# Tripartite Evolutionary Game Analysis of Shared Manufacturing by Manufacturing Companies under Government Regulation Mechanism

Authors: Peng Liu; Xiaoling Wei; Caiyun Liu
Journal: Discrete Dynamics in Nature and Society
 (2022)

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## Abstract

In order to study the decision-making behavior of the participating groups in shared manufacturing, this paper constructs a tripartite evolutionary game model of shared manufacturing by manufacturing companies under government regulation mechanism. Using evolutionary game theory, it is to analyze the evolutionary stable strategy (ESS) of the model. The utilization efficiency of government regulatory input and the influence of government nonregulation in the proportion of regulatory income are discussed. MATLAB numerical simulation is used to analyze the influence of different parameter changes on the evolution result. It is concluded that the initial sharing probability of manufacturing companies, the level of trust in the company, the government’s penalties for nonsharing parties, the utilization efficiency of government inputs and the rewards given to the government by the state all play a positive role in promoting shared manufacturing and government regulation of manufacturing companies. The lower the ratio of government nonregulation to the income of regulation is, the more active government regulation is. In addition, the shared income should be distributed reasonably. Therefore, in the shared manufacturing process, all the above factors should be considered.


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## Body

## 1. Introduction

With the rapid development of information technology, the sharing economy is deeply rooted in the hearts of the people. As a new model, the sharing economy provides a new direction for the transformation and development of traditional manufacturing. The development of shared manufacturing is an important measure to realize the optimal allocation of resources and improve the efficiency of resource utilization. The development of shared manufacturing can not only deal with the order imbalance problem of large companies in the off-peak season but also help small companies improve production efficiency and maximize profitability. Therefore, in the process of manufacturing companies participating in shared manufacturing, it is particularly important to study the relevant factors that affect the sharing parties’ participation in the sharing and how they affect the sharing parties.The concept of “shared manufacturing” was first proposed by Ellen [1] in 1990. With the continuous application of the shared manufacturing mode, He et al. [2] provided some reasons for the slow development of shared manufacturing in China. The concept, research status, and significance of shared manufacturing were introduced. Finally, the methods to improve the efficiency of shared manufacturing were presented, which help understand the shared manufacturing in the manufacturing industry in China currently. Jiang and Li [3] addressed a new factory model–shared factory and provided a theoretical architecture and some actual cases for manufacturing sharing. Yu et al. [4] proposed a dynamic Shared Manufacturing Service scheduling method in support of the technologies of Complex Network Analysis. Finally, an experiment for evaluating the efficiency of service matching was carried out to prove that Shared Manufacturing can provide better performance than Cloud Manufacturing and Social Manufacturing. Yu et al. [5] proposed the Blockchain-based Shared Manufacturing framework in support of the application of Cyber Physical Systems. The Blockchain-based Shared Manufacturing framework complementarily combined the blockchain and shared manufacturing, beneficial to promote both modes. Li and Jiang [6] proposed a brand-new Enhanced Self-organizing Agent in a sustainable shared factory, which helps the shared manufacturing resources realize cross-sharing with self-organizing communication and negotiation mechanisms. Xu et al. [7] investigated an online scheduling problem where one manufacturer owning two parallel identical machines may lease a number of external machines to satisfy its jobs via a manufacturing resource sharing platform. Li et al. [8] discussed the optimal conditions for choosing different business model by comparing maximizing self-revenues and maximizing social welfare in the context of shared manufacturing. Wang et al. [9] considered the credit problem to construct a resource allocation model and performed an enhanced Lagrangian coordination analysis to verify the effectiveness and efficiency of this method for resource allocation in the shared manufacturing environment. Rožman et al. [10] integrated blockchain technology into the concept of shared manufacturing by employing cross-chain solutions, proposed a hybrid method and concluded that the use of sidechain technology was reasonable. However, it is a long-term sharing process that the manufacturing enterprises share in the shared manufacturing environment, and then carry out the game of benefit distribution in the sharing. Therefore, it has certain theoretical and practical significance to study how to maximize the benefits of the shared members under the premise of ensuring the overall benefits of the resource-sharing manufacturing organization. On the one hand, the willingness to share resources is usually long-term. On the other hand, the sharing participants create resources and reach a sharing agreement to integrate their advantages, but their resource sharing behavior is often restricted and influenced by the sharing partners and cannot maximize their own interests, which is in line with the “bounded rationality” assumption of evolutionary game theory. Therefore, this study adopts the method of evolutionary game, trying to analyze the evolution trend of the dynamic sharing process of enterprise manufacturing resource sharing under the shared manufacturing environment, and measure the influence of various factors on the equilibrium strategy under different circumstances.The evolutionary game has been widely used in the literature. We will present a brief review on tripartite evolutionary game model as follows. Ji et al. [11] applied the evolutionary game to the green purchasing of the manufacturing industry and concluded that the manufacturing industry could form the patterns of sustainable development, and the supplier’s recycling capability directly determined how green a supply chain was. Luo et al. [12] used an evolutionary game to explore the influence of various parameters on the result of service derivatives and provided theoretical guidance for the implementation of service derivation by manufacturing enterprises. Wu et al. [13] constructed a tripartite evolutionary game model of government, industry, and university to analyze the strategic choices of the tripartite government, industry, university, and provide theoretical guidance for tripartite collaboration. Wang et al. [14] proposed a multiuser oriented manufacturing service allocation framework and drawn some managerial implications from the results that can help Cloud manufacturing platform operators to make better service allocation decision in the future. Xiao et al. [15] constructed a tripartite evolutionary game model among the local government, upstream and downstream manufacturers, and provided better suggestions for the game group through evolutionary game analysis. Zhu and Rong [16] constructed a tripartite evolutionary game model among drug manufacturers, third-party drug testing institutions and government regulatory agencies and gave some suggestions for the government to improve the drug supervision mechanism. Cui [17] constructed a tripartite game model of the enterprises, public and regulatory bodies, to analyze the impact of various related factors through simulation, and conduct analysis and research from both long-term and short-term perspectives. Wang [18] used the evolutionary game to solve the problem of urban parking difficulty and provided feasible suggestions for government, enterprise, and parking space owner through numerical simulation analysis. Wu et al. [19] applied the evolutionary game to the collaborative innovation of new energy automobiles and explored the impact of various related factors on new energy automobiles, universities and government through simulation analysis. Xu and Yang [20] established an evolutionary game model to solve the operation of rail-road intermodal transportation, analyzed the influence of government promotion and other related factors, and gave the influence trend of related factors. Xu et al. [21] used evolutionary game to analyze public health emergencies and put forward feasible suggestions. Zhu et al. [22] used the knowledge of evolutionary game theory to discuss the impact of incentive and penalty parameters on green credit. In fact, there are many studies on evolutionary games. Challet and Zhang [23] introduced and analyzed a simple evolutionary game. Friedman [24] present basic analytical tools of evolutionary game theory. Inspired by evolutionary game theory, Deng et al. [25] considered a biological and evolutionary perspective to study the combination of evidences. Some people applied the evolutionary game to the supply chains [26, 27], the solar PV power [28] and the shore power system [29], a two-person e-collaboration game [30] and online study groups [31]. There are also some studies that apply the evolutionary game to the construction industry, such as the construction and demolition waste recycling units’ green behavior [32], the green development performance [33] and the government’s reward–penalty mechanism on the decision-making process of production and recycling units, and the government’s effective incentive policies for the real estate enterprises [34]. Qi et al. [35] constructed an evolutionary game model between hard manufacturing resource and soft manufacturing resource enterprises in the cloud manufacturing. Hao and Zhao [36] constructed a three-group evolutionary game of manufacturing capacity sharing, and analyzed the factors that affect the sharing of the capacity sharing platforms, enterprises with manufacturing capacity and enterprises demanding manufacturing capacity.Although some scholars have studied the evolutionary game problem of enterprise manufacturing resource sharing in the cloud manufacturing environment, very few scholars have studied the evolutionary game problem in the shared manufacturing environment. At the same time, most scholars of evolutionary game only consider the cost and benefits of enterprise sharing. However, the level of trust may also affect their willingness to share. And, in an environment where the country vigorously develops shared manufacturing, the government can also participate in the regulation of shared manufacturing. Sharing companies can not only be secure because of government regulation, but also use government regulatory input to reduce costs. Therefore, this paper constructs an evolutionary game model considering the cost, income and trust level of manufacturing enterprises under the government regulation mechanism, more comprehensively analyzes the influence trend of various factors of manufacturing enterprises participating in shared manufacturing, and provides more favorable guarantee for manufacturing enterprises to participate in shared manufacturing.The rest of this paper is organized as follows. In Section2, it introduces the evolutionary game consisting of tripartite participants. In Section 3, we analyze Evolutionary Stable Strategy. Numerical simulation is given in Section 4. Finally, Section 5 provides conclusions.


