How Do Environmental Regulation and Media Pressure Influence Greenwashing Behaviors in Chinese Manufacturing Enterprises?

Abstract

Faced with mounting pressure to achieve high-quality green transformation, manufacturing enterprises are increasingly scrutinized for greenwashing behaviors. This study develops a novel hybrid modeling framework that combines evolutionary game theory with the SEIR epidemic model to investigate the dynamic interactions between environmental regulation, media pressure, and green innovation behavior. The model captures how strategic decisions among boundedly rational actors evolve over time under dual external pressures. Simulation results show that stronger environmental regulatory intensity accelerates the adoption of substantive green innovation and concurrently reduces the media pressure associated with greenwashing. Moreover, while social media disclosure has a limited impact during the early stages of greenwashing information diffusion, its influence becomes significantly amplified once a critical dissemination threshold is surpassed, rapidly transforming latent information into widespread public concern. This amplification triggers significant public opinion pressure, which, in turn, incentivizes local governments to enforce stricter environmental policies. The findings reveal a synergistic governance mechanism where environmental regulation and media scrutiny jointly curb greenwashing and foster genuine corporate sustainability.

1. Introduction

Over the past few decades, carbon dioxide emissions globally have been quite concerning [1]. As the leading contributor to global carbon emissions, China faces pressing challenges stemming from the excessive energy consumption of its manufacturing sector [2]. As high-carbon emission sectors, manufacturing enterprises not only exacerbate environmental pollution but also pose serious health risks for the communities nearby [3,4]. Faced with the pressure of emission reduction, substantive green innovation in the manufacturing sector plays a pivotal role in lowering the country’s overall carbon footprint [5]. However, some manufacturing enterprises often exaggerate their contribution to carbon emission reduction practices in pursuit of maximizing economic benefits and corporate reputation, which is defined as greenwashing behavior [6,7]. Greenwashing behaviors of manufacturing enterprises undermine the trust in genuine eco-friendly endeavors, mislead consumers and investors who are developing green innovation activities. Therefore, as China accelerates its green development agenda, the growing prevalence of greenwashing behaviors has emerged as a critical barrier to substantive green innovation. These deceptive practices distort environmental signals, erode stakeholder trust, and undermine the effectiveness of both regulatory frameworks and media oversight. This raises important questions about how external governance mechanisms can better detect and deter such behaviors.

To reduce CO₂ emissions that are caused by urbanization and industrialization, the Chinese government has formulated a series of environmental regulation policies centered around the goal of carbon neutrality by 2060 [8]. These policies have reinforced corporate environmental responsibility in the context of high-quality green development and have encouraged manufacturing enterprises to pursue substantive green innovation [9]. Additionally, as an important channel of information distribution matters, social media also plays a significant role in disclosing greenwashing behaviors of manufacturing enterprises [10]. Through the disclosure of environmental information on social media platforms [11], manufacturing enterprises are increasingly held accountable for reducing greenwashing behaviors. This transparency drives these companies to adopt low-carbon technologies [12,13], ultimately achieving the substantive green innovation. To enhance corporate social responsibility in environmental pollution governance, environmental regulation functions as a critical institutional mechanism for addressing greenwashing behaviors. Meanwhile, social media coverage, acting as an informal regulatory force, helps compensate for regulatory gaps and promotes more effective enforcement of environmental policies [14]. However, the mechanisms through which environmental regulation and media pressure mitigate greenwashing behaviors in manufacturing enterprises remain insufficiently understood.

Confronted with mounting pressure to reduce carbon emissions, an increasing number of manufacturing enterprises are advancing substantive green innovation in response to regulatory constraints and media scrutiny. In green innovation activities, multiple agents will make optimal decisions based on the maximization of their own interests [15,16,17]. However, the learning mechanism of stakeholders is still very limited in the complex decision-making process [18]. For this multi-stakeholder scenario, each game subject will be restricted by power struggles in greenwashing behaviors [19]. These factors contribute to information asymmetry and may lead to irrational decision-making in green innovation activities [20]. Nevertheless, the existing literature has concentrated on two main areas. First, a large body of empirical research utilizes panel and patent data to explore the relationship between environmental regulation and green innovation [21,22,23,24]. Second, econometric analyses have been conducted to assess the impact of media pressure on corporate green investment levels and environmental disclosure practices [25,26,27,28]. Despite growing concerns over greenwashing, few studies have explored how environmental regulation and media pressure interact to curb such behaviors in China’s manufacturing sector. Based on these potential flaws and criticisms, the objectives of this study are to solve the following issues: (1) What is the globally optimal strategy of manufacturing enterprises in the substantive green innovation? (2) To provoke corporate social responsibility in the environmental pollution governance, how are environmental regulation and media pressure used to reduce greenwashing behaviors of manufacturing enterprises? (3) In the governance of greenwashing behaviors within manufacturing enterprises, how can decision-makers leverage social media to enhance their strategic planning and broaden their influence?

To address these dilemmas, evolutionary game theory serves as a crucial mathematical modeling tool and has been extensively applied to analyze conflicts and cooperation among stakeholders [29,30,31]. Therefore, evolutionary game theory is essential for modeling adaptation and learning processes in strategic decision-making. Currently, epidemic models (such as the SIR, SIS, and SEIR models) are all widely employed to simulate the spread and dynamics of diseases within populations [32,33,34]. With the expansion of their applications, epidemic models have also been widely adopted to study phenomena beyond disease transmission, including information dissemination, online public opinion dynamics, and innovation diffusion [35,36,37]. Overall, this study develops a novel mathematical modeling approach by integrating the strengths of this novel hybrid modeling. This coupled framework enables a comprehensive examination of how environmental regulation and media pressure influence greenwashing behaviors among manufacturing enterprises. To date, research exploring the intersection of these factors using such an integrated model remains scarce. Based on this, the research gaps addressed in this paper are outlined as follows.

