Private Brand Product on Online Retailing Platforms: Pricing and Quality Management

Abstract

In recent years, online retailing platforms (ORPs) have increasingly introduced private brand (PB) products as a new profit source, reshaping market dynamics and affecting their commission revenues. This shift creates a strategic trade-off for the platform: maximizing PB product profits while maintaining commission income from national brand (NB) retailers. This paper examines the platform’s pricing and quality strategies for PB products, as well as its incentives to introduce them. We develop a game-theoretic model featuring a platform and a retailer, and derive results through equilibrium analysis and comparative statics. Special attention is given to the platform’s strategy when market power is asymmetric and the PB product is homogeneous. The analysis yields three key findings. Firstly, the platform is always incentivized to introduce a PB product, regardless of its brand value. Even when direct profit is limited, the platform can leverage the PB product to increase competitive pressure on the retailer and boost commission revenue. Secondly, when the PB product has low brand value, the platform adopts a cost-saving strategy with low quality for extremely low brand value, and a function-enhancing strategy with high quality for moderately low brand value. Thirdly, when the PB product has high brand value, the platform consistently prefers a function-enhancing strategy. This study contributes to the literature by systematically characterizing the platform’s strategic trade-offs in introducing PB products, highlighting its varied pricing and quality strategies across categories, and revealing the critical role of brand value in supply chain competition.

1. Introduction

With the rapid development of internet technologies, online shopping has become one of the main purchasing channels for consumers. In 2022, China’s online retail sales of physical goods reached CNY 11.96 trillion, accounting for 27.3% of total retail sales [1]. Online retail platforms (ORPs), such as Amazon in the United States and JD.com in China, have traditionally acted as intermediaries that connect buyers and sellers. In this model, retailers compete by offering national brand (NB) products, and the ORP earns a commission from each transaction.

In recent years, many large ORPs have begun to introduce private brand (PB) products. For example, Amazon launched Amazon Basics, and JD.com launched Jing Zao. This trend reflects a broader shift in global retail markets. According to a 2024 NielsenIQ survey, consumer acceptance of PB products has been rising across countries. In Germany, 61% of respondents reported an increase in PB purchases compared to previous years. Similar trends were observed in Saudi Arabia (59%), India (56%), and Colombia (56%), all above the global average of 50%. NIQ retail data further show that PB products achieved a 5.6% increase in value sales over the 12 months ending in the second quarter of 2024 [2]. This shift presents a strategic challenge for ORPs. While PB products offer an additional source of revenue, they also position the platform as a competitor to third-party retailers, which may result in reduced commission income. Therefore, ORPs must balance the goal of maximizing PB product profits with the need to maintain commission revenue from other sellers.

Existing literature on private brands has primarily focused on those introduced by manufacturers or retailers, who generally do not face the same conflicts of interest as ORPs. This study aims to address a gap in the literature by examining private brands launched by ORPs, with specific attention to the role of brand value and its influence on decisions related to pricing and quality.

Brand value refers to the investments sellers make in their brands, which confer a competitive advantage in the market and directly influence consumer product choices [3]. In this context, brand value pertains to the reputation and image associated with the ORP itself or with national brands. National brands establish their reputations gradually through sustained marketing efforts [4,5]. In contrast, ORPs such as JD.com have cultivated brand images based on the reliability of their platforms and the overall shopping experience they provide [6]. This platform-derived brand value can be further extended to their private brand products [7]. As a result, ORP private brands inherit the brand value of the platform rather than that of traditional retailers, creating a distinctive dynamic in the marketplace.

On the other hand, functional value refers to a product’s intrinsic quality, encompassing its functionality, durability, and performance. It represents the value created through product design and manufacturing, similar to the conventional notion of “quality ” commonly found in the literature.

The influence of ORP brand value on private brand products may differ across product categories. In categories dominated by national brands, such as smartphones or designer apparel, ORP private brands may demonstrate relatively weak brand value. In contrast, in categories without mature national brands, such as mobile phone accessories or small household appliances, ORP brand value may provide significant advantages.

To highlight the category-specific strategy of JD.com’s private brand Jing Zao, we searched the platform using the keywords ’2000 mAh power bank’ and ’children’s study desk and chair’ and compared the top five comparable products ranked after default. As shown in Figure 1, in the power bank category, Jing Zao focuses on basic functionality and adopts a low-price strategy, while competitors highlight unique features such as support for laptop charging or enhanced portability. In contrast, in the category of children’s study desk and chair, Jing Zao targets the premium segment with high-quality materials and rich functionality, pricing its products significantly above comparable alternatives.

These observations raise three key questions. First, when is it profitable for an ORP to introduce PB products, especially given the possible loss of commission income from existing retailers? Second, how should the ORP set the optimal price and functional value (quality) of its PB products across different categories, considering both competition and its brand value? Third, how does the ORP brand value affect its potential profitability?

To answer these questions, we develop a game theory model capturing the interaction between the ORP and a representative retailer within the same product category. Our analysis examines their strategic decisions and reveals the conditions under which introducing PB products benefits the ORP, as well as its effects on pricing, quality, and market competition.

Our model contributes to the existing literature by offering a comprehensive framework to understand the strategic implications when ORPs introduce private brands. We clarify the complex trade-offs faced by ORPs, the varied pricing and quality strategies they adopt, and the critical role of ORP brand value in the platform-based supply chain competition.

The rest of the paper is structured as follows: Section 2 reviews relevant literature and highlights our theoretical innovations. Section 3 builds the platform-based supply chain model and proposes the demand function. Section 4 computes equilibrium strategies. Section 5 analyzes product introduction motivations and explores the effect of brand values on private brand product positioning. Section 6 concludes the paper.

2. Literature Review

2.1. Private Brands in Traditional Supply Chains

The emergence and growth of PBs have significantly impacted the retail landscape, presenting both challenges and opportunities for national brand (NB) manufacturers and retailers [8]. A rich body of literature explores the manufacturer and retailer-driven PBs, examining their strategic implications, competitive strategies, and influence on consumer behavior.

Early research on PBs focused on understanding consumer choice between national and private brands. Baltas et al. [9] developed a nested logit model demonstrating asymmetric cross-brand substitutability in markets where both NB and PB products are available, emphasizing the need for strategic brand management considerations. Furthermore, Baltas and Doyle [10] used panel data to identify key determinants of consumer demand for PBs, highlighting the role of individual preferences and choice dynamics. In recent years, these studies have also been further expanded, focusing on the influence of PB quality tier [11], and consumer self-concept [12] on product choice. Moreover, Tran et al. [13] systematically identified factors such as regulatory focus, brand types, and attribute framing that affect consumer choices. However, most of these studies are empirical studies, with limited theoretical exploration.

As PBs gained traction, research attention shifted towards their impact on competing sellers. Amrouche and Zaccour [14] proposed a game-theoretic model that studies the rivalry between an NB manufacturer and a PB-offering retailer, exploring the conditions under which manufacturer incentives can secure larger shelf space for NBs. Zhang et al. [15] examined the strategic dynamics between manufacturer encroachment and retailer PB introductions. It finds that while PBs can counteract encroachment, cost-efficient premium PBs may enhance retailer credibility in market entry threats.

Another significant focus is the influence of PBs on channel dynamics and manufacturer strategies. Inderst and Shaffer [16] examined the impact of retailer-produced PBs on channel management, particularly focusing on pricing dynamics. Their findings underscored the necessity for manufacturers to adapt strategies in response to potential competition from PBs. Liu et al. [17] investigated advertising strategies within dual-channel supply chains, analyzing interactions between brands and channels. Their study provided insights into advertising effectiveness and channel performance, considering both brand competition and channel spillover effects.

Further studies investigate the role of brand image, advertising, and logistics decisions in the context of PB competition. Amrouche et al. [18] analyzed a differential game where a retailer sells a PB alongside a manufacturer brand, focusing on pricing and advertising strategies and their impact on brand goodwill. Karray and Martín-Herrán [19] expanded on this by incorporating brand advertising carryover effects and examining both complementary and competitive roles of advertising. They found that pricing and advertising decisions are influenced by brand image and competition intensity. Liu et al. [20] explored the role of logistics service selection and free brand spillover in a competitive supply chain with an NB and a PB, and highlighted the strategic interactions between the above two factors.

The quality of PBs and its impact on competition with NBs has also been a subject of investigation. Heese [21] explored how retailer-manufacturer interactions in product positioning are affected by the introduction of a PB. The study found that manufacturers can benefit from anticipating a retailer’s PB introduction when determining the NB’s quality and wholesale price. Chakraborty et al. [22] challenged the traditional assumption of lower PB quality, examining quality competition between an NB manufacturer and a PB retailer. Their analysis demonstrated that PBs may have higher quality than NBs even without cost advantages and highlighted the importance of considering quality decisions in private label strategies.

2.2. Private Brands in ORP Supply Chain

Existing literature on PBs has predominantly concentrated on those introduced by manufacturers or retailers. However, this body of research often overlooks the distinct challenges and opportunities faced by ORPs when introducing their own PBs, which differ significantly from traditional manufacturer or retailer-driven PB strategies.

