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

The paper investigates how government regulatory policies (subsidies, rewards, punishments) can motivate small and medium-sized manufacturing enterprises (SMMEs) in China to undertake digital transformation (DT), and how third-party demonstration enterprises (TDEs—large firms with DT capabilities) can guide SMMEs. DT promises innovation, revenue growth, customer stickiness, cost reduction, and efficiency gains, but SMMEs face high costs, resource constraints, and capability gaps. The study addresses: (1) conditions under which costs, subsidies, penalties, and guidance positively affect SMME DT; (2) whether it is better to subsidize SMMEs and TDEs versus subsidize SMMEs and punish TDEs; and (3) whether optimizing subsidy efficiency changes the optimal policy mix. To capture bounded rationality, dynamics, and information asymmetry among governments, TDEs, and SMMEs, the authors employ tripartite evolutionary game models to derive evolutionarily stable strategies (ESS) under regulated and unregulated regimes and under different SMME risk preferences.

The review clarifies distinctions among digitization, digitalization, and digital transformation (DT), emphasizing DT as a socio-cultural process integrating ICT to transform organizations and offering superior adaptability and value creation. SMMEs lag larger firms due to financial, knowledge, managerial, technical, and regulatory constraints, including limited financing, weak IT, and dependence on external technologies. Prior measures span maturity models, architecture and strategy design, risk assessment, implementation paths, IS improvements (enterprise perspective), capability frameworks and mechanisms (service providers), and diverse governmental instruments (opinions, plans, subsidies, penalties). However, integrated, dynamic, and rational models that include government’s regulatory role are scarce. Evolutionary game theory, accommodating bounded rationality and dynamic learning, has been used in related contexts (cloud services allocation, battery recycling EPR, industrial coordination with digital providers, fog federation stability, IoT offloading). This motivates a tripartite evolutionary game among governments, TDEs, and SMMEs for DT.

The study builds two tripartite evolutionary game models with players: Government (G), Third-party Demonstration Enterprises (TDEs), and SMMEs. Strategies: Government chooses to regulate with probability X (0–1); TDEs choose to guide SMMEs with probability Y; SMMEs choose to conduct DT using government-assigned resources with probability Z. Payoffs incorporate subsidies, rewards, penalties, and costs. Key parameters include: CG (government regulation cost), LG (social welfare loss when not regulating and SMMEs misuse resources), PE (penalty on SMMEs), RE (reward to SMMEs), PT (penalty on TDEs), RT (reward to TDEs), CE (SMME DT cost), RG (government social benefit if TDEs guide SMMEs), RNG (social benefit if SMMEs DT independently), RS (subsidy to SMMEs), RGE (SMME revenue when guided by TDEs), RNGE (SMME revenue when not guided), Cr (TDE guidance cost), RZT (TDE revenue from SMMEs for guidance), LT (TDE loss if not guiding while SMMEs DT). Payoff matrices are specified for cases when TDEs guide and when they do not. Model 1 (risk-neutral SMMEs with randomly shocked revenue): SMME DT revenues fluctuate with a mean-zero normal shock. Replicator dynamics for X, Y, Z are derived from the payoff matrices. After simplification, the system takes the form: dX/dt = X(1−X)(a−bZ), dY/dt = Y(1−Y)(cX + dZ − Cr), dZ/dt = Z(1−Z)(eX + f + g), with constants a,b,c,d,e,f,g defined by policy and payoff parameters. Ten equilibrium points (eight pure, two mixed) are identified; Jacobian eigenvalues determine local stability. Conditions for ESS are summarized, highlighting ideal ESS where Y=1 and Z=1: E3(0,1,1) (no regulation; TDEs guide; SMMEs DT) and E8(1,1,1) (regulation; TDEs guide; SMMEs DT). Propositions 1–2 provide threshold conditions on PT, CG, RE, LG, RS, Cr, RZT, LT, RGE, CE for E3 and E8 to be unique ESS. Model 2 (risk-averse SMMEs): SMME expected utility uses a mean–variance form E(U)=E(Π) − λ Var(Π), with λ the risk-aversion coefficient (λ=0 implies risk-neutral). Replicator dynamics incorporate risk terms: F(X)=X(1−X)[PT − RS − CG − Z(RE + PE + LG)], F(Y)=Y(1−Y)[X(RT + PT) + Z(RZT + LT) − Cr + λ Z^2 /2], F(Z)=Z(1−Z)[X(PE + RE) + RGE − CE − (λ/2)(Y − 1)^2]. Stability analysis yields multiple potential ESS; ideal ESS again include states where Y=1 and Z=1 (e.g., E3(0,1,1) and E5(1,0,1) depending on conditions). Propositions 3–4 establish how risk aversion shifts thresholds, generally requiring higher penalties to counteract inhibited SMME DT incentives. Numerical simulations: MATLAB simulations explore trajectories toward ESS (0,1,1) and (1,1,1) under parameter sets (provided in Table 11) and initial conditions X,Y,Z∈{0.2,0.7}. Simulations verify convergence to predicted ESS under the propositions, illustrate parameter regions with no ESS, and show switching paths between equilibria via policy changes (e.g., increasing PT, adjusting RE, RS, CG). Sensitivity analyses demonstrate transitions from non-ideal equilibria to ideal ones by tuning penalties and rewards.

