Introduction

The future of retail lies in omnichannel retailing, with both brand manufacturers and retailers exploring how to undergo the transformation and upgrade to omnichannel strategies (Chopra, 2015). In an omnichannel retail environment, businesses allow consumers to switch freely between all channel touchpoints, enabling them to experience seamless cross-channel services. Each channel touchpoint contributes a certain level of service utility or value to consumers, ultimately facilitating the completion of their shopping journey. As a result, omnichannel provides consumers with a consistent or seamless shopping experience (Brynjolfsson et al., 2013; Bell et al., 2014; Saghiri et al., 2017; Timoumi et al., 2022). However, achieving omnichannel strategic transformation remains a strategic challenge for brand manufacturers.

Globally, successful examples of omnichannel transformation are represented by retail giants such as Walmart, Apple, Xiaomi, Uniqlo, Amazon, Alibaba, and JD. These companies are powerful brands with ample financial resources, often adopting an integrated omnichannel strategy by investing in self-operated channels. For instance, Amazon’s acquisition of Whole Foods, Alibaba’s acquisition of Intime Department Store, and JD, originally an e-commerce platform, achieved omnichannel transformation by establishing physical stores. However, small and medium-sized brand manufacturers often find it challenging to implement integrated omnichannel strategies. This is mainly due to their smaller scale of operations, limited capital, difficulties in financing, and the high financial requirements and risks associated with integrated omnichannel strategies, which may exceed the risk tolerance of smaller players compared to large corporations or dominant brands.

With the rapid development of e-commerce platforms like Amazon and Taobao, these large platforms have provided infrastructure and operational convenience for small and medium-sized manufacturers to establish online channels. In the process of omnichannel transformation, these manufacturers still face the challenge of integrating offline and online channels to achieve true omnichannel retailing. Simply adding online channels is not sufficient for a genuine transformation into omnichannel retailers, as evidenced by the opposition from franchisees experienced by the shoe brand Daphne after establishing an online direct sales model (Qi, 2016). Additionally, when an integrated channel integration strategy fails, further exploration is needed on how manufacturers can collaborate with downstream physical retailers to implement contractual integration models.

Previous literature on omnichannel integration strategies has mostly focused on consumer and channel single touchpoints, where all shopping journeys are completed within a single channel (e.g., Cocco and Demoulin, 2022; Sharma and Fatima, 2024). However, there is limited research on channel migration behavior. Mehra et al. (2018) earlier considered consumers’ cross-channel shopping behavior, but they ignored omnichannel scenarios in which consumers switch between any channel touchpoint and failed to fully explain the nature of omnichannel. Specifically, this study will attempt to explore the following research questions:

  1. (1)

    What is the optimal collaboration strategy for small and medium-sized brand manufacturers in omnichannel transformation?

  2. (2)

    How can small and medium-sized brand manufacturers effectively integrate online and offline channel services to achieve omnichannel transformation?

  3. (3)

    How to understand consumers’ cross-channel experience behavior in an omnichannel scenario and its impact on channel integration strategies?

To address these research questions, this study starts by differentiating the characteristics of consumers’ cross-channel experience behavior and distinguishing the perceived service value differences between online and offline channel activities. These differences are then incorporated into a game theory model for analysis. Simultaneously, by constructing a dual-channel system involving brand manufacturers and traditional retailers, this study compares and analyzes performance before and after implementing channel integration strategies to identify the prerequisites for these strategies. Moreover, A sensitivity analysis focusing on key parameters was conducted to analyze the trends in wholesale prices, service levels, demand, and profits, providing crucial guidance for decision-makers. Finally, this study proposes a profit compensation mechanism for implementing channel integration strategies, thus offering practical and theoretical value.

Literature review

The literature related to this study is mainly divided into three aspects: retail channel integration, channel service strategy, and omnichannel retail operation.

First, the evolution of retail channel integrations has become a focal point in contemporary literature. Scholars emphasize the significance of seamless multichannel experiences for retailers to stay competitive in the dynamic marketplace. Neslin (2022) constructs a continuum framework of omnichannel integration that combines the customer journey (from search to purchase to aftersales) and channel selection (online versus offline) to generate a set of omnichannel strategies. It is suggested that omnichannel integration should consider customer journey and channel selection comprehensively, and formulate strategies according to consumers and marketing phenomena. Additionally, Zhang et al. (2024a, 2024b) point out that in omnichannel integration, personalization and connectivity influence the customer experience, while personal innovation and self-efficacy also play an important role. Optimizing the customer experience is the key to improving customer loyalty and has important implications for omnichannel retailers. Furthermore, Timoumi et al. (2022) review 50 empirical retail research papers published over the past 20 years, explore the impact of omnichannel retail marketing strategies on retailers’ internal cross-channel effects, and find that omnichannel integration strategies generally have a positive impact on retailers’ overall performance. Yin et al. (2022) find that omnichannel integration has a positive impact on brand experience and customer retention, but the specific effects vary depending on purchasing behavior and brand experience, and retailers should develop precise omnichannel strategies based on customer needs and purchasing behavior. However, while the above studies all examine the quality and effect of channel integration from a holistic perspective, this study innovatively refines channel integration, differentiates it from vertical integration, and considers contractual channel integration strategies.

Second, the retail landscape’s service strategy is a focal point in literature, with scholars delving into various aspects to understand and enhance customer experiences. Nguyen and Nguyen (2023) reveal key aspects of customer experience by analyzing online reviews of Vietnamese hotels on TripAdvisor, proposing an analytical model to understand customer emotions, and aiding hotels in enhancing their service quality. Gavrila Gavrila et al. (2023) find that proper application of robotic process automation can improve consumer satisfaction, emphasizing the need to consider end-user satisfaction in technology implementation. Shen and Wang (2024) discover that persona perception facilitates shared value creation, which subsequently affects customer experience. Tyrväinen et al. (2020) emphasize the importance of retail service with personalization and hedonic motivation, asserting that tailored interactions contribute significantly to customer satisfaction and loyalty. Furthermore, Meyer et al. (2023) explore the role of technology in service strategy, particularly in the context of service robots. The study suggests that service robots promise to revitalize physical retail value creation, but retail managers face the challenge of balancing the needs of customers and front-line employees in their implementation. Different from the above studies, this study also considers online and offline service levels, cross-channel consumer demand generated by service cooperation, and cross-channel service experience behaviors of consumers, to get closer to consumers’ actual shopping and service value realization in the omnichannel retail environment.

Last, omnichannel retail operations have garnered significant attention in the literature, reflecting the transformative impact of seamlessly integrating various channels. Song and Cheng (2023) establish a nonlinear constrained optimization model to analyze the impact of privacy issues on the strategy of traditional single-channel retailers in the transition to omnichannel sales, and propose the optimal revenue and pricing strategies for retailers facing profit-seeking and privacy-sensitive consumers in discount and full-price periods. Examining the role of technology, Thaichon et al. (2023) identify emerging issues including customer value, customer experience, in-store selection and online buying, and customer privacy concerns from a customer perspective. At the same time, key issues such as channel integration, personalization, and resource challenges are identified from a retailer’s perspective. Yang et al. (2022) explore how omnichannel strategies affect retailers’ physical store operations and found that the specific effects depend on product type and cost structure. The strategy may promote product market expansion and customer choice shift, with different effects on inventory and profit. Furthermore, Jiu (2022) investigates the operational strategies of omnichannel retailers in multi-cycle, multi-product, limited-capacity retail networks and finds that the robust two-stage approach of the “ship from store” strategy can optimize inventory management and reduce costs. Different from the above studies, this study analyzes the omnichannel operation strategy from the perspective of different channel service integration.

The model

Firms

This study considers a manufacturer producing a single product, which is distributed both through traditional retailers in offline channel and through online channel (e.g., Amazon, Taobao, and Tmall), as shown in Fig. 1. This retail system is considered because this mixed sales method is commonly seen in reality, such as Doggy Appliances, NVC Lighting, etc. Due to the maturity of the online retail market, the cost for merchants to open online channels is also relatively low, especially for small and medium-sized merchants, who can directly sell on major domestic e-commerce platforms such as Taobao, Tmall, JD.com, VIP.com, and Gome Online. For convenience, this study uses the subscript “o” to represent the online store, “r” to represent the offline physical retailer, and “c” to represent the integrated channel, respectively. The superscript “n” represents the situation without channel integration, while the superscript “i” represents the situation with channel integration.

