The Impact of Government Behavior on the Development of Cross-Border E-Commerce B2B Export Trading Enterprises Based on Evolutionary Game in the Context of “Dual-Cycle” Policy

Abstract

In 2020, the COVID-19 pandemic had a major impact on China’s foreign trade. Therefore, the Chinese government has proposed a “dual cycle” policy to promote economic development. In 2021, China’s cross-border e-commerce B2B exports accounted for 60 percent. Therefore, this paper studies the impact of government actions on the development of cross-border e-commerce B2B export enterprises under the background of “dual cycle” policy. First, the policies related to the cross-border e-commerce industry in the “dual circulation” policy are screened, and the LDA topic model is used to classify them, i.e., sorting by topic intensity as “fiscal policy”, “tax policy”, “customs clearance policy”, “payment policy” and “talent policy”. After that, based on the analysis results of the LDA topic model, a theoretical basis for the impact of different policies on cross-border e-commerce B2B export companies is established; then an evolutionary game model between the government and cross-border e-commerce B2B export enterprises is constructed. This article also carried out experiments to verify our analysis. The simulation results show that: (1) The government’s appropriate increase in subsidies, tax incentives, infrastructure investment, talent introduction and cultivation, optimized payment system, and supervision can promote enterprises to participate in cross-border e-commerce B2B export trading; (2) excessive government supervision reduces enterprises’ enthusiasm to participate in cross-border e-commerce B2B export trading; (3) the government’s subsidies, tax incentives, and supervision strength have the greatest impact on whether enterprises participate in cross-border e-commerce B2B export trading, followed by the government’s investment in cross-border e-commerce infrastructure, the introduction and cultivation of cross-border e-commerce talents, and the improvement of the payment system. Finally, this paper puts forward relevant policy recommendations to promote the development of cross-border e-commerce B2B export enterprises.

1. Introduction

The spread of COVID-19 has dealt a heavy blow to the global economy. Against the backdrop of the global economic downturn, in order to mitigate the impact of the epidemic on China’s economic development and stabilize its economic development, the Chinese government proposed, at the meeting of the Political Bureau of the CPC Central Committee on 30 July 2020, to accelerate the formation of a new development pattern in which the domestic market plays the main role and the domestic and foreign markets promote each other. The new policies introduced under this model are called “dual cycle” policies. The “dual cycle” policy aims to make full use of domestic and foreign markets and resources to achieve sustainable development.

China’s foreign trade grew 1.9% year on year despite unprecedented challenges due to the COVID-19 pandemic. Among them, cross-border e-commerce has achieved rapid development as an emerging industry. According to statistics, China’s cross-border e-commerce import and export in 2020 reached 231.244 billion dollars, up 31.1% year on year, among which exports reached 153.25 billion dollars, up 40.1%. China’s cross-border e-commerce is mainly export, and B2B export trade is an important part of China’s cross-border e-commerce trade, accounting for 60%. Thisindicates that China’s cross-border e-commerce B2B export trade becomes an important force in stabilizing foreign trade. The rapid development of China’s cross-border e-commerce B2B export trade cannot be separated from the support of the “dual circulation” policy.

At present, the “dual circulation” policy for cross-border e-commerce is divided into “domestic circulation” and “international circulation”. The policy of “domestic circulation” is conducive to the development of domestic cross-border industrial chain and the integration of domestic and foreign industrial chains. The “international circulation” policy realizes the rapid development of China’s cross-border e-commerce through overseas investment, construction of cross-border logistics, cross-border e-commerce bases and other ways.Based on this, it is of great practical significance to study the impact of the Chinese government’s behavioral decisions on cross-border e-commerce B2B export enterprises after proposing the “dual circulation” policy.

At present, the analysis of factors affecting the development of cross-border e-commerce is mainly divided into macro and micro environmental analysis. The analysis of macro-environmental factors mainly contains the analysis of the political environment, economic environment, technical environment, etc. Usually, scholars use macro data to analyze the development of cross-border points, mainly studying the shortcomings and development prospects of the cross-border e-commerce industry in the context of contemporary social economy and policy. The typicalresults are as follows: Yang and Ge [1] elaborated on the development of cross-border e-commerce in China, and using the proportion of cross-border e-commerce in foreign trade data, explained that cross-border e-commerce would be an important part of future foreign trade. Xie [2] believed that the development of cross-border e-commerce could not be separated from advanced information technology. He also proposed to apply blockchain technology to the cross-border e-commerce industry to build a cross-border cargo tracking system.In addition, taking the OECD (Organization for Economic Co-operation and Development) countries as an example, and using the panel data from 2000 to 2018 for econometric analysis, in the long run, He et al. [3] found that there was a significant positive correlation between international logistics and cross-border e-commerce. Moreover, He et al. [4] used principal component analysis and the gravity model to analyze the cross-border e-commerce data of several Southeast Asian countries and its impact on China’s cross-border e-commerce. They thought the development of cross-border e-commerce in Southeast Asia would benefit Chinese exports. Ma et al. [5] analyzed the panel data of 31 provinces in China from 2015 to 2018 and found that cross-border e-commerce was conducive to regional economic development. Ortiz et al. [6] examined the main variables affecting the development of e-commerce in European countries from 2003 to 2017. They found that these influencing variables had the characteristics of horizontal correlation, and there was a long-term equilibrium relationship between variables. Dospinescu et al. [7] explored those factors that affected the customer satisfaction of e-commerce in Romania and Moldova and found that there were differences in the factors that affected the customer satisfaction level of e-commerce in the two countries. Li [8] analyzed the impact of China’s cross-border e-commerce on China’s economic development from multiple perspectivesand believed that the development of cross-border e-commerce could change the structure of China’s foreign trade, promote China’s industrial upgrading and stimulate the growth of international trade. Moreover, Yin et al. [9] studied China’s export trade with one belt, one road countries andtheir gravity model was used in 2000 to 2018. The results showed that the development of cross-border e-commerce had a positive impact on export trade. Du et al. [10] used the spatial subcorrelation, multidimensional gravity model and spatial Durbin model to analyze international trade and cross-border e-commerce in “One Belt and One Road” countries, and found that there was no spatial autocorrelation effect in cross-border e-commerce, so geographical distance was not an important reason for the development of cross-border e-commerce. Chen et al. [11] analyzed the text content of “dual cycle” policy to establish its influence mechanism on the B2B export industry of cross-border e-commerce, and then built a system dynamics model to quantify the influence process. The modeling process and simulation results demonstrate that: (1) Infrastructure investment of cross-border e-commerce was most affected by policy lag, followed by government supervision and enterprise operation, while talent training of cross-border e-commerce and customs supervision were rarely affected by policy lag; (2) tax policy, customs clearance policy, and fiscal policy had greater effects on the promotion of cross-border e-commerce B2B exports, while the payment policy and talent policy had less impact on them; and (3) from the simulation results of policy combination, it could be seen that the regulatory environment (i.e., regulatory policies) was the most important factorto promote cross-border e-commerce B2B export trade, followed by financial support, customs environment, and business environment. Weng et al. [12] studied the impact of Xiamen municipal government policies on small and medium-sized cross-border e-commerce enterprises during the epidemic. Based on the study of policy effects, they put forward suggestions on how the government should improve cross-border e-commerce policies.

