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Innovative Technology Method Based on Evolutionary Game Model of Enterprise Sustainable Development and CNN–GRU

School of Management, Shandong University, Jinan 250100, China
School of Industry & Commerce, Shandong Management University, Jinan 250357, China
Author to whom correspondence should be addressed.
Sustainability 2023, 15(5), 4058;
Submission received: 3 February 2023 / Revised: 20 February 2023 / Accepted: 21 February 2023 / Published: 23 February 2023


Realizing the sustainable innovation growth of enterprises is one of the important research directions of management science. Traditional enterprise growth innovation methods cannot effectively estimate the emotional tendency of online public opinion (PO), and they cannot guide the effective growth of enterprises. For this reason, This paper proposes an enterprise growth innovation technology based on the evolutionary game (EG) model of sustainable development and deep learning (DL). Firstly, by obtaining the game payment matrix between network users and enterprises, combined with the deep neural network model, the PO evolution model of the enterprise growth network was constructed and solved. Then, a convolutional neural network (CNN) model was used to extract sequence features from global information, and a gated recurrent unit (GRU) was used to consider the context. A DL network model based on CNN–GRU was proposed. Finally, by introducing the EG model, a stable strategy was generated through the dynamic adjustment of the whole system, which improved the accuracy of online PO judgment. Through simulation experiments, the enterprise growth innovation method proposed in this paper was compared with the other three methods. The results show that the accuracy, precision, recall, and f1 value of this method are 92.21%, 89.33%, 91.86%, and 91.64%, respectively, which are better than the other three methods. This method is of great significance for promoting enterprise innovation technology and sustainable development of enterprises.

1. Introduction

Data flow and information sharing are crucial to the growth and innovation of enterprises. The data sharing community is an important promoter of enterprise innovation and open information sharing [1,2,3]. However, at present, enterprise innovation lacks an effective and scientific incentive mechanism, and generally faces challenges such as low enthusiasm for participation, a weak sense of belonging, insufficient motivation for knowledge generation, and a low degree of data sharing. The key to alleviating these problems is to build a reasonable and effective enterprise growth innovation model [4,5,6]. Therefore, it is of significance for this paper to propose a new method of evolutionary game theory and deep learning to solve the problem of enterprise growth. The emergence of game evolution provides new ideas for solving the problems faced by enterprise innovation [7,8]. At present, enterprise growth innovation is more oriented towards the technical means, industry competition, and enterprise performance considerations, and the role of incentive mechanisms in enterprise growth innovation has not been elucidated. Studies in this area have mainly considered subsidies for enterprise innovation itself, ignoring research on the impact of policy intervention on enterprise growth and innovation in different environments and with different policy combinations [9].
Exploring enterprise growth and innovation based on complex network evolution can solve policy barriers in industrial digital upgrading. A complex network evolution game model can describe the process of strategy evolution and the learning mechanism [10,11]. In recent years, the method of DL has been widely used to conduct research on enterprise growth and innovation, ensuring the transparency of innovation data sharing and circulation. Users can prevent data from being misused [12]. In addition, using the automatic execution of the smart contract of the DL model, the incentive mechanism of innovative data can be written into the smart contract, the reward and punishment information can be made public, and the process can be standardized to achieve transparency of reward and punishment. All data can be traced, which can not only protect the ownership of data, but also allows for checking of the authenticity of data information [13,14].
Enterprise growth and innovation is very important for an enterprise. Therefore, combining the complex network evolution game with DL and building a digital model of enterprise growth and innovation can help enterprises to better predict the trends and evolution of enterprise innovation, expand the scale of enterprise growth and innovation, standardize the innovation management process, and achieve rights to enterprise innovation, thus establishing an open enterprise growth and innovation ecosystem [15,16,17]. The statistical method of an evolutionary game is proposed by this paper, which solves the problem of enterprise innovation growth and uses the emotional tendency of network public opinion combined with a deep learning model to evaluate the growth and development of enterprises. The new method proposed in this paper is of significance to solving the problem of enterprise innovation. The framework of the remainder of the article is as follows: The Section 2 of the article describes the related research, and the Section 3 introduces the DL model. The Section 4 introduces the experiments and analysis, and the Section 5 presents the conclusions of the article.

