Supplier Encroachment Channel Selection on an Online Retail Platform

Abstract

Online retail platforms offer encroachment opportunities for suppliers to directly sell products to consumers on the online market. However, how to select appropriate encroachment channels poses a significant challenge for suppliers. To solve this problem, we take one supplier selling products through an indirect reselling channel on a third-party online retail platform (TORP) as the base model, and further consider that the supplier can choose TORP agency selling, the owned channel, or both to encroach onto the online market. We hereby establish game-theoretical models to analyze the optimal strategy of supplier encroachment, the TORP preference, and the equilibrium channel strategy. The findings show that the supplier is always willing to encroach onto the online market through its own channel. Additionally, when the commission rate is low, the supplier will further encroach via the TORP agency selling channel. The TORP provides the agency selling channel for the supplier only when the commission rate exceeds a certain threshold. If the channel competition is not very fierce (the competition intensity is lower than 0.852) and the commission rate is moderate, dual-channel encroachment is the equilibrium channel strategy; otherwise, supplier-owned-channel encroachment is the equilibrium strategy. We extend our main models by incorporating supplier blockchain adoption and the cost differences between both parties to enhance practical applicability.

1. Introduction

With the growing prominence of the platform economy, online platform shopping has seen a significant surge in popularity. In 2022, online sales made an impressive leap, reaching a total of USD 6.54 trillion [1]. This trend is further supported by an E-consultancy survey, which indicated that 87% of distributors noted that their customers prefer shopping on online platforms [2]. Third-party online retail platforms (TORPs) like Amazon, Taobao, and JD attract millions of users, offering suppliers substantial market opportunities and expansive online distribution channels [3]. Reputable brands such as IBM, Lenovo, Dell, Apple, and Nike are increasingly leveraging TORPs to enhance their profitability [4]. Many of these platforms originated as resellers by operating reselling channels, i.e., purchasing products in bulk from suppliers and then reselling them to consumers at a markup [5,6]. Over time, some TORPs have expanded their services to include agency channels, allowing suppliers to offer products directly to consumers. Amazon, for instance, launched its agency channel in 1999, and JD followed suit in 2013. Subsequently, many suppliers, including Haier, Midea, Samsung, and Asus Computer, have adopted a dual-channel strategy, selling their products through both agency and reselling channels on TORPs such as JD.

More recently, TORPs are no longer the only architects of the online channel. Giant suppliers are beginning to use their own retail platforms in addition to TORPs to sell products directly to consumers on the online market [7]. For example, Nike announced the official launch of its official online mall application, the Nike App Chinese version. Huawei sells electronics products through its own online platform V-mall and JD’s reselling channels. Xiaomi, the world’s fourth-largest smartphone supplier, sells its products not only through JD’s reselling and agency selling channels but also through Xiaomi Mall. Suppliers selling products through multiple types of online channels can expand the market by meeting consumers’ diverse online shopping preferences. To be specific, consumers who are familiar with TORPs prefer the reselling channel when they are concerned about convenient logistics and return services and the agency selling channel when they are concerned about guaranteeing genuine products. By comparison, consumers who want to enjoy membership rights prefer the online channel in the supplier-owned platforms. When the suppliers introduce owned or/and TORP agency selling channel based on TORP reselling channels to sell products directly to consumers, the supplier encroachment phenomenon arises [8,9,10], which will inevitably lead to competition between suppliers and TORPs on the market among various channels [11,12]. In this context, how to choose the appropriate encroachment strategy based on multi-channel competition is a significant decision-making issue faced by suppliers.

As discussed in the above cases, suppliers may have different encroachment options in practice, i.e., no encroachment, agency selling channel encroachment (Midea), supplier-owned-channel encroachment (Huawei), and dual-channel encroachment via both the agency selling channel and supplier-owned channel (Xiaomi). Scholars have conducted comparisons between no encroachment and agency selling encroachment [7,11,13], as well as between no encroachment and supplier-owned-channel encroachment [12,14], to identify the conditions under which the supplier adopts channel encroachment. However, studies comparing different encroachment models are scarce. Additionally, there is no research regarding dual-channel encroachment scenarios. To fill these research gaps, this paper considers dual-channel encroachment as a potential encroachment strategy and then provides a comprehensive comparative analysis for different encroachment models to examine the supplier’s encroachment strategy selection and the TORP preference strategy.

Specifically, this study seeks to provide valuable insights into the following questions: (a) Should a supplier encroach onto the online market through its own or/and TORP agency selling channels, and which is the optimal strategy of supplier encroachment? How do the key factors, namely, the competition intensity across different channels and the commission rate in the agency selling channel of the TORP, impact the supplier’s encroachment strategy? (b) How does the supplier’s online encroachment strategy influence the TORP? (c) What is the equilibrium channel strategy negotiated by both parties?

To deal with the aforesaid inquiries, for a platform supply chain with one supplier and one TORP, we take the reselling mode as the base model and then consider that the supplier can either choose single-channel encroachment through its own online channel or a TORP agency selling channel or dual-channel encroachment via the agency selling channel and its own channel simultaneously. On this basis, we propose four encroachment models and conduct the comparisons of equilibrium decisions and profits across these models. Several interesting findings are obtained. (a) The supplier always prefers encroachment on an owned channel, and whether it also encroach via the agency selling channel hinges on the TORP’s commission rate. (b) Supplier-owned-channel encroachment always hurts the TORP’s profit. The TORP prefers the use of only the reselling channel with a low commission rate, while it prefers both the agency selling and reselling channels with a high commission rate. (c) Supplier-owned-channel encroachment or dual-channel encroachment may be the equilibrium selling strategy. We also derive insights regarding the impact of the supplier adopting blockchain technology and the selling cost difference between both parties on the encroachment strategy, in turn. The results show that, compared to the case without blockchain, when the demand expansion effect with blockchain is large enough, the supplier has less preference to choose dual-channel encroachment, and this also reduces the TORP’s willingness to open the agency selling channel. In addition, when a cost difference exists, encroachment on an owned channel does not necessarily outweigh agency selling channel encroachment for the supplier.

The next sections of our paper are arranged as follows. Section 2 outlines an overview of the pertinent literature. Section 3 gives a detailed clarification of the models used in our work. The analysis of the encroachment strategy is provided in Section 4. Section 5 extends the main models to discuss the influences of blockchain application and selling cost difference on the supplier’s encroachment strategy. Section 6 provides the conclusions. All proof is in the Appendix A, Appendix B and Appendix C.

2. Literature Review

This work contributes to two bodies of related literature on channel selection in platform retail supply chains and supplier encroachment.

2.1. Channel Selection in Platform Retail Supply Chains

Online platforms play a critical sales role in industries [15,16], and researchers have examined various types of platforms, such as online retail platforms [17,18,19], sharing platforms [20], and logistics platforms [21]. Our paper specifically examines online retail platforms. Ryan et al. characterized the online retail platform as a bridge that connects consumers and sellers [22]. Yan et al. examined the inclination of both an e-retailer and a traditional retailer to participate in an online retail platform [23]. Choi and He assessed the effect of leasing services on the operations of fashion products via a TORP and concluded that the revenue-sharing arrangement is more efficient than the approach featuring a fixed service price [15]. Agency selling and reselling are the predominant selling modes of TORPs [24]. Some scholars focused on analyzing the channel selection decision between these two modes. Specifically, from the standpoint of the supplier, Liu et al. examined how suppliers strategically select between agency selling and reselling modes within the framework of platform financing [25]. Wei et al. explored the effects of interconnections among multiple suppliers on firms’ optimal selling mode decisions [3]. Tsunoda and Zennyo identified the online selling modes of suppliers by accounting for uncertain demand [26]. From the TORP perspective, Liu et al. analyzed TORP’s selling mode preferences by considering the combined effects of market scale and consumer-driven marketing [27]. Zhang and Hou assessed how private labels by electronic retailers influence TORP’s selling mode selection [28]. Chang et al. evaluated the impact of secured financing plans on a TORP’s marketing mode choices, discovering that a higher market risk fosters a greater inclination towards the marketplace mode [29]. The existing studies can also be categorized into three classes according to influencing factors, i.e., platform-related factors such as slotting fees [30,31] and commission rate [12], competition-related factors, including channel competition intensity [32] or product heterogeneity [33], and scenario-specific factors, e.g., online order fulfillment costs [34], sales efficiency [35], service level [36], strategic inventory [37], and information asymmetry [38]. Contrary to prior studies which have exclusively focused on agency selling and reselling channels, our research also takes supplier-owned channels into account. Furthermore, we comprehensively address the channel selection issue from both the supplier’s and the TORP’s perspective.

