Private Label Introduction and Sales Format Selection with Regard to e-Commerce Platform Supply Chain

Abstract

Largely motivated by the industrial practice in which a platform giant will encroach online retailing by introducing private label (PL) products, this paper aims to investigate the optimal introduction decision for a platform and identify the best sales format, between the reselling format and the agency format, for a manufacturer in an e-commerce platform supply chain. In response to these two sales formats, this paper characterizes and proposes three different PL product introduction strategies, including No Introduction, Partial Introduction, and Full Introduction. By developing a game-theoretic framework and applying the Karush–Kuhn–Tucker optimality, this paper examines the optimal PL product introduction decision and the best sales format. With analytical studies and numerical experiments, several significant implications are derived in this paper. For example, it is first found that the consumer preference for the platform and the quality of the PL products are two key factors influencing the platform’s PL product introduction, with associated effects differing notably. Secondly, improving the PL products’ quality does not necessarily lead to an increased profit for the platform. It will also not lead to a loss in profit for the manufacturer. Lastly, the best sales formats for the manufacturer are significantly influenced by the PL products’ introduction strategy chosen by the platform.

1. Introduction

1.1. Motivation

Online retailing has experienced significant success over the past two decades. In 2023, global e-commerce sales reached 5.8 trillion USD, which is nearly five times the amount recorded in 2014, with projections indicating that this figure will exceed 8 trillion USD by 2027 [1]. The platform company, as a cornerstone of online retailing, plays a critical role in facilitating online sales by initially providing a marketplace that connects sellers and buyers. Typically, it can be seen from both industry and academia that there are two common sales formats that manufacturers can choose for selling their current brand products (CB products) through the platform’s online marketplace [2], namely the reselling format and the agency format.

In the online reselling format, manufacturers first sell CB products to the platform, and the platform then resells these CB products to end consumers. In this case, the platform takes ownership of the CB products and acts as a reseller (e.g., Amazon and JD.com). In the online agency format, manufacturers own the CB products and sell them directly to consumers and pay sales commissions to the platform based on the shares of sales. In this case, the platform acts purely as an online marketplace (e.g., Tmall.com). A valuable research question arising here is how to assist manufacturers in selecting the best online sales format in the online marketplace.

Partly for improving the competitiveness and obtaining more profit shares on the online market, some giant e-platforms are entering the online retail markets originally owned by manufacturers by introducing private label products (PL products). The PL products coexist and compete with the CB products in the platform’s online marketplace. For example, Amazon, a leading e-commerce platform, launched its PL products in 2009. Another example is that Chinese e-commerce giants Tmall (which is a representative of a platform that mainly implements the online agency format) and JD.com (which is a representative of a platform that mainly implements the online reselling format) have introduced their PL brands, named Miaomanfen and Jingzhizao, respectively. However, the focus and categories of the PL products released on these leading e-platforms are different. It is particularly noteworthy that the PL products of Tmall are introduced and sold on Miaomanfen and are mainly daily necessities such as food, rice, and oil. While JD.com introduces and sells high-end products such as fashion, digital, and skin care, through Jingzhizao. The underlying reasons behind the platform’s decision on launching and selecting the PL products are unclear.

The introduction of PL products will inevitably have a crucial effect on the operation and the profitability of the e-commerce platform supply chain. Obviously, the launch of PL products introduced by a platform will compete with the CB products sold by manufacturers, which will affect the associated pricing decisions and thus, the profit distribution between the platform and the manufacturer, and ultimately modify a manufacturer’s choice of the optimal online sales format for its CB products. Therefore, it is worth examining the interplay between PL product introduction and sales format selection in an e-commerce platform supply chain.

1.2. Research Questions

Given the industry practice in which giant e-commerce platforms cannibalize an online retail market by introducing PL products with different sales formats, this paper aims to analyze and explore the best PL product introduction decision for a platform and the optimal sales format selection for a brand manufacturer, so as to reveal the mutual effects between PL product introduction and sales format selection. In more detail, this paper is going to answer the following research questions:

• (a). What are the optimal PL product introduction decisions for a platform with online reselling and agency formats?

• (b). What are the effects of a PL product’s quality on individual profitability with two different online sales formats?

• (c). How to select the best online sales format for a manufacturer?

• (d). How do sales format selection and PL product introduction strategy mutually affect each other in this e-platform supply chain?

There is a large group of studies that focus on the supply chain encroachment in a traditional supply chain [3,4]. However, the existing literature overlooks the situation where a giant e-commerce platform will be a potential entrant in an online retailing marketplace by introducing its PL products. The research gap lies between this paper and the existing literature is that this paper focuses on optimal encroachment decisions made by a platform within different online channel formats, as well as reveals the interplay between PL product introduction and sales format selection in an e-platform supply chain. To bridge the research gap and address the above research questions, this paper develops an e-platform supply chain consisting of one platform and one brand manufacturer, in which the Stackelberg game framework and the Karush–Kuhn–Tucker optimality conditions are employed to derive equilibrium decisions and the associated analysis.

1.3. Contributions and Organization

The contributions of this paper are twofold. Firstly, this paper explores the optimal PL introduction decision for the platform by characterizing three different strategies, namely No Introduction, Partial Introduction and Full Introduction. The results of our work indicate that the consumers’ preference for the platform and the PL products’ quality are two key factors that determine the platform’s PL product introduction decisions. In more detail, a higher consumer preference for the platform will obviously lead to the introduction of more PL products. However, the impacts of the PL product quality on introduction decisions are more complex and depend largely on the related consumers’ preferences for the platform and the PL product quality themselves. These results motivate the platform to select the optimal PL product introduction decisions and enrich related research on supply chain encroachment [5,6].

Secondly, this paper looks for the optimal sales format for the manufacturer in the presence of the PL product introduction by the platform. In response to this issue, this paper investigates the optimal sales formats with different PL product introduction strategies and finds that the PL product introduction strategy adopted by the platform plays a key role in the optimal sales format selection for the manufacturer. In different introduction strategies, the relevant factors determining the manufacturer’s sales format selection differ. These results can contribute to the existing studies and provide novel managerial implications of selecting the best online sales format [7,8].

The remainder of this article is organized as follows. Section 2 reviews the most related literature. Section 3 describes the problem statement in which the model settings are then formulated. The best PL product introduction decisions for the platform with online reselling format and online agency format are explored in Section 4 and Section 5, respectively. Section 6 focuses specifically on how the PL product quality affects the individual profitability with two different sales formats. The optimal sales format for manufacturers to sell CB products is studied in Section 7. Section 8 summarizes the main findings, limitations, and further research of this paper. For clarity, all proofs are summarized in the Appendix A.

2. Literature Review

2.1. Supply Chain Encroachment

Supply chain management has always been the focus of scholars’ attention. Many researchers concentrate on supply chain management mainly from the following aspects. The first line of research is operation decisions in supply chain management, such as pricing decision [9], quality improvement [10], sales effort [11], and among others. Another line of research is profit sharing in a supply chain, such as revenue sharing [12] and profit coordination [13]. The other one is the exploration of relationship in a supply chain, such as competition and cooperation [14], power structure [15], and fairness concern [16].

As a typical line of research in supply chain management, supply chain encroachment exhibits two sources of encroachment patterns, depending on who acts as the entrant. The first potential entrant who may enter the retailing market in a supply chain is the upstream supplier, referred to as supplier encroachment. The existing literature has illustrated that supplier encroachment will harm the retailer’s revenue because such an encroachment will discourage the selling efforts of retailers [17], incur more quality investments [18], and so forth. However, there are also studies showing that under certain market conditions, supplier encroachment can bring advantages to retailers through cooperation [19,20], enhancing supply chain transparency [21], incorporating optimal operation strategy [22], and easing channel conflict [23,24].

Another source of supply chain encroachment is retailer encroachment, which is achieved through the development of private label product and is relevant to our work. Numerous studies show that the encroachment of retailers increases competition with manufacturers, allowing manufacturers to lower wholesale prices and benefiting the retailers themselves. For instance, Zhang et al. [25] apply a game theory model to examine the trade-offs of manufacturer encroachment by developing direct-to-consumer channels and retailers’ adoption of private labels. Nie et al. [26] explore retailing encroachment by launching a private label product and manufacturer encroachment by selling national brand products to the end consumers directly. Shopova [27] studies how to launch private label products to compete directly with third parties in an online marketplace. Li et al. [28] investigate a competition situation where online retailers simultaneously sell the private label product directly and the product of the manufacturer with agency selling. Long and Amaldoss [29] study when and why platforms favor private brands in search advertising, and how this affects users and third parties. Zhang et al. [6] investigate the optimal encroachment decisions that may be made by the manufacturer or the e-retailer in an online retailing marketplace that are currently owned by multiple third-party retailers.