Existing research mainly focuses on the introduction strategies of ORPs for their PB products [23,24]. Wei and Xu [24] examined the impact of upstream manufacturer self-operation within the supply chain on the introduction of platform-owned brands. Their findings suggest that when the platform possesses decision-making advantages, the optimal introduction strategy depends on platform costs, consumer preferences for self-operated channels, the quality of national brand, and manufacturer self-operation strategies. However, in the absence of decision-making advantages, it is optimal for the platform to introduce high-quality PB products. Furthermore, Wang et al. [23] indicated that the introduction of market channels by contract manufacturers could impede the entry of ORP PB products.

Another concern is the impact of PB introduction on the benefits of competing sellers. The majority of existing literature believes that the introduction of PBs would encroach on the profits of manufacturers who sell similar types of products in the ORPs [25]. However, Li et al. [26] suggested that PBs may not always negatively impact manufacturer profitability. Instead, factors such as competition dampening, investment, and transfer incentives play crucial roles in determining manufacturer performance.

Scholars have also widely examined the influence of ORP PBs on other seller sales channels [27] and sales models [28,29,30]. ORP PBs may potentially threaten competing sellers on the platform, so competing sellers can decide whether to still sell their products through the ORP channel. For instance, Li et al. [27] explored the impact of the decision of the NB seller to fight or not against the platform’s private brand on the co-opetition relationship between the two sellers. They found that the NB seller’s optimal channel strategy depends on the expansion effect and the quality difference.

In addition, sellers on the ORP have the option to choose between two sales patterns: the agency pattern or the reseller pattern [31,32,33]. The choice of sales pattern significantly affects seller profits, thus attracting scholarly attention. For instance, Renlei and Jiajia [30] studied the impacts of PB’s introduction on manufacturer sale patterns in the ORP supply chain. The results found that the manufacturer preferred agency sales when the commission rate was moderate. In our study, we refer to the common profit-generation methods of ORPs, such as JD.com and Amazon, and focus mainly on the ORP agency sale pattern. In other words, these ORPs generate profits from commissions, which are a proportion of the revenue from sellers generated from the sales on the ORP [34,35,36].

For the ORP, revenue after launching the PB product consists of two parts: commission income and product sales. Prior studies suggest that the ORP faces a trade-off between these two sources when designing the PB product introduction strategy. Yu et al. [37] found that the commission rate plays a critical role in strategic decision-making: a lower commission rate leads to direct competition with the manufacturer, while a higher commission rate leads the retailer to prioritize the NB product. Liu et al. [29] also showed that the choice between agency and reselling models is mainly driven by the commission rate. Moreover, Long and Amaldoss [38] indicated that when adopting a self-preferencing strategy, the ORP needs to weigh commission income against revenue from selling the PB product. If commission income becomes relatively more important, the ORP may choose to downplay the PB product or instead promote the NB product.

In supply chain research, a product’s brand value is influenced not only by its intrinsic attributes but also, and more importantly, by the reputation and store image the ORP builds over time [4,5]. Studies in traditional retail consistently show that a retailer’s reputation can enhance the brand value of the products it sells, especially PB products [39,40,41]. As retail moves online, the ORP reputation plays a similarly important role in shaping consumer purchasing behavior [42]. Empirical evidence shows that the ORP reputation affects consumer perceptions of the PB product’s brand image, which in turn influences their willingness to purchase [43]. This suggests that the ORP can strengthen the competitiveness of its PB product in the short term without additional investment by leveraging its existing reputation. However, the literature offers limited analysis of the factors influencing brand value and their dynamic effects within the ORP supply chain. This study incorporates brand value into the analytical framework to examine its formation and impact in the ORP supply chain.

In comparison to the brand value extended from ORPs, research on PBs often focuses on cost-related factors that influence demand, with product quality being a key consideration. This is because the market positioning of new products is closely associated with both their pricing and quality. Enhancing product quality requires additional investments, prompting manufacturers to strive for an optimal quality level that maximizes their profitability [44,45]. However, in ORP supply chains, fewer studies have considered the quality of PBs. Some studies included quality factors in their models but did not consider the cost of improving product quality for the sake of simplifying the model [24,27]. Recently, ORPs have gradually emphasized the quality positioning of PB products, so this paper includes quality in the study and discusses the ORP optimal quality decision.

Table 1. Contrast of our research with the main related literature.

Related Studies	ORP Supply Chain	Private Brand	Optimal Quality Decision	Quality-Related Cost	Consumer Preference	Product Quality
Li et al. [26]	✓	✓
Wang et al. [23]	✓	✓			✓
Liu et al. [29]	✓	✓			✓
Wei and Xu [24]	✓	✓			✓	✓
Li et al. [27]	✓	✓			✓	✓
Chung and Lee [44]		✓	✓	✓		✓
Li et al. [45]		✓	✓	✓		✓
This study	✓	✓	✓	✓	✓	✓

shows the relevant literature in the ORP supply chain or PB context.

Table 1 summarizes key issues addressed in prior research within the context of ORP supply chains and private brands. The literature has primarily focused on aspects such as optimal quality decisions, quality-related costs, consumer preferences, and product quality. While these studies offer valuable insights into PB strategies, they fall short in explaining the specific challenges and implications of PB introduction by online retail platforms. Existing work has concentrated on PBs led by manufacturers or retailers, overlooking the distinct issues faced by platforms, such as the trade-off between PB profitability and commission revenue, as well as the strategic variations in pricing and quality across product categories.

Moreover, the value of a store or retailer brand has a significant influence on consumer preferences and purchase decisions, yet this dimension remains underexplored in current research. Although some scholars have considered the role of consumer preferences, few have examined how these preferences specifically affect decisions regarding PB products, particularly in relation to quality and pricing. This study addresses this gap by developing an integrated framework that incorporates the role of platform brand value. It investigates the introduction, pricing, and quality strategies of PBs on ORPs and analyzes how brand value shapes decision-making for private brand products, thereby filling a critical void in the existing literature.

3. The Model

3.1. Model Framework

This research establishes a game-theoretical model involving an Online Retailing Platform (ORP), with JD.com as an example, and a retailer. In this case, the retailer sells its products through the ORP. Similar settings can be found in existing research on platform environments [46,47]. We explore two models: (1) Base Model (BM): The retailer sells a single product on the ORP, referred to as the national brand (NB) product. The ORP earns a commission from the retailer sales, as depicted in Figure 2. (2) Competitive Platform Model (CPM): The ORP sells its Private Brand (PB) product in the same product category on the platform. Therefore, the ORP profits from both commission and PB product sales, as shown in Figure 2. Following Li et al. [26] and Xu et al. [48], we assume that the ORP directly controls the production and cost of the PB product, allowing us to better examine profit trade-offs and strategic decisions. In practice, e-commerce platforms can leverage their scale advantages to regulate product quality and cost through contracts with third-party manufacturers. This assumption is therefore supported by real-world practices.

In the Base Model, the retailer sets the market price $p_N$ for the NB product and pays the ORP a commission at a rate of r $(0<r<1)$, based on the market price. Following Tan and Carrillo [49], Tian et al. [50], we assume the commission rate is exogenous. ORP rates are generally stable over time for specific product categories (e.g., Amazon, JD.com). In a single-platform and single-retailer setting, platforms often set higher rates to ensure revenue [51], which may deviate from real-world practices. Thus, we focus on pricing and quality strategies under an exogenous rate, and briefly discuss endogenous rates in the limitations.

In the Competitive Platform Model, the ORP introduces a PB product and sets its price $p_E$, competing with the NB product in the market. The ORP profit comes from both commission and PB product sales. For simplicity, we assume the ORP only offers the PB product, while the retailer only offers the NB product. Consumers are assumed to be rational and evaluate products based on both functional value and brand value. They ultimately choose the product with the higher net utility, taking into account the price.

Broadly, functional value refers not only to product durability but also to additional features that enhance practicality [52,53], such as ergonomic design. Brand value refers to the utility consumers derive from the product brand itself. However, brand value does not always have a positive impact on products. A negative brand reputation can lead to consumer resistance towards the product. In this paper, the NB product brand value stems from the product brand itself, while the PB product brand value originates from the ORP reputation. In this study, the functional value and brand value of a product constitute its total value.

We normalize the brand value of the NB product to 1 and denote the relative brand value of PB products as $\theta >0$. This relative brand value depends entirely on the product category. Specifically, when $\theta >1$, consumers perceive the PB product brand value as higher than the NB product. For example, for cellphone accessories or small appliances where no dominant traditional brands exist in the market, JD.com’s Jing Zao products leverage the ORP reputation to achieve higher brand value. Conversely, when $\theta <1$, consumers perceive the PB product brand value as lower. For instance, in the mobile device market, established brands like Apple and Samsung have significant brand value advantages over similar products from JD.com’s private brand. Therefore, the ORP PB product brand value is relatively lower. Notably, $\theta =1$ represents the consumers perception of the same brand value for both products. For some products, like ink cartridges or fruits, consumers prioritize functionality and price over brand when making purchase decisions.