2.2. Supplier Encroachment

In light of the popularization of online retail platforms, supplier encroachment by selling products directly to consumers has become a scholarly focus. Ryan et al. explored a system where a supplier operates on its own channel and investigated whether the supplier encroaches onto a TORP’s agency selling channel [22]. Guan et al. found that supplier encroachment through its own channel alters the equilibrium disclosure strategy, which increases the retailer’s revenue under certain conditions [9]. Khouja et al. examined supplier encroachment through an independent distribution channel, an owned channel, or an agency selling channel and found that the scale of the retail-captive consumer is a significant factor in suppliers’ optimal distribution channel selection [39]. Furthermore, Cai argued that encroachment could prove advantageous for both upstream and downstream firms, particularly when the downstream firm possesses considerable channel privilege [40]. According to Chen and Chang, the primary factors influencing supplier encroachment are the level of channel competition and the costs of encroachment [41]. Yan et al. explored the impact of product endurance on the encroachment strategy via a two-stage model [42]. They showed that both stakeholders could gain advantages from encroachment, regardless of whether product endurance is high or not. Guan et al. investigated the relationship between supplier encroachment and inventory strategy, and demonstrated that both the supplier and the retailer are likely to enhance profitability through vertical competition [43]. Considering the investment spillover effect, Chen et al. analyzed supplier-owned-channel encroachment and found that both upstream and downstream firms achieve win–win outcomes from supplier encroachment [44]. Zhang et al. explored the equilibrium strategy of supplier encroachment via the TORP’s agency selling channel with two competing products [45]. Ha et al. analyzed the influence of the strategic relationship between a TORP and a supplier on the channel structure [12]. Additionally, they examined how information sharing interplays with the channel structure. Zhang et al. investigated the influences of supplier encroachment onto the TORP’s agency selling channel considering the service investment spillover effect [46]. He et al. examined the interplay between supplier-owned-channel encroachment and the TORP’s logistics integration strategy [47]. Li et al. studied how a supplier’s online market entry affects the TORP’s channel-sharing strategy [48]. Distinct from previous studies, our work concentrates on the selection of various encroachment channels. In addition to single-channel encroachment, we also examine the scenario of dual-channel encroachment.

2.3. Research Gaps and Our Contributions

To sum up, most existing studies on supplier encroachment are confined to single-channel encroachment via the agency selling of the TORP or the supplier-owned channel on the online market [12,35,42]. By contrast, we not only analyze the profitability of single-channel encroachment through the agency selling channel or supplier-owned channel, but also investigate dual-channel encroachment through these two selling channels to derive the optimal strategy of supplier encroachment. Moreover, previous studies analyze channel selection mainly from either the supplier’s or the TORP’s perspective, while our study probes into channel strategy comprehensively from the supplier’s view, the TORP’s preference, and the equilibrium channel strategy negotiated by both parties.

3. Models

3.1. Model Description

Our paper examines an online retail supply chain with a supplier (he, labeled M) and a TORP (she, labeled P). Assume that the supplier has sold his products via the indirect reselling channel of the TORP on the online market. On this basis, the supplier can choose the agency selling channel of the TORP, the supplier-owned channel, or both to encroach onto the online market. This assumption is significantly different from those in related studies focusing on single-channel encroachment, i.e., the supplier encroaches onto the online market either through the TORP’s agency selling channel or the supplier-owned channel [35,42]. Both single-channel and dual-channel encroachment are considered in our model. Additionally, the TORP has the right to decide whether to offer the supplier an agency selling channel or not. The operation processes in the three channels are illustrated in Figure 1. Specifically, in the reselling channel (R), the supplier sells his products to the TORP based on a wholesale price, and then the TORP resells them to consumers at a markup. In the agency selling channel (A), the supplier relies on the TORP to sell products directly. However, the supplier needs to pay commission fees (a certain percentage of sales revenue) to the TORP. In the owned channel (S), the supplier can directly sell his products to consumers.

This paper takes the reselling channel as the base model and then models the supplier-owned-channel or/and agency selling channel encroachment. Hence, there are in total four possible channel structures in this online retail supply chain: scenario R, only the reselling channel; scenario SR, supplier-owned-channel encroachment based on the reselling channel; scenario AR, agency selling channel encroachment based on the reselling channel; and scenario SAR, dual-channel encroachment through the owned and agency selling channels, based on the reselling channel.

In the following, the superscript of the parameters/variables $k=$ R, AR, SR, and SAR, respectively, represents each scenario. The subscript of the parameters/variables $iorj=a,r,s$ represents the agency selling channel, the reselling channel, and the supplier-owned channel, respectively. The notations used in the models are outlined in

Table 1. Notations and definitions.

Notations	Definitions
$u$	The commission rate of the agency selling channel
$m_i$ ${\tau }_{ij}$	The market capacity of channel $i$ The channel substitutability (competition intensity) between channel $i$ and channel $j$, $i,j=a,r,s$, $i\ne j$
$w^k$	The wholesale price in the reselling channel in Scenario $k$, $k=$ R, AR, SR, and SAR
$p_i^k$	The unit price of channel $i$ in Scenario $k$, $k$ = R, AR, SR, and SAR, $i=a,r,s$
$D_i^k$	The market demand of channel $i$ in Scenario $k$, $k=$ R, AR, SR, and SAR, $i=a,r,s$
${\pi }_M^k,{\pi }_P^k$	The profit of the supplier and the TORP in Scenario $k$, respectively, $k$ = R, AR, SR, and SAR

.

Additionally, to avoid overly complicated expressions and facilitate the comparisons of the equilibrium decisions and profits between different models, we assume that the selling cost in each channel is zero [20,33], and this assumption will be eased in Section 5.

3.2. Market Demand

Supplier encroachment alters the channel structure of an online retail supply chain. To compare all members’ decisions and profits to analyze single- and dual-channel encroachments with a variable channel structure and multi-channel competition, it is essential to derive demand functions under the above four scenarios, respectively. Considering that the R, SR, and AR scenarios are special cases of the SAR scenario, which has all three possible selling channels, i.e., the reselling channel, the agency selling channel, and the supplier-owned channel, we first analyze the SAR scenario. Following Singh and Vives [49], Ha et al. [12], and Jiang et al. [50], we establish a quadratic utility function of a representative consumer in the SAR system as follows1:

$$U={\displaystyle \sum _{i=a,r,s}\left(m_i{D}_i-\frac{D_i^2}{2}-p_i{D}_i\right)}-{\displaystyle {\sum }_{i,j\in \left\{a,r,s\right\},i\ne j}{\tau }_{ij}{D}_i{D}_j}$$

(1)

where ${\tau }_{ij}$ denotes the channel substitutability between channel $i$ and channel $j$, which can also be referred to as competition intensity between the two channels; and $m_i$ denotes the market capacity of channel $i$. To simplify the models and make the competition among different channels more comparable, without being influenced by the market fluctuations, it is assumed that the market capacity in each channel is normalized to 1 [51,52], and the competition intensity between any two channels is the same, i.e., ${\tau }_{ar}={\tau }_{as}={\tau }_{rs}=\tau$. Then, based on the consumer utility function, we can derive the demand functions in the SAR system as follows. See Appendix A for the proof.

