# What Role Should Government Play in the Personal Carbon Trading Market: Motivator or Punisher?

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## Abstract

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## 1. Introduction

## 2. Establishment of the Evolutionary Game Model

#### 2.1. Assumptions of the Evolutionary Game Model

#### 2.2. Establishment of the Replicator Dynamic Equations

## 3. Stability Analysis of the Evolutionary Game Model

#### 3.1. Stability Analysis for the Strategy of Government Departments

#### 3.2. Stability Analysis of the Strategy of CEEICA Individuals

#### 3.3. Stability Analysis for Their Strategies

## 4. Numerical Simulation

## 5. Discussion

## 6. Conclusions and Policy Suggestions

#### 6.1. Conclusions

#### 6.2. Policy Suggestions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Dynamic evolutionary paths for the strategies of government departments and CEEICA individuals: (

**a**) Condition No. 1; (

**b**) Condition No. 2; (

**c**) Condition No. 3; (

**d**) Condition No. 4; (

**e**) Condition No. 5; and (

**f**) Condition No. 6.

**Figure 2.**Dynamic evolutionary paths for each of the strategies under condition No. 1: (

**a**) Strategies of government departments; (

**b**) Strategies of CEEICA individuals.

**Figure 3.**Dynamic evolutionary paths for each of the strategies under condition No. 2: (

**a**) Strategies of government departments; (

**b**) Strategies of CEEICA individuals.

**Figure 4.**Dynamic evolutionary paths for each of the strategies under condition No. 3: (

**a**) Strategies of government departments; (

**b**) Strategies of CEEICA individuals.

**Figure 5.**Dynamic evolutionary paths for each of the strategies under condition No. 4: (

**a**) Strategies of government departments; (

**b**) Strategies of CEEICA individuals.

**Figure 6.**Dynamic evolutionary paths for each of the strategies under condition No. 5: (

**a**) Strategies of government departments; (

**b**) Strategies of CEEICA individuals.

**Figure 7.**Dynamic evolutionary paths for each of the strategies under condition No. 6: (

**a**) Strategies of government departments; (

**b**) Strategies of CEEICA individuals.

Symbol | Meaning |
---|---|

${T}_{A}$ | Initial carbon allowance of CEEICA individuals |

${T}_{H}$ | History carbon emissions of CEEICA individuals (i.e., the carbon dioxide emitted by CEEICA individuals in the last period) (${T}_{H}>{T}_{A}$). |

$p$ | Carbon price in the personal carbon trading market |

${K}_{N}$ | Reduced carbon emissions of CEEICA individuals (${K}_{N}$ times per unit of carbon emission reduction, $N=1,\text{}2$), where ${K}_{1}$ and ${K}_{2}$ represent the emission reductions obtained by following the “active plan” and “passive plan” strategy, respectively. |

${T}_{RN}$ | Actual carbon emissions of CEEICA individuals (${T}_{RN}={T}_{H}-{K}_{N}$, $N=1,\text{}2$), where ${T}_{R1}$ and ${T}_{R2}$ represent the emissions obtained by following the “active plan” and “passive plan” strategy, respectively (${T}_{R2}>{T}_{A}>{T}_{R1}$). |

${C}_{1}$ | Fixed cost for CEEICA individuals to participate in personal carbon trading (e.g., the cost for employing an independent party to validate or verify carbon emissions). |

${C}_{2}$ | Fixed cost for government departments for policy making and market management |

c | Cost of CEEICA individuals for reducing their per unit carbon emissions. |

$w$ | Public welfare obtained from the per unit carbon emissions reduction by CEEICA individuals (e.g., mitigating climate change and reducing energy consumption). |

$s$ | Subsidy for the per unit carbon emissions reduction when the actual carbon emissions of CEEICA individuals are less than the initial carbon allowance (i.e., the cost for government departments who played the “motivating policy”). |

$t$ | Carbon tax for the per unit carbon emissions when the actual carbon emissions of CEEICA individuals exceeded the initial carbon allowance (i.e., the benefit for government departments who played the “punitive policy”) |

Strategy Combinations | Payoff of Government Departments | Payoff of CEEICA Individuals |
---|---|---|

(G_{1}, P_{1}) | ${K}_{1}\times w-\left({T}_{A}-{T}_{R1}\right)\times s-{C}_{2}-\left({T}_{A}-{T}_{R1}\right)\times p$ | $\left({T}_{A}-{T}_{R1}\right)\times s-{K}_{1}\times c-{C}_{1}+\left({T}_{A}-{T}_{R1}\right)\times p$ |

(G_{1}, P_{2}) | ${K}_{2}\times w-{C}_{2}+\left({T}_{R2}-{T}_{A}\right)\times p$ | $-{K}_{2}\times c-{C}_{1}-\left({T}_{R2}-{T}_{A}\right)\times p$ |

(G_{2}, P_{1}) | ${K}_{1}\times w-{C}_{2}-\left({T}_{A}-{T}_{R1}\right)\times p$ | $-{K}_{1}\times c-{C}_{1}+\left({T}_{A}-{T}_{R1}\right)\times p$ |

(G_{2}, P_{2}) | ${K}_{2}\times w-{C}_{2}+\left({T}_{R2}-{T}_{A}\right)\times p+\left({T}_{R2}-{T}_{A}\right)\times t$ | $-{K}_{2}\times c-{C}_{1}-\left({T}_{R2}-{T}_{A}\right)\times p-\left({T}_{R2}-{T}_{A}\right)\times t$ |

