Synergistic Evolutionary Mechanism of Government–Enterprise Environmental Innovation Incentives and Sustainable Development: A Differential Game Approach

Against the backdrop of deepening the “Dual Carbon” goals and advancing the United Nations 2030 Agenda for Sustainable Development, the dynamic game characteristics and positive externalities of environmental innovation are becoming increasingly prominent. Aligning government industrial policy with sustainability goals requires understanding the dynamic strategic interactions between public environmental concern, government subsidies, and enterprise innovation investment. Departing from traditional static regression analysis, this paper constructs a continuous-time differential game between the government (the leader) and a representative environmental protection enterprise (the follower), incorporates public environmental concern into the payoff functions, and rigorously derives the feedback Stackelberg equilibrium using the Hamilton–Jacobi–Bellman (HJB) method. Four core scenarios—heterogeneity in public environmental concern, in the government subsidy cost coefficient, in the enterprise innovation cost coefficient, and path dependence of initial conditions—are simulated with complete, publicly released MATLAB code. The principal conclusions are quantitative rather than qualitative: (i) over the tested range of public concern θ ∈ [0.2, 2.0], the steady-state innovation stock rises monotonically from 2.9 to 73.5 and the equilibrium innovation input from 0.15 to 3.68, whereas the equilibrium subsidy ratio declines mildly from 0.49 to 0.35; (ii) raising the government subsidy cost coefficient β from 2.5 to 10 (a fourfold increase) reduces the steady-state innovation stock by approximately 12.7%, operating almost entirely through a sharp contraction of the equilibrium subsidy ratio (from 0.67 to 0.20); doubling β from the benchmark value of 5.0 to 10.0 reduces the steady-state stock by approximately 5.1%; (iii) raising the enterprise innovation cost coefficient α from 1.5 to 3 reduces both innovation input and steady-state stock by 50%, and the equilibrium subsidy ratio does not automatically compensate for higher costs; (iv) the initial innovation stock affects only the transition path—the system closes 95% of the gap in approximately 60 time units and reaches a unique steady state independent of initial conditions. One-at-a-time sensitivity analysis further shows that the depreciation rate and the enterprise-side cost coefficients are the most influential parameters. These findings, while illustrative in their calibrated magnitudes, offer dynamic, scenario-specific insights for designing sustainability-oriented innovation policies that combine transparent environmental information disclosure with efficient subsidy delivery and indirect R&D cost-reduction instruments.