Research on the Group Innovation Information-Sharing Strategy of the Industry–University–Research Innovation Alliance Based on an Evolutionary Game

Abstract

Based on various factors in information sharing between innovation alliance groups, this paper analyzes innovation information sharing under the influence of various factors and its evolutionary path to provide a reference for the decision-making of innovation information sharing between innovation alliance groups. Firstly, the paper analyzes the main factors influencing alliance group innovation information-sharing behavior. Secondly, based on the evolutionary game theory, an evolutionary game model of innovative information sharing under the cooperative trust degree of group decision-makers is constructed, and the related stable strategies are given. Finally, the sensitivity of innovative information-sharing strategies to key influencing factors is analyzed with the help of actual case data. The results show that a reasonable amount of innovation information sharing and fair profit distribution can improve the innovation information-sharing behavior among the industry–university–research alliance. Considering the trust degree of vertical partners, the alliance group pays more attention to the profit distribution ratio of collaborative innovation of the innovation alliance than the profit amount. When horizontal partner trust is considered, horizontal cooperation trust can promote information sharing among enterprises, universities, and research institutes in the short term but impedes information sharing among groups in the long term.

1. Introduction

The rapid development of the digital economy has led to heightened competitiveness and increased uncertainty in the enterprise product market. This has created a more complex and dynamic environment for technological innovation within enterprises. Relying solely on internal knowledge reserves is no longer sufficient for maintaining a competitive advantage in the market [1]. Therefore, the industry–university–research innovation alliance is born based on the flow and integration of technological innovation information. In the industry–university–research innovation alliance, enterprises, universities, and research institutes have different knowledge structures of innovation information, which makes the technical innovation business connections between these groups closer [2,3]. Compared with the external market environment, establishing the industry–university–research alliance with the enterprise as the link core can significantly reduce the cost of information acquisition for enterprises. Therefore, increasingly, enterprises choose to share innovation information with other groups in the innovation alliance to make up for their lack of technological innovation knowledge. As a kind of high-value information resource, the flow of innovative information between the industry–university–research innovation alliance can create new value growth points and high profits for enterprises and realize the improvement of the overall performance of the alliance [4,5]. However, from the perspective of the benefits of a single group, because a single group is often aimed at fair distribution and profit maximization, there is the leakage of alliance innovation information and the existence of individual groups “free riding”; thus, the innovation alliance will not completely choose to share innovative knowledge every time. At this time, the innovation alliance groups are highly dependent on each other. If the innovation information flow stops sharing, the alliance’s stability will be damaged. In this context, it is necessary to balance the benefits of different groups of innovation alliances from the perspective of enterprises, universities, and scientific research organizations. In addition, due to the persistence and uncertainty of technological innovation, the accumulation, expansion, and mutual flow of innovation information among enterprises, universities, and research institutes are characterized by dynamic evolution, and the sharing process of innovation information is affected by subjective and objective factors of decision-makers of various groups in the alliance. Therefore, exploring the group innovation information-sharing strategy of the industry–university–research innovation alliance based on an evolutionary game has important reference value for the benefit distribution decision of the innovation alliance.

Regarding research objects, [6] explored the formation process of a global collaborative innovation alliance under the influence of the Energy Internet. They pointed out that the differences between ordinary and standard essential patents led to ambiguities in the ownership of standard essential patents. Therefore, Chinese high-tech enterprises must promote the transformation of project ownership in cooperative innovation alliances from contracts to clauses, reconstruct the rules for attributing service inventions, and improve employees’ bargaining power. [7] reviewed and comprehensively analyzed relevant management, business, and psychology research methods. They argued that the intersection of these fields has evolved into a general consensus on the impact of governance choice decisions, cooperation motivations, partner selection decisions, performance, the increasing complexity and internationality of alliances, as well as the need for a multidisciplinary approach to decision-making in terms of applied theory and required data. Although the above literature points out the importance of establishing industry–university–research innovation alliances, there is still a lack of data support. For this reason, [8], based on a sample of 154 high-tech enterprises in Germany, adopted regression analysis to explore the relationship between the product concept stage, the actual R&D stage, and the cooperation types of different alliance enterprises. They found that the depth of horizontal and vertical cooperation between alliance groups has an important impact on their innovation ability. For example, the number of project participants, especially the number of university participants, will positively impact the performance, there is knowledge spillover between project groups, and the research center does not play a positive externality [9,10] analyzed the determinants of interregional innovation cooperation in European knowledge networks. They found that the basic gravitational mechanism drives the direction and intensity of interregional innovation cooperation in the EU; geographical distance is a barrier to interregional joint patent application, and border regions are generally inferior to non-border regions in terms of innovation cooperation intensity. It is suggested that the government should strengthen the level of international cross-border cooperation within the EU. Although these studies have analyzed the impact of innovation cooperation from the perspective of alliance construction and innovation patents of various groups in the alliance, specific group behavior is rarely involved. Therefore, [11] explored the group behavior of industry, university, and research innovation alliances based on the annual survey data of Spanish enterprises from 2005 to 2013. The study found that with the increase in the number of different types of partners, the possibility of patent licensing also increases, and the relevance of technological dissemination of policy interventions reduces the cost of establishing links between firms and other research organizations. Ref. [12] took 101 innovative SMEs as samples and pointed out that the application of social media in new product development should be accompanied by close cooperation between R&D and marketing. Social media can be used for both breakthrough and progressive innovation, but its effect on service innovation is greater than that of product innovation. However, after enterprises join the innovation alliance, compared with alliance cooperation intensity and government subsidies, enterprises’ ecological innovation strategy significantly impacts labor productivity. In contrast, the impact of public assistance through establishing an R&D cooperation agreement on the labor productivity of enterprises (non-ecological innovation enterprises) is lower, and the impact on ecological innovation enterprises is the same [13]. The above representative studies are only conducted from the perspective of the cooperation of industry–university–research innovation alliances, but in practice, there is both cooperation and competition among alliance groups. For example, for focus enterprises with weak or strong brands, cooperation with competitors does not always lead to the production of more environmentally friendly products. However, only when the cost-effectiveness of green innovation is not too great does cooperation with competitors for green innovation dominate [14]. In addition, [15] examined the moderating effects of three knowledge network contingency—technical complexity, knowledge diversity, and the stability of focus an inventor’s self-knowledge network—on the stability of a self-cooperation network and innovation and pointed out that the stability of a cooperation network participated by the core connected firms of an alliance presents an inverted U-shaped relationship with innovation performance.

