An Evolutionary Game Theory Study for Construction and Demolition Waste Recycling Considering Green Development Performance under the Chinese Government’s Reward–Penalty Mechanism
Abstract
:1. Introduction
2. Literature Review
2.1. CDW Recycling in the Government’s Reward–Penalty Mechanism
2.2. GDP
2.3. Application of Evolutionary Game Theory
3. Model Formulation
4. Evolutionary Game Model Analysis
4.1. Calculation of Stable Points
4.2. Evolutionary Equilibrium Stability Analysis
- (1)
- When 0 < m < m0 and 0 < k < k0, the ESS of this system is (0, 0).
- (2)
- When 0 < m < m0 and k0 < k < 1, or m0 < m < m1 and k1 < k < 1, the ESS of this system is (0, 1).
- (3)
- When m0 < m < 1 and 0 < k < k0, or m1 < m < 1 and k0 < k < k1, the ESS of this system is (1, 0).
- (4)
- When m0 < m < m1 and k0 < k < k1, the ESS of this system is (0, 1) or (1, 0).
- (5)
- When m1 < m < 1 and k1 < k < 1, the ESS of this system is (1, 1).
4.3. Evolutionary Equilibrium Stability Analysis in Case (4) by Parameter Variation
5. Numerical Simulations and Discussion
5.1. The Effect of GDP on the Game Equilibrium
5.2. The Effect of the Government’s reward–Penalty Mechanism on the Game Equilibrium
5.2.1. The Effect of Parameters λ and λ’
5.2.2. The Effect of Parameter α
6. Conclusions
Implications
Author Contributions
Funding
Conflicts of Interest
References
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Unit | Parameter | Definition |
---|---|---|
Government | λ | The subsidy rate when both players participate in the game with high quality |
λ’ | The subsidy rate when only one player participates in the game with high quality | |
α | Probability of government supervision | |
CDW production unit | m | Green development performance |
πp | Profit from passive participation | |
Δπp | Profit from free-riding | |
CP | Basic cost | |
CP’ | Additional cost | |
Fp | Fine | |
CDW recycling unit | k | Green development performance |
πr | Profit from non-high-quality production of remanufactured products | |
Δπr | Profit from free-riding | |
Cr | Basic cost | |
Cr’ | Additional cost | |
Fr | Fine |
CDW Recycling Unit | |||
---|---|---|---|
H(y) | NH(1−y) | ||
CDW production unit | AP (x) | ||
NP (1−x) | |||
Stable Point | a11 | a12 | a21 | a22 |
---|---|---|---|---|
(0, 0) | 0 | 0 | ||
(0, 1) | 0 | 0 | ||
(1, 0) | 0 | 0 | ||
(1, 1) | 0 | 0 | ||
(x*, y*) | 0 | − | − | 0 |
Det(J) | Tr(J) | Stability | |
---|---|---|---|
(0, 0) | + | − | ESS |
(0, 1) | − | ? | Saddle point |
(1, 0) | − | ? | Saddle point |
(1, 1) | + | + | Unstable point |
Point | 0 < m < m0, k0 < k < 1 | m0 < m < m1, k1 < k < 1 | ||||
---|---|---|---|---|---|---|
Det(J) | Tr(J) | Stability | Det(J) | Tr(J) | Stability | |
(0, 0) | − | ? | Saddle point | + | + | Unstable point |
(0, 1) | + | − | ESS | + | − | ESS |
(1, 0) | + | + | Unstable point | − | ? | Saddle point |
− | ? | Saddle point | ||||
(1, 1) | + | + | Unstable point | − | ? | Saddle point |
− | ? | Saddle point |
Point | m0 < m < 1, 0 < k < k0 | m1 < m <1, k0 < k <k1 | ||||
---|---|---|---|---|---|---|
Det(J) | Tr(J) | Stability | Det(J) | Tr(J) | Stability | |
(0, 0) | − | ? | Saddle point | + | + | Unstable point |
(1, 0) | + | + | Unstable point | − | ? | Saddle point |
− | ? | Saddle point | ||||
(0, 1) | + | − | ESS | + | − | ESS |
(1, 1) | − | ? | Saddle point | − | ? | Saddle point |
+ | + | Unstable point |
Point | Det(J) | Tr(J) | Stability |
---|---|---|---|
(0, 0) | + | + | Unstable point |
(0, 1) | + | − | ESS |
(1, 0) | + | − | ESS |
(1, 1) | + | + | Unstable point |
(x*, y*) | + | 0 | Central point |
Point | Det(J) | Tr(J) | Stability |
---|---|---|---|
(0, 0) | + | + | Unstable point |
(0, 1) | − | ? | Saddle point |
(1, 0) | − | ? | Saddle point |
(1, 1) | + | − | ESS |
Parameter | m | k | α | λ | λ’ |
↑ | ↑ | ↑ | ↑ | ↑ | |
S1 | ↓ | ↑ | U | U | ↑ |
Parameter | Value | Parameter | Value |
---|---|---|---|
(x0, y0) | (0.5, 0.5) | πp | 140 |
m | 0.3 | πr | 280 |
k | 0.4 | Δπp | 70 |
α | 0.2 | Δπr | 80 |
λ | 0.08 | CP | 35 |
λ’ | 0.12 | Cr | 270 |
Fp | 50 | CP’ | 14 |
Fr | 50 | Cr’ | 60 |
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Long, H.; Liu, H.; Li, X.; Chen, L. An Evolutionary Game Theory Study for Construction and Demolition Waste Recycling Considering Green Development Performance under the Chinese Government’s Reward–Penalty Mechanism. Int. J. Environ. Res. Public Health 2020, 17, 6303. https://doi.org/10.3390/ijerph17176303
Long H, Liu H, Li X, Chen L. An Evolutionary Game Theory Study for Construction and Demolition Waste Recycling Considering Green Development Performance under the Chinese Government’s Reward–Penalty Mechanism. International Journal of Environmental Research and Public Health. 2020; 17(17):6303. https://doi.org/10.3390/ijerph17176303
Chicago/Turabian StyleLong, Hongyu, Hongyong Liu, Xingwei Li, and Longjun Chen. 2020. "An Evolutionary Game Theory Study for Construction and Demolition Waste Recycling Considering Green Development Performance under the Chinese Government’s Reward–Penalty Mechanism" International Journal of Environmental Research and Public Health 17, no. 17: 6303. https://doi.org/10.3390/ijerph17176303