(1)

To explore the effect of environmental regulation and media pressure on greenwashing behaviors in manufacturing enterprises, a new tool of hybrid models is proposed. This integrated modeling approach enables a more accurate assessment of the influence exerted by environmental regulation and media pressure on greenwashing behaviors.

(2)

Based on the assumption of bounded rationality and the goal of interest maximization among agents, this study verifies the differentiated impacts of environmental regulation intensity and information disclosure intensity on the green innovation strategies of manufacturing enterprises. Accordingly, the main contribution of our findings lies in deepening the understanding of how environmental regulation and media pressure, particularly after their promulgation and dissemination, jointly influence and regulate greenwashing behaviors. This work addresses a notable gap in the literature by offering new insights into the collaborative governance mechanisms between regulatory authorities and media actors in promoting green corporate practices.

(3)

In light of China’s future goals in carbon peaking and carbon neutrality, the findings of this study offer valuable insights for the government in leveraging media pressure to enhance the effectiveness of environmental regulation policies. Accordingly, our results not only assist manufacturing enterprises in identifying optimal environmental strategies, but also provide evidence-based support for policymakers in designing more effective measures to deter greenwashing behaviors.

The remainder of this paper is organized as follows. Section 2 reviews the relevant literature on the effects of environmental regulation and media pressure on greenwashing behaviors. Section 3 introduces the proposed hybrid modeling framework. Section 4 presents the simulation results. Section 5 concludes the paper with key theoretical and practical implications.

2. Literature Review

2.1. Environmental Regulation and Its Impact on Greenwashing Behaviors

As government regulation, environmental regulation can shape the direction and intensity of green innovation through targeted policy instruments [37,38]. Environmental regulations are also widely implemented in controlling corporate greenwashing behaviors and have attracted widespread attention from scholars of the related fields [39,40,41]. Given the growing severity of global warming, environmental regulations play a pivotal role in mitigating environmental pollution and incentivizing manufacturing enterprises to adopt green technologies as part of their sustainability strategies [42,43,44]. Therefore, environmental regulation tools are widely used by scholars—for example, to improve energy transition performance [45], to promote the green innovation [46], and to reduce CO₂ emissions and accelerate zero carbon transition [47].

Faced with increasing pressure from environmental governance, scholars have recently focused on examining the effect of environmental regulations on corporate greenwashing behaviors. On the one hand, some researchers argue that stricter environmental regulations elevate operating costs for enterprises, and this effect has been defined as the “compliance cost-effect” [48,49,50,51,52]. For example, ref. [48] investigated the effect of environmental quality monitoring policy on corporate greenwashing behavior. Ref. [49] suggested that the energy policy can reduce corporate greenwashing behaviors by strengthening corporate environmental responsibility and environmental investment. Ref. [50] employed a two-period game model to analyze how competing manufacturing enterprises adopt green technologies under increasingly stringent environmental regulations while facing government supervision pressures. On the other hand, some scholars argue that well-designed environmental regulations can incentivize enterprises to internalize the external costs associated with green technological innovation and to reduce greenwashing behaviors, which have been defined as “backpressure regulation effect” [53,54,55,56,57]. For example, ref. [56] believed that reasonable environmental regulations contribute to forming an inverted U-shaped relationship between corporate income and the cost of greenwashing. Ref. [54] investigated the mechanisms through which both incentive-based and mandatory environmental regulations influence green innovation and greenwashing behaviors. Ref. [55] suggested that the interaction between policy instruments and environmental regulations can effectively incentivize firms to enhance the adoption of both cleaner production processes and end-of-pipe emission reduction strategies. Ref. [57] found that well-designed environmental regulations effectively facilitate the substitution of outdated production capacities with advanced technologies in innovative activities.

2.2. Media Pressure and Its Impact on Greenwashing Behaviors

Although environmental regulations are vital in governing corporate greenwashing behaviors, the governance of greenwashing behaviors still requires corporate environmental information disclosure by social media [58,59]. The social media concern about corporate greenwashing behaviors may not only increase the pressure on enterprises with excessive carbon emissions, but also supervise the government to enhance environmental regulation intensity [10,60,61,62]. Therefore, social media can promote environmental information disclosure and facilitate information sharing, which is an important tool to reduce corporate greenwashing behaviors and regulate the execution of environmental regulations [63].

As an important driving force of corporate environmental information disclosure, the media pressure on internet platforms is pivotal to a more equitable environment in controlling corporate greenwashing behaviors [59,64]. Existing research on the effect of media pressure on corporate greenwashing behaviors has mainly considered qualitative inquiries, econometric analyses, and game models [13,64,65,66,67,68]. For instance, ref. [64] suggested that public sentiment and emotional discourse are sensitive and responsive to climate policy measures by using a data-driven analysis of 256,717 English-language tweets. Ref. [65] found that greenwashing discourse on social media is predominantly shaped by a limited number of stakeholders. Ref. [67] explored the effect of social trust on greenwashing behaviors using the hierarchical linear model. Ref. [66] examined the effect of social media attention on corporate greenwashing using a sample of Chinese A-share. Ref. [13] suggested that a new media environment and green technological innovation have a synergistic effect on corporate production performance.

2.3. Brief Review

Nevertheless, prior studies on environmental regulation and media pressure have typically examined their effects in isolation—either analyzing variations in environmental regulatory intensity or focusing on the role of media pressure as an external governance mechanism for curbing corporate greenwashing. Most scholars have treated the impacts of environmental regulation and media pressure separately. However, as internal and external regulatory instruments, these two mechanisms can interact to produce a synergistic effect, contributing to more effective environmental collaborative governance.