$$D_a^{SAR}=\lambda \left[1-{\displaystyle \frac{1}{1-b}}{p}_a+{\displaystyle \frac{b}{2\left(1-b\right)}}(p_r+p_s)\right]$$

(2)

$$D_r^{SAR}=\lambda \left[1-{\displaystyle \frac{1}{1-b}}{p}_r+{\displaystyle \frac{b}{2(1-b)}}(p_a+p_s)\right]$$

(3)

$$D_s^{SAR}=\lambda \left[1-{\displaystyle \frac{1}{1-b}}{p}_s+{\displaystyle \frac{b}{2(1-b)}}(p_a+p_r)\right]$$

(4)

where $\lambda ={\displaystyle \frac{2-b}{2+b}}$ and $\tau ={\displaystyle \frac{b}{2-b}}$. It is evident that $\tau$ and $b$ are positively correlated and have the same value range, i.e., $\tau ,b\in \left[0,1\right]$. Hence, hereinafter, $b$ can be approximately treated as channel substitutability, i.e., competition intensity. In extreme cases, $b=0$ means that the agency selling, reselling, and owned channels are independent, while $b=1$ means that the three channels are completely substitutable.

Based on the demand function in the SAR system, the demand functions of the other three scenarios can be derived by utilizing the “channel exclusion method”, similar to Shen et al. [30]. Specifically, compared with the SAR system, the agency selling channel is excluded in the SR system. Then, we can set $D_a^{SAR}=0$ and derive the demand functions for the remaining two channels (reselling channel and supplier-owned channel) as follows:

$$D_r^{SR}={\displaystyle \frac{\left(2+b\right)\lambda }{4}}\left(2-{\displaystyle \frac{2-b}{1-b}}{p}_r+{\displaystyle \frac{b}{1-b}}{p}_s\right)$$

(5)

$$D_s^{SR}={\displaystyle \frac{\left(2+b\right)\lambda }{4}}\left(2-{\displaystyle \frac{2-b}{1-b}}{p}_s+{\displaystyle \frac{b}{1-b}}{p}_r\right)$$

(6)

Similarly, if we let $D_s^{SAR}=0$, the market demand functions in the AR system can be obtained as follows:

$$D_a^{AR}={\displaystyle \frac{\left(2+b\right)\lambda }{4}}\left(2-{\displaystyle \frac{2-b}{1-b}}{p}_a+{\displaystyle \frac{b}{1-b}}{p}_r\right)$$

(7)

$$D_r^{AR}={\displaystyle \frac{\left(2+b\right)\lambda }{4}}\left(2-{\displaystyle \frac{2-b}{1-b}}{p}_r+{\displaystyle \frac{b}{1-b}}{p}_a\right)$$

(8)

If we let $D_a^{SAR}=0$ and $D_s^{SAR}=0$, the market demand function in the R system is

$$D_r^R=1-p_r$$

(9)

The above market demand functions have three characteristics: (i) The total market demand under scenarios of no encroachment, single-channel encroachment, and dual-channel encroachment satisfies $3\lambda >2-b>1$, which shows that the total market can be expanded by adding new channels. (ii) The price-sensitive factor for the products in each channel under dual-channel encroachment, single-channel encroachment, and no encroachment meets ${\displaystyle \frac{\lambda }{1-b}}>{\displaystyle \frac{\left(2+b\right)\left(2-b\right)\lambda }{4\left(1-b\right)}}>1$. This is because more channels lead to a greater price comparison effect, which causes consumers to opt for products with lower prices, thereby increasing the sensitivity of product demand to price changes. (iii) The cross-price sensitivity factor under dual-channel encroachment and single-channel encroachment meets ${\displaystyle \frac{b}{2\left(1-b\right)}}<{\displaystyle \frac{\left(2+b\right)b}{4\left(1-b\right)}}$. It is because, when one channel is introduced, a more stable price level is often maintained among channels to reduce the possibility of consumers switching to other channels, and then the substitution effect from the competing channel becomes weaker.

4. Equilibrium Analysis

4.1. Equilibrium Decisions

In this section, we establish four models, i.e., the R, AR, SR, and SAR models. Then, the equilibrium decisions in the four models are derived, in turn.

4.1.1. Model R

In the R system, the supplier wholesales his products to the TORP, and the TORP resells them to consumers at a markup. The following is the Stackelberg game sequence: the supplier first sets the wholesale price; then, the TORP sets the reselling price. The supplier’s profit comes from the wholesale revenue in the reselling channel $w^R{D}_r^R$. The TORP’s profit comes from the markup within the reselling channel $(p_r^R-w^R)D_r^R$.

The profit functions in this model are as follows:

$${\pi }_M^R\left(w^R\right)=w^R{D}_r^R$$

(10)

$${\pi }_P^R\left(p_r^R\right)=(p_r^R-w^R)D_r^R$$

(11)

Using the backward induction method to solve Equations (10) and (11), we obtain the equilibrium decisions in the R model, as shown in Proposition 1.

Proposition 1.

In the R system, the equilibrium wholesale price is $w^{R\ast }={\displaystyle \frac{1}{2}}$, the equilibrium reselling price is $p_r^{R\ast }={\displaystyle \frac{3}{4}}$, the equilibrium market demand in the reselling channel is $D_r^{R\ast }={\displaystyle \frac{2-b}{8}}$, the equilibrium profit of the supplier is ${\pi }_M^{R\ast }={\displaystyle \frac{1}{8}}$, and the equilibrium profit of the TORP is ${\pi }_P^{R*}={\displaystyle \frac{1}{16}}$.

4.1.2. Model AR

In the AR system, the supplier sells products via the agency selling channel of the TORP in addition to the reselling channel. Then, the TORP resells products to consumers at a markup and charges the supplier the commission fee. The following is the Stackelberg game sequence: the supplier first determines the agency selling price and the wholesale price; then, the TORP determines the reselling price. The supplier’s profit is derived from the wholesale revenue in the reselling channel $w^{AR}{D}_r^{AR}$ and the direct sales minus the commission fees in the agency selling channel $(1-u)p_a^{AR}{D}_a^{AR}$. The TORP’s profit is derived from the commission income in the agency selling channel $u{p}_a^{AR}{D}_a^{AR}$ and the markup in the reselling channel $(p_r^{AR}-w^{AR})D_r^{AR}$.

The profit functions in this model are as follows:

$${\pi }_M^{AR}\left(w^{AR},p_a^{AR}\right)=w^{AR}{D}_r^{AR}+(1-u)p_a^{AR}{D}_a^{AR}$$

(12)

$${\pi }_P^{AR}\left(p_r^{AR}\right)=u{p}_a^{AR}{D}_a^{AR}+(p_r^{AR}-w^{AR})D_r^{AR}$$

(13)

Using the same method as Section 4.1.1 to solve Equations (12) and (13), we can obtain the equilibrium decisions in the AR model, as shown in Proposition 2.

Proposition 2.

In the AR system, the equilibrium wholesale price is $w^{AR*}={\displaystyle \frac{2+b(1-u)}{4-2b}}$, the equilibrium reselling price is $p_r^{AR*}={\displaystyle \frac{3-2b}{4-2b}}$, the equilibrium agency selling price is $p_a^{AR*}={\displaystyle \frac{1}{2}}$, the equilibrium market demand in the reselling channel is $D_r^{AR*}={\displaystyle \frac{2-b}{8}}$, the equilibrium market demand in the agency selling channel is $D_a^{AR*}={\displaystyle \frac{4-b}{8}}$, the equilibrium profit of the supplier is ${\pi }_M^{AR*}={\displaystyle \frac{3-b-2u}{8}}$, and the equilibrium profit of the TORP is ${\pi }_P^{AR*}={\displaystyle \frac{4u-b+1}{16}}$.

