# System Dynamics Analysis of Evolutionary Game Strategies between the Government and Investors Based on New Energy Power Construction Public-Private-Partnership (PPP) Project

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. The Mechanism of a Public-Private-Partnership (PPP) from the Game Perspective

#### 2.2. Theoretical Framing Analysis

#### 2.3. Evolutionary Game Model

#### 2.3.1. Game Payment Function

- (1)
- Participants in the game: the two participants in the evolution game of a new energy power construction PPP are the government and investors, and both of them have bounded rationality.
- (2)
- Participants’ behavior strategies: investors have two strategies, which are to actively cooperate and not to cooperate. An “active cooperation” (AC) strategy means that investors can cooperate with the government with a positive attitude to ensure the safety and smooth completion of projects, such as actively discussing construction plans, risk management, and regular maintenance of equipment. “Do not cooperate” (NC) refers to the inability of the project to go on-grid due to improper construction or management, resulting in social and economic losses. At the same time, the government has the duty to supervise and inspect investors, and it has two strategies that are, it supervises (S) and does not supervise (NS) whether investors actively cooperate. It can be seen as a result of the game between the government and investors whether investors actively cooperate with the government or not.
- (3)
- Probabilities of behavioral strategy: in the initial stage of the game between the government and investors, we suppose that the probability of the government choosing “S” is $x\left(0\le x\le 1\right)$, and then the probability of choosing “NS” is $1-x$. The probability of investors choosing “AC” is $y\left(0\le y\le 1\right)$, and then the probability of choosing “NC” is $1-y$. The game strategy combination is shown in Table 2.
- (4)
- Game payment functions: the revenue of the game matrix between the government and investors is shown in Table 3. The payment function of each strategy on game players are as follows.