From another perspective, researchers have primarily employed case studies and econometric methods to investigate the separate effects of environmental regulation and media pressure on corporate greenwashing. However, research on how these two mechanisms jointly reduce greenwashing in Chinese manufacturing enterprises remains scarce. Although numerous studies have examined the distinct functional roles of environmental regulation intensity, few have integrated media pressure into the analysis to assess how different forms of regulation interact to affect greenwashing practices in the manufacturing sector.

Distinctly from existing studies, this research employs an evolutionary game model to examine the impact of environmental regulation intensity on greenwashing behaviors in manufacturing enterprises. Subsequently, the SEIR epidemic model is developed to investigate how environmental pollution disclosure influences the diffusion of greenwashing. Through simulation and comparative analysis, the study identifies the optimal behavioral strategies adopted by manufacturing enterprises under varying intensities of dual regulatory mechanisms.

3. Approach

3.1. Problem Description

Greenwashing behavior in manufacturing enterprises reflects a dynamic power struggle among multiple stakeholders within the broader context of green innovation. This process involves local governments, social media, and manufacturing firms, all of which play distinct roles in advancing environmental collaborative governance. Under conditions of information asymmetry and uncertainty, enterprises’ green innovation decisions are increasingly shaped by both formal environmental regulation and informal media oversight.

On the one hand, government-imposed environmental policies can incentivize enterprises to assume greater social responsibility in green innovation. On the other hand, media pressure not only compels manufacturing enterprises to fulfill their environmental obligations, but also facilitates the enforcement of stricter regulatory policies by local authorities to curb greenwashing. As complementary regulatory forces, environmental regulation and media pressure contribute jointly to more effective environmental collaborative governance, thereby enhancing institutional oversight and accountability for greenwashing practices in the manufacturing sector.

3.2. Assumptions

Based on the problem description of various stakeholders in green innovation activities, this paper proposes some basic assumptions to establish a hybrid mathematical framework.

(1)

Assumptions for the evolutionary game model

Assumption 1.

In fierce market competition, manufacturing enterprises will rationally carry out production and operation activities based on their profit maximization. Therefore, manufacturing enterprises can adopt different behavioral strategies in market competition. Most of them will develop substantive green innovation under government environmental regulations, but there are still a small number of manufacturing enterprises who reject it.

Assumption 2.

According to the different governance concepts and performance competition between local governments, they will implement two strategies: environmental regulation and non-environmental regulation. To reduce greenwashing behaviors of manufacturing enterprises, the government generally adopts two methods to formulate environmental regulation policies: incentive measures and punitive measures. Suppose that the strengths of the two regulatory approaches are denoted by α and β ($\alpha ,\beta \in [0,1]$).

Assumption 3.

Suppose that the proportion of local governments adopting environmental regulation strategies is denoted by x ; hence, the proportion of those opting not to implement such regulations is$1-x$. Simultaneously, let$y$and$1-y$represent the proportions of manufacturing enterprises choosing to engage in substantive green innovation and greenwashing strategies, respectively, where$x\in [0,1]\mathit{,}$$y\in [0,1]$.

Due to the bounded rationality of agents in an iterated game, the optimal strategies of these stakeholders will be affected by power struggles and conflicts of interest. Therefore, the profit and loss variables of stakeholders in green innovation activities can be further assumed (see

Table 1. Variable definitions.

Variables	Descriptions	Sources
$V$	The normal benefit obtained of manufacturing enterprises by greenwashing behaviors	[49]
$\Delta V$	The additional innovation benefits of manufacturing enterprises through substantive green innovation	[69]
$C$	The production costs that manufacturing enterprises choose greenwashing strategies	[70]
$\Delta C$	Manufacturing enterprises incur additional green technological transformation costs when opting for substantive green innovation	[71]
$\alpha$	Intensity of incentive measures ($\alpha \in [0,1]$)	[37]
$\beta$	Intensity of regulatory penalties ($\beta \in [0,1]$)	[37]
$L_1$,$L_2$	Environmental regulation costs of incentive measures and regulatory penalties	[72]
$K$	Local governments will obtain social and economic benefits when manufacturing enterprises improve related technologies and equipment through substantive green innovation	[73]
$U_1$	If local governments do not adopt environmental regulations, they will suffer some losses (i.e., labor out-migration and the decline of government credibility) after social media exposure	[12]
$U_2$	After greenwashing behaviors of manufacturing enterprises are exposed by social media, they will suffer some economic losses (i.e., decline in reputation and product sales)	[66]
$U_3$	Local governments that adopt a non-environmental regulation strategy are subject to regulatory and administrative penalties imposed by the central government	[17]
$\epsilon$	The strength of environmental pollution information disclosure from social media	[74]

).

Based on the aforementioned assumptions, this study analyzes the evolutionary game among key stakeholders. Accordingly, the payoff matrix between manufacturing enterprises and local governments is presented in

Table 2. Game payoff matrix between manufacturing enterprises and local governments.

Manufacturing Enterprises	Local Governments
	Environmental Regulation	Non-Environmental Regulation
Substantive green innovation	$V+\Delta V-C_1-\Delta C_1+\alpha L_1$, $K-\alpha L_1$	$V+\Delta V-C_1-\Delta C_1$, $K-\epsilon U_3$
Greenwashing behavior	$V-C_1-\beta L_2-\epsilon U_2$, $\beta L_2$	$V-C_1-\epsilon U_2$, $-\epsilon U_1-\epsilon U_3$

.

(2)

Assumptions for the SEIR epidemic model

Assumption 4.

