# Can a Dynamic Reward–Penalty Mechanism Help the Implementation of Renewable Portfolio Standards under Information Asymmetry?

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Evolutionary Game Model of Power Sales Side RPS Regulation

**Assumption**

**1.**

**Assumption**

**2.**

**Assumption**

**3.**

**Assumption**

**4.**

**Assumption**

**5.**

**Assumption**

**6.**

**Assumption**

**7.**

## 4. System Dynamics Analysis of the Evolutionary Game Model

#### 4.1. System Dynamics Simulation of the Static Reward–Penalty Mechanism

#### 4.2. System Dynamics Simulation of the Dynamic Reward–penalty Mechanism

#### 4.3. Stability Analysis of Equilibrium Points

## 5. Impact Analysis of Exogenous Variables

#### 5.1. Impact of the RPS Quota Indicators

#### 5.2. Impact of the Green Certificate Price

#### 5.3. Impact of the Size of the Electricity Sales Market on the Evolution Process

## 6. Conclusions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Statistics of power sales companies in China as of August 2018 (Data sources: National Development and Reform Commission).

**Figure 10.**Evolutionary trend of the strategy selection for integrated power sales companies when ${\mathrm{P}}_{e}=0.05,0.1,\mathrm{and}0.15$.

**Figure 11.**Evolutionary trend of the strategic selection for independent power sales companies when ${\mathrm{P}}_{e}=0.05,0.1,\mathrm{and}0.15$.

**Figure 12.**Evolutionary trend of government regulators’ strategic selection when ${\mathrm{P}}_{e}=0.05,0.1,\mathrm{and}0.15$.

Government Regulates (x) | ||
---|---|---|

Independent power sales companies obeying $\text{}\left(z\right)$ | Independent power sales companies disobeying $\text{}\left(1-z\right)$ | |

Integrated power sales companies obeying ($\mathrm{y}$) | ${R}_{1}+{R}_{2}-{C}_{g}-{\mathrm{E}}_{1}-{\mathrm{E}}_{2}$ ${P}_{1}-{\mathrm{B}}_{1}+{\mathrm{E}}_{1}$ ${P}_{2}-{\mathrm{B}}_{2}+{\mathrm{E}}_{2}$ | ${R}_{1}+{\mathrm{F}}_{2}-{C}_{g}-{\mathrm{E}}_{1}$ ${P}_{1}-{\mathrm{B}}_{1}+{\mathrm{E}}_{1}$ ${\mathrm{O}}_{2}-{\mathrm{F}}_{2}$ |

Integrated power sales companies disobeying $\text{}\left(1-y\right)$ | ${R}_{2}+{\mathrm{F}}_{1}-{C}_{g}-{\mathrm{E}}_{2}$ ${\mathrm{O}}_{1}-{\mathrm{F}}_{1}$ ${P}_{2}-{\mathrm{B}}_{2}+{\mathrm{E}}_{2}$ | ${\mathrm{F}}_{1}+{\mathrm{F}}_{2}-{C}_{g}$ ${\mathrm{O}}_{1}-{\mathrm{F}}_{1}-{\mathrm{F}}_{2}$ ${\mathrm{O}}_{2}-{\mathrm{F}}_{1}-{\mathrm{F}}_{2}$ |

Government deregulates (1−x) | ||

Independent power sales companies obeying $\text{}\left(z\right)$ | Independent power sales companies disobeying $\text{}\left(1-z\right)$ | |

Integrated power sales companies obeying $\text{}\left(y\right)$ | ${R}_{1}+{R}_{2}-\mathrm{H}$ ${P}_{1}-{\mathrm{B}}_{1}$ ${P}_{2}-{\mathrm{B}}_{2}$ | ${R}_{1}-\mathrm{H}$ ${P}_{1}-{\mathrm{B}}_{1}$ ${\mathrm{O}}_{2}$ |

Integrated power sales companies disobeying $\text{}\left(1-y\right)$ | ${R}_{2}-\mathrm{H}$ ${\mathrm{O}}_{1}$ ${P}_{2}-{\mathrm{B}}_{2}$ | $-\mathrm{H}$ ${\mathrm{O}}_{1}$ ${\mathrm{O}}_{2}$ |