Fig. 1
figure 1

Channel structure.

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Additionally, this study considers a decentralized channel model, where the channel members make independent decisions, aiming to maximize their own profits. In terms of the game setting, following by the prior studies in modeling pricing and service level decisions such as Chen et al. (2008), Tsay and Agrawal (2000), and Fan et al. (2021), I assume that the manufacturer and retailer first conduct a Stackelberg game on the wholesale price, followed by a Nash game on the service level. When both parties engage in price negotiation, considering that small and medium-sized manufacturers are generally weaker, it is assumed that the retailer has price leadership (e.g., Wan et al. 2023). Furthermore, it is assumed that the product market is perfectly competitive, and the product selling price \(p\) is the market-clearing price. The retailer’s price leadership is reflected in its priority in claiming marginal profits.

Consumers

To capture the key characteristics of consumer choices in a multichannel environment, I employ a Hotelling-type model adapted for multichannel contexts (Hotelling, 1929; Tyagi, 2004; Liu and Zhang, 2006; Liu and Tyagi, 2011). Unlike the original Hotelling model where \(x\) represents physical location and \(t\) transportation cost, my framework interprets \(x\) as the consumer’s ideal channel preference and \(t\) as the adaptation cost to non-ideal channels, consistent with recent literature (e.g., Jiang and Srinivasan, 2016; Gao and Su, 2017; Nageswaran, Hwang, and Cho, 2024; Yin and Huang, 2025). Specifically, I assume that consumers are heterogeneous in their channel preferences, represented by a parameter \(x\) (interpreted as their ideal channel position), uniformly distributed along a line segment [0, 1]. This follows the classic Hotelling (1929) framework, where \(x\) denotes the consumer’s preferred “location” in a channel space, with 0 and 1 corresponding to purely offline and online preferences, respectively.

Following the adaptation cost interpretation in Hotelling-based literature (e.g., Dewan et al., 2003), I define \(t\) as the unit adaptation cost per distance, capturing the disutility a consumer incurs when their ideal channel preference (\(x\)) deviates from a channel’s position. This directly links to the utility reduction term, where \({h}_{j}\) is the distance between x and channel \(j\). For example, a consumer can purchase a Nike sports shirt from either a physical store or JD.com. Although consumers may have the same taste preference for the product style or other attributes (\(t\)), differences in their channel preference (\(x\)) can lead to different misfit costs. This setup ensures that a consumer’s utility decreases linearly with the “distance” to their preferred channel, aligning with spatial competition theory and its extensions to service channels (Liu and Zhang, 2006).

Let \(v\) represent the consumers’ valuation of the product, the consumer’s net utility from purchasing via channel \(j\) is thus \(v-t{h}_{j}\), where \(t{h}_{j}\) quantifies the total adaptation cost due to channel preference mismatch. Following the previous studies (e.g., Jiang and Srinivasan, 2016), I normalize the total number of consumers to 1. In addition, I assume that \(v\) is large enough to ensure that they will all buy the product, so that the market is fully covered (e.g., Li and Jain, 2016; Jiang and Srinivasan, 2016). This assumption helps to avoid discussions unrelated to the research question of this study, so that the research question focuses on the cross-channel experience effect of consumers. In addition, each consumer buys at most one unit of the product. To ensure the existence of an equilibrium solution, I assume that the unit marginal profit (\(p-c\)) of the product is sufficiently large.

Cross-channel experiencing behavior

Regardless of online shopping or offline shopping, consumers’ shopping experience is composed of multiple different service activities (Fan et al., 2022). Cross-channel consumers can shuttle between different channels and experience different online and offline shopping activities at the same time to complete shopping purposes. Following the way of cross-channel disutility transaction by Gao and Su (2017), the cross-channel disutility \(t{h}_{c}\) is a weighted sum of the adaptation costs from offline and online activities:

$$t{h}_{c}=t\left[\mathop{\underbrace{\alpha {h}_{r}}}\limits_{{\rm{Offline\; mismatch}}}+\mathop{\underbrace{\left(1-\alpha \right){h}_{o}}}\limits_{{\rm{Online\; mismatch}}}\right],$$
(1)

where \(\alpha\) reflects the proportion of activities requiring physical interaction (called “offline activity proportion”, such as try-ons, shopping guides, pick-up, return, and exchange), and \((1-\alpha )\) reflects the online-dominant activities (called “online activity proportion”, such as obtaining product information, pre-sale consultation, payment, and order placing); Also, \({h}_{r}=x\) for offline, \({h}_{o}=1-x\) for online. This formulation generalizes the classic Hotelling cost structure to hybrid channel contexts.

According to the empirical study of Sousa et al. (2015), different types of service activities bring different values to consumers through online and offline channels. Therefore, I assume that the proportion \(\beta \in (\mathrm{0,1})\) of perceived service value \({s}_{c}\) in cross-channel shopping comes from the offline channel (called “offline value proportion”); the other proportion \((1-\beta )\) of perceived service value \({s}_{c}\) comes from the online channel (called “online value proportion”). Let \({s}_{r}\) and \({s}_{o}\) denote the service value when buying solely offline or solely only, respectively. Following the way of cross-channel service value transaction by Fan et al. (2022), the service value received by consumers across channels can be derived by \({s}_{c}=\beta {s}_{r}+(1-\beta ){s}_{o}\). In addition, this study defines the service input cost as a quadratic function \({k}_{j}{s}_{j}^{2}\) to reflect the diseconomy of the scale of the service cost input, where \(j=r,o\). The quadratic cost function of service investment is widely used in economic and game-theoretic models, such as Wang (2022), Wang and Wang (2022), and Zhang et al. (2019a, 2019b). In addition, the service input cost of physical stores is usually higher than that of online channels (such as rent, decoration, labor, and other additional costs), so \({k}_{r} > {k}_{o}\).

Market demand

Based on the above analysis and prior studies in marketing and operation management (e.g., Iyer, 1998; Iyer and Kuksov, 2012; Kuksov and Liao, 2018), given the channel integration and service decisions, the net utility obtained by consumers from purchasing products in channel \(j\) can be represented as \({U}_{j}=v-t{h}_{j}+{s}_{j}-p\), where (i) \({h}_{r}=x\) for \(j=r\), (ii) \({h}_{o}=1-x\) for \(j=o\), and (iii) \({h}_{c}=\alpha {\rm{x}}+\left(1-\alpha \right)(1-{\rm{x}})\) and \({s}_{c}=\beta {s}_{r}+(1-\beta ){s}_{o}\) for \(j=c\). Next, I will derive the market demand functions under the case without and with channel integration.

Under the case without channel integration (i.e., case \(n\)), let \({x}_{{ro}}\) be the marginal consumer who is indifferent between the offline channel and online channel (i.e., \({U}_{r}={U}_{o}\)), which is equal to \(v-{tx}+{s}_{r}-p=v-t(1-x)+{s}_{o}-p\). I easily obtain that \({\hat{x}}_{{ro}}=\frac{1}{2}-\frac{{s}_{o}-{s}_{r}}{2t}\). That is, consumers with \(x\le {\hat{x}}_{{ro}}\) prefer to buy from the physical retailer, and those with \(x > {\hat{x}}_{{ro}}\) prefer to buy from the online store. Furthermore, I obtain that the offline channel demand is \({D}_{r}^{n}={\hat{x}}_{{ro}}\), and the online channel demand \({D}_{o}^{n}=1-{\hat{x}}_{{ro}}\). The results are shown in Fig. 2 (1). Thus, under the case \(n\), the demand functions are as follows:

$$\left({D}_{r}^{n},\,{D}_{o}^{n}\right)=\left(\frac{1}{2}-\frac{{s}_{o}-{s}_{r}}{2t},\,\frac{1}{2}+\frac{{s}_{o}-{s}_{r}}{2t}\right).$$
(2)
Fig. 2
figure 2

Schematic diagram of consumer segmentation.