According to the previous research of [75], the social media in the system at time $t$ was divided into four states.

① Susceptible ($S(t)$): Some social media have not received information about greenwashing behaviors of manufacturing enterprises.

② Escape ($E(t)$): Some social media have received information about the greenwashing behaviors of manufacturing enterprises, but it has not yet formed public opinion pressure in the dissemination.

③ Infected ($I(t)$): Social media have received information about greenwashing behaviors, and are competing to expose and disclose it on the internet. As the intensity of disclosure increases, it creates strong public opinion pressure.

④ Recover ($R(t)$): Local governments have implemented strict environmental regulations that have led manufacturing enterprises to improve their environmental performance. Thus, social media can reduce the dissemination of negative information about greenwashing behaviors.

Assumption 5.

Suppose that the social media ($A$) has disseminated the information about greenwashing behaviors. As the environmental pollution information is disclosed, the increase in the number of social media conforms to a logistic growth curve. Simultaneously, suppose that the effective information transmission rate is${\theta }_i=1-N^{\ast }/N$, where$N^{\ast }$is the real-time information volume, and N is the total information capacity.

Based on the above descriptions, the assumptions of specific parameters are shown in Figure 1. As illustrated in Figure 1, $(1-y){\theta }_1+\epsilon$ denotes the probability that a susceptible enterprise transitions to the escape state when it adopts greenwashing strategies. Conversely, when a manufacturing enterprise engages in substantive green innovation, $y{\theta }_1+\epsilon$ represents the probability that a susceptible enterprise transitions to the recovered state. In addition, $x{\theta }_2+\epsilon$ denotes the probability that an enterprise in the escape state transitions to the recovered state when local governments implement environmental regulation strategies. By contrast, when local governments do not adopt environmental regulation, $(1-x){\theta }_2+\epsilon$ denotes the probability that an enterprise in the escape state ($E(t)$) transitions to the infected state ($I(t)$). Therein, $\sigma$ represents the self-healing ability of infected social media in the information dissemination process.

3.3. Systematic Stability Analysis

(1)

Stability analysis of the evolutionary game model

Let $P_1$ denote the expected payoff of local governments when adopting environmental regulation strategies, and $P_2$ represent the expected payoff when choosing non-environmental regulation strategies. The average expected payoff of local governments is denoted by $\overline{P}$. These are defined as follows:

$$P_1=y(K-\alpha L_1)+(1-y)\beta L_2$$

(1)

$$P_2=y(K-\epsilon U_3)+(1-y)(-\epsilon U_1-\epsilon U_3)$$

(2)

$$\overline{P}=x{P}_1+(1-x)P_2$$

(3)

Similarly, let $Q_1$ denote the expected payoff of manufacturing enterprises that engage in substantive green innovation, and $Q_2$ is represent the expected payoff of those adopting greenwashing strategies. The average expected payoff of manufacturing enterprises is denoted by $\overline{Q}$. The corresponding equations are presented below:

$$Q_1=x(V+\Delta V-C_1-\Delta C_1+\alpha L_1)+(1-x)(V+\Delta V-C_1-\Delta C_1)$$

(4)

$$Q_2=x(V-C_1-\beta L_2-\epsilon U_2)+(1-x)(V-C_1-\epsilon U_2)$$

(5)

$$\overline{Q}=y{Q}_1+(1-y)Q_2$$

(6)

Based on the previous research of [76], replicator dynamic equations for local governments and manufacturing enterprises are formulated in Equations (7) and (8), respectively.

$$F(x)={\displaystyle \frac{dx}{dt}}=x(P_1-\overline{P})=x(1-x)[y(-\alpha L_1-\beta L_2-\epsilon U_1)+\beta L_2+\epsilon U_1+\epsilon U_3]$$

(7)

$$F(y)={\displaystyle \frac{dy}{dt}}=y(Q_1-\overline{Q})=y(1-y)[x(\alpha L_1+\beta L_2)+\Delta V-\Delta C_1+\epsilon U_2]$$

(8)

When $F(x)=0$ and $F(y)=0$, evolutionary equilibrium points in this model are (0, 0), (0, 1), (1, 0), (1, 1), ($x^{\ast }$,$y^{\ast }$). Based on the judgment method proposed by [77], the Jacobian matrix $J_1$ can be obtained as follows.

$$\begin{array}{l}{J}_1=\left[\begin{array}{l}{\displaystyle \frac{\partial F(x)}{\partial x}}\\ {\displaystyle \frac{\partial F(y)}{\partial x}}\end{array}\right.\left.\begin{array}{l}{\displaystyle \frac{\partial F(x)}{\partial y}}\\ {\displaystyle \frac{\partial F(y)}{\partial y}}\end{array}\right]=\left(\begin{array}{l}(1-2x)[y(-\alpha L_1-\beta L_2-\epsilon U_1)+\beta L_2+\epsilon U_1+\epsilon U_3]\\ y(1-y)(\alpha L_1+\beta L_2)\end{array}\right.,\\ \left.\begin{array}{l}x(1-x)(-\alpha L_1-\beta L_2-\epsilon U_1)\\ (1-2y)[x(\alpha L_1+\beta L_2)+\Delta V-\Delta C_1+\epsilon U_2]\end{array}\right)\end{array}$$

(9)

Furthermore, the determinant ($\det J_1$) and trace ($tr{J}_1$) of $J_1$ are shown in

Table 3. The $\det J_1$ and $tr{J}_1$.

