Frontiers | Digital marketing and social network effects in new energy vehicle diffusion: evolutionary dynamics in a dual-layer heterogeneous network

Digital marketing and social network effects in new energy vehicle diffusion: evolutionary dynamics in a dual-layer heterogeneous network

• 1. School of Management, Wuhan University of Technology, Wuhan, China

• 2. School of Economics and Management, Anqing Normal University, Anqing, China

Abstract

In the context of the carbon peaking and carbon neutrality strategy and the booming digital economy, the diffusion of new energy vehicles (NEVs) has become an important pathway for industrial green transformation. This study develops a dual-layer heterogeneous network evolutionary game model that integrates supply-side firms and demand-side consumers. Based on this model, we examine the effects of multiple government policies, digital marketing mechanisms, social network effects, underlying physical constraints, and network structure, as well as selected interactions among these mechanisms, on NEV diffusion. The findings reveal several critical insights. First, NEV diffusion exhibits a pronounced bimodal steady-state pattern and strong dependence on initial adoption conditions. It shows an S-shaped relationship with the initial consumer adoption base. Second, government policy transmission is asymmetric across the dual-layer network. Under standardized proportional policy changes, consumer purchase subsidies have a stronger effect on diffusion than technology transition subsidies and carbon prices. Third, digital marketing and social network effects are conditional on the prevailing market structure. When internal combustion engine vehicles initially hold an advantage, stronger marketing utility conversion, local bandwagon effects, and hub node influence can reinforce the incumbent position, whereas information overload weakens this exposure advantage. Fourth, charging anxiety and perceived technological risk constrain sustained NEV diffusion, while purchase subsidies can only partly compensate for severe charging constraints. Selected joint analyses and network robustness tests further show that diffusion outcomes depend on interactions among policy, behavioral, and physical mechanisms, while consumer-network connectivity and topology affect quantitative diffusion outcomes without overturning the main directional relationships. These findings highlight the importance of initial market conditions, cross-layer feedback, and network structure in shaping NEV diffusion and provide implications for policy design and firm strategy.

1 Introduction

In response to increasingly severe global environmental issues, governments and organizations worldwide have introduced a series of environmental policies [1]. The implementation of these policies is primarily aimed at promoting low-carbon transformation and upgrading across various industries. As a key sector in terms of energy consumption and carbon dioxide emissions, the transportation industry plays a critical role in achieving the carbon peaking and carbon neutrality goals through carbon reduction and pollution control. Against this backdrop, accelerating the transition from fossil fuels to clean energy in the transportation sector is not only a vital means of reducing environmental pollution but also an inevitable trend driving global industrial transformation and high-quality economic development.

As the core player in the transportation sector and a pillar industry of the national economy, the automotive industry represents the main battleground for promoting energy conservation and emissions reduction in transportation systems. In the context of green transformation, the widespread adoption of new energy vehicles (NEVs) helps address the energy crisis [2] and alleviate environmental pressures [3]. However, the market diffusion of NEVs is not merely a matter of technological substitution, but a complex process involving underlying physical constraints, the restructuring of consumer perceptions, and multidimensional network interactions and competition. In the current market, traditional internal combustion engine vehicles (ICEVs) continue to dominate because of their established market position. As a result, the diffusion of NEVs is constrained by limited consumer trust in NEV technologies and insufficient charging infrastructure. Consumer path dependence further impedes the widespread adoption of NEVs.

More critically, in the context of the digital economy, the environment for market diffusion has shifted, and competition is no longer confined to traditional physical spaces but has evolved into competition for consumer attention. Automakers are extensively leveraging digital marketing tools and algorithmic recommendation mechanisms in an attempt to gain dominance within social networks, which can influence consumer perceptions and technology adoption behavior. Therefore, a thorough understanding of the underlying mechanisms and multidimensional determinants of NEV diffusion can not only facilitate the implementation of the carbon peaking and carbon neutrality strategy but also provide valuable insights into promoting green technologies in complex network markets.

Despite the substantial body of literature that has advanced the understanding of the market diffusion of NEVs, several critical gaps remain in the context of highly digitalized and complex market environments. First, existing evolutionary analyses have paid limited attention to firms’ digital marketing behaviors, with most studies emphasizing policy interventions [4] and underlying physical constraints [5, 6]. This limits our understanding of how digital marketing exposure shapes consumer adoption behavior in technology competition. Second, although previous studies have considered firm-consumer interactions and co-evolution, the coupled evolution of firm strategies and consumer adoption across structurally distinct network layers remains insufficiently explored. In particular, limited attention has been paid to how within-layer heterogeneity shapes cross-layer market feedback. Third, the broader literature on NEV diffusion remains fragmented across policy, behavioral, and physical perspectives, with limited attention to interactions among these mechanisms. How policy incentives, digital marketing, social network effects, and physical constraints reinforce or offset one another therefore remains insufficiently understood. To address these gaps, this study investigates three core research questions: (1) How do firms’ digital marketing mechanisms affect consumer adoption and NEV diffusion? (2) How does the co-evolution of firm strategies and consumer adoption shape NEV diffusion within a dual-layer heterogeneous network? (3) How do policy incentives, digital marketing, social network effects, and physical constraints jointly shape NEV diffusion?

To answer these questions, this study develops a dual-layer heterogeneous network evolutionary game model involving both firms and consumers. The proposed framework incorporates government policies, digital marketing mechanisms, social network effects, and underlying physical constraints into the analysis of NEV diffusion. The main contributions of this study are threefold. First, this study extends the evolutionary analysis of NEV diffusion by incorporating firms’ digital marketing behavior alongside policy interventions, the social network effects, and physical constraints. It shows that the impacts of digital marketing and the social network effects depend on prevailing market conditions, while selected analyses further reveal reinforcing and compensatory relationships among key mechanisms. Second, this study develops a dual-layer heterogeneous network framework that jointly represents firm competition and consumer social interaction. The framework allows within-layer heterogeneity to shape cross-layer feedback through market demand and marketing exposure. The results further indicate that consumer-network structure can affect the quantitative diffusion outcome, highlighting network structure as an important boundary condition of the co-evolutionary diffusion process. Third, the findings provide practical insights for policy and firm decision-making by revealing differentiated policy transmission, the context-dependent effects of digital marketing and the social network effect, and the constraining role of physical constraints. Standardized policy comparisons and selected joint-effect analyses further support more targeted NEV promotion and marketing strategies.

The rest of this paper is organized as follows. Section 2 reviews the related literature. Section 3 outlines the methodology and model construction procedure. Section 4 presents the simulation results. Section 5 summarizes the main conclusions and proposes corresponding policy recommendations and management insights.

2 Literature review

2.1 Research on NEV diffusion

The diffusion of NEVs is a complex evolutionary process involving macro-level policy drivers, underlying physical constraints, and social network interactions. Existing research can be broadly grouped into two streams: studies examining macro-level policy interventions and underlying physical constraints, and studies focusing on consumer interactions and behavioral evolution within complex networks.

• Mechanisms of macro-level policy interventions and underlying physical constraints

Macro-policy incentives and underlying physical constraints are regarded as key factors influencing the diffusion of NEVs [7]. At the level of policy intervention, existing studies have examined the effects of multiple policy instruments and their combinations on NEV diffusion [8]. Research has shown that the dual-credit policy and carbon trading mechanisms affect firms’ research and development, technology diffusion, and market strategies within competitive and cooperative networks [4, 9]. Meanwhile, research on policy optimization for both supply and demand sides indicates that adaptive subsidy mechanisms can generate different evolutionary outcomes from fixed subsidy schemes [10]. Under market conditions characterized by the long-term coexistence of ICEVs and NEVs, dynamically adjusted and gradually phased-out subsidy policies have been shown to facilitate market transition [11]. These studies highlight the dynamic nature of policy intervention, indicating that policy effects may vary with the timing and path of policy adjustment [12]. Beyond the dynamic adjustment of specific policy instruments, recent research has also examined environmental policy uncertainty in the broader context of green technological change, particularly its implications for corporate green innovation [13].