No. | Condition | (X_{0},Y_{0}) | Equilibrium Point | $\mathit{Det}\left(\mathit{J}\right)$ | $\mathit{Tr}\left(\mathit{J}\right)$ | Result |
---|---|---|---|---|---|---|

1 | $\left({K}_{1}-{K}_{2}\right)\times c-\left({K}_{1}-{K}_{2}\right)\times p<\left({T}_{H}-{T}_{A}-{K}_{2}\right)\times t<\left({T}_{A}+{K}_{1}-{T}_{H}\right)\times s$ | ${X}_{0}<0$ ${Y}_{0}<0$ | ${B}_{1}\left(0,0\right)$ | $<0$ | Uncertain | SP |

${B}_{2}\left(1,0\right)$ | $>0$ | $>0$ | UP | |||

${B}_{3}\left(0,1\right)$ | $>0$ | $<0$ | ESS | |||

${B}_{4}\left(1,1\right)$ | $<0$ | Uncertain | SP | |||

2 | $\left({K}_{1}-{K}_{2}\right)\times c-\left({K}_{1}-{K}_{2}\right)\times p>\left({T}_{A}+{K}_{1}-{T}_{H}\right)\times s>\left({T}_{H}-{T}_{A}-{K}_{2}\right)\times t$ | ${X}_{0}>1$ ${Y}_{0}<0$ | ${B}_{1}\left(0,0\right)$ | $>0$ | $<0$ | ESS |

${B}_{2}\left(1,0\right)$ | $<0$ | Uncertain | SP | |||

${B}_{3}\left(0,1\right)$ | $<0$ | Uncertain | SP | |||

${B}_{4}\left(1,1\right)$ | $>0$ | $>0$ | UP | |||

3 | $\left({T}_{H}-{T}_{A}-{K}_{2}\right)\times t<\left({K}_{1}-{K}_{2}\right)\times c-\left({K}_{1}-{K}_{2}\right)\times p<\left({T}_{A}+{K}_{1}-{T}_{H}\right)\times s$ | $0<{X}_{0}<1$ ${Y}_{0}<0$ | ${B}_{1}\left(0,0\right)$ | $>0$ | $<0$ | ESS |

${B}_{2}\left(1,0\right)$ | $>0$ | $>0$ | UP | |||

${B}_{3}\left(0,1\right)$ | $<0$ | $<0$ | SP | |||

${B}_{4}\left(1,1\right)$ | $<0$ | $>0$ | SP | |||

4 | $\left({K}_{1}-{K}_{2}\right)\times c-\left({K}_{1}-{K}_{2}\right)\times p>\left({T}_{H}-{T}_{A}-{K}_{2}\right)\times t>\left({T}_{A}+{K}_{1}-{T}_{H}\right)\times s$ | ${X}_{0}<0$ ${Y}_{0}>1$ | ${B}_{1}\left(0,0\right)$ | $>0$ | $<0$ | ESS |

${B}_{2}\left(1,0\right)$ | $<0$ | Uncertain | SP | |||

${B}_{3}\left(0,1\right)$ | $<0$ | Uncertain | SP | |||

${B}_{4}\left(1,1\right)$ | $>0$ | $>0$ | UP | |||

5 | $\left({K}_{1}-{K}_{2}\right)\times c-\left({K}_{1}-{K}_{2}\right)\times p<\left({T}_{A}+{K}_{1}-{T}_{H}\right)\times s<\left({T}_{H}-{T}_{A}-{K}_{2}\right)\times t$ | ${X}_{0}>1$ ${Y}_{0}>1$ | ${B}_{1}\left(0,0\right)$ | $<0$ | Uncertain | SP |

${B}_{2}\left(1,0\right)$ | $>0$ | $>0$ | UP | |||

${B}_{3}\left(0,1\right)$ | $>0$ | $<0$ | ESS | |||

${B}_{4}\left(1,1\right)$ | $<0$ | Uncertain | SP | |||

6 | $\left({T}_{H}-{T}_{A}-{K}_{2}\right)\times t>\left({K}_{1}-{K}_{2}\right)\times c-\left({K}_{1}-{K}_{2}\right)\times p>\left({T}_{A}+{K}_{1}-{T}_{H}\right)\times s$ | $0<{X}_{0}<1$ ${Y}_{0}>1$ | ${B}_{1}\left(0,0\right)$ | $<0$ | $<0$ | SP |

${B}_{2}\left(1,0\right)$ | $<0$ | $>0$ | SP | |||

${B}_{3}\left(0,1\right)$ | $>0$ | $<0$ | ESS | |||

${B}_{4}\left(1,1\right)$ | $>0$ | $>0$ | UP |

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## Share and Cite

**MDPI and ACS Style**

Guo, D.; Chen, H.; Long, R.
What Role Should Government Play in the Personal Carbon Trading Market: Motivator or Punisher? *Int. J. Environ. Res. Public Health* **2019**, *16*, 1905.
https://doi.org/10.3390/ijerph16111905

**AMA Style**

Guo D, Chen H, Long R.
What Role Should Government Play in the Personal Carbon Trading Market: Motivator or Punisher? *International Journal of Environmental Research and Public Health*. 2019; 16(11):1905.
https://doi.org/10.3390/ijerph16111905

**Chicago/Turabian Style**

Guo, Daoyan, Hong Chen, and Ruyin Long.
2019. "What Role Should Government Play in the Personal Carbon Trading Market: Motivator or Punisher?" *International Journal of Environmental Research and Public Health* 16, no. 11: 1905.
https://doi.org/10.3390/ijerph16111905