Exclusive Product Strategies That Brick-and-Mortar Retailers Can Use to Address the Showrooming Effect

Abstract

Showrooming behavior on the part of consumers undoubtedly undermines the interests of brick-and-mortar (BM) retailers and hinders the growth of the physical economy. In response to this crisis, BM retailers can employ exclusive product strategies, although the questions of which specific strategy is most beneficial and what factors influence retailers’ choices remain unanswered. Based on utility theory and optimization theory, this paper investigates two strategies: the store exclusive brand (SEB) strategy and the well-known exclusive brand (WEB) strategy. First, we identify the pricing methods for both strategies employed by BM retailers, thereby revealing that the pricing of exclusive products under the SEB strategy should be higher than the corresponding pricing under the WEB strategy, whereas the pricing of nonexclusive products should be the opposite. Moreover, service levels should remain consistent under both strategies. Second, both strategies benefit retailers primarily by increasing their market share; interestingly, this process leads to the same overall growth in market share for BM retailers. Third, our analysis reveals that exclusive strategies always yield higher profits than nonexclusive strategies do. We also address the optimal choice between the SEB strategy and the WEB strategy for BM retailers. This choice depends on the relationship between the probability that a consumer can evaluate and purchase the best-fit product correctly online and the proportion of low-type consumers. If the former probability is low while the latter proportion is high, the SEB strategy is the best strategy. Otherwise, the WEB strategy is superior. Finally, numerical examples are provided to facilitate discussion of the effects of critical parameters on the outcomes of both strategies. Overall, this study explores the application of exclusive product strategies by BM retailers seeking to mitigate the negative effects of showrooming on service-oriented products; this research also emphasizes the crucial factors involved in the process of implementing these two strategies.

1. Introduction

As consumers become more sophisticated, consumer showrooming behavior (consumers visit a physical store with the goal of evaluating a product before making a purchase via an online channel that offers a lower price) is becoming a worldwide trend that is ubiquitous in the retail industry [1,2,3,4,5,6,7]. In particular, as online shopping becomes increasingly mainstream, an increasing number of online retailers choose to reduce consumer uncertainty by opening physical showrooms (PSs) to offer consumers more opportunities to experience their products. This approach undoubtedly further drives consumers’ showrooming behavior. Comscore reported that products featuring nondigital attributes (e.g., furniture, jade, or collectibles) or characterized by significant service attributes (e.g., automobiles or other appliances needing maintenance) are more prone to showrooming behavior. This occurs because consumers struggle to evaluate such products’ nondigital features or service quality through the online channel alone [8,9]. Even in the case of products for which complete information regarding numbers or parameters is available, such as lipsticks, foundations, and similar beauty products, consumers prefer to visit offline brick-and-mortar stores first to try these products and compare them before deciding whether to buy them directly in-store or to purchase the same products online.

Showrooming behavior on the part of consumers usually has adverse effects on the sales and profitability of brick-and-mortar (BM) retailers and thus represents a tremendous challenge for such stores (e.g., Walmart, Macy’s, and Target) [10], thereby exacerbating multichannel competition. We agree with Mehra, Kumar [11], who suggested that the exclusive product strategy can be used as a long-term strategy to counter consumers’ showrooming behavior, and we argue that products with significant service attributes are more conducive to obtaining benefits by employing an exclusive product strategy. In this study, exclusive products refer to those accessible only through specific sellers (including types such as exclusive agency and exclusive distribution), which consumers can hardly obtain via other channels. In contrast, nonexclusive products feature low purchase barriers, enabling consumers to acquire them from any seller. It should be clarified that the two are not completely disconnected; instead, they can be functionally similar products, both capable of meeting consumers’ core functional demands for this category of products. For example, the famous cosmetics brand SEPHORA has effectively catered to consumers’ showrooming needs and increased the number of store visits by adopting a strategy of coselling exclusive and nonexclusive brands in conjunction, along with providing complimentary services in multiple ways, whereas SEPHORA only needs to retain high-quality services [12]. Similar examples of adopting an exclusive product strategy include Macy’s decision to promote and sell certain brands, such as Tommy Hilfiger and T.J. Maxx [11,13], exclusively under special arrangements or as part of its store-exclusive offerings. In fact, these retailers prefer that the products that consumers prefer during showrooming are exclusive, with the goal of encouraging consumers to exhibit lasting preferences for and loyalty to their exclusive products and thus capitalizing on this advantage successfully. Red Star Macalline verified the value of comprehensive product demonstrations and consumer after-sales services in BM stores, and in this situation, consumer showrooming behavior does not represent a threat but rather a warning, which may offer companies the opportunity to stimulate sales by enhancing consumer engagement and improving service quality [14,15]. On this basis, a series of interesting and thought-provoking questions arises: What unique strategic approaches should BM retailers deploy to leverage market opportunities? What prerequisites and conditions are essential for the execution of these tailored strategies? What decision-making frameworks and logic should guide BM retailers in rolling out such strategies?

To answer these questions, we focus on products that exhibit prominent service attributes (either services pertaining to onsite service and guidance and advice before purchase or those pertaining to installation and maintenance after purchase) as our research objects. We investigate a sales system that consists of a BM retailer, an online retailer, and several heterogeneous consumers, and we develop a decision analysis model with the aim of determining whether a BM retailer should implement an exclusive product strategy. We were inspired by Mehra, Kumar [11], and business practices to design two types of exclusive product strategies: the store exclusive brand (SEB) strategy and the well-known exclusive brand (WEB) strategy. In light of the impacts of consumers’ showrooming behavior and the service efforts made by the BM retailer on consumer utility, we seek to answer the following questions:

(1)

How does the implementation of the two exclusive product strategies affect the pricing and product service levels associated with the BM retailer?

(2)

Are these two exclusive product strategies capable of enhancing the market share of the BM retailer?

(3)

What pivotal factors drive a BM retailer to choose an exclusive product strategy, and how does this retailer rely on these factors when making decisions?

Existing research primarily focuses on three main strands: ① analyzing the standalone impact of nonprice factors (e.g., service quality, brand reputation) on channel decisions; ② exploring the synergistic effects between showrooming and pricing strategies; ③ investigating the influence of exclusive product strategies on sellers’ optimal decisions and profitability. To date, no studies have integrated “non-price factors, showrooming, and exclusive product strategies” to examine their combined effects on firms’ channel choices and consumer behavior—this further validates the innovation and necessity of the present research. The contributions of our research to both theory and practice pertain mainly to the following three aspects. First, our model accounts for not only consumer showrooming behavior but also the impact of product valuation uncertainty and service perception differences on consumers’ expected utility comprehensively. Such considerations render the theoretical model used in this research closer to the reality of retail operations, thereby enriching the literature while simultaneously increasing the value of the results of this research with respect to the decision-making processes of BM retailers. Second, we construct three decision models: the nonexclusive brand (NEB) strategy, the SEB strategy, and the WEB strategy. These models are based on a process by which consumers are divided into two types, i.e., high and low, according to the costs they incur when visiting BM stores, as well as on the notion of service sensitivity, which is introduced to characterize the purchase utilities associated with different types of consumers with respect to all possible choices (i.e., purchases in BM stores, showrooming, and online purchases). We obtain the equilibrium conditions and results of these models and analyze the impact of various key parameters on the optimal equilibrium, which are useful for determining the pricing and service levels associated with products purchased via different channels for retailers. Third, we confirm that the exclusive product strategy can be an effective tool that BM retailers can use to counteract the negative effects of consumer showrooming behavior and provide managerial insights into the reasons why different types of exclusive product strategies should be chosen. We reveal that the implementation of exclusive product strategies can capture market share from online retailers, thus suggesting that BM retailers can increase their sales (and thus their revenues) by employing exclusive product strategies.

The remainder of this article is organized as follows. In Section 2, we review the relevant literature. Section 3 introduces the description of the model and the decision analysis. In Section 4, we explore three models, i.e., the benchmark model and two exclusive strategy models. In Section 5, we present various managerial insights based on a mathematical study and simulation. Finally, the conclusions of this research and corresponding directions for future studies are presented in Section 6. All explanations of the model and related proofs can be found in Appendix A and Appendix B, respectively.

2. Literature Review

This study is related to two streams of literature: the influence of nonprice factors in multichannel and omnichannel retail and consumer showrooming behavior. In this section, we review these literature streams and discuss how this study is related to them.

2.1. Influence of Nonprice Factors in Multichannel and Omnichannel Retail Contexts

The first stream of our work is related to the literature on multichannel and omnichannel retail operation decisions. As Ailawadi and Farris [16] observed, multichannel retail focuses more closely on the decisions made by the seller (for example, a brand seller) regarding which channel should be included in the channel operated by an independent company. In contrast, omnichannel retail management requires an investigation of the interactions among multiple channels operated by the same company (usually between online and offline channels). Early research on multichannel and omnichannel retail operation decisions focused primarily on channel selection and pricing strategies. For further research on multichannel and omnichannel retail, please refer to the relevant literature [14,17,18,19,20].

We focus on research on nonprice factors (such as sales and service effort) in multichannel and omnichannel retail. In fact, some scholars have given attention to the dimension of nonprice factors in the literature on multichannel and omnichannel retail [21,22,23,24,25,26]. The service effort strategies employed by retailers, such as promotions, advertising, and value-added services, may affect consumer demand [27,28]. Studies [29,30,31,32] have also demonstrated that retailers can increase demand and profit through promotional and advertising efforts. An increasing number of scholars have gradually begun to pay attention to the impact of nonprice factors on sales. Liu, Dan [33] focused on information sharing in the online retail supply chain for fresh produce, including the impact of preservation efforts and value-added services. Some studies have suggested that free value-added services, such as free breakfasts, parking, and Wi-Fi offered by hotels, also fall under the category of nonprice factors and positively affect consumers’ perceived price [34,35], especially in low- and high-demand conditions, and that value-added services are always beneficial [36]. However, some researchers have claimed that free products and free value-added services may not increase business value because of opportunity costs or hidden costs [37] or may undermine retailers’ interests as a result of consumers’ valuation biases [38].

Although the aforementioned studies all examined the impact of nonprice factors on multichannel and omnichannel retail, they overlooked the consideration of consumer showrooming behavior. In our research, we model the after-sales service effort invested by a BM retailer while explicitly considering consumer showrooming behavior. This is particularly meaningful because we find that each consumer’s sensitivity to after-sales service varies, meaning that even a high level of after-sales service effort by the BM retailer may not alter the showrooming behavior of some low-sensitivity consumers.

2.2. Consumer Showrooming Behavior

Our study also covers the research topic of “consumer showrooming behavior” in retail businesses. As Li, Zhang [39] reported, consumer showrooming behavior takes two main forms, namely, consumer showrooming behavior in omnichannel retail and corresponding behavior in multichannel retail.