## 2. The Evolutionary Game Consisting of Tripartite Participants

### 2.1. Model Description and Assumptions

The participation of manufacturing companies in shared manufacturing is characterized by the sharing of usage rights, and involves manufacturing sharing in multi-party, diverse and multimanufacturing links. Manufacturing enterprises can obtain the missing manufacturing capacity through shared manufacturing and reduce costs and technical risks; at the same time, they also bear the risk of additional costs and technology leakage, but they can make full use of their own enterprise advantages and obtain excess profits. In the shared service model of Shenyang Machine Tool, MouldLao and1688.com, there are many types of enterprises with shared manufacturing resources, including enterprises with manufacturing capacity and enterprises that demand manufacturing capacity. Combined with the researches of Wu et al. [13] and Qi et al. [35], this paper constructs an evolutionary game model based on government regulation to reduce the shared cost and risk of both parties. At the same time, this paper also considers the influence of trust benefits on the willingness of enterprises to cooperate. The relevant assumptions are as follows:(1)
There are three types of participants in shared manufacturing: the government, enterprises with manufacturing capacity (denoted as type A company), and enterprises requiring manufacturing capacity (denoted as type B company).(2)
The strategy of the two types of manufacturing companies is (sharing, not sharing), and the government’s strategy is (regulation and nonregulation). The probability of the type A company participating in the sharing isx, 0 ≤ x ≤ 1, and the probability of not participating in the sharing is 1 − x. The probability of a type B company participating in the sharing is y, 0 ≤ y ≤ 1, and the probability of not participating in the sharing is 1 − y. The probability of government regulation is z, 0 ≤ z ≤ 1. The probability of nonregulation is 1 − z. The three game groups are all “bounded rationality” and they choose their own strategies with a certain probability.(3)
Both types of companies do not participate in shared manufacturing. When the two types of companies operate independently, the cost isDi, and the income is Wi (i = 1, 2 for type A company and type B company, respectively).(4)
Both types of companies participate in shared manufacturing. In order to achieve resource sharing, the two types of companies need to invest additional sharing costCi and obtain trust income Li and shared income R. Among them, Li = γi∗Ti: γi, Ti are the trust level and potential trust income of the shared manufacturing parties, respectively. The shared income R is distributed in proportion to αi. The shared income of type A company is α1∗R, and the shared income of type B company is α2∗R, (α1 + α2 = 1). At this time, the utilization efficiency of the two types of companies for government regulation investment is βi.(5)
When one party does not participate in the sharing due to opportunism or other reasons, the other sharing party insists on the sharing behavior and sends a trustworthy signal to other subjects, thereby obtaining trust incomeLi and additional income Ri. The nonsharing party shall be subject to government punishments Si and loss Li for dishonesty. At this time, the sharing party’s utilization efficiency of government regulation investment is θi.(6)
When the government participates in regulation, the government needs to invest in regulation costCG. When only one party participates in the sharing, the government obtains the regulatory income RG, the fine Si, and the social income V. In order to promote the rapid development of shared manufacturing, when the government regulates two type of manufacturing companies to complete shared manufacturing, the state will give the government a reward M.(7)
When the government does not participate in regulation, there is no need to invest in costs. Since the government does not participate in regulation, the government income is reduced toλ times of the regulatory income, that is, the nonregulated income is λ∗RG.The model parameters are shown in Table1.Table 1
The model parameters.
i-Type of companies, (i = 1, 2 for type A company and type B company, respectively)x: probability of type A company participating in the sharingy: probability of type B company participating in the sharingz: probability of government’s regulationDi: cost of companies when they do not participate in the sharingWi: income of companies when they do not participate in the sharingCi: extra cost of companies when only one company participates in the sharingR: income of companies when they all participate in the sharingαi: proportion of income when they all participate in the sharingγi: trust level of companies when the company participates in the sharingTi: potential trust income when the company participates in the sharingLi: trust income. The loss of trust in nonsharing is −Li (Li = γi∗Ti)Ri: the additional income of company when only one company participate in the sharingSi: punishment of company that the company does not share by the governmentCG: cost of government’s regulationθi: utilization efficiency of government investment when one company does not participate in the sharingβi: utilization efficiency of government investment when both companies participate in the sharingRG: income of government’s regulationλ: the government’s nonregulation accounted for the proportion of income under regulationV: the social income of the government from the completion of shared manufacturingM: the reward given by the state to the government is due to the government’s regulation and completion of shared manufacturing