2. Related Research

At present, it is one of the urgent tasks of management to realize the sustainable growth of enterprises, organizations, and the whole national economic system. The focus of this issue is increasingly turning to the search for suitable innovative technologies. Through research and access to relevant information, it has been found that the research on enterprise growth innovation technology based on EG models and DL can solve the bottleneck of traditional enterprise innovation. Taking a technology park as the research object, Zhen and Yao [18] proposed a new evaluation model for enterprise technology innovation with DL, carried out through comprehensive evaluation. This method used the idea of combination prediction but did not propose an strategy for improving the innovation mode. Liu [19] classified the data of enterprises in time and space by studying their spatio-temporal characteristics. On this basis, a convolution method for prediction was proposed. However, the accuracy of this method for the prediction of innovation performance needs to be improved. Abudureheman et al. [20] created an enterprise evaluation method with six different perspectives. However, the evaluation system of this method was relatively complex and difficult to apply in practice. Zhang et al. [21] used a three-party differential dynamic game model to find that government subsidies contribute to the spread of enterprise digitalization, and that the level of industrial digitalization reaches Pareto optimality under the tripartite collaboration of the government, technology companies, and traditional enterprises. Wang et al. [22] took collaborative innovation risk as the starting point for their research. A method for analyzing the risk using DL was proposed, introducing synergetic effect and dynamic capability as intermediary variables and regulatory variables. However, this method did not analyze how to improve and reduce the risk from collaborative innovation. Yang and Wang [23] proposed a model of enterprise culture and technology with the DL method, taking the influence of enterprise technology innovation capability and enterprise culture on the enterprise itself as the research objects. However, this method did not consider the external factors affecting the development of enterprise innovation technology. Based on the data of listed companies, Chen et al. [24] constructed a fixed panel data model, and found that sufficient industry competition can change the information structure of the market and improve the speed of digital diffusion of enterprises. Huang et al. [25] found that improving profit margins and the level of digital collaboration of enterprises is conducive to the digital diffusion of cultural industries, by constructing game theory models and carrying out numerical simulations. Xiong [26], through relevant theoretical research, pre-surveys, and the construction of an appropriate measurement scale, put forward the corresponding relationship model by combining the methods of small and medium enterprises. However, this relationship model only analyzed the impact of network relationships, which has certain limitations. Bai [27] put forward relevant assumptions to construct a regression model and proposed a relationship model. However, this model only analyzed the stock price information, and its scope of application was limited. Hu [28] found that a good social network relationship is helpful to the digital diffusion of enterprises in the process of exploring the digital performance of enterprises based on social network theory. Zhao and Li [29] proposed to build a three-level ‘county, township, and village’ joint distribution system with the participation of e-commerce platforms. They first established and solved an evolutionary game model of a joint distribution alliance of express delivery enterprises. Finally, they analyzed the model by numerical simulation. It showed that the innovation growth of enterprises is related to factors such as excess return, early input cost, operation cost, cooperation risk, punishment cost, and enterprise learning absorption capacity. Jia et al. [30] proposed that the innovative growth of enterprises needs to use the open innovation model to obtain external knowledge, resources and skills, improve internal innovation performance, and achieve innovation catch-up. Dynamic capabilities can effectively promote the open innovation activities of enterprises. In addition, the different dimensions of dynamic capabilities, namely, perception ability, absorptive capacity, complementary ability, and coordination ability, also have a significant incentive effect on open innovation. Wang et al. [31] proposed an evolutionary game model between upstream and downstream enterprises, and explored the interaction between credit sales and green technology innovation through evolutionary equilibrium analysis, which provided theoretical support for the development of enterprise innovation technology. Haffar et al. [32] proposed to test the innovation strategy of commercial finance. By examining network capabilities and frugal innovation, he used quantitative research methods to provide great help for the innovation growth of commercial