# Game Analysis of Different Transportation Modes in a Corridor Considering Carbon Emission Costs
## 1 Introduction
Research in the cargo transportation market predominantly centers on consignors' transportation mode selection and the competition among different modes. [PERSON] et al. [4] (2019) utilized an n-player non-cooperative game to simulate the equilibrium outcomes of the Australian aviation market, estimating fares, frequencies, passenger numbers, and market shares for domestic competitors, thereby affirming the capability of game-theoretic models to mirror real-world transportation market dynamics. [PERSON] et al. [5] (2016) emphasized the significance of train technology in the competition between high-speed rail and airlines, proposing a three-stage game-theoretic model where the rail agency initially selects track technology and speed, followed by the determination of rail and airline frequencies, and ultimately, fare setting by each mode. [PERSON] et al. [6] (2019) explored competition along two Indian corridors, contrasting high-speed rail with bus and airline services through a three-stage entry game that assesses the high-speed rail entrant's speed choice, fare and frequency settings by alternative modes, and high-speed rail's market entry decisions. [PERSON] [7] (2015) employed a discrete selection model to identify key determinants in goods transportation mode choice. As game theory matures, international scholars have increasingly applied its concepts to cargo transportation's economic challenges. [PERSON] and [PERSON] [8] (2019) introduced a quantity-setting duopoly model in a railway passenger market, examining the welfare implications of duopoly versus monopoly scenarios based on operational costs and access charges. [PERSON] and [PERSON] [9] (2023) developed an evolutionary game model to refine decision-making in the interplay between civil aviation and high-speed rail, adjusting passenger ticket and carbon trading prices to foster the growth of the high-speed transportation system. [PERSON] et al. [10] (2023) developed a comprehensive optimization model for various transportation tasks and modes considering carbon emissions, aiming at transportation distance, transportation time, and carbon emissions. They optimized the path, transportation mode, and carbon dioxide emissions, providing a reference for logistics enterprises to carry out multimodal transportation. [PERSON] et al. [11] (2021) implemented a distributed architecture for an environmentally friendly traffic guidance system using an agent-based paradigm. The system utilizes real-time traffic data collection from multiple sources and provides multimodal transportation route recommendations to travelers through dedicated applications. Echoing the research methodologies of international scholars, Chinese experts have also extensively employed game theory tools to explore competitive dynamics. [PERSON] and [PERSON] [12] (2012) devised a modified Hotelling-Bertrand model to examine product differentiation, positioning airlines as profit maximizers against high-speed rail (HSR) operators, who aim to optimize a blend of welfare and profit due to their public ownership. Their analysis of a 600 km corridor in China revealed that increasing welfare weights leads to reduced HSR ticket prices and airfares, a decrease in flight frequency, and an increase in HSR frequency, with both flight and HSR frequencies rising as the business passenger segment expands. [PERSON] [13] (2008) formulated a Stackelberg game model for transportation mode selection, grounded in the fundamental principles of logistics transportation mode choice and the determinants influencing shippers' preferences. [PERSON] et al. [14] (2021) explored the competitive effects of frequent flight delays on HSR and air transport, developing a game-theoretical model to deduce the equilibrium strategies of both parties. Their findings indicate a gradual decline in revenues for both HSR and air transport as flight delays escalate.