In this study, PB and NB products compete on price in the market. Additionally, we assume the retailer on the ORP is relatively weaker. In contrast, the ORP, due to its size, possesses greater market power when launching PB products. Therefore, we consider the ORP as the market leader and the retailer as the follower. Consequently, in our game model, the ORP first sets the PB product price, and the retailer subsequently reacts by setting the NB product price. We ignore logistics and operational costs, as these can be absorbed into product prices and have a negligible impact on our analysis and conclusions. In

Table 2. Definition of parameters and variables.

Parameters
N	Index for National Brand (NB) product
E	Index for Private Brand (PB) product
$\theta$	The relative brand value of the PB product to the NB product, $\theta >0$
$\alpha ,\beta$	The functional values of the RB and PB products, $\alpha ,\beta >0$
r	The commission rate, $0<r<1$
$D_N,D_E$	The demands of the NB and PB products
${\Pi }_N,{\Pi }_E$	The profits of the retailer and the ORP
k	The sensitivity factor of cost, $k>0$
$c_N,c_E$	The unit cost of the NB and PB products
c	The integrated unit cost of the NB product with a commission rate of r $(c=\frac{c_N}{1-r})$
Variables
$p_N$	NB product price decided by the retailer
$p_E$	PB product price decided by the ORP

, we summarize the parameters and variables necessary for modeling our research.

3.2. Demands

This study normalizes the market size to 1, and assumes that consumers in the market have heterogeneous preferences for the functional value of products, with their sensitivity to functional value x being uniformly distributed within an interval $[0,1]$. The functional values of PB and NB products are represented by $\alpha$ and $\beta$, respectively, with $\alpha ,\beta >0$. When prices are equal, products with higher total value offer greater utility to consumers [54,55]. Considering brand preferences, the total utility consumers derive from purchasing the two products is $x\alpha$ and $\theta x\beta$, respectively [56]. Therefore, in the Base Model, the net utility consumers obtain from purchasing the NB product is:

$$U_N=x\alpha -p_N$$

(1)

In the Competitive Platform Model, the net utilities from purchasing different products are:

$$U_I=\left\{\begin{array}{cc}x\alpha -p_N,\hfill & \mathrm{if}I=N\hfill \\ \theta x\beta -p_E,\hfill & \mathrm{if}I=E\hfill \end{array}\right.$$

(2)

We assume consumers only purchase products when the net utility is greater than 0, accounting for market shrinkage due to price increases. Therefore, in the Base Model, consumer demand for the NB product is:

$$D_N=1-{\displaystyle \frac{p_N}{\alpha }}$$

(3)

Following the vertical differentiation model, in the Competitive Platform Model, we calculate $x_0$: $U_N(x_0;p_N,p_E)=U_E(x_0;p_N,p_E)$ to obtain the indifferent consumer $x_0={\displaystyle \frac{p_N-p_E}{\alpha -\theta \beta }}$. When $\alpha >\theta \beta$, $p_N<p_E$, or $\alpha <\theta \beta$, $p_N>p_E$, (the product with higher total value is priced lower), we will address this situation later. When $\alpha >\theta \beta$, $p_N>p_E$ (as shown in Figure 3), the NB product has a higher total value, and consumers more sensitive to product value will choose the NB product. By calculating $x^{\prime }$: $U_E\left(x^{\prime };p_N,p_E\right)=0$, we identify the zero-utility consumer $x^{\prime }={\displaystyle \frac{p_E}{\theta \beta }}$. Consumers $x\in [x^{\prime },x_0]$ who are less sensitive to product value and obtain utility greater than 0 will choose PB products. Similarly, when $\alpha <\theta \beta$, $p_N<p_E$, the PB product has a higher total value, and consumers with higher value perception will choose the PB product. Consumers who are less sensitive to product value and obtain utility greater than 0 will choose NB products. When $\alpha =\theta \beta$, the PB and NB products are homogeneous, and consumers derive the same total utility from either product, leading them to choose the lower-priced option. When both products are priced equally, consumers randomly choose one, resulting in equal market share.

Therefore, we obtain the demand for PB and NB products under the three scenarios in the Competitive Platform Model:

$$\alpha >\theta \beta :\left\{\begin{array}{c}{D}_N=1-{\displaystyle \frac{p_N-p_E}{\alpha -\theta \beta }}\hfill \\ D_E={\displaystyle \frac{p_N-p_E}{\alpha -\theta \beta }}-{\displaystyle \frac{p_E}{\theta \beta }}\hfill \end{array}\right.$$

(4)

$$\alpha <\theta \beta :\left\{\begin{array}{c}{D}_N={\displaystyle \frac{p_E-p_N}{\theta \beta -\alpha }}-{\displaystyle \frac{p_N}{\alpha }}\hfill \\ D_E=1-{\displaystyle \frac{p_E-p_N}{\theta \beta -\alpha }}\hfill \end{array}\right.$$

(5)

$$\alpha =\theta \beta :\left\{\begin{array}{cc}{D}_J=1-{\displaystyle \frac{p_J}{\alpha }},D_{-J}=0,\hfill & \hfill \mathrm{if}{p}_J<p_{-J}\\ D_J=D_{-J}={\displaystyle \frac{1}{2}}(1-{\displaystyle \frac{p_N}{\alpha }}),\hfill & \hfill \mathrm{if}{p}_J=p_{-J}\end{array}\right.(J\in \{N,E\})$$

(6)

Let $c_N=k{\alpha }^2$ and $c_E=k{\beta }^2$ represent the unit costs of NB and PB products, respectively [57].

$$\left\{\begin{array}{c}{\pi }_E=(p_E-c_E)D_E+r{p}_N{D}_N\hfill \\ {\pi }_N=[(1-r)p_N-c_N]D_N\hfill \end{array}\right.$$

(7)

4. Equilibrium Analysis

In this section, we present the price strategies before and after the PB product introduction. Based on the demand discussion, we solve for the partial equilibrium after introducing low-total-value PB products and high-total-value PB products, respectively. We then analyze the optimal strategies for identical-total-value products in the presence of unequal market power.

For a PB product with any given brand value, there are three scenarios based on functional value differences: (1) introducing a PB product with low total value, i.e., $\alpha >\theta \beta$, and (2) introducing a PB product with high total value, i.e., $\alpha <\theta \beta$, and (3) introducing a PB product with identical total value, i.e., $\alpha =\theta \beta$. We discuss the optimal price decisions separately. For simplicity, this section only considers the case where two products compete in the market, i.e., $D_E,D_N>0$.

4.1. The Base Problem: No PB Product Introduction

In the Base Model, only the NB product is sold on the ORP. Substituting the demand function Equation (3) into the retailer profit function, we find that profit is a strictly concave function of the NB product price. Using the first-order condition, we obtain the retailer monopoly price for the NB product.

$$p_N^B={\displaystyle \frac{\alpha +c}{2}}$$

(8)

where

$$c={\displaystyle \frac{c_N}{1-r}}$$

(9)

is the integrated marginal cost of the NB product with a commission rate of r. Correspondingly, the market demand for the NB product and the retailer profit are:

$$\left\{\begin{array}{c}{D}_N^B={\displaystyle \frac{\alpha -c}{2\alpha }}\hfill \\ {\pi }_N^B={\displaystyle \frac{(1-r){(\alpha -c)}^2}{4\alpha }}\hfill \end{array}\right.$$

(10)

In the Base Model, the ORP does not make any decisions and only earns commission revenue from the retailer NB product sales:

$${\pi }_E^B={\displaystyle \frac{r{(\alpha -c)}^2}{4\alpha }}$$

(11)

Generally, we assume that the integrated marginal cost of a product sold on the ORP is always lower than its total value, i.e., $c\le \alpha$. Therefore, $D_N^B\ge 0$. In a traditional monopoly model without ORP commission, the NB product cost is $c_N$, and the optimal monopoly price is ${\displaystyle \frac{\alpha +c_N}{2}}$. We can see that $c>c_N$, $p_N>{\displaystyle \frac{\alpha +c_N}{2}}$, which implies that the ORP commissions are passed on to consumers, resulting in higher product prices. Consequently, $D_N^B<{\displaystyle \frac{\alpha -c_N}{2\alpha }}$, market demand decreases accordingly. Additionally, the commission rate further reduces the total profit obtained by the ORP and the retailer, ${\pi }_N^B+{\pi }_E^B<{\displaystyle \frac{{(\alpha -c_N)}^2}{4\alpha }}$, while the total profit from selling NB products is distributed between the ORP and the retailer based on the commission rate.

4.2. PB Introducing Low-Total-Value Products

In this scenario, the ORP introduces a PB product with low total value, i.e., $\alpha >\theta \beta$. The market demands for PB and NB products are shown in equations Equation (4). We substitute the demand function into the retailer profit function and verify that the profit function is strictly concave in the NB product price. Using the first-order condition, we obtain the retailer optimal pricing strategy.

