The model, developed by Wanting Zhao, De Xia, and Yundong Zhang, is technically ambitious. The supply side is represented as a Watts-Strogatz small-world network of 200 firms, each choosing among four strategies: producing NEVs or internal combustion engine vehicles (ICEVs), combined with digital or traditional marketing. The demand side is a Barabási-Albert scale-free network of 1,000 consumers, whose connectivity mirrors real online social platforms—a few highly connected hubs and many sparsely linked users. The two layers are coupled functionally rather than through fixed one-to-one links: consumer adoption aggregates into market penetration, which drives firm payoffs, while firms’ technology and marketing choices determine the advertising exposure each consumer receives. Both populations update strategies asynchronously using the Fermi rule from statistical physics, comparing payoffs with connected neighbors under bounded rationality and noise.

Consumer utility in the model is a rich composite. It includes intrinsic vehicle value minus price, a purchase subsidy, a charging anxiety penalty that fades as NEV penetration grows, and a perceived technological risk term capturing worries about battery degradation and range. On top of this sit two distinctly digital ingredients. Marketing exposure is scaled by a consumer’s node degree, reflecting how platform algorithms target socially active users, and its utility follows a quadratic specification: exposure helps at moderate levels but triggers an information overload penalty that grows with the square of intensity. Social influence is borrowed from the Ising model of spin interactions, with a local bandwagon effect from neighbors plus a weighted term giving extra influence to hub nodes, whose degree serves as a proxy for their dissemination power.

The benchmark simulations, run for 150 periods and averaged over 100 Monte Carlo replications, produced a striking result: the steady-state distribution of NEV adoption is sharply bimodal. Most replications converge either to a low-adoption regime dominated by ICEVs or to a near-complete adoption regime, with very few outcomes in between. The Monte Carlo mean of roughly 0.53 is therefore an average across two divergent worlds, not a typical endpoint. Firm behavior mirrors this polarization in technology choice, yet digital marketing adoption stays close to one in almost every run—firms abandon traditional channels regardless of which technology wins.

The dependence on initial conditions follows a clean S-shaped curve. When the initial NEV adoption share is low, nearly all simulations stay stuck in the low-adoption regime. In an intermediate range, outcomes scatter widely and the probability of near-complete diffusion climbs steeply. At an initial adoption rate of 0.5, all 100 replications reach at least 95 percent NEV adoption. The mechanism is cross-layer reinforcement: a larger early user base strengthens pro-NEV social norms, eases charging anxiety as penetration rises, expands NEV demand, raises the payoff of NEV strategies for firms, and ultimately shifts the marketing exposure landscape further in NEVs’ favor. Early differences are amplified into divergent destinies.

Perhaps the most counterintuitive finding concerns digital marketing itself. Because ICEV-oriented firms initially dominate the market, they also hold the larger share of digital marketing exposure. Increasing the coefficient that converts marketing exposure into consumer utility therefore amplifies the incumbent’s advantage and suppresses NEV diffusion. Conversely, strengthening the information overload penalty—which hits the more heavily exposed ICEV option harder, quadratically—actually helps NEVs by eroding that exposure advantage. In other words, more advertising is not inherently good for the challenger technology; it depends entirely on who currently owns the attention. The same logic applies to social influence: stronger local conformity and stronger hub-node influence both reinforce whatever the majority already prefers, making it harder for NEVs to expand from a small base.

Government policy, by contrast, transmits asymmetrically through the two layers. The researchers standardized three instruments—a consumer purchase subsidy, a firm-side technology transition subsidy, and a carbon price—by scaling each proportionally from zero to twice its benchmark. The purchase subsidy, which directly improves consumer utility and demand, produced by far the strongest response, lifting steady-state adoption from about 0.10 when removed toward near-complete diffusion at double intensity. The technology transition subsidy and carbon price, which act only through firm payoffs, moved long-run outcomes far less. Policy effectiveness, the authors conclude, depends not just on intensity but on the channel through which a policy enters the coupled system.

Physical constraints proved to be hard boundaries that money can only partly buy down. Rising charging anxiety and perceived technological risk both suppressed consumer adoption and, through demand feedback, firm transition. Joint analyses showed that purchase subsidies can compensate for a weak initial market base, shifting the adoption threshold downward, and can partially offset charging constraints—but at sufficiently severe charging anxiety, even strong subsidies fail to sustain high adoption. Meanwhile, digital marketing utility and hub influence were found to act jointly, each amplifying the other’s incumbent-favoring effect. The lesson is sobering for policymakers: financial incentives cannot substitute for the infrastructure and reliability that make the technology genuinely attractive.

Robustness tests added an important nuance. Varying the firm network’s rewiring probability, neighborhood size, random seeds, and population size produced only modest changes, but the consumer network’s structure mattered substantially. Replacing the scale-free consumer layer with a small-world or Erdős-Rényi topology changed the quantitative diffusion level—near-complete diffusion emerged under a WS-WS configuration—without overturning the directional effects of the behavioral and policy parameters. Network structure, in other words, acts as a boundary condition on how large the effects are, even as the mechanisms themselves remain stable. This cautions against forecasting adoption from a single assumed social topology.

The practical implications are pointed. Early-stage efforts should concentrate on building the initial adopter base, because that base determines which basin of attraction the market falls into. Demand-side instruments deserve priority when the goal is market expansion, with firm-side support and carbon pricing playing complementary roles. Automakers should target NEV-oriented exposure effectiveness rather than raw marketing intensity, avoiding the overload regime, and should focus social-influence strategies on well-connected early adopters who can seed favorable local norms. Above all, the study reframes the electric vehicle transition as a problem of coupled networks and path dependence: the technology that wins is not necessarily the better one, but the one that starts with enough users, enough attention, and enough infrastructure to trigger the self-reinforcing loop before the incumbent’s advantage hardens into permanence.

Subject of Research: Evolutionary game modeling of new energy vehicle diffusion in a dual-layer firm-consumer heterogeneous network

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

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

Image Credits: AI Generated

DOI: 10.3389/fphy.2026.1972563

Keywords: new energy vehicles, digital marketing, social network effects, evolutionary game theory, dual-layer network, complex networks, government subsidies, carbon pricing, charging anxiety, information overload, technology diffusion, scale-free networks