In contrast to the existing literature, a fundamental difference between our work and previous studies is that this paper examines the encroachment decisions made by the platform within an e-commerce platform supply chain. Furthermore, to analyze the platform’s encroachment behavior, this paper explores three different PL product introduction strategies based on the market share proportion of the PL product relative to the CB product.

2.2. Online Sales Format

In view of the strong development of online sales, existing research mainly focuses on online retailing in the following aspects, i.e., pricing decision [30], value-added service provision [31], coordination [14], managing return policies [32,33], competition and cooperation [34], information sharing [35], consumer behavior [36,37], live-streaming selling [38], channel preference [39], omnichannel operations [40], selecting distribution channels [41], and new technology introduction [42].

With the ongoing research concerning online retailing, this paper aims to make a significant contribution to online sales format selection and the associated driving forces. Notably, both practice and academia have observed that two prevalent online sales formats, the reselling format and the agency format, are commonly employed within platform supply chains. Consequently, this study focuses on identifying key factors that determine the optimal choice of online sales format for platform supply chain. Abhishek et al. [43] examine how to determine the optimal sales format in an online marketplace including pure agency, pure reselling, and hybrid, in addition to an existing traditional physical channel. Their findings show that the competition among the online channels and its spillover effect into the traditional channel jointly play a critical role in determining the best online sales format. Hagiu and Wright [44] reveal that the optimal online sales format selection is largely dependent on who has more information advantages regarding the optimal marketing activity for involved product categories. Tian et al. [45] examine how the two competing suppliers distribute their substitutable products in an online marketplace and show that the two factors (i.e., the order-fulfillment cost and the upstream competition intensity) largely determine the optimal sales format selection for the online platform company. Zhang et al. [46] investigate the optimal sales format to sell new products online in the context of a secondary marketplace and indicate that the costs of the new and the second-hand products play different roles in the best sales format selection for the manufacturer. Lin et al. [2] pay attention to the optimal sales format selection for the supplier in the presence of the information sharing strategy provided by online intermediaries.

In contrast to the aforementioned studies, this paper examines the optimal sales format for the manufacturer in light of the introduction of private label (PL) products by online platforms. The introduction of the PL product is expected to compete with the CB product in the online retail marketplace. Furthermore, this paper explores the interaction between the manufacturer’s choice of sales format and the introduction of the platform’s PL product.

For clarity, Table 1 positions our paper in the presence of existing literature.

3. Model Setup

This paper conducts an e-commerce platform supply chain composed of one giant platform company (denoted as P) and one brand manufacturer (denoted as M). The brand manufacturer will sell the CB products via the platform’s online retailing marketplace, and if profitable, the platform may launch the PL products to cannibalize the online retail market. There are two typical sales formats that the brand name manufacturer can choose to sell its CB products on the platform’ online marketplace, that is, one is the reselling format and the other is the agency format. Figure 1 graphically depicts the structures of the two different online sales formats.

In more detail, with the online reselling format, the brand manufacturer first wholesales the CB products to the platform at a price of w, after which the platform resells the CB products to the end costumer at a price of $p_M$. In this case, the platform functions as a reseller. By contrast, with the online agency format, the brand manufacturer sells the CB product directly to the end customer at a price of $p_M$ through the platform’s online marketplace. In addition to this, the brand manufacturer has to pay the platform a commission (r) as a revenue share and thus retain the remaining portion ($1-r$) of the sales itself. In this context, the platform acts as a pure online marketplace. No matter which online sales format the brand manufacturer selects, the platform company will independently determine whether to introduce the PL products based on its profitability. If yes, the platform retails the PL products at a price of $p_P$ to the consumer.

• Consumer preferences. This paper considers that both the CB products and the PL products are substitutable. Consequently, consumers pose the same valuation (v) to both products, which is uniformly distributed between 0 and 1. To delineate the quality differences between the two types of products, we designate the quality of the CB products ($q_M$) as a benchmark and normalize it to 1, such that $q_M=1$. In contrast, the PL products’ quality ($q_P$) may fall into one of two categories: it can either be of relatively high quality, represented by $q_P>1$, or of relatively low quality, indicated by $q_P<1$. For clarity, denote $q_P=q$. This paper assumes a linear relationship between cost and product quality, which is a common assumption in the existing literature such as Shi et al. [51] and Li et al. [28]. Hence, we consider that the cost of the PL products is $C\left(q_P\right)=q$. With a normalized quality, we consider a fixed cost for the CB products and denote $C\left(q_M\right)=c$. Consumers will have different preferences for these two distribution sources according to their distinct trust levels in the manufacturer and the platform. $\theta$ represents the consumer’s preference for the platform relative to the manufacturer, and $\theta >0$ ($\theta <0$) stands for a higher (lower) consumer preference for the platform than for the manufacturer.

• Product demands. The following conducts utility functions to describe demands for the CB products and the PL products. Consumers are heterogeneous in their valuation of products, i.e., v. A consumer’s decision about which product to purchase depends largely on a combination of factors such as product quality, value, price, and personal preference for where the product is sold. In particular, when purchasing the CB products from the manufacturer, the consumer’s utility function can be determined as $u_M=1·v-p_M$. Correspondingly, when purchasing the PL products through the platform, the consumer’s utility function is $u_P=q·v-p_P+\theta$. Consumers will independently decide which product to purchase by maximizing their utility functions. That is, consumers with the valuation as $v\in \left\{u_P\left(v\right)>u_M\left(v\right)\right\}$ will choose the PL products; otherwise, they will choose to buy the CB products with $v\in \left\{u_M\left(v\right)>u_P\left(v\right)\right\}$ for the consumers. Therefore, the demands for these two types of products based on the quality of PL products (q) can be mathematically derived as follows:

  (1)$\left\{\begin{array}{c}{D}_P=1-{\displaystyle \frac{\theta +p_M-p_P}{1-q}}\\ D_M={\displaystyle \frac{\theta +p_M-p_P}{1-q}}-p_M\end{array}\right.\mathrm{if}q>1$

  and

  (2)$\left\{\begin{array}{c}{D}_P={\displaystyle \frac{\theta +p_M-p_P}{1-q}}-{\displaystyle \frac{p_P-\theta }{q}}\\ D_M=1-{\displaystyle \frac{\theta +p_M-p_P}{1-q}}\end{array}\right.\mathrm{if}q<1.$

• Introduction strategy. Because consumers independently decide which product to buy, several different scenarios can arise here for the relative demands of the two products. Essentially, relevant product demands depend heavily on the PL product characteristics such as quality, price, and consumer preferences. In this line of thinking, relative product demand is the platform’s specific response to the PL product introduction decision. Herein, this paper defines an introduction strategy to capture the specific product demands associated with Lemma 1.

Lemma 1.

Based on the relative demands for the CB and PL products, this paper characterizes three distinct strategies for introducing PL products to the platform. The specifics of these introduction strategies are detailed and intuitively displayed in Figure 2.

• (a). No introduction. In this scenario, the platform will not introduce the PL products, and only the CB products will be available to consumers in the online retailing market. Consequently, it follows that $D_P=0$ and $D_M>0$.

• (b). Partial introduction. In this scenario, the platform will introduce the PL products while simultaneously marketing both the PL products and the CB products to end consumers. Consequently, both products will be represented in the online retailing market. It thus holds that $D_P>0$ and $D_M>0$.

• (c). Full introduction. In this scenario, the platform will make every effort to promote and sell the PL products, resulting in the CB products losing their competitive advantage and ultimately being squeezed out of the market. Consequently, it follows that $D_P>0$ and $D_M=0$.

• Game sequences. As shown in Figure 3, given the commission rate r (Industrial practice illustrates that the platform updates and publishes all commissions for the relevant product categories on their official websites annually. For instance, JD.com sets product commissions across various categories, ranging from 0% to 20%. Consequently, this paper considers an exogenous commission. Such a setting is frequently observed in the existing literature [7,48]), the manufacturer firstly determines the sales format for the CB products, specifically choosing between the reselling format and the agency format. Secondly, the platform makes decisions regarding the introduction of PL products based on profitability considerations. Lastly, both the manufacturer and the platform independently make pricing decisions in response to the sales format selected by the manufacturer. In more detail, when the reselling format is chosen, the manufacturer sets the wholesale price for the CB products, while the platform charges the retail prices for both the PL and CB products. Conversely, when the agency format is selected, the manufacturer sets the retail price for the CB products, and the platform sets the retail price for the PL products. It is important to note that the platform typically holds greater bargaining powers over the manufacturer concerning pricing, channel control, and profit sharing. This paper assumes that the platform acts as a Stackelberg leader, with the manufacturer acting as the follower.

