# Game Analysis on the Evolution of Decision-Making of Vaccine Manufacturing Enterprises under the Government Regulation Model

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## Abstract

**:**

## 1. Introduction

- (1)
- This paper analyzes the competition and cooperation relationship and game strategy of the behavior decision-making of vaccine enterprises under the supervision of the government, and considers the third-party supervision as an environmental factor. Combined with the analysis of variables, it discusses the conditions that affect the evolution of the interaction between vaccine manufacturers and the government towards the direction of cooperation;
- (2)
- Based on the premise of bounded rationality, the decision-making process of vaccine manufacturing enterprises is regarded as a dynamic process of gradual learning. The evolutionary game model of government and vaccine manufacturing enterprises is constructed. The key factors affecting the game strategy of both sides are found by solving the model;
- (3)
- By analyzing the equilibrium point and stability of the evolutionary game between the government and vaccine manufacturers, the choice of the stable strategy of the two is studied. Then, through the changes of government punishment, third-party reports, and other parameters, using MATLAB simulation analysis, the evolution trend of the game of the behavior decision-making of vaccine enterprises is investigated under different government supervision modes, and reasonable countermeasures and suggestions are put forwarded to provide decision-making basis for government departments.

## 2. Methods

#### 2.1. Model Assumptions

**Hypothesis**

**1:**

**Hypothesis**

**2:**

**Hypothesis**

**3:**

#### 2.2. Model Symbol Description

## 3. Results

#### 3.1. Duplicate Dynamic Equation Construction

#### 3.2. Stability Analysis of Equilibrium Point

**Proposition**

**1.**

**Proof.**

- ${a}_{11}=(1-2x)\{y[({R}_{V2}+{F}_{V1}+{F}_{V2})(\alpha -\beta \lambda )]+{R}_{V1}-{R}_{V2}+\beta \lambda ({R}_{V2}+{F}_{V1}+{F}_{V2})\}$
- ${a}_{12}=x(1-x)({R}_{V2}+{F}_{V1}+{F}_{V2})(\alpha -\beta \lambda )$
- ${a}_{21}=y(1-y)\pi \psi (\beta \lambda -\alpha ){R}_{G}$
- ${a}_{22}=(1-2y)[\pi \psi (\alpha -\beta \lambda ){R}_{G}(1-x)+\lambda \pi {C}_{G2}-\psi {C}_{G1}]$

- (1)
- $trJ={a}_{11}+{a}_{22}0$ (trace condition);
- (2)
- $\mathrm{det}J=\left|\begin{array}{cc}{a}_{11}& {a}_{12}\\ {a}_{21}& {a}_{22}\end{array}\right|={a}_{11}{a}_{22}-{a}_{12}{a}_{21}0$ (Jacobian condition)

**Proposition**

**2.**

**Proposition**

**3.**

**Proof.**

## 4. Discussion

#### 4.1. The Impact of Government Punishment on the Evolutionary Behavior of Vaccine Companies

#### 4.2. The Impact of Active Regulation by Government Regulatory Departments on the Evolution of the Two Parties

#### 4.3. The Influence of Passive Government Regulation and Third-Party Reporting Probability on the Evolution of Both Parties

#### 4.4. The Influence of Power of the Government and Regulation on the Evolution of Both Parties

#### 4.5. The Influence of Corruption of Government and Awareness of People on the Evolution of Both Parties

## 5. Conclusions

#### 5.1. Raising Public Awareness of Public Safety

#### 5.2. Severe Punishment

#### 5.3. Improving Government Supervision

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The evolution path of game strategy. (

**a**) The evolution path is a closed loop of infinite cycle; (

**b**) (0,0) is an ESS; (

**c**) (1,0) is an ESS; (

**d**) (0,1) is an ESS; (

**e**) (1,1) is an ESS.

**Figure 3.**Cooperative probability simulation results of vaccine enterprises under government punishment.

**Figure 4.**Simulation results of the evolutionary game between the two parties under the condition that the success rate of government’s active supervision is increased.

**Figure 5.**Simulation results of the evolutionary game between the two parties under the circumstance that the success rate of government passive supervision is increased.

**Figure 6.**Simulation results of the evolutionary game between the two parties under the condition that the probability of third-party reporting is improved.

**Figure 7.**Simulation results of the evolutionary game between the two parties under the condition that power of the government and regulation is improved.

**Figure 8.**Simulation results of the evolutionary game between the two parties under the condition that corruption of government and awareness of people is improved.

**Table 1.**Influencing factors of drug (food) enterprise behavior decision under government supervision mode.

Scholars (Year) | Influencing Factors |
---|---|

Song Yan (2009) [37] | Income from qualified drugs and fake drugs. |

Cao Jiantao (2018) [13] | Additional benefit, benefit of inaction, positive utility, cost of implementation, government punishment. |

Song Yan (2016) [15] | Benefits of qualified drugs, safety costs, benefits of fake and inferior drugs, accident handling costs, government fines. |

Fang Yu (2010) [16] | Regulatory probability, regulatory cost, safety accident probability, violation cost, disposal cost, discount factor, social loss, penalty amount. |

Yan Jianzhou (2015) [18] | Regulatory cost, safety cost, penalty, legal liability cost, social cost, reputation loss. |

Liu Sukun (2011) [38] | Regulatory costs, normal earnings, excess earnings, penalties. |

Liu Sukun (2012) [39] | Supervision cost, reputation loss, degree of supervision, illegal earnings. Punishment, enterprise earnings, probability of illegal operation, probability of legal operation, probability of public report and verification of earnings. |

