apps. Moreover, the selection of the COSMOPlat case lies in the following specific reasons:

(1)

The COSMOPlat ecosystem has taken shape and been regarded as a pioneer in China’s Internet industry. However, in COSMOPlat’s initial stage, only a few complementors were able to access the platform. However, with the continuous development and deepening of the platform, the complementors within the ecosystem gradually increased and formed stable groups. In this process, platform enterprise and complementors have continuously interacted and innovated collaboratively, and the stable paths formed in the collaborative innovation process are similar to those discussed in this study: They are both affected by costs and benefits. Therefore, it is of great significance to evaluate the impact of platform enterprise input cost K, complementor input cost C, user value-added sharing coefficient t, data security H, speculative behavior F₁ and F₂, and value-added service S on the evolutionary equilibrium strategy of each innovation entity by using the examples of the COSMOPlat ecosystem. The second reason is data objectivity and accessibility. This study obtained primary information through surveys and interviews, supplemented by secondary information, such as enterprise annual reports, official website information, news reports, and industry reports. Furthermore, one of the authors of this paper worked for the Haier Group for about 7 years; accordingly, he deeply understands the innovation and development of the company, combining the process of building an ecosystem and promoting an ecological brand strategy based on COSMOPlat.

(2)

According to official statistics, by 2021, China had built more than 100 industrial Internet platforms, but only a small number of these platforms have developed steadily like COSMOPlat. Therefore, the collaborative innovation mechanisms of the innovation subjects in the COSMOPlat ecosystem can be references for industrial networking platforms that are still in their infancy. In this study, relevant parameters are assigned, with a unified unit of RMB one million. The initial willingness values of the three parties are set as x = y = z = 0.5, F₁ = 10, F₂ = 10, K = 10, L = 5, H = 5, E₄ = 20, E₂ = 40, E₅ = 10, C = 10, t = 0.5, S = 5, M = 6, satisfying the conditions of ${tE}_2+F_1-C>0$ and $({1-t)E}_2+F_2-M>0$ in Case 3. MATLAB R2022a was used for numerical simulation.

4.2. Sensitivity Analysis

4.2.1. The Impact of Platform Enterprise Input Cost and Value-Added Service on Sustainable Collaborative Relation

Figure 2 shows the impact of the input cost K of COSMOPlat on the sustainable collaborative relation in the system. As can be seen from Figure 2, the platform input cost K is assigned with three values of 5, 10, and 15, respectively, and all three parties start from the initial willingness of 0.5. The simulation results show that with an increase in the input cost K, the probability of the COSMOPlat choosing a governance strategy gradually increases at an accelerating pace.

When the input cost K is 5, COSMOPlat is in the initial stage of construction, focusing mainly on the construction of the platform architecture. At this time, COSMOPlat has a weak ability to attract external partners, and most of the cooperative complementors are existing partners, so it tends to implement an incentive strategy. When K is 10, the platform technology structure of COSMOPlat is completed and it has been approved as the “first national industrial Internet demonstration platform”. The influence of the platform gradually increases, which makes a large number of enterprises swarm into the ecosystem. At this point, the network effect of COSMOPlat continues to improve and it enters the stage of platform development. Consequently, it turns to a platform governance strategy. When K is 15, COSMOPlat begins to enter the stage of professional deepening, participating in the compilation of national intelligent manufacturing standards, and gradually leading to the construction of a new industrial ecosystem. Therefore, to strengthen the incentives and constraints on existing cooperative complementors and promote healthy competition among emerging complementors, COSMOPlat sticks to the governance strategy in order to enhance the overall competitiveness of the ecosystem.

Figure 3 shows the impact of COSMOPlat value-added services on the sustainable collaborative relation in the system. As can be seen from Figure 3, the value-added service S is assigned with three values of 0, 5, and 10, respectively, and all three parties start from an initial willingness of 0.5. The simulation results show that with an increase in the value-added service S, the probability of industry chain complementors choosing cooperation gradually increases at an accelerating pace. Currently, the value-added services provided by COSMOPlat for complementors mainly include basic service marketing, sales incentives, and platform access technical support. The low-code platform created by COSMOPlat can lower the development threshold of an enterprise. Enterprises and developers can realize rapid construction of business scenarios through drag-and-drop components and visual configuration, thus reducing the technical and human costs of enterprises’ digital transformation. In addition, by comparing S = 0 with S = 5 and S = 10, it can be seen that value-added services play a significant role in driving industrial chain complementors into the ecosystem. The more value-added services the COSMOPlat provides, the more willing complementors will be to cooperate and the faster the platform ecosystem will develop.