organizations such as SMEs. Costa et al. [33] realized digital transformation through digital technology, studied the field situation of three pulp and paper companies in Brazil, provided a practical basis for the sustainable development of enterprises, and provided theoretical support for the rapid development of enterprises. Shinkevich et al. [34] proposed that achieving sustainable growth of enterprises is one of the urgent tasks of management. They used descriptive statistics, correlation-regression analysis, and other methods to prove this in their research. Nastase et al. [35] proposed to analyze the business model of a company from the perspective of circular economy, and used a case study based on Evertoys to propose new strategies for the innovation model of the company. Lisin et al. [36] proposed innovative ideas for the financial sustainable growth of enterprises by analyzing ESG parameters, using regression models and Pearson correlation coefficients.
Trisyulianti et al. [37] proposed to design a sustainable performance management system, starting from the vision and mission of the enterprise, and put forward innovative methods for the sustainable development of the enterprise. Girdzijauskas et al. [38] proposed to establish a new inflation aggregate analysis model to analyze the sustainable growth of the economy. This research is also of great significance to the innovation and growth of the enterprise economy. Using the data regression model, Zhang et al. [39] proposed the sustainable development enterprise strategy, which provided constructive suggestions for the sustainable innovation and growth of enterprises. Morioka et al. [40] proposed to combine the concept of enterprise sustainability performance and sustainable business models, and used the sustainable innovation model to provide a valuable contribution to the innovation and growth of enterprises. Mandicak et al. [41] proposed a sustainable innovation design to realize the enterprise management process, which is of great significance for the sustainable development of the enterprise economy. Feng and Liu [42] proposed to use multiple linear regression models to study the sustainable development of enterprises, which is of great significance to the innovation and growth of enterprises. Ren and Li [43] discussed the digital transformation to promote the development of enterprise green innovation technology, which has an important impact on the sustainable development of enterprises. Storm and Smith [44] proposed a collaborative approach to stimulate the sustainable development of SMEs, which can increase the innovation opportunities of enterprises and open up new ways of thinking to meet new challenges. Kim et al. [45] discussed the mechanism of action in the process of enterprise management, and adopted the method of qualitative analysis to study the enterprise strategy, which has an important influence on the growth of the enterprise. Bhalla et al. [46] used regression models and structural equation models to conduct quantitative analysis of enterprises. This method is very important to the impact of enterprise performance, and it is also of great significance to the innovation growth of enterprises. Vrontis et al. [47] proposed the use of digital technology to influence the sustainability of the enterprise economy. This technology is of great significance for reducing the external crisis of enterprises and promoting the sustainable development of enterprises to a great extent. Wang and Huang [48] contributed to the sustainable development of enterprises by regulating the corporate control culture. Chatterjee et al. [49] used structural equation modeling technology to regulate the sustainable growth of SMEs, which has an important impact on the sustainable growth of enterprises. Tian et al. [50] used the panel data of listed companies to guide enterprises to use knowledge-intensive services to enhance the innovation growth of enterprises, which is of positive significance for the sustainable entrepreneurial growth of enterprises. Surya et al. [51] designed the sustainable development of enterprises by using the hypothesis method, and provided help for improving the sustainable innovation growth of enterprises through the combination of quantitative research and qualitative research. However, traditional enterprise growth innovation methods cannot effectively estimate the emotional tendency online and cannot guide enterprise growth. Therefore, this paper proposed an enterprise growth innovation technology method based on the EG model and DL. Compared with the traditional research on enterprise growth, the innovations of the proposed method were:
(1) EG theory was used to improve the accuracy of PO judgment through the process of imitation and learning among various game players;
(2) The DL network model based on CNN–GRU was able to extract the sequence features from global information while considering the contextual relationship, and improve the accuracy of PO judgment;
(3) Based on the characteristics of negative PO in the climax stage, the corresponding EG model and enterprise game pay-off matrix were established, which improved the prediction performance of the model for enterprise growth.