At the level of physical constraints, technological bottlenecks, high upfront costs, and infrastructure limitations constitute hard boundaries hindering the diffusion of NEVs [

]. Research indicates that while government policies can promote NEV diffusion and market penetration, technology remains the primary bottleneck constraining the NEV industry, and the driving force of technological progress on diffusion has substantially surpassed that of mere economic subsidies [

]. Furthermore, the scale of charging station deployment and network effects directly influence consumers’ perception of the technology [

], and the lack of relevant infrastructure is highly likely to trigger negative sentiments and weaken purchase intent [

• 2. Consumer interactions and dynamic evolution from a complex network perspective

With the introduction of complex system theory, scholars have gradually recognized that market diffusion is not merely the aggregation of isolated individual decisions, but is highly dependent on information interactions within social networks. At the macro-level network topology, research confirms the heterogeneous transmission characteristics and diffusion patterns of government subsidies across different topological structures, including scale-free networks, small-world networks, small-scale networks, and large-scale networks [17]. At the micro-level individual interaction stage, local information exchange among individuals has been proven to be an important mechanism for the diffusion of NEVs. Both evolutionary framework deductions based on supply-demand synergistic responses [18] and empirical consumer decision analyses [19] indicate that interactions between neighboring individuals profoundly shape the diffusion trajectories of NEVs. Even during the phase-out of government financial subsidies, the peer effects generated by online word-of-mouth can serve as an important self-reinforcing mechanism for the adoption of NEVs [20]. Different information interaction mechanisms yield distinct outcomes, as firms are more susceptible to negative information from peers compared to positive information [21]. In addition, opinion leaders situated at the core positions of social networks also attract substantial attention. Existing studies demonstrate that opinion leaders play a critical role in the adoption and promotion of new products [22, 23] and facilitate broader information dissemination [24].

Beyond the effects of individual drivers, recent studies have increasingly examined NEV diffusion by incorporating selected combinations of different influencing mechanisms within the same analytical framework. Government policy has been considered together with consumer social influence and infrastructure-related conditions in dual-layer network models [18]. Other studies have jointly examined charging infrastructure and government demonstration while accounting for spatial spillover effects in NEV diffusion [25]. Building on these multi-mechanism settings, a smaller body of research has further explored whether the effects of different mechanisms are jointly determined, conditional on one another, or connected through feedback processes. The effectiveness of NEV policies has been shown to vary across policy combinations and market characteristics [8], while peer-based imitation and demonstration can alter green innovation diffusion under mixed government policies [21]. Policy-driven and market-driven mechanisms may also reinforce one another in promoting NEV diffusion [26], and dynamic feedback between government intervention and market demand can reshape low-carbon technology diffusion outcomes [27]. Taken together, these studies suggest that different diffusion mechanisms may reinforce, offset, or condition one another. However, existing evidence remains concentrated on selected mechanism combinations, leaving broader interactions among policy, social, market, and physical mechanisms insufficiently understood.

2.2 Research on the impact of digital marketing on innovative product diffusion

Amid the rapid expansion of the digital economy, the information environment governing product diffusion has undergone profound transformations. A growing body of literature explores the dual effects of digital marketing on the diffusion of innovative products, particularly green products.

• Digital marketing empowerment and the adoption of green innovation

Digital marketing has been widely examined as an important mechanism influencing consumer adoption and the market diffusion of innovative and green products. Faced with “information overload” caused by the vast amount of market information, algorithmic recommendation systems have become an important digital marketing tool influencing consumer decision-making. Research has found that collaborative filtering and content-based recommendation mechanisms can effectively guide and enhance consumers’ purchase intentions by activating their social or personal identity [28]. Regardless of whether consumers fully trust algorithm-generated information, corporate algorithmic recommendations can significantly increase purchase intentions, demonstrating greater efficacy in guiding consumer decisions than opinion leaders [29].

Simultaneously, in a digital context, the dynamic evolution of user-generated content and online sentiment has significantly accelerated the market diffusion of new digital products [

]. Particularly in the current era of deep integration between the live-streaming economy and social networks, digital interactions not only enhance product accessibility for online consumers but also influence their adoption of green products [

]. In this context, social media influencers, as important agents in information dissemination [

], not only directly boost the purchase intent of target audiences through their credibility [

], but the framing of their messages (e.g., gain-loss framing) and the timing of their posts also determine the persuasive effectiveness of promoting green and sustainable products online [

• 2. The hindering effects of information complexity and emotional polarization

While emphasizing the positive role of digital marketing, some scholars have begun to focus on its potential negative impacts [37], particularly the complex negative effects that high-intensity digital marketing may induce online. Research indicates that the impact of digital marketing tools, such as online reviews, on new product diffusion is not a simple linear relationship; the interaction between the number of reviews and emotional polarity exhibits complex nonlinear characteristics [38]. Notably, high-intensity digital marketing tends to amplify emotional polarization within social networks, thereby weakening consumers’ attitudes toward adopting new products. Empirical tests reveal that emotional polarization on social media exacerbates the ambivalence of consumer attitudes, which in turn significantly reduces the willingness to adopt new products. Moreover, this inhibitory effect caused by information conflict is particularly pronounced in the early stages of an innovative product’s life cycle [39].

2.3 Complex network evolutionary game theory

Evolutionary game theory extends traditional game theory by relaxing the assumption of complete rationality and incorporating bounded rationality and iterative learning mechanisms into its mathematical framework, thereby providing an important theoretical tool for understanding how agents dynamically adjust their strategies in response to changing environments [40]. However, classical evolutionary game theory is typically based on the well-mixed population assumption, under which any two agents interact randomly with an equal probability [41]. While this assumption facilitates theoretical analysis, it is difficult to reconcile with real-world social, economic, and ecological systems, where interactions among agents are highly heterogeneous, nonlinear, and embedded within complex network structures rather than occurring randomly or under fully coupled conditions [42].

To overcome this limitation, scholars have integrated complex network theory into the evolutionary game framework, giving rise to complex network evolutionary game theory [43]. Compared with traditional evolutionary game models, this approach relaxes the well-mixed assumption by employing network topology to characterize heterogeneous connections among agents while simultaneously applying evolutionary game principles to describe their strategic decision-making processes [44]. Consequently, it provides a more realistic representation of strategic evolution in complex social systems and offers deeper insights into how network topology and local interactions jointly shape the dynamics of collective behavior [44].

In recent years, complex network evolutionary game theory has been widely applied to the study of cooperative behavior, technology diffusion, and innovation management [27, 45]. Previous studies have shown that this approach not only captures the complex interaction patterns among heterogeneous agents but also offers advantages in dynamic simulation, real-time strategy updating, and adaptive learning [40]. More importantly, it enables researchers to investigate how local interactions among micro-level agents give rise to adaptive evolution and emergent outcomes at the macro-system level under different policy interventions and market mechanisms.

The diffusion of new energy vehicles is inherently a complex adaptive process driven by the co-evolution of firms’ strategic decisions, consumer network interactions, and external environmental factors. This process involves the continuous evolution of strategies among heterogeneous agents while being fundamentally influenced by complex network structures. Therefore, complex network evolutionary game theory provides an appropriate theoretical framework for analyzing the coupling between micro-level behavioral evolution and macro-level diffusion outcomes and supports the construction of the dual-layer heterogeneous network model developed in this study.

2.4 Literature summary and research gaps

The above literature demonstrates that existing studies have achieved substantial progress in understanding policy drivers, underlying physical constraints, and social network effects in NEV diffusion, as well as the role of digital marketing in innovative and green product diffusion, providing a solid theoretical foundation for explaining market diffusion dynamics.

