Advanced game model of multi-agent environmental regulation strategy for sustainable production and consumption

Abstract

In response to escalating consumer demand for environmentally sustainable goods, China faces significant challenges in advancing green technology and ensuring sustainable production–consumption cycles through effective environmental governance. The eco-cost system supported by the European Union acts as a tool to convert consumer ecological preferences into manufacturing practices and provides regulators with quantifiable ecological metrics essential for meeting sustainability benchmarks. However, the practical application of the eco-cost framework to stimulate sustainable production–consumption dynamics in China is still an empirical question. This research examines the feasibility of the eco-cost system within China's sustainability strategy, using evolutionary game theory to model the interactions among consumers, producers, and regulators. The simulation predicts that consumer preference for eco-labeled products with lower eco-cost indices and their favored status among similar options will encourage manufacturers to initiate greening efforts, reducing environmental degradation in the production stage. This strategic consumer behavior is expected to lead to significant reductions in China's labor and fiscal expenditures, optimizing the dividends of resources, energy, and the environment. Empirical evidence supports the eco-cost system as an effective framework for China to achieve its sustainable production–consumption goals.

Appendices

Appendix

Analysis of the strategic stability of manufacturers:

$$ \begin{array}{*{20}c} {E_{11} = yz\left( {R_{P} - C_{{{\text{Ph}}}} + M_{P} } \right) + y\left( {1 - z} \right)\left( {R_{P} - C_{{{\text{Ph}}}} } \right) + \left( {1 - y} \right)z\left( {R_{P} - C_{{{\text{Ph}}}} + M_{P} } \right) + \left( {1 - y} \right)\left( {1 - z} \right)\left( {R_{P} - C_{{{\text{Ph}}}} } \right) } \\ \end{array} $$

(1)

$$ \begin{array}{*{20}c} { = z{\text{M}}_{{\text{P}}} + {\text{R}}_{{\text{P}}} - {\text{C}}_{{{\text{Ph}}}} } \\ \end{array} $$

(2)

$$ \begin{array}{*{20}c} {E_{12} = yz\left( { - C_{{{\text{pl}}}} - C_{P} - F_{P} } \right) + y\left( {1 - z} \right)\left( { - C_{{{\text{pl}}}} - C_{P} } \right) + \left( {1 - y} \right)z\left( {R_{P} - C_{{{\text{pl}}}} - C_{P} - B_{t} - F_{p} } \right)} \\ { + \left( {1 - y} \right)\left( {1 - z} \right)\left( {R_{p} - C_{{{\text{pl}}}} - C_{p} - B_{t} } \right) } \\ \end{array} $$

(3)

$$ \begin{array}{*{20}c} { = y\left( {B_{t} - R_{P} } \right) - zF_{p} + R_{P} - C_{P} - C_{{{\text{pl}}}} - B_{t} } \\ \end{array} $$

(4)

$$ \begin{array}{*{20}c} {\overline{{E_{1} }} = xE_{11} + \left( {1 - x} \right)E_{12} } \\ \end{array} $$

(5)

$$ \begin{array}{*{20}c} {{\raise0.7ex\hbox{${{\text{d}}x}$} \!\mathord{\left/ {\vphantom {{{\text{d}}x} {{\text{d}}t}}}\right.\kern-0pt} \!\lower0.7ex\hbox{${{\text{d}}t}$}} = x\left( {1 - x} \right)\left( {E_{11} - \overline{{E_{1} }} } \right) = x\left( {1 - x} \right)\left( {E_{11} - E_{12} } \right)} \\ \end{array} $$

(6)

$$ \begin{array}{*{20}c} { = x\left( {1 - x} \right)\left[ {y\left( {R_{P} - B_{t} } \right) + z\left( {M_{P} + F_{p} } \right) + C_{P} + C_{{{\text{Pl}}}} - C_{{{\text{Ph}}}} + B_{t} } \right]} \\ \end{array} $$

(7)

The first derivative of $x$ and the set $G\left( y \right)$ are, respectively:

$$ \begin{array}{*{20}c} {{\raise0.7ex\hbox{${{\text{d}}f\left( x \right)}$} \!\mathord{\left/ {\vphantom {{{\text{d}}f\left( x \right)} {{\text{d}}x}}}\right.\kern-0pt} \!\lower0.7ex\hbox{${{\text{d}}x}$}} = x\left( {1 - x} \right)\left[ {y\left( {R_{P} - B_{t} } \right) + z\left( {M_{P} + F_{p} } \right) + C_{P} + C_{{{\text{Pl}}}} - C_{{{\text{Ph}}}} + B_{t} } \right] } \\ \end{array} $$

