Evolutionary Game Analysis of Industrial Robot-Driven Air Pollution Synergistic Governance Incorporating Public Environmental Satisfaction

Abstract

Against the dual backdrop of worsening air pollution and industrial intelligent transformation, industrial robot technology has become an important means to promote air pollution synergistic governance. This study innovatively incorporates public environmental satisfaction and industrial robot application as dynamic mechanism variables, constructing an evolutionary game model involving the government, industrial enterprises, and the public. Through theoretical analysis and numerical simulation, the study reveals the influence mechanism of key cost–benefit parameters on stakeholders’ strategic interaction and the system’s evolution path. The conclusions are as follows: (1) The government’s environmental supervision directly affects enterprises’ green transformation willingness, and enterprises’ behavior reversely impacts public satisfaction and supervision effectiveness, forming a “supervision–response–feedback” closed-loop. (2) The cost and benefit parameters related to industrial robots are crucial for the evolution of the game system, and there is significant heterogeneity in their impact on the strategic choices of the three parties. The robot adaptation transformation of enterprise industrial depends on the comprehensive consideration of the transformation cost and the green benefits. Public supervision is regulated by both the supervision cost and the incentive benefit. The government regulation takes into account both the regulatory cost and the loss of social reputation. Various parameters dynamically regulate the system’s equilibrium by altering the party’s cost–benefit structure. (3) The application of industrial robots and the feedback of public environmental satisfaction form a coupling effect, jointly determining the long-term evolution direction of the game system. When the cost benefit and supervision incentives are well-matched, enterprises will actively promote the green transformation of industrial robots in order to achieve intelligent pollution control. The effectiveness of public supervision has also been fully realized. The dynamic adaptation of the two components can lead the system towards an efficient and stable equilibrium in air pollution governance.

1. Introduction

In recent years, China’s rapid industrialization and urbanization have driven improvements in the quality and efficiency of the economy. However, this process has also led to serious air pollution, including PM2.5, which has had a profound impact on the high-quality development of the economy and public health [1]. Facing the increasingly severe problem of air pollution, the shortcomings of the traditional governance model in terms of efficiency and effectiveness have become clear. There is an urgent need for artificial intelligence technology to provide systematic support, and industrial robots are precisely the core technological vehicle for achieving intelligent governance. In the “Several Opinions on Promoting the High-Quality Development of Environmental Protection Equipment Manufacturing”, China has clearly stated the need to develop intelligent pollution-control equipment, such as environmental protection robots, and to enhance air quality by strengthening technological innovation. The “Digital Transformation Plan for the National Ecological Environment Monitoring Network” issued in 2025 established the overall design for the digital transformation of the monitoring system. This plan encourages the utilization of artificial intelligence to establish an environmental monitoring center, thereby enhancing the ability to monitor air pollution. Therefore, the technological breakthroughs in China’s industrial robot industry and the deepening of the institutional reforms for air pollution governance jointly constitute the “supply side” and “demand side” of collaborative governance. As exemplary representatives of advanced production tools in the new productive forces, industrial robots not only facilitate industrial intelligent transformation but also align with the development concept of green, low-carbon growth [2]. Crucially, industrial robots have effectively reduced emissions by optimizing energy use and efficiency, enhancing pollution treatment capabilities, and driving green technological innovation [3]. Therefore, industrial robots are the key technological enablers of the transformation from endpoint governance to source-based prevention and control. Industrial robots can effectively reconfigure the unified logic between environmental and economic benefits, thereby becoming the core engine driving the synergistic governance of air pollution.

In the process of air pollution governance, the public, as the key feedback party, serves as both a social benchmark for measuring governance effectiveness and a driving force for optimizing the governance system. Therefore, incorporating public environmental satisfaction into the system is both theoretically and practically necessary. This governance is essentially a synergistic system in which multiple stakeholders interact through dynamic strategies to jointly shape the governance path in pursuit of different goals. While industrial robots provide technological support for air pollution governance, their actual environmental benefits still depend on governance systems and coordination among multiple parties Furthermore, as direct perceivers of environmental quality, the public’s expectations regarding air quality will affect their satisfaction [4]. The public’s environmental satisfaction, in turn, profoundly influences government regulation and enterprises’ decisions through social supervision and market selection. Specifically, the application of industrial robots in the green transformation of industrial enterprises can effectively reduce the emission intensity and total emissions of carbon dioxide and sulfur dioxide in the industry, promote green development, and achieve synergistic governance of environmental pollution and carbon emissions [5]. Meanwhile, the application of industrial robots contributes to reducing carbon dioxide emissions by promoting high-quality economic development [6]. In this process, population density plays a crucial supporting role [7]. This situation underscores the public’s role in understanding the mechanism linking industrial robot use to air pollution. Continuous improvements in air quality and the public’s subjective assessments of pollution governance efforts both positively influence residents’ sense of well-being [8] and effectively enhance the government’s environmental governance capabilities [9]. Public satisfaction also exerts a reciprocal influence on industrial enterprises’ environmental behavior and technology adoption decisions through social supervision and public opinion pressure. Therefore, establishing a tripartite, synergistic governance mechanism that is oriented towards public environmental satisfaction, guided by government regulations, and based on industrial enterprises’ responsibility to fulfill, becomes the key to maximizing the emission-reduction potential of industrial robots and promoting continuous improvement in air quality.

Existing related studies have richly revealed the influencing factors and pathways of air pollution governance, but they mostly explain its logic from a theoretical perspective or through empirical analysis. However, these studies failed to depict the systematic decision-making issues involving multiple parties in air pollution governance, nor did they account for the driving mechanisms of cutting-edge technologies such as artificial intelligence. In fact, industrial robots have already established a complete chain-driven model for monitoring and governance in various application scenarios, gradually becoming the core engine driving the synergistic governance of air pollution. In conclusion, this study aims to address the following issues. (1) How do variables such as regulatory intensity, special green subsidies for industrial robots, and reward and punishment systems interact with the application of industrial robots and public environmental satisfaction, thereby breaking through the traditional static research limitations of air pollution governance? (2) In the case of a three-party evolutionary game, how do the costs of each party affect the choice of strategies by the parties and the process of system co-evolution? (3) How does public environmental satisfaction dynamically influence government regulatory strategies, decisions on industrial enterprises’ robotization, and governance effectiveness through social supervision and public opinion pressure? The main contribution of this study lies in: (1) This study incorporates industrial robots as the core endogenous variable and public environmental satisfaction as a dynamic feedback factor into the analytical framework. This study breaks through the limitations of traditional static research and strengthens the core role and theoretical connection of robots in air pollution governance. (2) This study employs the evolutionary game theory approach to construct a multi-party decision-making model involving the government, industrial enterprises, and the public. This study regards the adaptation and transformation of robots as the core strategy of the enterprise, and comprehensively depicts the interaction and synergistic evolution path among multiple parties. (3) This study uses numerical simulation to identify the influence patterns of key parameters on the system evolution, providing a new perspective and decision-making basis for robot-driven air pollution synergistic governance.

2. Literature Review

2.1. Related Research on Promoting Air Pollution Governance by Industrial Robots

Industrial robots are a new type of intelligent manufacturing technology that deeply integrates digital technologies such as big data, 5G, and cloud computing. They can be remotely invoked and operated by setting system parameters, and are widely applied in multiple industrial fields [10]. Scholars have noted that industrial robots, as the core carrier of intelligent manufacturing, possess advantages such as high efficiency and stability, and thus have significant value and impact in the application of air pollution synergistic. And scholars explored the driving role of industrial robots from the perspectives of governance effectiveness and mechanisms. For instance, Usman et al. explored that the application of artificial intelligence technology has significantly enhanced the effectiveness in preventing and controlling the hazards of air pollution [11]. Acemoglu D and Restrepo P focused on the technical mechanism level. They showed that industrial robots, with their advantages such as high precision and high stability, can be used to continuously develop new equipment, providing a solid foundation for the application of environmental governance [12]. Yu et al. further focused on the structural efficiency of industrial robots, exploring their dual attributes of energy-efficiency improvement and green innovation-driven characteristics, and concluded that technology empowerment optimizes resource and energy efficiency and reduces air pollution [13].