Showrooming in the context of omnichannel retail entails that consumers check products in the physical store of a seller (company) but make purchases from the online store operated by the same seller (i.e., company) [39]. In an omnichannel environment, omnichannel retailers can use various methods (such as in-store tablets, salesperson recommendations, and quick response (QR) codes) to guide consumers to check their offline stores and then switch to their online stores to purchase; in this context, retailers can focus on omnichannel fulfillment to achieve a higher degree of operational efficiency. Therefore, the arrangement of offline showrooms is very important. Park, Dayarian [40] proposed a quantitative method that can be used to optimize retailers’ ability to demonstrate a product portfolio to maximize the functions that consumers want to experience when visiting an omnichannel showroom. This offline-to-online strategy, in turn, promotes consumer showrooming behavior. With respect to showrooming research in omnichannel retail, we recommend the research conducted by Li, Zhang [39], Cai and Lo [41], and Sharma, Starcevic [42] to readers because our research involves another type of showrooming, i.e., showrooming in multichannel retail.

Showrooming in the context of multichannel retail refers to a particular kind of free-riding behavior on the part of consumers, where consumers try a product in a physical store operated by one seller but purchase the same product from an online store operated by another seller [11,15,39,43]. Some researchers [4,44,45,46] have referred to showrooming in multichannel retail as “competitive showrooming”. Regardless of the definition of showrooming used, most previous studies on this topic have expressed negative views regarding this type of free-riding behavior on the part of consumers because, in this context, consumers choose a less expensive alternative to competing retailers (i.e., online retailers) [11,45,47,48].

Moreover, most studies on this topic [49,50,51,52] have reported that showrooming consumers (showroomers) may not exhibit a unified attitude or opinion regarding where to make their purchases before they arrive in a physical store. These consumers may be stimulated by the brand image of the physical store or the subsequent maintenance services provided by the physical retailer, and they may also be more affected by product strategies (i.e., exclusive strategies). This situation also indicates that showroomers are more inclined to shop around, change brands, and seek diversity with the goal of obtaining a better deal or better services than other types of consumers [49,53,54]. Therefore, the provision of differentiated exclusive products represents a long-term strategy that BM retailers can use as an effective counter to the negative effects of consumer showrooming [11]. In addition, service differentiation is crucial in this context because service homogeneity may offer fewer benefits to BM retailers that provide showrooms [53]. Therefore, to counter the negative effects of consumer showrooming, BM retailers have ample incentive to provide differentiated services.

Table 1. Differences and similarities between this study and previous studies.

Studies	Nonprice Factors	Showrooming Behavior	Exclusive Strategy
Basak, Basu [21], Feng, Liu [22], Nematollahi, Hosseini-Motlagh [23], Wang [25]	√
Gensler, Neslin [4], Li, Zhang [39], Park, Dayarian [40], Balakrishnan, Sundaresan [43], Schneider and Zielke [44], Frasquet and Miquel-Romero [46], Zhang, Dai [48]		√
Viejo-Fernández, Sanzo-Pérez [49], Quach, Barari [53], Nguyen, McClelland [54], Zhang and Wen [57]	√	√
Mehra, Kumar [11], Zhou, Yu [55], Kim, Lee [56], Ertekin, Gümüs [58]		√	√
Our paper	√	√	√

Note: A “√” indicates that the factor is considered in the present study.

summarizes the main literature closely related to our research topic. Although scholars have explored nonprice factors and showrooming behavior, studies on showrooms that simultaneously focus on nonprice factors and exclusive product strategies are still relatively rare. Our research is somewhat similar to the study conducted by Mehra, Kumar [11]; however, our study extends and differentiates itself in the following aspects. First, we fully consider the impacts of after-sales service efforts, a nonprice factor, on buyers and sellers in the process of studying the exclusive product strategy aimed at countering or exploiting the consumer showrooming effect. The level of effort involved in after-sales service entails certain service input costs, which change not only the profit functions of both the BM and online retailers but also the conditions under which consumers make purchase decisions. Second, we use a different consumer utility function. As consumers mature, an increasing number of them begin to value the after-sales value-added service of products. Accordingly, we introduce the sensitivity of consumers to the after-sales service of different channels as a way of characterizing the expected utility of consumers’ purchases, thereby providing a novel characterization of the uncertainty of consumers’ purchases. Changes in the consumer utility function lead to changes in the demand function. Moreover, the introduction of the level of after-sales service effort changes the profit functions and decision-making order of the two types of retailers during this process and ultimately renders the solution results essentially different from those obtained in previous research. Furthermore, we conduct a detailed analysis of the impact of changes in different parameter values on the effectiveness of exclusive strategies implemented by the BM retailer, thereby providing more targeted management insights for practice and adding new perspectives and practical guidance to the field. Naturally, some scholars have conducted research focusing on exclusive product strategies. For instance, Zhou, Yu [55] developed two game-theoretic models to explore whether live streaming platforms should promote brands from traditional retail platforms on a non-exclusive basis, and obtained a counterintuitive finding: when live streaming platforms adopt exclusive promotion, a higher commission rate may be beneficial to the brands. Kim, Lee [56] examined the impact of exclusive distribution on online retailers’ sales, as well as the moderating effects of product assortment (both breadth and depth) and intra-category competition intensity on this relationship. The results indicate that exclusive distribution can increase sales, and this effect is further strengthened with the improvement of product depth and the intensification of intra-category competition. However, these studies do not simultaneously address non-price factors and showrooming behavior.

3. Model

3.1. Retailer Behavior

This paper considers two retailers: a BM retailer and an online retailer. The BM retailer operates a BM store via the physical channel, which we label with subscript $s$. The online retailer operates an online store via the online channel, which we label with subscript $o$. It is assumed that these two retailers operate in the same product category and that the product price of each category is determined individually by the particular retailer in question. These products exhibit robust service attributes, which primarily take the form of product trials, guidance or suggestions, installation, debugging, maintenance, and other related services. Given the inherent convenience advantages exhibited by the BM retailer with respect to such services, the service level $s$ is determined by the BM retailer; in turn, the online retailer subsequently adheres to the service level $s$ established by the BM retailer. However, owing to the disparate levels of sensitivity to service exhibited by different consumers, we assume that the service sensitivity $x$ follows a Hotelling distribution ranging from 0–1, where $x=1$ denotes complete sensitivity to service effort, whereas $x=0$ denotes complete insensitivity to service effort. Therefore, the actual level of service perceived by consumers who choose the physical channel is $xs$. In contrast, while the online retailer offers service and adheres to the service level $s$ that has been established by the BM retailer, the absence of comprehensive product and service demonstrations via the online channel often exacerbates the challenges associated with the performance of service tasks, particularly in light of the inconvenience of remote services and the corresponding wait times. This situation, in turn, leads to a decreased level of service actually perceived by consumers when they make purchases via online channels. The difference in the perceived service level between the online and offline channels is denoted as $\epsilon$; consequently, the actual perceived service level for consumers who make purchases via online channels is represented as $x(s-\epsilon )$.

Furthermore, as mentioned above, consumer showrooming behavior significantly affects the profitability of BM retailers, particularly with respect to product categories that exhibit notable service attributes, which are more susceptible to showrooming behavior. Therefore, in this paper, we explore the possibility that BM retailers can adopt an exclusive product strategy to alleviate the adverse effects of consumer showrooming behavior. Moreover, for research purposes, we assume that all products within a specific category (i.e., exclusive products) are subject to independent decision-making, that price information is common knowledge that is shared between retailers and consumers, and that the unit marginal operating costs of both retailers are standardized to 0.

3.2. Consumer Behavior

Similar to the research of Mehra, Kumar [11], Lal R [59], we assume that products exhibit both digital and nondigital attributes and that consumers can evaluate these attributes with the goal of choosing the product that best suits their needs. Additionally, we assume that all consumers receive utility $v$ from their best-fit product. However, consumers who evaluate a product exclusively online are unable to make an accurate assessment of the product’s nondigital attributes; thus, the product that they select may not be the best fit for them. We suppose that the probability that a consumer’s best-fit product is selected correctly when the evaluation is performed solely online is $k$, where $0<k<1$, and the utility from any product that is not the consumer’s best-fit product is $v-\Delta$, where $0<\Delta <v$. Therefore, a consumer’s expected utility from a product that is selected online is $kv+(1-k)(v-\Delta )=v-(1-k)\Delta$. When $(1-k)\Delta$ is written as $\delta$, the expected utility of the product evaluated and purchased by the consumer directly online is $v-\delta$, in which context the values of $\delta$ and $v$ are known to both consumers and retailers.

Consumers incur different costs depending on the channel that they use. Furthermore, these costs differ across different consumers. In line with the suggestions of Coughlan and Soberman [60] and Mehra, Kumar [11], we assume the presence of two types of consumers in the market; we also assume that the costs they incur by visiting BM stores differ. One type of consumer is the low-type consumer, who visits BM stores at a lower cost because of his or her proximity to BM stores, whereas the other type of consumer is a high-type consumer, who is located far away from BM stores and therefore incurs high visit costs during such visits. The proportion of low-type consumers is $\lambda$, whereas that of high-type consumers is $1-\lambda$. The cost of visiting a BM store for low-type consumers is normalized to zero, whereas the corresponding cost for high-type consumers is denoted by $t$. Forman, Ghose [61] empirically established the existence of these costs, which have been discussed and analyzed accordingly in previous studies (e.g., Refs. [60,62,63]). To ensure equilibrium in the market allocation, similar to the approach employed by Mehra, Kumar [11], we assume that $t>\Delta >\delta$, thereby ensuring that some consumers prefer to evaluate and purchase online and do not always make purchases by engaging in showrooming behavior. In addition, we assume that visiting the online retailer’s website (online store) is costless for all consumers since it takes very little effort or time to visit such a website.

3.3. Decision Analysis

In light of relevant practical insights, we model a sequential game that involves two retailers and several consumers, in which context their decision-making processes are divided into three distinct stages.

(1)

Initially, the service level is established by the BM retailer, and it is subsequently mirrored by the online retailer.

(2)

Each retailer subsequently discloses its pricing strategy; this information is thus made accessible to competitors and all consumers. Concurrently, consumers visit each retailer’s store (or website) with the goal of obtaining pertinent product attribute information.

(3)

Finally, consumers make the decision to purchase and select their preferred purchase channel.

For the sake of enhanced clarity and readability, we present a summary of the notations in

Table 2. Notations.

Notations	Description
Decision variables
$p_i^j$	Retail price of product $i$ under $j$ strategy
$s^j$	Service level provided by the BM retailer under $j$ strategy
Parameters
$v$	Consumers’ perceived utility with respect to the best-fit product
$x$	Sensitivity to service effort on the part of a consumer, which follows a Hotelling distribution at [0,1]
$\epsilon$	Consumers’ perceived difference in service effort between the online and offline channels
$k$	The probability that a consumer can evaluate and purchase the best-fit product correctly when the evaluation is performed solely online
$\Delta$	Utility decreases for a consumer when the product purchased online is not the best-fit product ($0<\Delta <v$)
$\delta$	Expected utility for a consumer when the product is evaluated and purchased directly online ($\delta =(1-k)\Delta$)
$\lambda$	Proportion of low-type consumers
$t$	Cost of visiting the BM shore for high-type consumers
$c_o$	The inconvenience cost of receiving services for online consumers
$\alpha$	Proportion of customers who can buy the best-fit product in the BM store
$h$	Unit variable service cost borne by the online retailer
${\eta }_s$/${\eta }_o$	Unit service cost coefficient for the BM/online retailer (${\eta }_o>{\eta }_s$)
Superscript
$\hspace{1em} j=NEB/SEB/WEB$	Nonexclusive brand strategy/store exclusive brand strategy/well-known exclusive brand strategy
Subscripts
$s$	BM retailers or offline stores
$o$	Online retailers or stores
$i=sn/se/on$	Nonexclusive products of the BM retailer/exclusive products of the BM retailer/nonexclusive products of the online retailer
$l$/$h$	Low-type/high-type consumers

.