In addition, the micro-environmental factors mainly refer to the sum of factors that are closely related to the enterprise and directly affect the marketing capability and efficiency of the enterprise, mainly including cross-border e-commerce platforms, consumers, suppliers, and the internal environment of the enterprise. At present, the relevant literature on the analysis of cross-border e-commerce micro-environmental factors is as follows: According to the three major principles of cross-border export trade, such as main business, physical transaction and data availability, Sun and Wu [13] constructed performance evaluation indicators including operating ability, solvency, profitability and growth, and used the analytic hierarchy process and grey theory to analyze several cross-border e-commerce enterprises. The research results showed thatoperational capacity and solvency have the greatest impact on the performance of cross-border e-commerce enterprises. Furthermore, Elia et al. [14] studied the impact of digital technology on cross-border e-commerce in B2C business. They found that: (1) The application of digital technology could effectively promote the export business of cross-border e-commerce enterprises; (2) the impact of digital export on cross-border e-commerce enterprises was greater than that of traditional foreign trade enterprises. Ma and Liang [15] explored the influencing factors of export performance of cross-border e-commerce enterprises. Their study found that, as the duration of enterprises increases, the exports of cross-border e-commerce enterprises on platforms would show an ‘inverted U-shaped’ trend that rises and declines. Zuo [16] studied China’s export cross-border e-commerce ecosystem from the perspective of ecological chain and analyzed the relationship between China’s export cross-border e-commerce enterprises and the environment. Under the background of China’s economic reform and upgrading, Dai and Wang [17] studied how tax policies affected the industry norms and logistics transportation of cross-border e-commerce, indicating that China’s tax policies were an important thrust in the rapid development of cross-border e-commerce. Xu [18] believed that cross-border e-commerce business was a new trade mode that traditional foreign trade enterprises must face. This trade mode changed the operation mode of enterprises, provided them with a broader market and platform, and promotes their development. Sandhu et al. [19] found that the cross-border e-commerce platform could help the digital entrepreneurship ecosystem and turn the challenges faced by digital entrepreneurship into advantages. Chen and Yang [20] analyzed the data of 203 cross-border e-commerce enterprises and found that due to the homogenization of cross-border e-commerce platforms, the size of the network did not affect customers’ cross-border consumption intention. Chen and Yang [21] studied the impact of government policies on enterprise performance and found that, as an innovative business model, the government could promote the growth of enterprise performance by supporting the development of cross-border e-commerce business. Wang et al. [22] constructed three transnational logistics models, and their simulation results showed that cross-border e-commerce B2C could adjust product prices to maximize profits by considering cross-border logistics costs, tariffs and other factors. Bao et al. [23] analyzed the influence of product quality, cost control, brand image and enterprise strength on consumers’ consumption intention by constructing the influence model of consumer product evaluation on purchase intention. Taherdoost and Madanchian [24] analyzed customer satisfaction from the aspects of product performance, availability and quality, searched for the influencing factors of these three aspects, respectively, and proposed a plan to improve consumer satisfaction according to the research results. Goldman et al. [25] studied a sample of 446 small B2C e-retailers in Europe using structural equation model and alternative model, and found that the deployment of digital marketing strategy had a positive effect on the performance of cross-border e-commerce business. Kaynak et al. [26], Gomez-Herrea et al. [27] and Valarezo et al. [28] analyzed the factors influencing the development of cross-border e-commerce in Turkey, EU and Spain, and put forward valuable suggestions for cross-border e-commerce enterprises. Furthermore, in view of the financing dilemma of green innovation of manufacturers in the e-commerce supply chain, Liu and Peng [29] built a strategy evolution game model between manufacturers and e-commerce platforms and described the dynamic evolution law of manufacturers choosing green innovation and platforms choosing green financing. Combined with numerical simulation, the factors affecting green innovation and green financing decisions were analyzed and strategic suggestions were also proposed. By introducing the theory of social co-governance into the field of e-commerce intellectual property protection, Li et al. [30] built an evolutionary game model among the government, e-commerce platforms, and rights holders, and studies the conditions under the stakeholders form a stable equilibrium state under different constraints. Combined with numerical simulation, the influences of individual factors and factor combinations on the system stability were analyzed. The results showed that strictly controlling the action costs and response costs of all parties could enhance their willingness to actively deal with infringement issues; reasonable adjustment of the reward and punishment measures of government supervisory agencies could produce sufficient reverse shock and positive guidance to platform and operators; penalties should be imposed on government supervisory agencies that were not sufficiently supervised; government hasstrengthened the construction of the social environment for intellectual property protection, platforms have improved the social benefits of actively responding to infringement issues, and rights holders have increased the sense of acquisition. Also, it provided certain positive references and suggestions for the government to formulate relevant policies.

Through the above literature analysis, although many scholars studied the cross-border e-commerce industry from both macro and micro perspectives, very few scholars studied the impact of the “dual circulation” policy on cross-border e-commerce B2B export enterprises under the background of COVID-19. Based on this, by analyzing the policy environment factors, this paper analyzes the policy text of “dual circulation” to establish the influence mechanism of cross-border e-commerce B2B export enterprises by the “dual circulation” policy, and quantitatively analyzes the future development trends of cross-border e-commerce B2B export enterprises and government behavior choices. In addition, to quantitatively study the impact of the “dual circulation” policy on the development of cross-border e-commerce B2B export enterprises, this paper analyzes a series of policies related to the “dual circulation” policy proposed by the government, uses the LDA topic classification model to classify the policies, and analyzes the topic intensity and relevance of different types of policies to build a theoretical system of their impact on cross-border e-commerce B2B export enterprises. An evolutionary game model between the government and cross-border e-commerce B2B export enterprises is established to simulate the behavioral decision-making between the government and cross-border e-commerce B2B export enterprises after the “dual circulation” policy is proposed, and to obtain the impact of different decision-making behaviors of the government on cross-border e-commerce B2B export trading. Finally, according to the evolutionary game results, suggestions are made to promote the development of cross-border e-commerce B2B export enterprises. This paper can provide a reference for governments, formulating policies to support the development of cross-border e-commerce enterprises. In addition, the paper provides a reference value for the research on the impact of the “dual circulation” policy on other industries.

The paper is organized as follows: Section 2 provides the framework of the full paper; Section 3 classifies the “dual circulation” policy texts based on the LDA topic classification model; Section 4 constructs the evolution model of B2B export enterprises and cross-border e-commerce and simulates the influence of government behavior on cross-border e-commerce B2B export enterprises; Section 5 analyzes and discusses the simulation results; and Section 6 summarizes the whole paper and puts forward some relevant policy suggestions.

2. Research Framework

First, to study the game behavior between the government and B2B exporters of cross-border e-commerce in the context of the “dual circulation” policy, this paper selects the policies related to the cross-border e-commerce industry in the “dual circulation” policy and classifies the policy texts based on the LDA topic model. In total, they can be divided into “tax policy”, “fiscal policy”, “customs clearance policy”, “payment policy” and “talent policy”. At the same time, this paper analyzes the measures that the government will adopt to support the development of cross-border B2B export enterprises through high-frequency words and lay the theoretical foundation for the subsequent establishment of the evolutionary game behavior between the government and enterprises. Then, the game relationship between the government and cross-border B2B export enterprises is analyzed, and an evolutionary game model between the government and enterprises is constructed by combining the results of the policy text analysis above. Subsequently, the game behavior between government and enterprises is explored. Finally, the model simulation results are analyzed and discussed, and relevant conclusions are drawn. The detailed research framework of this paper is shown in Figure 1.

3. Analysis of Dual Circulation Policy Based on LDA Topic Model

In this section, this paper quantitatively analyzes the policy texts of “dual circulation” and mines the characteristics of policy texts. In particular, the LDA topic model is used to construct topic analysis based on words and documents, the text mining of China’s “dual circulation” policy is carried out, the high-frequency words, topic categories, and topic intensity are analyzed, and the “dual circulation” policy is studied for the following study. In the background, government actions provide support for the development of cross-border e-commerce B2B export enterprises.

3.1. Preprocessing of Policy Text

3.1.1. Data Source

Based on the rich, timely, and authoritative content of the “Pkulaw” database, this section selects it as the searching source for“dual circulation” policy text data. In addition, to prevent the omission of policy texts, simultaneous searches are conducted in each government department on the basis of the “Pkulaw” database to integrate and supplement the policy documents. In this paper, a total of 34 “dual circulation” policy texts on cross-border e-commerce issued from February 2020 to June 2021 are selected, and the categories of official documents are shown in Figure 2.