To further clarify the research boundaries of this study, Table 1 provides a systematic comparison of the core mechanisms and methodologies of recent representative studies. As shown in Table 1, existing research mainly investigates NEV diffusion from single-factor or selected multi-factor perspectives, including government policies, digital marketing, social network effect, and underlying physical constraints. Although some studies consider more than one mechanism, they generally focus on specific combinations rather than integrating these four dimensions within a unified framework. Consistent with the preceding review, a limited number of studies have further examined relationships between selected mechanisms, but such analyses remain confined to particular combinations. Consequently, a more integrated understanding of how these mechanisms jointly shape NEV diffusion remains limited.

Representative studies	Policy	Digital marketing	Social network	Physical constraints	Method
[8]	✓	×	×	✓	Stackelberg game
[46]	×	✓	✓	×	Empirical analysis/Survey data
[10]	✓	×	×	×	Complex network evolutionary games
[47]	✓	×	×	×	Complex network evolutionary games
[18]	✓	×	✓ (Herd effect)	✓	Complex networks and agent-based modelling
[4]	✓	×	×	×	Complex network evolutionary games
[5]	×	×	×	✓	Discrete choice experiments, agent-based model
[48]	✓	×	✓ (government-level information spillover network)	×	Dynamic topic model, net directed connectivity model
[25]	✓	×	×	✓	Spatial panel econometrics
This study	✓	✓	✓	✓	Complex network evolutionary games

Comparative summary of representative studies and the proposed framework.

✓ indicates that the study considers the corresponding factor, whereas × indicates that the factor is not included. Studies are presented in chronological order.

Against this background, several research gaps remain. First, in increasingly digitalized market environments, limited attention has been paid to firms’ digital marketing behavior in the evolutionary analysis of NEV diffusion, particularly to how digital marketing strategies shape consumer information exposure and NEV adoption. Second, although previous studies have examined interactions and co-evolution between firms and consumers, their strategic evolution within distinct heterogeneous network structures remains insufficiently characterized. In particular, how consumer adoption feeds back into firm strategy evolution through market demand remains inadequately explored. Third, few studies have simultaneously incorporated government policies, digital marketing mechanisms, social network effects, and underlying physical constraints within a unified analytical framework. Consequently, understanding of NEV diffusion under the combined influence of these mechanisms remains incomplete, and the reinforcing or compensatory relationships among selected mechanisms warrant further investigation.

To address these limitations, this study develops a dual-layer heterogeneous network evolutionary game model comprising a supply-side network of firms and a demand-side network of consumers. Consumer adoption affects firm strategy evolution through market demand, while evolving firm strategies feed back into consumer decisions through marketing exposure, thereby capturing the co-evolution between the two layers. Specifically, this study integrates multiple government policies, digital marketing mechanisms, social network effects (distinguishing between bandwagon effects and the influence of heterogeneous hub nodes), and underlying physical constraints into a unified analytical framework. Selected joint-effect analyses are further conducted to examine reinforcing and compensatory relationships among selected mechanisms. This framework is used to investigate the evolutionary dynamics of NEV diffusion under the combined effects of these mechanisms.

3 Model

This study develops a dual-layer heterogeneous network evolutionary game model comprising a firm layer and a consumer layer to explore the dynamic process of NEV diffusion in the digital economy. Specifically, the upper layer represents the competitive network among firms, while the lower layer denotes the consumer social network. The proposed dual-layer network constitutes a functionally coupled system. The two layers achieve cross-layer coupling through market demand feedback and marketing exposure, which jointly influence the evolutionary dynamics of NEV diffusion. The overall research framework is illustrated in Figure 1.

3.1 Network structure

• 1. Demand-side consumer layer: Barabási-Albert (BA) scale-free network

In digital social environments, consumer interaction networks often exhibit pronounced connectivity heterogeneity. Existing studies have shown that online social networks display scale-free characteristics, with a small number of highly connected nodes and many nodes having relatively few links [

]. The BA scale-free network reproduces this heterogeneous connectivity through the preferential-attachment mechanism, which is consistent with the structural characteristics observed in online consumer interaction networks [

]. Accordingly, this study adopts a BA scale-free network to represent the consumer layer. The network consists of

consumer nodes and is characterized by a heterogeneous degree distribution. Each newly added consumer node establishes

links with existing nodes according to the preferential-attachment mechanism, allowing a small number of highly connected hub nodes to emerge endogenously.

• 2. Supply-side firm layer: Watts-Strogatz (WS) small-world network

The evolution of automotive firms’ strategies is closely related to the structure of their interaction network. Previous studies on NEV diffusion have adopted WS small-world networks to represent strategic interactions among automotive manufacturers, with firms represented as nodes and their competitive interactions represented by network links [

]. Small-world networks are characterized by relatively high clustering and short average path lengths, allowing dense local interactions to coexist with relatively short paths across the broader network. These properties make the WS structure suitable for representing localized yet interconnected strategic interactions among automotive firms [

]. Accordingly, this study adopts a WS small-world network to represent the firm layer. The firm network consists of

nodes. During network initialization, each node

) nearest neighbors on each side of a regular ring lattice, resulting in

initial neighbors in total. Subsequently, with a rewiring probability

, one end of each edge is disconnected and randomly rewired to other nodes in the network. Self-loops and duplicate links are not allowed.

Existing evolutionary studies often model automotive firms as networked strategic agents while representing consumers through aggregate demand or predefined consumer types [10, 27]. Such representations capture demand-side heterogeneity to some extent, but do not explicitly account for the evolution of consumer adoption through social interactions within a consumer network. Following the dual-layer firm-consumer framework of Zhang and Han [18], this study therefore represents firms and consumers as two distinct network layers, allowing firm competition and consumer social interaction to evolve within their respective network structures.

Cross-layer interaction in the present model operates through market demand and marketing exposure rather than fixed one-to-one firm-consumer links. Related dual-layer studies also link firm and consumer dynamics through market demand and strategic feedback [18, 44]. This representation is consistent with the digital marketing setting considered here, in which consumers may be exposed to information from multiple firms rather than through stable pairwise relationships with individual firms. Consumer adoption decisions aggregate into the market penetration rate, which determines the relative demand for NEVs and ICEVs and thereby affects firm payoffs and subsequent strategy evolution. Conversely, the evolving composition of firms’ technology and marketing strategies determines the relative marketing exposure associated with NEVs and ICEVs. This exposure enters consumer utility and influences subsequent adoption decisions, while its intensity varies across consumers according to their network characteristics.

This coupling retains the distinct network structures and decision mechanisms of firms and consumers while allowing changes in either layer to affect incentives in the other. Relative to firm-centered network models that represent consumers through aggregate demand or predefined types, the dual-layer framework also incorporates consumer social interaction and the endogenous evolution of adoption into the analysis of firm strategy evolution. NEV diffusion is thus represented as a co-evolutionary process shaped by within-layer interactions and cross-layer market feedback.

3.2 Model assumptions

This study develops a dual-layer heterogeneous network evolutionary game model comprising firms and consumers. To define the analytical scope and behavioral rules of the model, the following assumptions are proposed.

Assumption 1The market consists of two types of dynamic agents, namely, firms and consumers, both of which are boundedly rational and operate under information asymmetry. Agents can observe and compare only the current payoffs or utilities of their directly connected neighbors within the same network layer. Strategy updating follows the Fermi rule [52].

Assumption 2The automobile market is assumed to operate under a competitive market setting, with NEV and ICEV prices fixed at benchmark levels within each simulation scenario [18]. Existing dynamic-game research shows that pricing adjustments under green consumer preferences can alter strategic outcomes and system stability [53]. To maintain focus on technology choices, marketing strategies, and consumer adoption, endogenous price competition is excluded from the present model. Firms compete for effective market share through their technology and marketing strategies.