• When government does not regulate:
  • Risk-neutral SMMEs: Increasing rewards to SMMEs (RE or RS) can alone ensure DT under TDE guidance (Proposition 1; ESS E3(0,1,1) if PT < CG + RE + LG + RS, Cr < RZT + LT, and RGE > CE).
  • Risk-averse SMMEs: Government must increase penalties on SMMEs (PE) and increase rewards for TDEs (RT) to effectively promote DT; higher risk aversion necessitates higher penalties (Proposition 3).
• When government regulates:
  • Risk-neutral SMMEs: Increasing penalties on both TDEs (PT) and SMMEs (PE) is effective while maintaining reward levels (Proposition 2; ESS E8(1,1,1) if PT > CG + RE + LG + RS, Cr − (RZT + LT + PT + RT) < 0, and CE − (RGE + PE + RE) < 0).
  • Risk-averse SMMEs: Increasing penalties on SMMEs or TDEs can suffice; minimal feasible penalties are higher than in the risk-neutral case (Proposition 4—discussed qualitatively).
• Optimal regulatory stance under risk aversion: Regulation is preferred; without regulation, DT may fail even with higher SMME penalties and TDE incentives.
• Deterrence effect: Heavy penalties effectively prevent SMMEs and TDEs from avoiding DT and guidance, respectively. As λ (risk-aversion) increases, the minimum effective penalty rises.
• Policy switching: Raising PT, or jointly raising PT and RE/RS, transitions systems from non-ideal equilibria (e.g., E1, E2, E5–E7) to ideal E8(1,1,1). Decreasing PT or increasing CG or increasing RE can move the system from E8 to E3 when PT < CG + RE.
• No-ESS regions: For certain parameter ranges (e.g., CG − PE − LG < PT < CG + RE and RGE < CE < RGE + RE + PE (risk-neutral); RGE < CE < RGE + RE + PE − λβ^2/2 (risk-averse)), models have no ESS regardless of initial conditions.
• Simulations (MATLAB) confirm convergence to the predicted ESS (0,1,1) and (1,1,1) under the stated thresholds and illustrate dynamic paths and sensitivity to policy parameters.

The findings address the research questions by linking policy instruments to behavioral equilibria under bounded rationality. (1) Factors that positively affect SMME DT include higher SMME rewards (RE/RS) in unregulated settings for risk-neutral firms; for risk-averse firms, penalties on SMMEs and rewards for TDEs are needed without regulation, while under regulation penalties (PE, PT) become the main levers. Cost and benefit thresholds (e.g., RGE > CE; Cr < RZT + LT) determine whether enterprises and TDEs adopt DT and provide guidance. (2) Subsidizing both SMMEs and TDEs is effective when not regulating; under regulation, maintaining rewards but increasing penalties is more efficient to ensure guidance and execution. (3) When optimizing subsidy efficiency, governments can favor penalty-focused strategies in regulated scenarios, preserving reward levels; in unregulated scenarios, reward-focused strategies for SMMEs (and TDE rewards if SMMEs are risk-averse) are preferred. Risk aversion substantially inhibits DT adoption, shifting optimal policies toward stronger penalties. Overall, the models illuminate how regulation choice and risk preferences jointly determine stable outcomes and provide actionable thresholds for policy design.

The study develops two tripartite evolutionary game models (risk-neutral and risk-averse SMMEs) to design government regulatory mechanisms for SMME digital transformation with TDE guidance. It identifies two ideal equilibria—no-regulation with rewards (E3) and regulation with penalties (E8)—and derives threshold conditions under which each becomes the unique ESS. Key insights: (i) feasible measures exist to prevent DT avoidance in both supervised and unsupervised contexts; (ii) SMME risk preferences critically shape optimal policies: reward-based levers for risk-neutral firms without regulation, penalty-based levers for regulated contexts and for risk-averse firms; (iii) strong deterrence from penalties curbs DT avoidance and guidance shirking. Managerially, governments should use rewards in laissez-faire settings and penalties under regulation, adjusting intensity to risk aversion, and avoid excessive fines that may backfire. Future work could extend beyond the governmental perspective to enterprise-side strategy optimization, incorporate richer behavioral factors, and empirically validate parameterization across sectors and regions.

• The analysis emphasizes the governmental perspective; enterprise-side optimization and heterogeneous firm behavior are not deeply explored.
• Models rely on simplified payoff structures, parameter thresholds, and mean–variance risk representation; real-world DT processes and risk perceptions may be more complex.
• Results are theory- and simulation-based without empirical estimation of parameters or field validation, potentially limiting generalizability.
• Context centers on Chinese SMMEs and policy instruments; applicability to other institutional settings may require adaptation.
• Some numerical and notation artifacts in presentation suggest potential typographical errors; precise calibration would benefit from standardized datasets.