4.2.2. The Impact of Input Cost and User Value-Added Sharing Coefficient of Industrial Chain Complementors on Sustainable Collaborative Relation

Figure 4 shows the impact of input cost of industrial chain complementors on sustainable collaborative relation in the system. As can be seen in Figure 4, the input cost C is assigned with values of 5, 10, and 15, respectively, and all three parties start from an initial willingness of 0.5. The simulation results show that with an increase in input cost C, the probability of choosing a cooperation strategy decreases at an accelerating pace. In the COSMOPlat ecosystem, there are two kinds of complementors: One is small- and medium-sized complementors whose input cost is 5 or 10, and the other is leading enterprises serving as complementors whose input cost is 15. It can be seen from the degree of willingness to cooperate in the simulation that small- and medium-sized enterprises as complementors are much more dependent on the platform than the leading enterprise. They rely on the technical solutions and digital transformation experiences provided by platform enterprises and create new momentum for the platform ecosystem through transforming and upgrading the platform. By contrast, leading companies create industry platforms together with COSMOPlat. Taking the strategic cooperation between Chery and COSMOPlat as an example, Chery used COSMOPlat to build the first mass-customized industrial Internet platform in the automobile industry and developed a new automobile Internet ecosystem with COSMOPlat. In turn, COSMOPlat drew on the development experience of Chery in the automobile industry to create a win–win situation.

Figure 5 shows the impact of the user value-added sharing coefficient of complementors on sustainable collaborative relations. The user value-added sharing coefficient refers to the ratio of value-added ecological revenue created by the operators of the COSMOPlat and complementors through differentiated profit models. Such revenue is shared by all stakeholders. As can be seen from Figure 5, the user value-added sharing coefficient t is assigned with three values of 0.2, 0.5, and 0.8, respectively, and all three parties start from an initial willingness of 0.5. The simulation results show that with an increase in the user value-added sharing coefficient t, the probability of the industrial chain complementors choosing the cooperation strategy gradually increases at an accelerating pace, while the probability of the innovation chain complementors choosing the cooperation strategy gradually decreases at an accelerating pace. This is because compared with the industrial chain complementors that directly deal with system users and output-integrated solutions, the innovation chain complementors are more likely to jointly develop key technologies with the COSMOPlat enterprise. Most of the services provided by the latter are incubation scenario projects, and the ecological benefits are mainly shared with the COSMOPlat enterprise. Therefore, the higher user value-added sharing coefficient assigned to the industrial chain complementors, the closer the cooperation between the industrial chain complementors and the innovation chain complementors, and the faster the ecosystem development speed.

4.2.3. The Impact of Data Security and Speculative Behaviors of Industrial Chain and Innovation China Complementors on Sustainable Collaborative Relation

Figure 6 shows the impact of data security of complementors on platform enterprise and sustainable collaborative relation. As can be seen in Figure 6, data security H is assigned with three values of 0, 5, and 10, respectively, and the three parties start from an initial willingness of 0.5. The simulation results show that with an increase in data security H, the probability of COSMOPlat operators choosing a governance strategy gradually increases at an accelerating pace. The cost of data security is reflected in the digital transformation process of complementors enabled by COSMOPlat. Most complementary companies are concerned about the security risks of cloud data, which leads to relatively conservative digital transformation of these enterprises currently. The “container-type” industrial Internet solution launched by COSMOPlat with the BaaS platform innovation system integrates all relevant enterprise infrastructure and hardware systems, and consequently, no data need to leave the factory, thus protecting the data privacy and security of the complementors. Additionally, after the transformation, the data of various departments within a complementary enterprise are interlinked, unified software login portals are used, and the workshop production data are captured in real-time. The production efficiency is, therefore, greatly improved, and the platform ecosystem, in turn, benefits from such improvement. Therefore, the input cost of data security drives the construction and improvement of the platform ecosystem.

Figure 7 and Figure 8 show the impact of speculative behavior of complementors on sustainable collaborative relation. It can be seen from Figure 7 and Figure 8 that the speculative behaviors F₁ and F₂ are assigned with three values of 0, 10, and 20, respectively, and all three parties start from an initial willingness of 0.5. The simulation results show that with an increase in the speculative costs F₁ and F₂, the probability of the complementors choosing the cooperation strategy gradually increases at an accelerating pace. The speculative behavior of industrial chain complementors mainly refers to passive participation after the achievement of certain innovation results in the innovation stage centering on user demand. The speculative behavior of innovation chain complementors is more related to the information leakage security problem in COSMOPlat. COSMOPlat only retains the design of core modules, and meanwhile, it jointly develops key generic technologies with innovation chain complementors. When comparing F₁ = 0, F₂ = 0 with F₁ = 10, and F₂ = 10, it can be seen that the cost of speculation is only a healthy factor to maintain the collaborative innovation of complementors. Even if the cost of speculation is set by COSMOPlat, complementors will still choose cooperation, which also indicates that collaborative innovation of the platform ecosystem is a self-evolving, self-growing, and self-driven win–win cooperation model.

