Differential Game Model of Collaborative Governance between Local Governments and Polluting Enterprises from the Perspective of Incentive Compatibility

Abstract

Dynamic coordination between regulatory authorities and industrial enterprises is essential for achieving sustainable manufacturing and intelligent environmental governance. This study develops an incentive-compatible differential game framework to investigate the collaborative optimization of local government regulation and enterprise emission reduction under dynamic pollution evolution. By incorporating pollution stock as the state variable and regulatory intensity together with enterprise abatement effort as control variables, a feedback Nash equilibrium and a cooperative Pareto-optimal strategy are systematically derived. A state-dependent dynamic transfer payment mechanism is further designed to guarantee incentive compatibility while preserving individual rationality, enabling both participants to converge toward cooperative decision-making through recursive feedback optimization. Numerical simulations demonstrate that the proposed mechanism significantly reduces long-term pollution accumulation, improves social welfare, and stabilizes the dynamic equilibrium under varying initial conditions. The framework establishes an effective dynamic control paradigm for intelligent environmental governance and provides valuable methodological references for distributed decision-making, networked optimization, and adaptive feedback systems in modern engineering applications, including digital industrial infrastructures and large-scale cyber-physical systems.