In the field of industrial robot driving, scholars have primarily conducted research on industrial structure upgrading, green innovation, and technological progress. Qin et al. explored, from the perspective of optimizing and upgrading the industrial structure, an intelligent development path centered on the application of industrial robots, which can effectively reduce the pollution emission intensity per unit output [5]. Based on this, Supekard et al. explored the practical application of industrial robots. They analyzed how to promote improvements in energy efficiency in the production process during the transformation and upgrading of the industrial structure [14]. Gan et al. conducted a study to explore the positive enabling effect of industrial robots on the green innovation of industrial enterprises by constructing two paths: reducing labor costs and adjusting the structure of human capital [15]. Lee et al. conducted a cross-national study using verification methods to examine measures taken to increase green R&D investment to enhance the application of industrial robots [16]. Furthermore, scholars have noted that industrial robots have facilitated the intelligent upgrading of pollution-detection and treatment facilities, thereby enhancing the technological level of governance and processing efficiency. Yin et al. conducted an empirical analysis to examine the effectiveness of industrial intelligence and verified the synergistic enhancement relationship between this effect and the technological absorption capacity [17]. Roy et al. further expanded the understanding of the technological effects of industrial robots in pollution governance. They analyzed the efficacy of robot technology in promoting the green transformation of industrial production systems by optimizing the clean production process [18]. Furthermore, industrial robots enhance the efficiency of governance and management processes, thereby enabling industrial enterprises to strengthen their green technological innovation efforts. As a result, industrial enterprises not only achieved quality improvement and efficiency enhancement, but also effectively reduced urban energy consumption and air pollution emissions [19].

Furthermore, the research on air pollution governance also focuses on the issue of synergistic participation by multiple parties. Scholars have revealed the complex and dynamic relationships among multiple parties through various methods. Shen et al. incorporated government regulation optimization and public participation empowerment into the research framework. They explored the core path for industrial enterprises to achieve synergistic benefits from pollution reduction and carbon emissions through the application of industrial robots [20]. Guo Jinhua et al. considered the dual influences of policy-driven factors and public pressure for green consumption and identified the factors influencing industrial enterprises’ robot adoption [21]. Furthermore, the public, driven by their desire for environmental satisfaction, uses social pressure and market selection to compel governments and enterprises to improve their behavior. This can lead to a positive interaction among the public, the government, and enterprises.

2.2. Related Research on Public Environmental Satisfaction

Public environmental satisfaction refers to the public’s subjective evaluation of the government’s environmental governance and response capabilities, and it also reflects the degree of public trust in the government [22]. Huang, from a social psychological perspective, by comparing the public’s experience of the environment with their psychological expectations, pointed out that the connotation of public environmental satisfaction is the public’s subjective assessment of the gap between the current environmental situation and their expectations [23]. Tang et al. analyzed the core indicators of ecological civilization construction performance and concluded that public satisfaction with the environment is the public’s direct perception of a good ecological environment [22]. This study, by reviewing the existing research literature, discovers that public environmental satisfaction is the comprehensive outcome of a “perception–pressure–response” closed-loop dynamic interaction and strategic game involving three factors: the government’s governance efficiency, industrial enterprises’ environmental behavior, and public social pressure.

There is a significant positive correlation between the government’s environmental protection image and public satisfaction with the environment. When the objective environment is unlikely to improve significantly in the short term, optimizing the government’s environmental image can be an effective way to enhance public environmental satisfaction [24]. From the perspective of the performance model, scholars generally believe that public evaluation and satisfaction mainly depend on the government’s performance [25]. When the public is satisfied with the government’s environmental performance, this satisfaction will translate into broader political support and more active public participation. Jia et al. investigated the pathways through which government environmental performance satisfaction is influenced and found that enhancing public environmental awareness and strengthening government credibility can effectively increase environmental satisfaction [26]. However, the transformation of government credibility and public satisfaction is always rigorously tested by the quality of the objective environment. Even if the government gains high public trust, if environmental quality does not achieve a substantial, perceptible improvement, satisfaction will still be undermined. Based on this, scholars have conducted multi-perspective discussions. Chen et al. examined the influencing factors of public environmental satisfaction from both positive and negative perspectives. They argued that the positive impact was the government’s strong enforcement of pollution control measures, while the negative impact was the perception of air pollution [27]. Jia et al. investigated strategies to enhance public participation and found that improving the government’s environmental governance performance can significantly promote sustainable public participation [26].

Furthermore, scholars have noted that industrial enterprises are the main sources of air pollution and constitute a key party in the application of green technologies. Industrial enterprise behavior is complexly associated with public environmental satisfaction. Enderle et al. explored, from a sustainable development perspective, the experiences and achievements of industrial enterprises in fulfilling environmental responsibilities and reducing waste emissions during their development [28]. Lund-Thomsen regarded the natural environment as an important stakeholder of enterprises, and argued that environmental responsibility is an inherent obligation that enterprises must undertake in the process of profit-making [29]. At the same time, green investment by industrial enterprises underpins their environmental performance. Public perception and trust are the key factors in enhancing their environmental satisfaction. Blacconiere et al. based on the positive effects of environmental information disclosure, examined how the market and the public regarded such disclosure as an important signal of a company’s environmental risk management capability [30]. Lan et al. found that public trust in industrial enterprises is negatively correlated with their willingness to engage in confrontational behavior, indicating that the pollution behavior of industrial enterprises will reduce public environmental satisfaction [31].

2.3. Implications and Shortcomings of Existing Research

The existing research provides the theoretical foundation for this study. The main implications are centered on three aspects: First, the existing literature clarifies, at the technical level, the mechanisms by which industrial robots achieve emission reduction through paths such as energy efficiency improvement, structural upgrading, and green innovation. Second, at the governance level, existing research reveals the feedback effect of public environmental satisfaction as a performance evaluation indicator on the government’s credibility, the reputation of enterprises, and public participation. Third, by involving the three main entities—the government, industrial enterprises, and the public—an interactive mechanism and policy coordination foundation for environmental governance is established. This research provides a basis for constructing the tripartite game model in this study.

In response to the aforementioned research, this study finds that although the academic community has conducted numerous studies into the pollution-control effects of industrial robots and public environmental satisfaction, there remains a significant gap in systematic research that combines these two aspects. First, existing research often treats public satisfaction as an exogenous or static variable, failing to incorporate it as an endogenous feedback mechanism within dynamic models. This study internalizes it as a dynamic feedback variable that links government regulation and corporate decision-making, revealing the dual roles of public satisfaction in the governance process involving multiple stakeholders, and further elaborating the micro-dynamic mechanism of multi-party collaborative governance. Second, existing research predominantly adopts a single-subject perspective or focuses solely on bilateral relationships such as “government–industrial enterprises” or “public–government,” lacking a systematic analysis that places all three parties within a unified dynamic game–theoretical framework. Especially in the context of multi-party collaborative governance, there is no comprehensive theoretical model regarding how the three parties can achieve collaborative evolution through strategic interaction. To address this research gap, this study constructs a three-party evolutionary game model of “government–industrial enterprises–public” by analyzing the strategy dependence and feedback mechanisms among the entities, thereby expanding the model’s boundaries and analytical dimensions in environmental governance research. Third, in the existing literature, studies on the emission-reduction effects of industrial robots mostly employ macroscopic measurement methods, failing to deeply explore the microscopic mechanisms underlying their impact. Furthermore, industrial robots are generally treated as exogenous technological shocks, failing to reveal their underlying logic in shaping corporate green production decisions from an evolutionary game–theoretical perspective. In view of this, this study incorporates industrial robots as a technological driving variable into the three-party evolutionary game framework. At the same time, long-term numerical simulations are introduced to visually depict the evolutionary paths and characteristics of the system under different policy parameters, providing a solid theoretical basis and methodological foundation for clarifying the evolutionary logic of environmental collaborative governance.

3. Problem Description and Model Assumptions

3.1. Problem Description

Industrial robots, as the core technical carrier for air pollution synergistic governance, can deeply empower pollution control through four key paths: source reduction, precise process pollution control, end-of-line automated treatment, and intelligent monitoring and feedback loop. Industrial robots can optimize production and pollution control parameters, increase raw material utilization, and reduce pollutant generation at the source. Industrial robots can also capture pollutants in real time and autonomously operate pollution control equipment, thereby avoiding secondary pollution. At the same time, industrial robots have promoted the total factor productivity of industrial enterprises, achieving the coordinated development of environmental benefits and production efficiency. For instance, in Guangzhou, the compound quadruped robot dog “Su·eGo” has been deployed for environmental monitoring. This robot dog can conduct real-time online monitoring of PM2.5, PM10, and nearly 15 types of harmful gases. The robotic dog significantly enhances the efficiency of regional air pollution monitoring and governance and serves as a crucial support for the green transformation of industrial enterprises and the resolution of air pollution governance challenges. This study focuses on three core parties: the government, industrial enterprises, and the public. This study is based on the background of the introduction and application of industrial robots, and explores the strategy interaction and synergistic evolution mechanism among the three parties guided by public environmental satisfaction, as shown in Figure 1.