4. Model Analysis

4.1. NEB Strategy

In the NEB strategy (which is used as the benchmark model), we consider three methods of purchase, including consumer showrooming behavior. The utility of different types of consumers under three purchasing methods is shown in Figure 1.

By comparing the utility of consumers under different purchase methods (see Appendix A for details), we can obtain the following market demand expressions for the BM and online retailers:

$$D_s^{NEB}=\lambda (1-x_l)+(1-\lambda )(1-x_h)$$

(1)

$$D_o^{NEB}=\lambda x_l+(1-\lambda )x_h$$

(2)

In summary, the profits obtained by the BM retailer and the online retailer are as follows:

$${\pi }_s^{NEB}=\left[\lambda (1-x_l)+(1-\lambda )(1-x_h)\right]p_{sn}-{\displaystyle \frac{1}{2}}{\eta }_s{s}^2$$

(3)

$${\pi }_o^{NEB}=\left[\lambda x_l+(1-\lambda )x_h\right](p_{on}-hs)-{\displaystyle \frac{1}{2}}{\eta }_o{s}^2$$

(4)

The relationship between the service cost and service level suggested by Tsay and Agrawal [64] is used here; that is, when the retailer provides service level $s$, the service cost paid is a quadratic function ${\displaystyle \frac{1}{2}}{\eta }_i{s}^2$, where ${\eta }_i>0\hspace{0.33em}(i=s,o)$ is the unit service cost coefficient. In addition, when online retailers provide after-sales service, they may even need to complete the corresponding after-sales service by relying on a third-party service outsourcing company due to the geographic dispersion of the customers who are involved in the offsite service. Therefore, the online retailer must pay not only a fixed service cost ${\displaystyle \frac{1}{2}}{\eta }_o{s}^2$ (equivalent to the authorization fee) but also the corresponding variable service fee $hs\cdot D_o^b$, where $h$ is the unit variable service cost.

Theorem 1.

In the NEB strategy, the optimal service level and prices for the BM retailer and the online retailer are as follows:

$$s^{NEB}={\displaystyle \frac{2h[c_o+2\epsilon -(1-\lambda )(t-\delta )]}{9\epsilon {\eta }_s-2h^2}}$$

(5)

$$p_{sn}^{NEB}={\displaystyle \frac{3\epsilon {\eta }_s[c_o+2\epsilon -(1-\lambda )(t-\delta )]}{9\epsilon {\eta }_s-2h^2}}$$

(6)

$$p_{on}^{NEB}={\displaystyle \frac{4h^2[c_o+2\epsilon -(1-\lambda )(t-\delta )]}{3(9\epsilon {\eta }_s-2h^2)}}-{\displaystyle \frac{1}{3}}[c_o-\epsilon -(1-\lambda )(t-\delta )]$$

(7)

The proof of Theorem 1 can be found in Appendix B. By analyzing the variation in key parameters ($k$ and $\lambda$) in the optimal equilibrium results of the BM and online retailers under the NEB strategy, Lemma 1 can be obtained.

Lemma 1.

(1)${\displaystyle \frac{\mathsf{\partial }{s}^{NEB}}{\mathsf{\partial }k}}<0$, ${\displaystyle \frac{\mathsf{\partial }{s}^{NEB}}{\mathsf{\partial }\lambda }}>0$; ${\displaystyle \frac{\mathsf{\partial }{p}_{sn}^{NEB}}{\mathsf{\partial }k}}<0$, ${\displaystyle \frac{\mathsf{\partial }{p}_{sn}^{NEB}}{\mathsf{\partial }\lambda }}>0$; when $2h^2<3\epsilon {\eta }_s$, = ${\displaystyle \frac{\mathsf{\partial }{p}_{on}^{NEB}}{\mathsf{\partial }k}}>0$, ${\displaystyle \frac{\mathsf{\partial }{p}_{on}^{NEB}}{\mathsf{\partial }\lambda }}<0$; otherwise, ${\displaystyle \frac{\mathsf{\partial }{p}_{on}^{NEB}}{\mathsf{\partial }k}}<0$ and ${\displaystyle \frac{\mathsf{\partial }{p}_{on}^{NEB}}{\mathsf{\partial }\lambda }}>0$.

(2) ${\displaystyle \frac{\mathsf{\partial }{D}_s^{NEB}}{\mathsf{\partial }k}}<0$, ${\displaystyle \frac{\mathsf{\partial }{D}_s^{NEB}}{\mathsf{\partial }\lambda }}>0$; ${\displaystyle \frac{\mathsf{\partial }{D}_o^{NEB}}{\mathsf{\partial }k}}>0$, ${\displaystyle \frac{\mathsf{\partial }{D}_o^{NEB}}{\mathsf{\partial }\lambda }}<0$.

(3) ${\displaystyle \frac{\mathsf{\partial }{\pi }_s^{NEB}}{\mathsf{\partial }k}}<0$, ${\displaystyle \frac{\mathsf{\partial }{\pi }_s^{NEB}}{\mathsf{\partial }\lambda }}>0$; ${\displaystyle \frac{\mathsf{\partial }{\pi }_o^{NEB}}{\mathsf{\partial }k}}>0$, ${\displaystyle \frac{\mathsf{\partial }{\pi }_o^{NEB}}{\mathsf{\partial }\lambda }}<0$.

Lemma 1 reveals that under the NEB strategy, the service level, product price, demand, and profit of the BM retailer decrease with the probability that a consumer can evaluate and purchase the best-fit product correctly when the evaluation is performed solely online ($k$) and increase with the proportion of low-type consumers ($\lambda$). The demand and profit of the online retailer exhibit the opposite trend; that is, these factors increase as $k$ increases and decrease as $\lambda$ increases. These results occur because the probability ($k$) reflects consumers’ comprehensive assessment of trust in online shopping platforms, the transparency of product information, and their satisfaction with the shopping experience. As $k$ increases, thus indicating a greater probability that consumers can easily find and evaluate products online that closely match their actual needs, consumers are more likely to complete their purchases online, thus negatively impacting the BM retailer. Even if the BM retailer tries to reverse this disadvantage by lowering product prices, it fails to change the situation of demand and profit losses; thus, the service level that it provides decreases accordingly. Unlike $k$, a higher value of $\lambda$ indicates a larger proportion of low-type consumers, which benefits the BM retailer. In this scenario, the BM retailer can increase product prices without significantly reducing demand. In fact, demand may even increase with an increase in $\lambda$, thus allowing the BM retailer to benefit from both a higher price and demand, which can further motivate the retailer to increase their service level.

In contrast, the effects of $k$ and $\lambda$ on the demand and profit of the online retailer are opposite to those observed with respect to the BM retailer. Specifically, while the process by which $k$ or $\lambda$ changes improve the situation of the BM retailer or the online retailer, it also causes the situation of the other party to deteriorate. However, notably, the influence of $k$ and $\lambda$ on the online retailer’s product pricing is dependent on the unit variable service cost ($h$) incurred by the online retailer. When $h$ is small, the effects of $k$ and $\lambda$ on the online retailer’s price are consistent with the impacts of these factors on demand and profit. Conversely, when $h$ is significant, this relationship of pricing is reversed.

4.2. Exclusive Product Strategy

4.2.1. SEB Strategy

In the SEB strategy, we first consider the decisions made by low-type customers who are aware of the store brand. In this context, the exclusive products sold by the BM retailer are SEB products, and the relevant information is known to customers. We assume that the probability that the exclusive product associated with the BM retailer store brand is the best-fit product for the consumer is $\alpha$. In other words, the proportion of customers who can buy the best-fit product in the BM store is $\alpha$. We also assume that the prices of an exclusive product and a nonexclusive product offered by the BM retailer are $p_{se}$ and $p_{sn}$, respectively, and that the online retailer sells a nonexclusive product at $p_{on}$. Figure 2 illustrates the decisions made by low-type customers in contexts featuring known SEB products. Through analysis (see Appendix A for details), under the SEB strategy, the total demand exhibited by low-type customers making purchases at the BM store, $D_s^{l-SEB}$, and the total profit obtained by the BM retailer, ${\pi }_s^{l-SEB}$ (excluding the service cost), are as follows:

$$D_s^{l-SEB}=\lambda \alpha (1-x_{\alpha })+\lambda (1-\alpha )(1-x_{(1-\alpha )})$$

(8)

$${\pi }_s^{l-SEB}=\lambda \alpha (1-x_{\alpha })p_{se}+\lambda (1-\alpha )(1-x_{(1-\alpha )})p_{sn}$$

(9)

The total demand exhibited by low-type customers making online purchases, $D_o^{l-SEB}$, and the total profit obtained by the online retailer, ${\pi }_o^{l-SEB}$ (excluding the service cost), are as follows:

$$D_o^{L,sb}=\lambda \left[\alpha x_{\alpha }+(1-\alpha )x_{(1-\alpha )}\right]$$

(10)

$${\pi }_o^{L,sb}=\lambda \left[\alpha x_{\alpha }+(1-\alpha )x_{(1-\alpha )}\right]p_o$$

(11)

Figure 3 explains the decisions made by high-type customers under the SEB strategy. Therefore, under the SEB strategy, the total demand of high-type customers who make purchases at the BM store, $D_s^{h-SEB}$, and the total profit obtained by the BM retailer ${\pi }_s^{h-SEB}$ (excluding the service cost) are as follows:

$$D_s^{h-SEB}=(1-\lambda )\alpha (1-x_{H1})+(1-\lambda )(1-\alpha )(1-x_{H1})$$

(12)

$${\pi }_s^{h-SEB}=(1-\lambda )\alpha (1-x_{H1})p_{se}+(1-\lambda )(1-\alpha )(1-x_{H1})p_{sn}$$

(13)

The total demand of high-type customers who make online purchases, $D_o^{h-SEB}$, and the total profit obtained by the online retailer, ${\pi }_o^{h-SEB}$ (excluding the service cost), are as follows:

$$D_o^{h-SEB}=(1-\lambda )x_{H1}$$

(14)

$${\pi }_o^{h-SEB}=(1-\lambda )x_{H1}{p}_{on}$$

(15)

On the basis of these analysis results regarding high- and low-type customers and in light of the service cost, the total demand and total profits of the BM retailer and the online retailer are as follows:

$$D_s^{SEB}=D_s^{l-SEB}+D_s^{h-SEB}$$

(16)

$$D_o^{SEB}=D_o^{l-SEB}+D_o^{h-SEB}$$

(17)

$${\pi }_s^{SEB}={\pi }_s^{l-SEB}+{\pi }_s^{h-SEB}-{\displaystyle \frac{1}{2}}{\eta }_s{s}^2$$

(18)

$${\pi }_o^{SEB}={\pi }_o^{l-SEB}+{\pi }_o^{h-SEB}-hs{D}_o^{SEB}-{\displaystyle \frac{1}{2}}{\eta }_o{s}^2$$

(19)

According to the previously described order of the game, we use backward induction to solve the model, and Theorem 2 can thus be obtained as follows:

Theorem 2.