4.2.1. Retailer Strategy

Following backward induction, as the follower, the retailer knows the ORP price decision and sets its price strategy to maximize profit. Therefore, we first consider the retailer decision. When $D_E,D_N>0$, we substitute the demand function into the retailer profit function and verify that the profit function is strictly concave in the NB product price. Then, using the first-order condition, we obtain the retailer optimal pricing strategy.

For any $p_E\ge 0$,

$$p_N\left(p_E\right)={\displaystyle \frac{1}{2}}(p_E+c)+{\displaystyle \frac{1}{2}}(\alpha -\theta \beta )$$

(12)

In the response function, the NB product price is positively correlated with the PB product price and the NB product cost. The NB product price comprises a reference price ${\displaystyle \frac{1}{2}}(p_E+c)$ based on the PB product price and a premium ${\displaystyle \frac{1}{2}}(\alpha -\theta \beta )$ based on the total value difference between the two products. The NB product price is higher when the PB product price is higher or when the NB product has a higher total value.

4.2.2. ORP Strategy

Using the retailer’s response Equation (12) response function wint low total value and the corresponding demand functions, the ORP profit is strictly concave in the PB product price. Setting its derivative to zero yields the partial-equilibrium price. When the ORP introduces a low-total-value PB product, the prices of both products at partial equilibrium are:

$$\left\{\begin{array}{c}{p}_E^L={\displaystyle \frac{\left(1+r\right)\delta +c+(2\mu -1)c_E}{2(2\mu -1)-r}}\hfill \\ p_N^L={\displaystyle \frac{(4\mu -1)\delta +(4\mu -r-1)c+(2\mu -1)c_E}{2\left[2\right(2\mu -1)-r]}}\hfill \end{array}\right.$$

(13)

where $\delta =\alpha -\theta \beta$, $\mu ={\displaystyle \frac{\alpha }{\theta \beta }}$. To ensure non-negative equilibrium, the unit cost of the PB product $c_E$ need satisfy certain conditions, that is $Z_1<(2\mu -1)<Z_2$, where $Z_1=(4\mu -r-3)c+(1-4\mu )\delta$, $Z_2=({\displaystyle \frac{r}{1-2\mu }}+1)c+({\displaystyle \frac{2r\mu }{1-2\mu }}+1)\delta$. By substituting $p_E^L$ and $p_N^L$ into the demand and profit functions under the competitive strategy, we obtain the market demands $D_E^L$ and $D_N^L$, as well as the platform profit ${\pi }_E^L$ and the retailer profit ${\pi }_N^L$ at equilibrium.

4.3. PB Introducing High-Total-Value Products

In this scenario, the ORP introduces a PB product with high total value, i.e., $\alpha <\theta \beta$. The market demands for PB and NB products are shown in equations Equation (5). We substitute the demand function into the retailer profit function and verify that the profit function is strictly concave in the NB product price. Using the first-order condition, we obtain the retailer optimal pricing strategy.

4.3.1. Retailer Strategy

As the retailer knows the OPR price decision $p_E$, it sets its price strategy to maximize profit. When $D_E,D_N>0$, we substitute the demand function into the retailer profit function. Then, we obtain the retailer optimal pricing strategy.

For any $p_E\ge 0$,

$$p_N\left(p_E\right)={\displaystyle \frac{1}{2}}(\alpha {\displaystyle \frac{p_E}{\theta \beta }}+c)$$

(14)

In the response function, $\frac{p_E}{\theta \beta }$ represents the ORP pricing per unit of product total value. In this scenario, the retailer strategy can be viewed as a pricing strategy that references the ORP unit product total value pricing.

4.3.2. ORP Strategy

Using the retailer response Equation (14) and demand function Equation (5), the ORP profit is strictly concave in the PB product price. Setting its derivative to zero yields the partial-equilibrium price. When the ORP introduces a high-total-value PB product, the prices of both products at partial equilibrium are:

$$\left\{\begin{array}{c}{p}_E^H={\displaystyle \frac{-2\delta +c+(2-\mu )c_E}{2(2-\mu )-\mu r}}\hfill \\ p_N^H={\displaystyle \frac{-2\mu \delta +\left[4-\mu (1+r)\right]c+(2-\mu )\mu c_E}{2\left[2\right(2-\mu )-\mu r]}}\hfill \end{array}\right.$$

(15)

where $\delta =\alpha -\theta \beta$, $\mu ={\displaystyle \frac{\alpha }{\theta \beta }}$. To ensure non-negative equilibrium, the unit cost of the PB product $c_E$ need satisfy certain conditions, $W_1<(2-\mu )c_E<W_2$, where $W_1=({\displaystyle \frac{4}{\mu }}-r-3)c+2\delta$, $W_2=({\displaystyle \frac{r\mu }{\mu -2}}+1)c+({\displaystyle \frac{2r\mu }{\mu -2}}-2)\delta$. Substituting $p_E^H$ and $p_N^H$ into the competitive demand and profit functions yields ${\pi }_E^H$, ${\pi }_N^H$.

4.4. The PB Product with Identical Total Value

For homogeneous PB products, i.e., $\alpha =\theta \beta$, we assume that the ORP market power is significantly stronger than that of the retailer. Therefore, unlike the game between two identical retailers, the final equilibrium will not necessarily settle at a state where the two products equally share the market. The ORP, leveraging its market advantage, can weigh the profits from PB product sales against the commission from NB products to maximize its overall profit. For homogeneous products, consumers with any value preference obtain the same total utility from purchasing either product. Therefore, they will choose the lower-priced product. When the prices of both products are the same, consumers will randomly choose one, resulting in equal demand for both products.

4.4.1. Retailer Strategy

When the PB product price is not higher than the NB product’s marginal cost, i.e., $0\le p_E\le c$, to avoid negative marginal profit, the retailer’s optimal strategy is to set the NB product price equal to its marginal cost, $p_N=c$, at which point ${\pi }_N=0$.

When the PB product price is higher than the NB product marginal cost but not higher than the NB product monopoly price, i.e., $c<p_E\le {\displaystyle \frac{\alpha +c}{2}}$, the retailer can choose a price slightly lower than the PB product price to capture the entire market. When $p_N<{\displaystyle \frac{\alpha +c}{2}}$, the retailer profit always increases as the price increases. Therefore, the retailer will increase the price as much as possible until $p_N=p_E-\epsilon$$(\epsilon \to 0^{+})$, which is its optimal strategy at $c<p_E\le {\displaystyle \frac{\alpha +c}{2}}$.

When the PB product price is higher than the NB product monopoly price, i.e., $p_E>{\displaystyle \frac{\alpha +c}{2}}$, the retailer optimal price is equal to the monopoly price $p_N={\displaystyle \frac{\alpha +c}{2}}$. At this point, the retailer obtains the optimal profit ${\pi }_N={\displaystyle \frac{(1-r){(\alpha -c)}^2}{4\alpha }}$.

In summary, we can obtain the retailer optimal response function:

For any $p_E\ge 0$,

$$p_N\left(p_E\right)=\left\{\begin{array}{ccc}c,\hfill & \hfill & \mathrm{if}0\le p_E\le c\hfill \\ p_E-\epsilon ,\hfill & \hfill & \mathrm{if}c<p_E\le {\displaystyle \frac{a+c}{2}}\hfill \\ {\displaystyle \frac{a+c}{2}},\hfill & \hfill & \mathrm{if}{p}_E>{\displaystyle \frac{a+c}{2}}\hfill \end{array}\right.$$

(16)

4.4.2. ORP Strategy

According to backward induction, we substitute the response function Equation (16) into the ORP profit function. The ORP makes its PB product pricing decision by weighing the PB product sales revenue against the commission revenue.

1.

$p_E\in [0,c]$

When the PB product price is lower than the NB product cost, i.e., $0\le p_E\le c$, according to Equation (16), the retailer pricing is $p_N=c$. Therefore, the ORP has two options: (1) set an equal price to compete with the NB product and share the market equally, that is, a competition strategy, or (2) set a lower price than the NB product to capture the entire market, that is, an exclusive PB product strategy. The ORP pricing decision depends on which option yields higher profits. Under both options, the PB product market demand is greater than 0, so it is necessary to ensure that the PB product marginal profit is non-negative, i.e., $p_E-c_E>0$.

When $p_E=c$, the non-negative marginal profit of the PB product is equivalent to $\theta \ge \sqrt{1-r}$, and the ORP total profit is ${\pi }_E={\displaystyle \frac{(\alpha -c)(rc+c-c_E)}{2\alpha }}$. When $p_E<c$, the ORP profit monotonically increases with the PB product price within the interval $[0,c)$. Therefore, the ORP adopts an exclusive PB product strategy, i.e., $p_E=c-\epsilon$$(\epsilon \to 0^{+})$, and the profit is ${\pi }_E={\displaystyle \frac{(a-c)(c-c_E)}{\alpha }}-\epsilon$. $\theta \ge \sqrt{1-r}$ ensures a non-negative marginal profit for the product. In contrast, when $0<\theta <\sqrt{1-r}$, the ORP needs to further increase the product price, i.e., $p_E>c$.

