# Research on Co-Opetition Mechanism between Pharmaceutical Enterprises and Third-Party Logistics in Drug Distribution of Medical Community

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Model Construction

#### Construction of Co-Opetition Model between Pharmaceutical Enterprises and 3PL Enterprises

**Assumption 1.**

**Assumption 2.**

**Assumption 3.**

**Assumption 4.**

**Assumption 5.**

## 4. Model Analysis

#### 4.1. Analysis of the Evolution Stability of Pharmaceutical Enterprise Strategy

- (1)
- When $y=\frac{\mu +{\delta}_{2}T-e-{n}_{m}}{{a}_{m}-e-{n}_{m}+{\delta}_{1}R+{\delta}_{2}T+\left(e-s\right)r}$, $F\left(x\right)=0$, at this point, the system is in a stable state for any value of $x$.
- (2)
- When $y>\frac{\mu +{\delta}_{2}T-e-{n}_{m}}{{a}_{m}-e-{n}_{m}+{\delta}_{1}R+{\delta}_{2}T+\left(e-s\right)r}$, $\left({a}_{m}-e-{n}_{m}+{\delta}_{1}R+{\delta}_{2}T+\left(e-s\right)r\right)y+e-\mu +{n}_{m}-{\delta}_{2}T<0$; therefore, ${F}^{\prime}\left(1\right)<0,{F}^{\prime}\left(0\right)0$. In this case, $x=1$ is an evolutionarily stable strategy—that is, the pharmaceutical enterprises eventually evolve to display cooperative behavior.
- (3)
- When $y<\frac{\mu +{\delta}_{2}T-e-{n}_{m}}{{a}_{m}-e-{n}_{m}+{\delta}_{1}R+{\delta}_{2}T+\left(e-s\right)r}$, $\left({a}_{m}-e-{n}_{m}+{\delta}_{1}R+{\delta}_{2}T+\left(e-s\right)r\right)y+e-\mu +{n}_{m}-{\delta}_{2}T>0$; therefore, ${F}^{\prime}\left(1\right)>0,{F}^{\prime}\left(0\right)0$. At this time, $x=0$ is an evolutionarily stable strategy—that is, the pharmaceutical enterprise will eventually evolve to display competitive behavior.

#### 4.2. Evolution Stability Analysis of 3PL Enterprise Strategy

- (1)
- When $x=\frac{e+{n}_{l}-\mu}{e-{a}_{l}+{n}_{l}+{\delta}_{1}R-{\delta}_{2}T+\left(e-s\right)\left(r-1\right)},F\left(y\right)=0$. At this point, regardless of the value that y takes, the system is stable.
- (2)
- When $x>\frac{e+{n}_{l}-\mu}{e-{a}_{l}+{n}_{l}+{\delta}_{1}R-{\delta}_{2}T+\left(e-s\right)\left(r-1\right)},\left(e-{a}_{l}+{n}_{l}+{\delta}_{1}R-{\delta}_{2}T+\left(e-s\right)\left(r-1\right)\right)x+\mu -e-{n}_{l}>0;$ therefore, ${F}^{\prime}\left(1\right)<0,{F}^{\prime}\left(0\right)>0$. In this case, y = 1 is the evolutionarily stable strategy, and the 3PL enterprise finally evolves to display cooperative behavior.
- (3)
- When $x<\frac{e+{n}_{l}-\mu}{e-{a}_{l}+{n}_{l}+{\delta}_{1}R-{\delta}_{2}T+\left(e-s\right)\left(r-1\right)},\left(e-{a}_{l}+{n}_{l}+{\delta}_{1}R-{\delta}_{2}T+\left(e-s\right)\left(r-1\right)\right)x+\mu -e-{n}_{l}<0$; therefore, ${F}^{\prime}\left(1\right)>0,{F}^{\prime}\left(0\right)<0$. In this case, y = 0 is the evolutionarily stable strategy, and the 3PL enterprise finally evolves to display competitive behavior.

