18th International Conference on Innovative Computing, Information and Control (ICICIC2024)
Onsite (Qinhuangdao, China) and Online, September 10-13, 2024

PS-8: ICICIC2024-WS05-07
Four-Party Evolutionary Game Analysis on Environmental Governanceof Heavy Polluting Enterprises
Lin Wang* and Xinyuan Bai
School of Economics and Management (School of Tourism), Dalian University, Dalian 116622, P. R. China*Corresponding author: wanglin2@dlu.edu.cn

Introduction

Mathematical Formulas

In order to improve the efficiency of environmental
governance of heavily polluting enterprises, this paper
researches the multi-body model of environmental
governance of heavily polluting enterprises in China,
and establishes a four-party evolutionary game modelby placing the central eco-environment protection
inspection team, local governments, heavily polluting
enterprises and social supervisors under a unifiedframework.

𝑥𝑥̇̇ = (𝑥𝑥 − 1)(𝐶𝐶1 − 𝐶𝐶1 𝜆𝜆1 − 𝐹𝐹𝐹𝐹 + 𝐹𝐹𝐹𝐹 + 𝐹𝐹𝐹𝐹𝐹𝐹 − 𝐹𝐹𝐹𝐹𝐹𝐹)= 𝑓𝑓𝐴𝐴1 − 𝑓𝑓𝐴𝐴1𝑥𝑥(1)Research Questions

Conclusion

Reviewing the literature, the existing studies
mostly focus on the two- or three-party games in thecentral and local governments, enterprises andsociety, but the real environmental governanceinvolves multi-party subjects and lacks comprehensive
research. This paper integrates central ecoenvironment protection inspection team, local
government, heavily polluting enterprises, and social
monitors into a unified framework. It constructs afour-party evolutionary game model and conducts
theoretical analyses to address the shortcomings ofprevious studies.

There are seven unstable equilibrium points in thebenchmark model, and the remaining nine areconditionally stable equilibrium points, and there is noabsolute ESS. The study suggests the following. (i)Heavily polluting enterprises with active pollution
control are a necessary condition for local
environmental governance to meet the standard. (ii)
Local governments that implement strict regulatory
strategies and heavily polluting enterprises that adopt
active pollution control strategies bring about better
operation of the environmental governance system. (iii)
The impact of social monitors’ participation is limited
and cannot fundamentally shake the strategic choicesof key players.
In order to improve and perfect the environmental
governance of heavily polluting enterprises, thefollowing policy recommendations are proposed. First,
incentivize heavily polluting enterprises to actively treatpollution. Local governments can encourage heavily
polluting enterprises to adopt environmental protection
measures through economic incentives. Second,
strengthen communication and coordination between
the central and local governments to jointly promote
environmental governance. Third, establish adiversified monitoring mechanism. The government
encourages and supports the establishment of ananonymous online reporting system using the Internetand social media platforms.

Methodologies
In this paper, the method of evolutionary game isused to construct a four-party evolutionary game model,
and numerical simulation analysis is carried out.

18th International Conference on Innovative Computing, Information and Control (ICICIC2024)
Onsite (Qinhuangdao, China) and Online, September 10-13, 2024

TablesPayoff matrix for the four-way game model of environmental governance.
Table 1. Payment matrix

Central Ecoenvironment
Protection
Inspection
Team:
StrictRegulation

Local Gov:
StrictRegulation

Heavily Polluting Enterprises:
Active Treatment
Social Monitors:
Social Monitors:
ActivePassive
Participation
Participation

Π1 =−C1 + α E− β C0Π 2 =−C2 + E − C0+B + P − bΠ 3 =−C3 + R + bΠ 4 =−C4 + ωL+ωE

Π 5 =−C1 + α E− β C0

Π 6 =−C2 + E −C0 + B + P − bΠ 7 =−C3 + R + b
Π 8 =−λ4C4 + ωL+ωE

Heavily Polluting Enterprises:
Negative Treatment
Social Monitors:
Social Monitors:
Active Participation
PassiveParticipation
Π 9 =−C1 + α E − β C0
Π13 =−C1 + α E − β C0