($x,y$)	$\det J_1$	$tr{J}_1$
(0,0)	$(\beta L_2+\epsilon U_1+\epsilon U_3)(\Delta V-\Delta C_1+\epsilon U_2)$	$(\beta L_2+\epsilon U_1+\epsilon U_3)+(\Delta V-\Delta C_1+\epsilon U_2)$
(0,1)	$(-\alpha L_1+\epsilon U_3)[-(\Delta V-\Delta C_1+\epsilon U_2)]$	$(-\alpha L_1+\epsilon U_3)+[-(\Delta V-\Delta C_1+\epsilon U_2)]$
(1,0)	$-(\beta L_2+\epsilon U_1+\epsilon U_3)(\alpha L_1+\beta L_2+\Delta V-\Delta C_1+\epsilon U_2)$	$-(\beta L_2+\epsilon U_1+\epsilon U_3)+(\alpha L_1+\beta L_2+\Delta V-\Delta C_1+\epsilon U_2)$
(1,1)	$-(-\alpha L_1+\epsilon U_3)[-(\alpha L_1+\beta L_2+\Delta V-\Delta C_1+\epsilon U_2)]$	$-(-\alpha L_1+\epsilon U_3)+[-(\alpha L_1+\beta L_2+\Delta V-\Delta C_1+\epsilon U_2)]$

. To obtain the evolutionary stability strategy (ESS) of this model, a corollary can be proposed in this paper.

Corollary 1.

If$\epsilon >{\displaystyle \frac{\alpha L_1}{U_3}}$ and$\epsilon >{\displaystyle \frac{\Delta C_1-\Delta V-\beta L_2-\alpha L_1}{U_2}}$, the point (1,1) is an ESS in this game model.

As can be seen from

Table 4. Evolutionary stability states under Corollary 1.

$(\mathit{x},\mathit{y}$)	$\mathbf{det}{\mathit{J}}_1$	$\mathit{t}\mathit{r}{\mathit{J}}_1$	States
(0,0)	+	+	Unstable
(0,1)	−	+, −	Saddle point
(1,0)	−	+, −	Saddle point
(1,1)	+	−	ESS

, point (1, 1) is an ideal evolutionary stable strategy in this model when $\epsilon >{\displaystyle \frac{\alpha L_1}{U_3}}$ and $\epsilon >{\displaystyle \frac{\Delta C_1-\Delta V-\beta L_2-\alpha L_1}{U_2}}$. In this scenario, the perfect strategies of local governments and manufacturing enterprises are adopting environmental regulation and substantive green innovation. Specifically, two basic conditions need to be met: ① The losses incurred by local governments in implementing environmental regulations exceed the incentives generated through regulatory policies for promoting substantive green innovation. ② The combined value of additional innovation benefits and green innovation incentives outweighs the total of additional innovation costs, environmental pollution taxes, and reputational losses due to social media exposure. Based on this, the phase diagram of local governments and manufacturing enterprises is presented in Figure 2.

(2)

Stability analysis of the SEIR epidemic model

In the complex strategic interactions between local governments and manufacturing enterprises, social media serves as an external observer that discloses and reports greenwashing behaviors based on the decision-making outcomes of both parties. The dissemination of greenwashing information through social media exhibits dynamics analogous to disease transmission, resembling an infection process. Based on the theory of information dissemination dynamics [33,35], an SEIR epidemic model is constructed to capture the state transitions in the spread of greenwashing-related information on social media. The model is presented as follows.

$$\left\{\begin{array}{l}{\displaystyle \frac{dS}{dt}}=A\epsilon -[(1-y){\theta }_1+\epsilon ]SI-(y{\theta }_1+\epsilon )S\\ {\displaystyle \frac{dE}{dt}}=[(1-y){\theta }_1+\epsilon ]SI-({\theta }_2+2\epsilon )E\\ {\displaystyle \frac{dI}{dt}}=[(1-x){\theta }_2+\epsilon ]E-\sigma I\\ {\displaystyle \frac{dR}{dt}}=\sigma I+(y{\theta }_1+\epsilon )S+(x{\theta }_2+\epsilon )E\end{array}\right.$$

(10)

Based on Equation (10), the diffusion threshold of SEIR epidemic model is calculated as $R_0={\displaystyle \frac{A\epsilon [(1-x){\theta }_2+\epsilon ]}{\sigma ({\theta }_2+2\epsilon )(y{\theta }_1+\epsilon )}}$. The evolution of diffusion thresholds is jointly influenced by the strategic interactions between local governments and manufacturing enterprises, as well as the intensity of greenwashing information dissemination on social media. Therefore, two corollaries of diffusion thresholds have been proposed based on Lyapunov’s stability theorem.

Corollary 2.

When$R_0\le 1$, the point $({\displaystyle \frac{A\epsilon }{y{\theta }_1+\epsilon }},0,0)$ is zero-equilibrium point in the SEIR epidemic model (see Appendix A and Appendix B for the proof process).

Proof. 

As derived in the Equation (10), the Jacobian matrix $J_2$ of the SEIR epidemic model is shown below:

$$J_2=\left[\begin{array}{l}-[(1-y){\theta }_1+\epsilon ]I-(y{\theta }_1+\epsilon ) 0 -[(1-y){\theta }_1+\epsilon ]S\\ [(1-y){\theta }_1+\epsilon ]I -({\theta }_2+2\epsilon ) [(1-y){\theta }_1+\epsilon ]S \\ 0 (x{\theta }_2+\epsilon ) -\sigma \end{array}\right]=\left[\begin{array}{l}{a}_{11}{a}_{12}{a}_{13}\\ a_{21}{a}_{22}{a}_{23}\\ a_{31}{a}_{32}{a}_{33}\end{array}\right]$$

(11)

By calculation, characteristic roots in Corollary 2 are denoted as ${\lambda }_1=-(y{\theta }_1+\epsilon )$,${\lambda }_2=-({\theta }_2+2\epsilon )$,${\lambda }_3=-\sigma$. Based on Lyapunov’s stability theorem, the point $({\displaystyle \frac{A\epsilon }{y{\theta }_1+\epsilon }},0,0)$ is an equilibrium point in the SEIR epidemic model when $R_0\le 1$. The inference results indicate that there will be no infected social media in the system. □

Corollary 3.