As can be seen from Figure 2, most of the “dual circulation” policy documents related to cross-border e-commerce are issued by the State Council and the Ministry of Commerce, and a small number of policies are issued by the State Administration of Taxation and the General Administration of Customs.

3.1.2. Preprocessing Text

Preprocessing complex text in natural language processing is necessary to ensure the reliability of the experiment, which includes constructing a dictionary, separating words, and removing stop words. The text preprocessing process is as follows: First, clean the non-Chinese characters in the text, second, use the Jieba word segmentation component in Python scripting language to perform word separation, and finally, use the self-built stop word dictionary to remove the deactivated words.

(1)

Clean the non-Chinese characters

Asnon-Chinese characters will interfere with the word segmentation results, this section uses regular expressions in the Python language to clean non-Chinese characters in 34 policy texts and removes English characters, numbers, and punctuation marks.

(2)

Construct dictionary

Search all the relevant dictionaries under the social science column in the Google web dictionaries, and download and build a professional domain dictionary. In this study, the stop word dictionary of Harbin Institute of Technology is adopted, which is convenient for preliminary word segmentation of text data.

(3)

Segment word

Use the Jieba word segmentation component in the Python language to perform word segmentation, and manually correct the segmentation results. Since Jieba word segmentation is not accurate for some policy texts, this paper refers to the word segmentation of Dai Di (2019), uses the NLPIR dictionary, and uses Jieba dictionary for word segmentation.

(4)

Remove stop word

After completing the word segmentation, filter the word segmentation results to remove irrelevant words. This section builds a stop word dictionary for special terms based on the stop word dictionary of Harbin Institute of Technology and filters the word segmentation results. Figure 2 shows a part of the word segmentation results.

It can be seen from the

Table 1. Results of part of the word segmentation.

Word Segmentation Results	Word Segmentation Results	Word Segmentation Results
Market regulation	cross-border	The electronic commerce
State Food and Drug Administration	retail	import
drug	The pilot	The Ministry of Finance
The Ministry of Commerce	The General Administration of Customs	Administration of Taxation
Market regulation	Import and export	regulatory
Customs clearance	management	audited
The tax policy	tariffs	rate
The consumption tax	The tax payable	pay
The State Council	data	Infrastructure construction

that removing stop words can effectively remove irrelevant words, and the text preprocessing results are better, which can meet the model requirements.

3.2. Topic Classification Analysis Based on LDA Topic Model

3.2.1. High Frequency Vocabulary and Its Distribution in Policy Texts

To better understand the characteristics of the “dual circulation” policy text, it is necessary to acquire the high-frequency vocabulary in the policy texts to analyze basic content and the focus of policy implementation. In this paper, the policy texts are analyzed and the top 20 keywords are ranked by using the frequency of words, and the results are shown in

Table 2. High-frequency vocabulary.

Vocabulary	Frequency	Vocabulary	Frequency
E-commerce	1739	Infrastructure	558
Commerce	946	Ministry of Finance	551
Customs	932	Tariff	543
Payment	851	Consumption	536
Logistics	843	Fiscal	532
Enterprise	838	Export	529
Cross-border	791	Employment	517
Talent	752	Information	461
State Council	573	Pilot zone	438
Supervision	565	Trade	427

.

To more intuitively observe the high-frequency words in the “dual circulation” policy text, this section arranges the words in descending order and selects the first 100 words to make a word cloud graph. The results are shown in Table 2. The words with higher frequency occupy a larger font size.

As can be seen from Figure 3, the “dual circulation” policy text pays great attention to the development of domestic e-commerce, many of which are related to the development of the cross-border e-commerce industry. In addition, the policy mentions multiple departments and requires them to play the functions of each department to support the development of cross-border e-commerce enterprises and industries in various aspects, including establishing pilot zones, improving infrastructure, and solving financing problems.

3.2.2. Determine the Optimal Number of Topics

This section first uses the LDA model for topic classification to obtain a number of topics and then uses the coherence score to determine the optimal number of topics. Coherence score is an index to evaluate the relevance of subject terms under each topic generated by the LDA topic model. The larger index indicates the more relevant subject terms within the topic, the less ambiguity within the topic, and the more accurate topic classification. Mimno [31] verified that when the Coherence Score is applied for topic classification, the classification results have a strong correlation with determination. Referring to Akhtar [32] for the calculation of the coherence score, the formula for the coherence score is as follows.

$$C_{UMass}=\frac{2}{N\times (N-1)}{\displaystyle \sum _{i=2}^N{\displaystyle \sum _{j=2}^i\log \frac{P(w_i,w_j)}{P(w_j)}}}$$

(1)

where $P(w_j)$ is the ratio of the number of documents containing $w_j$ to the total number of documents; $P(w_i,w_j)$ is the ratio of the number of documents containing $w_i$ and $w_j$ to the total number of documents; and N is the number of subject words under the topic. This paper calculates the relevance of topic words in each topic according to the coherence score and then takes the mean value as the coherence score of different topics. The calculation results of the coherence score for the different number of topics here are shown in Figure 4.

From Figure 4, the coherence score is the highest when the number of topics is five, which means that the optimal number of topics for “dual circulation” policy text classification is five.

3.2.3. Determination of Topic Types

In this section, the intensities of the five topics identified above are calculated and visualized with LDAvis to clearly understand the intensity of the different topics. Topic intensity is used to measure the relative component of each topic and its calculation is referred to the literature [31], as shown in Equation (2).

$$P_k=\frac{{\displaystyle \sum _i^n{\theta }_{ki}}}{N}$$

(2)

where N represents the number of documents, ${\theta }_{ki}$ represents the probability of the k^th topic in the i^th document; and $P_k$ represents the intensity of the k^th topic. The intensity of the five topics in this section is calculated by using Formula (2), as shown in

Table 3. Topic intensity.

Topic	Intensity
Fiscal policy	0.36
Tax policy	0.2633
Customs clearance policy	0.24
Payment policy	0.093
Talent policy	0.0433

.

As can be seen from Table 3, “fiscal policy” has the highest topic intensity, followed by “tax policy,”“customs clearance policy,”“payment policy,” and “talent policy. By analyzing the specific policy documents, we can find that the policy documents on “fiscal policy” include the government’s financial subsidies for cross-border e-commerce infrastructure construction, cross-border logistics construction, overseas warehouse construction, talent training, and other aspects. For example, enterprises whose cross-border e-commerce import and export transactions reach a certain scale are given financial support. This means that “fiscal policy” can support the development of the B2B industry of cross-border e-commerce in many aspects and at a deeper level, and its policy covers most aspects, so the topic intensity of “fiscal policy” is the strongest. At the same time, there are fewer policy documents corresponding to the topic of “talent policy”, so the intensity of these two topics is weaker.

After measuring the topic intensity, this section further uses the LDAvis visualization to understand the degree of correlation between topics. LDAvis selects the feature words that represent the topics by the degree of correlation between the feature words and the topics, and the LDAvis visualization helps people understand the relationship among topics in a holistic view. Each circle represents a topic. The larger circle represents the stronger intensity. The distance between the circles indicates the degree of correlation between the topics. The closer distance represents the greater degree of correlation between the topics. Figure 5 shows the LDAvis visualization results of the topics in this paper.

From Figure 5, Topic 1 (fiscal policy) has the strongest intensity, Topic 5 (talent policy) has the least intensity, the twoof which have the highest correlation, while Topic 4 (payment policy) is the least relevant to each topic. The “fiscal policy” is to subsidize enterprises or individuals who meet the conditions of financial subsidies, and “talent policy” relies on the cultivation and introduction of talents, which requires financial subsidies and a series of fiscal preferential policies. Therefore, the topic of “fiscal policy” isthe most closely related to the topic of “talent policy”. The topic of “payment policy” is optimizing the convenience and security of cross-border payment, and its topic feature words are special, so its correlation with other topics is low.