Table 2 summarizes all the notations.

4. Optimal PL Introduction Decision with the Reselling Format

In the reselling format, the manufacturer initially sells the CB products to the platform, which subsequently sells them to the end consumer via the online marketplace. In this scenario, the platform functions as a reseller. Additionally, the platform launches and markets its PL products on the marketplace. As a result, the platform is able to obtain profits from both the resale of the CB products and the sale of the PL products. As explained in the previous section, this paper assumes a fixed cost for the CB products (denoted as c) and a variable cost for the PL products (denoted as q). Accordingly, the resulting objective profit functions for both the manufacturer and the platform are confirmed as follows:

(3)$\begin{array}{c}{\pi }_P=\left(p_M-w\right)D_M+\left(p_P-q\right)D_P\\ s.t.\left\{\begin{array}{c}{D}_M\ge 0\\ D_P\ge 0\end{array}\right.\end{array},$

(4)${\pi }_M=\left(w-c\right)D_M.$

Utilizing the Karush–Kuhn–Tucker optimality conditions, the optimal introduction strategy for the platform and the respective equilibrium for the supply chain are derived in Proposition 1 (i.e., introducing low-quality PL products) and Proposition 2 (i.e., introducing high-quality PL products).

Proposition 1.

In the reselling format with introducing low-quality PL products, the optimal introduction strategy for the platform is derived as follows:

• (a) 

  When $\theta <{\displaystyle \frac{\left(1-c\right)q}{2-q}}$, the platform will choose the No Introduction  with the following equilibrium as $w={\displaystyle \frac{1+c\left(3-q\right)-q}{2\left(2-q\right)}}$, $p_M={\displaystyle \frac{3+c-2q}{4-2q}}$, $p_P={\displaystyle \frac{-2q^2+q\left(3+c-2\theta \right)+4\theta }{4-2q}}$, $D_M={\displaystyle \frac{1-c}{2\left(2-q\right)}}$, and $D_P=0$;

• (b) 

  When ${\displaystyle \frac{\left(1-c\right)q}{2-q}}⩽\theta ⩽1-c$, the platform will choose the  Partial Introduction  with the following equilibrium as $w={\displaystyle \frac{1+3c-\theta }{4}}$, $p_M={\displaystyle \frac{3+c-\theta }{4}}$, $p_P={\displaystyle \frac{2q+\theta }{2}}$, $D_M={\displaystyle \frac{1-c-\theta }{4\left(1-q\right)}}$, and $D_P={\displaystyle \frac{2\theta -q\left(1-c+\theta \right)}{4\left(1-q\right)q}}$;

• (c) 

  When $\theta >1-c$, the platform will choose the  Full Introduction  with the following equilibrium as $w=c$, $p_M={\displaystyle \frac{2-\theta }{2}}$, $p_P={\displaystyle \frac{2q+\theta }{2}}$, $D_M=0$, and $D_P={\displaystyle \frac{\theta }{2q}}$.

Consolidating Propositions 1 and 2, we clearly find that the platform uses three different strategies to introduce the PL products, which are dramatically dependent on the consumer’s relative preference for the platform ($\theta$). In particular, when consumers’ relative preference for the platform is sufficiently low (such as $\theta <{\displaystyle \frac{\left(1-c\right)q}{2-q}}$ with introducing low-quality PL products and $\theta <{\displaystyle \frac{q\left(1-c\right)}{2q-1}}$ with introducing high-quality PL products), the platform will choose not to introduce the PL products. In this case, only the CB products are provided on the online marketplace, and thus $D_M>0$ and $D_P=0$ hold, which is denoted as No Introduction strategy. With a higher consumers’ preference for the platform, the consumer will prefer the PL products sold by the platform rather than the CB products sold by the manufacturer. Hence, the platform will commit the Partial Introduction strategy with a mild consumer preference for the platform (such as ${\displaystyle \frac{\left(1-c\right)q}{2-q}}⩽\theta ⩽1-c$, with the introduction of low-quality PL products, and ${\displaystyle \frac{q\left(1-c\right)}{2q-1}}⩽\theta ⩽q\left(1-c\right)$, with the introduction of high-quality PL products). In this case, it holds that $D_M>0$ and $D_P>0$. However, when the consumer has a relatively high preference for the platform (such as $\theta >1-c$ with introducing low-quality PL products and $\theta >q(1-c)$ with introducing high-quality PL products), all consumers will buy the PL products, leading to $D_M=0$ and $D_P>0$, which is referred to as Full Introduction strategy. To clearly depict the optimal PL introduction decision, Figure 4 intuitively shows the specific introduction strategy for the platform in response to the relative consumer preference over the platform ($\theta$) and the quality of the PL products (q).

Proposition 2.

In the reselling format with introducing the high-quality PL products, the optimal introduction strategy for the platform is derived as follows:

• (a) 

  When $\theta <{\displaystyle \frac{q\left(1-c\right)}{2q-1}}$, the platform will choose the  No Introduction  with the following equilibrium as $w={\displaystyle \frac{1+c-q-3cq}{2-4q}}$, $p_M={\displaystyle \frac{\left(3+c\right)q-2}{4q-2}}$, $p_P={\displaystyle \frac{4q^2-2\theta +q\left(c+4\theta -3\right)}{4q-2}}$, $D_M={\displaystyle \frac{q\left(1-c\right)}{4q-2}}$, and $D_P=0$;

• (b) 

  When ${\displaystyle \frac{q\left(1-c\right)}{2q-1}}⩽\theta ⩽q\left(1-c\right)$, the platform will choose the  Partial Introduction  with the following equilibrium as $w={\displaystyle \frac{q+3cq-\theta }{4q}}$, $p_M={\displaystyle \frac{\left(3+c\right)q-\theta }{4q}}$, $p_P={\displaystyle \frac{2q+\theta }{2}}$, $D_M={\displaystyle \frac{\left(1-c\right)q-\theta }{4\left(q-1\right)}}$, and $D_P={\displaystyle \frac{q-cq+\theta -2q\theta }{4q-4q^2}}$;

• (c) 

  When $\theta >q\left(1-c\right)$, the platform will choose the  Full Introduction  with the following equilibrium as $w=c$, $p_M={\displaystyle \frac{2q-\theta }{2q}}$, $p_P={\displaystyle \frac{2q+\theta }{2}}$, $D_M=0$, and $D_P={\displaystyle \frac{\theta }{2q}}$.

Figure 4 shows that a higher consumers’ preference towards the platform combined with a low quality prompts the platform to launch the PL products into the online marketplace. This indicates that consumer preference for the platform and the quality of the PL products are two key factors influencing the platform’s PL product introduction decision. The subsequent discussion will illustrate this finding through industry practices. Founded in 1998, JD.com has emerged as a prominent e-commerce platform in China, focused on creating a marketplace for both consumers and manufacturers. Over the past two decades, as the market size has expanded, consumer confidence in JD.com has steadily risen. In 2018, JD.com officially debuted its private label brand, known as Jingzhizao, which is designed specifically for household products, particularly where comparable options in the CB product market fall short in quality.

5. Optimal PL Introduction Decision with the Agency Format

In the agency format, the manufacturer retains ownership of the CB products and engages in direct sales to end consumers. In this scenario, the platform acts as an online marketplace, facilitating these transactions and earning a commission on sales from the manufacturer. Furthermore, the platform actively develops and introduces its PL products, positioning it as a competitor to the CB products within the online marketplace. Consequently, the profit functions of both the manufacturer and the platform can be derived as follows, respectively:

(5)$\begin{array}{c}{\pi }_P=r·p_M{D}_M+\left(p_P-q\right)D_P\hfill \\ s.t.\left\{\begin{array}{c}{D}_M\ge 0\\ D_P\ge 0\end{array}\right.\hfill \end{array},$

(6)${\pi }_M=\left(\left(1-r\right)·p_M-c\right)D_M.$

In a similar manner, the agency format allows for the derivation of the optimal introduction strategy for the PL products on the platform, along with the corresponding equilibrium for the supply chain, as presented in Proposition 3 (for low-quality PL products) and Proposition 4 (for high-quality PL products), respectively.

Proposition 3.