In the synergistic governance system for air pollution, the three main parties-the government, industrial enterprise, and the public-have formed a close and dynamic connection regarding the introduction and application of industrial robots. The strategies of the three parties interact and evolve dynamically, as shown in Figure 2. Among them, the government, as the regulator, guides enterprises to introduce industrial robots through regulatory and incentive policies to facilitate their green transformation. Industrial enterprise, as the main party for robot application and emission reduction implementation, makes decisions on whether to undergo transformation based on cost–benefit considerations. The actions of industrial enterprises directly determine the effectiveness of industrial robots in reducing emissions, and thereby affect the success of air pollution governance and public environmental satisfaction. As the perceivers and supervisors of environmental quality, the public generates social pressure through feedback based on their satisfaction levels. The public not only forces enterprises to introduce industrial robots to achieve green transformation, but also urges the government to optimize regulatory strategies and implement relevant incentive and regulatory measures for the application of robots. The three parties have formed a close strategic linkage regarding the introduction and application of industrial robots, with mutual influence and mutual restraint. How to fully leverage the pollution governance empowerment effect of industrial robots through tripartite strategy collaboration, avoid falling into the governance predicament of “weak government regulation, extensive production by enterprises, and passive supervision by the public”, and achieve the positive evolution of the tripartite strategy, is the core issue that this study urgently needs to address.

3.2. Model Hypothesis

The above analysis reveals a competitive relationship among the three parties to conduct a more in-depth analysis, this study makes the following basic hypotheses:

H1. 

The government is Participant 1, the industrial enterprises are Participant 2, and the public is Participant 3. The government, industrial enterprises, and the public are all decision-makers with bounded rationality. Their strategic choices gradually evolve and stabilize at optimal strategies. At the initial stage, none of the party can predict the optimal strategy. Instead, they dynamically adjust their behavior by learning and imitating high-yield strategies during the game process. The system’s equilibrium state results from the long-term interaction and evolution of various methods, rather than from a one-time static game.

H2. 

The strategic options chosen by the government are {strict regulation, lenient regulation}. The probability of choosing strict regulation is $x$, while the probability of choosing lenient regulation is $1-x$, $x\in \left[0,1\right]$. “Strict regulation” means that the government will provide special technical subsidies and tax rate reductions to enterprises that have carried out green transformation by introducing industrial robots, directly reducing the overall costs of robot application transformation for these enterprises. At the same time, it will punish enterprises that have not introduced industrial robots and continue traditional production, raising the cost of non-transformation behavior, guiding enterprises to introduce industrial robots to achieve green transformation, and ensuring the effectiveness of air pollution control through the implementation of robot application through strict regulation. “Lenient regulation” means that neither subsidies and tax reduction incentives for enterprises to introduce industrial robots for green transformation were provided, nor were effective penalties and constraints imposed on enterprises that did not introduce industrial robots and maintained traditional high-pollution production. As a result, due to the lack of regulation, the air pollution governance effect of industrial robots could not be fully exerted.

The strategic options available to industrial enterprises are {robotic adaptation transformation, traditional extensive production}. The probability of taking an active transformation is $y$, then the probability of some enterprises choosing a passive transformation is $1-y$, $y\in \left[0,1\right]$. Industrial enterprises, as users of industrial robots, may either continue the negative transformation strategy of extensive production driven by profit motives or choose an active transformation strategy in response to policy incentives and reputation maintenance. “Robot Adaptation Transformation” refers to the process by which industrial enterprises introduce industrial robots to promote green transformation, integrating them deeply into the entire production process to achieve pollution control and emission reduction in all aspects. This approach enhances production efficiency, achieves a win-win situation between environmental and economic benefits, avoids pollution penalties, and accumulates green reputation to gain market advantages. “Traditional extensive production” refers to the situation in which industrial enterprises choose not to introduce industrial robots and instead maintain traditional production methods, continuing extensive operations with high energy consumption and high emissions. This approach not only misses out on the transformation opportunities offered by the development of industrial robots, but also fails to achieve pollution source control and efficient emission reduction, and to enhance production efficiency. Moreover, it faces multiple risks such as government fines for pollution, public claims, and damage to social reputation.

The strategic options chosen by the public are {active supervision, passive supervision}. The probability of choosing satisfaction-driven supervision is $z$, and the probability of choosing individual-interest-oriented supervision without willingness to supervise is $1-z$, $z\in \left[0,1\right]$. “Active supervision” refers to the situation where the public, through social supervision and public opinion pressure, forces enterprises to regulate their environmental behaviors, prompting enterprises to actively introduce industrial robots to implement green transformation. At the same time, the public also supervises the government to strictly implement relevant incentive and regulatory policies, ensuring that the emission reduction effect of industrial robots is fully exerted, and helping to enhance the overall effectiveness of air pollution governance. “Passive oversight” refers to the lack of effective public oversight of corporate environmental practices and external pressure from government regulation. This not only reduces enterprises’ motivation to introduce industrial robots for green transformation, but also makes it difficult for industrial robots to exert their air pollution governance effects. As a result, the collaborative dilemma in air pollution governance is exacerbated.

H3. 

The cost of strict government supervision is $C_1$. The degree of supervision is represented by coefficient $\alpha$, where $0<\alpha <1$. This cost primarily includes expenses related to environmental enforcement inspections, responding to public complaints, and verifying the implementation of industrial robotics applications. The government provides special green technology subsidies $G$ to industrial enterprises that undertake green transformation by introducing industrial robots, and sets a comprehensive tax rate reduction coefficient of $1-\gamma$, so that their actual tax burden becomes $\gamma$ times the base tax rate $t$ $\left(0<\gamma <1\right)$. At the same time, the government offers rewards $E$ for the public’s active supervision behavior, and imposes fines $F$ on enterprises that do not introduce industrial robots and continue to engage in traditional high-pollution production.

If the government opts for lenient regulation, there will be neither subsidies nor tax reduction incentives for enterprises to introduce industrial robots, nor will there be effective penalties imposed on polluting traditional production enterprises. In this situation, economic growth will suffer a loss of $P$ due to air pollution, and social reputation will also suffer a loss of $H_1$ due to the decline in public environmental satisfaction.

H4. 

When industrial enterprises adopt the “traditional extensive production” strategy, if they do not introduce industrial robots to maintain traditional production, they can obtain a short-term profit $R_2$. This strategy corresponds to an extensive mode of operation with high energy consumption and emissions, and there are no costs associated with the application of industrial robots or technical upgrade benefits. The benefits for industrial enterprises of adopting an active transformation strategy include the active introduction of industrial robots and their deployment in production. When industrial enterprises adopt the “robot adaptation transformation” strategy, the short-term benefits they obtain are $R_1$, and $R_1<R_2$. This situation is related to short-term factors such as equipment investment and production adjustments. Meanwhile, industrial enterprises need to bear the direct costs $C_2$ related to the green transformation, such as the equipment purchase premium for industrial robots, installation and maintenance, and technical training. They can also receive green technology subsidies $G$ and comprehensive tax rate reductions provided by the government. The actual tax burden is $\gamma$ times the base tax rate $t$. If an industrial enterprise opts for the “traditional extensive production” strategy without introducing industrial robots and causes pollution, in addition to paying the government fine $F$, it will also suffer a loss of social reputation $S$ due to air pollution, and a loss of social reputation $H_2$ due to the pollution behavior. Moreover, this loss will intensify as the public’s environmental satisfaction decreases.

H5. 

The public opts for active supervision with a cost of $C_3$, which includes expenditures such as environmental information collection and supervision feedback. At this point, they can receive supervision rewards  $E$ from the government. If industrial enterprises do not introduce industrial robots and cause air pollution, the public will suffer health losses  $L$  and will demand health loss compensation  $S$  from the polluting enterprises. If the public opts for passive supervision, they will not bear the costs of supervision as well as the related rewards and compensation benefits. If industrial enterprises fail to introduce industrial robots to maintain traditional production and cause pollution due to the lack of supervision constraints, the public will passively suffer from the corresponding health losses. Moreover, due to the absence of supervision, it will be difficult to promote green transformation in enterprises, and the government’s strict regulation will ultimately affect their environmental rights and satisfaction.

Based on the above assumptions, the parameter settings and definitions are shown in

Table 1. Parameter settings and definitions.

Parameters	Meaning
$C_1$	The regulatory costs of the government under strict supervision.
$\alpha$	The coefficient of the government regulatory intensity.
$G$	The government provides special green technology subsidies to industrial enterprises that introduce industrial robots and undertake green transformation.
$\gamma$	The ratio of the actual tax burden to the base tax rate.
$t$	Enterprises comprehensive tax rate benchmark value.
$E$	The government’s rewards for the public’s active supervision of environmental behavior.
$F$	Fines for enterprises that do not introduce industrial robots and continue with traditional high-pollution production methods.
$P$	The loss of economic growth due to air pollution.
$H_1$	The loss of social reputation due to the decline in public environmental satisfaction.
$R_1$	The short-term benefits that industrial enterprises obtain by choosing the “robotic adaptation transformation” strategy.
$R_2$	The short-term benefits of industrial enterprises choosing the “traditional extensive production” strategy.
$C_2$	Industrial enterprises bear the direct costs related to the green transformation, such as the equipment purchase premium, installation and maintenance, and technical training for industrial robots.
$S$	The compensation demanded by the public from polluting enterprises for health losses.
$H_2$	The loss of social reputation suffered by industrial enterprises due to their polluting activities.
$C_3$	The cost of public active supervision.
$L$	The health loss of the public resulting from air pollution caused by industrial enterprises’ failure to adopt industrial robots.