Assumption 3The state of a consumer at time is represented by , where denotes an NEV adoption state and denotes an ICEV adoption state. This state represents a consumer’s long-term technology adoption propensity and cognitive attitude, rather than short-term, high-frequency purchase decisions. According to the law of large numbers, the proportion of attitudes across the entire network approximates the actual demand base within the current vehicle replacement window.

Assumption 4Government intervention is represented by three exogenous policy variables: the consumer purchase subsidy, the technology transition subsidy, and the carbon price. The endogenous adjustment of these policy parameters over time is not modeled [18], and each policy variable remains constant within a given simulation run. Previous dynamic-game research shows that carbon regulation and policy intensity can alter firms’ strategic responses and system stability [54]. Accordingly, different policy levels are examined across experimental scenarios to evaluate their effects on system evolution. In experiments examining non-policy mechanisms, all three policy variables are held at their benchmark values.

The definitions of the key model parameters are summarized in Table 2.

Parameter category	Symbol	Definition
General parameters	Total number of nodes in the consumer layer and firm layer, respectively
BA scale-free network linking parameter, initial number of neighbors, and random rewiring probability in the WS small-world network, respectively
Set of locally connected neighbors of consumer , and degree of node
Market penetration rate of NEVs at time , and total number of active consumers entering the vehicle replacement window per unit time
Current-period market demand for NEVs and ICEVs
Baseline carbon emission quota per vehicle, and carbon price in the carbon emissions trading market
Consumer purchase subsidy for NEVs, and technology transition subsidy rate provided to firms
Algorithmic targeting sensitivity coefficient
Consumer layer	Consumer strategy set , and state variable of consumer at time , with for NEV and for ICEV, respectively
Intrinsic utility value of NEVs and ICEVs
Price sensitivity coefficient of consumers, and charging anxiety penalty coefficient
Technological-risk sensitivity coefficient, and perceived technological risk of NEVs
Digital marketing utility conversion coefficient, and information overload penalty coefficient
Heterogeneous social influence weight, and node influence index
Local basic bandwagon effect coefficient, and heterogeneous hub node influence coefficient
Individual long-term preference parameter, and intensity of individual preference heterogeneity
Noise factor in the consumer decision-making environment
Firm layer	Firm strategy set , and fixed technology transition investment required for NEV production
Number of firms adopting each of the four strategy combinations at time
Unit production costs of NEVs and ICEVs
Unit price of NEVs and ICEVs
Unit carbon emissions of NEVs and ICEVs (assuming )
Digital marketing expenditure, and traditional marketing expenditure
Exposure premium multiplier generated by digital marketing, and noise factor in the firm decision-making environment

Definitions of core parameters.

3.3 Model construction

3.3.1 Demand side: consumer utility

The strategy space of a consumer is defined as

denote the number of consumers adopting NEVs at time

. The market penetration rate of NEVs is therefore defined as

denote the total number of active consumers entering the vehicle replacement cycle per unit time. This demand is allocated according to the prevailing market penetration rate. Accordingly, the current-period demand for NEVs and ICEVs is given by

respectively. Consumers’ choices between NEVs and ICEVs are primarily influenced by the following four factors:

When evaluating alternative vehicle technologies, consumers consider not only intrinsic utility value and product price but also government purchase subsidies [10] and perceived technological risk. In addition, charging and range anxiety gradually diminish as NEV penetration increases, which is captured by the penalty term [18]. Perceived technological risk associated with battery degradation, driving range uncertainty, and material safety is represented by , whose effect is moderated by the technological-risk sensitivity coefficient .

In social media networks, consumers with more extensive social connections tend to generate more interactions and behavioral information, making them more likely to be identified and targeted by platform algorithms. Node degree is therefore used as a proxy for consumers’ network activity and visibility in algorithmic targeting. Considering the saturation effect of recommendation algorithms, marketing exposure cannot increase without bound. Let denote the technology type. The digital marketing exposure received by consumer node for technology type , denoted by , is defined in Equation 1:where denotes the degree of node , is the average degree of the network, and denotes the algorithmic targeting sensitivity coefficient, which governs the degree to which differences in consumers’ network activity are translated into heterogeneous recommendation exposure. Furthermore, denotes the proportion of firms adopting digital marketing for technology type at time , i.e., , .

Unlike the broadcast-style dissemination of traditional marketing, digital marketing is characterized by high-frequency and repeated information exposure, which may lead to information overload. As marketing exposure increases, its marginal utility declines and may become negative at sufficiently high exposure levels. Accordingly, the utility generated by digital marketing is formulated in Equation 2:where denotes the digital marketing utility conversion coefficient, and represents the information overload penalty coefficient. This quadratic specification captures the increasing penalty associated with intensive marketing exposure and information overload.

Consumers’ vehicle purchase decisions exhibit typical social learning characteristics and are continuously influenced by the opinions of their neighbors within the social network. To characterize the social network effects, this study draws on the local spin interaction concept from the Ising model, representing the opinion consensus between a consumer and their neighbors as social norm utility [18]. It is worth noting that the Ising model is adopted solely to describe local social interaction mechanisms. It does not assume that the entire consumer system follows the global energy minimization dynamics of the classic Ising model; rather, consumer strategies are still updated based on total utility using the Fermi rule in the evolutionary game [55].

Considering the degree heterogeneity in digital social networks, a small number of highly connected nodes generally possess stronger information dissemination capabilities. Therefore, building upon the conventional neighborhood interaction mechanism, a weighting mechanism based on node influence is introduced to characterize the impact of heterogeneous hub nodes on consumers’ social norm utility. To this end, this study defines the heterogeneous social influence weight of neighbor node relative to node as shown in Equation 3:where the node degree is adopted as a proxy variable for social influence. Future research may extend this specification to other network topology metrics.

Based on this, the social norm utility of node at time is formulated in Equation 4:where denotes the adoption state of consumer (+1 for NEV and −1 for ICEV), denotes the adoption state of consumer , is the set of locally connected neighbors of node ; and represent the degrees of nodes and , respectively. The first term represents the local basic bandwagon effect generated by connected neighbors, while the second term captures the heterogeneous social influence of hub nodes. The parameters and represent the local basic bandwagon effect coefficient and the heterogeneous hub node influence coefficient, respectively, and () is the node influence index, which controls the contribution of node degree to the social influence weight.

Consumers’ vehicle purchase decisions are influenced not only by rational economic value, marketing utility, and social norms but also by subjective factors such as long-term brand loyalty, technological propensity, and environmental preferences. Significant differences exist in the latent preferences of different consumers for NEVs and ICEVs. Therefore, this study introduces an individual long-term preference parameter (following a uniform distribution ), where represents consumer ’s degree of preference for NEVs, which remains constant throughout the consumer’s decision-making cycle. () is the intensity of individual preference heterogeneity. When , the consumer prefers NEVs; when , the consumer prefers ICEVs. A larger indicates more pronounced preference differences among consumers.

Integrating the above four components, the total utilities of consumer associated with the two strategies at time are formulated as shown in Equations 5, 6:

3.3.2 Supply side: firm strategy and payoffs

Within a competitive automotive market setting, firms choose among technology pathways and marketing channels. This gives rise to the strategy set

: NEV production with digital marketing,

: NEV production with traditional marketing,

denote the numbers of firms adopting the four strategy combinations at time

. Strategic heterogeneity among firms arises from their technology and marketing choices under different cost and institutional conditions.