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Under the case with channel integration (i.e., case \(i\)), let \({\hat{x}}_{{rc}}\) be the consumer who is indifferent between both offline channel and cross-channel (i.e., \({U}_{r}={U}_{c}\)), which is equal \(v-{tx}+{s}_{r}-p=v-t\left[\alpha x+\left(1-{\rm{\alpha }}\right)\left(1-x\right)\right]+\left[\beta {s}_{r}+\left(1-\beta \right){s}_{o}\right]-p\). I easily obtain that \({\hat{x}}_{{rc}}=\frac{1}{2}-\frac{\left(1-\beta \right)\left({s}_{o}-{s}_{r}\right)}{2\left(1-{\rm{\alpha }}\right)t}\). That is, consumers with \(x\le {\hat{x}}_{{rc}}\) prefer to buy from the physical retailer, and those with \(x > {\hat{x}}_{{rc}}\) prefer to buy from the cross-channel or online channel.

Then, let \({\hat{x}}_{{co}}\) be the consumer who is indifferent between both cross-channel and online channel (i.e., \({U}_{c}={U}_{o}\)), which is equal to \(v-t\left[\alpha x+\left(1-{\rm{\alpha }}\right)\left(1-x\right)\right]+\left[\beta {s}_{r}+\left(1-\beta \right){s}_{o}\right]-p=v-t(1-x)+{s}_{o}-p\). I easily obtain that \({\hat{x}}_{{co}}=\frac{1}{2}-\frac{\beta \left({s}_{o}-{s}_{r}\right)}{2{\rm{\alpha }}t}\). That is, consumers with \(x\le {\hat{x}}_{{co}}\) prefer to buy from the physical retailer or the cross-channel, and those with \(x > {\hat{x}}_{{co}}\) prefer to buy from the online channel.

The results are shown in Fig. 2 (1), one can observe that there shall be no cross-channel shopping consumers if and only if \({\hat{x}}_{{rc}}\ge {\hat{x}}_{{co}}\) holds. Therefore, it should satisfy \({\hat{x}}_{{rc}} < {\hat{x}}_{{co}}\), which leads to \(({\rm{\alpha }}-\beta )\left({s}_{o}-{s}_{r}\right) > 0\). Furthermore, I obtain that (i) the offline channel demand \({D}_{r}^{i}={\hat{x}}_{{rc}}\), (ii) the cross-channel consumption demand \({D}_{c}^{i}={\hat{x}}_{{co}}-{\hat{x}}_{{rc}}\), and (iii) the online channel demand \({D}_{o}^{i}=1-{\hat{x}}_{{co}}\). Thus, under case \(i\), the demand functions are as follows:

$$\left({D}_{r}^{i},{D}_{c}^{i},\,{D}_{o}^{i}\right)=\left(\frac{1}{2}-\frac{\left(1-\beta \right)\left({s}_{o}-{s}_{r}\right)}{2\left(1-{\rm{\alpha }}\right)t},\,\frac{\left({\rm{\alpha }}-\beta \right)\left({s}_{o}-{s}_{r}\right)}{2{\rm{\alpha }}\left(1-{\rm{\alpha }}\right)t},\,\frac{1}{2}+\frac{\beta \left({s}_{o}-{s}_{r}\right)}{2{\rm{\alpha }}{\rm{t}}}\right),$$
(3)
$${Subject\; to}:\,({\rm{\alpha }}-\beta )\left({s}_{o}-{s}_{r}\right) > 0.$$

Profit functions

If the channel provides cross-channel services to consumers after integration and there is cross-channel demand, part of the profit generated by the demand belongs to the manufacturer, and the rest belongs to the retailer. Among them, how the profit distribution ratio affects the channel integration decision will be discussed in detail in Numerical Analysis Section. At the same time, although the product price is the market-clearing price, because the manufacturer and the retailer respectively provide consumers with a certain level of service, the competition in the service dimension is formed, and the corresponding service cost needs to be paid. In addition, manufacturers will incur certain costs when they open direct stores on e-commerce platforms such as Taobao or Tmall. Therefore, referring to the research of Jiang et al. (2011), manufacturers will incur fixed costs \(F\) (such as entry fees) and unit costs or commission \(\sigma\) when selling products on e-commerce platforms. Since the fixed cost incurred by the manufacturer is a sunk cost, it is set to 0 and \(\sigma\) is small enough to ensure that the manufacturer will maintain the online channel. Therefore, the retailer’s profit \({\pi }_{r}\) and the manufacturer’s profit \({\pi }_{m}\) can be, respectively, expressed as follows:

$${\pi }_{r}=\left(p-w\right){D}_{r}-{k}_{r}{s}_{r}^{2},$$
(4)
$${\pi }_{m}=(p-c-\sigma ){D}_{o}+\left(w-c\right){D}_{r}-{k}_{o}{s}_{o}^{2}.$$
(5)

The Stackelberg game sequence is as follows: the retailer first proposes a marginal profit requirement to maximize its own profit, and then the manufacturer determines the wholesale price based on this marginal profit requirement and the market price. The game sequences are as follows: given the wholesale price and market price, the manufacturer and retailer simultaneously decide on the service level investment decisions for their respective channels to maximize their profits. The superscript “*” denotes the equilibrium and all model symbols used in this study can be found in Table 1.

Table 1 Summary of notions.
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Analysis

Benchmarking retail system without channel integration

In the channel structure of retailer-led price leadership, the retailer and the manufacturer first sign a long-term wholesale agreement. First, the retailer puts forward the marginal profit requirement \(m\), so the wholesale price \(w\) is determined immediately, namely \(w=p-m\). Next, the manufacturer and the retailer simultaneously decide the service level \({s}_{o}\) and \({s}_{r}\) for their respective channels. Finally, the consumers choose the channel to purchase the goods, and the manufacturer and the retailer realize their profits. According to this game sequence, Lemma 1 can be obtained by solving the game through backward induction.

Lemma 1

When there is no channel integration, the equilibrium wholesale price \({{w}^{n}}^{* }\), the of service levels of each channel \({{s}_{r}^{n}}^{* }\) and \({{s}_{o}^{n}}^{* }\), the market demand \({{D}_{r}^{n}}^{* }\) and \({{D}_{o}^{n}}^{* }\), and the profits of each party \({{\pi }_{r}^{n}}^{* }\) and \({{\pi }_{m}^{n}}^{* }\) are listed in Table 2, respectively.

Table 2 Results of equilibrium decision-making in the case of without channel integration and with channel integration.
Full size table

Proof

When there is no channel integration, referring to the Eqs. (4) and (5), one can obtain \({\pi }_{r}^{n}={m}^{n}{D}_{r}^{n}-{k}_{r}{{s}_{r}^{n}}^{2}\) and \({\pi }_{m}^{n}=\left(p-c-\sigma \right){D}_{o}^{n}+\left(p-{m}^{n}-c\right){D}_{r}^{n}-{k}_{o}{{s}_{o}^{n}}^{2}\). Next, Solving the game backwards. In stage 2 of the game, given \({m}^{n}\), the manufacturer and the retailer simultaneously decide the service level \({s}_{o}^{n}\) and \({s}_{r}^{n}\) to maximized their respective profit. As the profit function \({\pi }_{r}^{n}\) (\({\pi }_{m}^{n}\)) is concave concerning the service level \({s}_{r}^{n}\) (\({s}_{o}^{n}\)), on solving the first-order conditions \(\frac{\partial {\pi }_{r}^{n}}{\partial {s}_{r}^{n}}=\frac{\partial {\pi }_{m}^{n}}{\partial {s}_{o}^{n}}=0\), one can obtain \({s}_{r}^{n}({m}^{n})=\frac{{m}^{n}}{4{k}_{r}t}\) and \({s}_{o}^{n}({m}^{n})=\frac{{m}^{n}-\sigma }{4{k}_{o}t}\). Inserting \({s}_{r}^{n}({m}^{n})\) and \({s}_{o}^{n}({m}^{n})\), one can obtain \({\pi }_{r}^{n}\left({m}^{n}\right)=\frac{{m}^{n}({k}_{o}\left({m}^{n}+8{k}_{r}{t}^{2}\right)-2{k}_{r}({m}^{n}-\sigma ))}{16{k}_{o}{\rm{ks}}{t}^{2}}\). In stage 1 of the game, the retailer sets the marginal profit requirement \({m}^{n}\) to maximize its profit. As the profit function \({\pi }_{r}^{n}\left({m}^{n}\right)\) is concave concerning \({m}^{n}\), on solving the first-order condition \(\frac{\partial {\pi }_{r}^{n}\left({m}^{n}\right)}{\partial {m}^{n}}=0\), one can obtain \({{m}^{n}}^{* }=\frac{{k}_{r}(4{k}_{o}{t}^{2}+\sigma )}{2{k}_{r}-{k}_{o}}\). Inserting \({{m}^{n}}^{* }\), one can obtain the results summarized in Lemma 1.