Π10 =−C2 + E − C0 +B − Q + pf + ξ (∆f −HL )Π11 =−λ3C3 + R + RE− p ( f + ∆C3 ) − ξ (∆f+N)
Π12 =−C4 + ωL −

Π14 =−C2 + E − C0 +B − Q + pf
Π15 =−λ3C3 + R + RE− p( f + ∆C3 )Π16 =−λ4C4 + ωL −λ3−1ϕ E

λ3−1ϕ E + ξ ( H L + hωE )Local Gov:
LaxRegulation

Π17 =−C1 − α LΠ 21 =−C1 − α L −Π 25 =−C1 − α L − βλ2C0− βλ2C0 + uF

βλ2C0 + uF
Π 22 =−λ2C2 − L −λ2C0 − uF + P − λ2bΠ 23 =−C3 + R + λ2b
Π 24 =−λ4C4 − ϕL+ωE+uF
Π 26 =−λ2C2 − L − λ2C0

Π18 =−λ2C2 − L−λ2C0 − uF + P−λ2b − ∆C2
Π19 =−C3 + R+λ2bΠ 20 =−C4 − ϕ L+ hωL + ωE

Central Ecoenvironment
Protection
Inspection
Team:
LaxRegulation

Local Gov:
StrictRegulation

Π 37 =−λ1C1 + α E− β C0− β C0Π 34 =−C2 + E −Π 35 =−C3 + R + b
Π 36 =−C4 + ωL+ωE

βλ2C0 + uF
Π 30 =−λ2C2 − L −λ2C0 − uF − Q + qλ2 f
Π 31 =−λ3C3 + R +RE −q(λ2 f + ∆C3 )Π 32 =−λ4C4 − ϕ L−λ3−1ϕ E

λ3−1ϕ E + ξ (λ2 H L + hωE )Π 33 =−λ1C1 + α E

C0 + B + P − b−uF − Q + qλ2 f − ∆C2 +ξλ2 (∆f − H L )Π 27 =−λ3C3 + R + RE−q(λ2 f + ∆C3 ) −ξ (λ2 ∆f + N )Π 28 =−C4 − ϕ L + hωL −Π 29 =−C1 − α L −Π 38 =−C2 + E − C0+B + P − bΠ 39 =−C3 + R + b
Π 40 =−λ4C4 + ωL+ωE

Π 41 =−λ1C1 + α E− β C0Π 42 =−C2 + E − C0+ B − Q + pf +ξ (∆f − H L )Π 43 =−λ3C3 + R +RE − p ( f + ∆C3 ) −ξ (∆f + N )Π 44 =−C4 + ωL −

Π 45 =−λ1C1 + α E− β C0
Π 46 =−C2 + E − C0+ B − Q + pf
Π 47 =−λ3C3 + R +RE − p( f + ∆C3 )Π 48 =−λ4C4 + ωL
−λ3−1ϕ E

λ3−1ϕ E + ξ ( H L + hωE )Local Gov:
LaxRegulation

Π 49 =−λ1C1 − α LΠ 53 =−λ1C1 − α L −−βλ2C0 + vF

βλ2C0 + vF
Π 54 =−λ2C2 − L −λ2C0 − vF + P − λ2bΠ 55 =−C3 + R + λ2b
Π 56 =−λ4C4 − ϕL+ωE

Π 50 =−λ2C2 − L −λ2C0 − vF + P −λ2b − ∆C2
Π51 =−C3 + R + λ2bΠ52 =−C4 − ϕL+hωL + ωE

Π 57 =−λ1C1 − α L −βλ2C0 + vF
Π 58 =−λ2C2 − L −λ2C0 − vF − Q + qλ2 f−∆C2 + ξλ2 (∆f − H L )Π 59 =−λ3C3 + R + RE−q (λ2 f + ∆C3 ) −ξ (λ2 ∆f + N )Π 60 =−C4 − ϕ L + hωL−λ3−1ϕ E + ξ (λ2 H L +hωE )Π 61 =−λ1C1 − α L −βλ2C0 + vF
Π 62 =−λ2C2 − L −λ2C0 − vF − Q + qλ2 f
Π 63 =−λ3C3 + R +RE −q(λ2 f + ∆C3 )Π 64 =−λ4C4 − ϕ L−λ3−1ϕ E