### 2.2. Payoff Matrix and Replicator Dynamic Equation

Based on the above assumptions, the payoff matrix for the government and the shared manufacturing companies is shown in Table2.Table 2
The payoff matrix.
Type B company sharesType B company does not shareGovernment regulatesType A company sharesRG−CG+V+MRG−CG+S2W1−D1+α1R−C1+L1+β1CGW1−D1+R1−C1+L1+θ1CGW2−D2+α2R−C2+L2+β2CGW2−D2−L2−S2Type A company does not shareRG−CG+S1−CGW1−D1−L1−S1W1−D1W2−D2+R2−C2+L2+θ2CGW2−D2Government does not regulateType A company sharesλRG+VλRG+S2W1−D1+α1R−C1+L1W1−D1+R1−C1+L1W2−D2+α2R−C2+L2W2−D2−L2−S2Type A company does not shareλRG+S10W1−D1−L1−S1W1−D1W2−D2+R2−C2+L2W2−D2The expected payoffsU1S of type A company participating in the sharing and the expected payoffs U1N of type A company not participating in the sharing are:(1)U1S=yα1R+1−yR1+yzβ1CG+1−yzθ1CG−C1+L1+W1−D1,U1N=y−L1−S1+W1−D1.The expected payoffsU2S of type B company participating in the sharing and the expected payoffs U2N of type B company not participating in the sharing are:(2)U2S=xα2R+1−xR2+xzβ2CG+1−xzθ2CG−C2+L2+W2−D2,U2N=x−L2−S2+W2−D2.The expected payoffsUGS of government regulation and the expected payoffs UGN of government nonregulation are(3)UGS=x−xy+yRG+xyV+M+x1−yS2+1−xyS1−CG,UGN=x−xy+yλRG+xyV+x1−yS2+1−xyS1.Therefore, the replicator dynamic equation formed by the government and the shared manufacturing companies is(4)Fx=x1−xyα1R+1−yR1+yzβ1CG+1−yzθ1CG−C1+1+yL1+yS1Fy=y1−yxα2R+1−xR2+xzβ2CG+1−xzθ2CG−C2+1+xL2+xS2Fz=z1−zx−xy+y1−λRG+xyM−CG.,