In terms of research methods, [16] constructed an evolutionary game model by artificially analyzing the factors affecting the technological innovation cooperation behavior of the industry–university–research alliance under the changing mechanism of market products and the high-intensity administrative changes of the government and pointed out that reasonable government subsidies can promote the cooperation enthusiasm of the industry–university–research innovation alliance group, but strict administrative regulation and taxation hinder the improvement of the cooperation enthusiasm of the alliance group. Based on the data obtained by a questionnaire, [17] constructed an evaluation index of the green technology innovation ability of the industry–university–research innovation alliance with multi-group participation and measured the innovation ability of each group, pointing out that the influencing factors of the innovation ability of the industry–university–research innovation alliance group are mainly reflected in the aspects of innovation factor input, innovation output, and social welfare. These factors significantly impact the innovation patent output of the alliance group. Ref. [18] used fuzzy-set qualitative comparative analysis to identify previously unknown combinations leading to product/service innovation in 690 digital and non-digital startups. They found that combinations of different dimensions of product innovation and partner types can be explained in digital and non-digital contexts. The above research methods mainly focus on the evolutionary game model, questionnaire, and fuzzy qualitative comparison but ignore the benefits of alliance groups in the analysis process. The benefit of an alliance group determines the enthusiasm for alliance group cooperation.

For this reason, [19] used cooperative game theory to analyze the benefit distribution mechanism of technological innovation cooperation among enterprises. Based on the number of resources invested by enterprises in the technological innovation cooperation alliance, they constructed an income model of the innovation alliance of industry, university, and research institutes. They pointed out that the Shapley value analysis method could reasonably distribute the group’s profits, which would help improve the alliance’s stability. In addition, although enterprises’ technological innovation decisions have commonalities, different enterprise sizes have different decision-making mechanisms. Based on this, [20], based on evolutionary game theory, analyzed that the essence of the evolution of green technology innovation in manufacturing enterprises under multi-group cooperation is the encouragement of the government and the guidance of small and medium-sized enterprises. By connecting other industry–university–research innovation alliance groups, small and medium-sized enterprises can help the alliance evolve in a more open direction. Environmental regulation policies have a strong positive incentive effect on the dynamic, collaborative evolution of green technology innovation in urban agglomerations. Ref. [21] used a qualitative comparison method to determine the impact of cooperation between groups on the potential joint strength of the alliance’s green innovation tendency. They found seven equivalent paths to high innovation performance—cooperation with universities instead of private consultants, cooperation with universities and research institutes, and cooperation with universities and customers being the most decentralized. In terms of the two-group game, [22] used Steinberg game theory to investigate the effects of spillover rate, R&D efficiency, and competition level on the equilibrium solution by taking the same university or research institute’s participation in the industry–university–research alliance set up by two enterprises. They found that the investment level of universities or research organizations is not affected by the R&D efficiency of enterprises. However, its wholesale price is affected by the R&D efficiency of enterprises. Ref. [23] used experimental analysis to explore the evolutionary mechanism of knowledge-sharing decision-making. He pointed out that there is a behavioral spillover effect between knowledge-sharing decision-making and investment. Under exogenous conditions, the degree of symmetry of knowledge-sharing does not affect cooperation, and when participants can decide on knowledge, communication can promote cooperation more.

After reviewing the existing literature, it can be seen that: (1) The current research mainly analyzes the impact of policies and subsidies on the innovation capability and innovation output of innovation alliance enterprises from the perspective of the government, ignoring the close relationship between the development of innovation alliance and the behavior of innovation information-sharing groups, especially downplaying the impact on the interaction mechanism and innovation enthusiasm of core groups, and the sharing of innovation information is rarely involved [24,25,26]; (2) Although there have been relevant theoretical studies on the evolutionary game of the innovation alliance between enterprises, universities, and research institutes, these studies focus on the strategic choice of competition and cooperation between groups in the alliance, and the analysis methods on cooperation and competition are mostly limited to index design or the cooperative game between the two groups. The main reasons for the research are as follows: (1) The core of the alliance’s rapid development lies in the enterprise’s innovation output and the innovation information sharing among the groups [27,28]. If it is not included in the analysis framework, it will inevitably affect the interests of the groups of the alliance and then affect the output of the enterprise in the alliance and the technological innovation and innovation ability. (2) Although there are many indicators involved in measuring the innovation effect of the alliance, the final analysis still lies in the innovation enthusiasm of each group, that is, the willingness and degree of information sharing [27,28]. Meanwhile, the choice of strategies of each group will evolve with the change of time, and its evolutionary mechanism is complex and changeable [29]. In view of this, this paper first sorts out and describes the innovative information-sharing mechanism of enterprises, universities, research institutes, and other organizations in the industry–university–research innovation alliance. Secondly, the model hypothesis is proposed based on the innovative information-sharing mechanism of these organizations. Thirdly, an evolutionary game model under vertical cooperative trust and an evolutionary game model under horizontal cooperative trust are constructed, respectively, and the sensitivity of each group’s innovation information-sharing strategy to the main parameters is analyzed using numerical examples. Finally, the paper summarizes the research conclusions and puts forward relevant suggestions.

2. Model Construction

2.1. Problem Description

Because enterprises, universities, research institutes, and other organizations are in the process of cooperation, their respective information strategies are not exactly the same, and in the whole process of cooperation, different groups will adopt different strategies according to the actual situation. Universities share innovation information with enterprises, but enterprises do not share innovation information with universities. Of course, research institutes share information just like universities do. It is important to emphasize that innovation information will not be shared between universities and research institutes. The university’s strategy is to share information and not to share information, and the institute will adopt the same strategy. When universities adopt information-sharing strategies, research institutes may adopt information-sharing strategies or non-information-sharing strategies. The different strategies adopted by the research are based on the changes in the strategies of universities and enterprises. To sum up, we can see that the strategies of universities, enterprises, and research institutes have the characteristics of an evolutionary game.

The industry–university–research innovation alliance consists of three organizations: enterprises, universities, and research institutes. Enterprises are the core organizations of the alliance, connecting universities and research institutes as connection points. There are information differences among alliance groups. The core organizations of the alliance are enterprises, which share information with universities and research institutes, respectively. Vertical cooperation and trust exist among innovation alliance groups. As downstream enterprises, universities and research institutes do not share information but have horizontal cooperation trust, as shown in Figure 1. The alliance group has only two action strategies: sharing information and not sharing information. Under the influence of subjective and objective factors, the final action strategy of the enterprise in the innovation alliance can be obtained after many dynamic repeated games.

2.2. Model Hypothesis

In order to analyze the innovation information-sharing strategies of various groups in the industry–university–research innovation alliance, the following basic assumptions are proposed:

(1)

The core point of establishing the industry–university–research innovation alliance is that the alliance groups can share resources. From the perspective of enterprise innovation, the main purpose of establishing an industry–university–research innovation alliance between enterprises and universities and research institutes is to obtain innovative information from universities and research institutes, absorb it, and transform it into their own competitive advantages. Based on this, it can be assumed that enterprises, universities, and research institutes can share innovation information, and the amount of innovation information that enterprises can share is denoted as ${\Omega }_1$($K_1>0$), the amount of information shared by enterprises to universities and research institutes is denoted as ${\Omega }_{12}$ and ${\Omega }_{13}$, and the amount of information shared by universities and research institutes and enterprises is denoted as ${\Omega }_2$ and ${\Omega }_3$;

(2)