5. Findings and Discussion

(1)

The simulation results show that the evolution and development of a platform ecosystem are path-dependent and shaped by the development of the platform built by the platform enterprise. Platform enterprises and complementors form sustainable competitiveness through collaborative innovation. Based on the prediction and division of the evolution paths of the industrial Internet platform by existing scholars [16,37], this paper extends the study from platform to ecosystem. It verifies that the sustainability of platform ecosystem and platform development is a process of collaborative evolution, and sustainable collaborative innovation mechanisms can provide a foundation for the transition of a platform ecosystem.

(2)

This paper compares the research results with the value co-creation cooperation mechanism from an empowerment perspective [20] and the sharing incentive mechanism for a cloud manufacturing innovation ecosystem [38]. On this basis, the paper analyzes the unique role of collaborative innovation mechanisms in the sustainable development of a platform ecosystem. The similarities and differences among the three mechanisms are as follows:

Firstly, the three mechanisms deal with the same realistic subjects, i.e., industrial Internet platform ecosystems, and the ultimate goal of both the value cooperation mechanism and sharing incentive mechanism is to enhance the competitiveness of ecosystems.

Secondly, the three mechanisms emphasize different subject relations. For the study of value co-creation cooperation mechanism from the perspective of empowerment, the main emphasis is on the risks and benefits of SMEs’ access to the platform ecosystem. The sharing incentive mechanism for manufacturing innovation ecosystem emphasizes the sharing of knowledge with manufacturing service providers and integrators within an ecosystem. By contrast, from the perspective of platform sustainable development, a platform enterprise is no longer just commercial platforms, but also social platforms with social attributes. Hence, in order to drive sustainable ecological development, it is not enough to simply analyze the relationship among participants in the ecosystem. Therefore, based on previous studies, this paper expands the subject relationship from two to three parties, including scientific research institutions, universities, and other social groups.

Finally, the simulation subjects of the three mechanisms are different. The study of value co-creation and cooperation mechanisms, from an empowerment perspective, focuses on how simulation key factors influence the equilibrium state of system evolution. The sharing incentive mechanism for a cloud manufacturing innovation ecosystem focuses on how cloud manufacturing integrators design the corresponding incentive mechanisms to promote the knowledge-sharing initiative of cloud manufacturing suppliers. In this paper, the focus of the research is on a broader perspective. It not only fully discusses system evolution scenarios but also elaborates on the strategic behavior of complementors in detail.

6. Conclusions and Policy Implications

6.1. Conclusions

This paper adopts evolutionary game theory to build a three-party evolutionary game model, comprising platform enterprise, the industrial chain complementor, and the innovation chain complementor. Moving forward, how each innovation subject selects the collaborative innovation strategy during the evolution process is analyzed by embedding a sustainable value logic system. MATLAB R2022a is used to perform empirical simulation analysis of the COSMOPlat case and explore the influence of input cost, user value-added sharing coefficient, data security, speculative behavior, and value-added services on evolutionary equilibrium strategy. The main conclusions are as follows.

(1)

Depending on platform governance intensity, benefits of cooperation ecology, and cost of complementors, there are four evolutionary paths for the collaborative relation among the innovation entities in an ecosystem: (governance, competition, competition), (governance, cooperation, cooperation), (governance, cooperation, competition), and (governance, competition, cooperation). In the above four paths, platform enterprise chooses governance strategies, indicating that the sustainable interactive operation between platform enterprise and complementors in the ecosystem is carried out through the platform governance mechanism. The fact that cooperation and competition are both optional strategies for the complementors shows that the interaction behavior and the value creation mechanism between platform enterprise and the complementors are dynamic.

(2)

Platform enterprise will adopt different strategies at different stages of ecosystem evolution. In the initial stage of a platform, the platform enterprise tends to implement incentive strategies and provide value-added services. In this stage, the main purpose of the platform enterprise is to attract complementors to join the ecosystem. In the development and deepening stage of the platform, the platform enterprise tends to implement governance strategies. In this stage, the main purpose of the platform enterprise is to strengthen the incentives and constraints on the existing cooperative complementors and then to promote healthy competition among emerging complementors, which, consequently, enhances the overall competitiveness of the ecosystem.