From Lemma 1, it is easy to see that when the difference between online and offline channels is greater (a larger \(t\)), the wholesale price is smaller, the service level is higher, and the retailer’s profit is higher while the manufacturer’s profit is lower. It can be seen that channel differentiation is more beneficial to retailers, because the expansion of channel differentiation will slow down the competition among channels. Therefore, retailers with price leadership can increase their marginal profit requirement. In addition, the simultaneous improvement of the service level will benefit consumers. Comparing online and offline service levels, it can be seen that the service level of offline channels is lower than that of online channels, which is caused by the fact that the marginal service input cost of offline channels is higher than that of online channels, which also leads to the fact that the offline market demand is lower than that of the online market.

Omnichannel retail system with contractual channel integration

According to the previous analysis, when a manufacturer and a retailer sign an agreement for channel integration, once the condition of cross-channel consumption demand \({D}_{c}^{i}\) is established, some consumers in the original demand will switch to cross-channel shopping. Assuming that these consumers place orders online or offline randomly, the proportion \(\eta \in (\mathrm{0,1})\) of this type of consumers place orders online and the other proportion \(1-\eta\) of this type of consumers place orders offline. For the sake of comparison, the average value \(\eta\) is taken \(\frac{1}{2}\) in this section, and I will discuss in detail in Numerical Analysis Section the impact of the change in value \(\eta\) on the main conclusions. Specifically, the quantity of \({D}_{c}^{i}/2\) consumers place orders online, and the manufacturer makes a marginal profit of \(\left(p-c-\sigma \right)\) per unit of product; When the quantity of \({D}_{c}^{i}/2\) consumers who place orders offline, retailers earn a marginal profit of \(\left(p-w\right)\) per unit of product. Therefore, the manufacturer’s profit \({\pi }_{m}^{i}\) and the retailer’s profit \({\pi }_{r}^{c}\) in this case can be rewritten as follows:

$${\pi }_{r}^{i}=\left(p-w\right)\left({D}_{r}^{i}+\frac{{D}_{c}^{i}}{2}\right)-{k}_{r}{s}_{r}^{2},$$
(6)
$${\pi }_{m}^{i}=(p-c-\sigma )\left({D}_{o}^{i}+\frac{{D}_{c}^{i}}{2}\right)+\left(w-c\right)\left({D}_{r}^{i}+\frac{{D}_{c}^{i}}{2}\right)-{k}_{o}{s}_{o}^{2}.$$
(7)

Similar to the case without channel integration, in the channel structure with retailer price leadership, the retailer and the manufacturer first sign a long-term wholesale agreement, and the retailer first sets the marginal profit \(m\), so the wholesale price \(w\) is determined immediately. Next, the manufacturer and the retailer simultaneously decide the service level \({s}_{o}\) and \({s}_{r}\) of their respective channels. Finally, the consumers choose the channel to purchase the goods, and the manufacturer and the retailer realize the sales profit. According to this game sequence, Lemma 2 can be obtained by backward induction.

Lemma 2

Under the contractual channel integration mode, the equilibrium wholesale price \({{w}^{i}}^{* }\), the service levels \({{s}_{r}^{i}}^{* }\) and \({{s}_{o}^{i}}^{* }\), the market demands \({{D}_{r}^{i}}^{* }\), \({{D}_{c}^{i}}^{* }\), and \({{D}_{o}^{i}}^{* }\), and the firms’ profits \({{\pi }_{r}^{i}}^{* }\) and \({{\pi }_{m}^{i}}^{* }\) are listed in Table 2, respectively.

Proof

When there is no channel integration, referring to the eqs. (6) and (7), one can obtain \({\pi }_{r}^{i}=\left(p-w\right)\left({D}_{r}^{i}+\frac{{D}_{c}^{i}}{2}\right)-{k}_{r}{s}_{r}^{2}\) and \({\pi }_{m}^{i}=(p-c-\sigma )\left({D}_{o}^{i}+\frac{{D}_{c}^{i}}{2}\right)+\left(w-c\right)\left({D}_{r}^{i}+\frac{{D}_{c}^{i}}{2}\right)-{k}_{o}{s}_{o}^{2}\). Next, Solving the game backwards. In the stage 2 of the game, given \({m}^{i}\), the manufacturer and the retailer simultaneously decide the service level \({s}_{o}^{i}\) and \({s}_{r}^{i}\) to maximized their respective profit. As the profit function \({\pi }_{r}^{i}\) (\({\pi }_{m}^{i}\)) is concave concerning the service level \({s}_{r}^{i}\) (\({s}_{o}^{i}\)), on solving the first-order conditions \(\frac{\partial {\pi }_{r}^{i}}{\partial {s}_{r}^{i}}=\frac{\partial {\pi }_{m}^{i}}{\partial {s}_{o}^{i}}=0\), one can obtain \({s}_{r}^{i}({m}^{i})=\frac{{m}^{i}\left(\alpha +\beta -2\alpha \beta \right)}{8{k}_{r}t\left(1-\alpha \right)}\) and \({s}_{o}^{i}({m}^{i})=\frac{(\beta +\alpha (1-2\beta ))({m}^{i}-\sigma )}{8{k}_{o}t(1-\alpha )\alpha }\). Inserting \({s}_{r}^{i}({m}^{i})\) and \({s}_{o}^{i}({m}^{i})\), one can obtain \({\pi }_{r}^{i}\left({m}^{i}\right)=\frac{{m}^{i}({k}_{o}(32{k}_{r}{t}^{2}{(1-\alpha )}^{2}{\alpha }^{2}+{m}^{i}{(\alpha +\beta -2\alpha \beta )}^{2})-2{k}_{r}{(\alpha +\beta -2\alpha \beta )}^{2}({m}^{i}-\sigma ))}{64{k}_{r}{k}_{o}{t}^{2}{(1-\alpha )}^{2}{\alpha }^{2}}\). In the stage 1 of the game, the retailer sets the marginal profit requirement \({m}^{i}\) to maximize its profit. As the profit function \({\pi }_{r}^{i}\left({m}^{i}\right)\) is concave concerning \({m}^{i}\), on solving the first-order condition \(\frac{\partial {\pi }_{r}^{i}\left({m}^{i}\right)}{\partial {m}^{i}}=0\), one can obtain \({{m}^{i}}^{* }=\frac{{k}_{r}(16{k}_{o}{t}^{2}{(1-\alpha )}^{2}{\alpha }^{2}+{(\alpha +\beta -2\alpha \beta )}^{2}\sigma )}{(2{k}_{r}-{k}_{o}){(\alpha +\beta -2\alpha \beta )}^{2}}\). Inserting \({{m}^{i}}^{* }\), one can obtain the results summarized in Lemma 2.

Lemma 2 reveals that the larger \(\sigma\) the retailer is, the higher the profit will be, and vice versa. Therefore, it can be seen that the improvement of operational efficiency of online channels is detrimental to physical retailers. At the same time, the larger \(\sigma\) the channel is, the higher the offline channel service level is, and also the higher the online channel service level is. It can be seen that the low operating efficiency of the online channel will stimulate manufacturers to improve the service level, while the physical retailers will reduce the service level.

Sensitivity analysis

Next, I conduct a sensitivity analysis of the equilibrium results obtained from Lemmas 1 and 2, aiming to reveal the response trends of key variables to the cost parameters \({k}_{r}\) and \({k}_{o}\), as well as the channel preference parameter \(t\), under two scenarios: without channel integration (Case n) and with channel integration (Case i). The sensitivity analysis is based on partial derivative calculations. This method was selected due to its ability to quantify the impact of small changes in input variables on the output, offering insights into the relative importance of each factor. The analysis results are summarized in Tables 3 and 4, respectively.