3.3. Policy Topic Analysis

This section analyzes different policy topics based on the results of the LDA topic classification and studies what policy tools the government will use to support the development of cross-border e-commerce B2B export enterprises. In the “fiscal policy”, the government has given financial subsidies to the construction of cross-border e-commerce infrastructure, cross-border logistics, and overseas warehouse construction. In the “tax policy”, governments simplify the application procedures of preferential tax policies, innovate the retail export supervision system, introduce supervision measures for the return of cross-border e-commerce export commodities, and give income tax concessions for the small, medium, and micro cross-border e-commerce enterprises, etc., to enable cross-border e-commerce B2B export enterprises to develop better. In the “customs clearance policy”, the government mainly promotes the development of cross-border e-commerce B2B export enterprises by optimizing supervision methods and improving customs clearance efficiency. In the “payment policy”, the government continuously optimizes the convenience and security of cross-border payment to create a good payment environment for enterprises. Through the “talent policy”, the government introduces and trains industry leaders, professional and technical talents, and experienced management talents to promote the development of cross-border e-commerce models, thereby driving the development of enterprises.

To sum up, the government mainly gives financial subsidies and tax incentives, invests in cross-border e-commerce infrastructure construction, introduces and trains cross-border e-commerce talents, improves payment systems, and optimizes supervision methods to achieve cross-border e-commerce to support overseas e-commerce B2B export enterprises.

4. Evolutionary Game Model between the Government and Enterprises

In recent years, the spread of COVID-19 has takena heavy toll on China’s cross-border e-commerce industry. B2B export trading is the main body of cross-border e-commerce trade. However, cross-border e-commerce exporters face the risk of higher costs and market shrinkage. In response to this situation, the Chinese government has proposed a “dual circulation” policy to support the development of the cross-border e-commerce industry. Section 3 analyzes what policy tools the government will adopt to support the development of cross-border B2B exporters in the context of the “dual circulation” policy, and this section further examines the impact of government actions on cross-border B2B exporters. An evolutionary game model is established between the government and B2B exporters of cross-border e-commerce to reveal their dynamic evolution process.Subsequent, the MATLAB simulation is conducted to study the influence of different government behaviors on the development of cross-border e-commerce B2B exporters.

4.1. Analysis of the Game Relationship between Government and Enterprises

With the development of the Internet economy, the consumption habits of global consumers have gradually shifted from offline to online consumption. The growing scale of the cross-border e-commerce market becomes a pivotal way to boost China’s import and export trade. Against the background of the spreading COVID-19, cross-border e-commerce B2B export enterprises will face cross-border logistics stoppage, supply chain disruption, customs clearance efficiency slowdown, and other problems. Therefore, the “dual circulation” policy proposed by the government contributes to dealing with this problem. Under the “dual circulation” policy, the international logistics parks, cross-border e-commerce bases, and free trade zones established by the government provide important support for the development of cross-border e-commerce in China. At the same time, the continuous improvements of information service systems, such as cross-border trade public service platforms, cross-border payment regulations, and cross-border e-commerce infrastructure construction, promote the development of cross-border e-commerce in China.

The government should formulate a “dual circulation” policy to support the development of B2B exports of cross-border e-commerce and regulate cross-border e-commerce activities. On the one hand, it provides financial support, reduces enterprise tax rates, improves customs clearance efficiency, and improves cross-border e-commerce infrastructure to lower the cost of cross-border B2B export enterprises. On the other hand, the government should regulate enterprises, punish those that cheat on taxes and produce counterfeit products, optimize the market environment, and create a healthy development environment for enterprises.

Whether cross-border e-commerce B2B export enterprises choose to participate in export trade business under the background of COVID-19 is affected by relevant government policies and measures, and their chosen strategy also affects the government’s behavior strategy. Based on this, this section reveals the dynamic evolution process of the two based on the evolutionary game model between the government and enterprises and studies the impact of the government’s behaviors on cross-border B2B exporters based on MATLAB.

4.2. Evolutionary Game Model between Government and Enterprise

4.2.1. Basic Assumptions

According to the previous analysis of the game relationship between the government and enterprises, the following two assumptions are put forward:

Assumption 1: The subjects of the game are the government and the cross-border e-commerce B2B export enterprises, which are bounded rationality. Among them, the game behavior of the government aims to shore up the economic strength and seek industrial development, while the game behavior of the enterprise aims to improve the income of the enterprise.

Assumption 2: During the game, the two sides have different behavioral strategies. The government holds “support” and “ignore” strategy for cross-border e-commerce B2B export enterprises. The probability of choosing “support” is x, and the probability of choosing “ignore” is 1-x. The enterprise has “participate” and “not participate” choices. The probability of choosing “participate” is y, and the probability of choosing “not participate” is 1-y. According to the research of literature [32], the government’s “support” strategy is to encourage more enterprises to engage in cross-border e-commerce B2B export trading. By issuing the “tax policy”, “customs clearance policy”, “fiscal policy”, “payment policy” and “talent policy” within the “dual circulation” policy, it provides tax incentives and subsidy plans for cross-border e-commerce B2B export enterprises, reduces unnecessary superimposed tariffs, speeds up the customs clearance of goods, improves the cross-border payment system, and meets the talents needs of cross-border e-commerce enterprises. At the same time, it takes regulatory measures against enterprises’ fraudulent subsidies, tax evasion, and sales of fake and shoddy products, to provide a sound environment for enterprises and attract more enterprises to participate in cross-border e-commerce B2B export trading. The government’s “ignore” strategy means that it does not take incentives or interventions for enterprises to engage in cross-border e-commerce B2B export trading.

4.2.2. Parameter Setting

The relevant parameters and definition are shown in

Table 4. Basic parameter assumption.

Parameter	Definition
$A$	Financial subsidies to enterprise given by government
$a$	subsidy coefficient
$B$	Government’s tax incentive to enterprise
$b$	Tax incentive coefficient
$C$	Government’s investment in cross-border e-commerce infrastructure
$D$	Government’s investment in talent introduction and cultivation
$W$	Government’s investment in optimizing the payment system
$M$	Government’s punishment for enterprises that engage in fraud, tax evasion, and sales of counterfeit and shoddy products
$m$	Government’s supervision intensity
$E_1$	Enterprise’s additional benefits by government’s regulation
$C_1$	Cost when the government chooses “ignore” strategy
$E_2$	the income obtained by the enterprise relying on the original business method
$E_3$	Enterprise’s benefits when enterprise participate in the cross-border e-commerce B2B export trading trade
$E_4$	Government’s benefit from participating in the cross-border e-commerce B2B export trading
$C_2$	The cost of the enterprise participating in the cross-border e-commerce B2B export trading
$C_3$	opportunity cost for not participating in cross-border B2B export

.

When the government chooses the “support” strategy, it will support enterprises to participate in cross-border e-commerce B2B export trading. Suppose the government gives enterprises certain financial subsidies $A$. If the government subsidy coefficient is $a$, enterprises receive tax incentives $A\times a$. Suppose the government offers tax incentive $B$. If the tax incentive coefficient is b, enterprises receive tax incentive $B\times b$. The government’s investment in cross-border e-commerce infrastructure is C. The investment in talent introduction and cultivation is D. The investment in optimizing the payment system is W. The punishment for enterprises that engage in fraud, tax evasion, and sales of counterfeit and shoddy products is M. If the supervision intensity is m, the enterprise’s loss is $M\times m$. However, through optimizing the market environment, regulating industry order, and providing a sound development environment conducted by the government, enterprises can obtain additional benefits $E_1$. When the government chooses “ignore” strategy, it does not take interventions or incentives for enterprises to participate in cross-border e-commerce B2B export trading. It will cause certain social losses C₁, such as the chaos of the cross-border e-commerce B2B export industry and the decline of its international status.