#### 2.3.2. Evolutionarily Stable Strategy (ESS)

#### 2.4. System Dynamics (SD) Simulation Model

## 3. Case Study

#### 3.1. Data

#### 3.2. Results Analysis

## 4. Discussion

#### 4.1. Dynamic Reward

#### 4.2. Dynamic Punishment

## 5. Conclusions

- (1)
- The game system between the government and investors has four saddle points and one center point, and there is no ESS. System evolution is characterized by periodic behavior.
- (2)
- When the government implements dynamic bounty measures, the system evolution process is still a closed-loop with periodic motion. However, when the government implements dynamic punishment measures, the trajectory spiral of the evolution of game players tends to a stable focus, which indicates that the probability of the government supervision and investors’ cooperation gradually converge with the increase of time. Eventually, the equilibrium of ESS in the hybrid strategy can be reached.
- (3)
- The government can increase unit fine when making dynamic strategic adjustments, which will not only promote the active cooperation of investors, but also reduce the probability of government supervision, thereby reducing costs.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Cui, C.; Liu, Y.; Hope, A.; Wang, J. Review of studies on the public-private partnerships (PPP) for infrastructure projects. Int. J. Proj. Manag.
**2018**, 36, 773–794. [Google Scholar] [CrossRef] - National Energy Administration. Notice on Actively Promoting the Cooperation Model of Government and Social Capital in the Energy Sector. 2016. Available online: http://zfxxgk.nea.gov.cn/auto81/201604/t20160413_2232.htm?keywords (accessed on 31 March 2016).
- BJX Net. PPP Project Work Plan of China’s Provinces and Cities in 2018. 2018. Available online: http://huanbao.bjx.com.cn/news/20180314/885398.shtml (accessed on 14 March 2018).
- Yang, T.; Long, R.; Li, W. Suggestion on Tax Policy for Promoting the PPP Projects of Charging Infrastructure in China. J. Clean. Prod.
**2017**, 174, 133–138. [Google Scholar] [CrossRef] - Arbulú, I.; Lozano, J.; Rey-Maquieira, J. The challenges of tourism to waste-to-energy public-private partnerships. Renew. Sustain. Energy Rev.
**2017**, 72, 916–921. [Google Scholar] [CrossRef] - Akcay, E.C.; Dikmen, I.; Birgonul, M.T.; Arditi, D. Estimating the profitability of hydropower investments with a case study from Turkey. J. Civ. Eng. Manag.
**2017**, 23, 1002–1012. [Google Scholar] [CrossRef] - Nikitenko, S.M.; Goosen, E.V. Socio-economic development of territories based on the principles of public-private partnership in the sphere of comprehensive mineral exploration. In Proceedings of the International Scientific and Research Conference on Knowledge-Based Technologies in Development and Utilization of Mineral Resources, Novokuznetsk, Russia, 6–9 June 2017. [Google Scholar]
- Fantozzi, F.; Bartocci, P.; D’Alessandro, B.; Arampatzis, S.; Manos, B. Public-private partnerships value in bioenergy projects: Economic feasibility analysis based on two case studies. Biomass Bioenergy
**2014**, 66, 387–397. [Google Scholar] [CrossRef] - Wu, Y.; Xu, C.; Li, L.; Wang, Y.; Chen, K.; Xu, R. A risk assessment framework of PPP waste-to-energy incineration projects in China under 2-dimension linguistic environment. J. Clean. Prod.
**2018**, 183, 602–617. [Google Scholar] [CrossRef] - Emmanuel Cedrick, B.Z.; Long, W. Investment Motivation in Renewable Energy: A PPP Approach. Soc. Sci. Electron. Publ.
**2017**, 115, 229–238. [Google Scholar] - Song, J.; Song, D.; Zhang, X.; Sun, Y. Risk identification for PPP waste-to-energy incineration projects in China. Energy Policy
**2013**, 61, 953–962. [Google Scholar] [CrossRef] - Liu, J.; Wei, Q. Risk evaluation of electric vehicle charging infrastructure public-private partnership projects in China using fuzzy TOPSIS. J. Clean. Prod.
**2018**, 189, 211–222. [Google Scholar] [CrossRef] - Cai, L.R. System Dynamics Model for a Mixed-strategy Game of Environmental Pollution. Comput. Sci.
**2009**, 36, 234–238. [Google Scholar] - Kamarzaman, N.A.; Tan, C.W. A comprehensive review of maximum power point tracking algorithms for photovoltaic systems. Renew. Sustain. Energy Rev.
**2014**, 37, 585–598. [Google Scholar] [CrossRef] - Peng, B.; Gu, X.; Lu, Q. Analysis of Evolutionary Game of Stakeholders in Service-oriented Manufacturing Project Governance. J. Syst. Simul.
**2017**, 29, 595–608. [Google Scholar] - Shen, L.; Wang, Y. Collaboration of Public Service Contracting: An Evolutionary Game Analysis. Manag. Rev.
**2017**, 29, 219–230. [Google Scholar] - Zhao, X.; Zhang, Y. The System Dynamics (SD) Analysis of the Government and Power Producers’ Evolutionary Game Strategies Based on Carbon Trading (CT) Mechanism: A Case of China. Sustainability
**2018**, 10, 1150. [Google Scholar] [CrossRef] - Friedman, D. Evolutionary games in economics. Econometrica
**1991**, 59, 637–666. [Google Scholar] [CrossRef] - Ginits, H. Game Theory Evolving, 2nd ed.; Princeton University Press: Princeton, NJ, USA, 2009. [Google Scholar]
- Friedman, D. On economic applications of evolutionary game theory. J. Evol. Econ.
**1998**, 8, 15–43. [Google Scholar] [CrossRef][Green Version] - Zhao, X.G.; Jiang, G.W.; Li, A.; Li, Y. Technology, cost, a performance of waste-to-energy incineration industry in China. Renew. Sustain. Energy Rev.
**2016**, 55, 115–130. [Google Scholar] - State Statistical Bureau. China Energy Statistical Yearbook 2016; China Statistics Press: Beijing, China, 2017.
- State Statistical Bureau. China Environmental Statistics Yearbook 2016; China Statistics Press: Beijing, China, 2017.
- Zhao, X.G.; Zhang, Y.Z.; Ren, L.Z.; Zuo, Y.; Wu, Z.G. The policy effects of feed-in tariff and renewable portfolio standard: A case study of China’s waste incineration power industry. Waste Manag.
**2017**, 68, 711–723. [Google Scholar] - Song, J.; Sun, Y.; Jin, L. PESTEL analysis of the development of the waste-to-energy incineration industry in China. Renew. Sustain. Energy Rev.
**2017**, 80, 276–289. [Google Scholar] [CrossRef] - Li, Y.; Zhao, X.; Li, Y.; Li, X. Waste incineration industry and development policies in China. Waste Manag.
**2015**, 46, 234–241. [Google Scholar] [CrossRef] [PubMed] - CCGP Net. Pre-Confirmation of PPP Project for Waste Incineration Power Generation in Beihai City. 2017. Available online: www.ccgp.gov.cn/cggg/dfgg/cjgg/201711/t20171102_9099322.htm (accessed on 11 February 2017).
- Fan, R.; Dong, L. The dynamic analysis and simulation of government subsidy strategies in low-carbon diffusion considering the behavior of heterogeneous agents. Energy Policy
**2018**, 117, 252–262. [Google Scholar] [CrossRef] - Fang, G.; Tian, L.; Fu, M.; Sun, M. Government control or low carbon lifestyle? Analysis and application of a novel selective-constrained energy-saving and emission-reduction dynamic evolution system. Energy Policy
**2014**, 68, 498–507. [Google Scholar] [CrossRef]

