Optimizing subsidy strategies for high-speed railways: A Stackelberg game approach between local governments and railway operators

To offset railway losses, local governments frequently subsidise train services, yet disputes over subsidy amount and the number of trains commonly arise between GOV and CRC. To address this challenge, this study develops a Stackelberg game model based on the measurement of various types of revenue and expenses, in which GOV (as leaders) choose the subsidy amount required to operate trains and CRC (as followers) decides on the number of trains to operate. We use python language programming to call Gurobi solver to solve the game model. This model is validated using the Southern Sichuan Intercity Railway in Sichuan Province, China, as an example. The results indicate that there is a positive correlation between the number of trains operated by the CRC and the subsidies provided by the GOV. Excessive or insufficient subsidies can lead to a decrease in government benefits. The optimal and stable strategy for both parties is that GOV provides 0.943million CNY per train pair per month, while CRC operates 32 pairs of trains. GOV should be approximately 0.4 million CNY per train pair per month to ensure the normal operation of the railway line. Finally, we conducted a sensitivity analysis of passenger demand and financial costs, and the results showed that when determining subsidy strategies, the main consideration should be passenger demand rather than financial costs. This study has certain reference significance for construction and operation of high-speed railway.