From the construction purpose of the industry–university–research innovation alliance, the innovation information used by each participating group cannot be exactly the same. This is because the purpose of groups participating in innovation alliances is to exchange their own innovation information with each other, so this information is both the same and different. From the perspective of the benefits of innovation information sharing, it can be assumed that the performance of the innovation alliance jointly composed of enterprises, universities, and research institutes is obtained by sharing information among various groups, and this part of the performance can be regarded as the synergistic benefits between groups and the direct benefits generated by receiving information. The synergistic benefits between groups (measured via the synergistic benefits coefficient, denoted as ${\mu }_i$) are related to the total amount of information sharing [30,31]. The synergistic benefits generated by the innovation alliance will eventually be distributed to enterprises and universities, and enterprises and research institutes in the form of distribution; the distribution coefficient is denoted as ${\lambda }_i$. In addition, since the direct benefits generated by receiving information are related to the group’s ability to absorb and transform innovation information, the group’s absorption of innovation information and the trust between groups have an impact on the group’s absorption and sharing of innovation information, respectively, which can be assumed as ${\alpha }_i$($0<{\alpha }_i<1$) and ${\beta }_i$($0<{\beta }_i<1$), the unit value of the recorded information is ${\omega }_i>0,i=1,2,3$, and the group’s absorption capacity of innovative information is ${\theta }_i$($i=1,2,3$);

(3)

No matter whether enterprises, universities, or research institutes, they will incur costs when sharing innovation information. These originals are mainly comprised of information mining, transfer, human resources, and time costs. In view of this, it is assumed that the costs of sharing innovation information for enterprises, universities, and research institutes are, respectively, $M_i$($i=\{1,2,3\}$), the cost of information mining and transfer is denoted as $M_{1i}$, and the cost of human resources and time composition is denoted as $M_{2i}$. If we remember that the unit cost of sharing innovation information among groups is $l_i$, then, referring to the cost function form given by Wang et al. [32,33], the transfer cost before innovation information sharing of each group can be obtained as follows $M_{1i}=\frac{1}{2}{l}_i{\Omega }_i^2$. Further, the total cost of each group sharing innovation information is $M_i=M_{1i}+M_{2i}=\frac{1}{2}{l}_i{\Omega }_i^2+M_{2i}$;

(4)

Since the innovation alliance is an innovation community formed by enterprises as the link core, in which there is innovation information sharing between enterprises and universities, and between enterprises and research institutes, and universities and research institutes provide innovation information for enterprises, but there is no information sharing between research institutes and universities, it can be assumed that there is vertical cooperative trust between enterprises and universities. There is vertical cooperation trust between enterprises and research institutes, and the cooperation trust between enterprises and universities is denoted as ${\eta }_1$, while the cooperation trust between enterprises and research institutes is ${\eta }_2$;

(5)

The probability of the enterprise adopting the information-sharing strategy is $x$, and the probability of adopting the no-sharing strategy is $1-x$; the probability that the university adopts the information-sharing strategy is $y$, and the probability of adopting the no-sharing strategy is $1-y$; the probability that an information-sharing strategy is adopted by research institutes is $z$, and the probability of adopting the no-sharing strategy is $1-z$. The value range of the policy is $x,y,z\in [0,1]$.

2.3. Evolutionary Game Analysis of an Alliance Group under a Vertical Cooperative Trust

The benefits of each group in the industry–university–research innovation alliance are composed of direct benefits, collaborative benefits, and sharing costs. Among them, the direct benefit is the product of the information-sharing amount, information unit value coefficient, information absorption capacity, and information absorption willingness. In contrast, the synergistic benefit is the product of the synergistic benefit coefficient, income distribution coefficient, and the total information-sharing amount. Based on this, the innovative information-sharing benefits of each group in the alliance can be obtained, as shown in

Table 1. Benefits of innovation information sharing of each group in the industry–university–research innovation alliance.

Game Decision		Enterprise
		Share	Not Share
Colleges	Share	${\Omega }_{12}{\beta }_1{\omega }_1{\theta }_2{\alpha }_2+{\mu }_{12}{\lambda }_2({\beta }_1{\Omega }_{12}+{\beta }_2{\Omega }_2)-\frac{1}{2}{l}_2{\beta }_2^2{\Omega }_2^2-M_{22}$	$-\frac{1}{2}{l}_2{\beta }_2^2{K}_2^2-M_{22}$
		${\Omega }_2{\beta }_2{\omega }_2{\theta }_1{\alpha }_1+{\mu }_{12}{\lambda }_{12}({\beta }_1{\Omega }_{12}+{\beta }_2{\Omega }_2)-\frac{1}{2}{l}_1{\beta }_1^2{\Omega }_{12}^2-M_{21}$	${\Omega }_2{\beta }_2{\omega }_2{\theta }_1{\alpha }_1$
	Not share	${\Omega }_{12}{\beta }_1{\omega }_1{\theta }_2{\alpha }_2$	$0,0$
		$-\frac{1}{2}{l}_1{\beta }_1^2{\Omega }_{12}^2-M_{21}$
Research Institutes	Share	${\Omega }_{13}{\beta }_1{\omega }_1{\theta }_3{\alpha }_3+{\mu }_{13}{\lambda }_3({\beta }_1{\Omega }_{13}+{\beta }_3{\Omega }_3)-\frac{1}{2}{l}_3{\beta }_3^2{\Omega }_3^2-M_{23}$	$-\frac{1}{2}{l}_3{\beta }_3^2{\Omega }_3^2-M_{23}$
		${\Omega }_3{\beta }_3{\omega }_3{\theta }_1{\alpha }_1+{\mu }_{13}{\lambda }_{13}({\beta }_1{\Omega }_{13}+{\beta }_3{\Omega }_3)-l_1{\beta }_1^2{\Omega }_{13}^2-M_{21}$	${\Omega }_3{\beta }_3{\omega }_3{\theta }_1{\alpha }_1$
	Not share	${\Omega }_{13}{\beta }_1{\omega }_1{\theta }_3{\alpha }_3$	$0,0$
		$-\frac{1}{2}{l}_1{\beta }_1^2{\Omega }_{13}^2-M_{21}$

.

Enterprises make information-sharing decisions with universities and research institutes, respectively. Under a vertical cooperative trust, the cooperative relationship between the two does not affect the other. Therefore, the game between enterprises and universities is analyzed as an example.