Different business strategies involve trade-offs between costs and benefits. Producing NEVs requires a fixed technology transition investment

. The unit production costs of NEVs and ICEVs are denoted by

, respectively, while their market prices are represented by

Digital marketing incurs a higher marketing cost

, but provides firms with an exposure advantage through platform-mediated recommendation. This advantage is represented by an exposure premium multiplier

), which increases the relative market visibility of firms adopting digital marketing. In contrast, firms adopting traditional marketing receive only baseline exposure while incurring a lower marketing cost

). Accordingly, firms’ effective market shares within each technology segment are determined by their relative weighted exposure.

To support firms’ transition toward NEV production, the government provides a technology transition subsidy at a rate of , which offsets part of the fixed technology transition investment . Under the carbon emissions trading system, the baseline carbon emission quota per vehicle is denoted . The unit carbon emissions associated with NEVs and ICEVs are denoted by and , respectively, satisfying [9]. The carbon price in the carbon emissions trading market is denoted by . Consequently, in the carbon trading market, NEV-producing firms obtain positive carbon revenues, whereas ICEV-producing firms incur carbon compliance costs.

Based on the above model formulation, the payoff functions under the four strategic configurations are defined as follows:

Strategy (NEV + Digital Marketing):

Strategy (NEV + Traditional Marketing):

Note: Under the pairwise imitation rule, strategy payoffs are evaluated only for strategies currently represented in the firm population. Therefore, the corresponding denominators in Equations 7–10 remain positive whenever these payoffs are evaluated.

3.4 Evolutionary rules

This study employs the classical Fermi rule to describe the learning and strategy-updating processes of firms and consumers [

]. Within each simulation period, agents within both layers are updated asynchronously in random order, and successful strategy updates take effect immediately.

randomly selects a neighboring consumer

within the same network layer for comparison. The probability that consumer

adopts the strategy of neighbor

denote the utilities of consumers

represents the noise factor in the consumer decision-making environment, reflecting the uncertainty during consumers’ strategy updating.

Similarly, at time , firm randomly selects a neighboring firm within the firm layer for performance comparison. The probability that firm adopts the strategy of firm is given by Equation 12:where and denote the payoffs of firms and at time , respectively, and represents the noise factor in the firm decision-making environment, reflecting the uncertainty during firms’ strategy updating.

4 Numerical simulation and results

4.1 Network initialization and parameter calibration

The simulation environment is initialized according to the theoretical framework developed in

. Benchmark values are determined from two sources. Parameters with identifiable market, policy, or literature references are anchored to previous NEV studies and relevant policy information. Behavioral and structural parameters that lack directly observable empirical counterparts are calibrated according to their roles and relative scales in the utility and payoff functions. These values ​​should therefore be viewed as working benchmarks for the model rather than precise empirical estimates. Subsequent sensitivity and robustness analyses are used to assess whether the main findings depend on particular parameter or simulation settings.

reports the benchmark values ​​and their calibration basis.

Parameter	Value	Calibration basis
1,000, 200	Population sizes following Zhang and Han [18]
4, 4, 0.1	Structural benchmarks for network connectivity and rewiring; alternative settings are examined in network tests
0.2, 0.1, 0.1, 0.4, 0.4	Initial NEV adoption share following [18], marketing strategies are equally allocated within each technology
10000, 100	Model-scale benchmarks for market capacity and fixed technology transition investment
21, 15, 14, 11	Vehicle prices anchored to [9, 18]; production costs structurally calibrated with
1, 0.25	Both values ​​lie within representative ranges reported for NEV purchase and technology-support policies, is also consistent with related evolutionary research [10]
0.005, 27, 20, 30	Carbon price, quota, and lifecycle-emission settings following [9, 18]
30, 22.5, 0.5, 0.5	Utility-scale calibration balancing the higher NEV valuation against its price and risk disadvantages, with equal weights assigned to price and technological risk
3, 1.8, 4	Structural benchmarks for charging anxiety, perceived risk, and preference heterogeneity; is further examined in sensitivity analysis
1.2, 0.1, 1	Structural settings based on their functional roles in marketing exposure, marginal attenuation, and degree-sensitive recommendation
1, 1, 1.2	η follows Zhang and Han [18]; and are structural settings for hub-based influence
12, 2, 1.2	Structural benchmarks reflect higher digital-marketing costs and a moderate exposure advantage
0.1, 0.1	Following the Fermi noise setting for consumer and firm strategy updating in a related NEV diffusion study [18]

Benchmark parameter values and calibration basis.

The consumer layer is represented by a BA scale-free network with , and the firm layer by a WS small-world network with , following the population sizes adopted by Zhang and Han [18]. The BA linking parameter is , giving an average consumer degree of approximately eight. For the WS network, and , so each firm initially has four nearest neighbors before random rewiring. These network settings serve as structural baselines, with subsequent tests examining variations in network size, connectivity levels, rewiring probabilities, and topological structures.

Following the approach of Zhang and Han [

], the initial proportion of consumers adopting NEVs is set to

. The firm population is initialized with the same 20% share of NEV-producing firms. Within each technology, digital and traditional marketing strategies are assigned equal shares, giving initial proportions of 10%, 10%, 40%, and 40% for

. These initial shares are fixed, while their assignments to individual nodes are randomized in each replication. Consumers and firms update asynchronously according to the Fermi rule, with

]. All simulations are implemented in Python and conducted over 150 periods. Each experimental setting is independently replicated 100 times to account for stochastic variation, and the reported evolutionary trajectories are Monte Carlo means across these replications. Steady-state outcomes are calculated as the average over the final 20 periods of each simulation. Network realizations, node assignments, individual preference draws, and stochastic strategy-updating sequences are independently generated for each replication.

Market and policy parameters are calibrated, where possible, using values ​​reported in previous NEV studies. Representative vehicle prices are set to and (unit: 10,000 RMB), respectively [9]. Because directly comparable vehicle-level manufacturing costs are not available, and are used as effective unit production costs, preserving the higher cost of the NEV production pathway. The fixed technology transition investment is set to . Total market capacity is set to , corresponding to 50 demand units per representative firm under the benchmark firm population.

Policy settings include consumer purchase support, firm-side technology support, and carbon regulation. The consumer purchase subsidy and technology transition subsidy rate ​​are set to and , respectively. Both are within the ranges reported in relevant NEV policies. The value of is also consistent with that used in related evolutionary research [10]. The carbon price is , equivalent to RMB 50/tCO₂ [9]. The values , and tons follow lifecycle-emission settings used in related NEV studies [18].

Consumer and marketing coefficients without direct empirical counterparts are calibrated on the internal scale of the model. The baseline perceived values ​​are set to and . Price sensitivity and technological-risk sensitivity are both set to , assigning equal moderate weights to these two factors. Charging anxiety penalty coefficient and perceived technological risk are represented by and . Consumer heterogeneity follows , with . This zero-centered distribution introduces preference dispersion without imposing an aggregate preference for either technology. Because affects heterogeneous early adoption, its sensitivity is further examined in the Supplementary Material (Supplementary Figure S1).

Digital marketing is characterized by , , and , representing the digital marketing utility conversion coefficient, the information overload penalty coefficient, and the algorithmic targeting sensitivity coefficient, respectively. Firm-side marketing parameters are set to , and , with representing a moderate exposure advantage for digital marketing. For social network effects, the local basic bandwagon effect coefficient is set to [18]. The heterogeneous hub node influence coefficient and node influence index are set to and , respectively, providing a neutral baseline for hub influence while allowing highly connected consumers to exert moderately stronger effects.

Given the number of behavioral, market, and network parameters in the model, subsequent analyses focus on policy variables and parameters directly associated with the core examined mechanisms in this study. Network structure, initial conditions, and selected structural parameters are further evaluated through sensitivity and robustness tests, while non-focal parameters are maintained at the benchmark values ​​reported in Table 3.