**Figure 3.**The evolution of the probability of investors’ cooperation under different initial values.

**Figure 4.**The evolution of the probability of the government supervision under different initial values.

**Figure 6.**The system’s game process under dynamic reward. (

**a**) The probability of the government supervision under different rewards; (

**b**) the probability of investors’ cooperation under different rewards; (

**c**) the mixed game under dynamic rewards.

**Figure 7.**The system’s game process under dynamic punishment. (

**a**) The probability of the government supervision under different punishments; (

**b**) the probability of investors’ cooperation under different punishments; (

**c**) the mixed game under dynamic punishments.

Government’s Sole Proprietorship | Public-Private-Partnership (PPP) Mode | |
---|---|---|

Social capital participation | ${Y}_{-i}\left(k\right)-c$, ${U}_{i}\left({b}_{i}\right)+{U}_{-i}\left(b-{b}_{i}\right)$ | $\left(1-\varphi \right){Y}_{i}\left({b}_{e}-{b}_{m}\right)+{Y}_{-i}\left[k-\left({b}_{e}-{b}_{m}\right)-c\right]-c+{t}_{x}$, ${U}_{i}\left({b}_{e}\right)+{U}_{-i}\left(b-{b}_{m}\right)$ |

Social capital does not participate | ${Y}_{-i}\left(k\right)$, ${U}_{i}\left({b}_{i}\right)+{U}_{-i}\left(b-{b}_{i}\right)$ | ${Y}_{-i}\left(k\right)$, ${U}_{i}\left({b}_{e}\right)+{U}_{-i}\left(b-{b}_{m}\right)$ |

Game Players | Investors | ||
---|---|---|---|

$\mathbf{AC}\mathbf{\left(}\mathit{y}\mathbf{\right)}$ | $\mathbf{NC}\mathbf{(}\mathbf{1}\mathbf{-}\mathit{y}\mathbf{)}$ | ||

The government | S ($x$) | $\left(x,y\right)$ | $\left(x,1-y\right)$ |

NS ($1-x$) | $\left(1-x,y\right)$ | $\left(1-x,1-y\right)$ |

Game Players | Investors | ||
---|---|---|---|

$\mathbf{AC}\mathbf{\left(}\mathit{y}\mathbf{\right)}$ | $\mathbf{NC}\mathbf{(}\mathbf{1}\mathbf{-}\mathit{y}\mathbf{)}$ | ||

The government | S ($x$) | $\left({\pi}_{1},{u}_{1}\right)$ | $\left({\pi}_{2},{u}_{2}\right)$ |