## 2.1. Model Description and Assumptions

The participation of manufacturing companies in shared manufacturing is characterized by the sharing of usage rights, and involves manufacturing sharing in multi-party, diverse and multimanufacturing links. Manufacturing enterprises can obtain the missing manufacturing capacity through shared manufacturing and reduce costs and technical risks; at the same time, they also bear the risk of additional costs and technology leakage, but they can make full use of their own enterprise advantages and obtain excess profits. In the shared service model of Shenyang Machine Tool, MouldLao and1688.com, there are many types of enterprises with shared manufacturing resources, including enterprises with manufacturing capacity and enterprises that demand manufacturing capacity. Combined with the researches of Wu et al. [13] and Qi et al. [35], this paper constructs an evolutionary game model based on government regulation to reduce the shared cost and risk of both parties. At the same time, this paper also considers the influence of trust benefits on the willingness of enterprises to cooperate. The relevant assumptions are as follows:(1)
There are three types of participants in shared manufacturing: the government, enterprises with manufacturing capacity (denoted as type A company), and enterprises requiring manufacturing capacity (denoted as type B company).(2)
The strategy of the two types of manufacturing companies is (sharing, not sharing), and the government’s strategy is (regulation and nonregulation). The probability of the type A company participating in the sharing isx, 0 ≤ x ≤ 1, and the probability of not participating in the sharing is 1 − x. The probability of a type B company participating in the sharing is y, 0 ≤ y ≤ 1, and the probability of not participating in the sharing is 1 − y. The probability of government regulation is z, 0 ≤ z ≤ 1. The probability of nonregulation is 1 − z. The three game groups are all “bounded rationality” and they choose their own strategies with a certain probability.(3)
Both types of companies do not participate in shared manufacturing. When the two types of companies operate independently, the cost isDi, and the income is Wi (i = 1, 2 for type A company and type B company, respectively).(4)
Both types of companies participate in shared manufacturing. In order to achieve resource sharing, the two types of companies need to invest additional sharing costCi and obtain trust income Li and shared income R. Among them, Li = γi∗Ti: γi, Ti are the trust level and potential trust income of the shared manufacturing parties, respectively. The shared income R is distributed in proportion to αi. The shared income of type A company is α1∗R, and the shared income of type B company is α2∗R, (α1 + α2 = 1). At this time, the utilization efficiency of the two types of companies for government regulation investment is βi.(5)
When one party does not participate in the sharing due to opportunism or other reasons, the other sharing party insists on the sharing behavior and sends a trustworthy signal to other subjects, thereby obtaining trust incomeLi and additional income Ri. The nonsharing party shall be subject to government punishments Si and loss Li for dishonesty. At this time, the sharing party’s utilization efficiency of government regulation investment is θi.(6)
When the government participates in regulation, the government needs to invest in regulation costCG. When only one party participates in the sharing, the government obtains the regulatory income RG, the fine Si, and the social income V. In order to promote the rapid development of shared manufacturing, when the government regulates two type of manufacturing companies to complete shared manufacturing, the state will give the government a reward M.(7)
When the government does not participate in regulation, there is no need to invest in costs. Since the government does not participate in regulation, the government income is reduced toλ times of the regulatory income, that is, the nonregulated income is λ∗RG.The model parameters are shown in Table1.Table 1
The model parameters.
i-Type of companies, (i = 1, 2 for type A company and type B company, respectively)x: probability of type A company participating in the sharingy: probability of type B company participating in the sharingz: probability of government’s regulationDi: cost of companies when they do not participate in the sharingWi: income of companies when they do not participate in the sharingCi: extra cost of companies when only one company participates in the sharingR: income of companies when they all participate in the sharingαi: proportion of income when they all participate in the sharingγi: trust level of companies when the company participates in the sharingTi: potential trust income when the company participates in the sharingLi: trust income. The loss of trust in nonsharing is −Li (Li = γi∗Ti)Ri: the additional income of company when only one company participate in the sharingSi: punishment of company that the company does not share by the governmentCG: cost of government’s regulationθi: utilization efficiency of government investment when one company does not participate in the sharingβi: utilization efficiency of government investment when both companies participate in the sharingRG: income of government’s regulationλ: the government’s nonregulation accounted for the proportion of income under regulationV: the social income of the government from the completion of shared manufacturingM: the reward given by the state to the government is due to the government’s regulation and completion of shared manufacturing


## 2.2. Payoff Matrix and Replicator Dynamic Equation

Based on the above assumptions, the payoff matrix for the government and the shared manufacturing companies is shown in Table2.Table 2
The payoff matrix.
Type B company sharesType B company does not shareGovernment regulatesType A company sharesRG−CG+V+MRG−CG+S2W1−D1+α1R−C1+L1+β1CGW1−D1+R1−C1+L1+θ1CGW2−D2+α2R−C2+L2+β2CGW2−D2−L2−S2Type A company does not shareRG−CG+S1−CGW1−D1−L1−S1W1−D1W2−D2+R2−C2+L2+θ2CGW2−D2Government does not regulateType A company sharesλRG+VλRG+S2W1−D1+α1R−C1+L1W1−D1+R1−C1+L1W2−D2+α2R−C2+L2W2−D2−L2−S2Type A company does not shareλRG+S10W1−D1−L1−S1W1−D1W2−D2+R2−C2+L2W2−D2The expected payoffsU1S of type A company participating in the sharing and the expected payoffs U1N of type A company not participating in the sharing are:(1)U1S=yα1R+1−yR1+yzβ1CG+1−yzθ1CG−C1+L1+W1−D1,U1N=y−L1−S1+W1−D1.The expected payoffsU2S of type B company participating in the sharing and the expected payoffs U2N of type B company not participating in the sharing are:(2)U2S=xα2R+1−xR2+xzβ2CG+1−xzθ2CG−C2+L2+W2−D2,U2N=x−L2−S2+W2−D2.The expected payoffsUGS of government regulation and the expected payoffs UGN of government nonregulation are(3)UGS=x−xy+yRG+xyV+M+x1−yS2+1−xyS1−CG,UGN=x−xy+yλRG+xyV+x1−yS2+1−xyS1.Therefore, the replicator dynamic equation formed by the government and the shared manufacturing companies is(4)Fx=x1−xyα1R+1−yR1+yzβ1CG+1−yzθ1CG−C1+1+yL1+yS1Fy=y1−yxα2R+1−xR2+xzβ2CG+1−xzθ2CG−C2+1+xL2+xS2Fz=z1−zx−xy+y1−λRG+xyM−CG.,


