## 2 Problem Formulation  
### Problem Description and Assumptions  
The construction of the international land-sea transport corridor provides shippers with new port options. As shown in Figure 1, there are two potential transportation routes for the goods from the inland city \(i\) to the port \(K\) of country C, that is, route 1: city \(i\)--domestic port and A--destination port \(K\); route 2: city \(i\)--border port \(b\)--neighboring countries, and port B--destination port \(K\). As a result of the construction of a cross-border transport corridor, the hinterland originally belonging to port A will become the hinterland of common competition between port A and port B. As analyzed above, ports situated in varying geographical locations incur varying transportation costs and have varying market demands. Ports can influence consumers' choices by adjusting prices, enhancing service quality, or relocating. This strategy helps them expand their market share and boost profits. The Hotelling model, a classical game model addressing spatial disparities among competitors, can be applied to different port  
Figure 1: The alternative land–sea transportation routes for shippers. competition scenarios, addressing varying needs and preferences of consumers. In this article, we extend the classic model by expanding the one-dimensional spatial disparities to two dimensions, seeking a closer alignment with reality. Given that inland goods need to be transported by land to domestic ports or ports in neighboring countries and then shipped by sea to the destination port, this paper makes the following assumptions based on the Hotelling model. 1. Port: port A and port B are on a line of length 1, at 0 and 1, respectively (see Figure 2). The hinterlands of the two ports overlap, and they are in a competitive state. Both ports can provide the same transshipment loading and unloading services, and their service prices (i.e., port charges to be paid by cargo owners or shippers) are \(P_{A}\) and \(P_{B}\), respectively. It is assumed that the port costs (i.e., the costs of transshipment and handling services) provided by port A and port B are \(C_{A}^{port}\) and \(C_{B}^{port}\), respectively. The maritime transportation costs (i.e., sea freight to be paid by the cargo owner or shipper) from port A and port B to the overseas destination port K are \(C_{A}^{sea}\) and \(C_{B}^{sea}\), respectively. 2. Cargo owners or shippers: the cargo owner is at a certain point within the [0,1] range, and border port \(b\) is located between the cargo owner and port B, that is, \(0<x<b<1\). Cargo owners and port operators act rationally, making decisions based on their interests and anticipated outcomes. Cargo owners prioritize the most efficient transportation route, while port operators set port service prices to maximize profit or cargo throughput. For simplicity, we assume that cargo demand in the port's hinterland is inelastic, meaning the demand is constant. 3. Transportation model: The cargo owner in point x can select port A or port B to transfer the cargo to port K. The land transportation cost of goods from point x to port A is \(C_{A}^{land}(x)\), and the land transportation cost of goods from point \(x\) to port B is \(C_{B}^{land}(x)=C_{B}^{land}(b-x)+C_{bB}^{land}\), where \(C_{B}^{land}(b-x)\) is the domestic land transportation cost from point \(x\) to border port \(b\), and \(C_{bB}^{land}\) is the cross-border land transportation cost from border port b to port B. According to the above assumptions, the utility of transshipment of goods to port K by selecting port A or port B is as follows:  
\[U_{i}(x)= \begin{cases}U_{A}(x)=v-P_{A}-C_{A}^{land}(x)-C_{A}^{sea}-d\frac{Q_{A }}{h_{A}}\\ U_{B}(x)=v-P_{B}-C_{B}^{land}(b-x)-C_{bB}^{land}-C_{B}^{sea}-d\frac{Q_{B}}{h_{B }}\end{cases}