3. DL Model

3.1. Overall Structure

Based on the game pay-off matrix, combined with the deep neural network (DNN) model, the overall structure of the enterprise growth network PO evolution model was constructed. The research scheme framework is shown in Figure 1. It mainly included reputation, enterprise growth, reputation evolution, and stability strategy for the deep learning network.

3.2. EG Theory

EG is an improvement of traditional game theory by researchers. It is a process in which the static change process of the original game theory becomes a dynamic evolution process. In EG, with multiple market participants, each participant is bounded rationally. Each participant can clearly understand that individual decisions cannot achieve optimal behavior in practice. The strategies adopted each time are selected through the process of imitation and learning among various game players. Importantly, in EG, the entire system will produce stable strategies through dynamic adjustment. It is widely used and can be continuously improved in practice.

3.2.1. Basic Concepts of EG

When most members of the group choose a certain strategy, the final benefit obtained by this strategy is more stable than that obtained by other strategies. This strategy is called the evolutionary stability strategy, but it is not an absolutely advantageous strategy. The evolutionary stability strategy is defined as follows:
x Q is an evolutionary stable strategy. If y Q , y x , there exists α ¯ y 0 , 1 satisfying inequality (1).
v x , α y + 1 α x > v y , α y + 1 α x
α 0 , α ¯ y always satisfies inequality (1), where v represents the benefit of the hybrid strategy; Q represents the income matrix; y represents the mutation strategy; α ¯ y represents the constant related to y ; and α y + 1 α x represents a mixed population of the mutation strategy and stable strategy.
When a strategy gradually begins to evolve and develop in the game, this is the replication dynamic process. The mathematical expression is:
d δ 1 d t = δ 1 r r ¯ d δ 2 d t = δ 2 e e ¯
where δ 1 is the probability that A adopts 1; δ 2 is the probability that B adopts 2; r is the expected return of A when 1 is adopted; r ¯ is the average expected return of A; e is the expected return of B when 2 is adopted; and e ¯ is the average expected return of B.
We can take a two-dimensional first-order planar linear system as an example to illustrate the rules for judging. The expression is as follows:
x ˙ = m x + n y y ˙ = p x + q y
In the formula, m , n , p , and q are constants. Let A = m , n p , q , and
a = t r A = m + q b = det A = m q n p
where a represents the trace of the second-order matrix A; and b is the value of the determinant when the solution is the second-order A.

3.2.2. Characteristics and Classification of EG

EG includes the following four characteristics:
(1) The players will make adjustments according to different information. In the process of EG, dynamic changes are mainly emphasized;
(2) The object of study is the group, but the players in each game are uncertain. The players can not only be the internal game of a group, but also the mutual game between multiple groups;
(3) EG is a process of dynamic adjustment. During the adjustment, the system is likely to have multiple equilibria, but the final stable point is determined by the evolutionary path and the initial state;
(4) In the process of EG, there are often variations and trial and error, but the players may give up the original strategy and make the game system evolve to other equilibria through constant adjustment.
Games are involved in every field of life. There are many types of game theory, including two party or n-party games ( n 3 ), static and dynamic games, cooperative and non-cooperative games, symmetric and asymmetric games, and complete information and incomplete information games, etc. Symmetric and asymmetric games are determined by the number of groups. Symmetric games are mainly games within the same group. The income matrix established is symmetric. The asymmetric game is mainly reflected in the game between different groups. There are at least two participating groups and the established income matrix is asymmetric.

3.2.3. Differences from Classical Game Modeling

This paper discusses the differences between EG and traditional games concerning three aspects:
(1) Rational assumptions. The traditional game is completely rational. Completely rational refers to the participants’ perfect sense of adventure, degree of control, ability to perform accurate behavior, and self-inference of the market operation laws. It is inconsistent with reality; therefore, it is not suitable for dealing with practical problems and can only be used for theoretical discussion. However, the market judgment ability and inference ability of the market participants in EG theory are limited. The ability to obtain information is also limited, and the participants are often limited in rationality. Therefore, when choosing strategies, each player needs to go through an imitation and learning process at the same time. In this process, there will be many uncertain factors that affect the strategy choice of each participant.
(2) Equilibrium notion. Traditional game theory mainly discusses the equilibrium game and the Nash equilibrium, but this equilibrium point is a fixed point. In practice, the studied groups are generally in dynamic change, not only Nash equilibrium. However, traditional games find it difficult to describe the dynamic characteristics of groups. The equilibrium view in EG theory is an evolutionary stability strategy, which is consistent with reality, and can describe the local dynamic nature in the dynamic process of the game system, as well as more truly and reasonably predict the market decision-making behavior of participants.
(3) Research methods. In traditional game theory, calculus is usually used to determine the decision-making behavior of market participants, so static theory gradually tends to become dynamic. EG theory looks at the problem from the perspective of the whole market, and it regards the process of strategy adjustment of each participant as a process in which a dynamic system constrained by various influencing factors finally reaches equilibrium and stability. EG models usually require complex mathematical methods, such as Jacobian iteration and differential equations.