Table 3 Results of sensitivity analysis for the equilibrium outcomes in the case of without channel integration.
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Table 4 Results of sensitivity analysis for the equilibrium outcomes in the case of channel integration.
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As shown in Table 3, in the scenario without channel integration (Case n), the wholesale price \({{w}^{n}}^{* }\) increases monotonically with \({k}_{r}\) and decreases monotonically with \({k}_{o}\) and \(t\). The offline service level \({{s}_{r}^{n}}^{* }\) decreases monotonically with \({k}_{r}\), increases monotonically with \({k}_{o}\), and first decreases then increases monotonically with \(t\). The online service level \({{s}_{o}^{n}}^{* }\) decreases with \({k}_{r}\) and increases with \({k}_{o}\), both showing a positive correlation with \(t\). Furthermore, the profits of retailer (\({{\pi }_{r}^{n}}^{* }\)) and manufacturer (\({{\pi }_{m}^{n}}^{* }\)) first decrease and then increase with \({k}_{r}\).

According to Table 4, after introducing channel integration (Case i), the trends in wholesale price \({{w}^{i}}^{* }\), offline service level \({{s}_{r}^{i}}^{* }\), and online service level \({{s}_{o}^{i}}^{* }\) are influenced by \(\alpha\) and \(\beta\), exhibiting different patterns compared to the scenario without channel integration. Notably, the cross-channel demand \({{D}_{c}^{i}}^{* }\) also demonstrates sensitivity to the parameters. It is worth mentioning that the profits of retailer (\({{\pi }_{r}^{i}}^{* }\)) and manufacturer (\({{\pi }_{m}^{i}}^{* }\)) after integration show a more complex response to \({k}_{r}\), indicating that channel integration has a profound impact on profit distribution.

Overall, these sensitivity analysis results provide more insights into how various key economic variables change with different parameters, offering crucial guidance for decision-makers to formulate optimization strategies. By adjusting parameters such as cost coefficients, consumer preferences, and channel integration strategies, decision-makers can influence key indicators including wholesale prices, service levels, demand, and profits.

Comparative analysis

Combined with the above analysis and Lemmas, the conditions for cross-channel demand after omnichannel service integration can be obtained as described in the following Propositions:

Proposition 1

If and only if \(\alpha > \beta\) and \(\sigma < \frac{16{k}_{o}\left({k}_{r}-{k}_{o}\right){\left(1-\alpha \right)}^{2}{\alpha }^{2}{t}^{2}}{{k}_{r}{\left(\alpha +\beta -2\alpha \beta \right)}^{2}}\), there is cross-channel consumption demand.

Proof

If there is cross-channel consumption demand, the inequality \(({\rm{\alpha }}-\beta )\left({s}_{o}-{s}_{r}\right) > 0\) must be satisfied. Per Lemma 2, I have \({{s}_{o}^{i}}^{* }-{{s}_{r}^{i}}^{* }=\frac{16{k}_{o}({k}_{r}-{k}_{o}){(1-\alpha )}^{2}{\alpha }^{2}{t}^{2}-{k}_{r}{(\alpha +\beta -2\alpha \beta )}^{2}\sigma }{8{k}_{o}(2{k}_{r}-{k}_{o}){\left(1-\alpha \right)}^{2}{\alpha }^{2}{t}^{2}(\alpha +\beta -2\alpha \beta )}\), given \({k}_{r} > {k}_{o}\), such that \(8{k}_{o}\left(2{k}_{r}-{k}_{o}\right){\left(1-\alpha \right)}^{2}{\alpha }^{2}{t}^{2}\left(\alpha +\beta -2\alpha \beta \right) > 0\) always holds. \({{D}_{c}^{i}}^{* } > 0\) requires \(\sigma < \frac{16{k}_{o}\left({k}_{r}-{k}_{o}\right){\left(1-\alpha \right)}^{2}{\alpha }^{2}{t}^{2}}{{k}_{r}{\left(\alpha +\beta -2\alpha \beta \right)}^{2}}\) holds, which leads to \({\rm{\alpha }} > \beta\).

Proposition 1 shows that the premise of implementing a channel integration strategy is that the proportion of offline activities of consumers must be greater than the proportion of offline service value. Accordingly, the proportion of consumers’ online activities is smaller than the proportion of online service value. Take the typical omnichannel model of “buy-online-and-pick-up-in-store (BOPS)” as an example. This model gives full play to the advantages of fast information search on online platforms and convenient product experience in offline stores, respectively. Customers browsing product information through online e-commerce platforms and experiencing products in offline physical stores can form different service effects respectively. In addition, according to the consumer cross-channel experience of a subsidiary of IBM conducted by Edge Research in 2011, only 85% of the interviewed consumers felt the brand experience after channel integration (Lanlan and Li, 2018). Considering the differences between online and offline services and the intensity of individual consumers’ channel preferences, consumers will choose cross-channel shopping when the total utility obtained is greater than the total utility of pure online or pure offline shopping. Other consumers who prefer a single channel will choose their preferred channel to complete the shopping journey, which is consistent with intuitionistic. In addition, the unit cost of the online channel needs to be low enough to ensure that the manufacturer always introduces the online channel. Comparing the profit performance of all parties before and after adopting the channel integration strategy, the following Proposition can be obtained.

Proposition 2

(1) If \(\beta < \alpha \le \frac{1}{2}\) and \(\frac{8{k}_{o}(\alpha -{\alpha }^{2}){t}^{2}}{\alpha +\beta -2\alpha \beta } < \sigma < \frac{16{k}_{o}\left({k}_{r}-{k}_{o}\right){\left(1-\alpha \right)}^{2}{\alpha }^{2}{t}^{2}}{{k}_{r}{\left(\alpha +\beta -2\alpha \beta \right)}^{2}}\), such that \({{\pi }_{r}^{i}}^{* }\ge {{\pi }_{r}^{n}}^{* }\) and \({{\pi }_{m}^{i}}^{* }\le {{\pi }_{m}^{n}}^{* }\); (2) if \(\beta < \alpha \le \frac{1}{2}\) and \(\sigma \le \frac{8{k}_{o}(\alpha -{\alpha }^{2}){t}^{2}}{\alpha +\beta -2\alpha \beta }\), such that \({{\pi }_{r}^{i}}^{* }\le {{\pi }_{r}^{n}}^{* }\) and \({{\pi }_{m}^{i}}^{* }\le {{\pi }_{m}^{n}}^{* }\); (3) If \(\frac{1}{2} < \alpha \le 1\) and \(\beta < \alpha\), such that \({{\pi }_{r}^{i}}^{* } < {{\pi }_{r}^{n}}^{* }\) and \({{\pi }_{m}^{i}}^{* } > {{\pi }_{m}^{n}}^{* }\).