## 3. Evolutionary Stable Strategy Analysis

F(x) = 0, F(y) = 0, F(z) = 0 can get local equilibrium points: E1 (0, 0, 0), E2 (0, 0, 1), E3 (0, 1, 0), E4 (0, 1, 1), E5 (1, 0, 0), E6 (1, 0, 1), E7 (1, 1, 0), and E8 (1, 1, 1). In an asymmetric game, the evolutionary game equilibrium must be a strict Nash equilibrium, that is, a pure strategy equilibrium, and a mixed strategy must not be an evolutionary stable equilibrium. Therefore, only the above eight strategy stability conditions are discussed. The Jacobian matrix of this system is obtained as follows:(5)J=∂Fx∂x∂Fx∂y∂Fx∂z∂Fy∂x∂Fy∂y∂Fy∂z∂Fz∂x∂Fz∂y∂Fz∂z,where(6)∂Fx∂x=1−2xyα1R+1−yR1+yzβ1CG+1−yzθ1CG−C1+1+yL1+yS1,∂Fx∂y=x1−xα1R−R1−zβ1CG+zθ1CG+L1+S1,∂Fx∂z=x1−xyβ1CG+1−yθ1CG,∂Fy∂x=y1−yα2R−R2+zβ2CG−zθ2CG+L2+S2,∂Fy∂y=1−2yxα2R+1−xR2+xzβ2CG+1−xzθ2CG−C2+1+xL2+xS2,∂Fy∂z=y1−yxβ2CG+1−xθ2CG,∂Fz∂x=z1−z1−y1−λRG+yM,∂Fz∂y=z1−z1−x1−λRG+xM,∂Fz∂z=1−2zx−xy+y1−λRG+xyM−CG.According to the actual situation, when the additional net profit of the two manufacturing companies participating in the sharing is more significant than zero, the companies may participate in the sharing, that is,αiR−Ci + Li > 0. Using Lyapunov’s indirect method, we analyze the stability of the above eight equilibrium points.(1) WhenRi−Ci + Li > 0, (1, 1, 1) is the stable point. As long as one manufacturing company participates in the sharing, it can be profitable. After a long-term evolutionary game, both manufacturing companies will participate in the sharing, and the government will also participate in regulation. At this time, the manufacturing company is not highly affected by another manufacturing company. Therefore, this article does not consider such situations. When Ri−Ci + Li > 0, the local stability of the equilibrium points is analyzed by the Jacobian matrix, as shown in Table 3. Furthermore, the shared manufacturing evolutionary game phase diagram of manufacturing enterprises under government regulation is shown in Figure 1.Table 3
Analysis of local stability of equilibrium point of case (1).
Equilibrium pointEigenvaluesStabilityλ1Symbolλ2Symbolλ3SymbolE1(0, 0, 0)R1 − C1 + L1+R2 − C2 + L2+−CG−UnstableE2(0, 0, 1)R1 − C1 + L1 + θ1CG+, −R2 − C2 + L2 + θ2CG+, −CG+UnstableE3(0, 1, 0)α1R–C1 + 2L1 + S1+−[R2 − C2 + L2]−(1 −λ)RG − CG+, −UnstableE4(0, 1, 1)α1R + β1CG − C1 + 2L1 + S1+−[R2 − C2 + L2 + θ2CG]−, +−[(1 −λ)RG − CG]−, +UnstableE5(1, 0, 0)−[R1 − C1 + L1]−α2R–C2 + 2L2 + S2+(1 −λ)RG − CG−, +UnstableE6(1, 0, 1)−[R1 − C1 + L1 + θ1CG]−, +α2R + β2CG − C2 + 2L2 + S2+−[(1 −λ)RG − CG]+, −UnstableE7(1, 1, 0)−[α1R–C1 + 2L1 + S1]−−[α2R–C2 + 2L2 + S2]−(1 −λ)RG − CG  +  M+UnstableE8(1, 1, 1)–[α1R + β1CG − C1 + 2L1 + S1]−−[α2R + β2CG − C2 + 2L2 + S2]−−[(1 −λ)RG − CG  +  M]−ESSFigure 1
Strategy evolution phase diagram of case (1).Table 4
Analysis of local stability of equilibrium point of case (2).
Equilibrium pointEigenvaluesStabilityλ1Symbolλ2Symbolλ3SymbolE1 (0, 0, 0)R1 − C1 + L1−R2 − C2 + L2−−CG−ESSE2 (0, 0, 1)R1 − C1 + L1 + θ1CG+, −R2 − C2 + L2 + θ2CG+, −CG+UnstableE3 (0, 1, 0)α1R–C1 + 2L1 + S1+−[R2 − C2 + L2]+(1 −λ)RG − CG+, −UnstableE4 (0, 1, 1)α1R + β1CG − C1 + 2L1 + S1+−[R2 − C2 + L2 + θ2CG]−, +−[(1 −λ)RG − CG]−, +UnstableE5 (1, 0, 0)−[R1 − C1 + L1]+α2R–C2 + 2L2 + S2+(1 −λ)RG − CG−, +UnstableE6 (1, 0, 1)−[R1 − C1 + L1 + θ1CG]−, +α2R + β2CG − C2 + 2L2 + S2+−[(1 −λ)RG − CG]+, −UnstableE7 (1, 1, 0)−[α1R–C1 + 2L1 + S1]−−[α2R–C2 + 2L2 + S2]−(1 −λ)RG − CG  +  M+UnstableE8 (1, 1, 1)–[α1R + β1CG − C1 + 2L1 + S1]−−[α2R + β2CG − C2 + 2L2 + S2]−−[(1 −λ)RG − CG  +  M]−ESS(2) WhenRi − Ci + Li < 0, (0, 0, 0) and (1, 1, 1) are stable points. When only one party participates in the sharing, it will have a deficit. Thus, when a manufacturing company participates in the sharing, it is necessary to consider the probability of another company participating in the sharing, the level of trustworthiness, and the government’s participation probability. When Ri − Ci + Li < 0, the local stability of the equilibrium points is analyzed by the Jacobian matrix, as shown in Table 4. Furthermore, the shared manufacturing evolutionary game phase diagram of manufacturing enterprises under government regulation is shown in Figure 2.Figure 2
Strategy evolution phase diagram of case (2).


## 4. Numerical Simulation

This paper uses MATLAB to carry out the simulation analysis of the influence of different parameters on the strategy evolution result. The data set of this paper refers to the paper by Qi et al. [35]. The experimental data are x = 0.49, y = 0.49, z = 0.5; C1 = 20, C2 = 15, R = 40; α1 = 0.56, α2 = 0.44; γ1 = 0.7, γ2 = 0.6; T1 = 2, T2 = 2; R1 = 9, R2 = 6; S1 = 2, S2 = 1.5; θ1 = 0.8, θ2 = 0.6; β1 = 0.5, β2 = 0.4; CG = 4, RG = 8; λ = 0.4, M = 1.