.

3.3. Payment Matrix

Based on the above assumptions of the evolutionary game, the payment matrix among the government, industrial enterprises, and the public is derived, as shown in

Table 2. Payment matrix of the government, industrial enterprises, and the public.

Game Participants				Government
				$\mathbf{Strict} \mathbf{Regulation} (\mathit{x})$	$\mathbf{Lenient} \mathbf{Regulation} (1-\mathit{x})$
Public	Active supervision $(z)$	Industrial enterprises	Robotic adaptation transformation $(y)$	$-C_1+t\gamma R_1-E-G$ $R_1-C_2-t\gamma R_1+G$ $-C_3+E$	$-\alpha C_1+t{R}_1-P-H_1$ $-C_2+(1-t)R_1$ $-C_3$
			Lenient regulation $(1-y)$	$-C_1+t{R}_2-E+F$ $R_2-t{R}_2-F-S-H_2$ $-C_3-L+E+S$	$-\alpha C_1+t{R}_2-P-H_1+\alpha F$ $R_2-t{R}_2-\alpha F-H_2$ $-C_3-L$
	Passive supervision $(1-z)$	Industrial enterprises	Robotic adaptation transformation $(y)$	$-C_1+ t\gamma R_1-G$ $R_1-C_2-t\gamma R_1+G$ 0	$-\alpha C_1+t{R}_1-P$ $-C_2+(1-t)R_1$ 0
			Lenient regulation $(1-y)$	$-C_1+t{R}_2+F$ $R_2-t{R}_2-F-H_2$ $-L$	$-\alpha C_1+t{R}_2-P+\alpha F$ $R_2-t{R}_2-\alpha F-H_2$ $-L$

.

4. Model Construction and Analysis

4.1. Model Construction

The theoretical framework of evolutionary game theory encompasses fields such as game theory and evolutionary theory. Evolutionary game theory is typically used to study the evolutionary process of individual strategies in natural selection and population dynamics. This theory emphasizes that the behavioral strategies of game participants evolve dynamically over time. The evolutionary game theory then determines whether these strategies satisfy the evolutionary stable strategy (ESS) through stability analysis. To investigate decision-making for industrial robot-driven synergistic air pollution governance incorporating public environmental satisfaction, this study constructs a replication dynamic equation based on the approach of Taylor et al. [32] to describe the evolution of these strategies within the synergistic governance system for air pollution. Furthermore, this study combines evolutionary stable strategy analysis to examine the stability of equilibrium points, ultimately revealing the system’s collective strategy convergence direction and its long-term stability trend.

4.1.1. Analysis of Government Policy Stability

The expected benefit $E_{11}$ for the government choosing the strict regulatory strategy is:

$$\begin{array}{l}{E}_{11}=yz(-C_1+t\gamma R_1-E-G)+y(1-z)(-C_1+ t\gamma R_1-G)+\\ z(1-y)(-C_1+t{R}_2-E +F)+(1-y)(1-z)(-C_1+t{R}_2+F)\end{array}$$

(1)

The expected benefit $E_{12}$ for the government choosing the lenient regulatory strategy is:

$$\begin{array}{l}{E}_{12}=yz(-\alpha C_1+t{R}_1-P-H_1)+y(1-z)(-\alpha C_1+t{R}_1-P)+\\ z(1-y)(-\alpha C_1+t{R}_2-P -H_1+\alpha F)+(1-y)(1-z)(-\alpha C_1+t{R}_2-P+\alpha F)\end{array}$$

(2)

The average expected return $\overline{E_1}$ of the government’s strategy selection is:

$$\overline{E_1}=x{E}_{11}+(1-x)E_{12}$$

(3)

This leads to the replication dynamic equation $F(x)$ for the government’s choice strategy as follows:

$$\begin{array}{l}F(x)=dx/dt=x(E_{11}-\overline{E_1})=x (x-1)(C_1-F-P-\alpha C_1+\alpha F+y F+\\ zE+yG-z H_1-\alpha yF+ty{R}_1-\gamma ty{R}_1)\end{array}$$

(4)

4.1.2. Analysis of Industrial Enterprises’ Strategy Stability

The expected return $E_{21}$ for industrial enterprises choosing the robot adaptation transformation strategy is:

$$\begin{array}{l}{E}_{21}=xz[R_1-C_2-t\gamma R_1+G]+ x(1-z)[R_1-C_2-t\gamma R_1+G]+\\ z(1-x)[-C_2+R_1\left(1-t\right)]+(1-x)(1-z)[-C_2+R_1\left(1-t\right)]\end{array}$$

(5)

The expected return $E_{22}$ for industrial enterprises choosing the traditional extensive production strategy is:

$$\begin{array}{l}{E}_{22}=xz[R_2-t{R}_2-F-S-H_2]+ x(1-z)[R_2-t{R}_2-F- H_2]+\\ z(1-x)[R_2-t{R}_2-\alpha F-H_2]+(1-x)(1-z)[R_2-t{R}_2-\alpha F -H_2]\end{array}$$

(6)

The average expected return $\overline{E_2}$ for the selection strategy of industrial enterprises is:

$$\overline{E_2}=x{E}_{21}+(1-x)E_{22}$$

(7)

This leads to the replication dynamic equation $F(y)$ for industrial enterprises’ choice strategy as follows:

$$\begin{array}{l}F(y)=dy/dt=y(E_{21}-\overline{E_2})=-y(y-1)(H_2-C_2+R_1-R_2+\alpha F+\\ xF+xG-t{R}_1+t{R}_2-\alpha xF+tx{R}_1+xzS-\gamma tx{R}_1)\end{array}$$

(8)

4.1.3. Analysis of Public Strategy Stability

The expected benefit $E_{31}$ for the public choosing the active supervision strategy is:

$$\begin{array}{l}{E}_{31}=xy(-C_3+E)+x(1-y)(-C_3-L+E+S)+\\ y(1-x)(-C_3)+(1-x)(1-y)(-C_3-L)\end{array}$$

(9)

The expected benefit $E_{32}$ for the public choosing the passive supervision strategy is:

$$E_{32}=x(1-y)(-L)+(1-x)(1-y)(-L)$$

(10)

The average expected return $\overline{E_3}$ for the selection strategy of the public is:

$$\overline{E_3}=x{E}_{31}+(1-x)E_{32}$$

(11)

This leads to the replication dynamic equation $F(z)$ for industrial the public’s choice strategy as follows:

$$F(z)=dz/dt=z(E_{31}-\overline{E_3})=z(z-1) (C_3-xE-xS+xyS)$$

(12)

4.2. Stability Analysis of Equilibrium Strategies in the Game System

After conducting individual equilibrium strategy analyses for the government, industrial enterprises, and the public, this study further conducts an overall analysis of the stability of the air pollution governance game system. Based on Equations (4), (8) and (12), a replication dynamic equation system is constructed, as shown in Equation (13). The proof of the dynamic equation can be found in Supplementary Material File S1.

$$\left\{\begin{array}{l}F(x)=x(x-1)(C_1-F-P-\alpha C_1+\alpha F+y F+z E+yG-z H_1-\alpha yF+ty{R}_1-\gamma ty{R}_1)\\ F(y)=-y(y-1)(H_2-C_2+R_1-R_2+\alpha F+xF+xG-t{R}_1+t{R}_2-\alpha xF+tx{R}_1+xzS-\gamma tx{R}_1)\\ F(z)=z(z-1)(C_3-xE-xS+xyS)\end{array}\right.$$

(13)

Setting $F\left(x\right)=0,F\left(y\right)=0,F\left(Z\right)=0$, eight potential equilibrium points of the game system are obtained. It is considered that in asymmetric dynamic games, mixed strategies are not necessarily in evolutionarily stable equilibria. Therefore, this study conducts only an asymptotic stability analysis of the pure-strategy equilibrium points of the game system. The remaining points are all non-asymptotically stable states. To analyze the stability of the equilibrium point, a Jacobian matrix based on the replicative dynamic equation is constructed, as shown in Equations (14)–(23).

$$J=\left[\begin{array}{ccc}\begin{array}{l}\frac{\partial F(x)}{dx}\\ \frac{\partial F(y)}{dx}\\ \frac{\partial F(z)}{dx}\end{array}& \begin{array}{l}\frac{\partial F(x)}{dy}\\ \frac{\partial F(y)}{dy}\\ \frac{\partial F(z)}{dy}\end{array}& \begin{array}{l}\frac{\partial F(x)}{dz}\\ \frac{\partial F(y)}{dz}\\ \frac{\partial F(z)}{dz}\end{array}\end{array}\right]=\left[\begin{array}{ccc}\begin{array}{l}{a}_{11}\\ a_{21}\\ a_{31}\end{array}& \begin{array}{l}{a}_{12}\\ a_{22}\\ a_{32}\end{array}& \begin{array}{l}{a}_{13}\\ a_{23}\\ a_{33}\end{array}\end{array}\right]$$