In the agency format with introducing low-quality PL products, the optimal introduction strategies for the platform are given by the following:

• (a) 

  when $\theta <{\theta }_1\left(q\right)$, the platform will choose the  No Introduction  with the following equilibrium as $p_M={\displaystyle \frac{c+\left(1-q\right)\left(1-r\right)}{\left(2-q\right)\left(1-r\right)}}$, $p_P={\displaystyle \frac{2\left(1-r\right)\theta -q^2\left(1-r\right)+q\left(c+\left(1-r\right)\left(1-\theta \right)\right)}{\left(2-q\right)\left(1-r\right)}}$, $D_M={\displaystyle \frac{1-c-r}{\left(2-q\right)\left(1-r\right)}}$, and $D_P=0$;

• (b) 

  when ${\theta }_1\left(q\right)⩽\theta ⩽{\theta }_2\left(q\right)$, the platform will choose the  Partial Introduction  with the following equilibrium as $p_M={\displaystyle \frac{c\left(4-q-qr\right)+\left(1-r\right)\left(4-q\left(3-\theta \right)-2\theta \right)}{2\left(1-r\right)\left(4-q\left(2+r\right)\right)}}$, $p_P={\displaystyle \frac{q\left(c+\left(1-r\right)\left(3+r-q\left(2+r\right)\right)\right)+\left(1-r\right)\left(2-q-qr\right)\theta }{\left(1-r\right)\left(4-q\left(2+r\right)\right)}}$, $D_M={\displaystyle \frac{\left(1-r\right)\left(4-q\left(3-\theta \right)-2\theta \right)-c\left(4-q\left(3+r\right)\right)}{2\left(1-q\right)\left(1-r\right)\left(4-q\left(2+r\right)\right)}}$, and $D_P={\displaystyle \frac{q\left(c\left(2-q-qr\right)-\left(1-r\right)\left(2-q+2\left(1-q\right)r\right)\right)+{\left(2-q\right)}^2\left(1-r\right)\theta }{2\left(1-q\right)q\left(1-r\right)\left(4-q\left(2+r\right)\right)}}$;

• (c) 

  when $\theta >{\theta }_2\left(q\right)$, the platform will choose the  Full Introduction  with the following equilibrium as $p_M={\displaystyle \frac{c}{1-r}}$, $p_P={\displaystyle \frac{cq-\theta \left(1-r\right)}{1-r}}$, $D_M=0$, and $D_P={\displaystyle \frac{1-c-r}{q\left(1-r\right)}}$.

  In the above, ${\theta }_1\left(q\right)={\displaystyle \frac{q\left(2-q-r\left(q+2r-2qr\right)-c\left(2-q-qr\right)\right)}{{\left(2-q\right)}^2\left(1-r\right)}}$ and ${\theta }_2\left(q\right)={\displaystyle \frac{\left(4-3q\right)\left(1-r\right)-c\left(4-q\left(3+r\right)\right)}{\left(2-q\right)\left(1-r\right)}}$.

Generally, the strategies for optimal PL products introduction outlined in Propositions 3 and 4 for platforms with the agency format exhibit a resemblance to those employed by the platform with the reselling format. Specifically, regardless of the quality of the PL product, an increased consumer preference for the platform (i.e., $\theta$) will shift the platform to introduce the PL products. The platform will opt for the No Introduction strategy when $\theta$ is relatively low, choose the Partial Introduction strategy with a moderate $\theta$, and select the Full Introduction strategy with a high $\theta$.

Proposition 4.

In the agency format with introducing the high-quality PL products, the optimal PL introduction strategies for the platform are given by the following:

• (a) 

  when $\theta <{\theta }_3\left(q\right)$, the platform will choose the  No Introduction  with the following equilibrium as $p_M={\displaystyle \frac{1-r-q\left(1+c-r\right)}{\left(1-2q\right)\left(1-r\right)}}$, $p_P={\displaystyle \frac{q\left(2\left(1-q\right)\left(1-r\right)-c\right)}{\left(1-2q\right)\left(1-r\right)}}+\theta$, $D_M={\displaystyle \frac{q\left(c-1+r\right)}{\left(1-2q\right)\left(1-r\right)}}$, and $D_P=0$;

• (b) 

  when ${\theta }_3\left(q\right)⩽\theta ⩽{\theta }_4\left(q\right)$, the platform will choose the  Partial Introduction  with the following equilibrium as $p_M={\displaystyle \frac{q\left(c\left(1+r\right)+\left(1-r\right)\left(3+2\theta \right)\right)-4q^2\left(1+c-r\right)-\left(1-r\right)\theta }{2q\left(2-4q+r\right)\left(1-r\right)}}$, $p_P={\displaystyle \frac{4q^2\left(1-r\right)-\theta +r^2\theta +q\left(c-\left(1-r\right)\left(3-2\theta \right)\right)}{\left(4q-2-r\right)\left(1-r\right)}}$, $D_M={\displaystyle \frac{4q^2\left(1-c-r\right)+\left(1-r\right)\theta +q\left(c\left(3+r\right)-\left(1-r\right)\left(3+2\theta \right)\right)}{2\left(q-1\right)\left(4q-2-r\right)\left(1-r\right)}}$, and $D_P={\displaystyle \frac{q\left(\left(1-r\right)\left(1+2r-4\theta \right)-c\left(1+r\right)\right)+2q^2\left(c-\left(1-r\right)\left(1+r-2\theta \right)\right)+\left(1-r\right)\theta }{2\left(q-1\right)q\left(4q-2-r\right)\left(1-r\right)}}$;

• (c) 

  when $\theta >{\theta }_4\left(q\right)$, the platform will choose the  Full Introduction  with the following equilibrium as $p_M={\displaystyle \frac{c}{1-r}}$, $p_P={\displaystyle \frac{c-\left(1-r\right)\left(1-q-\theta \right)}{1-r}}$, $D_M=0$, and $D_P={\displaystyle \frac{1-c-r}{q\left(1-r\right)}}$.

  In the above, ${\theta }_3\left(q\right)={\displaystyle \frac{q\left(2\left(1-q\right)r^2-\left(1-c\right)\left(1-2q+r\right)\right)}{{\left(1-2q\right)}^2\left(1-r\right)}}$ and ${\theta }_4\left(q\right)={\displaystyle \frac{q\left(\left(1-c\right)\left(3-4q\right)-\left(3+c-4q\right)r\right)}{\left(1-2q\right)\left(1-r\right)}}$.

In this paper, we explore the impacts of the CB products’ cost and the commission rate on the threshold for the platform’s associated introduction strategy. Notably, our findings reveal that the cost of the CB products and the commission rate play different roles in shaping the platform’s introduction incentives. Regarding the cost of the CB products, further analysis shows that ${\displaystyle \frac{\partial {\theta }_i\left(q\right)}{c}}<0,i=1,2,3,4$. This clearly indicates that an increase in the cost of the CB products will deter the platform from launching the PL products. The underlying reason for this result is that a rise in cost diminishes the competitive edge of the brand manufacturer when the platform opts to introduce the PL products. Next, we illustrate the optimal PL introduction decisions to visually demonstrate the influence of the commission rate on the strategy involved. From Figure 5, we observe that a higher commission (see Figure 5b) corresponds to a larger area designated as No Introduction and reduced areas for Partial Introduction and Full Introduction. This indicates that higher commission rates will discourage the platform from launching the PL products in the online retailing market. This is reasonable, as a higher commission signifies greater profit sharing that the platform can obtain from the manufacturer for selling the CB products.

It is also seen from Figure 5 that the quality of the PL products plays a critical role in the platform’s introduction decision, which is largely determined by the quality type of the PL products and the consumer’s preference for the platform ($\theta$). When introducing low-quality PL products as $q<1$, an increase in the quality of the PL products will push the platform to introduce more PL products (i.e., from the Partial Introduction to the Full Introduction in Figure 5a) with a relatively high $\theta$ and will discourage the platform from introducing the PL products (i.e., from the Partial Introduction to the No Introduction in Figure 5a) with a relatively low $\theta$. On the other hand, when introducing high-quality PL products as $q>1$, an increase in the PL product quality will discourage the platform from introducing the PL products (i.e., from the Full Introduction to the Partial Introduction in Figure 5a) with a relatively high $\theta$ and will shift the platform to introduce more PL products (i.e., from the No Introduction to the Partial Introduction in Figure 5a) with a relatively low $\theta$. The above descriptions clearly depict how the quality of the PL products affects the platform’s PL product introduction incentive.

6. Impacts of PL Products’ Quality on the Individual Profitability

This section will examine the impacts of the quality of the PL products on the individual profitability, as expressed in Proposition 5.

Proposition 5.