4.1.3. Model SR

In the SR system, the supplier wholesales his products to the TORP and sells products through his own channel. Then, the TORP resells the products to consumers at a markup. The following is the Stackelberg game sequence: the supplier first sets the wholesale price on the reselling channel and the self-selling price on his own channel, after which the TORP determines the reselling price. The supplier’s profit comes partly from the wholesale revenue on the reselling channel $w^{SR}{D}_r^{SR}$ and partly from direct sales on the supplier-owned channel $p_s^{SR}{D}_s^{SR}$. The TORP’s profit comes from the markup in the reselling channel $(p_r^{SR}-w^{SR})D_r^{SR}$.

The profit functions in this model are as follows:

$${\pi }_M^{SR}\left(w^{SR},p_s^{SR}\right)=p_S^{SR}{D}_S^{SR}+w^{SR}{D}_r^{SR}$$

(14)

$${\pi }_P^{SR}\left(p_r^{SR}\right)=(p_r^{SR}-w^{SR})D_r^{SR}$$

(15)

Using the same method as Section 4.1.1 to solve Equations (14) and (15), we can obtain the equilibrium decisions in the SR model, as presented in Proposition 3.

Proposition 3.

In the SR system, the equilibrium wholesale price is $w^{SR*}={\displaystyle \frac{1}{2}}$, the equilibrium reselling price is $p_r^{SR*}={\displaystyle \frac{3-2b}{4-2b}}$, the equilibrium self-selling price is $p_s^{SR*}={\displaystyle \frac{1}{2}}$, the equilibrium market demand in the reselling channel is $D_r^{SR*}={\displaystyle \frac{2-b}{8}}$, the equilibrium market demand in the supplier-owned channel is $D_s^{SR*}={\displaystyle \frac{4-b}{8}}$, the equilibrium profit of the supplier is ${\pi }_M^{SR*}={\displaystyle \frac{3-b}{8}}$, and the equilibrium profit of the TORP is ${\pi }_P^{SR*}={\displaystyle \frac{1-b}{16}}$.

4.1.4. Model SAR

In the SAR system, the supplier wholesales his products to the TORP and sells products through both agency selling and owned channels; then, the TORP resells the products to consumers at a markup and charges the supplier the commission fee. The Stackelberg game sequence is as follows: the supplier first sets the wholesale, agency selling, and self-selling prices, after which the TORP determines the reselling price. The supplier’s profit comes from the wholesale revenue on the reselling channel $w^{SAR}{D}_r^{SAR}$, direct sales on the supplier-owned channel $p_s^{SAR}{D}_s^{SAR}$, and direct sales minus the commission fees on the agency selling channel $(1-u)p_a^{SAR}{D}_a^{SAR}$. The TORP’s profit comes partly from the commission income from the agency selling channel $u{p}_a^{SAR}{D}_a^{SAR}$ and partly from the markup in the reselling channel $(p_r^{SAR}-w^{SAR})D_r^{SAR}$.

The profit functions in this model are as follows:

$${\pi }_M^{SAR}\left(w^{SAR},p_a^{SAR},p_s^{SAR}\right)=p_s^{SAR}{D}_s^{SAR}+(1-u)p_a^{SAR}{D}_a^{SAR}+w^{SAR}{D}_r^{SAR}$$

(16)

$${\pi }_P^{SAR}(p_r^{SAR})=u{p}_a^{SAR}{D}_a^{SAR}+(p_r^{SAR}-w^{SAR})D_r^{SAR}$$

(17)

Using the same method as Section 4.1.1 to solve Equations (16) and (17), we can obtain the equilibrium decisions in the SAR model, as presented in Proposition 4.

Proposition 4.

In the SAR system, the equilibrium wholesale price is $w^{SAR*}={\displaystyle \frac{\left(1-b\right)\left[b^2{u}^2+8bu\left(1-u\right)-16(1-u)\right]}{2b^2{u}^2+32\left(1-u\right)b+32u-32}}$, the equilibrium self-selling price is $p_s^{SAR*}={\displaystyle \frac{2\left(1-u\right)\left(1-b\right)\left(4-bu\right)}{16(1-u)(1-b)-b^2{u}^2}}$, the equilibrium agency selling price is $p_a^{SAR*}={\displaystyle \frac{2\left(1-b\right)\left(bu-4u+4\right)}{16(1-u)(1-b)-b^2{u}^2}}$, the equilibrium reselling price is $p_r^{SAR*}={\displaystyle \frac{\left[b^2{u}^2-16\left(1-u\right)b-48u+48\right]\left(1-b\right)}{4\left[16(1-u)(1-b)-b^2{u}^2\right]}}$, the equilibrium market demand in the supplier-owned channel is $D_s^{SAR*}={\displaystyle \frac{\lambda \left[b^3{u}^2-8b^2\left(u^2-3u+2\right)-16b\left(u^2-4u+3\right)+64(1-u)\right]}{8\left[16(1-u)(1-b)-b^2{u}^2\right]}}$, the equilibrium market demand in the agency selling channel is $D_a^{SAR*}={\displaystyle \frac{\lambda \left[b^3{u}^2-8\left(2-u\right)b^2-16\left(3-2u\right)b-64u+64\right]}{8\left[16(1-u)(1-b)-b^2{u}^2\right]}}$, the equilibrium market demand in the reselling channel is $D_r^{SAR*}={\displaystyle \frac{2-b}{4(2+b)}}$, the equilibrium profit of the supplier is ${\pi }_M^{SAR*}={\displaystyle \frac{\lambda \left(1-b\right)\left[b^2{u}^2-16{\left(1-u\right)}^{2}b-32u^2+112u-80\right]}{8b^2{u}^2+128\left(1-u\right)b+128u-128}}$, and the equilibrium profit of the TORP is ${\pi }_P^{SAR*}={\displaystyle \frac{\lambda \left(1-b\right)\left[b^4{u}^4-32b^3{u}^2\left(3-2u\right)-32\left(9u^3-31u^2+32u-8\right)b^2-512\left(1+u\right){\left(1-u\right)}^{2}b+256\left(1+4u\right){\left(1-u\right)}^2\right]}{16{\left[b^2{u}^2+16\left(1-u\right)b+16u-16\right]}^2}}$.

4.2. Supplier Encroachment Analysis

This section compares the supplier’s and the TORP’s equilibrium decisions and profits in the above four models, based on which we identify the optimal strategy of supplier encroachment and the equilibrium channel strategy negotiated by both parties (the proofs of Corollaries 1–4 are in Appendix B).

Corollary 1.

(i) The unit prices of reselling and agency selling products in the AR system satisfy $p_r^{AR*}>p_a^{AR*}$; (ii) the reselling price and self-selling price in the supplier-owned channel in the SR system satisfy $p_r^{SR*}>p_s^{SR*}$; and (iii) the unit prices of the reselling, agency selling, and self-selling products in the SAR system satisfy. $\left\{p_r^{SAR*},p_a^{SAR*}\right\}>p_s^{SAR*}$.

Corollary 1 demonstrates that, in the AR system, the unit price of reselling products ($p_r^{AR*}$) always exceeds that of agency selling products ($p_a^{AR*}$). In the SR system, the unit price of reselling products ($p_r^{SR*}$) consistently surpasses that of self-selling products ($p_s^{SR*}$). The unit prices of reselling and agency selling products ($p_r^{SAR\ast },p_a^{SAR\ast }$) are always greater than those of self-selling products ($p_s^{SAR\ast }$) in the SAR system. These results reveal that, in the AR, SR, and SAR systems, the double marginalization problem caused by the markup behavior of the TORP in the reselling channel makes the unit price in this channel be higher than in other channels. Additionally, in the SAR system, to decrease the commission fees paid to the TORP and induce more consumers to steer towards the owned channel from the agency selling channel, the supplier sets a lower unit price for self-selling products compared to agency selling products.