Suppose that the income from information sharing in colleges and universities is ${\Theta }_{12}$, the benefits of not sharing information are ${\Theta }_{22}$, and the expected revenue is ${\overline{\Theta }}_2$. According to the payoff matrix in Table 1, the payoff of colleges and universities choosing to share information under a vertical cooperation trust is shown in Equation (1):

$$\begin{array}{c}{\Theta }_{12}=(1+{\eta }_1)[x({\Omega }_{12}{\beta }_1{\omega }_1{\theta }_2{\alpha }_2+{\mu }_{12}{\lambda }_1({\beta }_1{\Omega }_{12}+{\beta }_2{\Omega }_2)-\frac{1}{2}{l}_2{\beta }_2^2{\Omega }_2^2-M_{22})\\ +(1-x)(-\frac{1}{2}{l}_2{\beta }_2^2{\Omega }_2^2-M_{22})]-{\eta }_1[y({\Omega }_2{\beta }_2{\omega }_2{\theta }_1{\alpha }_1+{\mu }_{12}{\lambda }_{12}({\beta }_1{\Omega }_{12}+{\beta }_2{\Omega }_2)\\ -\frac{1}{2}{l}_1{\Omega }_{12}^2{\beta }_1^2-M_{21})+(1-y)(-\frac{1}{2}{l}_1{\Omega }_{12}^2{\beta }_1^2-M_{21})]\end{array}$$

(1)

The benefits of universities choosing not to share information are shown in Equation (2):

$${\Theta }_{22}=(1+{\eta }_1)x{\Omega }_{12}{\beta }_1{\omega }_1{\theta }_2{\alpha }_2-{\eta }_{1}y{\Omega }_2{\beta }_2{\omega }_2{\theta }_1{\alpha }_1$$

(2)

The expected income of colleges and universities is shown in Equation (3):

$${\overline{\Theta }}_2=y{\Theta }_{12}+(1-y){\Theta }_{22}$$

(3)

Thus, the replication dynamic equation is shown in Equation (4):

$$\begin{array}{c}F(y)=\frac{dy}{dt}=y({\Theta }_{12}-{\overline{\Theta }}_2)=y(1-y)({\Theta }_{12}-{\Theta }_{22})\hfill \\ =y(1-y)[(1+{\eta }_1)x{\mu }_{12}{\lambda }_2({\beta }_1{\Omega }_{12}+{\beta }_2{\Omega }_2)\hfill \\ -{\eta }_{1}y{\mu }_{12}{\lambda }_{12}({\beta }_1{\Omega }_{12}+{\beta }_2{\Omega }_2)-(1+{\eta }_1)(\frac{1}{2}{l}_2{\beta }_2^2{\Omega }_2^2+M_{22})\hfill \\ \hspace{1em}\hspace{1em}\hspace{1em}+{\eta }_1(\frac{1}{2}{l}_1{\Omega }_{12}^2{\beta }_1^2+M_{21})]\hfill \end{array}$$

(4)

Similarly, the replication dynamic equation of enterprises’ innovation information-sharing strategies in the innovation alliance can be obtained using:

$$\begin{array}{cc}\hfill F(y)& =\frac{dx}{dt}=x({\Theta }_{11}-{\overline{\Theta }}_1)=x(1-x)({\Theta }_{11}-{\Theta }_{21})\hfill \\ & =x(1-x)[(1+{\eta }_1)y{\mu }_{12}{\lambda }_{12}({\beta }_1{\Omega }_{12}+{\beta }_2{\Omega }_2)\hfill \\ & \hspace{1em}-{\eta }_{1}x{\mu }_{12}{\lambda }_2({\beta }_1{\Omega }_{12}+{\beta }_2{\Omega }_2)-(1+{\eta }_1)(\frac{1}{2}{l}_1{\Omega }_{12}^2{\beta }_1^2+M_{21})\hfill \\ & \hspace{1em}+{\eta }_1(\frac{1}{2}{l}_2{\beta }_2^2{\Omega }_2^2+M_{22})]\hfill \end{array}$$

(5)

To simplify the expression, set $X_{12}={\mu }_{12}{\lambda }_{12}\left({\beta }_1{\Omega }_{12}+{\beta }_2{\Omega }_2\right),$

$$\{\begin{array}{l}{X}_2={\mu }_{12}{\lambda }_2({\beta }_A{\Omega }_{12}+{\beta }_2{\Omega }_2)\\ M_{12}=\frac{1}{2}{l}_A{\Omega }_{12}^2{\beta }_1^2+M_{2A}\\ M_2=\frac{1}{2}{l}_2{\beta }_2^2{\Omega }_2^2+M_{21}\end{array}$$

If Equations (4) and (5) are set to 0, respectively, then the local equilibrium point can be obtained as $(0,0),(0,1),(1,0),(1,1)$ and $(x^{\ast },y^{\ast })$. Where $x^{\ast }=\frac{M_2}{X_2},y^{\ast }=\frac{M_{12}}{X_{12}}$. By taking partial derivatives of Equations (4) and (5), the Jacobian matrix of the game between the enterprise and the university can be obtained:

$$J=\left(\begin{array}{cc}\frac{\partial F(x)}{\partial x}& \frac{\partial F(x)}{\partial y}\\ \frac{\partial F(y)}{\partial x}& \frac{\partial F(y)}{\partial y}\end{array}\right)$$

(6)

The following can be obtained using:

$$\{\begin{array}{l}\frac{\partial F(x)}{\partial x}=(1-2x)[(1+{\eta }_1)y{X}_{12}-{\eta }_{1}x{X}_2-(1+{\eta }_1)M_{12}+{\eta }_1{M}_2]-x(1-x){\eta }_1{X}_2\\ \frac{\partial F(x)}{\partial y}=x(1-x)(1+{\eta }_1)X_{12}\\ \frac{\partial F(y)}{\partial y}=(1-2y)[(1+{\eta }_1)x{X}_2-{\eta }_{1}y{X}_{12}-(1+{\eta }_1)M_2+{\eta }_1{M}_{12}]-y(1-y){\eta }_1{X}_{12}\\ \frac{\partial F(y)}{\partial x}=y(1-y)(1+{\eta }_1)X_2\end{array}$$

Then, the determinant and trace of the matrix (6) are, respectively,

$$\begin{array}{cc}\hfill \det (J)& {=[(1-2x)[(1+{\eta }_1)y{X}_{12}-{\eta }_{1}x{X}_2-(1+{\eta }_1)M_{12}+{\eta }_1{M}_2]-x(1-x){\eta }_1{X}_2]}^{\ast }\hfill \\ & (1-2y)[(1+{\eta }_1)x{X}_2-{\eta }_{1}y{X}_{12}-(1+{\eta }_1)M_2+{\eta }_1{M}_{12}]-y(1-y){\eta }_1{X}_{12}\hfill \\ & -xy(1-x)(1-y){(1+{\eta }_1)}^2{X}_{12}{X}_2\hfill \end{array}$$

(7)

$$\begin{array}{cc}\hfill tr(J)& =[(1-2x)[(1+{\eta }_1)y{X}_{12}-{\eta }_{1}x{X}_2-(1+{\eta }_1)M_{12}+{\eta }_1{M}_2]-x(1-x){\eta }_1{X}_2]\hfill \\ & +[(1-2y)[(1+{\eta }_1)x{X}_2-{\eta }_{1}y{X}_{12}-(1+{\eta }_1)M_2+{\eta }_1{M}_{12}]-y(1-y){\eta }_1{X}_{12}\hfill \end{array}$$

(8)

Then, by putting the local equilibrium point into the above two equations, the local stability analysis results of the game can be obtained, as shown in

Table 2. Local stability analysis results of an evolutionary game of group innovation information sharing in the industry–university–research innovation alliance.

