# The Collaboration Mechanism of Agricultural Product Supply Chain Dominated by Farmer Cooperatives

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## Abstract

**:**

## 1. Introduction

- Analyze the members’ behavior of agricultural products supply chain dominated by farmer cooperatives and the possible reasons for failure to collaborate.
- Build a theoretical model and analyze the evolution process of tripartite strategy and evolutionarily stability strategy.
- Analyze how various factors affect the strategic decisions of members through numerical simulation.

## 2. Literature Review

## 3. Model Assumptions and Construction

**Assumption**

**1.**

**Assumption**

**2.**

**Assumption**

**3.**

**Assumption**

**4.**

**Assumption**

**5.**

## 4. Equilibrium Analysis of Tripartite Game Model

#### 4.1. Expected Revenue Function and Replication Dynamic Equation

#### 4.2. Analysis of Evolutionarily Stability Strategy

- (1)
- When $2\mathrm{L}<{\mathrm{C}}_{1}$, ${\mathrm{Q}}_{21}-{\mathsf{\alpha}}_{2}\mathrm{I}<{\mathrm{M}}_{21}$, and ${\mathrm{Q}}_{31}-{\mathsf{\alpha}}_{3}\mathrm{I}<{\mathrm{M}}_{31}$, the equilibrium $\left(0,0,0\right)$ is ESS. This shows that when the supervision cost of farmer cooperatives is higher than the penalty amount received from manufacturers and retailers, farmer cooperatives tend to “loose supervision”. If the amount of penalty for subordinate enterprises increases, the sum of the two penalties is higher than the supervision cost, and the stability strategy changes. If the difference between the additional income obtained by the manufacturers or the retailers from the farmer cooperative through collaboration and the collaboration cost is less than the “free-rider” income obtained from the farmer cooperative without the collaboration, then the two will tend to “non-collaboration”. The evolution strategy is shown in Figure 1.
- (2)
- When $1/2\mathrm{L}<{\mathrm{C}}_{1}$, ${\mathrm{Q}}_{21}-{\mathsf{\alpha}}_{2}\mathrm{I}>{\mathrm{M}}_{21}$, and $\mathsf{\delta}({\mathrm{Q}}_{31}+{\mathrm{Q}}_{32})-{\mathsf{\alpha}}_{3}\mathrm{I}<{\mathrm{M}}_{31}$, the equilibrium $\left(0,1,0\right)$ is ESS. This shows that when the supervision cost of farmer cooperatives is higher than half of the penalty amount of “non-collaboration” for manufacturers or retailers, then farmer cooperatives tend to “loose supervision”. If the difference between the additional income obtained from the farmer cooperatives and the collaboration input is higher than the “free-rider” income obtained from the farmer cooperatives, the manufacturers will choose the “collaboration” strategy. If the difference between the sum of the additional income obtained from the farmer cooperatives and the manufacturers and the collaboration input is less than the “free-rider” income from the farmer cooperatives for the retailers that do not collaborate, then the retailers will choose the “non-collaboration” strategy. The evolution strategy is shown in Figure 2.
- (3)
- When $\mathsf{\delta}({\mathrm{Q}}_{21}+{\mathrm{Q}}_{23})-{\mathsf{\alpha}}_{2}\mathrm{I}>{\mathrm{M}}_{21}$, and $\mathsf{\delta}({\mathrm{Q}}_{31}+{\mathrm{Q}}_{32})-{\mathsf{\alpha}}_{3}\mathrm{I}>{\mathrm{M}}_{31}$, the equilibrium $\left(0,1,1\right)$ is ESS. In this case, farmer cooperatives tend to “loose supervision”. If the manufacturers collaborate with farmer cooperatives and retailers, and the difference between the sum of the additional income obtained from them and the collaboration input is higher than the “free-rider” income obtained by the manufacturers without collaboration, then the manufacturers choose the strategy of “collaboration”. If the retailers collaborate with farmer cooperatives and manufacturers, and the difference between the sum of the additional income obtained from farmer cooperatives and manufacturers and the collaboration input is higher than the “free-rider” income obtained without adopting the collaboration strategy, the retailers will choose the “collaboration” strategy. The evolution strategy is shown in Figure 3.
- (4)