Proof

Per Lemmas 1 and 2, I have \({{\pi }_{m}^{i}}^{* }-{{\pi }_{m}^{n}}^{* }=\frac{(2\alpha -1)(\alpha -\beta )(\beta +\alpha (3-2\alpha -2\beta ))(192{{k}_{o}}^{2}{{k}_{r}}^{2}{t}^{4}{\left(1-\alpha \right)}^{2}{\alpha }^{2}+({k}_{r}^{2}-{k}_{o}^{2}){(\alpha +\beta -2\alpha \beta )}^{2}{\sigma }^{2})}{64{k}_{o}{(2{k}_{r}-{k}_{o})}^{2}{t}^{2}{(1-\alpha )}^{2}{\alpha }^{2}{(\alpha +\beta -2\alpha \beta )}^{2}}\) which leads to \({{\pi }_{m}^{i}}^{* }-{{\pi }_{m}^{n}}^{* }\le 0\) if \(\alpha \le \frac{1}{2}\), and \({{\pi }_{m}^{i}}^{* }-{{\pi }_{m}^{n}}^{* } > 0\) if \(\alpha > \frac{1}{2}\). Since \({{\pi }_{r}^{i}}^{* }-{{\pi }_{r}^{n}}^{* }=\frac{{k}_{r}\left(2\alpha -1\right)\left(\alpha -\beta \right)\left(\beta +\alpha \left(3-2\alpha -2\beta \right)\right)\left({\sigma }^{2}{\left(\alpha +\beta -2\alpha \beta \right)}^{2}-64{k}_{o}^{2}{t}^{4}{\left(1-\alpha \right)}^{2}{\alpha }^{2}\right)}{64{k}_{o}\left(2{k}_{r}-{k}_{o}\right){t}^{2}{\left(1-\alpha \right)}^{2}{\alpha }^{2}{\left(\alpha +\beta -2\alpha \beta \right)}^{2}}=\frac{{k}_{r}\left(2\alpha -1\right)\left(\alpha -\beta \right)\left(\beta +\alpha \left(3-2\alpha -2\beta \right)\right)}{64{k}_{o}\left(2{k}_{r}-{k}_{o}\right){t}^{2}}\left(\frac{\sigma }{\alpha -{\alpha }^{2}}+\frac{8{k}_{o}{t}^{2}}{\alpha +\beta -2\alpha \beta }\right)\left(\frac{\sigma }{\alpha -{\alpha }^{2}}-\frac{8{k}_{o}{t}^{2}}{\alpha +\beta -2\alpha \beta }\right)\), I have \(2{k}_{o}(1-\alpha )\alpha +{k}_{r}(2\alpha -1)(\alpha -\beta ) > 0\) holds when \(\alpha > \frac{1}{2}\); Given \(\sigma < \frac{16{k}_{o}\left({k}_{r}-{k}_{o}\right){\left(1-\alpha \right)}^{2}{\alpha }^{2}{t}^{2}}{{k}_{r}{\left(\alpha +\beta -2\alpha \beta \right)}^{2}}\) in Proposition 1, I have \(\sigma < \frac{8{k}_{o}(\alpha -{\alpha }^{2}){t}^{2}}{\alpha +\beta -2\alpha \beta }\) which leads to \(\frac{\sigma }{\alpha -{\alpha }^{2}}-\frac{8{k}_{o}{t}^{2}}{\alpha +\beta -2\alpha \beta } < 0\). Therefore, I obtain \({{\pi }_{r}^{i}}^{* }-{{\pi }_{r}^{n}}^{* } < 0\). Similarly, if \(\alpha \le \frac{1}{2}\), such that \(\sigma \le \frac{8{k}_{o}{t}^{2}}{\alpha +\beta -2\alpha \beta }\) which leads to \({{\pi }_{r}^{i}}^{* }-{{\pi }_{r}^{n}}^{* }\le 0\). If \(\frac{8{k}_{o}(\alpha -{\alpha }^{2}){t}^{2}}{\alpha +\beta -2\alpha \beta } < \sigma < \frac{16{k}_{o}\left({k}_{r}-{k}_{o}\right){\left(1-\alpha \right)}^{2}{\alpha }^{2}{t}^{2}}{{k}_{r}{\left(\alpha +\beta -2\alpha \beta \right)}^{2}}\), such that \({{\pi }_{r}^{i}}^{* }-{{\pi }_{r}^{n}}^{* }\ge 0\) holds.

As shown in Fig. 3, Proposition 2 shows that when the proportion of offline activities is large or the proportion of online activities is small, the implementation of the channel integration strategy is beneficial to the manufacturer but detrimental to the retailer. However, when the proportion of offline activities is small or the proportion of online activities is large, the implementation of channel integration strategy is always disadvantageous to the manufacturer; Channel integration is beneficial to retailers only when online channel costs are high, otherwise it is detrimental to both of them. Comparing the channel service level, it can be seen that when \(\frac{1}{2} < \alpha \le 1\) and \(\beta < \alpha\) there exists \({{s}_{o}^{n}}^{* } < {{s}_{o}^{i}}^{* }\). When \(\beta < \alpha \le \frac{1}{2}\) there exists \({{s}_{o}^{n}}^{* }\ge {{s}_{o}^{i}}^{* }\), it can be seen that a small proportion of offline activities will lead manufacturers to reduce online service investment. Meanwhile, when \(\frac{1}{2} < \alpha \le 1\) and \(\beta < \alpha\) there exists \({{w}^{i}}^{* } > {{w}^{n}}^{* }\), and when \(\beta < \alpha \le \frac{1}{2}\) there exists \({{w}^{i}}^{* }\le {{w}^{n}}^{* }\). A small proportion of offline activities will lead to a decrease in the manufacturer’s wholesale price. It can be concluded that when the proportion of offline activities is small or the proportion of online activities is large, manufacturers have no incentive to integrate channels. A similar principle holds for the other results of Proposition 2.

Fig. 3
figure 3

Profit comparison in the value range of α and β.

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Proposition 3

If \(\beta < \alpha \le \frac{1}{2}\), such that \({{\pi }_{T}^{i}}^{* }\le {{\pi }_{T}^{n}}^{* }\); if\(\,\frac{1}{2} < \alpha \le 1\) and \(\beta < \alpha\), such that \({{\pi }_{T}^{i}}^{* } > {{\pi }_{T}^{n}}^{* }\).

Proof

Per Lemmas 1 and 2, I have \(\begin{array}{ll}{{\pi }_{T}^{i}}^{* }-{{\pi }_{T}^{n}}^{* }=\left({{\pi }_{r}^{i}}^{* }+{{\pi }_{m}^{i}}^{* }\right)-\left({{\pi }_{r}^{n}}^{* }+{{\pi }_{m}^{n}}^{* }\right)\\=\frac{(2\alpha -1)(\alpha -\beta )(\beta +\alpha (3-2\alpha -2\beta ))(64{{k}_{o}}^{2}{k}_{r}\left({k}_{o}+{k}_{r}\right){t}^{4}{\left(1-\alpha \right)}^{2}{\alpha }^{2}+(3{{k}_{r}}^{2}-{{k}_{o}}^{2}-{k}_{o}{k}_{r}){(\alpha +\beta -2\alpha \beta )}^{2}{\sigma }^{2})}{64{k}_{o}{(2{k}_{r}-{k}_{o})}^{2}{t}^{2}{(1-\alpha )}^{2}{\alpha }^{2}{(\alpha +\beta -2\alpha \beta )}^{2}}\end{array}\); then, I have \(\left({{\pi }_{r}^{i}}^{* }+{{\pi }_{m}^{i}}^{* }\right)-\left({{\pi }_{r}^{n}}^{* }+{{\pi }_{m}^{n}}^{* }\right)\le 0\) when \(\beta < \alpha \le \frac{1}{2}\) holds, and \(\left({{\pi }_{r}^{i}}^{* }+{{\pi }_{m}^{i}}^{* }\right)-\left({{\pi }_{r}^{n}}^{* }+{{\pi }_{m}^{n}}^{* }\right) > 0\) when\(\,\frac{1}{2} < \beta < \alpha\) or \(\beta \le \frac{1}{2} < \alpha\) holds.

As shown in Fig. 3, Proposition 3 shows that when the proportion of offline activities is small or the proportion of online activities is large, the implementation of the channel integration strategy will reduce the total channel profit. On the contrary, when the proportion of offline activities is large or the proportion of online activities is small, the implementation of the channel integration strategy will increase the total channel profit. The reason is that in the former case, both parties will increase their service level and lead to cost pressure. In the latter case, on the contrary, both parties reduce the service level at the same time, thus saving the service cost. The underlying motivation comes from the consumer’s activity path, service heterogeneity and the difference in service cost efficiency between channels. The profit change of manufacturers and retailers determines their motivation to implement channel integration. When the proportion of offline activities is small or the proportion of online activities is large, retailers tend to integrate channels. When the proportion of offline activities is large or the proportion of online activities is small, the manufacturer prefers channel integration. Since the performance of both parties varies after channel integration, the cooperation suggestions as described in the following Proposition can be drawn.