4.2 Benchmark outcomes and diffusion thresholds

This section describes the long-run behavior of the coupled firm-consumer system under the benchmark parameter settings. It examines the distribution of steady-state outcomes across repeated simulations and evaluates how the initial consumer NEV adoption rate affects the diffusion outcome. The analysis therefore provides a benchmark for identifying the main features of NEV diffusion and its dependence on the initial market base.

Figure 2 presents the steady-state outcomes across 100 independent Monte Carlo replications. As shown in Figure 2A, consumer NEV adoption exhibits a pronounced bimodal distribution. Most replications approach either a low-adoption state or a near-complete adoption state, while relatively few remain at intermediate levels. The Monte Carlo mean is approximately 0.53. This value should therefore be interpreted as an average across heterogeneous long-run outcomes rather than as the steady state reached by a typical individual replication. A comparable polarization appears in the firm layer. Figure 2B shows that firm NEV transition is also concentrated near the two extremes. Digital marketing adoption behaves differently and remains close to one in almost all replications. Thus, the benchmark system displays substantial variation in technology adoption and transition outcomes, while firms’ marketing strategy choices are considerably more stable. The corresponding benchmark Monte Carlo mean trajectories of consumer NEV adoption and firm strategy evolution are reported in Supplementary Figure S2 in the Supplementary Material.

Figure 3 examines how the initial consumer NEV adoption rate () affects the evolutionary outcome. Figure 3A shows a nonlinear, S-shaped relationship between the initial NEV adoption rate and steady-state NEV adoption. At low initial adoption rates, most simulations remain in the low-adoption regime. The mean adoption rate rises rapidly over the intermediate range, where variation across replications is also greatest. At higher values ​​of , the system increasingly settles in the high-adoption regime. Figure 3B reports the probability of achieving near-complete NEV diffusion, measured as a steady-state consumer adoption rate of at least 0.95. The probability rises sharply with , reaches 1.0 at , and remains at this level thereafter within the examined range. Accordingly, represents the lowest tested initial adoption rate at which all 100 replications reach near-complete NEV diffusion under the benchmark setting.

Overall, the results show that NEV diffusion is characterized by strong path dependence and a clear dependence on the initial market base. Both consumer NEV adoption and firm NEV transition exhibit two distinct steady-state regimes, corresponding to low- and high-NEV outcomes. A higher initial NEV adoption rate increases the likelihood of near-complete NEV diffusion. This pattern arises from reinforcing feedback between the consumer and firm layers. A larger initial NEV user base strengthens pro-NEV social influence, reduces the disadvantage associated with charging constraints as market penetration increases, and expands aggregate NEV demand. Higher demand raises the relative payoff of NEV strategies and encourages firm transition toward NEVs. The accompanying shift in firm strategy composition can increase NEV-oriented market exposure and further support consumer adoption. This cross-layer feedback amplifies early differences in market penetration and produces the S-shaped, threshold-like diffusion pattern observed in Figure 3.

4.3 Effects of government policies

This section compares the effects of three government policy instruments on NEV diffusion: the consumer purchase subsidy for NEVs (), the firm technology transition subsidy rate (), and the carbon price (). These instruments differ in units and benchmark magnitudes, making direct comparison based on absolute parameter changes inappropriate. A dimensionless policy-intensity factor, , is therefore introduced to standardize their variation. In each experiment, the focal policy parameter is scaled by relative to its benchmark value, while the other two remain fixed at their benchmark levels. The factor varies from 0 to 2 in increments of 0.25, with representing removal of the focal policy, the benchmark level, and twice the benchmark intensity. This design allows the system responses to proportional changes in different policy instruments to be compared on a consistent basis, without assuming equivalence in fiscal cost or welfare effects.

Under the benchmark calibration, the standardized interval corresponds to a consumer purchase subsidy of 0–20,000 RMB, a technology transition subsidy rate of 0%–50%, and a carbon price of approximately 0–100 RMB/tCO_2. The benchmark values ​​are anchored to the policy and market conditions described in Section 4.1, while the wider interval is used to examine system responses under weaker and stronger policy scenarios. The endpoints therefore represent comparative sensitivity scenarios rather than equally typical levels of observed policy practice. The carbon-price range is also consistent with previous NEV research. Zhang and Han [18] adopted 50 RMB/tCO₂ as the benchmark carbon price for China and considered 0 and 100 RMB/tCO₂ as no emissions trading system and high-price scenarios, respectively. The range adopted here therefore remains within the carbon-price settings previously used for NEV diffusion analysis.

Figure 4 compares the Monte Carlo mean steady-state responses of consumers and firms under the standardized policy scale. By construction, the three policy curves meet at the benchmark outcome when . Figure 4A shows that consumer NEV adoption responds strongly to the purchase subsidy. The steady-state adoption rate is close to 0.10 when the subsidy is removed and rises steadily with policy intensity, approaching near-complete diffusion at the upper end of the examined range. The technology transition subsidy produces a much smaller change in consumer adoption, while the carbon-price curve remains close to the benchmark level across most of the interval. Figure 4B shows a similar pattern for firm NEV transition. Stronger purchase subsidies lead to a pronounced increase in the steady-state share of NEV strategies, whereas the effects of the transition subsidy and carbon price are comparatively limited. The close correspondence between the two panels reflects the coupling between consumer demand and firm technology choices.

Overall, equal proportional changes in the three policy instruments generate markedly different diffusion responses. The purchase subsidy produces the largest increase in both consumer NEV adoption and firm NEV transition because it directly improves the relative utility of NEVs and expands market demand. By contrast, the technology transition subsidy and carbon price both operate through the firm payoff function. The former reduces the fixed cost of NEV transition, whereas the latter changes the relative returns of NEV and ICEV strategies through their emission differences. Under the benchmark setting, these firm-side adjustments generate more limited changes in the long-run diffusion outcome. The diffusion effect of a policy therefore depends not only on its intensity, but also on the channel through which it enters the coupled consumer-firm system.

4.4 Effects of digital marketing mechanisms

This section examines how the digital marketing utility conversion coefficient () and the information overload penalty coefficient () affect NEV diffusion. The former captures the extent to which digital marketing exposure is converted into consumer utility, while the latter represents the penalty associated with intensive marketing exposure.

Figure 5 shows how and affect consumer NEV adoption and firm strategy evolution. Figure 5A shows that increasing reduces both consumer NEV adoption and firm NEV transition, while digital marketing adoption remains close to one. ICEV-oriented digital firms initially account for a larger share of the firm population, so a higher amplifies their existing exposure advantage and makes NEV diffusion more difficult. Figure 5B shows the opposite effect of . A higher information overload penalty increases NEV adoption and firm NEV transition by weakening the marketing advantage associated with the greater initial exposure of ICEVs.

Overall, the asymmetric effects of and can be traced to the marketing component of consumer utility. Under the benchmark initial firm composition, ICEV-oriented digital firms account for a larger share than NEV-oriented digital firms, giving ICEVs greater marketing exposure. A higher magnifies this exposure advantage and reinforces the incumbent position of ICEVs. In contrast, because the information-overload penalty increases quadratically with exposure, a higher imposes a larger utility loss on the more heavily exposed ICEV option, narrowing its relative utility advantage. The resulting shift in consumer demand is then transmitted to firm technology choices. Thus, digital marketing does not uniformly promote the diffusion of an emerging technology; its effect depends on the initial distribution of marketing exposure and how consumers translate that exposure into utility.

4.5 Effects of social network mechanisms

This section conducts sensitivity analyses on the local basic bandwagon effect coefficient () and the heterogeneous hub node influence coefficient (). The former captures conformity to neighboring consumer choices, while the latter reflects the influence of highly connected consumers in the network.

