Dynamic State Equations and Distributed Blockchain Control: A Differential Game Model for Optimal Emission Trajectories in Shipping Networks

The shipping industry, a cornerstone of global trade, faces emissions reduction challenges amid tightening environmental policies. Blockchain technology, leveraging distributed symmetric architectures, enhances supply chain transparency by reducing information asymmetry, yet its dynamic interplay with emissions strategies remains underexplored. This study employs symmetry-driven differential game theory to model four blockchain scenarios in port-shipping networks: no blockchain (N), port-led (PB), shipping company-led (CB), and a joint platform (FB). By solving Hamilton–Jacobi–Bellman equations, we derive optimal emissions reduction efforts, green investments, and blockchain strategies under symmetric and asymmetric decision-making frameworks. Results show blockchain adoption improves emissions reduction and service quality under cost thresholds, with port-led systems maximizing low-cost profits and shipping firms gaining asymmetrically in high-freight contexts. Joint platforms achieve symmetry in profit distribution through fee-trust synergy, enabling win–win outcomes. Integrating graph-theoretic principles, we have designed dynamic state equations for emissions and service levels, segmenting shippers by low-carbon preferences. This work bridges dynamic emissions strategies with blockchain’s network symmetry, fostering economic–environmental synergies to advance sustainable maritime supply chains.