Equilibrium Point	$\mathbf{det}(\mathit{J})$	$\mathit{t}\mathit{r}(\mathit{J})$
(0, 0)	$(-(1+{\eta }_1)M_{12}+{\eta }_1{M}_2)(-(1+{\eta }_1)M_2+{\eta }_1{M}_{12})$	$-M_{12}-M_2$
(0, 1)	$[(1+{\eta }_1)X_{12}-(1+{\eta }_1)M_{12}+{\eta }_1{M}_2][{\eta }_1{X}_{12}+(1+{\eta }_1)M_2-{\eta }_1{M}_{12}]$	$(1+2{\eta }_1)(X_{12}+M_2-M_{12})$
(0, 1)	$[(1+{\eta }_1)X_2-(1+{\eta }_1)M_2+{\eta }_1{M}_{12}][{\eta }_1{X}_2+(1+{\eta }_1)M_{12}-{\eta }_1{M}_2]$	$(1+2{\eta }_1)(X_2+M_{12}-M_2)$
(1, 1)	$\begin{array}{l}{[-(1+{\eta }_1)(X_{12}-M_{12})+{\eta }_1(X_2-M_2)]}^{\ast }\\ [-(1+{\eta }_1)(X_2-M_2)+{\eta }_1(X_{12}-M_{12})]\end{array}$	$-X_{12}-X_2+M_{12}+M_2$
$(x^{\ast },y^{\ast })$	$\frac{[{\eta }_1^2-{(1+{\eta }_1)}^2]M_{12}{M}_2[(X_2-M_2)(X_{12}-M_{12})]}{X_{12}{X}_2}$	$\begin{array}{l}-[\frac{{\eta }_1{M}_2}{X_2}(X_2-M_2)+\\ \frac{{\eta }_1{M}_{12}}{X_{12}}(X_{12}-M_{12})]\end{array}$

below.

According to the relevant knowledge of evolutionary game theory, when $\det (J)>0$ and $tr(J)<0$ are true, the stable strategy of an evolutionary game is the same as the local equilibrium point. It can be seen from Table 2 that determining the positive and negative of the determinant and trace corresponding to each equilibrium point is transformed into analyzing the value order of $X_{12}$ and $M_{12}$, and $X_2$ and $M_2$. The value order results are shown in

Table 3. Stability of an evolutionary game equilibrium point of group innovation information sharing in the industry–university–research innovation alliance.

Scenario	Equilibrium Point	$\mathbf{det}(\mathit{J})$	$\mathit{t}\mathit{r}(\mathit{J})$	ESS
$X_{12}>M_{12},X_2>M_2$	(0, 0)	$+$	$-$	(0, 0), (1, 1)
	(0, 1)	$+$	$+$
	(1, 0)	$+$	$+$
	(1, 1)	$+$	$-$
	$(x^{\ast },y^{\ast })$	$-$	$-$
$X_{12}>M_{12},X_2<M_2$	(0, 0)	$+$	$-$	(0, 0)
	(0, 1)	$+$	$+$
	(1, 0)	$-$	$-$
	(1, 1)	$-$	/
	$(x^{\ast },y^{\ast })$	$+$	/
$X_{12}<M_{12},X_2>M_2$	(0, 0)	$+$	$-$	(0, 0)
	(0, 1)	$-$	$-$
	(1, 0)	$+$	$+$
	(1, 1)	$-$	/
	$(x^{\ast },y^{\ast })$	$+$	/
$X_{12}<M_{12},X_2<M_2$	(0, 0)	$+$	$-$	(0, 0)
	(0, 1)	$-$	$-$
	(1, 0)	$-$	$-$
	(1, 1)	$+$	$+$
	$(x^{\ast },y^{\ast })$	$-$	$+$

. Here “+” means positive sign, “−” means negative sign, and “/” means uncertain sign; “ESS” stands for evolutionary stable strategy.

Scenario 1: If $X_{12}>M_{12},X_2>M_2$, the evolutionary stability points are (0, 0) and (1, 1). In this scenario, both enterprises and universities can benefit from sharing innovation information, and the final evolutionary result among innovation alliance groups is sharing or not sharing.

Scenario 2: If $X_{12}>M_{12},X_2<M_2$, the evolutionary stability point is (0, 0). In this scenario, the profits from sharing innovation information can compensate for the cost, while universities cannot. Therefore, universities do not share information, and the final evolutionary result between innovation alliance groups is no sharing.

Scenario 3: If $X_{12}<M_{12},X_2>M_2$, the evolutionary stability point is (0, 0). In this scenario, the benefits obtained by colleges and universities from sharing information are greater than their sharing costs, while the benefits of enterprises cannot compensate for their costs. Therefore, enterprises do not share information, and the final sharing strategy among innovation alliance groups is no sharing.

Scenario 4: If $X_{12}<M_{12},X_2<M_2$, the evolutionary stability point is (0, 0). In this scenario, the benefits obtained from information sharing between enterprises and universities cannot compensate for their sharing costs, so the final stability strategy among innovation alliance groups is no sharing.

From the above analysis, it can be seen that whether the sharing strategy among innovation alliance groups can achieve stable sharing depends on whether the enterprises themselves can benefit from information sharing. The final evolutionary result has nothing to do with the income gap among innovation alliance groups. The above is the analysis of sharing strategies between enterprises and universities, similar to that between enterprises and scientific research institutes, which will not be analyzed separately here.

2.4. Evolutionary Game Analysis under a Horizontal Cooperation Trust

Since horizontal cooperation trust occurs in enterprises at the same level of the industry–university–research innovation alliance, that is, between universities and research institutes, the utility of enterprises remains unchanged, and the utility of universities and research institutes influences each other. Assume that the trust coefficient of horizontal cooperation is $\psi (0<\psi <1)$ and that other assumptions are the same as those under a vertical cooperation trust.

When there is a horizontal cooperation trust between universities and research institutes, the set ${\Theta }_{12}^{\prime },{\Theta }_{22}^{\prime },\overline{{\Theta }_2^{\prime }}$ represents the university’s income from sharing information, the income from not sharing information, and the average income of the university, respectively. As shown in Table 1, the income from choosing to share information under a horizontal cooperation trust is

$$\begin{array}{cc}\hfill {\Theta }_{12}^{\prime }& =x[(1+\psi )({\Omega }_{12}{\beta }_1{\omega }_1{\theta }_1{\alpha }_2+X_2-M_2)-\psi ({\Omega }_{13}{\beta }_1{\omega }_1{\theta }_3{\alpha }_3+X_3-M_3)]\hfill \\ & \hspace{1em}+(1-x)[-(1+\psi )M_2+\psi M_3]\hfill \end{array}$$

(9)

The revenue of the university from not sharing information is

$${\Theta }_{22}^{\prime }=x[(1+\psi ){\Omega }_{12}{\beta }_1{\omega }_1{\theta }_2{\alpha }_2-\psi {\Omega }_{13}{\beta }_1{\omega }_1{\theta }_3{\alpha }_3]$$

(10)