The impactss of the PL products’ quality on individual profit are significantly dependent on the sales formats, the supply chain member, the introduction strategy, and the quality type of PL products, as intuitively illustrated in Table 3 and Table 4 (in Table 3 and Table 4, we use symbols “ ↑ ”, “ ↓ ”, “ $\uparrow \downarrow$ ” “ ∼ ”, “ — ” to represent the cases that the individual profit increases with, decreases with, firstly increases and then decrease with, is ambiguous of, and is independent of the PL products’ quality, respectively.).

It is observed from Table 3 that the effect of PL products’ quality on individual profits is significantly influenced by the introduction strategy selected by the platform. Regardless of the quality type of PL products, implementing the Full Introduction strategy means that an increase in PL products’ quality will lead to a reduction in the platform’s profitability while having no impact on the profits of the manufacturer. This occurs because the Full Introduction strategy allows the platform to capture all market potential, leaving the manufacturer with nothing. Conversely, when implementing the Partial Introduction strategy, an increase in the PL products’ quality will boost the manufacturer’s profits but diminish those of the platform. This finding suggests that under the Partial Introduction strategy, the platform lacks any incentive to improve the quality of the PL products. However, with the No Introduction strategy, the quality type of the PL products plays a crucial role in determining the relative effects of the PL products’ quality on individual profits. When introducing high (low)-quality PL products, the manufacturer’s profit will rise (fall), while the platform’s profit will decrease (increase) as the quality of the PL products increases. Even though the PL products may be excluded from the retail market under the No Introduction strategy, a higher quality of the PL products will still influence the pricing strategies of the CB products and subsequently affect the profit distribution between the platform and the manufacturer.

By comparing with Table 3, we highlight the differences in blue in Table 4. It is obvious from Table 4 that the effects of PL products’ quality on individual profits align similarly with the Full Introduction strategy across both the agency and reselling formats, a case we will not discuss further here. In contrast, the effects of the PL products’ quality on profitability demonstrate greater complexity with the No Introduction and Partial Introduction strategies in the agency format. Under the No Introduction strategy, an increase in the quality of the PL products initially boosts and then reduces the platform’s profit, regardless of whether high- or low-quality PL products are introduced. This indicates that the platform has the ability to choose the optimal PL products’ quality to enhance its profitability. However, under the Partial Introduction strategy, the effects of the PL products’ quality on individual profit are ambiguous and are significantly influenced by other factors, such as c and $\theta$.

In the following, we apply numerical analysis to explore how consumer preference for the platform (i.e., $\theta$) affects individual profit. As illustrated in Figure 6, a higher $\theta$ consistently increases the platform’s profit but negatively impacts the manufacturer, regardless of the sales format and the quality type of PL products. Furthermore, with the agency format, the manufacturer’s profit can exceed that of the platform, as demonstrated in Figure 6c,d with implementing the strategies of the No Introduction and the Partial Introduction. This occurs because, through the No Introduction strategy, the platform earns commission sales solely from the manufacturer, allowing the manufacturer to obtain greater revenue than the platform with a relatively low commission. Conversely, when the platform opts to introduce the PL products, its profit clearly rises while the manufacturer’s profit declines.

7. Optimal Sales Format for the Manufacturer

This section will explore the best sales format for the manufacturer, specifically addressing when the manufacturer should choose the reselling format and when it should opt for the agency one. The findings can be found in Proposition 6.

Proposition 6.

The key factors driving the optimal sales format for the manufacturer are largely dependent on the specific introduction strategy adopted by the platform (when adopting the Full Introduction strategy, the manufacturer obtains nothing and will not involve in the online retailing market), namely,

• (a) 

  when adopting the No Introduction strategy, regardless of the PL products’ quality type, the manufacturer will select

  $\left\{\begin{array}{cc}\mathit{agency}\mathit{format},& if{f}_1\left(c,r\right)\le 3\\ resellingformat,& otherwise\end{array}\right.$

  where $f_1\left(c,r\right)=3\left(2-c\right)c+7r-c\left(6+c\right)r-4r^2$;

• (b) 

  when adopting the Partial Introduction strategy, the optimal selling format decisions for the manufacturer are different in response to the PL products’ quality type, namely,

  • if introducing high-quality PL products, the manufacturer will select

    $\left\{\begin{array}{cc}\mathit{agency}\mathit{format},& if{h}_1\left(c,r,q,\theta \right)⩽4\\ resellingformat,& otherwise\end{array}\right.$

    where $h_1\left(c,r,q,\theta \right)={\displaystyle \frac{\left(1-r\right){\left(2-4q+r\right)}^2{\left(\theta -\left(1-c\right)q\right)}^2}{{\left(4q^2\left(1-c-r\right)+\theta \left(1-r\right)+q\left(c\left(3+r\right)-\left(1-r\right)\left(3+2\theta \right)\right)\right)}^2}}$;

  • if introducing low-quality PL products, the manufacturer will select

    $\left\{\begin{array}{cc}\mathit{agency}\mathit{format},& if{h}_2\left(c,r,q,\theta \right)<4\\ resellingformat,& otherwise\end{array}\right.$

    where $h_2\left(c,r,q,\theta \right)={\displaystyle \frac{\left(1-r\right){\left(4-q\left(2+r\right)\right)}^2{\left(1-c-\theta \right)}^2}{{\left(\left(1-r\right)\left(4-q\left(3-\theta \right)-2\theta \right)-c\left(4-q\left(3+r\right)\right)\right)}^2}}$.

It can be seen from Proposition 6 that the primary factors influencing the manufacturer’s decision regarding the optimal sales format are largely dependent on the introduction strategy selected by the platform. In greater detail, when implementing the No Introduction strategy, the manufacturer’s choice of sales format hinges on two main factors: the cost of the CB products and the commission (refer to Proposition 6), regardless of the PL products’ quality. This implies that with the No Introduction strategy, the quality of the PL products will affect the manufacturer’s profits whether with agency or reselling formats, but it does not influence the comparative profits between the reselling and agency formats. It is straightforward to deduce from Proposition 6 that when there is no commission (or cost), an increase in cost (or commission) will prompt the manufacturer to opt for the reselling format. Moreover, with positive values for both cost and commission, we observe that a greater commission corresponding with an increased cost will encourage the manufacturer to prefer the reselling format, as illustrated in Figure 7. This suggests that in situations where the platform does not promote the PL products, the manufacturer is likely to market the high-cost product via the reselling format, particularly with a higher commission, aligning with existing research [2,50].

Nevertheless, when implementing the Partial Introduction strategy, in addition to the product’s cost and commission, the quality of the PL products and consumer preferences related to the platform emerge as two crucial factors that influence the manufacturer’s choices regarding sales formats. In contrast to the No Introduction strategy, the quality type of PL products plays a significant role in the manufacturer’s decision-making process by impacting the specific thresholds associated with these factors (refer to Proposition 6). This clearly illustrates how the introduction strategy chosen by the platform influences the manufacturer’s choices of sales format, thereby enhancing the existing body of literature on optimal online sales format [7,52].

Furthermore, the numerical experiment is applied here to assess the joint selection of sales formats and introduction decisions, aiming to clarify how these elements mutually influence each other. It is initially observed from Figure 8 that with the Full Introduction strategy employed by the platform, the manufacturer does not need to enter the online retail market. Conversely, when the platform opts for the Partial Introduction strategy, a rise in the commission will incentivize the manufacturer to select the reselling format; meanwhile, an increase in consumer preference for the platform will lead the manufacturer to opt for the agency format. On the other hand, with the No Introduction strategy in play, an increased commission will prompt the manufacturer to prefer the reselling format, and the consumer’s preference for the platform does not impact the manufacturer’s choice. Regarding the quality of the PL products, introducing low-quality PL products (as seen in Figure 8a,b) shows that an increase in the quality of PL products will drive the manufacturer towards the reselling format. In contrast, when presenting high-quality PL products (as indicated by comparing Figure 8c,d), the manufacturer is more likely to choose the agency format.

8. Conclusions

Recently, numerous giant e-commerce platforms have been dedicated to launching their PL products, which compete with the manufacturer’s CB products sold on the online retailing marketplace. In light of this industry practice, this paper conducts an e-commerce supply chain analysis in which a platform will independently determine whether it will introduce its PL products with three different introduction strategies while the manufacturer will opt for two distinct sales formats. The equilibrium and analytical investigation are derived in response to the combination of the PL introduction strategy and the sales format. The purpose of this paper is to investigate the optimal PL product introduction for the platform and the sales format selection, as well as the interactive effects among them. The following concludes the paper with managerial insights, key findings, and limitations and future research.