- When $2\mathrm{L}<{\mathrm{C}}_{1}$, ${\mathsf{\alpha}}_{2}\mathrm{P}+{\mathrm{Q}}_{21}-{\mathsf{\alpha}}_{2}\mathrm{I}<{\mathrm{M}}_{21}-\mathrm{L}$, and ${\mathsf{\alpha}}_{3}\mathrm{P}+{\mathrm{Q}}_{31}-{\mathsf{\alpha}}_{3}\mathrm{I}<{\mathrm{M}}_{31}-\mathrm{L}$, the equilibrium $\left(1,0,0\right)$ is ESS. This shows that when the supervision cost of farmer cooperatives is lower than the penalty amount received from manufacturers and retailers, farmer cooperatives tend to adopt the “strict supervision”. The net income obtained when manufacturers adopt the “collaboration” strategy is less than the net income obtained without the “collaboration” strategy, then the manufacturers adopt the “non-collaboration” strategy. The net income obtained when manufacturers adopt the “collaboration” strategy means the difference between the reward distribution obtained due to the collaboration adding the additional income obtained from the collaborative farmer cooperatives and the collaboration input of the manufacturers. The net income obtained without the “collaboration” strategy means the difference between the “free-rider” income and the penalty amount. The net income obtained when retailers adopt the “collaboration” strategy is less than the net income obtained without the “collaboration” strategy, and then the retailers adopt the “non-collaboration” strategy. The net income obtained when retailers adopt the “collaboration” strategy means the difference between the reward distribution obtained due to the collaboration adding the additional income obtained from the collaborative farmer cooperatives and the collaboration input of the retailers. The evolution strategy is shown in Figure 4.
- (5)
- When $1/2\mathrm{L}>{\mathrm{C}}_{1}$, ${\mathsf{\alpha}}_{2}\mathrm{P}+{\mathrm{Q}}_{21}-{\mathsf{\alpha}}_{2}\mathrm{I}>{\mathrm{M}}_{21}-\mathrm{L}$, and ${\mathsf{\alpha}}_{3}\mathrm{P}+\mathsf{\delta}({\mathrm{Q}}_{31}+{\mathrm{Q}}_{32})-{\mathsf{\alpha}}_{3}\mathrm{I}<{\mathrm{M}}_{31}-\mathrm{L}$, the equilibrium $\left(1,1,0\right)$ is ESS. This shows that when the supervision cost of farmer cooperatives is less than half of the penalty amount received from retailers, farmer cooperatives tend to the “strict supervision”. The net income obtained when manufacturers adopt the “collaboration” strategy is higher than the net income obtained without the “collaboration” strategy, then the manufacturers adopt the “collaboration” strategy. The net income obtained when manufacturers adopt the “collaboration” strategy means the difference between the reward distribution obtained due to the collaboration adding the additional income obtained from the collaborative farmer cooperatives and the collaboration input of the manufacturers. The net income obtained without the “collaboration” strategy means the difference between the “free-rider” income and the penalty amount. The net income obtained when retailers adopt the “collaboration” strategy is less than the net income obtained without the “collaboration” strategy, and then the retailers adopt the “non-collaboration” strategy. The net income obtained when retailers adopt the “collaboration” strategy means the difference between the reward distribution obtained due to the collaboration adding the additional income obtained from the collaborative farmer cooperatives and manufacturers and the collaboration input of the retailers. The evolution strategy is shown in Figure 5.
- (6)
- When ${\mathsf{\alpha}}_{2}\mathrm{P}+\mathsf{\delta}({\mathrm{Q}}_{21}+{\mathrm{Q}}_{23})-{\mathsf{\alpha}}_{2}\mathrm{I}<{\mathrm{M}}_{21}-\mathrm{L}$, and ${\mathsf{\alpha}}_{3}\mathrm{P}+{\mathrm{Q}}_{31}-{\mathsf{\alpha}}_{3}\mathrm{I}>{\mathrm{M}}_{31}$, the equilibrium $\left(1,0,1\right)$ is ESS. In this case, farmer cooperatives tend to choose the “strict supervision”. The net income obtained when manufacturers adopt the “collaboration” strategy is less than the net income obtained without the “collaboration” strategy, then the manufacturers adopt the “non-collaboration” strategy. The net income obtained when manufacturers adopt the “collaboration” strategy means the difference between the reward distribution obtained due to the collaboration adding the additional income obtained from the collaborative farmer cooperatives and retailers and the collaboration input of the manufacturers. The net income obtained without the “collaboration” strategy means the difference between the “free-rider” income and the penalty amount. The net income obtained when retailers adopt the “collaboration” strategy is higher than the “free-rider” income without the “collaboration” strategy, then the retailers adopt the “collaboration” strategy. The net income obtained when retailers adopt the “collaboration” strategy means the difference between the reward distribution obtained due to the collaboration adding the additional income obtained from the collaborative farmer cooperatives and the collaboration input of the retailers. The evolution strategy is shown in Figure 6.