When the parameters satisfy $\theta \ge \sqrt{1-r}$, we compare the ORP profits under the above two pricing strategies. When the ORP reputation has an advantage, i.e., $\theta >1$, the ORP adopts an exclusive PB product strategy to achieve higher profits, i.e., $p_E=c-\epsilon$. When the ORP reputation is slightly weaker, i.e., $\sqrt{1-r}\le \theta \le 1$, it is more profitable for the ORP to share the market with the retailer.

In summary, for any $p_E\in [0,c]$,

$$p_E=\left\{\begin{array}{ccc}c-\epsilon ,\hfill & \hfill & \mathrm{if}\theta >1\hfill \\ c,\hfill & \hfill & \mathrm{if}\sqrt{1-r}\le \theta \le 1\hfill \\ >c,\hfill & \hfill & \mathrm{if}0<\theta <\sqrt{1-r}\hfill \end{array}\right.$$

(17)

2.

$p_E\in (c,+\infty )$

When the PB product price is higher than the NB product marginal cost but does not reach the NB product monopoly price, i.e., $c<p_E\le \frac{\alpha +c}{2}$, the corresponding NB product price is $p_N=p_E-\epsilon$, and the PB product is unsold. The ORP only obtains commission revenue. The ORP sets the PB product price at $p_E=\frac{\alpha }{2}+\epsilon$ to adjust the NB product price and demand, thereby obtaining the highest commission revenue ${\pi }_E=\frac{1}{4}\alpha r$.

When the ORP pricing is higher than the retailer monopoly price, i.e., $p_E>\frac{\alpha +c}{2}$, according to Equation (16), $p_N=\frac{\alpha +c}{2}$, the PB product will be rendered uncompetitive and experience no demand. This problem degenerates into the Base Problem, and the ORP cannot increase its revenue by introducing homogeneous PB products. Therefore, the ORP chooses to lower the price, i.e., $p_E\le \frac{\alpha +c}{2}$.

In summary, for the PB product price $p_E\in (c,+\infty )$, the pricing strategies for both products are:

$$\left\{\begin{array}{c}{p}_E=\frac{a}{2}+\epsilon \hfill \\ p_N=\frac{a}{2}\hfill \end{array}\right.$$

(18)

By comparing the ORP optimal profits in the two price decision spaces, $[0,c]$ and $(c,+\infty )$, we can draw the following conclusions:

Remark 1.

When the ORP has a good reputation, $\theta >1$, the ORP adopts different pricing strategies depending on the cost sensitivity k. When k is low, the ORP adopts an exclusive PB product strategy to achieve higher profits. Otherwise, the ORP prefers an unsold PB product strategy to profit entirely from commission.

Remark 1 demonstrates the ORP differentiated pricing strategies, mainly due to the following reasons. When $\theta >1$, the ORP chooses either an exclusive PB product strategy or an unsold PB product strategy. In the former case, the ORP only profits from selling the PB product, while in the latter case, the ORP only obtains commission. When introducing a homogeneous PB product ($\alpha =\theta \beta$), a higher $\theta$ leads to a lower $\beta$. When the cost sensitivity is higher, i.e., $k>\frac{1-r}{2\alpha }\left(1-\sqrt{\frac{\left({\alpha }^2-{\beta }^2\right)\left(1-r\right)}{{\alpha }^2-{\beta }^2\left(1-r\right)}}\right)$, the cost advantage of PB products is more significant, that is, $c_E(=k{\beta }^2)$ is lower, and the ORP can obtain higher marginal profits from PB product. As a result, the ORP profits more from the exclusive PB product than from merely collecting commissions on the NB product. The ORP sets a price $p_E^I=c-\epsilon$.

Conversely, when the cost sensitivity is lower, i.e., $k<\frac{1-r}{2\alpha }\left(1-\sqrt{\frac{\left({\alpha }^2-{\beta }^2\right)\left(1-r\right)}{{\alpha }^2-{\beta }^2\left(1-r\right)}}\right)$, in exclusive PB product strategy, the cost advantage of PB products is weaker, resulting in lower marginal profits. Even if the ORP can leverage its reputation advantage to introduce homogeneous products with low functional value, the reduction of functional value cannot significantly increase the marginal profit of the PB product. Therefore, the ORP profit from the exclusive PB product strategy will be lower than the commission obtained by adopting an unsold PB product strategy. Hence, the ORP sets the PB product price to maximize its commission revenue. The ORP will choose a price $p_E^I=\frac{\alpha }{2}+\epsilon$ for the PB product that maximizes its commission.

Remark 2.

When the ORP reputation is at a disadvantage, i.e., $0<\theta \le 1$, the ORP adopts an unsold PB product strategy, and all ORP profit is derived from commission.

Remark 2 indicates that the ORP decision is not affected by the cost sensitivity when $0<\theta \le 1$. Because the PB product is unsold at the partial equilibrium, the ORP only profits from commission. Therefore, the ORP profit is independent of cost. The specific analysis is as follows. When $0<\theta <\sqrt{1-r}$, the ORP reputation is at a significant disadvantage, considerably lower than that of the NB product. The ORP introduces a homogeneous PB product with high functional value, resulting in increased marginal costs. In this case, the PB product cost is higher than the NB product cost. If the ORP sets a price lower than the NB product cost, the marginal profit of the PB product will be negative. Therefore, the ORP adopts an unsold PB product strategy and sets a price to maximize commission revenue and achieve the highest profit, that is, $p_E^I=\frac{\alpha }{2}+\epsilon$, ${\pi }_E^I=\frac{1}{4}\alpha r$.

When the PB product brand value is slightly lower, i.e., $\sqrt{1-r}\le \theta \le 1$, the ORP introducing a homogeneous product implies a slightly higher functional value than the NB product. Correspondingly, the PB product cost increases. In price competition, if the ORP makes decisions within the interval $[0,c]$, according to Equation (17), its pricing will approach its marginal cost, making it impossible for the ORP to profit from the PB product. Instead, the ORP also turns to an unsold PB product strategy and makes the NB product capture the entire market. Therefore, the ORP sets the price $p_E^I=\frac{\alpha }{2}+\epsilon$ to maximize commission revenue. Overall, when the ORP reputation is at a disadvantage, the ORP pricing is consistent. Additionally, by comparing ORP profits before and after introduction, we verify that Proposition 2 still applies when introducing homogeneous products.

5. Analysis

5.1. Product Introduction Motivation and Competitive Pressure

Private brands offer ORPs a new avenue for profit generation. By introducing a PB product, the ORP not only benefits from commission but also from direct sales of the PB product [29,58]. However, the PB product competes with the existing NB product, potentially leading to decreased demand and prices for the NB product, thereby reducing ORP commission revenue and profits. On the other hand, the ORP can increase profits through PB product sales. The ORP is only motivated to introduce a PB product if its overall profit increases after introduction [59,60]. This section discusses the ORP motivation for introducing the product and the competitive pressure mechanism in detail.

First, we discuss the scenario of introducing a PB product with a low total value. In response to the ORP pricing of PB product, in addition to coexisting and competing with it, the retailer pricing can lead to the following situations: (1) setting a dominant price that makes the utility of indifferent consumers negative. As a result, all potential consumers deriving higher net utility from purchasing NB product, and the PB product is unsold, as shown in Figure 4a; (2) setting a cost price but the retailer still fail to capture market share, resulting in unsold NB products, as shown in Figure 4b.

In a Stackelberg game, the ORP, as the leader in price decisions, can anticipate the retailer price response and formulate its pricing strategy accordingly. Based on the market share outcome after decisions, we categorize the ORP pricing strategies into three types: Unsold PB product strategy, Two-product competition strategy, and exclusive PB product strategy. In the unsold PB product strategy, even though the PB product does not sell well, it remains in the market, and its price differs from the monopoly price of the NB product. In Section 4.2, we discussed the equilibrium under the two-product competition in detail.

In general, a higher brand value of a product constitutes its competitive advantage in the market, which helps PB products to capture a larger market share and marginal profit [4,61]. Consequently, under a two-product competition strategy, the higher sales profit of PB products compensates for the insufficient commission revenue, motivating the ORP to introduce PB products. However, it is worth discussing whether the ORP has an incentive to introduce PB products when their brand value lacks a distinct advantage. Product brand disadvantages may result in the ORP earning only meager profits from the sales of PB products, while a decrease in commissions due to market competition is inevitable. Under a two-product competition strategy, whether the profits from PB product sales can offset the decline in commission revenue remains a question. In fact, the ORP not only has pricing strategies under two-product competition but also can choose pricing for PB products’ unsold or exclusive markets.

To explore the ORP’s motivation for introduction, this paper focuses on alternative pricing strategies for PB products. If the ORP can achieve higher profits through these strategies compared to before product introduction, it indicates that the ORP still has the incentive to introduce PB products. This section discusses the ORP’s unsold PB product strategy, while the exclusive PB product strategy is provided in the Appendix B.