(3)

Industry chain complementors are more dependent on platform enterprise than innovation chain complementors, and they are more significantly influenced by value-added services and users’ value-added sharing coefficient. Compared with the joint research and development of key technologies between innovation chain complementors and platform enterprise, industry chain complementors rely more on industrial replication schemes and technologies of the platform enterprise to achieve transformation, so they are highly dependent on platform enterprise. In the simulation sensitivity analysis, it is found that the more value-added services and users’ value-added sharing coefficient provided by the platform enterprise for industrial chain complementors, and the closer the cooperation between industrial chain complementors and innovation chain complementors, the faster the ecosystem development speed.

(4)

The investment of platform enterprise in data security drives construction and improvements in the ecosystem. Speculation behavior is also a healthy factor, indicating that the collaborative innovation of a platform ecosystem is a self-evolving, self-growing, self-driven, and sustainable win–win cooperation mechanism. Data security is the key factor that prevents most complementary enterprises from accessing the platform. Making heavier investments in data security by platform enterprises can encourage complementary enterprises to enter the ecosystem, thus allowing platform enterprises to reap ecological benefits more quickly. In addition, the speculative cost can effectively constrain the cooperative behavior of the complementary enterprise.

6.2. Policy Implications

(1)

Industrial Internet platform enterprises should take the responsibility of building the infrastructure of the ecosystem and be good at applying incentives and governance mechanisms for complementors. When a platform is first built, a platform enterprise should increase the subsidy for industrial chain complementors, aiming at increasing the scale of platform users and attracting innovation chain complementors to join the platform, with a positive network scale effect. When the platform has grown with a certain network effect, the platform enterprise should implement the governance strategy as much as possible to regulate the value network of the complementors in the industrial and innovation chains, and to promote healthy competition within the network of complementors. However, this period is not completely governed, and platform enterprises can give appropriate subsidies to the complementors in the industry and innovation chains to compensate for the increase in the cost of collaborative innovation cooperation.

(2)

Complementors in the industrial chain are suggested to make use of the enabling role of platform enterprise to realize transformation and upgrading. It is necessary for traditional manufacturing enterprises, as industrial chain complementors, to enter the ecosystem at the beginning of construction of the industrial Internet platform and realize transformation through the empowerment of the platform enterprise in terms of solutions and technologies, so as to create momentum for subsequent collaborative cooperation. However, enterprises should also be careful not to rely excessively on the resources given by platform enterprises. It is only beneficial to form their unique core competitiveness in subsequent development.

(3)

It is necessary for innovation chain complementors to make a keen judgment of the evolutionary stage of the industrial Internet platform-based ecosystem they are about to enter and assess the gap between the benefits of cooperation and the expected benefits. Since, at the beginning of the construction of an industrial Internet platform, the focus is not on technological innovation in products and services, the best choice for innovation chain complementors is to enter a platform that is in the development or deepening stage. Complementors in the collaborative innovation chain can determine the stage of the ecosystem by the strategy implemented by the platform enterprise, the size of the ecosystem, and the number of participants.

(4)

With the implementation of measures for the healthy and sustainable development of the platform economy, social environmental value and potential consumption demand can play a crucial role in the sustainable development of a platform ecosystem. Under the mechanism of sustainable innovation, industrial Internet platform enterprises must deepen collaboration and cooperation with their complementors in terms of social environment and potential consumer demand. On the one hand, industrial Internet platform enterprises need to carry out collaborative innovation with both economic and social complementors. On the other hand, it is also necessary for industrial Internet platform enterprises to meet consumers’ potential demands in terms of interaction value, experience value, and scene value, creating social value for the development of a new or extensible sustainable innovation mechanism.

6.3. Limitations and Future Work

This paper analyzes the evolution paths and collaborative innovation mechanisms of platform ecosystems with the aid of theoretical models, and it draws several conclusions, but there are still some limitations: (1) The focus of this paper mainly concerns the collaborative innovation interaction among platform enterprises, industry chain complementors, and innovation chain complementors, without considering the role of other social agents, such as government and users, in depth. (2) This study mainly considers the collaboration between platform enterprises and complementors and does not consider the competition among the complementors on the same side. In the future, it is necessary to further adapt the theoretical models to an actual governance environment to improve the effectiveness of governance strategies. At the same time, further exploration into the competition among complementors on the same side should also be a focus of scholars’ future research on platform collaborative innovation mechanisms.