The expected revenue of the university is

$$\begin{array}{cc}\hfill \overline{{\Theta }_2^{\prime }}& =y{\Theta }_{12}^{\prime }+(1-y){\Theta }_{22}^{\prime }=xy[(1+\psi )({\Omega }_{12}{\beta }_1{\omega }_1{\theta }_2{\alpha }_2+X_2-M_2)\hfill \\ & -\psi ({\Omega }_{13}{\beta }_1{\omega }_1{\theta }_3{\alpha }_3+X_3-M_3)]+y[-(1+\psi )M_2+\psi M_3]\hfill \\ & \hspace{1em}\hspace{1em}\hspace{1em}+x(1-y)[(1+\psi )\gamma {\Omega }_{12}{\beta }_1{\omega }_1{\theta }_2{\alpha }_2-\psi \gamma {\Omega }_{13}{\beta }_1{\omega }_1{\theta }_3{\alpha }_3]\hfill \end{array}$$

(11)

To simplify the formula, set

$$\begin{array}{c}{X}_3={\mu }_{13}{\lambda }_3({\beta }_1{\Omega }_{13}+{\beta }_3{\Omega }_3)\\ M_3=\frac{1}{2}{l}_3{\beta }_3^2{\Omega }_3^2+c_{23},X_{13}={\mu }_{13}{\lambda }_{13}({\beta }_1{\Omega }_{13}+{\beta }_3{\Omega }_3)\\ M_1=\frac{1}{2}{l}_1{\beta }_1^2({\Omega }_{12}^2+{\Omega }_{13}^2)+2c_{21}\end{array}$$

Thus, the replication dynamic equation of the strategy of sharing innovative information among universities in the alliance can be obtained using:

$$F_1(y)=\frac{dy}{dt}=y({\Theta }_{12}^{\prime }-\overline{{\Theta }_2^{\prime }})=y(1-y)[x(1+\psi )X_2-\psi x{X}_3-(1+\psi )M_2+\psi M_3]$$

(12)

Similarly, the replication dynamic equation for studying the strategy of sharing innovative information in the alliance can be obtained using:

$$F_1(z)=\frac{\mathrm{dz}}{dt}=z({\Theta }_{13}^{\prime }-\overline{{\Theta }_3^{\prime }})=z(1-z)[x(1+\psi )X_3-\psi x{X}_2-(1+\psi )M_3+\psi M_2]$$

(13)

The replication dynamic equation of the strategy of sharing innovation information of enterprises in the alliance can be obtained using:

$$F_1(x)=x(1-x)(y{X}_{12}+z{X}_{13}-M_1)$$

(14)

Respectively to enterprises, universities, and research institutes, the replicated dynamic equation is equal to zero, and available local equilibrium (0, 0), (0, 1), (0, 0), (0, 1, 1), (0, 1), (1, 1), (1, 0), (1, 1, 1), and $(x^{\ast },y^{\ast },z^{\ast })$. Where the value of $y^{\ast }$ and $z^{\ast }$ is equal to the value under vertical fairness.

$$x^{\ast }=\frac{(1+\psi )M_2-\psi M_3}{(1+\psi )X_2-\psi X_3}\mathrm{or}{x}^{\ast }=\frac{(1+\psi )M_3-\psi M_2}{(1+\psi )X_3-\psi X_2}$$

The Jacobian matrix can be obtained by taking the partial derivatives for x, y, and z of the above replicated dynamic equations $F_1(x),F_1(y),F_1(z)$, respectively,

$$J^{\prime }=\left(\begin{array}{ccc}{J}_{11}^{\prime }& J_{12}^{\prime }& J_{13}^{\prime }\\ J_{21}^{\prime }& J_{22}^{\prime }& J_{23}^{\prime }\\ J_{31}^{\prime }& J_{32}^{\prime }& J_{33}^{\prime }\end{array}\right)=\left(\begin{array}{ccc}\frac{\partial F_1(x)}{\partial x}& \frac{\partial F_1(x)}{\partial y}& \frac{\partial F_1(x)}{\partial z}\\ \frac{\partial F_1(y)}{\partial x}& \frac{\partial F_1(y)}{\partial y}& \frac{\partial F_1(y)}{\partial z}\\ \frac{\partial F_1(z)}{\partial x}& \frac{\partial F_1(z)}{\partial y}& \frac{\partial F_1(z)}{\partial z}\end{array}\right)$$

(15)

In Equation (15), there is

$$\begin{array}{c}{J}_{11}^{\prime }=(1-2x\left)\right(y{\mathrm{X}}_{12}+z{X}_{13}-M_1),J_{21}^{\prime }=y(1-y)[(1+\psi )X_2-\psi X_3]\\ J_{13}^{\prime }=x(1-x)X_{AC},J_{22}^{\prime }=(1-2y)\{[(1+\psi )X_2-\psi X_3]x-(1+\psi )M_2+\psi M_3\}\\ J_{23}^{\prime }=J_{32}^{\prime }=0;J_{31}^{\prime }=z(1-z)[(1+\psi )X_3-\psi X_2],J_{12}^{\prime }=x(1-x)X_{12}\\ J_{33}^{\prime }=(1-2z)\{[(1+\psi )X_3-\psi X_2]x-(1+\psi )M_3+\psi M_2\}\end{array}$$

If the local stable point is substituted into the Jacobian matrix, the other elements of the matrix except the main diagonal are equal to 0, where $J_{11}^{\prime },J_{22}^{\prime },J_{33}^{\prime }$ are the three eigenvalues of the Jacobian matrix, respectively. The values of eigenvalues $J_{11}^{\prime },J_{22}^{\prime },J_{33}^{\prime }$ in each equilibrium point of the game are shown in

Table 4. Local stability analysis results of the group innovation information-sharing evolutionary game for the industry–university–research innovation alliance.

Locally Stable Point	${\mathit{J}}_{11}^{\prime }$	${\mathit{J}}_{22}^{\prime }$	${\mathit{J}}_{33}^{\prime }$
(0, 0, 0)	$-M_1$	$-(1+\psi )M_2+\psi M_3$	$-(1+\psi )M_3+\psi M_2$
(0, 0, 1)	$X_{13}-M_1$	$-(1+\psi )M_2+\psi M_3$	$(1+\psi )M_3-\psi M_2$
(0, 1, 0)	$X_{12}-M_1$	$(1+\psi )M_2-\psi M_3$	$-(1+\psi )M_3+\psi M_2$
(0, 1, 1)	$X_{12}+X_{13}-M_1$	$(1+\psi )M_2-\psi M_3$	$(1+\psi )M_3-\psi M_2$
(1, 0, 0)	$M_1$	$(1+\psi )X_2-\psi X_3-(1+\psi )M_2+\psi M_3$	$(1+\psi )X_3-\psi X_2-(1+\psi )M_3+\psi M_2$
(1, 0, 1)	$-X_{13}+M_1$	$(1+\psi )X_2-\psi X_3-(1+\psi )M_2+\psi M_3$	$-(1+\psi )X_3+\psi X_2+(1+\psi )M_3-\psi M_2$
(1, 1, 0)	$-X_{12}+M_1$	$-(1+\psi )X_2+\psi X_3+(1+\psi )M_2-\psi M_3$	$(1+\psi )X_3-\psi X_2-(1+\psi )M_3+\psi M_2$
(1, 1, 1)	$-X_{12}-X_{13}+M_1$	$-(1+\psi )X_2+\psi X_3+(1+\psi )M_2-\psi M_3$	$-(1+\psi )X_3+\psi X_2+(1+\psi )M_3-\psi M_2$

.