## 5. Numerical Simulation and Discussion

#### 5.1. The Impact of Supervision Cost on Evolutionary Game

#### 5.2. The Impact of Additional Income on Evolutionary Game

#### 5.3. The Impact of “Free-Rider” Income on Evolutionary Game

#### 5.4. The Impact of Synergy Coefficient on Evolutionary Game

#### 5.5. The Impact of Reward and Punishment Mechanism on Evolutionary Game

## 6. Conclusions and Enlightenment

## 7. Limitations and Future Research

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 8.**Effect of additional income on strategy. (

**a**) The additional income ${\mathrm{Q}}_{21}$; (

**b**) the additional income ${\mathrm{Q}}_{31}$.

**Figure 9.**Effect of “free-rider” income on strategy. (

**a**) The additional income ${\mathrm{M}}_{21}$; (

**b**) the additional income ${\mathrm{M}}_{31}$.

**Figure 11.**Effect of reward and punishment mechanism on strategy. (

**a**) The reward amount $\mathrm{P}$; (

**b**) the punishment amount $\mathrm{L}$.

Farmer Cooperative | Manufacturer | Retailer | |
---|---|---|---|

Collaboration (y) | Non-Collaboration (1 − y) | ||

Strict supervision (x) | ${\mathrm{B}}_{1}-{\mathrm{C}}_{1}-{\mathsf{\alpha}}_{1}\mathrm{I}+\mathsf{\delta}({\mathrm{Q}}_{12}+{\mathrm{Q}}_{13}),$ ${\mathrm{B}}_{2}-{\mathsf{\alpha}}_{2}\mathrm{I}+{\mathsf{\alpha}}_{2}\mathrm{P}+\mathsf{\delta}({\mathrm{Q}}_{21}+{\mathrm{Q}}_{23}),$ ${\mathrm{B}}_{3}-{\mathsf{\alpha}}_{3}\mathrm{I}+{\mathsf{\alpha}}_{3}\mathrm{P}+\mathsf{\delta}({\mathrm{Q}}_{31}+{\mathrm{Q}}_{32})$ | ${\mathrm{B}}_{1}-{\mathrm{C}}_{1}-{\mathsf{\alpha}}_{1}\mathrm{I}+\mathrm{L}+{\mathrm{Q}}_{13},$ ${\mathrm{B}}_{2}+{\mathrm{M}}_{21}+{\mathrm{M}}_{23}-\mathrm{L}$, ${\mathrm{B}}_{3}-{\mathsf{\alpha}}_{3}\mathrm{I}+{\mathrm{Q}}_{31}+{\mathsf{\alpha}}_{3}\mathrm{P}$ | Collaboration (z) |