Corollary 2.

(i) The unit prices of agency selling products in the AR and SAR systems satisfy $p_a^{AR*}<p_a^{SAR*}$; (ii) the unit prices of the supplier-owned channel in the SR and SAR systems satisfy $p_s^{SR*}>p_s^{SAR*}$; and (iii) the unit price of agency selling products in the AR system and that of the supplier-owned channel in the SR system satisfy $p_a^{AR*}=p_s^{SR*}$.

Corollary 2 demonstrates that the unit price of agency selling products in the SAR system ($p_a^{SAR*}$) is higher than in the AR system ($p_a^{AR*}$), whereas the unit price of self-selling products in the SAR system ($p_s^{SAR*}$) is lower than in the SR system ($p_s^{SR*}$). These results reveal that, when the supplier further encroaches via the owned channel based on the AR system to operate the SAR system, he will raise the price for agency selling products in order to induce more consumers to shift towards the owned channel from the agency selling channel and obtain more revenue via the owned channel. For a similar reason, when the supplier further encroaches via an agency selling channel based on the SR system to operate the SAR system, he will lower the unit price for self-selling products to maintain the market share in the owned channel. Moreover, the unit price of agency selling products in the AR system ($p_a^{AR*}$) is the same as the unit price of self-selling products in model SR ($p_s^{SR*}$). This is because, from supplier profit Equations (12) and (14) in the AR and SR systems, we know that the supplier, as the leader, can independently set the unit prices of agency selling and self-selling products without considering the TORP’s decision regarding the unit price of the reselling products; in addition, the functional forms of the demand $D_a^{AR}$ and $D_s^{SR}$ are identical, so $p_a^{AR*}=p_s^{SR*}$ holds.

Corollary 3.

(i) The wholesale prices of the reselling channel in the four systems satisfy $w^{R*}=w^{SR*}>w^{SAR*}>w^{AR*}$. (ii) The unit prices of the reselling products in the four systems satisfy the following conditions: if $u>\overline{u}={\displaystyle \frac{4(1-b)\left(\sqrt{b^3-3 b^2+4}+2 b-2\right)}{b(b^2-7 b+8)}}$, $p_r^{R*}>p_r^{SAR*}>p_r^{AR*}=p_r^{SR*}$; otherwise, $p_r^{R*}>p_r^{AR*}=p_r^{SR*}>p_r^{SAR*}$.

Corollary 3 shows that, for the reselling channel, the wholesale prices in the R and SR systems are identical ($w^{R*}=w^{SR*}$) and the highest out of all wholesale prices, followed by the wholesale price in the SAR system ($w^{SAR\ast }$), while that in the AR system ($w^{AR\ast }$) is the lowest. That is, only encroachment on an owned channel does not vary the wholesale pricing decision of the supplier in the reselling channel. Additionally, when the supplier encroaches via the agency selling channel (AR) or the dual channel (SAR), he will set wholesale prices in the reselling channel that are lower than those under the scenarios of no encroachment (R) and owned-channel encroachment (SR) to lead the TORP to reduce the reselling price, alleviating the competition between the agency selling channel and the reselling channel. Compared to the AR and SAR systems, the finding shows that the supplier sets a wholesale price in the SAR system that is higher than that in the AR system because he wants to drive the TORP to raise the reselling price in the SAR system, motivating more consumers to choose the supplier-owned channel.

In the four systems, the unit price of reselling products in the R system ($p_r^{R*}$) is the highest. This is because the reselling channel is the sole sales channel in this system, the TORP will set the highest reselling price to increase her marginal profit. Based on the result in Corollary 2 (iii) that the unit price of agency selling products in the AR system and that of self-selling products in the SR systems are the same, the TORP, as the follower, will set the same unit price for reselling products in these two systems, i.e., $p_r^{AR*}=p_r^{SR*}$. If the commission rate is higher (lower) than the threshold $\overline{u}$, the unit price of reselling products in the SAR system ($p_r^{SAR*}$) is greater (smaller) than in the AR system ($p_r^{AR*}$). It can be explained as follows. According to Corollary 2 (i), compared to the AR system, the supplier sets a higher price in the agency selling channel in the SAR system. Now, if the commission rate is relatively high, the supplier will further raise the agency selling price to reduce demand in this channel, thereby resulting in the TORP benefitting little from the agency selling channel in the SAR system. In this situation, the TORP will definitely elevate the reselling price to extract more profit in the reselling channel, leading to $p_r^{SAR*}>p_r^{AR*}$. By contrast, if the commission rate is relatively low, the TORP can take the strategy of “quick returns and small margins” in both the reselling and agency selling channels in the SAR system; thus, $p_r^{AR*}>p_r^{SAR*}$.

Corollary 4.

The total market demands in the four systems satisfy the following conditions: when $u<u_0={\displaystyle \frac{4\left(1-b\right)\left(\sqrt{2 b^4-8 b^3+12 b^2-16 b+16}+4 b-4\right)}{b\left(b^3-4 b^2-2 b+8\right)}}$, $D^{SAR*}>D^{AR*}=D^{SR*}>D^{R*}$; otherwise, $D^{AR*}=D^{SR*}>D^{SAR*}>D^{R*}$.

Corollary 4 demonstrates that, when the commission rate is lower than the threshold $u_0$, the total market demand in the SAR system ($D^{SAR*}$) is the greatest. On the contrary, when it is higher than $u_0$, the total market demand in the AR ($D^{AR*}$) and SR ($D^{SR*}$) systems becomes the greatest. The total market demand in the R system ($D^{R*}$) is always the smallest, regardless of the commission rate. The reason behind the above results is that a lower commission rate can help the supplier sell more products by encroaching onto the online market through dual channels. With the commission rate increasing, to avoid paying high commission fees to the TORP, the supplier will increase the unit price of the agency selling products to motivate some consumers to transfer from this channel to the owned channel. In addition, the unit prices of the reselling and supplier-owned channels also increase with the commission rate increasing ($\partial p_r^{SAR*}/\partial u>0$ and $\partial p_s^{SAR*}/\partial u>0$). Hence, given that the unit prices of all three selling channels in the SAR system increase, the total market demand in this system decreases to lower values than in the AR and SR systems.

In the following, we investigate the supplier’s encroachment strategy selection, the TORP’s preference, and the equilibrium channel strategy negotiated by both parties, as illustrated in Proposition 5 and Figure 2.

Proposition 5.

(i) For the supplier, if $u<u_1={\displaystyle \frac{4(1-b)\left[b^2-\sqrt{3}(b^2-2b)+4b-8\right]}{b^4-10b^3+6b^2+32b-32}}$ , ${\pi }_M^{SAR*}>Max\left\{{\pi }_M^{R*},{\pi }_M^{AR*},{\pi }_M^{SR*}\right\}$; otherwise, ${\pi }_M^{SR*}>Max\left\{{\pi }_M^{R*},{\pi }_M^{AR*},{\pi }_M^{SAR*}\right\}$. (ii) For the TORP, if$u<u_2=b/4$, ${\pi }_P^{R*}>Max\left\{{\pi }_P^{AR*},{\pi }_P^{SR*},{\pi }_P^{SAR*}\right\}$; otherwise, ${\pi }_P^{AR*}>Max\left\{{\pi }_P^{R*},{\pi }_P^{SR*},{\pi }_P^{SAR*}\right\}$. (iii) If $u_2<u<u_1$ and $b\le b\approx 0.852$, the equilibrium selling strategy negotiated by the supplier and the TORP is SAR; in other cases, it is SR.