### 4.1. The Influence of the Initial Sharing Probability

Considering that the sharing willingness of the three-party game subject is not clear, the initial sharing probability of the game subject is set to (0.5, 0.5, 0.5). In order to study the influence of the initial sharing probability on the evolutionary game path, the initial sharing probabilities are set to (0.8, 0.5, 0.5), (0.5, 0.2, 0.5), (0.6, 0.6, 0.5), (0.5, 0.5, 0.2) and (0.45, 0.45, 0.45), respectively. Then, we analyze the influence of different initial probabilities on the evolutionary results. The evolutionary stable strategy of the system is shown in Figures3(a) and 3(b).Figure 3
Numerical simulation diagram of initial sharing probability.
(a)(b)By analyzing Figure3, we can see that on the basis of the initial sharing probability of (0.5, 0.5, 0.5), if the manufacturing company or the government actively participates in the sharing, the manufacturing company and the government will participate in the shared manufacturing after a long-term evolutionary game. It is found by comparison that the greater the initial sharing probability of the game subject, the more likely the three parties in the game are to participate in the sharing and the faster the tendency. On the contrary, the three parties in the game do not tend to participate in the sharing and the faster the tendency. It can also be seen from Figure 3 that manufacturing companies always react before the government.


### 4.2. The Influence of the Shared Income Distribution Ratio of Shared Manufacturing Companies

The shared income distribution ratio of shared manufacturing companies is set to (α1 = 0.56, α2 = 0.44), (α1 = 0.65, α2 = 0.35), (α1 = 0.51, α2 = 0.49) and (α1 = 0.48, α2 = 0.52), respectively. Then, we analyze the influence of the shared income distribution ratio of shared manufacturing companies on the evolutionary results. The evolutionary stable strategy of the system is shown in Figures 4(a) and 4(b).Figure 4
Numerical simulation diagram of the distribution ratio of shared income.
(a)(b)By analyzing Figure4, we can see that the shared incomes should be distributed reasonably. When the share of revenue distribution ratio is within a reasonable range, because manufacturing companies with a high share of revenue share will increase their willingness to participate in shared manufacturing, all three parties in the game participate in shared manufacturing after a long-term evolutionary game. If the income distribution ratio exceeds the reasonable distribution range, because the willingness of manufacturing companies to participate in shared manufacturing with a low shared income ratio will decrease, all three parties in the game will do not participate in shared manufacturing after a long-term evolutionary game.


### 4.3. The Influence of the Trust Level of the Shared Manufacturing Companies

The trust levels of the two parties of the shared manufacturing companies is set as (r1 = 0.7, r2 = 0.6), (r1 = 0.8, r2 = 0.7), (r1 = 0.5, r2 = 0.4) and (r1 = 0.3, r2 = 0.2), respectively. Then, we analyze the influence of the trust level of shared manufacturing companies on the evolutionary results. The evolutionary stable strategy of the system is shown in Figures 5(a) and 5(b).Figure 5
Numerical simulation diagram of the level of trust.
(a)(b)By analyzing Figure5, we can see that the higher the level of trust between the two parties of shared manufacturing companies, the more the government and manufacturing companies tend to participate in shared manufacturing and the faster the tendency. Conversely, the less the government and manufacturing companies tend to participate in shared manufacturing and the faster the tendency.


### 4.4. The Influence of the Utilization Efficiency of Government Input When One Company Does Not Participate in the Sharing

The utilization efficiency of government input when a party does not participate in the sharing is set to (θ1 = 0.8, θ2 = 0.6), (θ1 = 0.7, θ2 = 0.6), (θ1 = 0.5, θ2 = 0.45) and (θ1 = 0.3, θ2 = 0.3), respectively. Then, we analyze the effect of changes in the utilization efficiency of government input on the outcome of the evolutionary game when one company does not participate in the sharing. The evolutionary stable strategy of the system is shown in Figures 6(a) and 6(b).Figure 6
Numerical simulation diagram of utilization efficiency of government investment when one party does not participate in the sharing.
(a)(b)By analyzing Figure6, we can see that the more efficient the use of government input when one party of the shared manufacturing company does not participate in the sharing, the more the government and manufacturing companies tend to participate in shared manufacturing and the faster the tendency. Conversely, the less the government and manufacturing companies tend to participate in shared manufacturing and the faster the tendency.


### 4.5. The Influence of the Utilization Efficiency of Government Input When All Parties of Shared Manufacturing Company Participate in the Sharing

The utilization efficiency of government input when all parties of shared manufacturing companies participate in the sharing is set to (β1 = 0.6, β2 = 0.5), (β1 = 0.5, β2 = 0.4), (β1 = 0.4, β2 = 0.3) and (β1 = 0.3, β2 = 0.2), respectively. Then, we analyze the effect of changes in the utilization efficiency of government input on the outcome of the evolutionary game when both companies of shared manufacturing company participate in the sharing. The evolutionary stable strategy of the system is shown in Figures 7(a) and 7(b).Figure 7
Numerical simulation diagram of the utilization efficiency of government investment when the two parties participate in the sharing.
(a)(b)By analyzing Figure7, we can see that the more efficient the use of government input is when shared manufacturing companies are participating in the sharing, the more the government and manufacturing companies tend to participate in shared manufacturing and the faster the tendency. Conversely, the less likely the government and manufacturing companies are to participate in shared manufacturing and the faster the tendency.


