Government regulatory policies for digital transformation in small and medium-sized manufacturing enterprises: an evolutionary game analysis

Digital transformation (DT) is reshaping the manufacturing industry globally, offering significant benefits such as enhanced innovation, increased revenue, and improved efficiency. However, SMMEs often face challenges in adopting DT due to limited resources, high costs, talent shortages, and unclear transformation pathways. This study focuses on the critical role of government regulatory policies in overcoming these obstacles. Governments frequently employ subsidy schemes, subsidizing either SMMEs directly or TDEs that assist SMMEs with DT. Punishments for non-compliance also play a role. Existing literature primarily addresses DT adoption by individual actors, neglecting the dynamic interactions between governments, SMMEs, and TDEs. This research aims to address this gap by developing a three-party evolutionary game model to explore the optimal strategies for each party and how government policies influence DT adoption under different scenarios. The study addresses three key research questions: 1. Under what conditions do factors like SMMEs and TDEs expenses and government subsidies positively affect DT in SMMEs, and how do these factors exert their influence? 2. Is it better for governments to subsidize SMMEs and TDEs, or subsidize SMMEs while penalizing TDEs? 3. If the government's goal shifts from optimizing DT results in SMMEs to optimizing subsidy efficiency, does the optimal reward/punishment scheme change?

The literature review distinguishes between digitization, digitalization, and DT, emphasizing DT's unique advantages in terms of content, adaptability, coverage, and value creation. Existing research often focuses on individual actors in DT (e.g., SMMEs or service providers), neglecting the interconnectedness of multiple participants. SMMEs face specific DT challenges, including financial constraints, knowledge gaps, management competency limitations, and technological dependence. The literature highlights various methods to facilitate DT in SMMEs, including maturity models, enterprise architecture design, risk assessment, and implementation pathways. However, the literature largely overlooks the crucial regulatory role of governments and the use of subsidies, rewards, and punishments to influence the DT behaviors of SMMEs and TDEs. Evolutionary game theory is presented as a suitable framework for analyzing the dynamic interactions between these multiple stakeholders, particularly in situations involving bounded rationality and information asymmetry.

The study employs evolutionary game theory to model the dynamic interactions among governments, TDEs, and SMMEs. Two tripartite evolutionary game models are constructed: Model 1 considers risk-neutral SMMEs, while Model 2 incorporates the risk aversion of SMMEs using a mean-variance model. Each model analyzes the strategic choices of the three players—government regulation (or lack thereof), TDE guidance (or lack thereof), and SMME DT adoption (or lack thereof)—and their respective payoffs. Replicator dynamic equations are derived for each model, representing the evolution of the probabilities of each strategy over time. The equilibrium points (including evolutionarily stable strategies or ESSs) are analyzed to identify stable states of the system and how they depend on various parameters, such as government subsidies, rewards, and penalties, the costs incurred by SMMEs and TDEs, and the risk aversion of SMMEs. Numerical simulations using MATLAB are conducted to verify the theoretical findings and illustrate the evolutionary paths under different parameter values and initial conditions. Sensitivity analysis is performed to examine the impact of changes in key parameters on the system's equilibrium states.

The study's key findings are summarized in four propositions: **Proposition 1:** When government regulation is absent, and under certain conditions (low government regulation costs, profitable DT for SMMEs, and profitable guidance for TDEs), the unique ESS is where governments do not regulate, TDEs guide SMMEs, and SMMEs adopt DT. In this scenario, increasing governmental rewards for SMMEs effectively promotes DT. **Proposition 2:** When government regulation is present, and under certain conditions (high penalties outweighing government regulation costs, profitable DT for SMMEs, and profitable guidance for TDEs), the unique ESS is where governments regulate, TDEs guide SMMEs, and SMMEs adopt DT. In this scenario, increasing penalties for both TDEs and SMMEs effectively promotes DT. **Proposition 3:** When SMMEs are risk-averse and government regulation is absent, and under certain conditions (low government regulation costs, profitable DT for SMMEs, and profitable guidance for TDEs adjusted for risk aversion), the ESS is where governments do not regulate, TDEs guide SMMEs, and SMMEs adopt DT. In this case, adjusting rewards and penalties to account for risk aversion becomes crucial. **Proposition 4:** When SMMEs are risk-averse and government regulation is present, and under certain conditions (high penalties to offset risk aversion and government regulation costs, profitable DT for SMMEs, and profitable guidance for TDEs adjusted for risk aversion), the ESS is where governments regulate, TDEs guide SMMEs, and SMMEs adopt DT. Increasing penalties for SMMEs or TDEs alone can be effective in this scenario. Numerical simulations validate these propositions. The simulations demonstrate that various parameter combinations lead to different stable states, and that the risk aversion of SMMEs significantly impacts the effectiveness of governmental policies. The sensitivity analysis shows how changes in key parameters (e.g., penalties, rewards, costs) affect the transition between different stable states.

The findings highlight the importance of context-specific policy design for DT promotion. The optimal strategy for the government depends on the risk preferences of SMMEs and whether the government chooses to actively regulate or not. The results suggest that a purely reward-based approach may be sufficient when SMMEs are risk-neutral and government supervision is deemed unnecessary or too costly. However, when SMMEs are risk-averse, a regulatory framework with appropriate penalties may be more effective. The model's ability to capture dynamic interactions and incorporate risk preferences provides valuable insights into designing effective DT policies.

This study contributes to the literature by providing a dynamic and nuanced analysis of government regulatory policies in promoting DT among SMMEs. The evolutionary game models offer a framework for understanding the complex interplay between government intervention, TDE guidance, and SMME behavior. The findings highlight the importance of considering the risk preferences of SMMEs when designing DT policies and suggest that a combination of rewards and penalties, along with government regulation in cases of risk aversion, can be most effective. Future research could explore the impact of other factors, such as information asymmetry and technological advancements, on the DT process.

The study's limitations include the simplifying assumptions made in the model, such as the representation of risk aversion using a mean-variance model and the focus on a specific set of policy instruments. The model does not explicitly account for the heterogeneity among SMMEs or TDEs. Furthermore, the generalizability of the findings may be limited to the context of the Chinese manufacturing sector. Future research could address these limitations by incorporating more complex features and expanding the scope of analysis.