Consistent with the previous method, we first discuss the retailer strategy and then substitute it into the ORP profit function to discuss the ORP strategy.

5.1.1. Retailer Strategy

For any given PB product price, we solve for $D_E=0$ to obtain the threshold price $p_N=\mu p_E$ for the exclusive NB product. When $p_N\le \mu p_E$, i.e., $\frac{p_N}{\alpha }\le \frac{p_E}{\theta \beta }$, the NB product will capture the entire market. The demand functions are:

$$\left\{\begin{array}{c}{D}_N=1-\frac{p_N}{\alpha }\hfill \\ D_E=0\hfill \end{array}\right.$$

(19)

By comparing the retailer optimal profits in the exclusive market and competition market, we find that when $p_E\ge \frac{c+\delta }{2\mu -1}$, the retailer will achieve higher profits by adopting an exclusive NB product strategy. Substituting the demand function Equation (19) into the profit, we obtain the retailer response function:

$$p_N\left(p_E\right)=\left\{\begin{array}{ccc}\mu p_E,\hfill & \hfill & \mathrm{if}\frac{c+\delta }{2\mu -1}\le p_E\le \frac{\theta \beta (\alpha +c)}{2\alpha }\hfill \\ \frac{\alpha +c}{2},\hfill & \hfill & \mathrm{if}{p}_E>\frac{\theta \beta (\alpha +c)}{2\alpha }\hfill \end{array}\right.$$

(20)

When $\frac{c+\delta }{2\mu -1}\le p_E\le \frac{\theta \beta \left(\alpha +c\right)}{2\alpha }$, the retailer can set a price strategy to capture the entire market share. Since the retailer profit increases by $p_N$, the optimal price for the NB product is $\mu p_E$.

When $p_E>\frac{\theta \beta \left(\alpha +c\right)}{2\alpha }$, the retailer can also capture the entire market share. However, due to the excessively high $p_E$, the PB product completely loses its competitiveness and the pricing constraint. At this time, the market is equivalent to the monopoly market in the Base Problem, and the retailer profit reaches its maximum at $p_N=\frac{\alpha +c}{2}$.

5.1.2. ORP Strategy

Based on the response function Equation (20), we substitute the demand function into the ORP profit function and solve for the ORP decision when the NB product captures the entire market and the PB product is unsold.

When the PB product reaches a sufficiently high price level, i.e., $p_E\ge \frac{\theta \beta \left(\alpha +c\right)}{2\alpha }$, the NB product price reaches the monopoly price $\frac{\alpha +c}{2}$. Therefore, this problem degenerates into the Base Problem, and the ORP introducing the PB product will not increase its total profit. Hence, the ORP will lower the PB product price. Then, we can obtain the following equilibrium.

The partial equilibrium in the unsold PB product strategy is:

$$p_E^L=\left\{\begin{array}{cc}\frac{1}{2}\theta \beta ,\hfill & \hfill \mathrm{if}2c\le \theta \beta \\ \frac{c+\delta }{2\mu -1},\hfill & \hfill \mathrm{if}2c>\theta \beta \end{array}\right.$$

(21)

$$p_N^L=\left\{\begin{array}{cc}\frac{1}{2}\alpha ,\hfill & \hfill \mathrm{if}2c\le \theta \beta \\ \frac{\mu (c+\delta )}{2\mu -1},\hfill & \hfill \mathrm{if}2c>\theta \beta \end{array}\right.$$

(22)

When the PB product price decreases, i.e., $\frac{c+\delta }{2\mu -1}\le p_E<\frac{\theta \beta \left(\alpha +c\right)}{2\alpha }$, the ORP profit comes entirely from commission revenue since the NB product captures the whole market, and the ORP pricing strategy is related to the NB product cost. When the NB product has a cost advantage, i.e., $2c\le \theta \beta$, the ORP can adjust the PB product price to maximize its commission revenue. However, when the NB product cost advantage is not significant, i.e., $2c>\theta \beta$, the ORP profit gradually decreases within the decision space $[\frac{c+\delta }{2\mu -1},\frac{\theta \beta \left(\alpha +c\right)}{2\alpha })$, and therefore, the ORP pricing strategy is $p_E^L=\frac{c+\delta }{2\mu -1}$.

5.1.3. Product Introduction, Motivation, and Competitive Pressure

When the ORP total profit increases by introducing a PB product with low total value, we believe the ORP is motivated to introduce such a product. By comparing the ORP profits in the Base Problem and the unsold PB product strategy, we obtain a meaningful conclusion.

Proposition 1.

When adopting an unsold PB product strategy, the ORP can obtain higher commission revenue than in the NB product monopoly market. Therefore, the ORP is motivated to introduce the PB product with a low total value.

Proof: When the NB product has a cost advantage, $2c\le \theta \beta$, the PB product optimal price is $p_E^L=\frac{1}{2}\theta \beta$, and the ORP profit is ${\pi }_E^L=\frac{1}{4}\alpha r>{\pi }_E^B=\frac{r{(\alpha -c)}^2}{4\alpha }$, which is higher than the profit in the NB monopoly. When the NB product does not have a cost advantage, $2c>\theta \beta$, the PB product price is $p_E^L=\frac{c+\delta }{2\mu -1}$, ${\pi }_E^L=\frac{\alpha r(\alpha -c)(c+\delta )}{{(2\alpha -\theta \beta )}^2}>{\pi }_E^B$, and the ORP profit is still higher than in the NB monopoly. Therefore, under any condition, the ORP benefits from introducing the PB product with a low total value.

When $p_E\in [\frac{c+\delta }{2\mu -1},\frac{\theta \beta (\alpha +c)}{2\alpha })$, the NB product captures the entire market share. However, the partial equilibrium in this case differs from the monopoly market in the Base Problem because the ORP and the retailer have different optimal strategies. Within this PB product price range, although the PB product is unsold, it still exists in the market, and the two products compete on price. At partial equilibrium, the demand for the PB product is 0. If the retailer increases $p_N$, the demand for the PB product will increase, and the NB product market share will be squeezed, leading to a decrease in profit. Therefore, the NB product cannot reach the monopoly price $\frac{\alpha +c}{2}$.

In this case, the NB product price is constrained by the ORP pricing. Therefore, to increase commission revenue, the ORP adjusts the PB product price to exert “competitive pressure” on the retailer, leading to a decrease in the NB product price. The NB product price $p_N^L=\frac{1}{2}\alpha$ (or $p_N^L=\frac{\mu (c+\delta )}{2\mu -1}$) is lower than monopoly price $p_N^B$, while the NB product demand increases. Ultimately, the ORP commission revenue reaches its maximum.

When the ORP introduces a PB product with low total value, the ORP decision space, $p_E\in [\frac{c+\delta }{2\mu -1},\frac{\theta \beta (\alpha +c)}{2\alpha })$, results in an unsold PB product. Based on the principles of game theory, the ORP profit after introducing the product must be at least as high as the revenue in this subspace. Therefore, the ORP profit significantly increases after introducing the private brand. In conclusion, the ORP is motivated to introduce the PB product with a low total value. For PB products with high total value, the above conclusions are still valid, and solutions can be found in the Appendix D.

Proposition 2.

Considering the unsold PB product strategy, we obtain the following conclusions:

• For product categories of any brand value, the ORP always has an incentive to introduce it due to profit growth.
• The ORP can exert “competitive pressure” on the retailer by setting the PB product price, adjusting the NB product price, and demand to maximize the ORP commission revenue.

Proposition 2 suggests that the ORP has an incentive to introduce PB products regardless of brand value. In practice, major platforms often launch PB products across multiple categories. JD.com, for example, has introduced Jing Zao in digital accessories, furniture, and apparel, offering both a premium line and a lower-cost version under Hui Xun for lower-tier markets. PB products have generally provided strong returns across categories. The NielsenIQ report “Finding Harmony on the Shelf: 2025 Global Outlook on Private Label & Branded Products” indicates that, as of the third quarter of 2024, global private brand sales experienced a year-over-year increase of 4.3%. Moreover, 53% of surveyed consumers worldwide reported an increase in their purchase of private brand products [62]. In 2020, Amazon offered 111 private label brands encompassing 22,717 products [63]. Additionally, 9% of Amazon’s sales in the apparel, footwear, and accessories categories came from its private label offerings, with total sales projected to reach $25 billion by 2022 [64]. Since its launch in 2017, Jing Zao has achieved notable success. On Singles’ Day in 2020, its wooden children’s desk set generated over CNY 20 million in sales. Hui Xun has reached 25 million users [65], 72% of whom are from third- to sixth-tier cities, with revenue doubling year-on-year [66]. By 2022, Jing Zao saw nearly 400% growth in orders and customers, and a 147% increase in search volume [66]. Even in lower-performing categories like apparel, the ORP continues to invest in PB products. This suggests that its goals include not only direct PB profits but also influencing NB pricing and demand to boost overall commission income.