Proposition 5 and Figure 2 demonstrate that the supplier (i) always prefers to encroach onto the online market via the owned channel, and whether he should also encroach via the TORP’s agency selling channel or not depends on the commission rate and the competition intensity. Specifically, when the commission rate is lower than a specific threshold ($u_1$), the supplier can gain more revenue by performing dual-channel encroachment and thus prefers the SAR system. By contrast, when the commission rate is higher than $u_1$, more revenue from agency selling products goes to the TORP, causing the supplier’s revenue to decrease. Thus, the supplier will give up the agency selling channel. We can also verify this from the equilibrium solutions. As the commission rate increases, it can be proven that the increasing rate of the selling price in the agency selling channel is faster than in the owned and reselling channels, i.e., $\partial p_a^{SAR\ast }/\partial u>\max \left\{\partial p_s^{SAR\ast }/\partial u,\partial p_r^{SAR\ast }/\partial u\right\}>0$. This motivates consumers to turn from the agency selling channel to the other two channels, and, thus, in this context, the supplier prefers the SR system. On the other hand, with the competition among the three channels becoming intense, $u_1$ decreases ($\partial u_1/\partial b<0$). This means that intensifying competition will force the supplier to abandon dual-channel encroachment at a lower commission rate and only choose owned-channel encroachment to weaken the substitutive effect of the agency selling products on the reselling and self-selling products.

(ii) The TORP does not hope to face competition from the supplier-owned channel, i.e., supplier-owned-channel encroachment will always damage TORP interests. If the commission rate in the agency selling channel is less than $b/4$, the TORP prefers to offer only the reselling channel; on the contrary, when the commission rate is more than $b/4$, the TORP will choose to provide the supplier with the agency selling channel. It can thus be easily understood that a relatively low commission rate cannot bring enough commission fees to the TORP. Hence, the TORP will not offer an agency selling channel to the supplier. By contrast, with a relatively high commission rate, the TORP can earn more commission fees from agency selling products, thus preferring to provide the supplier with the agency selling channel.

(iii) The equilibrium channel strategy negotiated by the supplier and the TORP is either supplier-owned-channel or dual-channel encroachment. Specifically, if the competition between different channels is not very intense ($b\le 0.852$), when the commission rate lies within a certain range, the equilibrium selling strategy is dual-channel encroachment; otherwise, it is supplier-owned-channel encroachment. This is because the supplier has the power to introduce the owned channel or not, while the TORP can decide whether to offer an agency selling channel to the supplier. From the perspective of the supplier, he can always expand the market and obtain more revenue by introducing the owned channel, so owned-channel encroachment is the dominant strategy of the supplier. From the viewpoint of the TORP, when the commission rate is relatively low, she is unwilling to provide the agency selling channel, and, thus, the equilibrium channel strategy negotiated by both parties is supplier-owned-channel encroachment. When the commission rate reaches the corresponding threshold, the TORP chooses to provide the supplier with an agency selling channel. Hence, the equilibrium channel strategy becomes dual-channel encroachment. However, when the commission rate continues to rise beyond a certain threshold, although the TORP wishes to offer the agency selling channel to the supplier, the latter will not choose this channel to sell products, as shown in Figure 2a. Therefore, the equilibrium selling strategy in this context changes back to supplier-owned-channel encroachment. Furthermore, if the competition among different channels is very intense ($b>0.852$), regardless of the value of the commission rate, the supplier will always give up the agency selling channel and only choose owned-channel encroachment. Therefore, the equilibrium channel strategy is supplier-owned-channel encroachment.

5. Extensions

In this section, we investigate two variants of the main models: blockchain technology application and selling cost difference between the supplier and the TORP. Below, we analyze each extended model, present the findings, and derive managerial insights.

5.1. Extension 1: Blockchain Technology Applications

In the main models, we assume the market capacity in each channel to be constant, i.e., $m_i=1$. In this extension, we consider the case of a supplier using blockchain technology to expand the market. In recent years, blockchain technology has been increasingly used in platform retail supply chains. Blockchain endows the online market with information invariance and permanent accessibility and ensures that consumers can access immutable real data on online retail platforms [53]. For example, Nike uses a dynamically encrypted NFC chip in conjunction with blockchain for product traceability. IBM applies blockchain to offer consumers detailed information about the sources and origins of their food products [54,55]. Hence, the implementation of blockchain can enhance consumer trust in product quality, increase their willingness to purchase products, and, thus, expand the market capacity on online retail platforms [56].

If we denote ${\tilde{m}}_i(i=a,r,s)$ as the market capacity in channel i when the supplier applies blockchain technology, based on the above analysis, ${\tilde{m}}_i>m_i=1$ is satisfied. For model tractability, we let ${\tilde{m}}_a={\tilde{m}}_r={\tilde{m}}_s=m>1$. However, adopting blockchain technology will incur a unit cost $c_b$ for the supplier. For example, blockchain as a service product incurs a cost of USD 0.29 per allocated CPU hour (IBM Blockchain Platform). The introduction of this cost aligns with the assumptions proposed by the literature [57,58] and is considered an exogenous parameter. By incorporating the expanded market capacity ${\tilde{m}}_i$ and the blockchain application cost $c_b$ into the main model, we can establish game-theoretical models with blockchain in the four systems (scenarios BR, BSR, BAR, and BSAR, respectively, correspond to the application of blockchain technology in the R, SR, AR, and SAR systems). Using the backward induction method, we can derive the equilibrium outcomes. Then, we can perform a comparative static analysis and conduct comparisons on equilibrium decisions between the four systems. The detailed outcomes and proof are in Appendix C. The main results are as follows:

Lemma 1.

When the supplier adopts blockchain technology, the impacts of an expanded market capacity and unit blockchain application cost on the equilibrium prices and demands are as follows: (i) ${\displaystyle \frac{\partial w^{k*}}{\partial m}}>0,{\displaystyle \frac{\partial p_i^{k*}}{\partial m}}>0,{\displaystyle \frac{\partial D_i^{k\ast }}{\partial m}}>0$ and (ii) ${\displaystyle \frac{\partial w^{k*}}{\partial c_b}}>0,{\displaystyle \frac{\partial p_i^{k*}}{\partial c_b}}>0,{\displaystyle \frac{\partial D_i^{k*}}{\partial c_b}}<0$, where $k$ = BR, BAR, BSR, BSAR and $i=a,s,r$.

Lemma 1 (i) indicates that, when the supplier adopts blockchain technology, the more significant the market capacity expanded by blockchain, the higher the total market demand in all four systems, which gives the supplier and the TORP more pricing power. Thus, they will increase prices in the three selling channels. Lemma 1 (ii) states that, when the supplier adopts blockchain to expand the market capacity, with the increase in unit blockchain application costs, the wholesale and selling prices in all four systems increase, while the total market demand decreases. It is straightforward that, since the supplier must bear the blockchain application costs, he needs to increase the wholesale price to offset the extra costs; in this context, the TORP will also raise the unit price of reselling products to maintain marginal profit. Accordingly, the unit prices in the agency selling and supplier-owned channels also increase. Consumers are less willing to buy products because of higher prices in the three selling channels, leading to the total market demand in each model decreasing.

Corollary 5.

When the supplier adopts blockchain technology, the unit prices of reselling, agency selling, and self-selling products and the total market demand for the BAR and BSR systems satisfy the following conditions: (i) $p_a^{BAR*}>p_s^{BSR*}$, $p_r^{BAR*}>p_r^{BSR*}$, and $D^{BAR*}<D^{BSR*}$. (ii) When $u<{\displaystyle \frac{m-c_b}{m+c_b}}$, $p_a^{BAR*}<p_r^{BAR*}$; otherwise, $p_a^{BAR*}>p_r^{BAR*}$.

