## 3 Analysis of Port Competition Mode and Equilibrium Result
\(\square\)  
The higher the maritime transportation cost of port B and the cost of cross-border land transportation to port B, the more competitive port A will be in terms of transport costs, making it more attractive for cargo. As a result, this would lead to an increase in both the equilibrium price and the demand for port A, while causing a decrease in the equilibrium price and demand for port B. Therefore, even though the area near port B has a proximity advantage, the significant costs associated with cross-border and maritime to port B could reduce its attractiveness to hinterland goods, putting it at a disadvantage in competition with port A. If the sum of the land transport cost, maritime transport cost, and port cost when the shipper selects port B is greater than the sum of the land transport cost, maritime transport cost, and port cost when the shipper selects port A (that is, the total transportation cost when selecting port B is greater than the total transportation cost when choosing port A), then the profit of port A increases with the increase in \(C_{B}^{sea}-C_{A}^{sea}\). However, if the total transportation cost for the shipper to select port B is less than the total transportation cost for selecting port A, meaning that selecting port A does not offer a cost advantage over port B for the shipper, then the profit of port A will not increase with the increase in \(C_{B}^{sea}-C_{A}^{sea}\). Taking port A as an example, it can be seen in Equation (19) that \(\pi_{A}^{*}\) is a quadratic function with respect to \(C_{B}^{sea}-C_{A}^{sea}\). When \(C_{B}^{sea}-C_{A}^{sea}\in\left[-\infty,\ -C_{B}^{leaf}-(2+b)\sum\limits_{m=1}^{M}w_{m} \left(\delta^{m}+\varepsilon\frac{1}{\overline{V}^{m}}\right)-2H_{B}-H_{A}-C_{ B}^{port}+C_{A}^{port}\right]\), \(\pi_{A}^{*}\) decreases as \(C_{B}^{sea}-C_{A}^{sea}\) increases, while when \(C_{B}^{sea}-C_{A}^{sea}\in\left[\ -C_{B}^{land}-(2+b)\sum\limits_{m=1}^{M}w_{m} \left(\delta^{m}+\varepsilon\frac{1}{\overline{V}^{m}}\right)-2H_{B}-H_{A}-C_ {B}^{port}+C_{A}^{port},+\infty\right]\), \(\pi_{A}^{*}\) increases as \(C_{B}^{sea}-C_{A}^{sea}\) increases. \(\square\)  
This indicates that \(C_{B}^{sea}-C_{A}^{sea}\in\left[-\infty,\ -C_{B}^{leaf}-(2+b)\sum\limits_{m=1}^{M}w_{m} \left(\delta^{m}+\varepsilon\frac{1}{\overline{V}^{m}}\right)-2H_{B}-H_{A}-C_ {B}^{port}+C_{A}^{port}\right]\), that is, \(C_{B}^{sea}+C_{B}^{port}+\sum\limits_{m=1}^{M}w_{m}\left(\delta^{m}(b-x)+ \varepsilon\frac{b-x}{\overline{V}^{m}}\right)+C_{bB}^{land}+H_{B}\leq C_{A} ^{port}+C_{A}^{sea}+\sum\limits_{m=1}^{M}w_{m}\left(\delta^{m}x+\varepsilon \frac{x}{\overline{V}^{m}}\right)+H_{A}\), although the maritime transportation cost advantage of port A is more obvious with the increase in \(C_{B}^{sea}-C_{A}^{sea}\), and the total transportation costs to be paid by shippers when they select port B are smaller than the total cost to be paid when they select port A. In this scenario, despite the increase in \(C_{B}^{sea}-C_{A}^{sea}\), the maritime transportation cost advantage of port A cannot offset the land transport cost advantage of port B, and shippers will still select port B for cargo transportation. Consequently, the demand for goods in port A decreases, and the equilibrium profit of port A decreases with the increase in \(C_{B}^{sea}-C_{A}^{sea}\). However, when \(C_{B}^{sea}-C_{A}^{sea}\in\left[-C_{B}^{land}-(2+b)\sum\limits_{m=1}^{M}w_{m} \left(\delta^{m}+\varepsilon\frac{1}{\overline{V}^{m}}\right)-2H_{B}-H_{A}-C_ {B}^{port}+C_{A}^{port},+\infty\right]\), that is when \(C_{B}^{sea}+C_{B}^{port}+\sum\limits_{m=1}^{M}w_{m}\left(\delta^{m}(b-x)+ \varepsilon\frac{b-x}{\overline{V}^{m}}\right)+C_{bB}^{land}+H_{B}\geq C_{A} ^{port}+C_{A}^{sea}+\sum\limits_{m=1}^{M}w_{m}\left(\delta^{m}x+\varepsilon \frac{x}{\overline{V}^{m}}\right)+H_{A}\), the total transportation costs to be paid by shippers when they select port A are smaller than the total cost to be paid when they select port B.