5.2. Product Vertical Differentiation

In practice, for product categories with varying brand values, ORPs develop unique product positioning for PB products. Specifically, ORPs strategically adjust product price and functional value to optimize their profits. In this section, we analyze the impact of PB product functional value on ORP and NB’s decision and profit under the following two scenarios: (1) when the ORP offers a PB product with lower brand value, i.e., $0<\theta <1$, and (2) when the ORP offers a PB product with higher brand value, i.e., $\theta \ge 1$.

Equations (13) and (15) show the relationship between the brand value of PB products and the optimal pricing strategy when two products coexist in the market. By taking the derivative of these two equations with respect to $\beta$, we can obtain the following proposition.

Proposition 3.

When ORP adopts Two-product competition strategy and meets $k>k^{\ast }$, $\frac{\partial p_E^L}{\partial \beta }$ and $\frac{\partial p_E^H}{\partial \beta }$ are both positive. Therefore, the ORP will increase the PB product price with the increase of functional value β. See Appendix for proof.

k refers to the cost coefficient. A higher k implies that quality improvements significantly increase production costs. In this case, the platform must raise the PB product price accordingly, leading to a positive partial derivative, i.e., $\frac{\partial p_E^L}{\partial \beta }>0$. The ORP then faces a trade-off between cost and quality: higher quality requires a higher price, weakening the PB product price advantage over the NB product and reducing its market share.

In practice, many retailers reduce costs while maintaining quality to enhance cost-effectiveness. For example, Jing Zao on JD.com uses a C2M model to match demand and eliminate intermediaries. By bulk purchasing core components, it lowers the cost coefficient, achieving “lower prices for equal quality” and “better quality at the same price.” Its collaboration with Luthai on shirts using premium 200-count cotton, priced under CNY 300, became the top seller in its price range, exceeding market expectations.

In addition, the results in Section 5.1 show that to maximize profit, the platform may adopt an unsold PB product strategy ($D_E=0$) or monopolize the entire market ($D_R=0$). In this case, the above conclusion no longer holds. Therefore, to observe the impact of product functional value on the optimal pricing decisions of the platform in all cases, we need to consider three cases simultaneously: $D_E=0\&D_R>0;D_E>0\&D_R>0;D_E>0\&D_R=0$. Moreover, the derivative results of platform profit with respect to product functional value are complex and difficult to intuitively show the impact of product functional value on the platform and the national brand profit. Therefore, considering that the impact of product functional value on the platform and national brand pricing decisions and profits is complex, we use numerical simulation to visualize this result.

First of all, to facilitate calculation, we standardize $\alpha$ as 1, and $\beta$ represents the relative difference in functional value between the platform product and the NB product. Secondly, the JD.com platform manual shows that for most product categories, including daily necessities, electronic products, etc., the commission rate charged by the JD.com platform is 8% [67]. Therefore, we refer to this rule and set $r=0.08$. The parameter k represents the cost coefficient of the product functional value. For ease of presentation, we assign it a value of 0.1. Furthermore, we expand the parameter space in the subsequent analysis to examine the robustness of our findings.

5.2.1. The PB Product with Lower Brand Value

We first set $\theta =0.5$ to estimate the impact of the PB product functional value on equilibrium. As depicted in Figure 5c, an increase in the PB product functional value leads to a gradual reduction in the disparity between the two products. This diminishes the PB product’s competitive disadvantage and compels the retailer to lower its product price to maintain market competitiveness. However, enhancing functional value also incurs higher costs for the ORP, necessitating an increase in the PB product price. As illustrated in Figure 5b, this price increase significantly reduces demand for the PB product, while demand for the NB product rises. The ORP profit comprises both commission revenue and PB product profit. At this juncture, as shown in Figure 5d, commission revenue experiences a slight decline due to the decrease in retailer profit. Nonetheless, PB product profit remains the dominant contributor to total ORP profits, resulting in an overall trend of initial increase followed by a decrease as $\beta$ increases.

As the PB product functional value continues to increase, the ORP raises the price to offset the excessively high marginal cost, leading to a decline in product demand. A threshold, denoted by ${\beta }_1$, exists such that when the functional value exceeds this threshold ( $\beta >{\beta }_1$), the ORP profit from the PB product falls below the commission revenue that it would obtain by adopting an unsold PB product strategy. Consequently, the ORP relinquishes its PB product market share and shifts its focus to profiting from commission. Further increases in the PB product functional value result in corresponding price increases, hindering its ability to gain market share. Therefore, the ORP’s sole source of profit becomes commission revenue. The point in the figures signifies the equilibrium state after the introduction of a homogeneous PB product. Notably, price, demand, and profit exhibit continuity at this point.

Figure 5 suggests that when the ORP faces a substantial disadvantage in brand value, e.g., $\theta =0.5$, a cost-saving strategy proves to be optimal. The cost-saving strategy refers to the case in which the platform offers the PB product with fewer functions than the NB product, i.e., $\beta <\alpha$, reducing costs and prices to capture market share and maximize profit.

Figure 6 depicts the impact of PB product functional value when $\theta =0.8$. Initially, as functional value increases, equilibrium price, demand, and profit exhibit trends akin to those observed in $\theta =0.5$. The ORP profit initially rises with increasing functional value $\beta$, but then declines until $\beta ={\beta }_1^{\prime }$. Then, the ORP solely derives profit from commission. However, as functional value continues to increase, the trends of these variables shift significantly.

Differing from the case when $\theta =0.5$, as the product functional value continues to increase, there exists a threshold ${\beta }_2$ such that when $\beta >{\beta }_2$, the ORP profit from two-product competition is higher than the commission revenue obtained by the unsold PB product strategy. At this point, as $\beta$ increases, the ORP profit initially rises before eventually declining. In addition, the PB products suffer fewer disadvantages in brand value compared to the case when $\theta =0.5$. Therefore, for the same total value, the PB product boasts both a lower cost and price compared to the case when $\theta =0.5$. This ensures the continued market competitiveness of the PB product, allowing the ORP to profit from its sales. In essence, a two-product competition strategy maximizes ORP profits.

Figure 6d illustrates the ORP profit composition when $\theta =0.8$. Notably, when $\beta >{\beta }_2$, the ORP profit from the PB product significantly surpasses commission. Consequently, when the ORP brand value is moderately low, e.g., $\theta =0.8$, a function-enhancing strategy is recommended. The function-enhancing strategy refers to offering the PB product with more functions than the NB product, i.e., $\beta >\alpha$, allowing the platform to attract consumers who perceive higher functional value and to increase marginal returns, thereby maximizing profit. Importantly, both the cost-saving and function-enhancing strategies represent functional value decisions determined by the product brand value.

A comparison of cases $\theta =0.5$ and $\theta =0.8$ highlights the significance of brand value in determining product market share. Brand value can offset disadvantages in product functionality and is an inherent benefit derived from ORP reputation, incurring no additional costs. Conversely, improvement in functional value often leads to increased costs that are ultimately passed on to consumers. Consequently, for products with the same total value, the brand value advantage can result in cost savings, lower product prices, and subsequently, higher demand and profit. Figure 7a–d expands the range of $\theta$, and further verifies these findings.

The analysis reveals that ORP is more profitable under a differentiated PB product strategy, i.e., $\alpha \gg \theta \beta$ or $\alpha \ll \theta \beta$. This conclusion aligns with existing research findings suggesting that firms can derive positive benefits from differentiated products, while price competition for similar products can harm firms’ earnings [68,69]. In line with real-world practices, ORP develops two-product competition strategies for differentiated PB products, while profiting from selling the products and collecting commissions to maximize profits.

To maximize profits, ORP develops distinct functional value strategies for PB products with varying brand values. Figure 7 illustrates that with the increase of $\theta$, the impact of platform product function value on profit changes significantly: When $\theta$ is small, the $\beta$ that makes the platform profit maximum is smaller; When $\theta$ is larger, the $\beta$ that makes the platform the most profitable is larger. In other words, when the brand value of PB products is extremely low, the platform tends to adopt a cost-saving strategy, and with the decrease of brand value, the corresponding optimal functional value also decreases.

Conversely, when the PB product has moderately low brand value, ORPs can achieve greater profits through enhanced product functionality, thus opting for a function-enhancing strategy. In this case, product functional value and brand value do not exhibit a positive correlation. Because a lower functional value helps control marginal costs, enabling the ORP to maintain marginal profit. However, as brand value increases, consumers become more willing to pay the price premium associated with higher functional value. Consequently, ORPs can capitalize on this willingness to pay by improving PB product functionality to make more profit.

Corollary 1.

For the PB product with low brand value, i.e., $0<\theta <1$,

• The optimal price and functional value are influenced by the product brand value. When brand value is extremely low, the ORP adopts a cost-saving strategy, reducing product functionality and setting competitive prices. Conversely, with moderately low brand value, the ORP pursues a function-enhancing strategy by improving product functionality and setting higher prices.