3.3. Enterprise Game Pay-off Matrix

Suppose that there are two strategies for enterprises to choose when considering the strategy of network users: enthusiasm and robustness. If user enthusiasm is defined as k 1 , and user robustness is defined as k 2 , then k 1 + k 2 = 1 . If the enterprise enthusiasm is l 1 , and the enterprise robustness is l 2 , then l 1 + l 2 = 1 . The fixed income of network users is recorded as w 1 . When the network users have high enthusiasm, and the benefits brought by enthusiasm are recorded as P 1 , their own income parameter is a , and the cost is H 1 . When network users have high robustness and transmit robustness, the profit and loss parameter is b , and the cost is H 2 . When the logistics enterprise is active, the loss of network users in pursuit of robustness is Q 1 . In the case of logistics enterprises pursuing robustness, the waiting cost of network users’ demand enthusiasm is H 3 . The fixed income of logistics enterprises is W 2 . When logistics enterprises choose to pursue enthusiasm, the cost is H 4 , and the economic benefit is P 2 . When a logistics enterprise chooses robustness, the loss of the enterprise’s credibility is Q 2 .
According to the above definitions, the game pay-off matrix between network users and logistics enterprises was obtained [52], as shown in Table 1.
In Table 1, k 1 and k 2 represent the enthusiasm and robustness of users, respectively, and l 1 and l 2 represent the enthusiasm and robustness of enterprises, respectively.
The expected benefits and average benefits of user enthusiasm and robustness are, respectively, expressed as
S U 1 = l 1 H 1 1 + a H 3 + l 1 H 3 S U 2 = H 2 + l 1 P 1 l 1 Q 1 + W 1 1 b S ¯ U = k 1 S U 1 + k 2 S U 2
The expected income and average income of positive rumor-dispelling strategies and negative rumor-dispelling strategies of logistics enterprises are, respectively, expressed as follows:
S E 1 = H 4 + W 2 + P 2 k 1 Q 1 S E 2 = W 2 Q 2 S ¯ E = l 1 S E 1 + l 2 S E 2

3.4. Evolution Model of Enterprise Growth Network PO

It is worth noting that PO can form a huge scale in a short time under the influence of online media, which greatly accelerates the evolution of enterprise PO. The online PO evolution process of enterprises has four stages: incubation, diffusion, outbreak, and decay. Compared with positive enterprise online PO, Internet users care about enterprise PO events, and negative PO spreads more rapidly. Therefore, the transition time between the diffusion period and the outbreak of negative PO of enterprises is greatly reduced. These two stages can be regarded as one stage (i.e., the upsurge period). The conceptual model of enterprise negative PO of three parties is shown in Figure 2.
The spread of enterprise-related negative information is short-term and rapid. Most enterprises are in the upsurge period of PO when responding to PO events. Therefore, the corresponding EG model should be established with characteristics of the enterprise’s negative PO in the upsurge stage.

3.5. Model Solution and Stability Analysis

According to Table 1 and Formula (5), the user’s replication dynamic equation is
D X = d x d t = x S U 1 S ¯ U = x 1 x y Q 2 W 2 + Q 2 H 4
Let D X = 0 , and we obtain x = 0 , x = 1 or y = Q 2 H 4 Q 2 + W 2 . When y = y = Q 2 H 4 Q 2 + W 2 , D X is always 0, so the system reaches a stable state no matter what value x is. When y < y , D x = 0 < 0 , so x = 0 is the evolutionary stability strategy of the game equation. When y > y , D x = 1 < 0 , so x = 1 is the evolutionary stability strategy of the game equation. Through the introduction of the above cases and the description of previous methods [53], the user’s replicated dynamic phase map is shown in Figure 3.
Similarly, the replicated dynamic equation of enterprise can be obtained as follows:
D Y = d y d t = y S E 1 S ¯ E = Y 1 Y x Q 2 + W 2 + H 2 P 1 1 + w 1
Let D Y = 0 , and we obtain y = 0 , y = 1 or x = P 1 1 + w 1 H 2 Q 2 + W 2 . When x = x = P 1 1 + w 1 H 2 Q 2 + W 2 , D Y is always 0, so the system reaches a stable state no matter what value x is. When x < x , D y = 0 < 0 , so y = 0 is the evolutionary stability strategy of the game equation. When x > x , D y = 1 < 0 , so y = 1 is the evolutionary stability strategy of the game equation. Through the introduction of the above cases and the description of previous methods [53]. The enterprise’s replicated dynamic phase map is shown in Figure 4.