8.1. Key Findings

• Optimal PL introduction strategy for the platform. It is found that there are two primary factors determining the PL introduction decisions. They are a consumer’s preference toward a platform and the quality of the PL products, with ensuing different effects on the introduction incentive. To be specific, when consumers show a greater preference for the platform, the platform will be consistently encouraged to encroach the online retailing market by introducing more PL products. In contrast, the quality of the PL products has a complex effect on the platform’s PL product introduction. In more detail, when consumer preference is very low or high, an increase in the PL products’ quality will deter the platform from encroachment, whereas it will discourage (or promote) the platform from introducing the PL products if the PL product’s quality is relatively low as $q<1$ (or high as $q>1$) with a moderate consumer preference.

• Optimal sales format selection for the manufacturer. This paper finds that the best sales formats for the manufacturer are significantly influenced by the PL products’ introduction strategy chosen by the platform. Specifically, with the No Introduction strategy chosen by the platform, the primary factors assisting the manufacturer in selecting the best sales format are the product cost and the commission, without the consideration of the quality of the PL products. Conversely, with the Partial Introduction strategy chosen by the platform, in addition to the product cost and commission, the manufacturer must also consider consumers’ preference regarding the platform and the PL products’ quality.

• How does the PL products’ quality affect individual profitability? A higher PL product quality will not absolutely lead to more revenues for the platform, nor does it guarantee a loss for the manufacturer. This result is significantly influenced by the PL introduction strategy employed by the platform, the PL product type, and the sales format chosen by the manufacturer. For instance, with the Partial Introduction strategy, a higher quality of the PL product may be advantageous for the manufacturer while negatively impacting the platform, particularly in the online reselling format, regardless of the PL products’ quality type. In the context of the No Introduction strategy, selecting an optimal quality level for the PL products is crucial for the platform’s interests.

8.2. Managerial Insights

Firstly, this paper assists the platform in determining the optimal PL product introduction strategy in response to the two different sales modes chosen by the manufacturer. It shows that the consumer preference toward the platform and the quality of the PL products are the two key factors, based on which the platform decides the specific introduction strategy. Take the industrial practice as an example. JD.com and Tmall, two leading e-commerce platforms, serve as an online marketplace at their early stage, that is, the consumer preference toward the platform is relatively low. They both began to introduce the PL products after two decades of foundation. The quality of PL products exhibited in these two platforms are also different, namely Tmall pays more attention to the necessities, while JD.com introduces more high-quality products.

Secondly, this paper provides guidelines for the manufacturer on how to select the optimal sales format in the presence of the PL product introduced by the platform. The factors determining the manufacturer’s sales format are different and largely reliant on the PL introduction implemented by the platform. When the platform chooses not to introduce the PL product, the two elements determining the sales format that the manufacturer should focus on are product cost and the commission. In addition to these two factors, the manufacturer should evaluate the consumers’ preference for the platform and pay attention to the quality of the PL products when selecting the optimal sales format with the Partial Introduction.

8.3. Limitations and Further Research

Despite the efforts in addressing the PL products introduction and the selection of sales formats within an e-commerce platform supply chain, several constraints and avenues for further exploration exist in our work. Firstly, this study examines the optimal PL products introduction strategy related to both the online reselling and online agency formats. Evidence from the industrial practice indicate shows that certain companies simultaneously market their goods through both the reselling and agency formats. Therefore, it is realistic to analyze the PL introduction strategy for platforms that employ such a mixed sales format. Next, this paper concentrates exclusively on the online retailing channel while overlooking the traditional physical channel. In fact, the physical channel run by the manufacturer significantly influences the platform’s PL introduction on online channel, making it a topic worthy of further investigation. Thirdly, this paper addresses a deterministic demand scenario for both CB and PL products. A challenging but valuable topic would be to examine related situations that involve stochastic demands for these two product types. Finally, it is essential to pursue an investigation of the PL introduction decision in a competitive context, such as involving two rival platforms within a platform supply chain.

Author Contributions

Conceptualization, Z.L.; Methodology, Z.Z.; Software, T.T.; Validation, J.T.; Formal analysis, Z.Z. and T.T.; Investigation, Z.L.; Writing—original draft, Z.Z. and T.T.; Writing—review & editing, J.T.; Supervision, Z.L. and J.T. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

No new data were created or analyzed in this study.

Conflicts of Interest

The authors declare no conflicts of interest.

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures and Tables

Figure 1. Two different sales formats with platform’s PL product introduction.

Figure 2. Three different introduction strategies of the platform.

Figure 3. Game sequences of this paper.

Figure 4. Three different PL introduction strategies with the reselling format.

Figure 5. Three different PL introduction strategies with the agency format.

Figure 6. Individual profits with different selling formats and PL product quality.

Figure 7. Sales format selection with the No Introduction strategy.

Figure 8. Joint online sales format selection and introduction strategy.

Table 1

Positioning of this paper in the literature.

Papers	Supply Chain Encroachment	PL Introduction	Introduction Strategy	Reselling Format	Agency Format	Sales Format Selection
Yoon [23]	√
Zhang and Zhang [47]				√	√
Zhang et al. [48]				√	√	√
Li et al. [49]			√	√
Shopova [27]		√
Li et al. [28]	√	√			√
Zhang et al. [50]				√	√	√
Long and Amaldoss [29]		√			√
Zhang et al. [6]	√			√	√
Our paper	√	√	√	√	√	√

Table 2

List of notations.

Indexes
j	Product j, where $j\in \{M,P\}$, and M stands for the CB products sold by the manufacturer, P represents the PL products sold by the platform.
k	Introduction strategy k, where $k\in \{N,P,F\}$, and N, P and F referring to No Introduction, Partial Introduction and Full Introduction, respectively.
s	Participant s, where $s\in \{M,P\}$ and M refers to the manufacturer and P stands for the platform.
Parameters
v	Consumer’s valuation of the product.
$q_j$	The quality of product j, where $j\in \{M,P\}$. For clarity, denote $q_M=1$ and $q_p=q$.
$\theta$	Consumer’s relative preference for the platform over that to the manufacturer.
c	Unit cost of the CB products.
r	Commission rate.
${\pi }_s^k$	Profit of participant s with introduction strategy k.
Decision variables
w	The wholesale price of the CB products.
$p_j$	Retail price of product j, $j=M,P$.
$D_j$	Demand of product j, $j=M,P$.

Table 3

The impacts of the PL products’ quality on individual profits with the reselling format.

	$\mathit{q}>1$			$\mathit{q}<1$
	No	Partial	Full	No	Partial	Full
${\pi }_M$	↑	↑	—	↓	↑	—
${\pi }_P$	↓	↓	↓	↑	↓	↓

Table 4

The impacts of the PL products’ quality on individual profits with the agency format.

	$\mathit{q}>1$			$\mathit{q}<1$
	No	Partial	Full	No	Partial	Full
${\pi }_M$	↑	∼	—	↓	∼	—
${\pi }_P$	↑↓	∼	↓	↑↓	∼	↓

Appendix A

Appendix A.1. Proof of Proposition 1

In the reselling format with introducing the low-quality PL product, letting $t=p_M-w$ and the objective profit of the manufacturer ${\pi }_M=\left(w-c\right)\left({\displaystyle \frac{t+w+\theta -p_P}{1-q}}-t-w\right)$. Obviously, ${\pi }_M$ is concave on w as ${\displaystyle \frac{{\partial }^2{\pi }_M}{\partial w^2}}={\displaystyle \frac{2q}{1-q}}<0$. Applying the first order condition, it is easy to derive the optimal wholesale price for the manufacturer as $w={\displaystyle \frac{cq-qt-\theta +p_P}{2q}}$.

