Subsidy policy design and optimal pricing decisions of high-speed rail express

High-speed rail express (HSRE) plays an important role in promoting industrial development and reducing carbon emissions. This study addresses the issues of the government subsidies and pricing decisions of HSRE operators under decentralized (DE) and centralized (CE) decision-making frameworks. A two-stage analysis framework is proposed: The first stage addresses the issue of government subsidies amount and starting subsidy distances, while the second stage focuses on determining the optimal pricing decisions of HSRE operators after government subsidies are withdrawn. The proposed model is validated by the HSRE service between Chengdu and Kunming. The results indicate that the subsidy amount per ton km in the initial phase is positively correlated with the transportation distance of HSRE. The longer the transportation distance, the larger the subsidy amount should be. Meanwhile, the results reveal that while centralized decision-making consistently enhances overall profits, its impact on HSRE and RE services exhibits significant distance-dependent heterogeneity, mutual profit improvement for both transport modes only materializes under medium-distance scenarios. These findings provide new sights for operational optimization and subsidy pricing decisions of HSRE.