### 4.6. The Influence of Government Nonregulation in the Proportion of Regulatory Income

The ratio of government nonregulation to the income of regulation is set asλ = 0.3, λ = 0.4, λ = 0.5 and λ = 0.6, respectively. Then, we analyze the effect of the government’s nonregulation accounted for the proportion of income under regulation on the evolutionary results. The evolutionary stable strategy of the system is shown in Figures 8(a) and 8(b).Figure 8
Numerical simulation diagram of the proportion of government’s nonregulation to the income of regulation.
(a)(b)By analyzing Figure8, we can see that the higher the proportion of government’s nonregulation in the income of regulation, the less the government and manufacturing companies tend to participate in shared manufacturing and the faster the tendency. Conversely, the more the government and manufacturing companies tend to participate in shared manufacturing and the faster they tend to.


### 4.7. The Influence of the Punishment by the Government

The nonsharing party is punished by the government as (4, 3), (2, 1.5), (1.5, 1.2), and (0.6, 0.4), respectively. Then, we analyze the effect of the punishment by the government on the evolutionary results. The evolutionary stable strategy of the system is shown in Figures9(a) and 9(b).Figure 9
Numerical simulation diagram of the government’s penalty for the nonsharing party.
(a)(b)By analyzing Figure9, we can see that the more the government penalizes the nonsharing party, the more the government and manufacturing companies tend to participate in shared manufacturing and the faster the tendency. Conversely, the less the government and manufacturing companies tend to participate in the shared manufacturing and the faster the tendency.


### 4.8. The Influence of the Reward Given by the State

The rewards given to the government by the state are set asM = 1, M = 0.8, M = 0.6 and M = 0.2, respectively. Then, we analyze the effect of the reward given by the state on the evolutionary results. The evolutionary stable strategy of the system is shown in Figures 10(a) and 10(b).Figure 10
Numerical simulation diagram of government award given by the state.
(a)(b)By analyzing Figure10, we can see that the more reward the state give to the government, the more the government and manufacturing companies tend to participate in shared manufacturing and the faster the tendency. Conversely, the less the government and manufacturing companies tend to participate in shared manufacturing and the faster the tendency.


## 4.1. The Influence of the Initial Sharing Probability

Considering that the sharing willingness of the three-party game subject is not clear, the initial sharing probability of the game subject is set to (0.5, 0.5, 0.5). In order to study the influence of the initial sharing probability on the evolutionary game path, the initial sharing probabilities are set to (0.8, 0.5, 0.5), (0.5, 0.2, 0.5), (0.6, 0.6, 0.5), (0.5, 0.5, 0.2) and (0.45, 0.45, 0.45), respectively. Then, we analyze the influence of different initial probabilities on the evolutionary results. The evolutionary stable strategy of the system is shown in Figures3(a) and 3(b).Figure 3
Numerical simulation diagram of initial sharing probability.
(a)(b)By analyzing Figure3, we can see that on the basis of the initial sharing probability of (0.5, 0.5, 0.5), if the manufacturing company or the government actively participates in the sharing, the manufacturing company and the government will participate in the shared manufacturing after a long-term evolutionary game. It is found by comparison that the greater the initial sharing probability of the game subject, the more likely the three parties in the game are to participate in the sharing and the faster the tendency. On the contrary, the three parties in the game do not tend to participate in the sharing and the faster the tendency. It can also be seen from Figure 3 that manufacturing companies always react before the government.


## 4.2. The Influence of the Shared Income Distribution Ratio of Shared Manufacturing Companies

The shared income distribution ratio of shared manufacturing companies is set to (α1 = 0.56, α2 = 0.44), (α1 = 0.65, α2 = 0.35), (α1 = 0.51, α2 = 0.49) and (α1 = 0.48, α2 = 0.52), respectively. Then, we analyze the influence of the shared income distribution ratio of shared manufacturing companies on the evolutionary results. The evolutionary stable strategy of the system is shown in Figures 4(a) and 4(b).Figure 4
Numerical simulation diagram of the distribution ratio of shared income.
(a)(b)By analyzing Figure4, we can see that the shared incomes should be distributed reasonably. When the share of revenue distribution ratio is within a reasonable range, because manufacturing companies with a high share of revenue share will increase their willingness to participate in shared manufacturing, all three parties in the game participate in shared manufacturing after a long-term evolutionary game. If the income distribution ratio exceeds the reasonable distribution range, because the willingness of manufacturing companies to participate in shared manufacturing with a low shared income ratio will decrease, all three parties in the game will do not participate in shared manufacturing after a long-term evolutionary game.


## 4.3. The Influence of the Trust Level of the Shared Manufacturing Companies

The trust levels of the two parties of the shared manufacturing companies is set as (r1 = 0.7, r2 = 0.6), (r1 = 0.8, r2 = 0.7), (r1 = 0.5, r2 = 0.4) and (r1 = 0.3, r2 = 0.2), respectively. Then, we analyze the influence of the trust level of shared manufacturing companies on the evolutionary results. The evolutionary stable strategy of the system is shown in Figures 5(a) and 5(b).Figure 5
Numerical simulation diagram of the level of trust.
(a)(b)By analyzing Figure5, we can see that the higher the level of trust between the two parties of shared manufacturing companies, the more the government and manufacturing companies tend to participate in shared manufacturing and the faster the tendency. Conversely, the less the government and manufacturing companies tend to participate in shared manufacturing and the faster the tendency.


## 4.4. The Influence of the Utilization Efficiency of Government Input When One Company Does Not Participate in the Sharing

The utilization efficiency of government input when a party does not participate in the sharing is set to (θ1 = 0.8, θ2 = 0.6), (θ1 = 0.7, θ2 = 0.6), (θ1 = 0.5, θ2 = 0.45) and (θ1 = 0.3, θ2 = 0.3), respectively. Then, we analyze the effect of changes in the utilization efficiency of government input on the outcome of the evolutionary game when one company does not participate in the sharing. The evolutionary stable strategy of the system is shown in Figures 6(a) and 6(b).Figure 6
Numerical simulation diagram of utilization efficiency of government investment when one party does not participate in the sharing.
(a)(b)By analyzing Figure6, we can see that the more efficient the use of government input when one party of the shared manufacturing company does not participate in the sharing, the more the government and manufacturing companies tend to participate in shared manufacturing and the faster the tendency. Conversely, the less the government and manufacturing companies tend to participate in shared manufacturing and the faster the tendency.