(8)

$$ \begin{array}{*{20}c} {G\left( y \right) = y\left( {R_{P} - B_{t} } \right) + z\left( {M_{P} + F_{p} } \right) + C_{P} + C_{{{\text{Pl}}}} - C_{{{\text{Ph}}}} + B_{t} } \\ \end{array} $$

(9)

Analysis of the strategic stability of consumers:

$$ \begin{array}{*{20}c} {E_{21} = xz\left( {V_{t} + M_{t} } \right) + x\left( {1 - z} \right)V_{t} + \left( {1 - x} \right)z\left( {V_{t} + M_{t} } \right) + \left( {1 - x} \right)\left( {1 - z} \right)V_{t} } \\ \end{array} $$

(10)

$$ \begin{array}{*{20}c} { = zM_{t} + V_{t} } \\ \end{array} $$

(11)

$$ \begin{array}{*{20}c} {E_{22} = xz\left( {V_{t} - C_{t} - F_{p} } \right) + x\left( {1 - z} \right)\left( {V_{t} - C_{t} } \right) + \left( {1 - x} \right)z\left( {V_{t} - C_{t} + B_{t} - F_{t} } \right)} \\ { + \left( {1 - x} \right)\left( {1 - z} \right)\left( {V_{t} - C_{t} + B_{t} } \right)} \\ \end{array} $$

(12)

$$ \begin{array}{*{20}c} { = xz\left( {F_{t} - F_{p} } \right) - xB_{t} - zF_{t} + B_{t} - C_{t} + V_{t} } \\ \end{array} $$

(13)

$$ \begin{array}{*{20}c} {\overline{{E_{2} }} = xE_{21} + \left( {1 - x} \right)E_{22} } \\ \end{array} $$

(14)

$$ \begin{array}{*{20}c} {F\left( y \right) = {\raise0.7ex\hbox{${{\text{d}}y}$} \!\mathord{\left/ {\vphantom {{{\text{d}}y} {{\text{d}}t}}}\right.\kern-0pt} \!\lower0.7ex\hbox{${{\text{d}}t}$}} = y\left( {1 - y} \right)\left( {E_{21} - \overline{{E_{2} }} } \right) = y\left( {1 - y} \right)\left( {E_{21} - E_{22} } \right) } \\ \end{array} $$

(15)

$$ \begin{array}{*{20}c} { = y\left( {1 - y} \right)\left( {xz\left( {F_{p} - F_{t} } \right) + xB_{t} + z\left( {F_{t} + M_{t} } \right) - B_{t} + C_{t} } \right)} \\ \end{array} $$

(16)

Analysis of the strategic stability of China government regulators:

$$ \begin{array}{*{20}c} {E_{31} = xy\left( { - C_{g} - M_{P} - M_{t} + A_{g} } \right) + x\left( {1 - y} \right)\left( { - C_{g} - M_{P} + F_{t} + A_{g} } \right)} \\ { + \left( {1 - x} \right)y\left( { - C_{g} + F_{p} - M_{t} } \right) + \left( {1 - x} \right)\left( {1 - y} \right)\left( { - C_{g} + F_{P} + F_{t} - D_{g} } \right) } \\ \end{array} $$

(17)

$$ \begin{array}{*{20}c} { = - xyD_{g} + x\left( {A_{g} + D_{g} - F_{P} - M_{P} } \right) + y\left( {D_{g} - F_{t} - M_{t} } \right) + F_{P} - D_{g} - C_{g} + F_{t} } \\ \end{array} $$

(18)

$$ \begin{array}{*{20}c} {E_{32} = xyA_{g} + x\left( {1 - y} \right)A_{g} + \left( {1 - x} \right)y\left( 0 \right) + \left( {1 - x} \right)\left( {1 - y} \right)\left( { - D_{g} - T_{g} } \right) } \\ \end{array} $$

(19)

$$ \begin{array}{*{20}c} { = xy\left( { - D_{g} - T_{g} } \right) + x\left( {A_{g} + D_{g} + T_{g} } \right) + y\left( {D_{g} + T_{g} } \right) - D_{g} - T_{g} } \\ \end{array} $$

(20)

$$ \begin{array}{*{20}c} {\overline{{E_{3} }} = xE_{31} + \left( {1 - x} \right)E_{32} } \\ \end{array} $$

(21)

$$ \begin{array}{*{20}c} {{\raise0.7ex\hbox{${{\text{d}}z}$} \!\mathord{\left/ {\vphantom {{{\text{d}}z} {{\text{d}}t}}}\right.\kern-0pt} \!\lower0.7ex\hbox{${{\text{d}}t}$}} = z\left( {1 - z} \right)\left( {E_{31} - \overline{{E_{3} }} } \right) = z\left( {1 - z} \right)\left( {E_{31} - E_{32} } \right) } \\ \end{array} $$

(22)