# A Study on Inter-Regional Cooperation Patterns and Evolution Mechanism of Traditional and Renewable Energy Sources

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methodology

## 3. Construction of Evolutionary Game System Model

#### 3.1. Description of Evolutionary Game Nexus

#### 3.2. Modeling Assumptions

#### 3.3. Payoff Analysis of Different Cooperative Strategies

#### 3.4. System Dynamics Model of Evolutionary Game

## 4. Stable Conditions of Evolutionary Game Strategy

#### 4.1. Acquisition of Equilibrium Points

#### 4.2. Stable Conditions of Equilibrium Points

## 5. Discussion of Evolutionary Results

#### 5.1. Case Basis

^{8}, with a total cost of RMB 8.64 × 10

^{8}.

^{6}tons of coal-fired energy consumption and 4.9 × 10

^{5}tons of carbon dioxide emissions will be reduced. If the average coal-fired price in the Guizhou market is RMB 600 per ton and the carbon trading price is RMB 42.58 per ton, the added storage value of saving coal-fired energy and the environmental value in Guizhou are RMB 14.4 × 10

^{8}and RMB 0.208642 × 10

^{8}, respectively, and the added value of the power industry is approximately RMB 47.87224 × 10

^{8}. In October, the growth rates of coal and power industries were 5.7% and 10.4%, respectively. Assuming that this is due to the corresponding influence coefficient, in line with our hypothesis, we can estimate the RPS quota’s completion for the Guizhou provincial government by “WFERYG” cooperation, i.e., 18.434%. What’s more, considering that it is difficult to evaluate the failure cost of the opportunity benefits, owing to reducing the traditional thermal power generation in Guizhou, for convenience, let the failure cost of the opportunity benefits equal the power-generation cost of the Yunnan area.

#### 5.2. Effect of Sensitive Parameters on the Cooperative Strategy’s Evolutionary Path

#### 5.2.1. Sensitivity Analysis of Sharing Cooperative Parameters When Sharing Cost Is Symmetric

#### 5.2.2. Sensitivity Analysis of Sharing Cooperative Parameters When Sharing Cost Is Asymmetric

**Case 1.**The failure cost of the opportunity gains is less than the RES power-generation cost ($\pi <c$).

**Case 2.**The failure cost of the opportunity gains is far more than the RES power-generation cost ($\pi >c$).

## 6. Conclusions

#### 6.1. Research Conclusions

#### 6.2. Limitations and Suggestions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

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

${\mathit{\lambda}}_{1}^{*}$ | ${\mathit{\lambda}}_{2}^{*}$ | ||

${X}_{1}^{*}(0,0)$ | 0 | 0 | Unstable point |

${X}_{2}^{*}(1,0)$ | 0 | 0 | Unstable point |

${X}_{3}^{*}(0,1)$ | 0 | 9.6385 | Unstable point |

${X}_{4}^{*}(1,1)$ | 12.7728 | 32.0498 | Unstable point |

${X}_{5}^{*}(0.43,0.32)$ | −1.7580 | −2.9834 | $ESS$ |

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**Figure 2.**The SD flow diagram of the evolution of cooperative strategies between governments A and B.

**Figure 13.**Evolutionary result of mixed strategy ${X}_{5}^{*}({x}^{*},{y}^{*})$ under dynamic proportional allocation schema.

**Figure 14.**Evolutionary result of mixed strategy ${X}_{5}^{*}({x}^{*},{y}^{*})$ with the increase in $\pi $ value.

Government A | Government B | |
---|---|---|

$\mathbf{Sharing}\mathbf{Cooperation}\left(\mathit{y}\right)$ | $\mathbf{No}-\mathbf{Sharing}\mathbf{Cooperation}(1-\mathit{y})$ | |

Sharing cooperation ($x$) | $\left(\begin{array}{l}\ell {r}_{1}+\alpha \delta {r}_{2}+\lambda {r}_{3}-e-\theta (\pi +c)\\ e+(1-\alpha )\delta {r}_{2}+(\delta +0.1)e-(1-\theta )(\pi +c)\end{array}\right)$ | $\left(\begin{array}{l}\ell {r}_{1}+\alpha \delta {r}_{2}+\lambda {r}_{3}-e-\pi \\ e+(\delta +0.1)e-c\end{array}\right)$ |

No-sharing cooperation ($1-x$) | $\left(\begin{array}{l}\ell {r}_{1}+\delta {r}_{2}+\lambda {r}_{3}-e-\pi \\ e+(1-\alpha )\delta {r}_{2}+(\delta +0.1)e-c\end{array}\right)$ | $\left(\begin{array}{l}\ell {r}_{1}+\delta {r}_{2}+\lambda {r}_{3}-e-\pi \\ e+(\delta +0.1)e-c\end{array}\right)$ |

Equilibrium Points | Eigenvalues | Asymptotic Stability | |
---|---|---|---|

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

${X}_{1}(0,0)$ | $(\alpha -1)\delta {r}_{2}$ | $(1-\alpha )\delta {r}_{2}$ | Instability |