When the enterprise chooses “not participate”, the income obtained by the enterprise relying on the original business method is $E_2$. The opportunity cost for not participating in cross-border B2B export is $C_3$, including seizing its own market share due to other companies participating in cross-border e-commerce B2B export trading. The benefits when enterprise participate in the cross-border e-commerce B2B export trading trade are $E_3$, including the increase of the enterprise’s influence, which in turn promotes an increase in operating income, etc. The government’s benefit from participating in the cross-border e-commerce B2B export trading is $E_4$, for example, promoting the transformation and upgrading of China’s foreign trade and driving the development of other industries in the supply chain. The cost of the enterprise participating in the cross-border e-commerce B2B export trading is $C_2$, such as labor costs and publicity costs.

4.2.3. Game Model Result

From the above analysis, the payment matrix of the government and enterprises is obtained, and the results are shown in

Table 5. Payoff matrix of the evolutionary game between the government and enterprises.

Objects		Enterprise
		Participate (y)	not Participate (1 − y)
government	support	$E_4-A\times a-B\times b-C-D-W+M\times m$	$-C-D-W$
	($x$)	$E_2+A\times a+B\times b+E_1+E_3-M\times m-C_2$	$E_2-C_3$
	ignore	$E_4-C_1$	$-C_1$
	($1-x$)	$E_2+E_3-C_2$	$E_2-C_3$

.

According to the payoff matrix of the evolutionary game between the government and enterprises in Table 5, we get:

(1)

Expected benefits of the government’s choice of “support” strategy U₁₁

$$U_{11}=y(E_4-A\times a-B\times b+M\times m)-(C+D+W)$$

(3)

Expected benefits of the government’s choice of “ignore” strategy $U_{12}$

$$U_{12}=y{E}_4-C_1$$

(4)

Average expected benefit of government strategy $\overline{U_1}$

$$\overline{U_1}=xy(M\times m-A\times a-B\times b)-x(C+D+W-C_1)+y{E}_4-C_1$$

(5)

According to the principle of the dynamic equation, the replication dynamic equation corresponding to the government’s choice of “support” strategy is:

$$\begin{array}{cc}\hfill F(x)& =\frac{dx}{dt}=x(U_{11}-\overline{U_1})\hfill \\ & =x(1-x)[y(M\times m-A\times a-B\times b)-(C+D+W)+C_1]\hfill \end{array}$$

(6)

(2)

Expected benefits of the enterprise’s choice of “participate” strategy $U_{21}$

$$U_{21}=x(A\times a+B\times b+E_1-M\times m)+(E_2+E_3-C_2)$$

(7)

(3)

Expected benefits of the enterprise’s choice of “not participate” strategy $U_{22}$

$$U_{22}=E_2-C_3$$

(8)

Average expected benefit of enterprise strategies $\overline{U_2}$

$$\overline{U_2}=y{U}_{21}+(1-y)U_{22}$$

(9)

According to the principle of the dynamic equation, the replication dynamic equation corresponding to the enterprise’s choice of “participate” strategy is:

$$\begin{array}{cc}\hfill F(y)& =\frac{dy}{dt}=y(U_{21}-\overline{U_2})\hfill \\ & =y(1-y)[x(A\times a+B\times b+E_1-M\times m)+E_3+C_3-C_2]\hfill \end{array}$$

(10)

4.2.4. Equilibrium Point Results

(1)

Equilibrium point results

According to the above system and joint replication dynamic equation, making $F(x)=0$ and $F(y)=0$, five equilibrium points (0,0), (1,0), (0,1), (1,1), ($x^{*}=\frac{C_2-C_3-E_3}{A\times a+B\times b+E_1-M\times m}$,$y^{\ast }=\frac{C+D+W-C_1}{M\times m-A\times a-B\times b}$) can be obtained.

(2)

Jacobian Matrix Analysis

The equilibrium point derived by replicating the dynamic equations needs to be determined by the stability determination rule of the Jacobi matrix to be considered as an evolutionary stable strategy (ESS) of the system. When the partial equilibrium point satisfies both the following two conditions:

$$Det(J)=\left|\begin{array}{cc}{a}_{11}& a_{12}\\ a_{21}& a_{22}\end{array}\right|=a_{11}{a}_{22}-a_{12}{a}_{21}>0$$

(11)

$$Tr(J)=a_{11}+a_{22}<0$$

(12)

This equilibrium point is an evolutionary stable strategy (ESS) of the system, otherwise, it is an unstable or the saddle point of the system.

The Jacobi matrix of the above system is

$$J=\left[\begin{array}{cc}{a}_{11}& a_{12}\\ a_{21}& a_{22}\end{array}\right]=\left[\begin{array}{cc}F{(x)}_x& F{(x)}_y\\ F{(y)}_x& F{(y)}_y\end{array}\right]$$

(13)

$$F{(x)}_x=(1-2x)[y(M\times m-A\times a-B\times b)-(C+D+W)+C_1]$$

(14)

$$F{(x)}_y=x(1-x)(M\times m-A\times a-B\times b)$$

(15)

$$F{(y)}_x=y(1-y)(A\times a+B\times b+E_1-M\times m)$$

(16)

$$F{(y)}_y=(1-2y)[x(A\times a+B\times b+E_1-M\times m)+E_3-C_2+C_3]$$

(17)

The values and traces of the determinant of the Jacobi matrix for the five partial equilibrium points are calculated and solved to obtain the results shown in

Table 6. Jacobian matrix results.

Partial Equilibrium Points	$\mathit{T}\mathit{r}(\mathit{J})<0$	$\mathit{D}\mathit{e}\mathit{t}(\mathit{J})>0$
(0,0)	$C_1-C-C_2+C_3-D+E_3-W$	$-(C_3-C_2+E_3)\times (C-C_1+D+W)$
(1,0)	$\begin{array}{c}C-C_1+D+W-C_2+C_3\\ +E_1+E_3+A\times a+B\times b-M\times m\end{array}$	$\begin{array}{c}(C-C_1+D+W)\times (C_3-C_2+E_1+E_3\\ +A\times a+B\times b-M\times m)\end{array}$
(0,1)	$\begin{array}{c}{C}_1-C+C_2-C_3-D-E_3-\\ W-A\times a-B\times b+M\times m\end{array}$	$\begin{array}{c}(C_3-C_2+E_3)\times (C-C_1+D+\\ W+A\times a+B\times b-M\times m)\end{array}$
(1,1)	$C-C_1+C_2-C_3+D-E_1-E_3+W$	$\begin{array}{c}-(C_3-C_2+E_1+E_3+A\times a+B\times b-M\times m)\\ \times (C-C_1+D+W+A\times a+B\times b-M\times m)\end{array}$
($x^{\ast }$, $y^{\ast }$)	0	$\frac{\alpha }{\beta }$

.

α and β are calculated as follows:

$$\begin{array}{c}\alpha =(C_3-C_2+E_3)\times (C-C_1+D+W)\times (C_3-C_2+E_1+E_3+A\times a+B\times b-M\times m)\times \\ (C-C_1+D+W+A\times a+B\times b-M\times m)\end{array}$$

$$\beta =(A\times a+B\times b-M\times m)\times (E_1+A\times a+B\times b-M\times m)$$

4.2.5. Evolutionary Stability Strategy Analysis

When the partial equilibrium point satisfies $Tr(J)$ < 0 and $Det(J)$ > 0, the system will be in a stable state. Combined with the above Jacobi matrix, the stability analysis of the equilibrium point is performed.

(1) When the partial equilibrium point (0,0) satisfies $Det(J)$ > 0,it means $C_3$−$C_2$+$E_3$ < 0 and −$C$+$C_1$−$D$− W < 0, at this time $Tr(J)$ < 0, so (0,0) is a stable point. At this moment, the government will finally choose the “ignore” strategy when the cost of supporting enterprises to participate in cross-border e-commerce B2B export trading is greater than the social loss they pay when they choose to ignore. Therefore, the government will choose the “ignore” strategy. While the benefits of participating in cross-border e-commerce B2B export trading are lower than participation costs, enterprises will eventually give up their participation.