NS ($1-x$) | $\left({\pi}_{3},{u}_{3}\right)$ | $\left({\pi}_{4},{u}_{4}\right)$ |

Local Equilibrium Point | $\mathbf{det}\left(\mathit{J}\right)$ | $\mathit{t}\mathit{r}\left(\mathit{J}\right)$ | Stability |
---|---|---|---|

$\left(0,0\right)$ | - | ± | Saddle Point |

$\left(0,1\right)$ | - | ± | Saddle Point |

$\left(1,0\right)$ | - | ± | Saddle Point |

$\left(1,1\right)$ | - | ± | Saddle Point |

$\left({x}^{\ast},{y}^{\ast}\right)$ | - | 0 | Center Point |

Variables | Value | Unit |
---|---|---|

The economic benefit of unit power generation ($ECB$) | 0.66 | Yuan/kWh |

The environmental benefit of unit power generation ($ENB$) | 0.68 | Yuan/kWh |

The human resource fee of unit power generation ($GSC$) | 0.11 | Yuan/kWh |

The subsidy of unit power generation ($US$) | 0.04 | Yuan/kWh |

The compensatory payment of unit power generation ($CP$) | 0.14 | Yuan/kWh |

The levelized cost of electricity of the project ($LCOE$) | 0.91 | Yuan/kWh |

The on-grid price of the project ($p$) | 0.65 | Yuan/kWh |

Installed capacity | 5.4 × 10^{6} | kW |

Annual utilization hours | 6000 | Hour |

Local Equilibrium Point | $\mathbf{det}\left({\mathit{J}}^{\prime}\right)$ | $\mathit{t}\mathit{r}\left({\mathit{J}}^{\prime}\right)$ | Stability |
---|---|---|---|

$\left(0,0\right)$ | - | ± | Saddle Point |

$\left(0,1\right)$ | - | ± | Saddle Point |

$\left(1,0\right)$ | - | ± | Saddle Point |

$\left(1,1\right)$ | - | ± | Saddle Point |

$\left(\begin{array}{l}\frac{LCOE-US-CP-p}{UF+y\times b},\\ \frac{\left(1-{y}^{2}\right)\times UF-GSC}{b}\end{array}\right)$ | - | 0 | Center Point |

Local Equilibrium Point | $\mathbf{det}\left({\mathit{J}}^{\u2033}\right)$ | $\mathit{t}\mathit{r}\left({\mathit{J}}^{\u2033}\right)$ | Stability |
---|---|---|---|

$\left(0,0\right)$ | - | ± | Saddle Point |

$\left(0,1\right)$ | - | ± | Saddle Point |

$\left(1,0\right)$ | - | ± | Saddle Point |

$\left(1,1\right)$ | - | ± | Saddle Point |

$\left(\begin{array}{l}\frac{LCOE-US-CP-p}{\left(1-y\right)\times UF+b},\\ \frac{\left(1+{y}^{2}\right)\times UF-GSC}{UF+b}\end{array}\right)$ | + | - | ESS |

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**MDPI and ACS Style**

Gao, L.; Zhao, Z.-Y. System Dynamics Analysis of Evolutionary Game Strategies between the Government and Investors Based on New Energy Power Construction Public-Private-Partnership (PPP) Project. *Sustainability* **2018**, *10*, 2533.
https://doi.org/10.3390/su10072533

**AMA Style**

Gao L, Zhao Z-Y. System Dynamics Analysis of Evolutionary Game Strategies between the Government and Investors Based on New Energy Power Construction Public-Private-Partnership (PPP) Project. *Sustainability*. 2018; 10(7):2533.
https://doi.org/10.3390/su10072533

**Chicago/Turabian Style**

Gao, Lei, and Zhen-Yu Zhao. 2018. "System Dynamics Analysis of Evolutionary Game Strategies between the Government and Investors Based on New Energy Power Construction Public-Private-Partnership (PPP) Project" *Sustainability* 10, no. 7: 2533.
https://doi.org/10.3390/su10072533