(14)

$$a_{11}=(2x-1)(C_1-F-P-\alpha C_1+\alpha F+yF+zE+yG-z{H}_1-\alpha yF+ty{R}_1-\gamma ty{R}_1)$$

(15)

$$a_{12}=x(x-1)(F+G-\alpha F+t{R}_1-\gamma t{R}_1)$$

(16)

$$a_{13}=x(x-1)(E-H_1)$$

(17)

$$a_{21}=-y(y-1)(F+G-\alpha F+t{R}_1+zS-\gamma t{R}_1)$$

(18)

$$a_{22}=(-2y+1)(H_2-C_2+R_1-R_2+\alpha F+xF+xG-t{R}_1+t{R}_2-\alpha xF+tx{R}_1+xzS-\gamma tx{R}_1)$$

(19)

$$a_{23}=xy(1-y)S$$

(20)

$$a_{31}=z(1-z)(E+S-yS)$$

(21)

$$a_{32}=xz(z-1)S$$

(22)

$$a_{33}=(2z-1)(C_3-xE-xS+xyS)$$

(23)

This study substitutes each equilibrium point into the Jacobian matrix and, by calculating the eigenvalues at each point, obtains the corresponding Jacobian matrices, as shown in

Table 3. Eigenvalues of the Jacobian matrices corresponding to each equilibrium point.

Equilibrium Point	${\mathit{\lambda }}_1$	${\mathit{\lambda }}_2$	${\mathit{\lambda }}_3$
$E_1(0,0,0)$	$F-C_1+P+\alpha C_1-\alpha F$	$\begin{array}{l}{H}_2-C_2+R_1-R_2+\alpha F\\ -t{R}_1+t{R}_2\end{array}$	$-C_3$
$E_2(0,1,0)$	$P-G-C_1+\alpha C_1-t{R}_1+\gamma t{R}_1$	$\begin{array}{l}{C}_2-H_2-R_1+R_2-\alpha F\\ +t{R}_1-t{R}_2\end{array}$	$-C_3$
$E_3(0,0,1)$	$\begin{array}{l}F-E-C_1+H_1+P+\\ \alpha C_1-\alpha F\end{array}$	$\begin{array}{l}{H}_2-C_2+R_1-R_2+\alpha F\\ -t{R}_1+t{R}_2\end{array}$	$C_3$
$E_4(0,1,1)$	$\begin{array}{l}{H}_1-E-G-C_1+P+\\ \alpha C_1-t{R}_1+\gamma t{R}_1\end{array}$	$\begin{array}{l}{C}_2-H_2-R_1+R_2-\alpha F \\ +t{R}_1-t{R}_2\end{array}$	$C_3$
$E_5(1,0,0)$	$C_1-F-P-\alpha C_1+\alpha F$	$\begin{array}{l}F-C_2+G+H_2+R_1-\\ R_2+t{R}_2-\gamma t{R}_1\end{array}$	$E-C_3+S$
$E_6(1,1,0)$	$C_1+G-P-\alpha C_1+t{R}_1-\gamma t{R}_1$	$\begin{array}{l}{C}_2-F-G-H_2-R_1+\\ R_2-t{R}_2+\gamma t{R}_1\end{array}$	$E-C_3$
$E_7(1,0,1)$	$\begin{array}{l}{C}_1+E-F-H_1-P-\\ \alpha C_1+\alpha F\end{array}$	$\begin{array}{l}F-C_2+G+H_2+R_1-\\ R_2+S+t{R}_2-\gamma t{R}_1\end{array}$	$C_3-E-S$
$E_8(1,1,1)$	$\begin{array}{l}{C}_1+E+G-H_1-P-\\ \alpha C_1+t{R}_1-\gamma t{R}_1\end{array}$	$\begin{array}{l}{C}_2-F-G-H_2-R_1+\\ R_2-S-t{R}_2+\gamma t{R}_1\end{array}$	$C_3-E$

.

The stability of each equilibrium point fluctuates with changes in parameter values, and the system’s evolution path changes accordingly. Therefore, this study examines the system’s stability by varying parameter conditions across the eight scenarios described below. Based on Lyapunov’s first method [33], the signs of the eigenvalues of the Jacobian matrix can be used to determine the stability of the equilibrium point; that is, if the real parts of all three eigenvalues of the Jacobian matrix are less than 0, then this equilibrium point is evolutionarily stable. If the real parts of the three eigenvalues of the Jacobian matrix are all greater than 0, then this point is unstable. If there are 1 or 2 eigenvalues in the Jacobian matrix whose real parts are positive, then this point is a saddle point. The specific content is shown in

Table 4. Eigenvalues of the Jacobian matrices corresponding to each equilibrium point and stability analysis.

Equilibrium Point	Real Part Symbol	Stable Conditions	Stability Results
$E_1(0,0,0)$	$(-,-,-)$	$F - C_1+ P+ \alpha C_1-\alpha F<0$; $H_2-C_2+R_1- R_2+\alpha F-t{R}_1+t{R}_2<0$; $-C_3<0$	ESS
$E_2(0,1,0)$	$(-,-,-)$	$P+\alpha C_1<t{R}_1-\gamma t{R}_1+G+C_1$; $C_2-H_2<\alpha F+R_1-t{R}_1-R_2+t{R}_2$; $-C_3<0$	ESS
$E_3(0,0,1)$	$(\times ,\times ,+)$	$F-E-C_1+H_1+P+\alpha C_1-\alpha F$; $H_2-C_2+R_1-R_2+\alpha F-t{R}_1+t{R}_2$; $C_3$	Saddle point
$E_4(0,1,1)$	$(\times ,\times ,+)$	$H_1-E-G-C_1+P+\alpha C_1-t{R}_1+\gamma t{R}_1$; $C_2-H_2-R_1+R_2-\alpha F +t{R}_1-t{R}_2$; $C_3$	Saddle point
$E_5(1,0,0)$	$(-,-,-)$	$C_1-F-P-\alpha C_1+\alpha F<0$; $F+G<C_2-H_2-R_1+\gamma t{R}_1+R_2-t{R}_2$; $E+S<C_3$	ESS
$E_6(1,1,0)$	$(-,-,-)$	$C_1+G<\gamma t{R}_1-t{R}_1+P+\alpha C_1$; $C_2-R_1+R_2-t{R}_2+\gamma t{R}_1<F+G+H_2$; $E<C_3$	ESS
$E_7(1,0,1)$	$(-,-,-)$	$C_1+E-F-H_1-P-\alpha C_1+\alpha F<0$; $F+G<C_2-H_2-R_1+R_2-S-t{R}_2+\gamma t{R}_1$; $C_3<E+S$	ESS
$E_8(1,1,1)$	$(-,-,-)$	$C_1+ E + G< \gamma t{R}_1-t{R}_1+ H_1+ P +\alpha C_1$; $C_2<F+G+ H_2+ R_1-\gamma t{R}_1+ t{R}_2-R_2+S$; $C_3<E$	ESS

Note: $\times$ indicates an uncertain symbol.

.

This study primarily explores the strategy selection for industrial robot-driven air pollution control, taking into account synergistic air pollution governance that incorporates public environmental satisfaction, as well as factors that influence the government’s choice of regulation strategies. Therefore, this study sets the government’s strategy as a strict regulation. Furthermore, this study selected $E_6(1,1,0)$, $E_7(1,0,1)$, and $E_8(1,1,1)$ as the three equilibrium points for discussion. Based on this, this study mainly highlights the decisive role of industrial robot application in achieving balance and stability.

Situation 1: When $C_1+G<\gamma t{R}_1-t{R}_1+P+\alpha C_1$, $C_2-R_1+R_2-t{R}_2+\gamma t{R}_1<F+G+H_2$ and $E<C_3$, the eigenvalues of the Jacobian matrix corresponding to $E_6(1,1,0)$ are all less than 0. The strategy combination has evolved stably toward (strict government regulation, robot adaptation transformation, and passive public supervision). In this situation, although the government needs to bear the regulatory costs in the short term, the intelligent monitoring and automatic pollution control capabilities of industrial robots can significantly reduce the regulatory costs $C_1$ such as environmental protection law enforcement and robot on-site verification by the government, improve the pollution control performance and reduce economic losses $P$. The long-term cost savings in regulation and the increase in social benefits are sufficient to cover the industrial robot application subsidies $G$ and the tax reduction expenditures. Therefore, the government will adopt a strict regulatory strategy. Industrial robots reduce the marginal cost of enterprise transformation $C_2$ by optimizing production processes, enhancing energy utilization efficiency, and implementing source reduction measures, and generating efficiency gains and green reputation benefits. When the comprehensive benefits of robot applications exceed the investment costs, industrial enterprises will actively implement robot adaptation transformation. With the stable use of industrial robots in industrial enterprises and strict government regulation, air quality and public environmental satisfaction have significantly improved. The marginal benefits of public supervision have decreased, and ultimately, the public tends to engage in passive supervision.