3.6. DL Network Model Based on CNN–GRU

CNN has unique advantages in feature extraction, and GRU has functions that CNN does not. Therefore, the two models can be used together. The model uses the CNN convolution layer to extract local features, and then the GRU layer uses feature sorting to understand the input text sorting. Its structure is shown in Figure 5.
The model has four main steps:
(1) Word vectors are used to represent text. This is consistent with the above description and will not be repeated here;
(2) CNN is used to extract text features. The matrix is used for word embedding. The convolution kernel extracts local features. When the word vector is 96 dimensions, 250 filters with sizes of 3 × 100, 4 × 100, 5 × 100 are used. Padding is set to VALID, and strides is set to 1. The pooling discards unused features and retains useful features.
(3) GRU is used to obtain context information.
(4) The classifier is used to classify text orientation. Text orientation classification inputs the full connection into the activation function. The dropout mechanism is used, and the dropout probability is 20%.

3.7. CNN

The CNN network is a multilayer supervised learning network, as shown in Figure 6.
As can be seen from Figure 6, the input layer is used to input the features of the CNN network to be trained. For NLP tasks, this feature is a feature vector representing the text. The pooling layer is connected behind the convolution. Its role is to down-sample features according to certain rules.

3.8. GRU

Because of the complex structure of LSTM, some researchers have combined a recurrent neural network with LSTM, which is called a Gated Recurrent Unit (GRU). In this structure, the cell state and hidden state are combined, making this model simpler than the standard LSTM structure, as shown in Figure 7.

4. Experiments and Analysis

4.1. Experimental Environment Configuration

A lab PC was used as the hardware environment for the experiment, and the algorithm implementation language was Python. The configuration shown in Table 2 was used for the research.

4.2. Datasets

In order to ensure the objectivity of the results, the data set of the emotion analysis task needed to be from a representative website or social platform. The Simplifyweibo_4_moods dataset was the standard dataset used in the experimental part of this paper [54]. The basic information of the dataset is introduced below, and some processing was carried out according to the task requirements.
The Simplifyweibo_4_moods dataset is a standard dataset based on the microblog platform, which contains more than 360,000 microblog data points with four types of emotional tags. There are about 200,000 pieces of data labeled with joy emotion tags, and about 100,000 pieces of data labeled with disgust, anger, and depression emotion tags. The data are from Sina Weibo and can be obtained directly through crawlers. Because disgust, anger, and depression are all negative emotional experiences, and they are similar in the description of some words and sentences, the model can be difficult to learn. Therefore, according to the different emotional tendencies of the data in the dataset, the label items of the entire data set were simplified and divided into two emotional directions: positive emotions and negative emotions. The specific processing method was to first integrate the data labeled as disgust, anger, and depression in the data set, and then label the negative emotion data after removing or reprocessing any ambiguous data. Similarly, data labeled as happy in the data set were also processed, and the data containing positive emotions were labeled as such. The positive emotional data was labeled as 1, and the negative emotional data was labeled as 0.
After the dataset was relabeled and reclassified, part of the data in the standard data set was randomly selected for model training. The distribution statistics of the dataset in this experiment are shown in Table 3 below.

4.3. Evaluation Indicators

A standard was needed to evaluate the model. The confusion matrix shown in Table 4 below is usually used as the standard.
In Table 4, TP indicates cases where the actual classification is P and P is predicted. FN indicates cases where the actual classification is P and N is predicted. FP indicates cases where the actual classification is N and P is predicted. TN indicates cases where the actual classification is N and N is predicted. P is positive and N is negative.
On this basis, four evaluation indicators were used: accuracy A, precision P, recall R, and F1. The specific calculation process is shown in Equations (9)–(12).
A = T P + T N T P + T N + F P + F N
P = T P T P + F P
R = T P T P + F N
F 1 = 2 P R P + R

4.4. Model Training

For training, the selection of an iteration number is very important. A low iteration number will lead to incomplete model training, and the results from incomplete training will not reflect the real performance of the model. A high iteration number will lead to excessive model training time, and unnecessary consumption of computer resources. Based on the size of the dataset and the experimental environment, we selected an iteration number between 0 and 15, and the GRU Hidden Size was 128. We recorded the accuracy and loss after each epoch, as shown in Figure 8.