Corollary 5 demonstrates that blockchain application will lead to the change in some conclusions related to the AR and SR systems from Corollary 1 to Corollary 4, which are obtained in the case without blockchain. To be specific, because the supplier bears both the blockchain application costs and the commission fee in the BAR system, he will set a higher unit price for agency selling products in this system compared to self-selling products in the BSR system, meaning that $p_a^{BAR*}>p_s^{BSR*}$. Due to a higher $p_a^{BAR*}$, more consumers will flow to the supplier-owned channel, leading the TORP to set a higher unit price for reselling products in the BAR system than the BSR system to gain more margin profit, i.e., $p_r^{BAR*}>p_r^{BSR*}$. Consequently, the BSR system yields a higher total market demand than the BAR system, i.e., $D^{BSR*}>D^{BAR*}$. Moreover, when the commission rate exceeds the threshold, the unit price of agency selling products ($p_a^{BAR*}$) is even higher than that of reselling products ($p_r^{BAR*}$) in the BAR system. This is because, with the increase in the commission rate, the supplier raises the unit price of agency selling products and induces more consumers to turn to the reselling channel to reduce commission fees, weakening the substitution effect of agency selling on the reselling channel.

Next, we focus on how blockchain application affects the supplier’s encroachment strategy and equilibrium channel strategy through a profit analysis for both parties. First, it must be noted that the supplier chooses to apply blockchain technology only when he can benefit from it. Hence, the supplier judiciously weighs the demand expansion effect and the additional costs of blockchain application to ensure its profitability. Figure 3 illustrates an example of the optimal joint selection of blockchain application and channel encroachment strategies for the supplier, given the expanded market capacity of $m=1.2$. The findings show that, when the blockchain application cost is $c_b=0.18$, the supplier adopts a mixed strategy for blockchain application in the dual-channel encroachment region. Specifically, as depicted in Figure 3a, if the commission rate is below the threshold, the supplier opts for blockchain application (BSAR region); otherwise, due to a relatively high commission fee, the supplier opts out of it (SAR region) to curtail the expenses. In owned-channel encroachment region, the supplier always chooses to apply blockchain technology (BSR region) because he is free from paying the TORP commission fees. However, as the blockchain application cost $c_b$ escalates to 0.2, as described in Figure 3b, the supplier applies blockchain technology in the owned-channel encroachment region and does not apply it in the dual-channel encroachment region, irrespective of the commission rate. In sum, Figure 3 reveals that the supplier does not apply blockchain technology in all regions because the expanded market capacity is not large enough compared to the blockchain application cost. Given that it is a tough challenge to derive all the possibilities for the above situation, in the following, we will only concentrate on the scenario in which the expanded market capacity is sufficiently large to ensure that the supplier can always benefit from blockchain application in both owned-channel and dual-channel encroachment regions.

In the following, we select the parameters as $m=1.5$ and $c_b=0.1$ to make sure that the supplier always applies blockchain and then delve into the influence of the commission rate and competition intensity among the three channels on the supplier encroachment strategy. By comparing the equilibrium profits of all four systems, we obtain Figure 4 and Proposition 6.

Proposition 6.

When the demand expansion effect is large enough that the supplier always chooses to apply blockchain technology, the following conditions apply: (i) For the supplier, if $u<u_3$, ${\pi }_M^{BSAR*}>Max\{{\pi }_M^{BR*},{\pi }_M^{BAR*},{\pi }_M^{BSR*}\}$; otherwise, ${\pi }_M^{BSR*}>Max\{{\pi }_M^{BR*},{\pi }_M^{BAR*},{\pi }_M^{BSAR*}\}$. (ii) For the TORP, when $u<u_4$, ${\pi }_P^{BR*}>Max\{{\pi }_P^{BAR*},{\pi }_P^{BSR*},{\pi }_P^{BSAR*}\}$; when $u_4<u<u_5$, ${\pi }_P^{BAR*}>Max\{{\pi }_P^{BR*},{\pi }_P^{BSR*},{\pi }_P^{BSAR*}\}$; and when $u>u_5$, ${\pi }_P^{BR*}>Max\{{\pi }_P^{BAR*},{\pi }_P^{BSR*},{\pi }_P^{BSAR*}\}$. (iii) If $u_4<u<u_3$ and $b<b_2$, the equilibrium channel strategy negotiated by the supplier and the TORP is BSAR; otherwise, it is BSR (see $u_3$, $u_4$, $u_5$, and $b_2$ in Appendix A).

Proposition 6 (i) shows that, when the demand expansion effect is large enough to ensure that the supplier always applies blockchain, they will still choose owned-channel or dual-channel encroachment according to the commission rate. Specifically, if the commission rate is less than the threshold $u_3$, the supplier will opt for dual-channel encroachment; otherwise, they prefer owned-channel encroachment. The reason is the same as that in Proposition 5. Moreover, we can verify that $\partial u_3/\partial b<0$ and $\partial u_3/\partial c_b<0$, i.e., as the competition intensity among different channels or the blockchain application cost increases, the supplier will abandon dual-channel encroachment at a lower commission rate and choose only owned-channel encroachment to eliminate the substitutive effect exerted by the agency selling channel on the reselling channel, as well as reduce the blockchain application costs.

Proposition 6 (ii) demonstrates that, similarly to the main models without blockchain application, supplier-owned-channel encroachment is detrimental to the TORP. Additionally, when the commission rate is low (less than $u_4$), the TORP prefers only the reselling channel; when the commission rate is moderate ($u_4<u<u_5$), the TORP can gain more revenue by opening both the agency selling and reselling channels. However, different from the main models, when the commission rate is high (more than $u_5$), the TORP instead gives up the agency selling channel and only provides the reselling channel. This finding is counter-intuitive. The rationale behind this is that, facing a high commission rate, aligned with Corollary 5 (ii), the supplier sets a higher unit price in the agency selling channel than in the reselling channel, leading a portion of consumers to turn to the reselling channel. In this situation, even if the commission rate is high, the decrease in the market demand makes the agency selling channel less profitable for the TORP. Hence, the TORP only offers the reselling channel. On the whole, blockchain application will reduce the TORP’s willingness to offer the agency selling channel.

Proposition 6 (iii) shows that the equilibrium channel strategy negotiated by both parties is either the BSR or BSAR system, for the same reason as Proposition 5. But, compared to Figure 2c, the BSAR region in Figure 4c becomes smaller because the supplier abandons the dual channel and chooses owned-channel encroachment at a lower commission rate. Hence, compared to the case without blockchain, owned-channel encroachment is more likely to be the equilibrium channel strategy when the supplier applies blockchain technology.

5.2. Extension 2: The Selling Cost Difference Between the Supplier and the TORP

In the main models, we consider that the supplier and the TORP have the same efficiency in selling products. In practice, TORPs usually have more professional sales capabilities and cost advantages over the supplier in terms of sales. Specifically, compared to TORPs, it is difficult for suppliers to exhibit economies of scale when providing pre-sales, after-sales, logistics, and distribution services in their own channels, so they need to invest more human and material resources to overcome this disadvantage. In this extension, without the loss of generality, we normalize the selling cost in retail channels of the TORP to be zero and assume that the supplier bears a positive unit selling cost $c$ in his own channel. To avoid a tedious discussion, we take the value of $c$ as 0.1 (we find that the relevant conclusions are robust for different values of $c$). Then, we explore the impacts of this cost difference on the supplier’s encroachment strategy and equilibrium channel strategy. The profit functions and equilibrium solutions in models R and AR are consistent with Section 4, so we only provide the profit functions of models SR and SAR below.