When$R_0>1$, the non-zero equilibrium point$(S^{*},E^{*},I^{*})$is computed by Equation (10). If $R_0>1$, the point $(S^{*},E^{*},I^{*})$ is an equilibrium point in the SEIR epidemic model.

Proof 3.

As derived in the Equation (10), point $(S^{*},E^{*},I^{*})$ is calculated below: $S^{*}={\displaystyle \frac{({\theta }_2+2\epsilon )\sigma }{[(1-y){\theta }_1+\epsilon ][(1-x){\theta }_2+\epsilon ]}}$, $I^{*}={\displaystyle \frac{A\epsilon [(1-y){\theta }_1+\epsilon ][(1-x){\theta }_2+\epsilon ]-\sigma ({\theta }_2+2\epsilon )(y{\theta }_1+\epsilon )}{\sigma [(1-y){\theta }_1+\epsilon ]({\theta }_2+2\epsilon )}}$, $E^{*}={\displaystyle \frac{\sigma }{[(1-x){\theta }_2+\epsilon ]}}{I}^{*}$. By further calculations, the characteristic roots in Corollary 3 are denoted as ${\lambda }_4=-[(1-y){\theta }_1+\epsilon ]I^{*}-(y{\theta }_1+\epsilon )$, ${\lambda }_5=-({\theta }_2+2\epsilon )$, ${\lambda }_6=-\sigma$. Based on Lyapunov’s stability theorem, the point $(S^{*},E^{*},I^{*})$ constitutes an equilibrium of the SEIR model when the condition is $R_0>1$. The inference suggests that the strategic decisions of both local governments and manufacturing enterprises remain uncertain, thereby exacerbating the spread of greenwashing information on social media. □

According to the results of Corollaries 1–3, the further analysis of these models is summarized below: ① The strategic interactions between local governments and manufacturing enterprises are primarily driven by their respective payoffs. Over time, the evolutionary trajectories converge toward the equilibrium point (1, 1). This means that the perfect strategies of local governments and manufacturing enterprises are adopting environmental regulations and developing substantive green innovation. ② As greenwashing behaviors are increasingly exposed via social media, the dynamics of information dissemination transition from susceptible to either escape or infected states. In response, both local governments and enterprises iteratively adjust their strategies based on changing payoff conditions. ③ When the intensity of greenwashing information dissemination by social media increases, the strategies of both players evolve toward an ESS. This highlights the pivotal role of media pressure in shaping the regulatory responses of local governments and the innovative behaviors of manufacturing enterprises. Based on this, the phase diagram of information dissemination based on the SEIR epidemic model is presented in Figure 3.

4. Result and Discussion

4.1. Parameter Specification

As a method of dynamic simulation, the simulation of a numerical example can solve risk power struggles between different stakeholders. For some complex situations, the numerical example is the most effective method to address some complex questions. To obtain the initial parameters of the numerical example, parameter values in this paper have been investigated by multiple channels, such as personal investigations and secondary sources. Based on this, the selection of initial parameters has the following steps:

Step 1: In this paper, we have chosen China’s manufacturing enterprises as a research case. Based on the characteristics of resource-intensive, high-polluting industries, the research team selected two typical manufacturing companies. These companies include Harbin Electric Corporation and Harbin Heating Company. The data collection process is shown in

Table 5. The data collection process in this paper.

Data Source	Data Description
Questionnaire surveys	To obtain simulation parameters in the evolutionary game model, the questionnaire survey was distributed to relevant domain experts, government managers, and executives by e-mails.
In-depth interviews	Based on the statistical results of questionnaire surveys, we conducted a semi-structured interview with government managers and executives.
Online reporting	The media coverage of greenwashing behaviors in two manufacturing enterprises was collected.
Internal materials	Internal materials and website information in two companies were used as auxiliary references.

.

Step 2: Our research team tracked the relevant reports from local official and social media regarding the greenwashing behavior of these manufacturing enterprises. By questionnaire survey and media coverage, initial parameters in the SEIR epidemic model can be obtained.

Step 3: To ensure the reliability and validity of the numerical analysis, the range of exploratory values is divided and used as the basis for the benchmark simulations. Following extensive discussions within the research team, the parameter values for the models were determined accordingly (see

Table 6. The rates of change for different exploration values in these models.

Parameters	${\mathit{L}}_1,{\mathit{L}}_2$	$\mathit{\alpha },\mathit{\beta }$	${\mathit{U}}_1,{\mathit{U}}_2,{\mathit{U}}_3$	$\mathbf{\Delta }\mathit{V}$	$\mathbf{\Delta }{\mathit{C}}_1$	$\mathit{A}$	${\mathit{\theta }}_1,{\mathit{\theta }}_2$
Initial values	50–70%	40–90%	30–50%	>40%	>50%	30–50%	40–90%

).

4.2. Simulation Results

(1)

Initial game strategy

In the initial stage of decision-making, the selection of game strategies among local governments and manufacturing enterprises will gradually approach (1,1) over time. To evaluate the impact of initial game strategies, we set the initial proportions of regulatory adoption and substantive green innovation at 0.2, 0.5, and 0.8, respectively. Simulation results are illustrated in Figure 4.