(2) When the partial equilibrium point (1,0) satisfies $Det(J)$ > 0, it means $C$−$C_1$+$D$+$W$ < 0 and $-C_2$+$C_3$+$E_1$+$Aa$+$Bb$−$Mm$ < 0, at this time $Tr(J)$ > 0, so (1,0) is an unstable point. When the government chooses the “ignore” strategy, the social loss caused by it is greater than the investment of the “support” strategy. Therefore, the government will support enterprises participating in cross-border e-commerce. However, while the cost of participating in cross-border e-commerce and the risks they face are greater than their income, enterprises will decline enthusiasm and choose not to participate in cross-border e-commerce B2B export trading.

(3) When the partial equilibrium point (0,1) satisfies $Det(J)$ > 0, it means $C_3$−$C_2$+$E_3$ > 0 and $C$−$C_1$+$D$+ $W$+$Aa$+$Bb$−$Mm$ > 0, at this time $Tr(J)$ < 0, at this moment < 0, so (0,1) is a stable point. When the government chooses the “support” strategy, the financial subsidies, tax incentives, investment in infrastructure, and efforts in the introduction and cultivation of talents to enterprises are higher than the benefits that the enterprise can obtain from enterprises participating in the cross-border e-commerce B2B export trading, the government cost will be greater than the social loss of adopting the “ignore” strategy, and the government will choose the “ignore” strategy. The opportunity cost paid by the enterprise for not participating in the cross-border e-commerce B2B export trading and the benefits obtained by participating in this business are combined. When the sum is greater than its participation cost, it means that the company can obtain more profits by participating in the cross-border e-commerce B2B export trading, so the company will choose the “participate” strategy.

(4) When the partial equilibrium point (1,1) satisfies $Det(J)$ > 0 and $Tr(J)$ < 0, it means $C$−$C_1$+$D$+$W$+$Aa$+$Bb$−$Mm$ < 0, $C_3$−$C_2$+$E_1$+$E_3$+$Aa$+$Bb$–$Mm$ > 0.When an enterprise chooses to participate in the cross-border e-commerce B2B export trading, the income that the enterprise can obtain from the government’s “support” strategy is greater than its income that does not participate, and the enthusiasm for participation will increase and eventually choose e-commerce B2B export trading. The social returns that the government can obtain through the cross-border e-commerce B2B export trading are greater than the costs invested by the “support” strategy, and it will eventually choose the “support” strategy.

4.3. Simulation of the Evolutionary Game Model between Government and Enterprises

In this section, MATLAB is used to simulate the above game model, and variables such as the government’s subsidy coefficient, tax incentive coefficient, investment in the construction of cross-border e-commerce infrastructure, the cost of introducing and cultivating cross-border e-commerce talents, the investment in improving the payment system and the government’s supervision are also adjusted to observe the dynamic evolution process of government and enterprises. Finally, corresponding conclusions are drawn on this basis.

4.3.1. Evolutionary Stability Simulation Analysis

MATLAB software is used to verify the correctness of the evolutionary paths and results of the above scenarios utilizing numerical simulations, and to provide a reference for the subsequent analysis of government behavior.

(1)

Simulation of partial equilibrium point (0,0)

When $C_3$ − $C_2$ + $E_3$ < 0 and −$C$ + $C_1$ − $D$ − W < 0, assuming that $A$= 2.8, $a$= 0.5, $B$ = 3.9, $b$ = 0.5, $C$ = 2.4, $D$ = 2.6, $W$ = 1.5, $M$ = 1.5, $m$ = 0.53, $E_1$ = 0.42, $E_2$ = 0.61, $E_3$ = 0.55, $E_4$ = 2, $C_1$ = 1, $C_2$ = 2, $C_3$ = 1 are met, the initial values of the government and enterprise strategy choice are set to (0.5,0.5), and the simulation results are shown in Figure 6.

According to the simulation results, the system converges to the point (0,0) in this case, which is consistent with the above analysis of the evolutionary stabilization strategy. Because when the government chooses the “support” strategy, the investment is greater than the social loss caused by adopting the “ignore” strategy, the government will give up the “support” strategy and no longer care about whether enterprises choose to participate in B2B export trading of cross-border e-commerce or not. When the government chooses the “ignore” strategy, the cost of participation will be greater than the benefit, and the enterprises will give up participating in the business, and the final evolutionary stabilization strategy of the government and enterprises is (ignore, not participate).

(2)

Simulation of partial equilibrium point (0,1)

When $C$ − $C_1$ + $D$ + $W$ < 0 and $-C_2$ + $C_3$ + $E_1$ + $A\times a$ + $B\times b$ − $M\times m$ < 0, assuming that $A$ = 2.8, $a$ = 0.5, $B$ = 3.9, $b$ = 0.5, $C$ = 2.4, $D$ = 2.6, $W$ = 1.3, $M$ = 3.5, $m$ = 0.53, $E_1$ = 0.42, $E_2$ = 0.61, $E_3$ = 0.55, $E_4$ = 2, $C_1$ = 6.7, $C_2$ = 3.5, $C_3$ = 1 are met, the initial values of the government and enterprise strategy choice are set to (0.5,0.5), and the simulation results are shown in Figure 7.

According to the simulation results, in this case, the system converges to point (0,1), which is consistent with the above-mentioned evolutionary stability strategy analysis. When the investment in supporting enterprises to participate in cross-border e-commerce B2B export trading is less than the social loss caused by adopting the “ignore” strategy, the government will continue to choose the “support” strategy. Whileenterprises can obtain government support, the cost of their participation is still too high. Therefore, they are less enthusiastic about the participation and will finally, give up participating in the business. At this time, the evolutionary stabilization strategy of the government and enterprises is (support, not participate).

(3)

Simulation of partial equilibrium point (1,0)

$C_3$ − $C_2$ + $E_3$ > 0 and $C$ − $C_1$ + $D$ + $W$ + $A\times a$ + $B\times b$ − $M\times m$ > 0, assuming that $A$ = 2.8, $a$ = 0.5, $B$ = 3.9, $b$ = 0.5, $C$ = 2.4, $D$ = 2.6, $W$ = 1.3, $M$ = 3.5, $m$ = 0.53, $E_1$ = 0.42, $E_2$ = 0.61, $E_3$ = 2.55, $E_4$ = 2, $C_1$ = 6.7, $C_2$ = 3.5, $C_3$=2 are met, the initial values of the government and enterprise strategy choice are set to (0.5,0.5), and the simulation results are shown in Figure 8.

It can be seen from the simulation results that the system converges to point (0,1) in this case, which is consistent with the analysis of the above evolutionary stability strategy. As the result of the theoretical analysis in the previous section, although the government adopts the “ignore” strategy and does not take intervention or incentive measures on whether enterprises participate in the cross-border e-commerce B2B export trading or not, due to the rapid development of cross-border e-commerce B2B exports, enterprises participating in this business can get the greater benefit, so they will eventually participate. At this time, the evolutionary trend strategy of government and enterprises is (ignore, participate).

(4)

Simulation of partial equilibrium point (1,1)

$C$ − $C_1$ + $D$+$W$ + $A\times a$ + $B\times b$ − $M\times m$ < 0,$C_3$ − $C_2$ + $E_1$ + $E_3$ + $A\times a$ + $B\times b$ − $M\times m$ > 0, assuming that $A$ = 2.8, $a$ = 0.5, $B$ = 3.9, $b$ = 0.5, $C$ = 2.4, $D$=1.6, $W$ = 1.3, $M$ = 3.5, $m$ = 0.53, $E_1$ = 0.42, $E_2$ = 0.61, $E_3$ = 2.55, $E_4$ = 2, $C_1$ = 8.7, $C_2$ = 3.5, $C_3$=2 are met, the initial values of the government and enterprise strategy choice are set to (0.5,0.5), and the simulation results are shown in Figure 9.