External Variable | Definition | Value |
---|---|---|

${C}_{g}$ | Cost of regulation | 30 |

$\mathrm{H}$ | Loss of deregulation | 30 |

${P}_{e}$ | The price of green certificate | 0.1 |

$f$ | Unit punishment | 0.5 |

${q}^{T}$ | The RPS quota | 0.09 |

${q}_{1}^{1}$ | The initial quota of integrated power sales companies | 0.03 |

${q}_{1}^{2}$ | The ultimate quota of integrated power sales companies | 0.15 |

${W}_{1}$ | Total sales of integrated power sales companies | 40 |

${q}_{2}^{1}$ | The initial quota of independent power sales companies | 0.02 |

${q}_{2}^{2}$ | The ultimate quota of independent power sales companies | 0.13 |

${W}_{2}$ | Total sales of independent power sales companies | 30 |

${d}_{1}$ | Unit revenue of integrated power sales companies | 0.08 |

${d}_{2}$ | Unit revenue of independent power sales companies | 0.1 |

${g}_{1}$ | Unit power sales profits of integrated power sales companies | 0.005 |

${g}_{2}$ | Unit power sales profits of independent power sales companies | 0.003 |

$t$ | Unit social benefits | 0.5 |

$e$ | Unit reward | 0.1 |

Intermediate Variable | Definition | Formulation |
---|---|---|

${\mathrm{B}}_{i}$ | Gross green certificate cost | ${\mathrm{B}}_{i}={P}_{e}\left({q}_{i}^{2}-{q}_{i}^{1}\right){W}_{i}$ |

${\mathrm{F}}_{i}$ | Gross penalty | ${\mathrm{F}}_{i}=f\left({q}^{T}-{q}_{i}^{1}\right){W}_{i}$ |

${\mathrm{O}}_{i}$ | Gross opportunity revenue | ${\mathrm{O}}_{i}={d}_{i}{P}_{e}\left({q}_{i}^{2}-{q}_{i}^{1}\right){W}_{i}$ |

${P}_{i}$ | Gross power sales profits | ${P}_{i}={g}_{i}{W}_{i}$ |

${R}_{i}$ | Gross social benefits | ${R}_{i}=t\left({q}_{\mathrm{i}}^{2}-{q}_{\mathrm{i}}^{1}\right){W}_{i}$ |

${\mathrm{E}}_{i}$ | Gross reward | ${\mathrm{E}}_{i}=e\left({q}_{i}^{2}-{q}^{T}\right){W}_{i}$ |

Equilibrium Point | Eigenvalues | Attributes | ||
---|---|---|---|---|

${\mathrm{O}}_{1}=\left(0,0,0\right)$ | 2.25 | –0.3184 | –0.273 | Saddle point |

${\mathrm{O}}_{2}=\left(1,0,0\right)$ | –2.25 | 1.6826 | 1.857 | Saddle point |

${\mathrm{O}}_{3}=\left(0,1,0\right)$ | 0 | 0.3184 | –0.273 | Saddle point |

${\mathrm{O}}_{4}=\left(0,0,1\right)$ | –0.002 | –0.3184 | 0.273 | Saddle point |

${\mathrm{O}}_{5}=\left(1,1,0\right)$ | 0 | –1.3016 | 1.827 | Saddle point |

${\mathrm{O}}_{6}=\left(1,0,1\right)$ | 0.002 | 1.6016 | –1.885 | Saddle point |

${\mathrm{O}}_{7}=\left(0,1,1\right)$ | –0.122 | 0.3184 | 0.273 | Saddle point |

${\mathrm{O}}_{8}=\left(1,1,1\right)$ | 0.122 | –0.1616 | –0.657 | Saddle point |

${\mathrm{O}}_{9}=\left(0.257,0.771,0.903\right)$ | –1.172 | –0.391 | –0.257 | Stable point |

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**MDPI and ACS Style**

Xin, X.
Can a Dynamic Reward–Penalty Mechanism Help the Implementation of Renewable Portfolio Standards under Information Asymmetry? *Symmetry* **2020**, *12*, 670.
https://doi.org/10.3390/sym12040670

**AMA Style**

Xin X.
Can a Dynamic Reward–Penalty Mechanism Help the Implementation of Renewable Portfolio Standards under Information Asymmetry? *Symmetry*. 2020; 12(4):670.
https://doi.org/10.3390/sym12040670

**Chicago/Turabian Style**

Xin, Xing.
2020. "Can a Dynamic Reward–Penalty Mechanism Help the Implementation of Renewable Portfolio Standards under Information Asymmetry?" *Symmetry* 12, no. 4: 670.
https://doi.org/10.3390/sym12040670