In the SEB strategy, the optimal service level and product pricing for the BM and online retailers are as follows:

$$s^{SEB}={\displaystyle \frac{2h\left[c_o+2\epsilon +\alpha (\Delta k+\lambda \delta )-(1-\lambda )(t-\delta )\right]}{9\epsilon {\eta }_s-2h^2}}$$

(20)

$$p_{se}^{SEB}={\displaystyle \frac{3\epsilon {\eta }_s\left[2c_o+4\epsilon +2\alpha (\Delta k+\lambda \delta )-2(1-\lambda )(t-\delta )+3\Delta (1-\alpha )\right]-2\Delta h^2(1-\alpha )}{2(9\epsilon {\eta }_s-2h^2)}}$$

(21)

$$p_{sn}^{SEB}={\displaystyle \frac{3\epsilon {\eta }_s\left[2c_o+4\epsilon +2\alpha (\Delta k+\lambda \delta )-2(1-\lambda )(t-\delta )-3\alpha \Delta \right]+2\alpha \Delta h^2}{2(9\epsilon {\eta }_s-2h^2)}}$$

(22)

$$p_{on}^{SEB}={\displaystyle \frac{4h^2\left[c_o+2\epsilon +\alpha (\Delta k+\lambda \delta )-(1-\lambda )(t-\delta )\right]}{3\left(9\epsilon {\eta }_s-2h^2\right)}}-{\displaystyle \frac{1}{3}}\left[c_o-\epsilon +\alpha (\Delta k+\lambda \delta )-(1-\lambda )(t-\delta )\right]$$

(23)

The proof of Theorem 2 can be found in Appendix B. By analyzing the variation in key parameters ($k$ and $\lambda$) in the optimal equilibrium results of the BM and online retailers under the SEB strategy, Lemma 2 can be obtained.

Lemma 2.

(1) ${\displaystyle \frac{\mathsf{\partial }{s}^{SEB}}{\mathsf{\partial }k}}<0$, ${\displaystyle \frac{\mathsf{\partial }{s}^{SEB}}{\mathsf{\partial }\lambda }}>0$; ${\displaystyle \frac{\mathsf{\partial }{p}_{se}^{SEB}}{\mathsf{\partial }k}}={\displaystyle \frac{\mathsf{\partial }{p}_{sn}^{SEB}}{\mathsf{\partial }k}}<0$, ${\displaystyle \frac{\mathsf{\partial }{p}_{se}^{SEB}}{\mathsf{\partial }\lambda }}={\displaystyle \frac{\mathsf{\partial }{p}_{sn}^{SEB}}{\mathsf{\partial }\lambda }}>0$; when $2h^2<3\epsilon {\eta }_s$, ${\displaystyle \frac{\mathsf{\partial }{p}_{on}^{SEB}}{\mathsf{\partial }k}}>0$, ${\displaystyle \frac{\mathsf{\partial }{p}_{on}^{SEB}}{\mathsf{\partial }\lambda }}<0$; otherwise, ${\displaystyle \frac{\mathsf{\partial }{p}_{on}^{SEB}}{\mathsf{\partial }k}}<0$ and ${\displaystyle \frac{\mathsf{\partial }{p}_{on}^{SEB}}{\mathsf{\partial }\lambda }}>0$.

(2) ${\displaystyle \frac{\mathsf{\partial }{D}_{se}^{SEB}}{\mathsf{\partial }k}}<0$, ${\displaystyle \frac{\mathsf{\partial }{D}_{se}^{SEB}}{\mathsf{\partial }\lambda }}>0$; ${\displaystyle \frac{\mathsf{\partial }{D}_{sn}^{SEB}}{\mathsf{\partial }k}}<0$, ${\displaystyle \frac{\mathsf{\partial }{D}_{sn}^{SEB}}{\mathsf{\partial }\lambda }}>0$; ${\displaystyle \frac{\mathsf{\partial }{D}_s^{SEB}}{\mathsf{\partial }k}}<0$, ${\displaystyle \frac{\mathsf{\partial }{D}_s^{SEB}}{\mathsf{\partial }\lambda }}>0$; ${\displaystyle \frac{\mathsf{\partial }{D}_o^{SEB}}{\mathsf{\partial }k}}>0$, ${\displaystyle \frac{\mathsf{\partial }{D}_o^{SEB}}{\mathsf{\partial }\lambda }}<0$.

(3) ${\displaystyle \frac{\mathsf{\partial }{\pi }_s^{SEB}}{\mathsf{\partial }k}}<0$, ${\displaystyle \frac{\mathsf{\partial }{\pi }_s^{SEB}}{\mathsf{\partial }\lambda }}>0$; ${\displaystyle \frac{\mathsf{\partial }{\pi }_o^{SEB}}{\mathsf{\partial }k}}>0$; ${\displaystyle \frac{\mathsf{\partial }{\pi }_o^{SEB}}{\mathsf{\partial }\lambda }}<0$.

Analogous to Lemma 1, Lemma 2 describes how the optimal equilibrium outcomes for the BM and online retailers evolve with changes in key parameters ($k$ and $\lambda$) under the SEB strategy. The patterns of these outcomes under the SEB strategy are closely in line with those observed under the NEB strategy. Given that the BM retailer sells both store-exclusive products and nonexclusive items under the SEB strategy, the parameters $k$ and $\lambda$ simultaneously influence the pricing of both product types. Notably, $k$ and $\lambda$ have not only the same increasing or decreasing effects on exclusive and nonexclusive product prices but also the same rate of change with respect to the prices of both product types (${\displaystyle \frac{\mathsf{\partial }{p}_{se}^{SEB}}{\mathsf{\partial }k}}={\displaystyle \frac{\mathsf{\partial }{p}_{sn}^{SEB}}{\mathsf{\partial }k}}$, ${\displaystyle \frac{\mathsf{\partial }{p}_{se}^{SEB}}{\mathsf{\partial }\lambda }}={\displaystyle \frac{\mathsf{\partial }{p}_{sn}^{SEB}}{\mathsf{\partial }\lambda }}$). This consistency is primarily because $k$ and $\lambda$ share identical structural relationships with respect to the optimal pricing decisions for both exclusive and nonexclusive products sold by the BM retailer. The price difference between these two product types relies primarily on $\epsilon$, ${\eta }_s$, $h$ and $\Delta$ ($p_{se}^{SEB}-p_{sn}^{SEB}=(9\epsilon {\eta }_s-2h^2)\Delta$).

The basis for the exclusive product strategy decisions made by BM retailers is whether such a strategy can offer them more benefits. By comparing the optimal profits generated under the NEB and SEB strategies when those strategies are employed by the BM retailer, Corollary 1 can be obtained as follows:

Corollary 1.

The BM retailer can benefit from adopting the SEB strategy, as the optimal profits in the two different models satisfy ${\pi }_s^{SEB}>{\pi }_s^{NEB}$.

Corollary 1 indicates that BM retailers can indeed alleviate the negative impacts of customer showrooming behavior and improve their profits by implementing the SEB strategy.

4.2.2. WEB Strategy

With respect to the WEB strategy, we assume that when the BM retailer implements the WEB strategy, the prices of that retailer’s exclusive and nonexclusive products are $p_{se}$ and $p_{sn}$, respectively, whereas the price of the online retailer’s products (which are associated with a non-well-known brand) is $p_{on}$. Since the brand in question is well known, customers already know whether the exclusive product at the BM store is the best-fit product and thereby decide whether to visit the BM store. This situation is different from the corresponding situation under the SEB strategy. In the SEB situation, customers do not know whether the BM store-exclusive product is the best-fit product in advance; thus, they must first decide whether to visit the BM store. Only when customers choose to visit the BM store can they discover whether the exclusive product of SEB is the best-fit product. We use Figure 4 to illustrate the decision-making behavior of low-type customers under the WEB strategy.

Through analysis (see Appendix A for details), we can conclude that $\lambda \alpha (1-x_{l\alpha })$ customers buy exclusive products at price $p_{se}$ in the BM store, $\lambda (1-\alpha )(1-x_{l(1-\alpha )})$ customers buy nonexclusive products at price $p_{sn}$ in the BM store, and $\lambda \left[\alpha x_{l\alpha }+(1-\alpha )x_{l(1-\alpha )}\right]$ customers buy nonexclusive products online at price $p_{on}$ by engaging in showrooming.

Therefore, under the WEB strategy, the total demand of low-type customers who make purchases at the BM store, $D_s^{l-WEB}$, and the total profit obtained by the BM retailer, ${\pi }_s^{l-WEB}$ (excluding the service cost), can be expressed as follows:

$$D_s^{l-WEB}=\lambda \alpha (1-x_{l\alpha })+\lambda (1-\alpha )(1-x_{l(1-\alpha )})$$

(24)

$${\pi }_s^{l-WEB}=\lambda \alpha (1-x_{l\alpha })p_{se}+\lambda (1-\alpha )(1-x_{l(1-\alpha )})p_{sn}$$

(25)

Correspondingly, the total demand of low-type customers who make online purchases after engaging in showrooming in the BM store, $D_o^{l-WEB}$, and the total profit obtained by the online retailer, ${\pi }_o^{l-WEB}$ (excluding the service cost), are as follows:

$$D_o^{l-WEB}=\lambda \left[\alpha x_{l\alpha }+(1-\alpha )x_{l(1-\alpha )}\right]$$

(26)

$${\pi }_o^{l-WEB}=\lambda \left[\alpha x_{l\alpha }+(1-\alpha )x_{l(1-\alpha )}\right]p_{on}$$

(27)

Next, we consider the decision-making behavior exhibited by high-type customers under the WEB strategy, as illustrated in Figure 5.

We can conclude that $(1-\lambda )\alpha (1-x_{h\alpha })$ customers buy exclusive products at price $p_{se}$ in the BM store, $(1-\lambda )(1-\alpha )(1-x_{h(1-\alpha )})$ customers buy nonexclusive products at price $p_{sn}$ in the BM store, and $(1-\lambda )\left[\alpha x_{h\alpha }+(1-\alpha )x_{h(1-\alpha )}\right]$ customers buy nonexclusive products at price $p_{on}$ online.

Therefore, under the WEB strategy, when high-type consumers make purchases at the BM store, the total demand $D_s^{h-WEB}$ and the total profit ${\pi }_s^{h-WEB}$ (excluding the service cost) for the BM retailer are as follows:

$$D_s^{h-WEB}=(1-\lambda )\alpha (1-x_{h\alpha })+(1-\lambda )(1-\alpha )(1-x_{h(1-\alpha )})$$

(28)

$${\pi }_s^{h-WEB}=(1-\lambda )\alpha (1-x_{h\alpha })p_{se}+(1-\lambda )(1-\alpha )(1-x_{h(1-\alpha )})p_{sn}$$

(29)

The total demand $D_o^{H,kb}$ and the total profit ${\pi }_o^{H,kb}$ (excluding the service cost) for the online retailer when high-type customers make purchases online are as follows:

$$D_o^{h-WEB}=(1-\lambda )\left[\alpha x_{h\alpha }+(1-\alpha )x_{h(1-\alpha )}\right]$$

(30)

$${\pi }_o^{h-WEB}=(1-\lambda )\left[\alpha x_{h\alpha }+(1-\alpha )x_{h(1-\alpha )}\right]p_{on}$$

(31)

On the basis of the results of this analysis of high- and low-type customers and in light of the service cost, the total demand and total profit of the BM retailer and the online retailer under the WEB strategy are as follows:

$$D_s^{WEB}=D_s^{l-WEB}+D_s^{h-WEB}$$

(32)

$$D_o^{WEB}=D_o^{l-WEB}+D_o^{h-WEB}$$

(33)

$${\pi }_s^{WEB}={\pi }_s^{l-WEB}+{\pi }_s^{h-WEB}-{\displaystyle \frac{1}{2}}{\eta }_s{s}^2$$

(34)

$${\pi }_o^{WEB}={\pi }_o^{l-WEB}+{\pi }_o^{h-WEB}-hs\cdot D_o^{WEB}-{\displaystyle \frac{1}{2}}{\eta }_o{s}^2$$

(35)

By using the backward induction method to solve the formulas presented above, we can obtain Theorem 3 as follows:

Theorem 3.