${\mathrm{B}}_{1}-{\mathrm{C}}_{1}-{\mathsf{\alpha}}_{1}\mathrm{I}+\mathrm{L}+{\mathrm{Q}}_{12}$, ${\mathrm{B}}_{2}-{\mathsf{\alpha}}_{2}\mathrm{I}+{\mathrm{Q}}_{21}+{\mathsf{\alpha}}_{2}\mathrm{P}$, ${\mathrm{B}}_{3}+{\mathrm{M}}_{31}+{\mathrm{M}}_{32}-\mathrm{L}$ | ${\mathrm{B}}_{1}-{\mathrm{C}}_{1}-{\mathsf{\alpha}}_{1}\mathrm{I}+2\mathrm{L}$, ${\mathrm{B}}_{2}+{\mathrm{M}}_{21}-\mathrm{L}$, ${\mathrm{B}}_{3}+{\mathrm{M}}_{31}-\mathrm{L}$ | Non-Collaboration (1 − z) | |

Loose supervision (1 − x) | ${\mathrm{B}}_{1}-{\mathsf{\alpha}}_{1}\mathrm{I}+\mathsf{\delta}({\mathrm{Q}}_{12}+{\mathrm{Q}}_{13}$), ${\mathrm{B}}_{2}-{\mathsf{\alpha}}_{2}\mathrm{I}+\mathsf{\delta}({\mathrm{Q}}_{21}+{\mathrm{Q}}_{23}$), ${\mathrm{B}}_{3}-{\mathsf{\alpha}}_{3}\mathrm{I}+\mathsf{\delta}({\mathrm{Q}}_{31}+{\mathrm{Q}}_{32}$) | ${\mathrm{B}}_{1}-{\mathsf{\alpha}}_{1}\mathrm{I}+{\mathrm{Q}}_{13}$, ${\mathrm{B}}_{2}+{\mathrm{M}}_{21}+{\mathrm{M}}_{23}$, ${\mathrm{B}}_{3}-{\mathsf{\alpha}}_{3}\mathrm{I}+{\mathrm{Q}}_{31}$ | Collaboration (z) |

${\mathrm{B}}_{1}-{\mathsf{\alpha}}_{1}\mathrm{I}+{\mathrm{Q}}_{12}$, ${\mathrm{B}}_{2}-{\mathsf{\alpha}}_{2}\mathrm{I}+{\mathrm{Q}}_{21}$, ${\mathrm{B}}_{3}+{\mathrm{M}}_{31}+{\mathrm{M}}_{32}$ | ${\mathrm{B}}_{1}-{\mathsf{\alpha}}_{1}\mathrm{I}$, ${\mathrm{B}}_{2}+{\mathrm{M}}_{21}$, ${\mathrm{B}}_{3}+{\mathrm{M}}_{31}$ | Non-Collaboration (1 − z) |

Equilibrium Points | Eigenvalues | ||
---|---|---|---|

${\mathit{\lambda}}_{1}$ | ${\mathit{\lambda}}_{2}$ | ${\mathit{\lambda}}_{3}$ | |

$\left(0,0,0\right)$ | $2\mathrm{L}-{\mathrm{C}}_{1}$ | ${\mathrm{Q}}_{21}-{\mathsf{\alpha}}_{2}\mathrm{I}-{\mathrm{M}}_{21}$ | ${\mathrm{Q}}_{31}-{\mathsf{\alpha}}_{3}\mathrm{I}-{\mathrm{M}}_{31}$ |

$\left(0,1,0\right)$ | $\mathrm{L}-2{\mathrm{C}}_{1}$ | ${\mathsf{\alpha}}_{2}\mathrm{I}-{\mathrm{Q}}_{21}+{\mathrm{M}}_{21}$ | $\mathsf{\delta}({\mathrm{Q}}_{31}+{\mathrm{Q}}_{32})-{\mathsf{\alpha}}_{3}\mathrm{I}-{\mathrm{M}}_{31}$ |

$\left(0,0,1\right)$ | $\mathrm{L}$ | $\mathsf{\delta}({\mathrm{Q}}_{21}+{\mathrm{Q}}_{23})-{\mathrm{M}}_{21}-{\mathsf{\alpha}}_{2}\mathrm{I}$ | ${\mathsf{\alpha}}_{3}\mathrm{I}+{\mathrm{M}}_{31}-{\mathrm{Q}}_{31}$ |