Figure 6 shows how and affect consumer NEV adoption and firm strategy evolution. Figure 6A shows that increasing reduces both consumer NEV adoption and firm NEV transition, while digital marketing adoption remains close to one. Because ICEVs dominate the initial consumer market, stronger local conformity reinforces the prevailing choice within consumer neighborhoods and makes it more difficult for NEVs to expand from a small user base. Figure 6B shows a similar effect of . Greater hub node influence gives more weight to highly connected consumers and, under the initial ICEV majority, tends to reinforce the incumbent technology throughout the network. The similar responses to and indicate that both local conformity and heterogeneous influence can preserve the incumbent advantage when NEVs begin from a minority position.

Overall, both forms of social influence reinforce the prevailing market structure. Their effect is therefore conditional on the initial composition of the consumer network rather than inherently favorable to NEV diffusion. Under the benchmark setting, where ICEVs initially hold the majority, stronger local conformity and hub influence amplify this incumbent advantage and hinder the transition toward NEVs.

4.6 Effects of underlying physical constraints

This section examines the effects of the charging anxiety penalty coefficient () and the perceived technological risk of NEVs (). The former captures the constraint associated with charging conditions, while the latter reflects consumers’ perceived risk of NEV technology.

Figure 7 shows how and affect consumer adoption and firm strategy evolution. Figure 7A shows that increasing suppresses both consumer NEV adoption and firm NEV transition. Low charging anxiety supports near-complete NEV diffusion, whereas higher values ​​of lead to progressively lower adoption and transition outcomes. A stronger charging penalty reduces the relative utility of NEVs, weakens consumer adoption, and consequently lowers NEV demand. Figure 7B shows a similar negative effect of . Higher perceived technological risk reduces consumer NEV adoption and firm NEV transition by lowering the perceived utility of NEVs and weakening market demand. Digital marketing adoption remains close to one across the tested values ​​of both parameters.

Overall, charging conditions and perceived technological risk constrain NEV diffusion primarily through consumer utility, with their effects subsequently transmitted to firm technology choices through market demand. The persistence of digital marketing adoption even when NEV diffusion remains low also suggests that marketing activity cannot fully offset unfavorable physical conditions. These results underline the importance of charging accessibility and technological reliability for sustained NEV diffusion.

4.7 Joint effects of key diffusion mechanisms

This section examines the joint effects of selected mechanisms identified in the preceding analyses. The analysis considers the interaction between the initial NEV adoption base () and consumer purchase subsidy (), the combined effects of digital marketing utility conversion coefficient () and the heterogeneous hub node influence coefficient (), and the interaction between consumer purchase subsidy () and charging anxiety ().

Figure 8 shows how the initial NEV adoption base () and consumer purchase subsidy () jointly shape the steady-state diffusion outcome. NEV adoption increases with both a larger initial user base and a higher purchase subsidy. More importantly, the iso-adoption contours shift toward lower values ​​of as increases. A stronger purchase subsidy can therefore partly compensate for a weak initial market base and reduce the initial adoption level required to achieve a given diffusion outcome. This compensating effect becomes less important once the initial NEV user base is already sufficiently large.

Figure 9A examines the joint effects of digital marketing utility conversion coefficient () and the heterogeneous hub node influence coefficient (). Higher values ​​of either parameter reduce NEV adoption under the benchmark market structure, and their combined increase moves the system further toward the low-adoption region. The downward shift of the iso-adoption contours indicates that, as one mechanism becomes stronger, a smaller increase in the other is sufficient to produce the same reduction in NEV adoption. Digital marketing utility and hub node influence therefore jointly reinforce the initial advantage of the incumbent technology.

Figure 9B shows a different interaction between the consumer purchase subsidy () and charging anxiety (). Higher charging anxiety lowers NEV adoption, whereas a stronger purchase subsidy shifts the iso-adoption contours upward. Thus, higher subsidies allow the system to sustain a given adoption level under more severe charging constraints. This compensating effect is nevertheless limited. At sufficiently high levels of charging anxiety, even strong purchase subsidies cannot maintain high NEV adoption.

Overall, the joint analyses show that NEV diffusion is shaped by interactions among market conditions, behavioral mechanisms, policy incentives, and physical constraints. Purchase subsidies can partly offset an unfavorable initial market base and charging conditions, while digital marketing utility and hub node influence can jointly strengthen the incumbent advantage. These results indicate that the effect of any single mechanism depends on the conditions created by other components of the diffusion system.

4.8 Effects of network settings and robustness analysis

This section examines the sensitivity of NEV diffusion to network parameters, stochastic realizations, network topology, and network size. These tests assess whether the main simulation results depend on particular structural or stochastic settings.

Figure 10 examines the network parameters of the two layers. Figure 10A shows that increasing the BA linking parameter reduces both consumer NEV adoption and firm NEV transition, while digital marketing adoption remains close to one. Under the initial ICEV majority, greater consumer connectivity tends to reinforce the prevailing choice in social interactions, making early NEV diffusion more difficult. In contrast, Figure 10B shows only limited variation as the WS rewiring probability changes. The diffusion outcome is therefore more sensitive to consumer-network connectivity than to firm-network rewiring within the tested ranges.

Figure 11 provides additional checks on the firm network and stochastic realizations. Varying the WS neighborhood size produces relatively modest differences in the steady-state outcomes. The five random-seed sets also generate similar evolutionary patterns and steady-state levels. These results indicate that the benchmark outcome is not confined to a particular firm-network neighborhood size or random realization.

Figure 12 further relaxes the benchmark network assumptions. Figure 12A shows that network topology can change the quantitative diffusion outcome. The WS-WS structure leads to near-complete NEV diffusion, while ER-WS also produces a higher adoption level than the benchmark BA-WS structure. By comparison, changing the firm-layer topology while retaining a BA consumer network produces smaller differences. Figure 12B shows some variation across network sizes, but the main evolutionary pattern remains similar. This size test is conducted with total market demand held fixed.

Overall, the results reveal both structural sensitivity and robustness. Consumer-network connectivity and topology affect the level of NEV diffusion, indicating that network structure is an important boundary condition of the evolutionary process. The results are comparatively less sensitive to the tested firm-network parameters, random-seed sets, and network sizes. Additional simulations under the WS-WS configuration further show that the directional effects of the main behavioral and policy parameters remain broadly consistent (Supplementary Figures S3–S5), although the steady-state diffusion levels differ from those under the benchmark topology. These results indicate that the directional effects are not confined to the benchmark BA-WS configuration, while their quantitative magnitudes remain dependent on the underlying network structure.

5 Conclusion and implications

5.1 Conclusion

Using NEVs as the research context, this study develops a dual-layer heterogeneous network evolutionary game model that links consumer adoption and firm strategy evolution through market demand feedback and marketing exposure. The framework integrates government policies, digital marketing mechanisms, social network effects, underlying physical constraints, and network structure to investigate the dynamic evolutionary mechanisms of NEV diffusion. The main conclusions are as follows.

• NEV diffusion exhibits a pronounced bimodal steady-state structure and strong dependence on the initial consumer adoption base. Under the benchmark setting, the system tends to evolve toward either an ICEV-dominated low-adoption regime or an NEV-dominated high-adoption regime, with relatively few intermediate outcomes. As the initial NEV adoption rate increases, steady-state adoption follows a nonlinear S-shaped transition and the likelihood of reaching the high-adoption regime rises markedly. This result highlights the importance of initial market conditions in shaping threshold-like diffusion outcomes within a coupled firm-consumer network.

• Government policies exhibit asymmetric transmission effects within the dual-layer network. Under standardized proportional changes, consumer purchase subsidies generate the strongest diffusion response, increasing both consumer NEV adoption and firm NEV transition. By contrast, technology transition subsidies and carbon prices mainly affect firm payoffs and produce more limited changes in long-run diffusion under the benchmark setting. This result shows that policy effects depend not only on policy intensity, but also on the channel through which different instruments enter the coupled system.