In the WEB strategy, the optimal service level and product pricing for the BM and online retailers are as follows:

$$s^{WEB}={\displaystyle \frac{2h\left[c_o+2\epsilon +\alpha (\Delta k+\lambda \delta )-(1-\lambda )(t-\delta )\right]}{9\epsilon {\eta }_s-2h^2}}$$

(36)

$$p_{se}^{WEB}={\displaystyle \frac{3\epsilon {\eta }_s\left[2c_o+4\epsilon +(3-\alpha )(\Delta k+\lambda \delta )-2(1-\lambda )(t-\delta )\right]-2h^2(1-\alpha )(\Delta k+\lambda \delta )}{2(9\epsilon {\eta }_s-2h^2)}}$$

(37)

$$p_{sn}^{WEB}={\displaystyle \frac{3\epsilon {\eta }_s\left[2c_o+4\epsilon -\alpha (\Delta k+\lambda \delta )-2(1-\lambda )(t-\delta )\right]+2h^2\alpha (\Delta k+\lambda \delta )}{2(9\epsilon {\eta }_s-2h^2)}}$$

(38)

$$p_{on}^{WEB}={\displaystyle \frac{4h^2\left[c_o+2\epsilon +\alpha (\Delta k+\lambda \delta )-(1-\lambda )(t-\delta )\right]}{3(9\epsilon {\eta }_s-2h^2)}}-{\displaystyle \frac{1}{3}}\left[c_o-\epsilon +\alpha (\Delta k+\lambda \delta )-(1-\lambda )(t-\delta )\right]$$

(39)

The proof of Theorem 3 can be found in Appendix B. By analyzing the variation in key parameters ($k$ and $\lambda$) in the optimal equilibrium results of the BM and online retailers under the WEB strategy, Lemma 3 can be obtained.

Lemma 3.

(1) ${\displaystyle \frac{\mathsf{\partial }{s}^{WEB}}{\mathsf{\partial }k}}<0$, ${\displaystyle \frac{\mathsf{\partial }{s}^{WEB}}{\mathsf{\partial }\lambda }}>0$; ${\displaystyle \frac{\mathsf{\partial }{p}_{sn}^{WEB}}{\mathsf{\partial }k}}<0$, ${\displaystyle \frac{\mathsf{\partial }{p}_{sn}^{WEB}}{\mathsf{\partial }\lambda }}>0$, ${\displaystyle \frac{\mathsf{\partial }{p}_{se}^{WEB}}{\mathsf{\partial }\lambda }}>0$; when $2h^2<3\epsilon {\eta }_s$, ${\displaystyle \frac{\mathsf{\partial }{p}_{se}^{WEB}}{\mathsf{\partial }k}}>0$, ${\displaystyle \frac{\mathsf{\partial }{p}_{on}^{WEB}}{\mathsf{\partial }k}}>0$, ${\displaystyle \frac{\mathsf{\partial }{p}_{on}^{WEB}}{\mathsf{\partial }\lambda }}<0$; otherwise, ${\displaystyle \frac{\mathsf{\partial }{p}_{se}^{WEB}}{\mathsf{\partial }k}}<0$, ${\displaystyle \frac{\mathsf{\partial }{p}_{on}^{WEB}}{\mathsf{\partial }k}}<0$ and ${\displaystyle \frac{\mathsf{\partial }{p}_{on}^{WEB}}{\mathsf{\partial }\lambda }}>0$.

(2) When $2h^2<3\epsilon {\eta }_s$, ${\displaystyle \frac{\mathsf{\partial }{D}_{se}^{WEB}}{\mathsf{\partial }k}}>0$; otherwise, ${\displaystyle \frac{\mathsf{\partial }{D}_{se}^{WEB}}{\mathsf{\partial }k}}<0$; ${\displaystyle \frac{\mathsf{\partial }{D}_{se}^{WEB}}{\mathsf{\partial }\lambda }}>0$, ${\displaystyle \frac{\mathsf{\partial }{D}_{sn}^{WEB}}{\mathsf{\partial }k}}<0$, ${\displaystyle \frac{\mathsf{\partial }{D}_{sn}^{WEB}}{\mathsf{\partial }\lambda }}>0$; ${\displaystyle \frac{\mathsf{\partial }{D}_s^{WEB}}{\mathsf{\partial }k}}<0$, ${\displaystyle \frac{\mathsf{\partial }{D}_s^{WEB}}{\mathsf{\partial }\lambda }}>0$; and ${\displaystyle \frac{\mathsf{\partial }{D}_o^{WEB}}{\mathsf{\partial }k}}>0$, ${\displaystyle \frac{\mathsf{\partial }{D}_o^{WEB}}{\mathsf{\partial }\lambda }}<0$.

(3) ${\displaystyle \frac{\mathsf{\partial }{\pi }_s^{WEB}}{\mathsf{\partial }k}}<0$, ${\displaystyle \frac{\mathsf{\partial }{\pi }_s^{WEB}}{\mathsf{\partial }\lambda }}>0$; ${\displaystyle \frac{\mathsf{\partial }{\pi }_o^{WEB}}{\mathsf{\partial }k}}>0$, ${\displaystyle \frac{\mathsf{\partial }{\pi }_o^{WEB}}{\mathsf{\partial }\lambda }}<0$.

Lemma 3 characterizes the ways in which the optimal equilibrium outcomes for the BM and online retailers vary with key parameters ($k$ and $\lambda$) under the WEB strategy, and the results that overlap with Lemma 1 and Lemma 2 are not reiterated here. Notably, under the WEB strategy, the monotonicity of the price $p_{se}^{WEB}$ of the BM retailer’s exclusive products with respect to changes in $k$ is no longer fixed. Similar to the discussion of the SEB strategy, by comparing the optimal profits obtained by the BM retailer between the NEB strategy and the WEB strategy, we can obtain Corollary 2 as follows:

Corollary 2.

The BM retailer can benefit by implementing the WEB strategy, as the optimal profits obtained through the two different models satisfy ${\pi }_s^{WEB}>{\pi }_s^{NEB}$.

Corollary 2 indicates that BM retailers can also alleviate the negative impacts of customer showrooming behavior and improve their profits by implementing the WEB strategy. In this context, we confirm that both the SEB and WEB strategies can benefit BM retailers and help them achieve their goal of increasing profits. Therefore, we must compare and study the two exclusive product strategies of SEB and WEB in further detail with the goal of identifying the conditions under which BM retailers make choices regarding the type of exclusive product strategy that they should implement.

4.2.3. Analysis of the Exclusive Product Strategy

In this section, we conduct a further comparative analysis of and subsequently interpret the equilibrium results obtained under the NEB, SEB, and WEB strategies. The focus of this section is on which of the two exclusive product strategies, i.e., SEB or WEB, is more beneficial for BM retailers and which strategy can enhance their profits or competitive advantages more effectively.

On the basis of Theorems 1–3, we can derive a comparative analysis of the optimal decision equilibria for the BM and online retailers under different strategies, as presented in Proposition 1.

Proposition 1.

Under the three product strategies of NEB, SEB, and WEB, the optimal decisions for the BM retailer and the online retailer satisfy the following relationships:

(1) $s^{NEB}<s^{SEB}=s^{WEB}$.

(2) $p_{se}^{WEB}<p_{se}^{SEB}$; when $2h^2<3\epsilon {\eta }_s$, $p_{sn}^{SEB}<p_{sn}^{WEB}<p_{sn}^{NEB}$; otherwise, $p_{sn}^{SEB}<p_{sn}^{NEB}<p_{sn}^{WEB}$.

(3) When $2h^2<3\epsilon {\eta }_s$, $p_{on}^{NEB}>p_{on}^{SEB}=p_{on}^{WEB}$; otherwise $p_{on}^{NEB}<p_{on}^{SEB}=p_{on}^{WEB}$.

The proof of Proposition 1 is presented in Appendix B. Regarding the optimal service level for the BM retailer, Proposition 1 (1) first indicates that, compared with the nonexclusive product strategy (NEB), the BM retailer will provide a higher level of service when implementing an exclusive product strategy (SEB or WEB). Specifically, the proprietary nature of exclusive products ensures a relatively stable market share for the BM retailer, which corresponds to the consumer segment that prefers exclusive products. As a result, the BM retailer has a stronger incentive to offer a high level of service with the goals of stabilizing their market position and attracting potential demand. This fact also explains why businesses that offer exclusive products or implement exclusive product strategies, such as SEPHORA (mentioned in the introduction), typically provide a higher level of service than do general comprehensive retailers (such as Walmart).

Regarding the optimal product pricing for the BM retailer, Proposition 1 (2) first indicates that the BM retailer tends to charge higher prices for exclusive products and lower prices for nonexclusive products under the SEB strategy, whereas the opposite is true under the WEB strategy; this situation can be described by $p_{se}^{WEB}<p_{se}^{SEB}$ and $p_{sn}^{SEB}<p_{sn}^{WEB}$. This tendency occurs because the exclusive products sold under the SEB strategy are proprietary to the BM retailer and thus function as monopolistic offerings that can enable the BM retailer to extract greater marginal profits from each unit sold, whereas a pricing approach that favors thin profits and high sales volumes is adopted with respect to nonexclusive products. In contrast, under the WEB strategy, whether exclusive products are suitable for consumers is known beforehand. The BM retailer can benefit from appropriate reductions in the prices of exclusive products, which can attract consumers to their offline stores, and any losses incurred owing to the reduction in exclusive product prices can be compensated for by appropriate increases in the prices of nonexclusive products. Furthermore, the price of nonexclusive products is always lower when the BM retailer employs the SEB strategy than when the retailer employs the NEB strategy, whereas the pricing relationship between the WEB and NEB strategies with respect to nonexclusive products varies depending on the value of $3\epsilon {\eta }_s-2h^2$. This situation occurs because under the SEB strategy, the BM retailer not only sells exclusive products associated with its own brand and nonexclusive products simultaneously but also sets a higher price for exclusive products than would be the case for nonexclusive products under the NEB strategy ($p_{se}^{SEB}>p_{sn}^{NEB}$). Therefore, under the SEB strategy, the BM retailer must obtain high profits from its exclusive products while reducing the price of nonexclusive products with the goal of improving its competitiveness. Unlike the conditions under the SEB strategy, while the prices of exclusive products under the WEB strategy remain higher than the prices of nonexclusive products under the NEB strategy ($p_{se}^{WEB}>p_{sn}^{NEB}$), further analysis reveals that when $2h^2<3\epsilon {\eta }_s$, the online retailer reduces prices under both the SEB and WEB strategies ($p_{on}^{SEB}=p_{on}^{WEB}<p_{on}^{NEB}$). This situation forces the BM retailer to lower the prices of nonexclusive products with the goal of maintaining a competitive edge and stabilizing its market share, thus resulting in $p_{sn}^{WEB}<p_{sn}^{NEB}$. Correspondingly, when $2h^2>3\epsilon {\eta }_s$, the online retailer increases product prices under both the SEB and WEB strategies ($p_{on}^{NEB}<p_{on}^{SEB}=p_{on}^{WEB}$), thus prompting the BM retailer to raise the prices of nonexclusive products in response to the goal of maximizing profits under the WEB strategy, as indicated by $p_{sn}^{NEB}<p_{sn}^{WEB}$. In summary, regarding nonexclusive product prices for the BM retailer, when $2h^2<3\epsilon {\eta }_s$, the pricing hierarchy is $p_{sn}^{SEB}<p_{sn}^{WEB}<p_{sn}^{NEB}$; in contrast, when $2h^2>3\epsilon {\eta }_s$, the order becomes $p_{sn}^{SEB}<p_{sn}^{NEB}<p_{sn}^{WEB}$.