Substituting w into Equation (3), we shall apply the Lagrangian and the Karush-Kuhn-Tucker optimality principle to derive the platform’s optimization problem as follows:$$\begin{array}{c}L=\left(p_M-w\right)D_M+\left(p_P-q\right)D_P+{\mu }_1{D}_M+{\mu }_2{D}_P,\hfill \\ {\displaystyle \frac{\partial L}{\partial t}}=-{\displaystyle \frac{q^2+c{q}^2+2q^{2}t+q\theta -2q{p}_P+q^2{\mu }_1-q{\mu }_2}{2\left(-1+q\right)q}}=0,\hfill \\ {\displaystyle \frac{\partial L}{\partial p_P}}={\displaystyle \frac{-3q+cq+4q^2+2qt-\theta +2q\theta +\left(2-4q\right)p_P+q{\mu }_1+{\mu }_2-2q{\mu }_2}{2\left(-1+q\right)q}}=0,\hfill \\ {\mu }_1{D}_M=-{\displaystyle \frac{\left(cq+qt+\theta -p_P\right){\mu }_1}{2\left(-1+q\right)}}=0,\hfill \\ {\mu }_2{D}_P={\displaystyle \frac{\left(-\theta +q\left(-2+c+2q+t+2\theta \right)+\left(1-2q\right)p_P\right){\mu }_2}{2\left(-1+q\right)q}}=0,\hfill \end{array}$$ where $u_1$ and $u_2$ are Lagrangian multipliers that can be either zero or positive, based on which four cases are derived as given by:

• Case 1 (No Introduction): For the case of $u_1=0$ and $u_2>0$, based on the Complementary Relaxation Theorem, it follows $D_M>0$ and $D_P=0$, which yields ${\mu }_2={\displaystyle \frac{\theta +q\left(1-c-2\theta \right)}{2q-1}}$. Thus, the necessary optimality condition with this case is $\theta <{\displaystyle \frac{q\left(1-c\right)}{2q-1}}$. The optimal decisions for the platform in this case are obtained as follows: $t={\displaystyle \frac{1-c}{2}}$ and $p_P={\displaystyle \frac{-2q^2+q\left(3+c-2\theta \right)+4\theta }{4-2q}}$.

• Case 2 (Partial Introduction): For the case of $u_1=0$ and $u_2=0$, based on the Complementary Relaxation Theorem, it follows that $D_M>0$ and $D_P>0$. Thus, the necessary optimality condition with this case is ${\displaystyle \frac{q\left(1-c\right)}{2q-1}}\le \theta \le \left(1-c\right)q$. The optimal decisions for the platform in this case are obtained as follows: $t={\displaystyle \frac{1-c}{2}}$ and $p_P={\displaystyle \frac{2q+\theta }{2}}$.

• Case 3 (Full Introduction): For the case of $u_1>0$ and $u_2=0$, based on the Complementary Relaxation Theorem, it follows that $D_M=0$ and $D_P>0$, which yields ${\mu }_1=c+{\displaystyle \frac{\theta }{q}}-1$. Thus, the necessary optimality condition with this case is $\theta >\left(1-c\right)q$. The optimal decisions for the platform in this case are obtained as follows: $t=1-c-{\displaystyle \frac{\theta }{2q}}$ and $p_P={\displaystyle \frac{2q+\theta }{2}}$.

• Case 4 (No Production): For the case of $u_1>0$ and $u_2>0$, based on the Complementary Relaxation Theorem, it follows that $D_M=D_P=0$, based on which we ignore this case in this paper.

By substituting the corresponding decisions of the platform, it is easy to obtain the price decision of the manufacturer and the associated product demands, as shown in Proposition 1. □

Appendix A.2. Proof of Proposition 2

In the reselling format with introducing the high-quality PL product, letting $t=p_M-w$ and the objective profit of the manufacturer ${\pi }_M=\left(w-c\right)\left(1-{\displaystyle \frac{t+w+\theta -p_P}{1-q}}\right)$. Obviously, ${\pi }_M$ is concave on w as ${\displaystyle \frac{{\partial }^2{\pi }_M}{\partial w^2}}=-{\displaystyle \frac{2}{1-q}}<0$. Applying the first order condition, it is easy to derive the optimal wholesale price for the manufacturer as $w={\displaystyle \frac{1+c-q-t-\theta +p_P}{2}}$.

Substituting w into Equation (3), we shall apply the Lagrangian and the Karush-Kuhn-Tucker optimality principle to derive the platform’s optimization problem as given by:$$\begin{array}{c}L=\left(p_M-w\right)D_M+\left(p_P-q\right)D_P+{\mu }_1{D}_M+{\mu }_2{D}_P,\hfill \\ {\displaystyle \frac{\partial L}{\partial t}}={\displaystyle \frac{-2q{p}_P+q\left(-1+c+2q+2t+\theta +{\mu }_1\right)-q{\mu }_2}{2\left(-1+q\right)q}}=0,\hfill \\ {\displaystyle \frac{\partial L}{\partial p_P}}={\displaystyle \frac{-2\theta +q\left(-3-c+2q-2t+\theta \right)-2\left(-2+q\right)p_P+2{\mu }_2-q\left({\mu }_1+{\mu }_2\right)}{2\left(-1+q\right)q}}=0,\hfill \\ {\mu }_1{D}_M={\displaystyle \frac{\left(-1+c+q+t+\theta -p_P\right){\mu }_1}{2\left(-1+q\right)}}=0,\hfill \\ {\mu }_2{D}_P={\displaystyle \frac{\left(q^2-q\left(1+c+t-\theta \right)-2\theta -\left(-2+q\right)p_P\right){\mu }_2}{2\left(-1+q\right)q}}=0,\hfill \end{array}$$ where $u_1$ and $u_2$ are Lagrangian multipliers that can be either zero or positive, based on which four cases are derived in the following:

• Case 1 (No Introduction): For the case of $u_1=0$ and $u_2>0$, based on the Complementary Relaxation Theorem, it follows $D_M>0$ and $D_P=0$, which yields ${\mu }_2={\displaystyle \frac{\theta +q\left(1-c-2\theta \right)}{2q-1}}$. Thus, the necessary optimality condition with this case is $\theta <{\displaystyle \frac{q\left(1-c\right)}{2q-1}}$. The optimal decisions for the platform in this case are obtained as follows: $t={\displaystyle \frac{1-c}{2}}$ and $p_P={\displaystyle \frac{4q^2-2\theta +q\left(c+4\theta -3\right)}{4q-2}}$.

• Case 2 (Partial Introduction): For the case of $u_1=0$ and $u_2=0$, based on the Complementary Relaxation Theorem, it follows that $D_M>0$ and $D_P>0$. Thus, the necessary optimality condition with this case is ${\displaystyle \frac{q\left(1-c\right)}{2q-1}}\le \theta \le \left(1-c\right)q$. The optimal decisions for the platform in this case are obtained as follows: $t={\displaystyle \frac{1-c}{2}}$ and $p_P={\displaystyle \frac{2q+\theta }{2}}$.

• Case 3 (Full Introduction): For the case of $u_1>0$ and $u_2=0$, based on the Complementary Relaxation Theorem, it follows that $D_M=0$ and $D_P>0$, which yields ${\mu }_1=c+\theta -1$. Thus, the necessary optimality condition with this case is $\theta >\left(1-c\right)$. The optimal decisions for the platform in this case are obtained as follows: $t=1-c-{\displaystyle \frac{\theta }{2}}$ and $p_P={\displaystyle \frac{2q+\theta }{2}}$.

• Case 4 (No Production): For the case of $u_1>0$ and $u_2>0$, based on the Complementary Relaxation Theorem, it follows that $D_M=D_P=0$, based on which we ignore this case in this paper.

By substituting the corresponding decisions of the platform, Proposition 2 is easy to be proved. □

Appendix A.3. Proof of Proposition 3

In the agency format with introducing the low-quality PL product, it is easy to find that ${\pi }_M$ is concave on $p_M$ as ${\displaystyle \frac{{\partial }^2{\pi }_M}{\partial p_M^2}}=-{\displaystyle \frac{2}{1-q}}<0$. Applying the first order condition, the optimal retail price for the manufacturer is obtained as $p_M={\displaystyle \frac{c+\left(1-r\right)\left(1-q-\theta \right)+\left(1-r\right)p_P}{2\left(1-r\right)}}$.