#### 4.3. Evolutionary Stability Analysis of the System

## 5. Numerical Simulation

#### 5.1. Initial Evolution Path Analysis

#### 5.2. Sensitivity Analysis of Important Parameters of Evolutionary Stability of Pharmaceutical Enterprises and 3PL Enterprises

## 6. Evolutionary System Optimization of Pharmaceutical Enterprises and 3PL Enterprises

#### 6.1. Static Premium and Penalty Mechanism

#### 6.2. Dynamic Premium and Penalty Mechanism

## 7. Conclusions

- (1)
- The cooperation and stability strategy of the drug distribution system of the county medical community is positively correlated with the incremental income of the cooperation between the two parties, liquidated damages and the degree of incentive and restraint. For pharmaceutical enterprises, cooperative incremental benefits are more sensitive, while 3PL enterprises are more sensitive to liquidated damages.
- (2)
- The income distribution ratio needs to be set reasonably in order to achieve a “win–win cooperation” situation. Values that are too high or too low will cause competition between pharmaceutical enterprises and 3PL enterprises.
- (3)
- Numerical simulations intuitively reveal the different evolution paths of pharmaceutical enterprises and 3PL enterprises and further verify the correctness of the theoretical analysis.
- (4)
- The static premium and penalty mechanism fails to dynamically adjust according to the behaviors of pharmaceutical enterprises and 3PL enterprises, thus failing to provide a stability control strategy for the system, while the dynamic premium and penalty mechanism links the behavior of the subject with the intensity of rewards and punishments and effectively controls the system’s stability.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The phase diagram of the co-opetition of drug distribution in the county medical community.

**Figure 9.**Evolution results of pharmaceutical enterprises (

**a**) and 3PL enterprises (

**b**) under the static premium and penalty mechanism.

**Figure 10.**Evolution paths of pharmaceutical enterprises (

**a**) and 3PL enterprises (

**b**) under the static premium and penalty mechanism.

**Figure 11.**Evolution paths of pharmaceutical enterprises and 3PL enterprises under the dynamic premium and penalty mechanism.

Parameter | Definition | Range |
---|---|---|

${P}_{m}$ | Basic income of pharmaceutical enterprises in logistics distribution | ${P}_{m}>0$ |

${P}_{l}$ | Basic income of 3PL enterprises in logistics distribution | ${P}_{l}>0$ |

$S$ | Excess return of cooperation between pharmaceutical enterprises and 3PL enterprises | $S>0$ |

$e$ | Cost of maintaining cooperation between pharmaceutical enterprises and 3PL enterprises | $e>0$ |

$r$ | Profit distribution ratio of pharmaceutical enterprises in cooperation with 3PL | $r\in \left[0,1\right]$ |

${a}_{m}$ | Competition income of pharmaceutical enterprises when they compete and cooperate with 3PL enterprises | ${a}_{m}>0$ |

$\mu $ | Cost of competition default of pharmaceutical enterprises or 3PL enterprises | $\mu >0$ |

${\eta}_{l}$ | Third-party logistics enterprises bear the cost of cooperation maintenance when pharmaceutical enterprises compete and 3PLenterprises cooperate | ${\eta}_{l}>0$ |

${a}_{l}$ | The 3PL enterprises’ competitive income when pharmaceutical enterprises cooperate and 3PL enterprises compete | ${a}_{l}>0$ |

${\eta}_{m}$ | The 3PL bear the cost of cooperation maintenance when pharmaceutical enterprises cooperate and 3PL enterprises compete | ${\eta}_{m}>0$ |

${\delta}_{1}$ | Incentive coefficient of pharmaceutical enterprises to 3PL enterprises | ${\delta}_{1}>1$ |

$R$ | Incentive cost of pharmaceutical enterprises to 3PL enterprises | $R>0$ |

${\delta}_{2}$ | Restriction coefficient for pharmaceutical enterprises to compete with 3PL enterprises | ${\delta}_{2}>1$ |

$T$ | Restriction cost of pharmaceutical enterprises to 3PL enterprises | $T>0$ |

$x$ | Probability of pharmaceutical enterprises choosing cooperation | $x\in \left[0,1\right]$ |

$1-x$ | Probability of pharmaceutical enterprises choosing competition | $1-x\in \left[0,1\right]$ |

$y$ | Probability of 3PL enterprises choosing cooperation | $y\in \left[0,1\right]$ |

$1-y$ | Probability of 3PL enterprises choosing competition | $1-y\in \left[0,1\right]$ |

${E}_{A1}$ | Expected benefits of pharmaceutical enterprises cooperation | ${E}_{A1}\in \left[-\infty ,+\infty \right]$ |

${E}_{A2}$ | Expected benefits of pharmaceutical enterprises competition | ${E}_{A2}\in \left[-\infty ,+\infty \right]$ |

${E}_{A}$ | Average income of pharmaceutical enterprises adopting mixed strategy | ${E}_{A}\in \left[-\infty ,+\infty \right]$ |

${E}_{B1}$ | Expected benefits of 3PL enterprises to choose cooperation | ${E}_{B1}\in \left[-\infty ,+\infty \right]$ |

${E}_{B2}$ | Expected benefits of 3PL enterprises to choose competition | ${E}_{B2}\in \left[-\infty ,+\infty \right]$ |

