## 3 Methods and Modeling
### Modeling  
Considering that a dual-channel cross-border supply chain consists of one overseas supplier and two CBEC merchants, one applied advanced IT in the supply chain (hereinafter referred to as Merchant 1), while the other did not (hereinafter referred to as Merchant 2). The cross-border supply chain model was constructed as below (Figure 1). The parameters in the model are presented as follows (Table 1). To effectively analyze price and service competition, the following assumptions are made:  
* The dual-channel products are identical. Specifically, the product from Merchant 1 is the same as that from Merchant 2. This assumption is adopted to focus on the competition in service differentiation rather than product attributes, as the core of this research lies in exploring how IT-enabled service differentiation influences supply chain decisions and performance. By abstracting away product attribute differences, we can more clearly observe the role of service quality in driving consumer choice and merchant competition. * Consumers are assumed to be rational actors who make purchasing decisions based on utility maximization. This assumption is grounded in the reality of e-commerce environments, where consumers typically have access to ample product and service information. Rational consumer choice provides a solid foundation for formulating demand functions and analyzing market equilibrium. It enables us to model consumer \begin{table}
\begin{tabular}{c c} \hline \hline
**Notation** & **Representation** \\ \hline \(p_{i}\) & The product sale price. \(p_{1}\) is the price in Merchant 1’s channel, \(p_{2}\) is the price in Merchant 2’s channel. \(\Delta p=p_{1}-p_{2}\) \\ \(\lambda\) & The basic product valuation of the consumer; \(\lambda\in[0,1]\). \\  & The service level provided by the merchants. \(s_{1}\) is the service level of Merchant 1; \(s_{2}\) is the service level of Merchant 2. Merchant 1 can provide better services using IT, so \(s_{1}>s_{2}\). The service differentiation between the merchants is \(\Delta s=s_{1}-s_{2}\). \\  & The service cost paid by the merchants. \(C_{1}\) represents Merchant 1; \(C_{2}\) represents Merchant 2. Referring to the definition of cost function in economic principles, \(C(s)=\eta S^{2}/2\). \(\eta\) is the service cost coefficient, representing the efficiency of IT investment in converting service differentiation into cost. \\  & The channel preference (loyalty) of consumers. \(\delta_{1}\) is the probability of \\ \(\delta_{i}\) & purchasing from Merchant 1, \(\delta_{2}\) is the probability of purchasing from Merchant 2; \\  & without loss of generality, assume \(\delta_{1}>\delta_{2}\). \(\Delta\delta=\delta_{1}-\delta_{2}\). \\ \(\alpha\) & The consumer’s sensitivity to the product price; \(\alpha\in[0,1]\). \\ \(\beta\) & The consumer’s sensitivity to the service level; \(\beta\in[0,1]\). \\ \(D_{i}\) & The market demand function. \(D_{1}\) is the market demand of Merchant 1, \(D_{2}\) is the market demand of Merchant 2. \\ \(\pi_{i}\) & The profit function. \(\pi_{1}\) is the profit of Merchant 1, \(\pi_{2}\) is the profit of Merchant 2. \\  & \(\pi\) is the overall profit of the supply chain. \\ \(U_{i}\) & The consumer utility from product purchasing. \(U_{1}\) is the utility of purchasing from Merchant 1, \(U_{1}\) is the utility of purchasing from Merchant 2. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The parameters in the channel model. Figure 1: The structure of the cross-border supply chain. responses to different service and pricing strategies, thereby offering insights into how merchants can optimize their decisions to attract consumers and enhance profitability. * Without loss of generality, both merchants are assumed to confront unit market demand and only account for service costs, with other costs being zero. This assumption reflects the characteristics of cross-border e-commerce, particularly in scenarios involving digital services and information-based offerings.