It can be seen from the simulation results that the system converges to the point (1,1) in this case, which is consistent with the analysis of the above evolutionary stability strategy. The benefit of choosing the “support” strategy is higher than the “ignore” strategy, so the government will choose the “support” strategy. The benefit of the “participate” strategy is higher than the “not participate” strategy, so the enterprises will choose to participate. At this time, the evolutionary stabilization strategy of the government and enterprises is (support, participate).

4.3.2. Analysis on Government and Enterprise Behavior

This section uses the MATLAB numerical simulation method to analyze the impacts of government subsidies, tax incentives, government investment in cross-border e-commerce infrastructure construction, efforts to introduce and cultivate cross-border e-commerce talents, improve payment systems, and supervision intensity on enterprise strategies. The relevant parameters in the model are set as follows: A = 2.8, a = 0.5, B = 3.9, b = 0.5, C = 2.4, D = 1.6, W = 1.5, M = 3.5, m = 0.4, E₁ = 0.42, E₂ = 0.61, E₃ = 0.55, E₄ = 2, C₁ = 8.7, C₂ = 3.5, C₃ = 2. Before themodel isadopted, the initial probabilities that the government chooses to support and the probability that enterprises choose to participate in the cross-border e-commerce B2B export trading are both assumed to be 0.5.

(1)

Intensity of subsidies

Government subsidy means the financial subsidies to enterprises engaged in cross-border e-commerce B2B export trading for reducing operating costs. By changing the intensity of subsidies, the impact of subsidies on the willingness of enterprises to participate in cross-border e-commerce B2B export trading is simulated. The subsidy intensity is set to 0.3, 0.5, and 0.7, respectively. The larger the value is, the larger the government subsidy amount and the wider the subsidy range will be. The corresponding evolutionary game results are shown in Figure 10.

From the simulation results, it can be known that by increasing the subsidy, the government can stimulate the enterprises to a certain extent and increase their willingness to participate in the cross-border e-commerce B2B export trading. When the government subsidy is 0.3, the operation cost is high due to the insufficient government subsidy, which makes enterprises choose not to participate. When the government subsidy is 0.5 and 0.7, the government can stimulate enterprises through subsidy. Enterprises can make profits by participating in cross-border e-commerce B2B export trading, so finally choose to participate. At the same time, in the early stage of enterprises participating in cross-border e-commerce B2B export trading, the incentive effect of government subsidies on enterprises is relatively high. However, when the cross-border e-commerce B2B export trade market develops rapidly, the incentive effect of government subsidies on enterprises will be weakened. This is because participation will also be affected by factors such as market environment and industry prospects. When an enterprise can make profits by participating in the business, the incentive effect of government subsidies on the business will be diminished.

(2)

Intensity of tax incentives

Tax incentives refer to preferential tax policies to reduce the amount of tax paid by enterprises and the operating costs of enterprises. Here, by changing the intensity of government tax incentives, the impact of tax incentive on the willingness of enterprises to participate in cross-border e-commerce B2B export trading is simulated. The government tax incentive intensity is set to 0.3, 0.5, and 0.7, respectively. The larger the value is, the larger the coverage of the government’s tax incentive policies and the lower the partial tax rate levied on enterprises will be. The corresponding evolutionary game model results are shown in Figure 11.

From the simulation results, it can be seen that changing the intensity of tax incentives can positively impact enterprises’ willingness to participate in cross-border e-commerce B2B export trading so that the probability of enterprises participating in cross-border e-commerce B2B export trading is accelerated. When the tax incentive intensity increases from 0.3 to 0.5, the probability curve of enterprises’ evolution toward participating in the business changes more obviously. When the tax incentive intensity increases from 0.5 to 0.7, the probability of enterprises’ evolution toward participating in the business slows down.

(3)

Intensity of investment

The impact of government investment in cross-border e-commerce infrastructure construction on the willingness of enterprises to participate in cross-border e-commerce B2B export trading is simulated. The investments are set to 0.96, 2.4, and 3.84, respectively. Under this setting, the larger values imply that the government pays more importance to the construction of cross-border e-commerce infrastructure, i.e., the larger the investment amount results in faster construction speed, including improving the construction of logistics facilities, accelerating the planning and construction of cross-border parks, port areas, transportation, and security information infrastructure. The corresponding evolutionary game results are shown in Figure 12.

From the simulation results, it can be seen that, when the government’s investment in cross-border e-commerce infrastructure gradually increases, it can improve the enthusiasm of enterprises to participate in cross-border e-commerce B2B export trading and make them evolve toward participation faster. In contrast, when the government’s investment in cross-border e-commerce infrastructure increases from 2.4 to 3.84, the promotion effect of cross-border e-commerce infrastructure investment on enterprises’ choice of cross-border e-commerce B2B export trading changes insignificantly. This is because initially, enterprises increased their enthusiasm for participation due to the government’s large investment in cross-border e-commerce infrastructure, however, under the premise of limited financial resources, the government is unable to give reasonable support to enterprises in terms of financial subsidies and tax incentives, which will slow down its evolution toward participation, so the government’s investment in cross-border e-commerce infrastructure should be kept within a reasonable range.

(4)

Efforts to introduce and cultivate cross-border e-commerce talent

This section measures the government’s efforts to introduce and cultivate cross-border e-commerce talent by varying the investment in the introduction and cultivation of cross-border e-commerce talent. By changing the investment, the impact of efforts to introduce and cultivate cross-border e-commerce talents on the willingness of enterprises to participate in cross-border e-commerce B2B export trading is simulated. The government’s efforts to introduce and cultivate cross-border e-commerce talents are set to 0.96, 1.6, and 2.24, respectively. Under this setting, the larger values indicate that government can provide more industry leaders, professional and technical talents, and experienced management talents for enterprises to engage in cross-border e-commerce B2B export trading, promoting cross-border e-commerce B2B export trade business development. The corresponding evolutionary game results are shown in Figure 13.

It can be seen from the simulation results that when the government’s efforts to introduce and cultivate cross-border e-commerce talents increase from 0.96 to 2.24, although the evolution of participation accelerates, the effect is not obvious. The reason is that the goal of introducing and cultivating cross-border e-commerce talent is to enable enterprises involved in cross-border e-commerce B2B export trading to develop better, but for other enterprises, the number of talents has no impact on their decision for choosing participation. Based on this, the government’s efforts to introduce and cultivate cross-border e-commerce talents should be kept within a reasonable range.

(5)

Intensity of improving the payment system

By changing the intensity of improving the payment system, the impact on the willingness of enterprises to participate in cross-border e-commerce B2B export trading is simulated. Our simulation sets the government’s intensity to 0.9, 1.5, and 2.1, respectively. The larger value implies that the government will optimize the convenience and security of cross-border payments promptly, thus improving the security of cross-border transactions and reducing the cost of cross-border online shopping. An optimized payment system can expand the scale of cross-border online shopping, which is ultimately beneficial for enterprises to participate in cross-border e-commerce B2B export trading. The corresponding evolutionary game results are shown in Figure 14.

From the simulation results, it can be seen that the impact of changing the government’s efforts to improve the payment system and the introduction and cultivation of cross-border e-commerce talents on the willingness of enterprises to participate in cross-border e-commerce B2B export trading is relatively similar. When the government’s efforts to improve the payment system increase from 0.9 to 2.1, the evolution of enterprises to participate in cross-border e-commerce B2B export trading accelerates, but the promotion effect is not obvious. The reason is that although improving the cross-border payment system can improve the convenience and security of cross-border payments, most companies’ cross-border payments are made through online bank transfers, which are relatively convenient and safe. Due to the nature of cross-border e-commerce B2B export trading, enterprises do not consider high-frequency small cash transactions, so the existing payment system is sufficient to meet their daily cross-border transaction needs. Therefore, the decision of participating in cross-border e-commerce B2B export trading does not depend on whether the payment system is perfect or not. A decade ago, even though the payment system for domestic transactions was not perfect, the profitability of participating in foreign trade business led to the emergence of a large number of foreign trade enterprises in China.