$\left(0,1,1\right)$ | $-{\mathrm{C}}_{1}$ | ${\mathsf{\alpha}}_{2}\mathrm{I}+{\mathrm{M}}_{21}-\mathsf{\delta}({\mathrm{Q}}_{21}+{\mathrm{Q}}_{23})$ | ${\mathsf{\alpha}}_{3}\mathrm{I}+{\mathrm{M}}_{31}-\mathsf{\delta}({\mathrm{Q}}_{31}+{\mathrm{Q}}_{32})$ |

$\left(1,0,0\right)$ | ${\mathrm{C}}_{1}-2\mathrm{L}$ | ${\mathrm{Q}}_{21}+{\mathsf{\alpha}}_{2}\mathrm{P}+\mathrm{L}-{\mathrm{M}}_{21}-{\mathsf{\alpha}}_{2}\mathrm{I}$ | ${\mathrm{Q}}_{31}+{\mathsf{\alpha}}_{3}\mathrm{P}+\mathrm{L}-{\mathrm{M}}_{31}-{\mathsf{\alpha}}_{3}\mathrm{I}$ |

$\left(1,1,0\right)$ | $2{\mathrm{C}}_{1}-\mathrm{L}$ | ${\mathsf{\alpha}}_{2}\mathrm{I}+{\mathrm{M}}_{21}-{\mathrm{Q}}_{21}-{\mathsf{\alpha}}_{2}\mathrm{P}-\mathrm{L}$ | $\mathsf{\delta}\left({\mathrm{Q}}_{31}+{\mathrm{Q}}_{32}\right)+{\mathsf{\alpha}}_{3}\mathrm{P}+\mathrm{L}-{\mathsf{\alpha}}_{3}\mathrm{I}-{\mathrm{M}}_{31}$ |

$\left(1,0,1\right)$ | $-\mathrm{L}$ | $\mathsf{\delta}\left({\mathrm{Q}}_{21}+{\mathrm{Q}}_{23}\right)+{\mathsf{\alpha}}_{2}\mathrm{P}+\mathrm{L}-{\mathsf{\alpha}}_{2}\mathrm{I}-{\mathrm{M}}_{21}$ | ${\mathsf{\alpha}}_{3}\mathrm{I}+{\mathrm{M}}_{31}-{\mathrm{Q}}_{31}-{\mathsf{\alpha}}_{3}\mathrm{P}-\mathrm{L}$ |

$\left(1,1,1\right)$ | ${\mathrm{C}}_{1}$ | ${\mathsf{\alpha}}_{2}\mathrm{I}+{\mathrm{M}}_{21}-\mathsf{\delta}\left({\mathrm{Q}}_{21}+{\mathrm{Q}}_{23}\right)-{\mathsf{\alpha}}_{2}\mathrm{P}-\mathrm{L}$ | ${\mathsf{\alpha}}_{3}\mathrm{I}+{\mathrm{M}}_{31}-\mathsf{\delta}\left({\mathrm{Q}}_{31}+{\mathrm{Q}}_{32}\right)-{\mathsf{\alpha}}_{3}\mathrm{P}-\mathrm{L}$ |

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**MDPI and ACS Style**

Huo, Y.; Wang, J.; Guo, X.; Xu, Y.
The Collaboration Mechanism of Agricultural Product Supply Chain Dominated by Farmer Cooperatives. *Sustainability* **2022**, *14*, 5824.
https://doi.org/10.3390/su14105824

**AMA Style**

Huo Y, Wang J, Guo X, Xu Y.
The Collaboration Mechanism of Agricultural Product Supply Chain Dominated by Farmer Cooperatives. *Sustainability*. 2022; 14(10):5824.
https://doi.org/10.3390/su14105824

**Chicago/Turabian Style**

Huo, Yujia, Jiali Wang, Xiangyu Guo, and Yang Xu.
2022. "The Collaboration Mechanism of Agricultural Product Supply Chain Dominated by Farmer Cooperatives" *Sustainability* 14, no. 10: 5824.
https://doi.org/10.3390/su14105824