Regarding the optimal product pricing for the online retailer, Proposition 1 (3) first indicates that the implementation of an exclusive product strategy affects the optimal pricing decisions made by the online retailer. Second, the optimal product pricing for the online retailer under an exclusive product strategy remains unaffected by the type of exclusive product strategy. This result is primarily because the implementation of an exclusive product strategy by the BM retailer disrupts the existing market equilibrium, thus prompting the online retailer to adjust its product pricing in response to this shift. However, only when the unit variable service cost ($h$) borne by the online retailer is relatively small in comparison with consumers’ perceived difference in service ($\epsilon$) and the unit service cost coefficient of the BM retailer (${\eta }_s$), specifically when $2h^2<3\epsilon {\eta }_s$, does the online retailer opt to reduce prices ($p_{on}^{SEB}=p_{on}^{WEB}<p_{on}^{NEB}$) following the implementation of an exclusive product strategy by the BM retailer with the goal of minimizing the corresponding loss of market share. Conversely, when $2h^2>3\epsilon {\eta }_s$, the online retailer bears a higher unit variable service cost, a price reduction aimed at mitigating such demand loss may result in increased variable service costs, which may not be economically viable. Therefore, a wiser choice for the online retailer might be to increase product prices, thereby reducing demand with the goals of decreasing expenditures on variable service costs and maximizing profits based on a combination of high prices ($p_{on}^{NEB}<p_{on}^{SEB}=p_{on}^{WEB}$), low demand, and low variable service costs.

Furthermore, on the basis of the optimal pricing and service level, we can obtain the changes in the market share of the BM retailer and the online retailer before and after the implementation of exclusive product strategies, as described in Proposition 2.

Proposition 2.

(1) The implementation of an exclusive product strategy can help the BM retailer obtain more market share from the online retailer, as indicated by $D_s^j-D_s^{NEB}>0$, $D_o^j-D_o^{NEB}<0$, and $\left|D_s^j-D_s^{NEB}\right|=\left|D_o^j-D_o^{NEB}\right|$.

(2) The SEB and WEB strategies do not alter the overall market share of the BM retailer and the online retailer during the process of implementing exclusive product strategies, namely, $D_s^{SEB}=D_s^{WEB}$ and $D_o^{SEB}=D_o^{WEB}$; however, under different exclusive product strategies, some consumers shift their preferences between the BM retailer’s exclusive and nonexclusive products. That is, certain consumers who choose nonexclusive products under the SEB strategy will choose exclusive products under the WEB strategy, which is reflected in $D_{se}^{WEB}-D_{se}^{SEB}=D_{sn}^{SEB}-D_{sn}^{WEB}$.

The proof of Proposition 2 is presented in Appendix B. Proposition 2 first indicates that these exclusive product strategies can indeed increase the market share of BM retailers, thus breaking with the norm that consumer showrooming behavior typically causes BM retailers to suffer losses while leading online retailers to benefit from it. Second, the increases in the market share of the BM retailer entailed by the SEB and WEB strategies are identical, thus indicating that the two exclusive product strategies have the same effect on the total market share of the BM and online retailers. However, for the BM retailer, according to Proposition 1, owing to the different high- and low-pricing methods that this retailer adopts under the two exclusive product strategies, some of the demand included in its market share shifts between exclusive and nonexclusive products. This shift occurs mainly because the pricing of exclusive products is higher under the SEB strategy than under the WEB strategy ($p_{se}^{WEB}<p_{se}^{SEB}$), which causes some consumers to choose nonexclusive products under the SEB strategy but to switch to exclusive products under the WEB strategy (and vice versa). Therefore, the choice of an exclusive product strategy cannot be based solely on the market share or pricing decisions made by the BM retailer. In light of the inverse relationship between demand for exclusive and nonexclusive products and their pricing, a deeper analysis of the impact of exclusive product strategies on the profitability of the BM retailer is imperative. By comparing the profits obtained by the BM retailer under both the SEB and WEB strategies, Proposition 3 can be obtained as follows.

Proposition 3.

(1) When $0<k\le {\displaystyle \frac{1}{2}}$, if $({\displaystyle \frac{k}{1-k}}{)}^2<\lambda \le 1$, the BM retailer should choose the SEB strategy; if $0\le \lambda \le ({\displaystyle \frac{k}{1-k}}{)}^2$, the BM retailer should choose the WEB strategy.

(2) When $k>{\displaystyle \frac{1}{2}}$, the BM retailer should choose the WEB strategy.

Figure 6 graphically illustrates the correspondence between this relationship and the exclusive product strategy employed by the BM retailer. The probability $k$ that a consumer can evaluate and purchase the best-fit product correctly online reflects the combined impacts of the product category and the marketing means implemented by the online retailer, which is treated as an exogenous variable in this paper. In retail practice, decision makers can evaluate the approximate value of $k$ on the basis of questionnaire interviews or statistical analyses of online sales and return information from previous years, thereby offering support for their choice to implement exclusive product strategies. Accordingly, for product categories that feature a relatively low number of nondigital attributes or for customers who have access to higher levels of evaluation technology, this situation usually produces a high value of $k$, and the BM retailer thus identifies the implementation of an exclusive product strategy based on the WEB strategy as a better choice. WEB-type exclusive products are more familiar to consumers than SEB-type exclusive products are; in addition, the former are better able to cater to consumer preferences and thus drive more customer traffic to retailers. For example, the layout of SEPHORA’s “FBeauty” concept store in Shanghai, China, fully reflects its forward-thinking approach to beauty retail. The store not only displays and sells products from internationally renowned brands but also offers exclusive brands (such as XOVE, PAT McGRATH LABS, Courrèges, and TATCHA) as well as its own private label (SEPHORA’s eponymous brand). This comprehensive range of brands and product categories effectively attracts consumers to SEPHORA’s physical stores. Additionally, the SEPHORA Shanghai concept store offers three levels of experience: self-exploration for customers, virtual makeup try-on via tablets, and full makeup consultations. By combining digital smart tools with beauty assistants (BAs), the store enhances its service capabilities, fully meets consumer experience demands, and successfully converts showrooming consumers into actual buyers, thereby increasing profitability. This finding is in line with the conclusions reported by Mehra, Kumar [11]. When the value of $k$ is low, consumers find it difficult to evaluate and purchase the best-fit products online, thus increasing the likelihood that consumers will find the best-fit products at the BM retailer. Nevertheless, the BM retailer opts to adopt an SEB strategy specifically in scenarios where there is a significant presence of low-type consumers (larger $\lambda$) because the BM retailer has more opportunities to showcase its products to consumers and to utilize SEB-type products to implement differentiation strategies, which can allow it to obtain more marginal profits ($p_{se}^{SEB}>p_{se}^{WEB}$). Otherwise, the BM retailer adopts the WEB strategy, as high-type consumers visit BM stores only if their ideal products are available there, whereas the SEB-type products offered by the BM retailer remain unknown to this segment of consumers.

5. Numerical Analysis and Simulation

The fundamental motivation for BM retailers to employ exclusive product strategies lies in the ability of such strategies to mitigate or prevent the negative impacts of consumer showrooming behavior, with the ultimate goal of increasing the retailer’s profitability. On the basis of the analyses presented in Lemmas 1–3 and Proposition 3, the decisions concerning whether a BM retailer should implement an exclusive product strategy and which type of exclusive product strategy it should implement depend primarily on the probability $k$ that a consumer can correctly evaluate and purchase the best-fit product solely online, as well as the proportion $\lambda$ of low-type consumers. In this section, we first explore the characteristics of the optimal profits obtained by the BM retailer relative to the changes in $k$ and $\lambda$ by conducting numerical experiments to verify and support the preceding theoretical analysis. Second, we explore the impacts of other parameters on the optimal profits obtained by the BM retailer under different strategies. In line with the utility theory upon which this research model is constructed and the constraining relationships among relevant variables and parameters, we assign the following values to the parameters involved in this section of the study: $k=0.4$, $\lambda =0.85$, $\alpha =0.5$, $h=0.005$, $t=0.002$, $\Delta =0.0003$, $\epsilon =0.002$, $c_o=0.001$, ${\eta }_o=1.25$, and ${\eta }_s=1$. Only when we explore the impact of changing a parameter’s value is such a parameter treated as a variable; otherwise, these parameters take the values assigned here. This approach is relatively common in the field of retail operations management, and similar approaches have been taken by Mehra, Kumar [11], Liu, Yuan [65], Liu and Feng [66].

In line with the research approach discussed above, we first fix the values of other parameters to observe the impact of variation in the probability $k$ that a consumer can correctly evaluate and purchase the best-fit product solely online on the profits obtained by the two retailers. Figure 7a,b visually illustrate the trajectories of the profits obtained by the BM retailer ${\pi }_s^j$ and the profits obtained by the online retailer ${\pi }_o^j$ as these values change with $k$ under the $j$ strategy ($j=NEB/SEB/WEB$). We provide the following observations to illustrate the impact of $k$ on the profits obtained by the two retailers.

Observation 1.

Regardless of whether the BM retailer implements an exclusive product strategy, an increase in the probability $k$ that consumers can evaluate and purchase the best-fit product online always inhibits the growth of the retailer’s profit but has a positive effect on the profits obtained by the online retailer.