4.5. Comparative Analysis

For the proposed enterprise growth innovation method based on the EG model and DL, the methods in [19,20,23] were used for experimental analysis on the Simplifyweibo_4_moods dataset. The final calculation results are shown in Table 5.
As can be seen from Table 5, when using the Simplifyweibo_4_moods dataset, the proposed enterprise growth innovation method based on the EG model and DL was superior to the other three comparison methods in the four evaluation indicators. The accuracy A, precision P, recall R, and F1 values reached 92.21%, 89.33%, 91.86%, and 91.64%, respectively. The accuracy of the proposed method was improved by 6.76%, 7.69%, and 11.76%, respectively, compared with the other three comparison methods. This was because the whole system in the EG model can generate stable strategies through dynamic adjustment, and each participant can clearly understand whether the individual decision can achieve the optimal behavior in practice, which greatly improves the classification accuracy. In addition, the GRU network can eliminate the problem of gradient disappearance, reduce the time interval between obtaining input and making decisions, improve the feature sampling process, and improve the comprehensive performance of the model.

4.6. Application of the Game Pay-off Matrix Model

Steady state results of enterprise growth under different policy combinations are shown in Table 6.
In addition, in order to further reveal the role of government policies in the interaction mechanism of micro-enterprise decision making, a comparative analysis was conducted on the average income of enterprises in the growth stage. The results are shown in Figure 9 and Figure 10, where T represents the proportion of the digital subsidy.
It can be seen from Table 6 and Figure 9 and Figure 10 that when the subsidy proportion η increases by 0.025 in 0.1 , 0.2 , the enterprise growth breadth under the evolutionary steady state is 11%, 17%, 29%, 48%, and 68%, respectively. When the high-tech certification influence λ increases by 0.02 steps in 0.1 , 0.2 , the enterprise growth breadth in the evolutionary steady state is 28%, 65%, 86%, 98%, and 100%, respectively. Horizontal comparison shows that the high-tech certification influence has a greater role in enterprise growth than the digital subsidy proportion.

4.7. Comparison of Evolution Curves

The following is a comparative analysis of the evolution curve of the proposed model with the methods in [19,20,23]. The evolution curve reflects the enterprise growth with trends in PO. The results are shown in Figure 11.
It can be seen from Figure 11 that under the same initial sharing proportion, the proposed model achieved data sharing saturation faster than the other comparison methods. The proposed model can achieve data sharing at an earlier game stage, improve the efficiency of data sharing, and is more conducive to the growth of enterprises and the guidance of PO.

5. Conclusions

To solve the problem that traditional enterprise growth innovation methods cannot effectively estimate the emotional tendency of online PO and guide enterprise growth, this paper proposes an enterprise growth innovation method based on a sustainable development EG model and DL model. The experimental results showed that EG theory can make the whole system produce a stable strategy through dynamic adjustment, which can be widely used and constantly improved in practice. By solving the enterprise game pay-off matrix, this method can effectively understand the factors that affect the growth of enterprises. The introduction of GRU into the traditional CNN network can solve the problem of gradient disappearance, reduce the time interval between obtaining input and making decisions, and improve the detection accuracy.
In short, because it does not consider the complex relationship structure in the enterprise and the emotional tendencies of enterprise personnel in a specific environment, this will have an impact on the forecast of sustainable growth of enterprises. In order to improve the sustainable development of enterprises, innovative technologies are used to continuously promote the healthy growth of enterprises. The following suggestions are about the sustainable innovation and growth of future enterprises:
  • Focus on how to accurately predict the growth of enterprises considering the complex relationship structure in social enterprises, so as to have a precise positioning for the growth of enterprises.
  • Pay attention to the change in enterprise relationship structure over time, and promote the sustainable development of enterprises from the applicability and improvement strategy of the enterprise growth innovation method.
  • Focus on the complex relationship structure in the enterprise and the trend in emotional public opinion of enterprise personnel in a specific environment, so as to accurately predict the development of enterprises.