Situation 2: When $C_1+E-F-H_1-P-\alpha C_1+\alpha F<0$, $F+G<C_2-H_2-R_1+R_2-S-t{R}_2+\gamma t{R}_1$ and $C_3<E+S$, the eigenvalues of the Jacobian matrix corresponding to $E_7(1,0,1)$ are all less than 0. The strategy combination has evolved stably toward (strict government regulation, traditional extensive production, and active public supervision). In this situation, industrial enterprises did not adopt industrial robots but continued to use high-carbon, extensive production methods, resulting in high pollution emission intensity, significant regulatory difficulties, and increased regulatory costs. However, the government can make up for the regulatory expenses $C_1$ by imposing heavy fines $F$ on polluting enterprises. At the same time, in order to avoid the economic losses $P$ caused by air pollution and the reputational damage $H_1$ resulting from a decline in public satisfaction, the government will still maintain a strict regulatory strategy. Furthermore, the current cost of purchasing robots is high, and short-term returns are not significant, resulting in a negative net benefit for industrial enterprises in terms of robot transformation. At this point, industrial enterprises would rather bear the heavy fines $F$ and suffer the reputational damage $H_1$ than carry out the robot adaptation transformation. At the same time, the extensive production methods of enterprises have caused air pollution, harmed public health and led to lower satisfaction levels. The government rewards $E$ and the enterprise compensations $S$ that the public actively supervision are higher than the supervision costs $C_3$. Therefore, the public opts for the active monitoring strategy. Therefore, the government should increase special subsidies and tax exemptions for the application of industrial robots, and strengthen supervision and penalty measures. The public should actively participate in environmental supervision and promptly express their environmental demands, thereby encouraging industrial enterprises to accelerate the transformation towards robot adaptation.

Situation 3: When $C_1+ E + G < \gamma t{R}_1-t{R}_1+ H_1+ P +\alpha C_1$, $C_2<F+G+ H_2+ R_1-\gamma t{R}_1+ t{R}_2-R_2+S$ and $C_3<E$, the eigenvalues of the Jacobian matrix corresponding to $E_8(1,1,1)$ are all less than 0. The strategy combination has evolved stably around (strict government regulation, robot adaptation transformation, and active public supervision). In this situation, relying on industrial robots to achieve full-process pollution control and emission reduction can significantly reduce the government regulatory costs $C_1$. The comprehensive gains subject to strict government supervision, namely the avoided reputational damage $H_1$, the avoided economic losses $P$, the saved costs from lenient supervision $\alpha C_1$, and the reduced taxes, all combined, are much greater than the total cost. Therefore, it is economically feasible for the government to implement strict supervision. Furthermore, the extensive application of industrial robots can help enterprises in the industrial sector improve quality, increase efficiency, reduce pollution and emissions. Coupled with multiple incentives such as government subsidies and tax reductions, the net benefits of robot adaptation transformation are significantly higher than those of traditional, less efficient production methods. Therefore, robot adaptation transformation in industrial enterprises is a rational choice. At the same time, the public can receive government rewards $E$ for their active supervision. This, in turn, promotes the robot adaptation transformation in industrial enterprises, thereby effectively improving air quality. At this point, the benefits of public active supervision outweigh the costs. The three parties achieve a synergistic win-win. This balance indicates that industrial robots are the core technical support for achieving efficient, synergistic governance and are also the key condition for achieving the dual goals of air pollution governance and improving public satisfaction. In conclusion, the government should improve subsidy and supervision mechanisms, and the public should actively participate in environmental supervision. Together, they should guide industrial enterprises to incorporate the application of industrial robots into their long-term development strategies and jointly enhance the effectiveness of air pollution governance.

5. Numerical Simulation

To ensure the robustness of the evolutionary results of the game system, to guarantee that the core parameters and basic assumptions align with actual governance scenarios, and to visually observe the system’s evolutionary trend, this study conducts numerical simulation analysis of the constructed three-party evolutionary game model. The simulation process uses a control-variable approach: a single core variable is varied to assess its impact on the system’s stability strategy, while the values of the other variables remain constant. Parameter assignment involves selecting multiple authoritative data sources across various dimensions. At the policy level, we refer to the macro data on policy subsidies, tax exemptions, and administrative penalties for industrial pollution control as provided in the “China Intelligent Manufacturing Industry Development Report (2023–2024)” and the “China Environmental Statistical Yearbook” issued by the Ministry of Industry and Information Technology. At the enterprise level, based on the annual reports of representative manufacturing enterprises such as Gree Electric Appliances, we extract micro-level data related to the transformation costs and tax incentives for industrial robots. At the same time, this study draws on the parameter assignment ideas of Yu [34] and Zhang et al. [35], and applies standardized scaling and dimensionless processing to the above macro and micro data to eliminate differences in units and regional and industrial deviations in actual values. This will ensure that the parameters reflect only the relative magnitudes of the variables, rather than their actual amounts, thereby guaranteeing the generality and universality of the simulation results. The specific values of the relevant parameters are shown in

Table 5. Initial assignments of key parameters.

Parameter	Assignment	Parameter	Assignment	Parameter	Assignment
$C_1$	10	$R_1$	18	$F$	4
$C_2$	20	$R_2$	35	$P$	6
$C_3$	5	$G$	3	$H_1$	6
$\alpha$	0.7	$E$	6	$S$	5
$H_2$	3	$\gamma$	0.5	$t$	0.2
$L$	6

.

5.1. Simulation Analysis of Initial Probability

Considering that the government, industrial enterprises, and the public all have a strong desire for collaborative air pollution governance driven by industrial robots, the initial values for the three parties are set as $x=0.5,y=0.5,z=0.5$. By substituting the initial values of the key parameters for the three parties into Equation (13), it can be seen that simultaneous changes in the initial intentions of the three parties have different effects on the evolutionary trajectories, as shown in Figure 3. The horizontal axis in the figure represents the passage of time, while the vertical axis reflects the probability of the parties’ strategy choices. The curve depicts the process of behavioral evolution. As shown in the figure, the threshold for simultaneous changes in the initial intentions of the three stakeholders is 0.5. As time went by, when the value was below this threshold, due to the high initial procurement, adaptation, and maintenance costs of industrial robots, as well as insufficient policy incentives and transformation benefits, industrial enterprises rapidly evolved to the traditional, extensive production strategy. When the emission reduction and efficiency improvement achieved by industrial enterprises through robot application exceed this threshold, the compliance benefits gradually become apparent. The transition towards robot adaptation stabilizes and converges, which also drives the government to move more quickly towards stricter regulations. The public’s achievement of balance has been relatively slow. As a result, the improvement in environmental quality and the increase in satisfaction eventually converge towards a passive supervision strategy. Ultimately, when $t$ equals 2.5, the evolutionary equilibrium point eventually converges to $(1,0,1)$, and the evolutionary game achieves equilibrium. The stable results of the initial probabilities indicate that the initial costs for industrial enterprises to adopt industrial robots are relatively high, and that there may be insufficient policy incentives and market returns. Industrial enterprises lack the motivation for green transformation, so their strategies tend to focus on traditional and extensive production methods. Industrial enterprises lack the motivation for green transformation, so their strategies tend to focus on traditional and extensive production methods. Therefore, measures such as strengthening policy incentives, overcoming technical barriers, and improving demonstration guidance can be adopted to increase industrial enterprises’ initial willingness to use industrial robots and accelerate the evolution of the system towards stable, balanced, and synergistic governance.

5.2. Sensitivity Analysis of Third-Party Costs

This study first changes the values of the government’s costs for strict regulation $C_1$, the costs of industrial enterprises’ green transformation $C_2$, and the costs of public active supervision $C_3$, while keeping the other parameter values unchanged. Then, substitute these values into Equation (13) to conduct the sensitivity analysis of the three-party costs, as shown in Figure 4. When $C_1$ equals 0 or 10, the probabilities of the evolutionary strategies for the government and the public are both 1. As the government’s costs for strict regulation increase, the speed at which it evolves toward the stable state of “strict regulation” slows. When $C_1$ increases to 30, the government’s strategy shifts from proactive to passive and finally stabilizes at 0. When $C_2=0$, the evolutionary equilibrium steady state of industrial enterprises converges to 0. As $C_2$ increases to 20, 40, and 60, industrial enterprises evolve toward a stable state of “passive transformation,” shifting their evolutionary equilibrium from convergence toward 1 to convergence toward 0. When $C_3=0,4$, the evolutionary equilibrium steady state of the public converges to 1. When $C_3 = 8$, the evolution rate of public supervision slows down. As $C_3$ rises to 12, the equilibrium steady state of the public strategy converges to 0. At this point, the public strategy evolves towards the “passive supervision” state.