Firstly, at the equilibrium point (1, 0, 0), since $J_{11}^{\prime }=M_1>0$ always holds, the point (1, 0, 0) is not an evolutionary stable point. Secondly, if $(1+\psi )M_2<\psi M_3$, $(1+\psi )M_3>\psi M_2$ is true, then at the equilibrium point (0, 1, 1), the eigenvalues $J_{11}^{\prime },J_{22}^{\prime },J_{33}^{\prime }$ are greater than or equal to 0, so the equilibrium point (0, 1, 1) is not an evolutionary stable point. Finally, for other equilibrium points, the values of eigenvalues $J_{11}^{\prime },J_{22}^{\prime },J_{33}^{\prime }$ at other points are positive or negative, as shown in

Table 5. Scenario analysis results corresponding to the equilibrium point of the evolutionary game of group innovation information sharing in the industry–university–research innovation alliance.

Scenario	Equilibrium Point	${\mathit{J}}_{11}^{\prime }$	${\mathit{J}}_{22}^{\prime }$	${\mathit{J}}_{33}^{\prime }$	ESS
$X_{AC}>M_A,X_{AB}>M_A$	(0, 0, 0)	$-$	$-$	$+$	(1, 0, 1)
$(1+\psi )M_2>\psi M_3,(1+\psi )M_3<\psi M_2$	(0, 0, 1)	$+$	$-$	$-$
$(1+\psi )X_3>\psi X_2,(1+\psi )X_2<\psi X_3$	(0, 1, 0)	$+$	$+$	$+$
	(1, 0, 1)	$-$	$-$	$-$
	(1, 1, 0)	$-$	$+$	$+$
	(1, 1, 1)	$-$	$+$	$-$
$X_{13}>M_1,X_{12}>M_1$	(0, 0, 0)	$-$	$+$	$-$	(1, 1, 0)
$(1+\psi )M_2<\psi M_3,(1+\psi )M_3>\psi M_2$	(0, 0, 1)	$+$	$+$	$+$
$(1+\psi )X_3<\psi X_2,(1+\psi )X_2>\psi X_3$	(0, 1, 0)	$+$	$-$	$-$
	(1, 0, 1)	$-$	$+$	$+$
	(1, 1, 0)	$-$	$-$	$-$
	(1, 1, 1)	$-$	$-$	$+$
$X_{13}>M_1,X_{12}>M_1$	(0, 0, 0)	$-$	$+$	$+$	(1, 1, 1)
$(1+\psi )M_2<\psi M_3,(1+\psi )M_3<\psi M_2$	(0, 0, 1)	$+$	$+$	$-$
$(1+\psi )X_2>\psi X_3,(1+\psi )X_3>\psi X_2$	(0, 1, 0)	$+$	$-$	$+$
	(1, 0, 1)	$-$	$+$	$-$
	(1, 1, 0)	$-$	$-$	$-$
	(1, 1, 1)	$-$	$-$	$-$
$(1+\psi )M_2>\psi M_3,(1+\psi )M_3<\psi M_2$	(0, 0, 0)	$-$	$-$	$-$	(0, 0, 0)
	(0, 0, 1)	/	$-$	$+$
	(0, 1, 0)	/	$+$	$-$
	(1, 0, 1)	/	/	/
	(1, 1, 0)	/	/	/
	(1, 1, 1)	/	/	/

.

Scenario 1: If $X_{13}>M_1$, $X_{12}>M_1$$(1+\psi )M_2>\psi M_3$, $(1+\psi )M_3<\psi M_2$, $(1+\psi )X_3>\psi X_2$, $(1+\psi )X_2<\psi X_3$, then (1, 0, 1) is the stable point of the evolutionary game, that is, when the enterprises in the alliance obtain more income after sharing innovation information than their cost, and the research institutes obtain more income after sharing innovation information than the universities and the sharing cost is lower, the final evolutionary result is that the enterprises share information with the research institutes and the universities do not share information.

Scenario 2: If $X_{13}>M_1$, $X_{12}>M_1$, $(1+\psi )M_2<\psi M_3$, $(1+\psi )M_3>\psi M_2$, $(1+\psi )X_3<\psi X_2$, $(1+\psi )X_2>\psi X_3$, then (1, 1, 0) is the stable point of the evolutionary game, that is, when the benefits of innovation information shared by enterprises in the alliance are greater than their costs, when the benefits of information sharing by enterprises are higher than their costs, and the sharing benefits of universities are higher than and the sharing costs are lower than those of scientific research institutes, the final evolutionary result is information sharing between enterprises and universities. Scientific research institutes do not share information.

Scenario 3: If $X_{13}>M_1$, $X_{12}>M_1$, $(1+\psi )M_2<\psi M_3$, $(1+\psi )M_3<\psi M_2$, $(1+\psi )X_2>\psi X_3$, $(1+\psi )X_3>\psi X_2$, then (1, 1, 1) is the evolutional stable point, that is, when the enterprise’s income from information sharing is higher than its cost, and under the influence of a horizontal cooperation trust, universities and research institutes think that their profit is higher, and the alliance group will eventually choose to share information.

Scenario 4: If $(1+\psi )M_2>\psi M_3,(1+\psi )M_3<\psi M_2$, the point (0, 0, 0) is the evolutionally stable point. Under the influence of a horizontal cooperation trust, when universities and research institutes think that their sharing cost is higher than that of the other party, the final sharing strategy of the alliance group is not to share.

3. Analysis of Numerical Examples

3.1. Analysis of Examples under a Vertical Cooperation Trust

Based on the theoretical analysis under a vertical cooperation trust, it can be seen that only when $X_{12}>M_1,X_2>M_2$, the enterprise’s sharing strategy can be stable in sharing. Based on the previous experiments, we obtained the actual value range of the relevant parameters. In order to analyze the dynamic relationship between different parameters, we take specific values of related parameters. Therefore, the simulation in this paper is carried out under this premise, assuming that the parameter assignment of the model species is

$${\Omega }_{12}={\Omega }_2=10,{\beta }_1={\beta }_2=0.5,{\mu }_{12}=2,{\lambda }_{12}={\lambda }_2=0.5,{\eta }_1=0.3,l_1=l_2=0.3,c_{2A}=c_{2B}=10.$$

Table 6. Sensitivity of information-sharing probability of colleges and universities to information-sharing probability of enterprises.