In practice, JD.com serves as an example that verifies our findings. The ORP introduced its private brand, Jing Zao, which includes cordless jump ropes as part of its sports product line. However, the well-established sports brand Keep already enjoys a strong presence on the ORP and widespread consumer recognition. Consequently, the brand value of Jing Zao products is considerably lower than that of Keep. In response, Jing Zao has opted to omit advanced features such as app connectivity and data synchronization from its cordless jump ropes, focusing instead on meeting basic consumer needs. This strategy has allowed Jing Zao to offer its products at half the price of Keep-branded jump ropes, attracting a substantial customer base due to the significant price difference.

In contrast, when it comes to air fryer products, there are already well-known brands in the market, such as SUPOR and Midea. However, Jing Zao small appliances have gained popularity among young consumers due to their quality assurance. To increase profit, Jing Zao added extra features such as a panoramic visual window and rapid heating to their air fryers, along with a slight price increase. Some consumers perceive these additional features as significantly enhancing convenience, leading them to choose Jing Zao products.

5.2.2. The PB Product with Higher Brand Value

In this section, we discuss product positioning for higher brand value PB products, i.e., $\theta \ge 1$. As illustrated in Figure 8, when PB products possess a brand advantage, the marginal cost of enhancing product total value is relatively low, resulting in a price advantage for the PB product. Consequently, there exists a lower functional value at which the PB product captures the entire market, driving NB product demand to zero. As functional value increases, the PB product price also rises to maintain marginal profit, but remains lower than that of the NB product. This allows the PB product to maintain its dominant market share. At this juncture, the PB product generates a high marginal profit, eliminating any incentive for the ORP to share the market with the retailer.

However, as functional value continues to increase, the PB product cost also rises, eventually leading to a price higher than that of the NB product. There exists a threshold such that when $\beta >{\beta }_4$, NB product demand increases, resulting in market competition between the two products. Given that ORP profit is primarily driven by PB product profit, the ORP sets the optimal price to balance the PB product price and demand, maximizing profit at a higher functional value and a higher price. The trend observed when $\theta =1.8$ is similar to that when $\theta =1.5$, with the PB product functional value being higher when ORP profit is maximized (see Appendix E for figures).

Similarly, we expand the range of $\theta$ to further validate our previous conclusions, as presented in Figure 9a–d. Additionally, we estimate the impact of brand value on the optimal functional value of the product. Figure 9 demonstrates that when the ORP enjoys a reputational advantage, i.e., $\theta \ge 1$, brand value and the ORP functional value decision exhibit a positive correlation. Moreover, for the PB product with higher brand value, ORPs can achieve greater profits by enhancing functional value.

Corollary 2.

For the PB product with high brand value, i.e., $\theta \ge 1$,

• The ORP mainly adopts a function-enhancing strategy by improving product functionality and setting higher prices.

In practice, numerous electrical appliance manufacturers have introduced hairdryers as part of their small household appliance product lines. However, few brands on JD.com have achieved widespread recognition. The hairdryer launched by JD.com’s private brand, Jing Zao, has gained favor among consumers. Consequently, compared to conventional hairdryers, Jing Zao’s product incorporates additional features such as intelligent temperature control and gear memory, significantly enhancing its functional value. Despite being priced nearly three times higher than ordinary hairdryers, Jing Zao’s hairdryers have been well-received by consumers, generating substantial profit for the Jing Zao brand.

5.2.3. Sensitivity Analysis

To test the robustness of our conclusions, we conduct a sensitivity analysis on the commission rate r and the functional value cost coefficient k. Since commission rates on e-commerce platforms rarely exceed 20% [50,70], we set $r\in \{0.05,0.08,0.15,0.20\}$. To ensure the platform remains profitable, we set $k\in \{0.05,0.10,0.15,0.20\}$. Results from Figure 10 and Figure 11 show that variations in r and k do not change the direction of platform profit or the choice of PB product strategy, confirming the robustness of our findings. Notably, when k is relatively low (e.g., $k=0.05$), the platform tends to prefer the function-enhancing strategy, as shown in Figure 10a. However, even in this case, there still exists a threshold $\theta ={\theta }^{\ast }$ (${\theta }^{\ast }<0.5$) such that the platform chooses the cost-saving strategy when brand value falls below it. Conversely, when the platform brand value is low, variations in the commission rate have a notable influence on the platform profit. However, this influence is significantly diminished when the brand value is high. Moreover, the platform strategic decisions remain consistent across different levels of commission rates. Therefore, the core conclusion remains valid.

6. Conclusions

A recent trend has witnessed major Online Retailing Platforms (ORPs) launching their own private brands as a new avenue for profit. Existing studies have mainly focused on private brands introduced by manufacturers or retailers, overlooking the distinct challenges and opportunities encountered by ORPs. These include the inherent conflict between maximizing private brand profits and sustaining commission revenues from other retailers, the impact of ORP brand value on private brand positioning, and the varied price and quality strategies employed across different product categories. To address this gap, this study develops a game-theoretical model that captures the interactions between an ORP and a representative retailer competing within the same product category on the platform. Our analysis explores the strategic decisions of both players and offers insights into the conditions favoring the introduction of a private brand for the ORP, along with implications for product pricing, quality, and market competition. Specifically, we also analyze the ORP strategies for homogeneous private brand products under unequal market power. We have obtained the following research findings.

Firstly, in a product category where the private brand product has either a higher or lower brand value, the ORP always has the incentive to introduce a PB product into that category. Even for insufficient profit from a private brand, the ORP can exert competitive pressure on the retailer, thereby increasing commission and stimulating the motivation for product introduction. Secondly, when the PB product has lower brand value, the platform opts for a cost-saving strategy with low quality if the brand value is very low, but switches to a function-enhancing strategy with high quality when the brand value is moderately low. Finally, when the PB product brand value is higher, the platform consistently prefers a function-enhancing strategy.

This study on the ORP private brand makes several potential contributions. Firstly, when introducing private brands, the ORP faces a trade-off between maximizing profits from its private brand and maintaining the commissions earned from other retailers’ sales. This study addresses the ORP complex price and quality decisions by constructing a platform-based supply chain model. Secondly, different from conventional retail brands, the private brands of ORPs inherit the brand value derived from the ORP reputation. Therefore, this study considers the influence of ORP brand value on private brand positioning, as well as the diverse price and quality strategies employed across different product categories.

This study assumes a fixed, exogenous commission rate. In practice, ORPs adjust commissions in response to competition and profit goals. Recent research has endogenized commission rates, showing that ORPs tend to raise them under retailer competition and lower them under cooperation [71]. When the platform determines the optimal commission rate, the current vertical product differentiation enables OEM manufacturers to benefit from PB invasion [72]. In this study’s setting, the ORP launch of the PB product intensifies competition with the NB product, especially when commission revenue is crucial. When the two products are highly homogeneous (i.e., $\alpha -\theta \beta \to 0$), raising the commission can ease price competition and improve profits. If the PB product has lower brand value, the ORP may offer higher functional value to justify a higher commission, even matching the NB product in functionality. If the PB product has a higher brand value, the ORP may still prefer a higher functional value but reduce it slightly to maintain commission income. In multi-platform markets, high commissions may discourage retailer participation or lead to exit, limiting the platform’s ability to raise rates. Future research could endogenize commissions to explore their interaction with PB strategies in such environments.

For simplicity, this study assumes the ORP directly manages PB production. In reality, platforms often outsource production to third-party manufacturers. Prior research shows that outsourcing increases cost pressures and quality control challenges for manufacturers, while also affecting the retailer costs and product strategy [73,74]. In this setting, weak cost or quality control by manufacturers raises production and oversight costs for high-functional-value PB products. This reduces profit margins and increases reliance on commission revenue, making cost-saving strategies more attractive. Conversely, strong control enables lower costs, supporting function-enhancing strategies for high-brand-value products, consistent with this study’s conclusions. Future work could incorporate manufacturers into the model to examine optimal PB strategies under different platform–manufacturer power structures.

Furthermore, our model considers a single online retailer and a single national brand retailer, who interact through a Stackelberg game framework. This modeling choice greatly simplifies the analytical setting, allowing us to derive the key insights of this study. However, in real-world scenarios, online retail platforms typically host numerous retailers. Even within a single product category, multiple retailers often offer similar or overlapping products. Prior research has shown that the number of retailers on a platform can significantly influence both the platform’s decision to introduce private brands and its optimal commission structure [75]. Specifically, as the number of retailers increases, intensified competition and limited market potential lead to reduced profits for individual retailers. Conversely, this heightened competition allows the platform to capture a larger share of the market profit. Such dynamics are likely to impact the platform’s incentives for introducing private brands, potentially weakening its motivation to do so. Therefore, future research could extend the current model by incorporating multiple retailers to examine how retailer count influences the platform’s private brand introduction decisions, and further investigate whether the platform is strategically motivated to attract additional retailers.

This study has several limitations that suggest avenues for future research. Firstly, it considers only short-term brand value driven by ORP reputation, without accounting for the long-term effects of persistent low functional value strategies. In future research, we plan to develop a dynamic model that captures the evolution of consumer preferences over time and accounts for potential quality risks under stringent market regulation. This framework will enable an analysis of how platforms should optimally adjust their quality and pricing strategies in the long run as consumer preferences and the brand value of private brands evolve.