Further analysis reveals that all three parties are highly sensitive to their respective costs, and changes in costs directly influence the evolution direction of the system through the application mechanism of industrial robots. For the government, the regulation costs determine the extent of its supervision, subsidies and penalties for enterprises’ robot adaptation transformation. When the costs remain within a reasonable range, the advantage of government strict regulation in terms of returns is highly significant. Once the cost exceeds the threshold, at this point the total revenue is less than the cost incurred, the government will opt for a lenient regulatory strategy. At the industrial enterprise level, the transformation cost directly determines the economic feasibility of applying industrial robots. As the purchase and adaptation of robots far exceed expected returns, this will dampen industrial enterprises’ enthusiasm for transformation. At the same time, it will also inversely weaken the government’s governance momentum and lead to the failure of public supervision. At the public level, the increase in supervision costs will reduce external constraints on enterprises, making them more likely to maintain traditional, extensive production methods. This results in an inability to fully leverage the pollution control and emission reduction capabilities of industrial robots. Therefore, the cost optimization mechanism can be used to enhance each party’s positive behavior. First, the government should optimize the regulatory process and reduce the regulatory costs for the application of industrial robots. Second, industrial enterprises can incorporate the robot adaptation transformation into their long-term development strategies. By applying robots on a large scale and upgrading technologies, they can reduce the costs of purchasing and maintaining industrial robots, converting short-term investments into long-term competitiveness. Third, we should establish a digital supervision platform. By leveraging online platforms and establishing a linkage mechanism, we can reduce supervision costs. Through social supervision, enterprises can be encouraged to accelerate the application of industrial robots and jointly enhance the effectiveness of air pollution governance.

5.3. Sensitivity Analysis of the Benefits from the Green Transformation of Industrial Enterprises

This study first changes the value assigned to the benefit $R_1$ for industrial enterprises choosing the “robot adaptation transformation” strategy, while keeping the values of other parameters unchanged. Then, substitute these values into Equation (13) respectively, and obtain the sensitivity analysis of the green transformation benefits of industrial enterprises, as shown in Figure 5. This study conducts a sensitivity analysis on the benefits of robot adaptation transformation in industrial enterprises and explores the impact of the benefit mechanism on the evolution trajectories of the three parties. When the benefits of industrial enterprise robot adaptation transformation $R_1$ keep increasing, the stable strategy of the system will shift from $E_7(1,0,1)$ to $E_2(0,1,0)$. $R_1$ exhibits a negative correlation with the rate of evolution toward proactive strategies among the government and the public, and a positive correlation with the rate of evolution toward proactive transformation strategies among industrial enterprises. Specifically, when $R_1$ is assigned a value of 0, 18, or 36, the rate at which the government and the public evolve towards the positive strategy state and converge to 1 increase. Industrial enterprises have evolved to a stable state of “Traditional extensive production”, and the rate of evolution converging to 0 has slowed down. When R1 is set to 54, the government and public strategies shift from positive to negative, ultimately converging to a stable state of 1. Industrial enterprises evolve from a negative to a positive stable state and eventually stabilize at 1.

Further analysis reveals that industrial enterprises have a high sensitivity to the robot adaptation transformation benefit $R_1$. Changes in the benefit will alter the strategies of each party and will also trigger a chain reaction on the overall synergistic state of the system. The $R_1$ upgrade will directly increase the profits of industrial enterprises, weakening their willingness to maintain the traditional extensive production model. When reaching a certain threshold, industrial enterprises will, in pursuit of maximizing profits, actively adopt the robot adaptation transformation strategy. When industrial enterprises undergo proactive transformation, pollution control effectiveness improves, the pressure and costs of government regulation decrease, and the government is likely to adopt a more lenient regulatory approach. At the same time, improvements in environmental quality have also reduced the need for supervision and weakened the public’s motivation to actively supervise. Therefore, the positive effect of $R_1$ can be strengthened through corresponding mechanisms: The government can establish strict green product standards, increase subsidies for the purchase of industrial robots, and enhance the expected returns for enterprises’ transformation. Industrial enterprises can enhance production efficiency and their ability to control pollutants at the source by continuously implementing technological iterations and upgrades. The public can prioritize purchasing products with environmental certification in their decision-making, and this preference for green consumption can directly expand enterprises’ profit space.

5.4. Sensitivity Analysis of Punishment and Reputation Mechanisms

This study first changes the penalty $F$ imposed by the government on industrial enterprises, the social reputation loss resulting from air pollution $S$, and the social reputation loss caused by the decline in public environmental satisfaction $H_1$. All other parameter values remain unchanged. Then, substitute these values into Equation (13) respectively, and obtain the sensitivity analysis of the punishment and reputation mechanism, as shown in Figure 6. As can be seen from the figure, as $F$, $S$, and $H_1$ increase, the system’s stability strategy will shift from $E_5(1,0,0)$ to the rational stable point $E_8(1,1,1)$, and the evolution rates of the active strategies of the three parties are positively correlated with these three parameters. Specifically, at the government level, as $F$ and $H_1$ continue to increase, the rate of evolution of the government’s strict regulation continues to rise and eventually stabilizes at 1. For enterprises, when $F$ and $S$ increase, industrial enterprises tend to evolve towards a negative state and converge to 0 at a slower rate. When $F$ reaches a certain threshold, that is, when $F>15$, the industrial enterprise strategy changes from negative to positive and eventually stabilizes at 1. For the public, as $S$ increases from 0 to 15, the corresponding public supervision curve shows that the evolution rate accelerates at this point, and the probability of the public strategy gradually rises from 0.1 and eventually stabilizes at 1.

Further analysis reveals that an increase in $H_1$ indicates that the decline in satisfaction caused by air pollution will directly undermine the government’s credibility. When $F$ and $S$ are sufficiently high, the strategic choices of industrial enterprises will undergo a fundamental transformation. The greater the intensity of punishment and compensation, the greater the losses enterprises incur when maintaining extensive production. Industrial enterprises, to avoid hefty fines and ongoing environmental risks, will actively introduce industrial robots to support green transformation. By relying on industrial robots, its source reduction and intelligent pollution control capabilities can reduce pollution risks during the production process, enabling compliance with environmental regulations while also enhancing production efficiency. Based on this, a constraint-and-incentive mechanism is established for the application of industrial robots, and the synergy between technology and the system is strengthened. The government has strengthened environmental law enforcement. By relying on industrial robot monitoring data, the government has improved verification efficiency and reduced regulation costs. This has significantly increased the probability of penalties for enterprises’ excessive production and failure to implement robot-based emission reduction technologies. The public uses robots to monitor data in real time for precise supervision. This not only enhances the effectiveness of supervision, improves air quality and environmental satisfaction, but also enables the acquisition of government rewards and enterprise compensation, forming a positive incentive loop. At the same time, the government, taking into account the transformation costs of industrial robots and their emission reduction efficiency, has established a reasonable penalty and compensation mechanism. This will impose greater constraints on enterprises’ efforts to actively control pollution and reduce emissions, thereby encouraging them to fully leverage the emission reduction capabilities of industrial robots.

5.5. Sensitivity Analysis of Government Incentive Compensation Mechanism

This study first modifies the allocation of the special technical subsidies $G$ for enterprises implementing green transformation through the introduction of industrial robots, as well as the rewards $E$ for public active supervision. All other parameter allocations remain unchanged. Then, substitute these values into Equation (13) respectively, and obtain the sensitivity analysis of the government incentive compensation mechanism, as shown in Figure 7. As $G$ and $E$ increase, the evolution rates of the government and industrial enterprises change, but their stable strategies remain the same. As $G$ and $E$ increase, the evolution rates of the government and industrial enterprises change, but their stable strategies remain unchanged. As $G$ and $E$ increase, the government evolves to a stable state of 1, and the rate of evolution gradually slows down. The probability of the public’s strategy increases from 0.4 and eventually stabilizes at 1.

Further analysis reveals that different parties have varying sensitivities to the relevant incentives. Industrial enterprises have limited sensitivity to the special green technology subsidy $G$. Although higher subsidies can somewhat enhance the transformation motivation of these enterprises, due to insufficient incentive intensity and the fact that transformation costs and risks have not been fully covered, industrial enterprises will ultimately maintain the traditional extensive production mode. For the government, the increased subsidies for robot technology and rewards for public supervision would place an excessive financial burden, making it difficult to sustain large-scale subsidies in the long term. The public is highly sensitive to supervision rewards. An increase in rewards can directly enhance the net benefits of supervision and strengthen the external constraints on enterprises’ production behaviors. Therefore, a differentiated incentive mechanism can be adopted to enhance the positive effects. The government can adopt a combined model of progressive subsidies and private capital investment. In the early stage, the government moderately increased the subsidy ratio. Later on, as the benefits from robot adaptation transformation of industrial enterprises increased, the subsidy was gradually reduced. Apart from maintaining their vigilance through government incentives, the public can collectively opt to purchase green products. This will expand the green revenue space for enterprises based on their green consumption preferences. This way, through the combined efforts of supervision and consumption, industrial robots can reduce pollution emissions throughout the production process, thereby enhancing the synergistic effectiveness of air pollution governance.