(6)

Intensity of government supervision

By changing the intensity of government supervision, we simulate its impact on the willingness of enterprises to participate in cross-border e-commerce B2B export trading. Set the supervision intensity to 0.4, 0.6, and 0.8, respectively. The larger value indicates the stricter supervision. When the enterprise engages in illegal operations, sells counterfeit and shoddy products, and participates in other illegal activities, the government will impose higher penalties on the enterprise. Punishment is enforced to purify the market environment. The corresponding evolutionary game results are shown in Figure 15.

From the simulation results, it can be seen that, when the supervision intensity is increased from 0.4 to 0.6, the government intensifies the supervision of enterprises’ fraudulent subsidies, tax evasion, sales of fake and shoddy products, and other behaviors, which effectively regulates the market order of cross-border e-commerce B2B export trade, creates healthy development environment for enterprises participating in cross-border e-commerce B2B export trading. Therefore, intensifying supervision can push enterprises to participate in cross-border e-commerce B2B export trading. When the supervision intensity increases from 0.6 to 0.8, the government’s supervision intensity is further enhanced. Whileit can more effectively supervise enterprises, due to its excessive supervision, the government will invest more manpower and material resources in supervision, which leads to limited support in financial subsidies, cross-border e-commerce infrastructure construction, improvement of payment systems, and introduction and cultivation of cross-border e-commerce talents. It eventually makes enterprises not participate in cross-border e-commerce B2B export trading. Based on this, the government’s appropriate increase in supervision will promote enterprises to participate in cross-border e-commerce B2B export trading, but excessive supervision will make enterprises not participate in the end.

5. Analysis and Discussion

This section further discusses the analysis of the simulation results and the limitations of the study.

5.1. Simulation Result

Based on the above simulation results, the following conclusions can be drawn:

(1) The influence intensity of “fiscal policy”, “taxation policy” and “customs clearance policy” is high, while the influence intensity of “payment policy” and “talent policy” is low.

(2) The topic correlation between “fiscal policy” and “talent policy” is the largest, and the correlation between “payment policy” and other policies is the lowest.

(3) Once the government appropriately increases subsidies, tax incentives, investment in cross-border e-commerce infrastructure construction, talent introduction and training, improvement of payment systems, and supervision, these actions can promote enterprises to participate in cross-border e-commerce B2B export trading.

(4) Government subsidies, tax incentives, and supervision have the greatest impact on whether enterprises participate in cross-border e-commerce B2B export trading, followed by government investment in cross-border e-commerce infrastructure, introduction and cultivation of cross-border e-commerce talents, and improvement of the payment system.

(5) The government’s appropriate increase in supervision will help promote enterprises to participate in cross-border e-commerce B2B export trading, while excessive supervision will occupy too much manpower and material resources of the government, which may be unable to give support in financial subsidies or cross-border e-commerce infrastructure construction, finallyreducing the enthusiasm of enterprises.

5.2. Limitations

There are still the following limitations in this paper that need further research:

(1) This paper only studies the evolutionary game relationship between the government and cross-border e-commerce B2B export enterprises under the background of the “dual circulation” policy. In the follow-up research, the game relationship between enterprises and the government in the remaining sub-sectors of the cross-border e-commerce industry, such as the impact of government actions on the cross-border e-commerce retail export industry, can be further explored.

(2) While considering the impact of government behavior on corporate behavior, the influence of upstream suppliers and downstream consumers of cross-border e-commerce B2B export enterprises on the decision-making behavior of enterprises is not considered, which can be further discussed in the future?

6. Conclusions

This paper uses the LDA topic classification model [33] to classify the “dual circulation” policy documents, which are divided into five types and sorted in descending order of topic intensity: Fiscal policy, taxation policy, customs clearance policy, payment policy, and talent policies. These five types can promote enterprises to participate in cross-border e-commerce through government financial subsidies, investment in cross-border e-commerce infrastructure construction, introduction and cultivation of cross-border e-commerce talents, and improvement of payment systems. Then, an evolutionary game model [34] between the government and enterprises is constructed, and MATLAB is used for simulation analysis.

Compared tothe existing literature, this paper has the following innovations, which are as follows:

(1) When current scholars study the impact of the “dual circulation” policy on cross-border e-commerce, they do not further consider the impact of the “dual circulation” policy on cross-border e-commerce B2B export enterprises, and most of them analyze the effect by constructing the statistical indicators system based on macroeconomic indicators. By quantifying and classifying the “dual circulation” policy texts, measuring and analyzing the topic intensity of different types of policies, this paper determines the impact process of the “dual circulation” policy on cross-border e-commerce B2B export enterprises, and finally establishes the relationship between the government and enterprises. The evolutionary game model in the experiments simulates the impact of the different decision-making behaviors of the government on the cross-border e-commerce B2B export enterprises under the background of the “dual circulation” policy.

(2) Compared toother studies, this paper specifically analyzes the types and implementation process of the “dual circulation” policy and quantifies the government’s supportive behavior, which can more intuitively analyze the impact of the government’s supportive behavior on enterprises. Its quantitative analysis process can provide a reference for future research on the impact of the “dual circulation” policy on companies in other industries.

In addition, based on the above simulation results, this paper puts forward policy suggestions to promote the development of cross-border e-commerce B2B export enterprises as follows:

(1)

Implement fiscal policies to promote trade growth

From the simulation results of government and enterprise behavior analysis, it can be seen that the government’s financial subsidies can significantly promote enterprises to participate in cross-border e-commerce B2B export trading. Therefore, the Chinese government needs to keep increasing financial subsidies to step up the development of cross-border e-commerce B2B export trade. In terms of policy structure, the government should adjust the expenditure structure, actively raise funds, intensify special financial support for cross-border e-commerce B2B export enterprises, and promote the development of cross-border e-commerce B2B export industry clusters to stimulate the development of cross-border e-commerce B2B export enterprises.

(2)

Improving the social service environment

From the above evolutionary game simulation results, it can be seen that the government can optimize the social service environment by intensifying investment in cross-border e-commerce infrastructure construction, introducing and cultivating cross-border e-commerce talents, and improving the payment system, thereby creating a beneficial business environment for enterprises. Through the above three measures, the government can accelerate the logistics and transportation of cross-border e-commerce, effectively promote the growth of cross-border e-commerce practitioners and the improvement of related talent reserves, and improve the security of cross-border payments, to eliminate possible development bottlenecks that the cross-border e-commerce B2B export enterprises may confront in the future. Therefore, the government should pay attention to the social service environment, strengthen the construction of cross-border e-commerce industrial parks, improve the infrastructure of cross-border logistics, reduce logistics costs, optimize the cross-border payment system, and focus on the training of professional application-oriented talents for cross-border e-commerce in China, to lay a solid foundation and create a sound environment for the long-term development of e-commerce B2B export in China.

(3)

Optimize supervision measures

The government’s optimization of the regulatory measures for the cross-border e-commerce B2B industry can effectively improve the cross-border e-commerce market environment. A good market environment will help improve the enthusiasm of cross-border e-commerce B2B exporters and facilitate the development of enterprises [35]. The government should further determine the access standards for cross-border e-commerce B2B export trade, appropriately raise its access threshold, and optimize the market service environment. The quality inspection department should strictly control the quality inspection of circulating goods, and strictly crack down on the production and sale of counterfeit goods. The government should improve and complete the corporate credit system in a timely manner to avoid the disclosure of consumers’ information and other violations of consumers’ rights. In addition, the government can innovate the supervision mode of cross-border e-commerce, use advanced information technology to electronically monitor cross-border e-commerce commodities, and record enterprises and commodities to achieve efficient supervision.