Model SR:

$${\overline{\pi }}_M^{SR}({\overline{w}}^{SR},{\overline{p}}_s^{SR})={\overline{p}}_s^{SR}{\overline{D}}_s^{SR}+{\overline{w}}^{SR}{\overline{D}}_r^{SR}-c{\overline{D}}_s^{SR}$$

(18)

$${\overline{\pi }}_P^{SR}({\overline{p}}_r^{SR})=({\overline{p}}_r^{SR}-{\overline{w}}^{SR}){\overline{D}}_r^{SR}$$

(19)

Model SAR:

$${\overline{\pi }}_M^{SAR}({\overline{w}}^{SAR},{\overline{p}}_s^{SAR},{\overline{p}}_a^{SAR})={\overline{p}}_s^{SAR}{\overline{D}}_s^{SAR}+(1-u){\overline{p}}_a^{SAR}{\overline{D}}_a^{SAR}+{\overline{w}}^{SAR}{\overline{D}}_r^{SAR}-c{\overline{D}}_s^{SAR}$$

(20)

$${\overline{\pi }}_P^{SAR}({\overline{p}}_r^{SAR})=u{\overline{p}}_a^{SAR}{\overline{D}}_a^{SAR}+({\overline{p}}_r^{SAR}-{\overline{w}}^{SAR}){\overline{D}}_r^{SAR}$$

(21)

Using the backward induction method, we obtain the equilibrium outcomes. The detailed outcomes and proof are in Appendix C. By conducting comparisons on equilibrium decisions and both parties’ profits between the four systems, the main results are obtained, as shown in Figure 5 and Proposition 7.

Proposition 7.

When there is a selling cost difference between the supplier and the TORP, (i) The supplier’s agency selling channel encroachment will occupy a dominant area. (ii) The TORP’s preferred selling strategy in this scenario is still reselling or both agency selling and reselling. (iii) The equilibrium channel strategy negotiated by both parties may be AR, SR, or SAR.

Proposition 7 demonstrates that, in the presence of the selling cost difference, for the supplier, owned-channel encroachment or dual-channel encroachment is no longer always superior to agency selling channel encroachment. Specifically, facing a high selling cost in the owned channel and a low commission fee in the agency selling channel, the supplier, who weighs the selling cost and the commission fee, will choose agency selling channel encroachment under certain circumstances (i.e., region AR in Figure 5). As the TORP does not bear the cost, no matter how large the selling cost difference is, she still chooses the R or AR systems for the same reasons as Proposition 5. Hence, the equilibrium selling strategies may be AR, SR, or SAR systems.

6. Conclusions and Managerial Implications

6.1. Conclusions

With the burgeoning expansion of retail platforms on the online market, suppliers can distribute products to consumers via diverse selling channels. To cater to this trend, we take one supplier selling products through the reselling channel on a TORP as the base model and further consider that the supplier can choose the agency selling channel of the TORP, the owned channel, or both to encroach onto the online market. We use game-theoretical models combined with numerical analysis to examine the optimal strategy of supplier encroachment, the TORP’s preference, and the equilibrium channel strategy. We obtained the following findings:

For the supplier, owned-channel encroachment or dual-channel encroachment is strictly superior to agency selling encroachment or no encroachment. Thus, the supplier will always choose owned-channel encroachment, and whether he should encroach onto the online market via the agency selling channel depends on the commission rate of the TORP. Specifically, when the commission rate is lower than a certain threshold, the supplier chooses dual-channel encroachment; otherwise, he will opt for only owned-channel encroachment. However, from the perspective of the TORP, supplier-owned-channel encroachment is always detrimental. The TORP prefers the reselling channel with a low commission rate, and both the agency selling and reselling channels with a high commission rate. Since it is the TORP who decides whether to provide the agency selling channel for the supplier, dual-channel encroachment is the equilibrium channel strategy only when the commission rate is at a moderate level and the competition among different channels is not very fierce. Otherwise, the equilibrium strategy is supplier-owned-channel encroachment.

We further extend the main models by considering blockchain application by the supplier and the selling cost difference between both parties, respectively. We find that the supplier does not necessarily choose to apply blockchain technology unless the demand expansion effect is sufficiently large. When the supplier can always benefit from blockchain application, he prefers owned-channel encroachment or dual-channel encroachment. However, the supplier will give up dual-channel encroachment and switch to owned-channel encroachment at a lower commission rate. Blockchain application also reduces the TORP’s willingness to open the agency selling channel. Specifically, when the commission rate is low, the TORP prefers only the reselling channel; when it is moderate, she prefers both agency selling and reselling; and, when it is high, counter-intuitively, she gives up the agency selling channel and only provides the reselling channel. Therefore, compared to the main models without blockchain application, it is more likely that supplier-owned-channel encroachment will be the equilibrium strategy with blockchain application.

When there is the selling cost difference between the supplier-owned channel and the TORP’s agency selling and reselling channels, we find that, for the supplier, owned-channel encroachment does not necessarily outweigh agency selling channel encroachment. Specifically, under a low commission rate and a large competition intensity, only agency selling channel encroachment will be better than supplier-owned encroachment and dual-channel encroachment. The TORP’s preferred selling strategy is still reselling or both agency selling and reselling. Hence, the equilibrium strategy negotiated by both parties turns out to be agency selling channel encroachment, supplier-owned-channel encroachment, or dual-channel encroachment.

6.2. Managerial Implications

As mentioned above, Huawei adopts supplier-owned-channel encroachment to sell the electronic products on JD’s or Amazon’s reselling channel, while Xiaomi employs dual-channel encroachment. Following this, we will connect our main findings to strategic recommendations for the stakeholders in the platform supply chain, as outlined in

Table 2. Managerial implications and recommendations.

Management Implications	Recommendations
Optimize Channel Selection to Enhance Competitiveness	Suppliers like Xiaomi should prioritize dual-channel encroachment strategies. For instance, Xiaomi selling through its own online store and the agency selling and reselling channels of TORPs like Amazon can maximize market coverage and profits. However, suppliers should also flexibly adjust their channel choices based on the commission rates set by Amazon and JD.com.
Develop Flexible Channel Strategies	TORPs like Amazon and JD.com should adjust their channel strategies based on the commission rates. When the commission rates are low, TORPs should only provide the reselling channel for the suppliers. At moderate or high commission rates, offering both agency selling and reselling channels to attract suppliers can improve the TORPs’ interests. Additionally, high commission rates may require TORPs like Amazon to re-evaluate channel structures to prevent suppliers from solely relying on owned channels.
Strategic Consideration of Blockchain Application	Suppliers like Xiaomi can enhance supply chain traceability and efficiency by adopting blockchain technology, but only if it can significantly expand the market demand. TORPs like Amazon should assess the impact of blockchain on channel strategies and market competition to ensure that its application fosters collaboration and mutual growth between the TORPs and the suppliers. For example, Xiaomi using blockchain to ensure product authenticity on Amazon can build consumer trust and drive sales growth.
Consider Sales Cost Differences to Formulate Precise Strategies	Suppliers like Huawei must account for sales cost differences between its own channels and TORPs like Amazon’s agency/reselling channels when choosing their encroachment strategies. In the cases of a low commission rate and high competition intensity, agency selling channel encroachment (e.g., selling through Amazon) is more advantageous.
Achieve Equilibrium and Synergy in Channel Strategies	Suppliers like Xiaomi and TORPs like Amazon should negotiate effectively to achieve balanced and synergistic channel strategies. Amazon should flexibly optimize channel structures to encourage suppliers to choose win–win encroachment strategies. Suppliers, in turn, should dynamically adjust their channel choices based on market competition intensity and commission rate changes to maintain a competitive edge in a multi-channel environment.

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Finally, we discuss three directions for future study. First, in Section 5.1, we mainly examine encroachment strategy selection for the supplier when the market expansion effect is sufficiently large to ensure that he can always benefit from blockchain application, and it will be a promising research topic to analytically derive the optimal joint selection of blockchain application and channel encroachment strategies for the supplier when the expansion effect is not large enough. Second, the proliferation of live-streaming platforms has expanded the channels available for supplier encroachment. Thus, the inclusion of live streaming as an encroachment channel deserves more investigation. Third, nowadays, artificial intelligent (AI) technologies have been gradually applied to the production stage of suppliers [59] and incorporated into the marketing strategies of platforms [60]. One can further examine the influence of AI adoption on supplier encroachment in a platform supply chain.