Figure 4 depicts the optimal stable strategy equilibrium point (1,1) in initial game strategies. This means that manufacturing enterprises and local governments will eventually evolve into strategies (developing substantive green production, adopting stricter environmental regulations). The stricter the environmental regulation, the more pronounced its effect on achieving equilibrium. As the proportion of local governments implementing regulatory policies increases, manufacturing enterprises have also carried out substantive green innovations to meet legal emission reduction standards. In the initial state of evolutionary games, the intensity of greenwashing information dissemination and the strength of environmental regulations are key factors influencing the greenwashing behaviors of manufacturing enterprises. Therefore, it is essential to examine the evolutionary dynamics of all participating agents with respect to these two regulatory dimensions.

(2)

The effect of environmental regulations

Environmental regulation, as a key policy instrument for governments, is of vital importance for compelling manufacturing enterprises to adopt cleaner and more efficient production methods that result in lower greenwashing behaviors. Simulation results are presented in Figure 5 and Figure 6.

As illustrated in Figure 5, the speed of the evolution of substantive green innovation behaviors begins to rise when the environmental regulation intensity has increased. This indicates a positive correlation between regulatory stringency and the speed of green innovation adoption. However, stronger regulations also result in higher enforcement costs for local governments. When these costs exceed a certain threshold, local governments may shift from a regulatory to a non-regulatory stance. Figure 6 further demonstrates that, when the information is in a susceptible or latent state, the impact of government regulation is limited, and the evolution patterns remain largely unchanged. Over time, however, stronger environmental regulation significantly accelerates the transition of greenwashing information from the infected state to the recovered state. These findings highlight the dual effects of environmental regulation on both enterprise behavior and the dissemination of greenwashing information on social media.

Although environmental regulations may impose certain regulatory costs on local governments, necessary regulatory policies can accelerate the evolution rate of substantive green innovation behaviors among manufacturing enterprises. And these regulations also can effectively alleviate the media pressure related to greenwashing behaviors of manufacturing enterprises. However, once manufacturing enterprises decrease their greenwashing behaviors, local governments can gradually weaken the intensity of environmental regulations. In the face of a public opinion crisis of greenwashing information dissemination, local governments should not overly evade risks or emphasize the minimization of environmental regulatory costs. Instead, they should decisively adopt strict environmental regulatory policies to accelerate the evolution rate of substantive green innovation behavior. Additionally, the greenwashing information dissemination brought about by tendentious social media reports will be rapidly reduced with the increase in the intensity of environmental regulations.

(3)

The effect of media pressure

Media pressure serves as a critical external governance mechanism for controlling greenhouse gas emissions and mitigating environmental pollution. Public concern expressed through social media regarding corporate greenwashing not only exerts pressure on manufacturing enterprises to pursue substantive green innovation, but also plays a supervisory role in prompting governments to strengthen environmental regulatory efforts. The outcomes of the numerical simulations are presented in Figure 7 and Figure 8.

As illustrated in Figure 7, when the dissemination speed of greenwashing information on social media is relatively low, local governments tend to adopt non-regulatory strategies. However, as media exposure intensifies, governments become increasingly inclined to implement environmental regulatory policies. Meanwhile, manufacturing enterprises exhibit a high sensitivity to the intensity of greenwashing information dissemination. According to Figure 8, the degree of media disclosure has a limited impact on the infectious state of greenwashing information in the early stages of dissemination. Once dissemination surpasses a critical threshold; however, the spread of greenwashing-related information rapidly expands to broader segments of the social media network. Specifically, higher intensity in the dissemination of greenwashing information is associated with a slower rate of relief from media pressure. In other words, sustained high-intensity media exposure imposes continuous pressure on both local governments and manufacturing enterprises, compelling enterprises to reduce greenwashing behaviors. When media pressure reaches a critical level, it can act as a forcing mechanism, driving manufacturing enterprises toward the adoption of substantive green innovation measures.

From the above analysis, the intensity of greenwashing information dissemination exerts a significant influence on the strategic behavior of both local governments and manufacturing enterprises. On the one hand, widespread diffusion generates strong public opinion pressure, prompting governments to intervene with more stringent environmental regulations. On the other hand, media pressure can promote manufacturing enterprises to pursue green transformation and adopt cleaner production practices. Consequently, media pressure serves as an effective external regulatory force in curbing greenwashing behaviors.

4.3. Discussion

The above numerical example proved that the collaborative governance of environmental regulation and media pressure have significantly reduced greenwashing behaviors. Our research team believes that possible reasons are that the dual regulation of government and media stimulates a reputation insurance effect, which can help manufacturing enterprises more actively engage in substantive green innovation. Therefore, this paper will further discuss the above simulation results.

(1)

Several studies have confirmed that environmental regulation plays a significant role in promoting green innovation among enterprises, which can stimulate the Porter effect [72,73,78]. The findings of this paper further suggest that differentiated environmental regulations have different dominant levels of greenwashing behaviors. To maximize the function of government environmental governance, the stricter environmental regulation is, the more appreciable may be its effects [79]. Once manufacturing enterprises decrease their greenwashing behaviors, local governments can gradually weaken the intensity of environmental regulations. However, when regulatory costs reach a critical value, the regulatory effect of environmental regulations on greenwashing behaviors of manufacturing enterprises may be reduced. The possible reason is that the cost-effective of environmental regulation may pass on the green innovation output of manufacturing enterprises [80]. These findings agree with [49], who believed that stricter environmental regulation intensity has a higher inhibitory effect on corporate greenwashing behaviors of China’s energy companies. Especially, stricter environmental regulations can force high-polluting enterprises to develop substantive green innovation [70]. Also, the intensity of environmental regulation needs to be dynamically adjusted based on the evolution of greenwashing behaviors in considering the cost of environmental regulation.