• Digital marketing has context-dependent effects on NEV diffusion. It can reinforce the existing market advantage of the incumbent technology. When ICEVs initially hold greater market exposure, a higher digital marketing utility conversion coefficient strengthens this advantage. By contrast, a stronger information overload penalty weakens it. This finding indicates that digital marketing does not inherently favor an emerging technology, and its diffusion effect depends on the relative exposure positions of competing technologies.

• Social network effects tend to reinforce the diffusion advantage of the initial market leader. Stronger local basic bandwagon effects and heterogeneous hub node influence both favor the prevailing technology when ICEVs dominate the initial market. This makes consumers more likely to follow the existing ICEV majority and reduces the space for NEVs to expand from a small initial user base. This result indicates that the effect of social influence is conditional on the initial composition of the consumer network.

• Underlying physical constraints play an important role in NEV diffusion, with charging anxiety and perceived technological risk acting as two major barriers to sustained adoption. Both factors reduce consumer adoption and weaken firm transition toward NEVs. The joint analysis further shows that consumer purchase subsidies can partly offset charging constraints, but this compensating effect becomes limited as charging anxiety increases. These findings highlight the importance of physical conditions in determining the extent to which economic incentives can translate into sustained NEV diffusion.

• NEV diffusion is jointly shaped by policy incentives, market conditions, behavioral mechanisms, and network structure. Consumer purchase subsidies can partly compensate for a weak initial market base, while digital marketing utility and hub node influence can jointly reinforce incumbent advantages. Network tests further show that consumer connectivity and topology affect quantitative diffusion outcomes, whereas the main directional relationships remain broadly consistent across the examined structural and stochastic settings. This finding identifies network structure as an important boundary condition for the magnitude of diffusion outcomes, while showing that the main mechanism relationships are not confined to a single network setting.

5.2 Implications

Based on the findings of this study, the following managerial and policy implications are proposed for policymakers and NEV firms.

• Policymakers and NEV firms should place greater emphasis on cultivating consumers’ initial willingness to adopt NEVs during the early stage of NEV market development. A weak initial adoption base can make subsequent diffusion more difficult to sustain. Early-stage efforts should therefore focus on improving consumers’ awareness, acceptance, and willingness to adopt NEVs, thereby enlarging the initial group of potential adopters. Building a stronger initial adoption base can create more favorable conditions for subsequent market diffusion and self-reinforcing feedback.

• Policymakers should place greater emphasis on the transmission channels of different policy instruments when designing support for NEV diffusion. Policy instruments that enter the consumer and firm layers through different channels may generate markedly different market responses. When the primary objective is to expand market adoption, greater attention can be given to demand-side instruments that directly influence consumer decisions, while firm-side support and carbon regulation can serve complementary roles. Considering these transmission differences can improve the alignment between policy instruments and specific diffusion objectives.

• NEV firms should tailor digital marketing strategies to the relative market exposure of competing technologies. Stronger digital marketing does not necessarily improve the competitive position of NEVs when incumbent technologies already hold an exposure advantage. Firms should therefore focus on improving the effectiveness of NEV-oriented exposure rather than simply increasing marketing intensity, while avoiding excessive exposure that may intensify information overload. A better balance between market visibility and exposure intensity can create more favorable conditions for digital marketing to support NEV diffusion.

• NEV firms should focus social influence strategies on well-connected consumers and early adopters during the early stage of market diffusion. Firms can give greater attention to improving NEV recognition and acceptance among these consumers and encouraging their interactions with surrounding users. Their adoption can help create favorable local social influence and reduce the reinforcing effect of the existing ICEV majority. Such targeted engagement may improve the conditions for NEVs to diffuse beyond early local groups.

• Policymakers and NEV firms should strengthen the physical conditions that support sustained consumer adoption. Financial incentives alone may have limited effects when charging inconvenience and concerns about technological reliability remain pronounced. Policymakers can place greater emphasis on charging accessibility, while NEV firms can continue improving product reliability, safety, and technological maturity. Reducing these underlying constraints can provide a more stable foundation for economic and market-based measures to support long-term NEV diffusion.

• Policymakers and NEV firms should incorporate consumer-network heterogeneity into diffusion assessment and market planning. Expected adoption outcomes may vary across markets with different patterns of consumer connectivity and social interaction. Policy evaluation and market forecasting should therefore avoid relying on a single assumed network structure and, where feasible, examine alternative network configurations or interaction scenarios. Accounting for such structural heterogeneity can improve the robustness of diffusion assessments and reduce the risk of overinterpreting predictions obtained under one specific network setting.

5.3 Limitations and future research

Although this study examines multiple underlying mechanisms of NEV diffusion, several limitations remain and provide directions for future research.

First, the model combines literature-based benchmark values ​​with structurally calibrated behavioral and network parameters. These settings are intended to provide internally consistent simulation benchmarks rather than precise empirical estimates. Although the sensitivity and robustness analyses reduce dependence on particular parameter values ​​and stochastic realizations, the results also show that consumer-network structure can affect quantitative diffusion outcomes. Future research could use survey data, market observations, or platform-based behavioral data to estimate key parameters and reconstruct more realistic consumer interaction networks. Such empirical calibration would allow stronger validation of the simulated diffusion patterns and their quantitative implications.

Second, this study focuses on consumers and firms as the two endogenous strategic actors in the functionally coupled dual-layer network. Firm strategies are limited to four technology and marketing combinations, while other relevant actors, such as digital platforms, charging infrastructure providers, and upstream suppliers, are not modeled endogenously. This simplification may leave some broader interactions within the NEV ecosystem unexplored. Future research could incorporate additional stakeholders and richer strategy spaces to examine multi-actor coevolution, while cross-market studies could further assess the applicability of the identified mechanisms under different institutional and market conditions.

Third, government policies, carbon prices, and digital marketing parameters are treated as exogenous and remain constant within each simulation. This assumption helps isolate the mechanisms examined in this study but does not capture policy uncertainty, adaptive policy adjustment, changes in digital marketing conditions, or external shocks. Future research could introduce time-varying policies, policy uncertainty, adaptive marketing mechanisms, external shocks, and delayed responses to examine how changing external conditions reshape diffusion trajectories and cross-layer feedback.

Statements

Data availability statement

The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding author.

WZ: Conceptualization, Data curation, Formal Analysis, Methodology, Software, Validation, Visualization, Writing – original draft, Writing – review and editing. DX: Project administration, Resources, Supervision, Validation, Visualization, Writing – original draft, Writing – review and editing. YZ: Formal Analysis, Software, Validation, Visualization, Writing – review and editing.

Funding

The author(s) declared that financial support was received for this work and/or its publication. This study is funded by the National Natural Science Foundation of China (72172112, 72404214).

Conflict of interest

The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Generative AI statement

The author(s) declared that generative AI was used in the creation of this manuscript. ChatGPT was used solely to enhance the language of this manuscript. The authors take full responsibility for the final content.

Any alternative text (alt text) provided alongside figures in this article has been generated by Frontiers with the support of artificial intelligence and reasonable efforts have been made to ensure accuracy, including review by the authors wherever possible. If you identify any issues, please contact us.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

Supplementary material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fphy.2026.1972563/full#supplementary-material

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Summary

digital marketing, dual-layer heterogeneous network, evolutionary game, government policy, new energy vehicles, social network effect

Zhao W, Xia D and Zhang Y (2026) Digital marketing and social network effects in new energy vehicle diffusion: evolutionary dynamics in a dual-layer heterogeneous network. Front. Phys. 14:1972563. doi: 10.3389/fphy.2026.1972563

Kaipeng Hu, Yunnan University of Finance And Economics, China

Longfei Li, Chinese Academy of Sciences (CAS), China

Ming Li, Southeast University, China

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