The findings described in Observation 1 are in line with the properties outlined in Lemmas 1–3 regarding retailers’ profits as a function of $k$. This consistency demonstrates the agreement between the numerical experiments and the theoretical analysis, thereby reinforcing the credibility and applicability of this theory. For BM retailers, a higher value of $k$ implies that consumers can more easily compare, evaluate, and purchase products online, which decreases their likelihood of visiting offline stores and subsequently harms the profits obtained by BM retailers. Conversely, a higher value of $k$ benefits online retailers since it indicates enhanced online evaluation capabilities among consumers and suggests higher conversion rates, stronger reputations, and greater trust in the practices of online retailers. For example, as consumers’ online evaluation skills improve, Best Buy begins to face stiff competition from online retailers such as Amazon, which can suppress profit growth for many BM retailers, including Best Buy itself. Consequently, Best Buy was required to adjust its pricing and actively explore an omnichannel retail model that incorporated both online and offline sales with excellent service and close collaboration with suppliers. In contrast, Amazon fosters trust and reliance among consumers by offering them an interactive, comprehensive platform that users can use to access detailed product descriptions as well as high-resolution images and videos or to read other consumer reviews and Q&A sections, thereby driving sales and profit growth for Amazon.

Similar to the numerical analysis conducted with respect to changes in $k$, we fix the values of all parameters except the proportion of low-type consumers, i.e., $\lambda$, to investigate the impacts of changes in $\lambda$ on the profits obtained by the two retailers. Figure 8a,b visually demonstrate the trajectories of the profits obtained by the BM retailer ${\pi }_s^j$ and the profits obtained by the online retailer ${\pi }_o^j$ under the $j$ strategy ($j=NEB/SEB/WEB$) as $\lambda$ changes; the detailed results are described in Observation 2.

Observation 2.

Regardless of whether the BM retailer implements an exclusive product strategy, an increase in the proportion of low-type consumers $\lambda$ always has a positive effect on the growth of the profits obtained by the BM retailer, whereas it has a negative effect on the profits obtained by the online retailer.

Clearly, the results described in Observation 2 are in line with the properties outlined in Lemmas 1–3 regarding the changes in profits obtained by retailers as $\lambda$ varies. In fact, as the proportion of low-type consumers $\lambda$ increases, this change indicates an increase in the number of consumers who are willing or able to visit BM stores conveniently. This value thus serves as a positive indicator for BM retailers, as more store visits directly increase foot traffic and sales opportunities. Additionally, BM retailers can exploit in-store product displays, experiences, and exceptional service to increase the likelihood of impulse purchases and maintain customer loyalty, which may lead to increased profits. In contrast, for online retailers, an increase in the proportion of low-type consumers $\lambda$ may indicate intensified market competition. Specifically, when more consumers visit BM stores, this situation first indicates a decrease in online traffic for online retailers. Second, to attract customers, online retailers may need to offer more competitive pricing, which can further squeeze their profit margins. For example, IKEA, a home furnishing retail brand with a focus on the physical store experience, offers consumers a delightful in-store experience: they can personally try out furniture, experience layouts of various furnishings, and draw inspiration from the displays presented in the store. As the proportion of low-type consumers $\lambda$ increases, more individuals are drawn to BM retailers such as IKEA to experience and purchase products, thereby increasing the profits obtained by such retailers. Conversely, as a prominent e-commerce platform in China, JD.com offers customers a wide range of online shopping options. However, as $\lambda$ increases, a segment of consumers who might have chosen to shop online may switch to BM stores or engage in showrooming practices, resulting in a partial or complete loss of customers for online retailers. Especially when consumers discover that it is more convenient and cost-effective to purchase home appliances or household items from nearby BM stores, they may prefer to visit these stores in person to experience such products, compare prices, and take the purchased items home directly. In such cases, an increase in $\lambda$ could have a negative effect on the profits obtained by online retailers such as JD.com because their sales are influenced by competition from BM stores as well as shifts in consumers’ shopping behavior.

In fact, the ultimate goal of retailers’ pricing and service level decisions is to maximize their profits; thus, with respect to other parameters, we analyze the impacts of numerical changes on the profits obtained by retailers.

Table 3. Impacts of other parameters on the profits obtained by retailers.

	Profits	NEB		SEB		WEB
Parameters		${\pi }_s^{NEB}$	${\pi }_o^{NEB}$	${\pi }_s^{SEB}$	${\pi }_o^{SEB}$	${\pi }_s^{WEB}$	${\pi }_o^{WEB}$
$\alpha$		-	-	↑	↓	↑	↓
$\epsilon$		First↓then↑	First↓then↑	First↓then↑	First↓then↑	First↓then↑	First↓then↑
$h$, $c_o$, $\Delta$		↑	↓	↑	↓	↑	↓
$t$, ${\eta }_s$		↓	↑	↓	↑	↓	↑
${\eta }_o$		-	↓	-	↓	-	↓

Note: “↑” indicates that the corresponding profit increases with the parameter; “↓” indicates that the corresponding profit decreases with the parameter.

summarizes the effects of parameters such as $\alpha$, $\epsilon$, and $h$ on the profits of both the BM and online retailers under three strategies, i.e., NEB, SEB, and WEB.

Table 3 reveals Observation 3, which illustrates the relationship between the profits obtained by retailers and changes in various parameters.

Observation 3.

(1) ${\pi }_s^{NEB}$ and ${\pi }_o^{NEB}$ do not vary with $\alpha$; furthermore, ${\pi }_s^j$ increases with $\alpha$, whereas ${\pi }_o^j$ decreases with $\alpha$ ($j=SEB,\hspace{0.33em}WEB$).

(2) ${\pi }_s^j$ and ${\pi }_o^j$ first decrease but then increase with $\epsilon$ ($j=NEB,\hspace{0.33em}SEB,\hspace{0.33em}WEB$).

(3) ${\pi }_s^j$ increases with $h$, $c_o$ and $\Delta$, whereas ${\pi }_o^j$ decreases with $h$, $c_o$ and $\Delta$ ($j=NEB,\hspace{0.33em}SEB,\hspace{0.33em}WEB$).

(4) ${\pi }_s^j$ decreases with $t$ and ${\eta }_s$, whereas ${\pi }_o^j$ increases with $t$ and ${\eta }_s$ ($j=NEB,\hspace{0.33em}SEB,\hspace{0.33em}WEB$).

(5) ${\pi }_s^j$ is not affected by ${\eta }_o$, whereas ${\pi }_o^j$ decreases with ${\eta }_o$ ($j=NEB,\hspace{0.33em}SEB,\hspace{0.33em}WEB$).

$\alpha$, which represents the probability that a BM retailer’s store brand or well-known brand products are the most suitable choice for consumers, reflects the degree of alignment between the exclusive products offered by the BM retailer and consumers’ preferences. However, since the NEB strategy does not involve exclusive products, changes in $\alpha$ do not affect ${\pi }_s^{NEB}$ and ${\pi }_o^{NEB}$. Moreover, $\alpha$ serves as an indicator of consumer satisfaction with the retailer’s exclusive offerings, and it is influenced not only by product attributes but also by various other factors, such as in-store experience, brand loyalty, and trust. Especially when products require professional guidance or personalized services (e.g., trying on clothing or testing cosmetics), products pertaining to store brands or well-known brands are often displayed in a more beautiful and attractive manner in BM stores. These displays allow consumers to interact directly with the brand, and they offer consumers access to professional presales and after-sales services or other brand-related experiences. This approach not only increases consumers’ brand loyalty and trust but also improves the match between consumers and these products. Conversely, replicating such brand loyalty and trust can be challenging in an online environment, thus leading to issues such as incomplete information and inferior shopping experiences for online retailers. Hence, the profit obtained by the BM retailer typically increases with $\alpha$, whereas the profit obtained by the online retailer decreases with $\alpha$.

$\epsilon$ captures consumers’ perceived difference in service levels between the online and offline channels. When $\epsilon$ is small, it indicates that consumers perceive no significant difference in service levels between the online and BM retailers, thus suggesting that the online retailer has effectively emulated or replicated the services offered by the BM store. In such cases, the BM retailer may lose motivation to improve its service level. Such a decrease in motivation, in turn, may lead to consumer dissatisfaction or distrust in the services provided by both the BM and the online retailer, thereby potentially causing consumers to switch to competitors and subsequently reducing these retailers’ sales and profits. As $\epsilon$ further increases and reaches a certain level, consumers can clearly perceive differences in service levels between the online and offline channels, even if the online retailer attempts to maintain parity with the BM retailer. These perceptions are due primarily to disparities in the service experience, convenience, social interaction, and security available via each channel. The significance of this perceived difference in service levels thus becomes a driving force that can encourage retailers to improve their services. BM retailers may enhance the store environment, improve product displays, and provide professional service personnel to improve the shopping experience for consumers; in turn, online retailers may optimize website interfaces, improve logistics and delivery, strengthen after-sales services, and increase the levels of online service that they provide. When these improvement measures are implemented, consumers are likely to reassess their shopping choices, thus leading to a potential influx of both returning and new customers. Consequently, as the perceived difference in service levels increases, retailers that adapt successfully and meet consumer demands may obtain increased profits.

The impacts of $h$, $c_o$ and $\Delta$ on the profits obtained by both the online and BM retailers exhibit certain similarities. Specifically, these factors positively affect the profits obtained by the BM retailer while negatively influencing the profits obtained by the online retailer. Specifically, $h$, $c_o$ and $\Delta$ can all be viewed as unfavorable factors for the online retailer, and an increase in these values can put the online retailer at a disadvantage in competition with the BM retailer. More specifically, $h$ reflects the magnitude of the variable service cost per unit borne by the online retailer; accordingly, a higher $h$ increases the costs incurred by the online retailer, thus leading to inevitable price hikes, which may lead to the loss of price competitiveness, reduced demand, and profit squeezing, in which context the competing BM retailer may seize the opportunity to obtain more market share, enhance its brand image, and achieve growth in terms of sales and profits. Given the inconvenience costs incurred by online or showrooming consumers during the service process, the higher $c_o$ is, the lower the net utility that consumers derive from online or showrooming purchases, as the higher inconvenience cost offsets some or all of the utility they can obtain from lower prices or other advantages offered by online stores. Conversely, BM stores typically offer a more intuitive product experience, the instant availability of merchandise, and face-to-face customer service, all of which can reduce consumers’ inconvenience costs. Hence, in such scenarios, more consumers may prefer to purchase from BM stores, especially when they need professional guidance or must make purchases urgently, thereby highlighting the evident advantages of BM stores. $\Delta$ represents the decrease in utility for consumers when the product they purchase online is not the best-fit product. The magnitude of this factor reflects consumers’ tolerance of and sensitivity toward unsuitable purchases. A larger $\Delta$ indicates greater demand for product suitability on the part of consumers; when unsuitable products are purchased, their utility is thus significantly affected. Hence, a larger $\Delta$ for the online retailer may signify higher return rates, an increase in negative reviews, increased customer acquisition costs, and decreased trust, which consequently reduce the retailer’s competitiveness and profit margins. In contrast, for the BM retailer, this scenario could represent an opportunity to attract consumers and boost market share, thereby driving profit growth.