${X}_{2}(1,0)$ | $(1-\alpha )\delta {r}_{2}$ | $c-(1-\theta )(\pi +c)+(1-\alpha )\delta {r}_{2}$ | Instability |

${X}_{3}(0,1)$ | $(\alpha -1)\delta {r}_{2}$ | $\pi -\theta (\pi +c)+(\alpha -1)\delta {r}_{2}$ | Condition (11) |

${X}_{4}(1,1)$ | $(1-\alpha )\delta {r}_{2}-\pi +\theta (\pi +c)$ | $(\alpha -1)\delta {r}_{2}-c+(1-\theta )(\pi +c)$ | Condition (15) |

${X}_{5}(\tilde{x},\tilde{y})$ | ${\tilde{\lambda}}_{1}$ | ${\tilde{\lambda}}_{2}$ | Condition (16) |

Stable Points | Condition of Stable Points | ID |
---|---|---|

${X}_{3}(0,1)$ | $\pi -\theta (\pi +c)+(\alpha -1)\delta {r}_{2}<0$ | (11) |

${X}_{4}(1,1)$ | $(1-\alpha )\delta {r}_{2}-\pi +\theta (\pi +c)<0$, $(\alpha -1)\delta {r}_{2}-c+(1-\theta )(\pi +c)<0$ | (15) |

${X}_{5}(\tilde{x},\tilde{y})$ | ${\tilde{\lambda}}_{1}<0$, ${\tilde{\lambda}}_{2}<0$ | (16) |

Symbol | Definition | Initial Value | Units |
---|---|---|---|

${r}_{1}$ | Storage value of saving coal-fired energy | 14.4 | 10^{8} RMB |

${r}_{2}$ | Environmental value of carbon abatement | 0.208642 | 10^{8} RMB |

${r}_{3}$ | Government A’s added economic value | 47.87224 | 10^{8} RMB |

$e$ | Government A’s expense for RES alternative | 6.7824 | 10^{8} RMB |

$c$ | RES power-generation cost | 8.64 | 10^{8} RMB |

$\pi $ | Failure cost of opportunity gains | 8.64 | 10^{8} RMB |

$\ell $ | Influence coefficient of ${r}_{1}$ | 5.7 | % |

$\lambda $ | Influence coefficient of ${r}_{3}$ | 10.4 | % |

$\delta $ | RPS volume completed by government B | 18.434 | % |

$\theta $ | Government A’s cost’s allocated proportion | 50 | % |

$\alpha $ | Government A’s environmental benefits’ allocated proportion | 50 | % |

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

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

${X}_{1}(0,0)$ | −0.019231 | 0.019231 | Saddle point |

${X}_{2}(1,0)$ | 0.019231 | 0.019231 | Unstable point |

${X}_{3}(0,1)$ | −0.019231 | −0.019231 | $ESS$ |

${X}_{4}(1,1)$ | 0.019231 | −0.019231 | Saddle point |

${X}_{5}(\tilde{x},\tilde{y})$ | / | / | / |

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

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

${X}_{1}(0,0)$ | −0.019231 | 0.019231 | Saddle point |

${X}_{2}(1,0)$ | 0.019231 | 1.019231 | Unstable point |

${X}_{3}(0,1)$ | −0.019231 | −1.019231 | $ESS$ |

${X}_{4}(1,1)$ | 1.019231 | −1.019231 | Saddle point |

${X}_{5}(\tilde{x},\tilde{y})$ | 0.019601 | −0.019601 | Saddle point |

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

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

${X}_{1}(0,0)$ | −0.019231 | 0.019231 | Saddle point |

${X}_{2}(1,0)$ | 0.019231 | −0.480769 | Saddle point |

${X}_{3}(0,1)$ | −0.019231 | 0.480769 | Saddle point |

${X}_{4}(1,1)$ | −0.480769 | 0.480769 | Saddle point |

${X}_{5}(\tilde{x},\tilde{y})$ | 0.018491 | −0.018491 | Saddle point |

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## Share and Cite

**MDPI and ACS Style**

Shang, B.; Jiang, T.; Bao, Z.
A Study on Inter-Regional Cooperation Patterns and Evolution Mechanism of Traditional and Renewable Energy Sources. *Sustainability* **2022**, *14*, 16022.
https://doi.org/10.3390/su142316022

**AMA Style**

Shang B, Jiang T, Bao Z.
A Study on Inter-Regional Cooperation Patterns and Evolution Mechanism of Traditional and Renewable Energy Sources. *Sustainability*. 2022; 14(23):16022.
https://doi.org/10.3390/su142316022

**Chicago/Turabian Style**

Shang, Bo, Taotao Jiang, and Zheshi Bao.
2022. "A Study on Inter-Regional Cooperation Patterns and Evolution Mechanism of Traditional and Renewable Energy Sources" *Sustainability* 14, no. 23: 16022.
https://doi.org/10.3390/su142316022