Proposition 4

When \(\frac{1}{2} < \alpha \le 1\) and\(\,\beta < \alpha\), if the manufacturer subsidizes \(A\in ({\underline{A}},\bar{A})\) to the retailer, the adoption of channel integration strategy can achieve Pareto improvement of channel performance, where \({\underline{A}}=\frac{{k}_{r}\left(2\alpha -1\right)\left(\alpha -\beta \right)\left(\beta +\alpha \left(3-2\alpha -2\beta \right)\right)\left(64{k}_{o}^{2}{t}^{4}{\left(1-\alpha \right)}^{2}{\alpha }^{2}-{\sigma }^{2}{\left(\alpha +\beta -2\alpha \beta \right)}^{2}\right)}{64{k}_{o}\left(2{k}_{r}-{k}_{o}\right){t}^{2}{\left(1-\alpha \right)}^{2}{\alpha }^{2}{\left(\alpha +\beta -2\alpha \beta \right)}^{2}}\) and \(\bar{A}=\frac{(2\alpha -1)(\alpha -\beta )(\beta +\alpha (3-2\alpha -2\beta ))(192{{k}_{o}}^{2}{{k}_{r}}^{2}{t}^{4}{\left(1-\alpha \right)}^{2}{\alpha }^{2}+({k}_{r}^{2}-{k}_{o}^{2}){(\alpha +\beta -2\alpha \beta )}^{2}{\sigma }^{2})}{64{k}_{o}{(2{k}_{r}-{k}_{o})}^{2}{t}^{2}{(1-\alpha )}^{2}{\alpha }^{2}{(\alpha +\beta -2\alpha \beta )}^{2}}\).

Proof

Per Lemmas 1 and 2 and Proposition 2, I have \({{\pi }_{m}^{i}}^{* }-{{\pi }_{m}^{n}}^{* }=\frac{(2\alpha -1)(\alpha -\beta )(\beta +\alpha (3-2\alpha -2\beta ))(192{{k}_{o}}^{2}{{k}_{r}}^{2}{t}^{4}{\left(1-\alpha \right)}^{2}{\alpha }^{2}+({k}_{r}^{2}-{k}_{o}^{2}){(\alpha +\beta -2\alpha \beta )}^{2}{\sigma }^{2})}{64{k}_{o}{(2{k}_{r}-{k}_{o})}^{2}{t}^{2}{(1-\alpha )}^{2}{\alpha }^{2}{(\alpha +\beta -2\alpha \beta )}^{2}}\), which indicates that the profit of manufacturers will increase after adopting channel integration strategy when\(\,\frac{1}{2} < \beta < \alpha\) or \(\beta < \frac{1}{2} < \alpha\). Also, since \({{\pi }_{r}^{n}}^{* }-{{\pi }_{r}^{i}}^{* }=\frac{{k}_{r}\left(2\alpha -1\right)\left(\alpha -\beta \right)\left(\beta +\alpha \left(3-2\alpha -2\beta \right)\right)\left({\sigma }^{2}{\left(\alpha +\beta -2\alpha \beta \right)}^{2}-64{k}_{o}^{2}{t}^{4}{\left(1-\alpha \right)}^{2}{\alpha }^{2}\right)}{64{k}_{o}\left(2{k}_{r}-{k}_{o}\right){t}^{2}{\left(1-\alpha \right)}^{2}{\alpha }^{2}{\left(\alpha +\beta -2\alpha \beta \right)}^{2}}\), which indicates that the retailer’ profits will shrink under the same situation. Therefore, if the retailer receives a certain subsidy and the subsidy is greater than the profit loss, it will have an incentive to participate in service cooperation. For the manufacturer, the subsidy must be less than the increase in its profit, otherwise the manufacturer will not participate in service cooperation. Therefore, subsidy \(A\) must be somewhere between the two, as shown in Proposition 3 as \({{\pi }_{r}^{i}}^{* }+{{\pi }_{m}^{i}}^{* } > {{\pi }_{r}^{n}}^{* }+{{\pi }_{m}^{n}}^{* }\), so \({{\pi }_{m}^{i}}^{* }-{{\pi }_{m}^{n}}^{* } > {{\pi }_{r}^{n}}^{* }-{{\pi }_{r}^{i}}^{* }\) is satisfied.

Proposition 4 shows that under the premise that the overall channel profit is improved, the channel integration goal can be achieved through the appropriate benefit distribution mechanism. In practice, the manufacturer can sign a service cooperation agreement with the retailer to agree on the way of benefit distribution or subsidy, to realize the contractual channel integration mode. Compared with the integrated channel integration strategy, the contractual channel integration strategy saves more capital cost and time cost, and can achieve a “win-win” result while providing omnichannel services for consumers. Otherwise, the channel cannot achieve the equilibrium result after integration, that is, the two parties will not provide omnichannel services through cooperation.

Numerical analysis

In the previous section, for the sake of comparison, I took the average value \(\frac{1}{2}\) for the cross-channel demand profit distribution ratio \(\eta\), and this section will use numerical simulation to analyze the impact \(\eta \in (\mathrm{0,1})\) on the above main conclusions. The derivation process of Lemma 2 is repeated, and I can obtain \({{\pi }_{r}^{i}}^{* }=\frac{{k}_{r}{(4{k}_{o}{t}^{2}{(1-\alpha )}^{2}{\alpha }^{2}+{(\alpha \eta +\beta (1-\alpha -\eta ))}^{2}\sigma )}^{2}}{16{k}_{o}(2{k}_{r}-{k}_{o}){t}^{2}{(1-\alpha )}^{2}{\alpha }^{2}{(\alpha \eta +\beta (1-\alpha -\eta ))}^{2}}\) and \({{\pi }_{m}^{i}}^{* }=p-c-8\left(2{{k}_{o}}^{2}-6{k}_{o}{k}_{r}+7{{k}_{r}}^{2}\right)\sigma -\frac{48{k}_{o}{{k}_{r}}^{2}{t}^{2}{\left(1-\alpha \right)}^{2}{\alpha }^{2}}{{\left(\alpha \eta +\beta \left(1-\alpha -\eta \right)\right)}^{2}}+\frac{({k}_{r}^{2}-{k}_{o}^{2}){(\alpha \eta +\beta (1-\alpha -\eta ))}^{2}{\sigma }^{2}}{{k}_{o}{t}^{2}{(1-\alpha )}^{2}{\alpha }^{2}}\). Firstly, I analyze the impact of \(\eta\) on the profits of the manufacturer and the retailer. Let \({k}_{r}=10\), \({k}_{o}=8\), \(t=1\), \(\beta =0.3\), \(p=100\), \(c=20\), \(\sigma =15\), and \(\alpha =0.6\) or \(\alpha =0.4\). Then, I examine the changing trend of the profits of each channel member in \(\eta \in (\mathrm{0,1})\), respectively, as shown in Figs. 4 and 5 (where the solid line represents the profits after channel integration, and the dotted line represents the profits before channel integration, the same below).

Fig. 4
figure 4

Channel member profits in \(\eta\) when \(\alpha =0.6\).

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Fig. 5
figure 5

Channel member profits in \(\eta\) when \(\alpha =0.4\).

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As shown in Figs. 4 and 5, firstly, a bigger \(\eta\) is more beneficial to the manufacturer and less beneficial to the retailer, and vice versa. Secondly, given \(\alpha\), when \(\eta\) is large enough, the channel integration is beneficial to the manufacturer but unfavorable to the retailer, which is consistent with Proposition 2. When \(\eta\) is small enough, the channel integration is unfavorable to the manufacturer but beneficial to the retailer, which is also consistent with Proposition 2. In particular, unlike Proposition 2, even if \(\frac{1}{2} < \alpha \le 1\) and \(\beta < \alpha\) are satisfied, when \(\eta\) is small enough, channel integration is bad for the manufacturer but good for the retailer. This finding indicates that the trend of channel membership changes after channel integration is moderated by the proportion \(\alpha\) of demand profit distribution across channels. Finally, when channel integration is large, it is ultimately beneficial for the manufacturer even if the cross-channel demand profit of channel integration belonging to the online channel is less.

Next, I analyze the impact of \(\eta\) on the total profit of the channel. Keep the values of the above parameters unchanged, and investigate the changing trend of the total channel profit in \(\eta \in (\mathrm{0,1})\) given \(\alpha =0.6\) and \(\alpha =0.4\), respectively, as shown in Figs. 6 and 7.

Fig. 6
figure 6

Total channel profit in \(\eta\) when \(\alpha =0.6\).

