# Game Analysis of Different Transportation Modes in a Corridor Considering Carbon Emission Costs
## 1 Introduction  
Entering the 21 st century, a surge in economic activities and e-commerce expansion has led to a growing demand for small-batch, multi-batch, and time-sensitive goods in the logistics market. In response, logistics companies specializing in express freight are vigorously enhancing their service quality and speed. This effort challenges the traditional express freight models and unveils new prospects for the advancement of high-speed rail freight. Managed by China Railway Express, high-speed rail express signifies a significant transformation in railway freight transportation, leveraging daily high-speed rail EMU trains for the expedited delivery of goods. Launched initially on the Beijing-Shanghai high-speed railway in early 2014, this service expanded rapidly. By the end of 2019, it had achieved comprehensive coverage across major cities, including municipalities directly under the Central Government, provincial capitals, and key prefecture-level cities in the central and eastern regions, marking a significant shift in competitive dynamics among various transportation modes within the express freight corridor. The innovation of this study lies in the introduction of a novel dynamic game model that analyzes the competitive dynamics among different transportation modes within the context of the \"Belt and Road\" initiative, particularly emphasizing the advantages of high-speed rail express under carbon emission tax conditions. The academic contributions include:  
1. A comprehensive utility function that integrates five key factors: transportation cost, speed, safety, reliability, and convenience. 2. The introduction of carbon emission tax as a crucial component of transportation costs, with a quantitative analysis of its impact on transportation mode selection. 3. Empirical validation of the model's effectiveness, providing theoretical support for policymakers and logistics enterprises. Numerous studies highlight the high-speed railway (HSR)'s significant contribution to emission reduction, surpassing other transportation modes. [PERSON] et al. (2013) [1] delineated the carbon emission phases throughout HSR's lifecycle--infrastructure construction, operation, and recovery--providing specific formulas for calculating carbon dioxide emissions at each phase. Despite higher emissions during the construction phase, HSR's overall lifecycle emissions are lower than highways', showing a decreasing trend with higher ridership rates, thus affirming HSR's effective emission reduction capabilities. [PERSON] et al. (2016) [2] discussed the balance between carbon emissions saved by shifting transport demand from air to HSR and those generated by increased HSR demand, considering the established rapid air transport framework. They argued that the environmental impact of air travel on local air pollution and climate change varies with flight duration, crew size, fuel usage, and the airport's proximity to urban centers, especially for suburban airports. Conversely, HSR's environmental impact largely hinges on the mix of power generation sources, track length, and energy consumption. [PERSON] et al. (2022) [3] examined HSR's effects on the economy and environment in China's impoverished counties, assessing the environmental benefits difference between conventional railways and HSR. Utilizing a time-varying difference-in-difference approach, they quantified HSR's impact on carbon dioxide emissions, revealing a 10.3% emission reduction in counties with railway access compared to those without, with HSR operations specifically showing greater emission reductions than conventional railways. The pricing strategy of high-speed rail express plays a pivotal role in determining the variety and volume of goods it attracts. Analyzing this pricing issue requires a clear understanding of the relationships between various transportation modes and shippers within the express freight corridor.