(2)

As a supplementary force of government regulation, media pressure is an important external regulatory tool to disclose manufacturing enterprises’ greenwashing behaviors by disseminating greenwashing information [66]. The degree of social media disclosure has little impact on its infectious state in the early stages of greenwashing information dissemination [68,81]; however, once a certain threshold of dissemination is crossed, the media pressure can provide a certain external regulation in the lower greenwashing behaviors of manufacturing enterprises. There are some research efforts that also report the above findings [82,83]. By the investigation of greenwashing behaviors in manufacturing enterprises, research teams found that the lack of effective regulation is the biggest obstacle to governing greenwashing behaviors of manufacturing enterprises. Meanwhile, many scholars have indicated that environmental regulation and social media carried important indications in disclosing enterprises’ greenwashing behaviors [7,49,74]. These studies have often overlooked the synergistic governance effect of environmental regulation and social media.

(3)

Environmental regulation and social media play different functional roles in controlling the greenwashing behaviors of manufacturing enterprises [52,84]. First, strict environmental regulation can compel manufacturing enterprises to reduce emissions, while also encouraging them to pursue substantive green innovation [85], and the dissemination of greenwashing information driven by tendentious social media reports tends to decline significantly as the intensity of environmental regulation increases [49]. Second, the higher intensity of greenwashing information dissemination can bring sustained media pressure on local governments and manufacturing enterprises [83,86]. Therefore, it should introduce the media pressure and environmental regulation to regulate greenwashing behaviors and give full play to the positive role of environmental collaborative governance in reducing greenwashing behaviors, which ultimately achieves substantive green innovation.

5. Conclusions and Implications

5.1. Conclusions

To investigate the effects of environmental regulation and media pressure on corporate greenwashing behaviors, this study integrates evolutionary game theory with the SEIR epidemic model to construct a dynamic decision-making framework. The proposed models are validated through numerical simulations, and the main conclusions are as follows:

(1)

Stricter environmental regulations imposed by local governments significantly curb greenwashing behaviors among manufacturing enterprises. However, such regulatory efforts entail increasing costs for governments, while the high cost of genuine green innovation continues to constrain enterprises. Furthermore, the process of greenwashing is inherently stochastic. When greenwashing information on social media remains in its early (susceptible or latent) stages, environmental regulation has limited impact. Nevertheless, in the long run, the relaxation of regulatory intensity may trigger a resurgence of greenwashing behaviors, potentially leading to secondary outbreaks of greenwashing information dissemination on social platforms.

(2)

The social media concern about greenwashing behaviors may not only pressurize green innovation activities of manufacturing enterprises, but also supervise the government to enhance environmental regulation intensity. As the exposure of social media continues to increase, local governments are more willing to adopt environmental regulation strategies. At the same time, the higher the intensity of greenwashing information dissemination in social media, the slower the rate of relief for media pressure. However, we should also note that social media is keen on hot and short-term news events in the greenwashing information dissemination, which often shifts media attention with the emergence of new hotspots. Therefore, the local government should encourage social media to establish a long-term follow-up reporting mechanism for disclosing greenwashing behaviors. So, social media will become an important external regulatory tool that continuously exposes corporate greenwashing behaviors.

(3)

Given the dynamic and adaptive nature of greenwashing behavior, regulatory intensity should be flexibly adjusted in accordance with its associated costs. Meanwhile, the media pressure also can promote substantive green innovation in manufacturing enterprises. As internal and external regulatory tools, environmental regulation and media pressure can jointly generate the effect of environmental collaborative governance. Especially, it is necessary to further expand the scope of social media’s authority and establish a legal guaranteed mechanism of social media. Therefore, the function of environmental collaborative governance for environmental regulation and media pressure can be fully utilized, which is crucial in regulating the greenwashing behaviors of manufacturing enterprises.

5.2. Implications

The findings of this study offer three key theoretical contributions. First, the co-evolution theory has been expanded by revealing the evolutionary process of multi-agent decision-making. This can be used to better understand the collaborative evolutionary relationship of stakeholders in controlling the greenwashing behaviors of manufacturing enterprises. Second, it also extends collaborative governance theory by analyzing different impact effects of environmental regulation and media pressure in reducing greenwashing behaviors; and relevant findings may have important implications for improving the collaborative governance of greenwashing behaviors among stakeholders. Finally, this paper confirms the effectiveness of different intensities between environmental regulation and media pressure on the governance of greenwashing behaviors, which is of significant value for the high-quality green innovation and green transformation in manufacturing enterprises.

In practice, the research results of this paper also have three implications for controlling the greenwashing behaviors of manufacturing enterprises. First, stricter environmental regulation can encourage manufacturing enterprises to actively adopt the strategies of substantive green innovation in the initial stage. To enhance regulatory effectiveness, policymakers should adapt the intensity of environmental regulations in accordance with the dynamic evolution of greenwashing practices. Second, media pressure can provide a certain external regulation for reducing greenwashing behaviors. Third, effective collaborative governance between environmental regulations and social media in different regions plays a pivotal role for the containment of greenwashing behaviors. So, public participation and official media should be introduced to address the greenwashing behaviors of manufacturing enterprises based on the environment collaborative multi-agent governance.

5.3. Limitations and Future Study

Nevertheless, certain limitations remain. (1) As a regulatory force in addressing greenwashing behaviors in manufacturing enterprises, media pressure can effectively complement the limitations of environmental regulations. However, this paper does not delve into how to ensure that social media can monitor and report on greenwashing behaviors in the long term. (2) On the basis of personal investigations, expert experiences, and group discussions, the simulation of numerical examples can solve risk power struggles between different stakeholders. It needs to be further validated the practicality of these models by using the real data. Therefore, the limitations of the above research are also the focus that needs to be paid attention to in the next step of research.