${E}_{B}$ | Average income of 3PL enterprises adopting mixed strategy | ${E}_{B}\in \left[-\infty ,+\infty \right]$ |

$F\left(x\right)$ | Replication dynamic equation for pharmaceutical enterprises to choose cooperation strategies | $F\left(x\right)\in \left[-\infty ,+\infty \right]$ |

$F\left(y\right)$ | Replication dynamic equation for 3PL enterprises to choose cooperation strategies | $F\left(y\right)\in \left[-\infty ,+\infty \right]$ |

Pharmaceutical Enterprise | 3PL Enterprise | |
---|---|---|

$\mathbf{Cooperation}\left(\mathit{y}\right)$ | $\mathbf{Competition}\left(1-\mathit{y}\right)$ | |

cooperation $\left(x\right)$ | ${P}_{m}+r\left(s-e\right)-{\delta}_{1}R$, ${P}_{l}+\left(1-r\right)\left(s-e\right)+{\delta}_{1}R$ | ${P}_{m}+\mu -e-{\eta}_{m}+{\delta}_{2}T,$ ${P}_{l}+{a}_{l}-\mu -{\delta}_{2}T$ |

competition $\left(1-x\right)$ | ${P}_{m}+{a}_{m}-\mu $, ${P}_{l}+\mu -e-{\eta}_{l}$ | ${P}_{m},$ ${P}_{l}$ |

Equilibrium Point | $\mathit{d}\mathit{e}\mathit{t}\left(\mathit{J}\right)$ | $\mathit{t}\mathit{r}\left(\mathit{J}\right)$ |
---|---|---|

$O\left(0,0\right)$ | $\left(\mu -e-{n}_{m}+{\delta}_{2}T\right)\ast \left(\mu -e-{n}_{l}\right)$ | $\left(\mu -e-{n}_{m}+{\delta}_{2}T\right)+\left(\mu -e-{n}_{l}\right)$ |

$A\left(1,0\right)$ | $\left(e-\mu +{n}_{m}-{\delta}_{2}T\right)\ast $ $\left(\mu -{a}_{l}+{\delta}_{1}R-{\delta}_{2}T+\left(e-s\right)\left(r-1\right)\right)$ | $\left(e-\mu +{n}_{m}-{\delta}_{2}T\right)+$ $\left(\mu -{a}_{l}+{\delta}_{1}R-{\delta}_{2}T+\left(e-s\right)\left(r-1\right)\right)$ |

$B\left(0,1\right)$ | $\left(\mu -{a}_{m}-{\delta}_{1}R-r\left(e-s\right)\right)\left(e-\mu +{n}_{l}\right)$ | $\left(\mu -{a}_{m}-{\delta}_{1}R-r\left(e-s\right)\right)+\left(e-\mu +{n}_{l}\right)$ |

$C\left(1,1\right)$ | $-\left(\mu -{a}_{m}-{\delta}_{1}R-r\left(e-s\right)\right)\ast $ $\left[-\left(\mu -{a}_{l}+{\delta}_{1}R-{\delta}_{2}T+\left(e-s\right)\left(r-1\right)\right)\right]$ | $-\left(\mu -{a}_{m}-{\delta}_{1}R-r\left(e-s\right)\right)$ $-[\left(\mu -{a}_{l}+{\delta}_{1}R-{\delta}_{2}T+\left(e-s\right)\left(r-1\right)\right)$ |

$D\left({x}^{*},{y}^{*}\right)$ | $\ast $ | 0 |

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## Share and Cite

**MDPI and ACS Style**

Li, Z.; Xia, T.; Shen, W.; Chen, S.
Research on Co-Opetition Mechanism between Pharmaceutical Enterprises and Third-Party Logistics in Drug Distribution of Medical Community. *Int. J. Environ. Res. Public Health* **2023**, *20*, 609.
https://doi.org/10.3390/ijerph20010609

**AMA Style**

Li Z, Xia T, Shen W, Chen S.
Research on Co-Opetition Mechanism between Pharmaceutical Enterprises and Third-Party Logistics in Drug Distribution of Medical Community. *International Journal of Environmental Research and Public Health*. 2023; 20(1):609.
https://doi.org/10.3390/ijerph20010609

**Chicago/Turabian Style**

Li, Zhao, Tie Xia, Wanzhi Shen, and Sheng Chen.
2023. "Research on Co-Opetition Mechanism between Pharmaceutical Enterprises and Third-Party Logistics in Drug Distribution of Medical Community" *International Journal of Environmental Research and Public Health* 20, no. 1: 609.
https://doi.org/10.3390/ijerph20010609