Enterprise Information-Sharing Probability	t = 0.00	t = 0.50	t = 1.00	t = 1.50	t = 2.00	t = 2.50	t = 3.50
0.00	0.00	0.71	0.82	0.10	0.10	0.10	0.10
0.10	0.00	0.77	0.85	0.10	0.10	0.10	0.10
0.20	0.00	0.79	0.89	0.10	0.10	0.10	0.10
0.30	0.00	0.82	0.93	0.10	0.10	0.10	0.10
0.40	0.00	0.84	0.98	0.10	0.10	0.10	0.10
0.50	0.00	0.87	0.10	0.10	0.10	0.10	0.10
0.60	0.00	0.89	0.10	0.10	0.10	0.10	0.10
0.70	0.00	0.91	0.10	0.10	0.10	0.10	0.10
0.80	0.00	0.95	0.10	0.10	0.10	0.10	0.10
0.90	0.00	0.98	0.10	0.10	0.10	0.10	0.10
1.00	0.00	0.99	0.10	0.10	0.10	0.10	0.10

shows the sensitivity of the university information-sharing probability to enterprise information-sharing probability.

As shown in Table 6, when the level of information sharing among innovation alliance groups is 10, the probability of innovation information sharing in universities increases with the increase of enterprise information-sharing probability, and the convergence rate of innovation information-sharing probability in universities increases rapidly, and tends to be stable as time goes on.

3.2. Sensitivity of the Enterprise Innovation Information-Sharing Evolution Strategy to Information-Sharing Volume

Keeping the other parameters in the initial simulation constant, the information-sharing level among innovation alliance groups is changed to ${\Omega }_{12}={\Omega }_2\in [10,40]$. Based on this,

Table 7. Sensitivity of the enterprise sharing innovation information evolution strategy to information sharing volume.

Information-Sharing Volume among Groups	t = 0.01	t = 0.02	t = 0.03	t = 0.04	t = 0.05	t = 0.06	t = 0.07
10	0.31	0.28	0.34	0.45	0.69	0.89	0.98
15	0.38	0.34	0.39	0.46	0.71	0.90	1.00
20	0.46	0.42	0.57	0.69	0.86	0.98	1.00
25	0.55	0.51	0.68	0.79	0.98	1.00	1.00
30	0.67	0.63	0.78	0.84	1.00	1.00	1.00
35	0.78	0.72	0.88	1.00	1.00	1.00	1.00
40	0.86	0.99	1.00	1.00	1.00	1.00	1.00

shows the sensitivity of enterprise strategy evolution to the amount of information sharing among alliance groups.

As shown in Table 7, with the increasing amount of information sharing among innovation alliance groups, the evolution of enterprise strategy becomes more stable, and enterprises will choose to share innovation information more. When the amount of information sharing among groups increases to 40, the convergence speed of enterprise strategy is the strongest. The reason for this phenomenon may be that when the innovation alliance group shares too much information with the enterprise, the enterprise will absorb all the information and turn it into its profit, increasing the internal innovation input and, in turn, improving its knowledge absorption and sharing ability.

3.3. Sensitivity of the Innovation Information-Sharing Evolution Strategy to Vertical Cooperation Trust Coefficient

Keeping other parameters unchanged in the initial simulation, the cooperation trust between enterprises and universities in the innovation alliance group is set as ${\eta }_1\in [0,0.8]$. Based on this, the sensitivity of enterprise strategy evolution to the trust coefficient of vertical cooperation can be obtained, as shown in

Table 8. Sensitivity of the enterprise innovation information-sharing evolution strategy to vertical cooperation trust coefficient.

Trust Coefficient of Cooperation between Enterprises and Universities	t = 0.01	t = 0.02	t = 0.03	t = 0.04	t = 0.05	t = 0.06
0	0.00	0.00	0.00	0.00	0.00	0.00
1	0.21	0.32	0.41	0.43	0.50	0.63
2	0.34	0.41	0.56	0.51	0.55	0.74
3	0.36	0.53	0.64	0.62	0.68	0.89
4	0.47	0.65	0.70	0.77	0.79	0.99
5	0.59	0.74	0.84	0.86	0.98	1.00
6	0.69	0.84	0.91	0.98	1.00	1.00
7	0.78	0.97	0.98	1.00	1.00	1.00
8	0.85	0.99	1.00	1.00	1.00	1.00

.

As shown in Table 8, with the increasing trust coefficient of vertical cooperation between enterprises and universities, the evolution of the enterprise strategy tends to be more stable, and enterprises will choose to share innovative information more. When the trust coefficient of vertical cooperation between enterprises and universities is 8, the convergence speed of enterprise strategy is the strongest. The reason for this phenomenon may be from the perspective that the information obtained by enterprises can be converted into profits. When the cooperation trust between universities and enterprises increases, universities will be more willing to share core technical information with universities. Then, universities will gain more innovation benefits, so they will be more willing to share their own innovation information.

4. Conclusions and Management Suggestions

Based on various factors in the information sharing of innovation alliance, this paper analyzes the decision-making of innovation information sharing among innovation alliance groups under the influence of various factors and its evolutionary path to provide references for the decision-making of innovation information sharing among industry–university–research innovation alliance groups. First, the paper analyzes the main factors influencing the innovative information-sharing behavior of alliance groups. Secondly, based on the evolutionary game theory, an evolutionary game model of innovative information-sharing under the cooperative trust degree of group decision-makers is constructed, and the related stable strategies are given. Finally, the sensitivity of innovative information-sharing strategies to key influencing factors is analyzed with the help of actual case data. The research shows that:

(1)

The appropriate amount of innovation information sharing can promote the stability of the innovation group alliance among enterprises, universities, and research institutes. If the amount of innovation information sharing continues to increase, especially when it exceeds the absorption capacity of enterprises, it will not be conducive to the information-sharing intention of the industry–university–research innovation alliance with enterprises as the link core;

(2)

From the perspective of a cooperation trust between enterprises, universities and enterprises and research institutes, compared with the income distribution strategy between innovation alliances, each group pays more attention to the cooperation trust between groups, and the trust is related to the psychological expectations of each specific decision-maker;

(3)

With the increasing amount of information sharing among innovation alliance groups, the evolution of an enterprise strategy becomes more stable, and enterprises will choose to share innovation information more;

(4)

The probability of innovation information sharing in colleges and universities increases with the increase of enterprise information-sharing probability and the convergence rate of innovation information-sharing probability in colleges and universities increases rapidly and tends to be stable as time goes on;

(5)

With the increasing trust coefficient of vertical cooperation between enterprises and universities, the evolution of an enterprise strategy tends to be more stable, and enterprises will choose to share innovative information more.

Based on the above research conclusions, this paper suggests that in order to promote the rapid development of the industry–university–research innovation alliance composed of enterprises, universities, and research institutes, the government should formulate relevant policies to provide guidance, especially focusing on the cooperation trust of all participating groups. In the case of cooperation trust, each group should pay more attention to its own interests and the unity of the interests of the alliance, avoid paying too much attention to the individual benefits of each group, and focus on the analysis of the enthusiasm of each group to share innovation information (sharing probability) and strive to ensure the fair distribution of the common benefits of the alliance among all groups.

The innovations of this paper are as follows:

(1)

In terms of research methods, the evolutionary game method adopted in this paper can more accurately describe the information-sharing behavior among enterprises, universities, and research institutes. In particular, the innovation information-sharing behavior of enterprises is described more dynamically;

(2)

In terms of research objects, this paper is significantly different from other relevant studies. It distinguishes universities and research institutes and finds that they have the same and different strategies in the process of information sharing, which is obvious.