## 4.5. The Influence of the Utilization Efficiency of Government Input When All Parties of Shared Manufacturing Company Participate in the Sharing

The utilization efficiency of government input when all parties of shared manufacturing companies participate in the sharing is set to (β1 = 0.6, β2 = 0.5), (β1 = 0.5, β2 = 0.4), (β1 = 0.4, β2 = 0.3) and (β1 = 0.3, β2 = 0.2), respectively. Then, we analyze the effect of changes in the utilization efficiency of government input on the outcome of the evolutionary game when both companies of shared manufacturing company participate in the sharing. The evolutionary stable strategy of the system is shown in Figures 7(a) and 7(b).Figure 7
Numerical simulation diagram of the utilization efficiency of government investment when the two parties participate in the sharing.
(a)(b)By analyzing Figure7, we can see that the more efficient the use of government input is when shared manufacturing companies are participating in the sharing, the more the government and manufacturing companies tend to participate in shared manufacturing and the faster the tendency. Conversely, the less likely the government and manufacturing companies are to participate in shared manufacturing and the faster the tendency.


## 4.6. The Influence of Government Nonregulation in the Proportion of Regulatory Income

The ratio of government nonregulation to the income of regulation is set asλ = 0.3, λ = 0.4, λ = 0.5 and λ = 0.6, respectively. Then, we analyze the effect of the government’s nonregulation accounted for the proportion of income under regulation on the evolutionary results. The evolutionary stable strategy of the system is shown in Figures 8(a) and 8(b).Figure 8
Numerical simulation diagram of the proportion of government’s nonregulation to the income of regulation.
(a)(b)By analyzing Figure8, we can see that the higher the proportion of government’s nonregulation in the income of regulation, the less the government and manufacturing companies tend to participate in shared manufacturing and the faster the tendency. Conversely, the more the government and manufacturing companies tend to participate in shared manufacturing and the faster they tend to.


## 4.7. The Influence of the Punishment by the Government

The nonsharing party is punished by the government as (4, 3), (2, 1.5), (1.5, 1.2), and (0.6, 0.4), respectively. Then, we analyze the effect of the punishment by the government on the evolutionary results. The evolutionary stable strategy of the system is shown in Figures9(a) and 9(b).Figure 9
Numerical simulation diagram of the government’s penalty for the nonsharing party.
(a)(b)By analyzing Figure9, we can see that the more the government penalizes the nonsharing party, the more the government and manufacturing companies tend to participate in shared manufacturing and the faster the tendency. Conversely, the less the government and manufacturing companies tend to participate in the shared manufacturing and the faster the tendency.


## 4.8. The Influence of the Reward Given by the State

The rewards given to the government by the state are set asM = 1, M = 0.8, M = 0.6 and M = 0.2, respectively. Then, we analyze the effect of the reward given by the state on the evolutionary results. The evolutionary stable strategy of the system is shown in Figures 10(a) and 10(b).Figure 10
Numerical simulation diagram of government award given by the state.
(a)(b)By analyzing Figure10, we can see that the more reward the state give to the government, the more the government and manufacturing companies tend to participate in shared manufacturing and the faster the tendency. Conversely, the less the government and manufacturing companies tend to participate in shared manufacturing and the faster the tendency.


## 5. Conclusions

In order to adapt to the new wave of sharing economy, the manufacturing industry needs to quickly complete the transition to the new development trend of shared manufacturing. This paper constructs a tripartite evolutionary game model of manufacturing companies participating in shared manufacturing under the government regulation mechanism considering the trust level of manufacturing companies and the influence of government regulation. We use MATLAB to analyze the impact of relevant factors on the willingness of the government and manufacturing companies to participate in shared manufacturing. The main conclusions include: if the initial sharing probability of the government or manufacturing companies is high, it will attract other companies to participate in shared manufacturing. Participating in shared manufacturing can increase additional income for manufacturing companies. In the sharing, manufacturing companies must rationally distribute shared benefits. The level of trust in manufacturing companies, government punishments, utilization efficiency of government regulatory inputs, and state reward will all actively promote government and manufacturing companies to participate in shared manufacturing. The higher the ratio of government nonregulation to the revenue of regulation, the lower the probability that the government and companies will participate in shared manufacturing.We got some managerial implications according to the influence trend and stable conditions of various factors. Manufacturing companies should actively participate in shared manufacturing and attract more companies to participate in shared manufacturing to increase additional benefits. When companies participate in shared manufacturing, they should not only pursue maximization of their own interests, but reasonably distribute shared benefits under the premise of ensuring the profitability of themselves. Manufacturing companies should actively participate in shared manufacturing to increase the level of trust and make full use of government regulatory investment to maximize benefits. The government should increase the penalties for nonsharing parties. The state should increase the reward given to the government to regulate and complete shared manufacturing.The future work of this research is as follows. Firstly, the competitiveness of products or service produced by manufacturing companies participating in shared manufacturing in the existing market is going to be discussed. Secondly, it is wise to analyze the quality and market feedback of the products or services produced in shared manufacturing. Thirdly, the evolutionary game model of manufacturing companies in sharing manufacturing considering speculative income will be studied. Fourthly, we will be to consider tripartite evolutionary game model of shared manufacturing led by core manufacturing enterprises with Empirical Research.



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*Source: 7706727-2022-03-23.xml*