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Fig. 7
figure 7

Total channel profit in \(\eta\) when \(\alpha =0.4\).

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As shown in Figs. 6 and 7, firstly, a bigger \(\eta\) is more beneficial to the integrated channel, and vice versa. Secondly, given \(\alpha\), when \(\eta\) is large enough, channel integration will increase the total channel profit, which is consistent with Proposition 3. When \(\eta\) is small enough, the channel integration will reduce the total channel profit, which is also consistent with Proposition 3. In particular, unlike Proposition 3, channel integration will reduce total channel profits even if\(\,\frac{1}{2} < \alpha \le 1\) and \(\beta < \alpha\) are satisfied when \(\eta\) is small enough. This finding indicates that the total channel profit after channel integration is moderated by the proportion of cross-channel demand profit distribution, and the more cross-channel demand profit belonging to the online channel, the more beneficial the overall channel is. Finally, when the channel integration \(\alpha\) is large enough, the total channel profit can be increased even if the cross-channel demand profit of the online channel is less.

Conclusions

In the context of retail, omnichannel strategies are gaining prominence, with a focus on delivering a consistent shopping experience across various channels. Recognizing the growing acceptance of omnichannel retail in both industry and academia, this study investigates the implementation of omnichannel strategies, particularly the integration between manufacturers’ online direct sales channels and physical retailers, under the assumption of retail price leadership. By combining empirical research findings, the study differentiates consumer cross-channel shopping activities and their perceived service values, delineating the utility and demands of such activities. Employing game theory, the study comprehensively analyzes the effects and feasibility of channel integration.

The research reveals several key findings: First, the cross-channel demands may only exist when the proportion of offline activities (e.g., in-store browsing, product trial) exceeds the proportion of offline service value (e.g., customer assistance, return services), measured in terms of consumer utility contribution. Second, channel integration may result in a win-lose or lose-lose situation, depending on the proportions of offline and online activities. This finding echoes the empirical research of Zhang et al. (2019a, 2019b), who discovered that integrating online and offline channels may hurt offline channel profits and total profits in the short term, but will increase offline channel profits and total profits in the long term. Third, providing subsidies to retailers by manufacturers can improve the overall channel profitability, particularly when offline activities dominate or online activities are minimal. Fourth, the effective channel integration conditions can be adjusted by appropriately distributing the profits generated from cross-channel demands between online and offline channels. Last, the sensitivity analysis results show that, without integration, the wholesale prices and service levels change monotonically with the online service cost coefficient, offline service cost coefficient, and channel preference intensity, while profits first decrease and then increase (with the offline service cost coefficient). After integration, influenced by the proportion of offline channel activities and the service value proportion, the trends become more complex.

The practical implications of this study are substantial, offering valuable insights for businesses looking to optimize their channel integration strategies. A central theme throughout the analysis is the evolving role of consumer experience as a driver of strategic decision-making in omnichannel environments. By prioritizing the experiential dimensions of shopping—such as convenience, consistency, personalization, and satisfaction—businesses can align their integration strategies with consumer expectations. This research highlights three key takeaways, each with broader applications beyond retail. These implications can help organizations across industries better navigate the complexities of integrating online and offline channels, and in doing so, maximize operational efficiency, enhance consumer experiences, and drive profitability.

First, this study proposes a contractual channel integration strategy that can significantly reduce the investments and time needed for businesses to expand their market presence. By engaging in strategic partnerships, companies can extend their reach without having to rely solely on building or maintaining their own infrastructure. For example, Nike’s integration strategy—coordinated through partnerships with both online and offline retailers—mirrors the cooperative structure outlined in the game-theoretic model. Nike effectively aligns incentives by distributing marketing and logistical responsibilities, similar to the profit-sharing mechanisms discussed in the findings of this study. This integration strategy provided Nike with the ability to reach more consumers while minimizing the costs of establishing new brick-and-mortar locations. The integration of these diverse channels also enhanced Nike’s omnichannel experience, making it easier for customers to interact with the brand across platforms. More importantly, it enabled a seamless and engaging customer journey across platforms, thereby deepening brand loyalty and enhancing the overall consumer experience.

However, there are instances where product-related factors may outweigh service considerations, particularly in industries where product differentiation, brand prestige, or exclusivity play a central role. For example, in luxury goods markets, product availability and exclusivity might be prioritized over service accessibility. In the model of this study, such cases can be interpreted as scenarios where the consumer utility derived from product attributes dominates the utility from service interaction, reducing the effectiveness of service-based channel integration. A luxury brand like Louis Vuitton might choose to limit the number of retail partners and focus on a more controlled, high-end customer experience, both online and in-store. Even here, the curation of consumer experience remains vital, albeit with a stronger emphasis on exclusivity and brand engagement. As such, product-related factors—such as brand positioning, perceived value, and customer loyalty—may sometimes be more crucial than service expansion considerations.

Second, the insights gained from this study extend beyond the retail sector to other industries where the convergence of digital and physical channels can improve service delivery. For instance, in the hospitality industry, hotels and airlines are increasingly implementing omnichannel services to streamline consumer touchpoints and elevate guest experiences. Consider a hotel chain that collaborates with an airline to offer integrated booking and check-in services. Customers can book flights and hotel rooms through a unified platform, and check into both their flight and hotel using a single mobile app. This integration streamlines the travel experience and provides the companies with valuable data on consumer preferences, helping them target marketing efforts more effectively.

Moreover, in healthcare, omnichannel strategies are gaining traction as well. Hospitals and healthcare providers are integrating telemedicine with in-person visits to create more seamless patient experiences. For example, patients might schedule appointments through a digital platform, conduct virtual consultations, and receive follow-up care either remotely or at a physical location, depending on the nature of their condition. Such integration ensures continuity of care and significantly enhances the patient experience, not only improving convenience for patients but also enhancing operational efficiencies for healthcare providers, allowing them to optimize resources and reach more patients.

Last, this study provides a profit distribution mechanism that can help businesses manage channel integration in a way that aligns the incentives of all parties involved. This mechanism is particularly useful for businesses like Unilever, whose integration strategy—offering subsidies and promotional support to retail partners—parallels the cooperative outcomes modeled in the game-theoretic analysis. Unilever’s strategy of offering incentives and subsidies to retailers in exchange for promoting its products in both digital and physical stores has helped drive sales and foster long-term partnerships. The outcome is a more cohesive and satisfying consumer experience, as brands and partners collaborate to provide unified messaging, product availability, and service quality across platforms. By distributing a portion of the profits generated through omnichannel sales, Unilever ensures that its retail partners are motivated to allocate resources to the promotion of its brand, enhancing the overall performance of the channel network.

This profit-sharing model is not limited to consumer goods or retail industries. In the technology sector, for instance, companies that provide cloud-based services might collaborate with third-party vendors to promote their offerings. By offering commissions or rebates to these vendors for each new customer they bring on board, cloud service providers can expand their market share without incurring the full cost of customer acquisition. Similarly, in the financial services sector, banks and fintech companies could engage in profit-sharing agreements with digital platforms that help them reach new customers, ensuring mutual benefits and incentivizing cooperation across channels.

However, the study has limitations. One notable limitation is the primary focus on the perspective of manufacturers and retailers. To enhance the comprehensiveness of understanding, future research should delve into the impact on consumers with a greater emphasis on their real-world shopping experiences. This includes examining how factors such as time spent shopping, transportation costs, and service levels influence purchase decisions, particularly in the context of online shopping (Zhang et al., 2024a, 2024b). Moreover, while the study assumes a retail price leadership scenario, it is important to acknowledge that different pricing structures may yield distinct implications. Future research should investigate the effects of various pricing strategies on omnichannel dynamics to provide a more robust understanding of the market. Additionally, the study could benefit from a more extensive exploration of the competition under different online channels, as well as a platform-to-platform competition (Liu et al., 2024). As these elements continue to influence retailers’ or other service providers’ decisions strategically, a nuanced understanding of their impact on omnichannel strategies is crucial. By incorporating these insights, future research can offer a more holistic view of the omnichannel retail environment, ensuring that the understanding aligns with the complexities of real-world shopping experiences. Only by centering consumer experiences at the heart of analysis can future studies fully capture the strategic and operational nuances of omnichannel integration.