Jiang Shubo (2009) [40] | Control cost, penalty amount, compensation amount, regulatory probability. Disguised cost, income from superior goods, income from inferior goods, excess income. |

Zhao, L (2018) [41] | Government regulations, product output, product revenue, regulatory cost. |

Game Players | Government Regulatory Authority | ||
---|---|---|---|

$\mathbf{Active}\text{}\mathbf{Regulation}(\mathit{y})$ | $\mathbf{Passive}\text{}\mathbf{Regulation}(1-\mathit{y})$ | ||

vaccine manufacturers | Self-discipline ($x$) | ${R}_{V1}-{C}_{V}$, $-\frac{{C}_{G1}}{\pi}$ | $\lambda ({R}_{V1}-{C}_{V})+(1-\lambda ){R}_{V1}$, $\lambda (-\frac{{C}_{G2}}{\psi})$ |

non-self-discipline ($1-x$) | $(1-\alpha ){R}_{V2}-\alpha ({F}_{V1}+{F}_{V2})-{C}_{V}$, $\alpha {R}_{G}-\frac{{C}_{G1}}{\pi}$ | $\lambda [(1-\beta ){R}_{V2}-\beta ({F}_{V1}+{F}_{V2})-C{}_{V}]+(1-\lambda ){R}_{V2}$, $\lambda [\beta ({R}_{G}-\frac{{C}_{G2}}{\psi})+(1-\beta )(-\frac{{C}_{G2}}{\psi})]$ |

Local Equilibrium Points | ${\mathit{a}}_{11}$ | ${\mathit{a}}_{12}$ | ${\mathit{a}}_{21}$ | ${\mathit{a}}_{22}$ |
---|---|---|---|---|

$(0,0)$ | ${R}_{V1}-{R}_{V2}+\beta \lambda ({R}_{V2}+{F}_{V1}+{F}_{V2})$ | 0 | 0 | $\pi \psi (\alpha -\beta \lambda ){R}_{G}+\lambda \pi {C}_{G2}-\psi {C}_{G1}$ |

$(0,1)$ | ${R}_{V1}-{R}_{V2}+\alpha ({R}_{V2}+{F}_{V1}+{F}_{V2})$ | 0 | 0 | $-[(\alpha -\beta \lambda ){R}_{G}+\lambda \pi {C}_{G2}-\psi {C}_{G1}]$ |

$(1,0)$ | $-[{R}_{V1}-{R}_{V2}+\beta \lambda ({R}_{V2}+{F}_{V1}+{F}_{V2})]$ | 0 | 0 | $\lambda \pi {C}_{G2}-\psi {C}_{G1}$ |

$(1,1)$ | $-[{R}_{V1}-{R}_{V2}+\alpha ({R}_{V2}+{F}_{V1}+{F}_{V2})]$ | 0 | 0 | $-(\lambda \pi {C}_{G2}-\psi {C}_{G1})$ |

$({x}^{\ast},{y}^{\ast})$ | 0 | M | N | 0 |

**Table 4.**Stability analysis equilibrium points when $\alpha >\epsilon >\beta \lambda >0$ or $0<\alpha <\epsilon <\beta \lambda $.

Local Equilibrium Points | $\mathbf{det}\mathit{J}$ | $\mathit{t}\mathit{r}\mathit{J}$ | Results |
---|---|---|---|

$(0,0)$ | - | uncertain | Saddle point |

$(0,1)$ | - | uncertain | Saddle point |

$(1,0)$ | - | uncertain | Saddle point |

$(1,1)$ | - | uncertain | Saddle point |

$({x}^{\ast},{y}^{\ast})$ | + | 0 | Center point |

Parameter | ${\mathit{C}}_{\mathit{G}}{}_{1}$ | ${\mathit{C}}_{\mathit{G}}{}_{2}$ | ${\mathit{R}}_{\mathit{G}}$ | $\mathit{\alpha}$ | $\mathit{\beta}$ | $\mathit{\lambda}$ | ${\mathit{R}}_{\mathit{V}1}$ | ${\mathit{R}}_{\mathit{V}}{}_{2}$ | ${\mathit{F}}_{\mathit{V}1}$ | ${\mathit{F}}_{\mathit{V}2}$ | ${\mathit{C}}_{\mathit{V}}$ | $\mathit{\pi}$ | $\mathit{\psi}$ |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Value | 1 | 5 | 3 | 0.3 | 0.8 | 0.4 | 2 | 6 | 4 | 2 | 1 | 1 | 1 |

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## Share and Cite

**MDPI and ACS Style**

Zhang, N.; Yang, Y.; Wang, X.; Wang, X.
Game Analysis on the Evolution of Decision-Making of Vaccine Manufacturing Enterprises under the Government Regulation Model. *Vaccines* **2020**, *8*, 267.
https://doi.org/10.3390/vaccines8020267

**AMA Style**

Zhang N, Yang Y, Wang X, Wang X.
Game Analysis on the Evolution of Decision-Making of Vaccine Manufacturing Enterprises under the Government Regulation Model. *Vaccines*. 2020; 8(2):267.
https://doi.org/10.3390/vaccines8020267

**Chicago/Turabian Style**

Zhang, Na, Yingjie Yang, Xiaodong Wang, and Xinfeng Wang.
2020. "Game Analysis on the Evolution of Decision-Making of Vaccine Manufacturing Enterprises under the Government Regulation Model" *Vaccines* 8, no. 2: 267.
https://doi.org/10.3390/vaccines8020267