Substituting w into Equation 5, we shall apply the Lagrangian and the Karush-Kuhn-Tucker optimality principle to derive the platform’s optimization problem as follows:$$\begin{array}{c}L=r·p_M{D}_M+\left(p_P-q\right)D_P+{\mu }_1{D}_M+{\mu }_2{D}_P,\hfill \\ {\displaystyle \frac{\partial L}{\partial p_P}}={\displaystyle \frac{c}{2\left(1-q\right)\left(1-r\right)}}+{\displaystyle \frac{q\left(3-2q+\left(1-q\right)r\right)+\left(2-q-qr\right)\theta -\left(4-q\left(2+r\right)\right)p_P+q{\mu }_1-\left(2-q\right){\mu }_2}{2\left(1-q\right)q}}=0,\hfill \\ {\mu }_1{D}_M=-{\displaystyle \frac{\left(c-\left(1-r\right)\left(1-q-\theta \right)-\left(1-r\right)p_P\right){\mu }_1}{2\left(1-q\right)\left(1-r\right)}}=0,\hfill \\ {\mu }_2{D}_P={\displaystyle \frac{\left(q\left(c+\left(1-q\right)\left(1-r\right)\right)+\left(2-q\right)\left(1-r\right)\theta -\left(2-q\right)\left(1-r\right)p_P\right){\mu }_2}{2\left(1-q\right)q\left(1-r\right)}}=0,\hfill \end{array}$$ where $u_1$ and $u_2$ are Lagrangian multipliers that can be either zero or positive, based on which four cases are derived in the following:

• Case 1 (No Introduction): For the case of $u_1=0$ and $u_2>0$, based on the Complementary Relaxation Theorem, it thus follows $D_M>0$ and $D_P=0$, which yields ${\mu }_2={\displaystyle \frac{4\left(1-r\right)\theta +q^2\left(-c\left(1+r\right)+\left(1-r\right)\left(1+2r+\theta \right)\right)+2q\left(c-\left(1-r\right)\left(1+r+2\theta \right)\right)}{{\left(2-q\right)}^2\left(-1+r\right)}}$. Thus, the necessary optimality condition with this case is $\theta <{\displaystyle \frac{q\left(2-q-r\left(q+2r-2qr\right)-c\left(2-q-qr\right)\right)}{{\left(2-q\right)}^2\left(1-r\right)}}$. The optimal decision for the platform in this case is obtained as follow: $p_P={\displaystyle \frac{2\left(1-r\right)\theta -q^2\left(1-r\right)+q\left(c+\left(1-r\right)\left(1-\theta \right)\right)}{\left(2-q\right)\left(1-r\right)}}$.

• Case 2 (Partial Introduction): For the case of $u_1=0$ and $u_2=0$, based on the Complementary Relaxation Theorem, it thus follows that $D_M>0$ and $D_P>0$. Thus, the necessary optimality condition with this case is ${\displaystyle \frac{q\left(2-q-r\left(q+2r-2qr\right)-c\left(2-q-qr\right)\right)}{{\left(2-q\right)}^2\left(1-r\right)}}\le \theta \le {\displaystyle \frac{\left(4-3q\right)\left(1-r\right)-c\left(4-q\left(3+r\right)\right)}{\left(2-q\right)\left(1-r\right)}}$. The optimal decision for the platform in this case can be easily obtained as follows: $p_P={\displaystyle \frac{q\left(c+\left(1-r\right)\left(3+r-q\left(2+r\right)\right)\right)+\left(1-r\right)\left(2-q-qr\right)\theta }{\left(1-r\right)\left(4-q\left(2+r\right)\right)}}$.

• Case 3 (Full Introduction): For the case of $u_1>0$ and $u_2=0$, based on the Complementary Relaxation Theorem, it follows that $D_M=0$ and $D_P>0$, which yields ${\mu }_1={\displaystyle \frac{c\left(4-q\left(3+r\right)\right)-\left(1-r\right)\left(4-q\left(3-\theta \right)-2\theta \right)}{q\left(1-r\right)}}$. Thus, the necessary optimality condition with this case is $\theta >{\displaystyle \frac{\left(4-3q\right)\left(1-r\right)-c\left(4-q\left(3+r\right)\right)}{\left(2-q\right)\left(1-r\right)}}$. The optimal decision for the platform in this case is obtained as follow: $p_P={\displaystyle \frac{c-\left(1-r\right)\left(1-q-\theta \right)}{1-r}}$.

• Case 4 (No Production): For the case of $u_1>0$ and $u_2>0$, based on the Complementary Relaxation Theorem, it follows that $D_M=D_P=0$, based on which we ignore this case in this paper.

By substituting the corresponding decisions of the platform, Proposition 3 is thus formulates. □

Appendix A.4. Proof of Proposition 4

In the agency format with introducing the high-quality PL product, it is easy to find that ${\pi }_M$ is concave on $p_M$ as ${\displaystyle \frac{{\partial }^2{\pi }_M}{\partial p_M^2}}={\displaystyle \frac{2q\left(1-r\right)}{1-q}}<0$. Applying the first order condition, the optimal retail price for the manufacturer is obtained as $p_M={\displaystyle \frac{cq+\left(p_P-\theta \right)\left(1-r\right)}{2q\left(1-r\right)}}$.

Substituting w into Equation (5), we shall apply the Lagrangian and the Karush-Kuhn-Tucker optimality principle to derive the platform’s optimization problem as follows:$$\begin{array}{c}L=r·p_M{D}_M+\left(p_P-q\right)D_P+{\mu }_1{D}_M+{\mu }_2{D}_P,\hfill \\ {\displaystyle \frac{\partial L}{\partial p_P}}={\displaystyle \frac{q\left(\left(3-4q\right)\left(1-r\right)-c\right)+\left(1-2q+r\right)\left(1-r\right)\theta -\left(1-r\right)\left(2-4q+r\right)p_P-q\left(1-r\right){\mu }_1-\left(1-2q-r+2qr\right){\mu }_2}{2\left(1-q\right)q\left(1-r\right)}}=0,\hfill \\ {\mu }_1{D}_M={\displaystyle \frac{\left(cq+\theta -r\theta -\left(1-r\right)p_P\right){\mu }_1}{2\left(1-q\right)\left(1-r\right)}}=0,\hfill \\ {\mu }_2{D}_P=\left(1+{\displaystyle \frac{\left(1-2q\right)\left(1-r\right)\theta -cq-\left(1-2q\left(1-r\right)-r\right)p_P}{2\left(1-q\right)q\left(1-r\right)}}\right){\mu }_2=0,\hfill \end{array}$$ where $u_1$ and $u_2$ are Lagrangian multipliers that can be either zero or positive, based on which four cases are derived in the following:

• Case 1 (No Introduction): For the case of $u_1=0$ and $u_2>0$, based on the Complementary Relaxation Theorem, it follows $D_M>0$, $D_P=0$, and ${\mu }_2={\displaystyle \frac{q\left(\left(1-c\right)\left(1-2q\right)+r-cr-2\left(1-q\right)r^2\right)}{{\left(1-2q\right)}^2\left(-1+r\right)}}-\theta$. Thus, the necessary optimality condition with this case is $\theta <{\displaystyle \frac{q\left(2\left(1-q\right)r^2-\left(1-c\right)\left(1-2q+r\right)\right)}{{\left(1-2q\right)}^2\left(1-r\right)}}$. The optimal decision for the platform in this case is obtained as follow: $p_P={\displaystyle \frac{q\left(2\left(1-q\right)\left(1-r\right)-c\right)}{\left(1-2q\right)\left(1-r\right)}}+\theta$.

• Case 2 (Partial Introduction): For the case of $u_1=0$ and $u_2=0$, based on the Complementary Relaxation Theorem, it follows that $D_M>0$ and $D_P>0$. Thus, the necessary optimality condition with this case is ${\displaystyle \frac{q\left(2\left(1-q\right)r^2-\left(1-c\right)\left(1-2q+r\right)\right)}{{\left(1-2q\right)}^2\left(1-r\right)}}\le \theta \le {\displaystyle \frac{q\left(\left(1-c\right)\left(3-4q\right)-\left(3+c-4q\right)r\right)}{\left(1-2q\right)\left(1-r\right)}}$. The optimal decision for the platform in this case can be easily obtained as follow: $p_P={\displaystyle \frac{q\left(c+\left(1-r\right)\left(3+r-q\left(2+r\right)\right)\right)+\left(1-r\right)\left(2-q-qr\right)\theta }{\left(1-r\right)\left(4-q\left(2+r\right)\right)}}$.

• Case 3 (Full Introduction): For the case of $u_1>0$ and $u_2=0$, based on the Complementary Relaxation Theorem, it follows that $D_M=0$ and $D_P>0$, which yields ${\mu }_1=3-4q-{\displaystyle \frac{c\left(3-4q+r\right)}{1-r}}+{\displaystyle \frac{\left(2q-1\right)\theta }{q}}$. Thus, the necessary optimality condition with this case is $\theta >{\displaystyle \frac{q\left(\left(1-c\right)\left(3-4q\right)-\left(3+c-4q\right)r\right)}{\left(1-2q\right)\left(1-r\right)}}$. The optimal decision for the platform in this case is obtained as follow: $p_P={\displaystyle \frac{cq+\theta \left(1-r\right)}{1-r}}$.

• Case 4 (No Production): For the case of $u_1>0$ and $u_2>0$, based on the Complementary Relaxation Theorem, it follows that $D_M=D_P=0$, based on which we ignore this case in this paper.

Proposition 4 thus derives by substituting the corresponding decisions of the platform. □

Appendix A.5. Proof of Propositions 5 and 6

Based on the respective equilibrium across different scenarios, the associated individual profit can be easily addressed, based on which Propositions 5 and 6 formulate and we will not elaborate it here. □

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