Author Contributions

H.Z.: Conceptualization, methodology, validation, visualization, writing—original draft. X.X.: Project administration, resources, writing—review and editing, conceptualization. All authors have read and agreed to the published version of the manuscript.


This research received no external funding.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Data are contained within the article.

Conflicts of Interest

The authors declare no conflict of interest.


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Figure 1. Enterprise growth innovation model based on the EG model and DL.
Figure 1. Enterprise growth innovation model based on the EG model and DL.
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Figure 2. Evolutionary conceptual model of an enterprise negative PO network.
Figure 2. Evolutionary conceptual model of an enterprise negative PO network.
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Figure 3. Replicated dynamic phase map of the user.
Figure 3. Replicated dynamic phase map of the user.
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Figure 4. Replicated dynamic phase map of the enterprise.
Figure 4. Replicated dynamic phase map of the enterprise.
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Figure 5. DL network model based on CNN–GRU.
Figure 5. DL network model based on CNN–GRU.
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Figure 6. Basic structure of the CNN network.
Figure 6. Basic structure of the CNN network.
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Figure 7. Basic structure of the GRU network.
Figure 7. Basic structure of the GRU network.
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Figure 8. Change in the accuracy and loss with each epoch.
Figure 8. Change in the accuracy and loss with each epoch.
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Figure 9. Steady state income when subsidy proportion changes.
Figure 9. Steady state income when subsidy proportion changes.
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Figure 10. Steady state income when the influence of high-tech certification changes.
Figure 10. Steady state income when the influence of high-tech certification changes.
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Figure 11. Evolution curve of enterprise growth and PO tendency with different methods.
Figure 11. Evolution curve of enterprise growth and PO tendency with different methods.
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Table 1. Game pay-off matrix.
Table 1. Game pay-off matrix.
l 1 l 2
User k 1 H 3 + W 1 1 + a + P 1
W 2 Q 2
H 2 + W 1 1 b + P 1 Q 1
H 4 + W 2 + P 2 + Q 1
k 2 H 2 + W 1 1 b + P 1 Q 1
H 4 + W 2 + P 2 + Q 1
H 2 + W 1 1 b
W 2 Q 2
Table 2. Experimental environment configuration.
Table 2. Experimental environment configuration.
OSWindows 7 64 bit
CPUIntel (R) Core (TM) i7-6700
Memory16 GB
Programming languagePython 3.5.4
DL frameworkKeras 2.2.4
Table 3. Data set distribution statistics.
Table 3. Data set distribution statistics.
Data DistributionTraining SetValidation SetTest Set
Table 4. Confusion matrix.
Table 4. Confusion matrix.
Table 5. Calculation results of evaluation indicators of different algorithms.
Table 5. Calculation results of evaluation indicators of different algorithms.
Method A/%P/%R/%F1/%
Proposed method92.2189.3391.8691.64
Ref. [19]85.4583.6286.3185.66
Ref. [20]84.5281.3582.0582.97
Ref. [23]80.4580.6280.8180.52
Table 6. Steady state results of enterprise growth under different policy combinations.
Table 6. Steady state results of enterprise growth under different policy combinations.
CombinationSpan CombinationSpan
η = 0.1 , λ = 0.1 10% η = 0.1 , λ = 0.12 30%
η = 0.125 , λ = 0.1 15% η = 0.1 , λ = 0.14 70%
η = 0.15 , λ = 0.1 30% η = 0.1 , λ = 0.16 85%
η = 0.175 , λ = 0.1 50% η = 0.1 , λ = 0.18 98%
η = 0.2 , λ = 0.1 70% η = 0.1 , λ = 0.2 100%
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Zhang, H.; Xu, X. Innovative Technology Method Based on Evolutionary Game Model of Enterprise Sustainable Development and CNN–GRU. Sustainability 2023, 15, 4058.

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Zhang H, Xu X. Innovative Technology Method Based on Evolutionary Game Model of Enterprise Sustainable Development and CNN–GRU. Sustainability. 2023; 15(5):4058.

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Zhang, Hongni, and Xiangyi Xu. 2023. "Innovative Technology Method Based on Evolutionary Game Model of Enterprise Sustainable Development and CNN–GRU" Sustainability 15, no. 5: 4058.

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