In contrast to $h$, $c_o$, and $\Delta$, $t$ and ${\eta }_s$ can be viewed as detrimental factors for the BM retailer. An increase in the values of these factors positively affects the profits obtained by the online retailer ${\pi }_o^j$ but negatively affects the profits obtained by the BM retailer ${\pi }_s^j$. Specifically, $t$ signifies the cost incurred by high-type consumers when they visit BM stores. As $t$ increases, the frequency with which high-type consumers visit BM stores decreases, thus leading to reduced customer traffic, sales volume, and profits for the BM retailer. Additionally, this situation can cause various issues for the BM retailer, such as excess inventory, a tarnished brand image, and decreased market competitiveness. These impacts are even more pronounced when high-type consumers represent a larger proportion of the customer base in BM stores (i.e., when $\lambda$ is relatively small). The costs incurred by consumers when they visit BM stores constitute a multifaceted concept, including financial expenses, time, effort, and psychological and emotional factors; furthermore, these costs are influenced by consumers’ personal preferences, economic status, and shopping habits, as well as store characteristics. However, if BM retailers can enhance their merchandise mix and service quality, thereby providing consumers with a superior shopping experience that increases their willingness to visit these stores, the negative impacts of rising store visit costs can be mitigated. For example, Starbucks attracts many consumers by offering a comfortable environment, fast Wi-Fi, friendly service, and delicious coffee, and has introduced loyalty cards and membership programs to encourage repeat visits. Similarly, Haidilao is known for its exceptional service and delicious hotpot; this company provides a pleasant dining atmosphere and offers additional customer benefits such as free fruit and manicure services. The service cost coefficient ${\eta }_s$ reflects the costs incurred by the BM retailer when it provides a certain level of service; this coefficient highlights the expense that the retailer must bear to deliver unit service. A higher ${\eta }_s$ signifies that the BM retailer must bear greater service costs at the same service level. The service cost coefficient is typically proportional to the operational costs, labor costs, and complexity of the service provided. An increased service cost coefficient can lead to a variety of issues, such as reduced profits, decreased competitiveness, and increased investment needs. In contrast, an increase in the service cost coefficient for the BM retailer represents an opportunity for the online retailer, as it allows the latter to showcase its advantages in pricing, service, customer reach, and marketing strategies. By seizing this opportunity, the online retailer can increase its market competitiveness, attract more consumers to make online purchases, and ultimately obtain increased profits. For example, while Barnes & Noble, a prominent physical bookstore chain in the U.S., offers unique value in terms of reading experiences, cultural exchanges, and community events, an increase in its service cost coefficient (due to rising rents, labor, electricity, etc.) has led consumers to shift toward online platforms such as Amazon when purchasing books. This shift has contributed to Amazon’s continuous market share growth in the book industry, whereas physical bookstores such as Barnes & Noble have faced declining sales.

As the unit service cost coefficient for the online retailer, ${\eta }_o$ reflects the costs incurred by the online retailer when it provides a specific level of service. The characteristics of this coefficient and its impact on the online retailer are analogous to the preceding analysis of ${\eta }_s$ in terms of its effects on the BM retailer; thus, we do not discuss these characteristics further. However, it is worth noting that the BM retailer’s profit remains unaffected by variations in ${\eta }_o$. This situation is related primarily to our modeling assumptions and the sequence of the game. As described in “Section 3: Model description and decision analysis”, we assume that the BM retailer determines the service level $s$, which is then followed by the online retailer. This sequential game thus unfolds as follows. First, the BM retailer determines the service level; then, both the BM retailer and the online retailer independently determine their particular retail prices; and finally, consumers make purchase decisions and determine their preferred mode of acquisition.

6. Conclusions

The prevalence of online channels has led to the emergence of showrooming behavior, in which consumers prioritize visiting BM retailers’ offline stores to experience products but then switch to online retailers when making purchases; such behavior may often disrupt the existing market balance and damage BM retailers. In this context, the development of effective strategies to counter showrooming behavior has become an urgent issue for BM retailers. Our research aims to explore a set of effective strategies that can be used to offset or mitigate the negative effects of showrooming, thereby providing practical solutions to BM retailers while establishing a balance among players in the market and establishing a stable market environment. We employ mathematical modeling and game theory to explore the feasibility and effectiveness of the exclusive product strategies used by BM retailers to alleviate the adverse impacts of consumer showrooming behavior. In light of the brand influence of exclusive products, two strategies, i.e., SEB and WEB, are discussed. Our analysis derives equilibrium prices, service levels, and the corresponding characteristics of the demand and profit functions, thereby offering clear decision-making guidance for both the BM and online retailers.

6.1. Main Findings

Alongside the benchmark model that does not consider exclusive product strategies, we construct three strategic models, i.e., NEB, SEB, and WEB, with the goal of providing decision support for BM retailers regarding whether they should adopt an exclusive product strategy and how they can choose an appropriate type of exclusive product strategy. Our main findings are as follows.

First, BM retailers adjust their product pricing and service levels after they implement an exclusive product strategy. Specifically, first, such retailers typically set higher prices for exclusive products under the SEB strategy with the goal of reflecting their uniqueness and brand value. Simultaneously, to balance the price competitiveness of their overall product portfolio, BM retailers reduce the prices of nonexclusive products with the aim of attracting more consumers. Second, when BM retailers adopt the WEB strategy, the adjustments made to nonexclusive product prices are influenced by the decisions made by online retailers. If the unit variable service cost borne by online retailers is relatively low, those retailers tend to lower their product prices after the implementation of an exclusive product strategy with the goal of obtaining market share. In these cases, BM retailers usually choose to emulate this price reduction with the aim of remaining competitive. Conversely, if the unit variable service cost borne by online retailers is relatively high, those retailers tend to increase their product prices, and BM retailers tend to follow suit by increasing the prices of nonexclusive products with the goal of preserving their profits.

Second, exclusive product strategies can help BM retailers increase their market share, but different strategies have varying impacts on the structure of demand for exclusive and nonexclusive products. First, the implementation of exclusive product strategies alters consumers’ purchase choices, particularly by redirecting some consumers who originally intended to purchase online or to engage in showrooming to make purchases at BM stores. This shift is primarily due to the uniqueness and exclusivity of exclusive products, which enable BM retailers to attract and retain more customers, especially those who exhibit strong preferences for exclusive products. Simultaneously, as mentioned, following the implementation of exclusive product strategies, BM retailers emulate online retailers by adjusting the prices of their nonexclusive products with the goal of establishing a balance between profitability and competitiveness. Second, although both types of exclusive product strategies generate the same increase in overall demand, the WEB strategy results in higher demand for exclusive products and lower demand for nonexclusive products. This disparity may be because well-known brands are characterized by established significant levels of brand recognition and consumer trust. Despite the overall increase in demand resulting from both strategies, the demand for exclusive products exhibits a more prominent increase under the WEB strategy because of the high level of recognition and trust associated with established brands, thereby suppressing the demand for nonexclusive items. Under the SEB strategy, owing to the relatively low popularity of the store’s private brand, the difference in demand between exclusive and nonexclusive products may be smaller. This explanation accounts for the contrasting structures observed regarding the demand for exclusive and nonexclusive products between the two strategies.

Third, the exclusive product strategy can indeed serve as an effective tool that BM retailers can use to circumvent the negative impacts of consumer showrooming behavior, thereby ensuring that those retailers always benefit from the adoption of this strategy. However, the dominance of the SEB or WEB strategies depends on the probability that consumers may evaluate and purchase the best-fit products online, as well as on the proportion of low-type consumers. When the probability that consumers can evaluate and purchase best-fit products online is low, and the proportion of low-type consumers is relatively high, the SEB strategy can generate higher profits for BM retailers. Otherwise, the BM retailers should choose the WEB strategy.

Furthermore, the consistency between numerical research and theoretical analysis also indicates that BM retailers can benefit from the implementation of exclusive product strategies. By employing such strategies and providing consumers with superior service and shopping experiences, BM retailers are able not only to attract a larger consumer base to their BM stores but also to increase their sales and profit margins. These benefits, in turn, offer them advantageous positions in the prevalent competitive landscape, which is characterized by showrooming practices on the part of consumers. Inevitably, as online retailers respond to this paradigm shift, they are compelled to adjust their strategic approaches to counteract the influence of exclusive product strategies adopted by their BM counterparts. Hence, it is imperative to offer relevant managerial insights that are grounded in the key findings of our theoretical explorations.

6.2. Managerial Insights

In light of the theoretical analysis and findings discussed, the following managerial insights for BM retailers are proposed.

First, BM retailers should continuously monitor market changes and consumer behavior with the goals of clarifying their brand positioning and selecting appropriate exclusive product strategies. Typically, the SEB strategy permits BM retailers to cultivate a distinct brand image by designing and promoting their own branded products. The advantage of this strategy lies in the complete control over product design, manufacturing, and marketing that it offers the retailer, thereby ensuring alignment between the product’s uniqueness and the store’s overall positioning. Conversely, the WEB strategy aims to attract customers and boost sales by exploiting the influence and consumer loyalty of established, well-known brands. By engaging in collaborations with these brands, BM retailers can quickly gain consumer trust and recognition, thereby reducing the difficulty and costs of market promotion. Therefore, in practice, if the target market values product uniqueness and innovation and if consumers have a limited ability to evaluate products online or find their preferred products online, the SEB strategy may be more suitable. Alternatively, if brand recognition and reputation are prioritized and if consumers either possess strong online evaluation skills or the probability that consumers can find the best-fit products online is high, the WEB strategy might prove to be advantageous.

Second, the optimization of product assortment and pricing strategies should be emphasized. When BM retailers implement an exclusive product strategy, they must optimize their product mix and pricing approach with the goals of ensuring the effectiveness of their strategies and maximizing their profits. Exclusive products should be priced higher to reflect their uniqueness and brand value, whereas nonexclusive products’ prices can be adjusted flexibly on the basis of market demand and competition with the aim of maintaining competitiveness. This pricing strategy not only highlights the distinctiveness of exclusive products, thus enabling BM retailers to achieve higher marginal revenues, but also demonstrates the flexibility of nonexclusive offerings, thereby allowing these retailers to balance profitability with competitiveness by adjusting their prices.

Third, enhancing service quality and the shopping experience is crucial. When BM retailers choose SEB or WEB-exclusive product strategies, they should strive to increase their service standards and enhance their shopping experience. By providing consumers with professional product consultations, excellent after-sales services, and a comfortable shopping environment, consumer satisfaction and loyalty can be increased. This approach not only encourages more consumers to make offline purchases but also bolsters the brand image and reputation of BM retailers.

6.3. Limitations and Directions for Future Research

The aim of this study is to transform consumers’ showrooming behavior by transforming its potentially negative impact on BM retailers into a positive effect through the introduction of an exclusive product strategy. This approach is designed to enhance the competitiveness and profitability of BM stores while providing customers with a superior and more personalized shopping experience. However, certain assumptions made in our analysis may not hold in reality, thus highlighting certain limitations of our research. For instance, our study focuses solely on a duopoly competitive environment involving only a single BM retailer and a single online retailer. However, in the actual retail market, multiple BMs and online retailers coexist and compete in various contexts, such as price, product quality, service, product delivery speed, and the shopping experience. Additionally, we assume that both exclusive and nonexclusive products belong to a singular product category, whereas in reality, it is more common for retailers to sell multiple types of products simultaneously. Furthermore, our research relies primarily on static analysis, thereby overlooking dynamic changes and long-term effects in the market. In contrast, in the real world, market conditions, consumer preferences, and competitive strategies are all subject to change over time. Certainly, these limitations highlight various directions for future research on this topic. Possibilities such as exploring a competitive environment featuring multiple BMs and online retailers, examining the relationships among various types of exclusive and nonexclusive products, and developing dynamic models that are capable of capturing market fluctuations and long-term impacts represent viable directions for future investigations.