6. Research Conclusions and Implications

6.1. Research Conclusions

Based on the synergistic governance model, this study takes public environmental satisfaction as the dynamic feedback variable and industrial robot application as the technical driving factor. By constructing and analyzing the evolutionary game model among the government, industrial enterprises, and the public, this study systematically reveals the strategic interactions and dynamic evolutionary patterns among multiple actors in air pollution control driven by industrial robots. The study also clarifies the multi-scenario influence mechanism of different policy parameters on the system’s evolution path and stable equilibrium. The main conclusions are as follows.

The three parties, through the application of industrial robots, have formed a closed-loop, dynamic, synergistic governance mechanism of “supervision-response-feedback”. The intensity of government environmental regulation directly affects enterprises’ willingness to introduce industrial robots for green transformation. The effectiveness of enterprises’ implementation of industrial robot adaptation transformation inversely determines the level of public environmental satisfaction and the effectiveness of government regulation. And the public’s Supervision actions will further prompt the government to optimize its regulatory strategies and encourage enterprises to deepen the application of industrial robots in reducing emissions. The strategic choices of the three parties interact with and evolve dynamically.

The cost–benefit parameters of industrial robot application are key factors driving the evolution of the synergistic governance game system for air pollution. The influence mechanisms of each parameter on the strategic choices of the three parties exhibit significant heterogeneity. The robot adaptation transformation strategies of industrial enterprises reflect the comprehensive consideration of the transformation costs and green benefits of robot applications. The behavior of public supervision is regulated by both the cost of supervision and the benefits of incentives. Moreover, the effectiveness of supervision is closely related to the intelligent monitoring data support provided by industrial robots. The choice of government regulatory strategies is based on a comprehensive consideration of various factors such as the regulatory costs of industrial robot applications, the requirements for performance assessment, and the potential loss of social reputation. Each parameter dynamically regulates the evolution path and equilibrium outcome of the game system by altering the cost–benefit structure of the main party.

The coupling mechanism between the application of industrial robots and the feedback of public environmental satisfaction jointly determines the long-term evolution path of the synergistic governance game system for air pollution. Among them, the application of industrial robots serves as the core technical support, while public environmental satisfaction represents the key feedback driving force. When the transformation costs of industrial robots exceed the expected returns of the enterprise, the enterprise will actively introduce and implement industrial robots for green transformation, fully leveraging their technical capabilities to reduce source emissions and achieve precise pollution control. When the cost of public supervision is low and the incentives are sufficient, the public can achieve efficient supervision, and the constraining effect and feedback function can be fully exerted. By effectively designing mechanisms to achieve dynamic adaptation of industrial robot technology empowerment and public environmental satisfaction feedback incentives, it is possible to promote the evolution of the game system towards a high-level equilibrium for air pollution governance.

6.2. Theoretical Implications

This study has expanded and deepened the existing theories in the following aspects:

First, this study internalizes public environmental satisfaction as a game feedback variable, overcoming the limitations of treating it as an exogenous or static indicator in previous studies. This enriches the theoretical connotation of how artificial intelligence technology can empower public participation in environmental governance. By embedding it within the tripartite game structure of the government–industrial enterprises–public, the study reveals the dynamic regulatory role of public satisfaction as a key transmission node in the “perception–pressure–response” closed loop of the synergistic governance system. This setting enriches the theoretical connotation of public participation in environmental governance, thereby promoting the transmission path for the application of industrial robot emission reduction technologies, and providing a new analytical perspective for understanding the governance logic of the synergy between technology and society [36].

Second, this study constructs an evolutionary game model involving the government, industrial enterprises, and the public. This study systematically depicts the complexity and evolution path of the strategic interactions among the three parties in the context of the introduction of industrial robot technology. Compared with previous studies that mainly focused on the “government–enterprise” or “government–public” pairwise relationships, or adopted static analytical frameworks, this study incorporates the application of industrial robots as a core technological driving variable into the game system. This study systematically depicts the strategic interaction relationship among the three parties regarding industrial robot adaptation transformation, regulatory verification, and technical supervision. This study reveals the interdependence, feedback mechanism, and nonlinear evolution characteristics of the strategies chosen by each party, and improves the dynamic analysis framework for the synergistic governance of multiple parties under technological embedding. This study provides a reference model paradigm for the research on environment governance that empowers similar technologies. At the same time, this aligns with the call to understand the dynamic analysis framework of multi-party synergistic governance [37].

Finally, this study integrates the mathematical analysis of evolutionary game theory with multi-scenario numerical simulation. This study innovates the quantitative decision-making research method for industrial robot-driven air pollution governance systems, enhancing the explanatory power and predictive ability of the theoretical model for actual governance scenarios. This study, through mathematical derivation, clearly defines the evolutionary equilibrium conditions for the relevant parameters of industrial robot applications. Subsequently, this study conducts multi-dimensional sensitivity analysis based on numerical simulation, visually presenting the threshold values and action rules of key parameters such as the transformation cost and application benefits of the robot on the evolution path of the system. This compensates for the limitations of pure analytical models in terms of their adaptability to real-world situations. This method combines the quantitative analysis of technical variables with the dynamic analysis of evolutionary games, providing a new methodological reference for the operational research of complex technical-enabled governance systems.

6.3. Practical Implications

Based on the research findings, the following policy recommendations are proposed:

First, optimize the government’s environmental regulation system and establish a dynamic governance mechanism suitable for the application of industrial robots. In the initial stage, the investment cost for the adaptation and transformation of industrial robots should be reduced. Later on, as the green benefits of the enterprises increase, the incentive measures should be gradually adjusted accordingly. At the same time, strengthen environmental protection law enforcement and the pollution compensation mechanism. Relying on the intelligent monitoring data of industrial robots to enhance the efficiency of pollution behavior investigation and reduction in regulatory costs. Integrate public environmental satisfaction and the emission reduction achievements of enterprises’ industrial robot applications into the government performance assessment, and enterprise reputation and credit evaluation systems, and establish a complete institutional loop for supervision, incentives, and feedback.

Second, guide industrial enterprises to undergo green strategic transformation and to achieve deep integration of industrial robots into the entire production process. Integrate industrial robots into the long-term development strategy of industrial enterprises, fully leveraging their technical advantages in source emission reduction, precise pollution control, and intelligent operation and maintenance. These methods can achieve a coordinated improvement in both environmental benefits and production efficiency. Meanwhile, industrial enterprises should enhance their operational transparency by actively disclosing environmental information and regularly releasing sustainable development reports that cover key environmental performance indicators, such as energy consumption and emissions.

Third, establish a sound mechanism for public participation in digitalization and leverage industrial robot technology to empower the public with efficient supervision capabilities. Enhance the public’s awareness of environmental protection and their willingness to supervise by means of conducting environmental education campaigns and establishing environmental reward systems, thereby guiding the public to shift from mere awareness to actual action. Build a digital supervision platform based on real-time monitoring data from industrial robots, open key data for environmental monitoring, and reduce the costs of public information collection and supervision feedback. This can achieve precise and efficient public supervision. At the same time, we should establish smooth digital supervision channels, lower the threshold for public supervision, and improve supervision efficiency.

7. Limitations of the Research and Future Prospects

This study still has some limitations. In the future, this study can be further expanded from the following three aspects.

First, the coupling between industrial robots and the game model is insufficient. This study indirectly characterizes the effect of robot application through parameters such as transformation costs and benefits. This study did not set the intensity of robot application and the speed of technology diffusion as explicit decision variables. The direct driving mechanism of robots on the strategic choices of the game participants is not particularly prominent. Subsequent studies can incorporate the proportion of robot applications and emission reduction efficiency as endogenous variables into the model, accurately presenting the governance logic driven by technology. Second, the model assumptions and parameters lack sufficient empirical support. The hypotheses and simulation parameters were mainly based on literature review and scenario setting, and no empirical tests were conducted using regional panel data or enterprise micro-research data. The robustness and practical applicability of the conclusion are limited. Future research can construct econometric models to empirically assess the heterogeneous impact of industrial robot application on air pollution governance, as well as the moderating effect of public environmental satisfaction within it. At the same time, future research can compare empirical results with the parameter ranges of the numerical simulation, calibrate the model parameters, and make the model’s equilibrium results more consistent with actual governance scenarios. Third, the governance parties and the research scenarios are relatively limited. This study merely constructs a tripartite game framework, without including key parties such as the central government, environmental protection organizations, and financial institutions, nor does it cover complex scenarios such as cross-regional joint prevention and control. Subsequent research can expand the multi-party, multi-level synergistic evolutionary game model to comprehensively analyze the multi-party interactions and strategy coupling mechanisms in the air pollution synergistic governance system.