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Article

Simultaneous or Sequential? Supplier Product Launch Strategy through E-Commerce Channels with Different Models

School of Management, Jiangsu University, Zhenjiang 212013, China
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Author to whom correspondence should be addressed.
J. Theor. Appl. Electron. Commer. Res. 2024, 19(3), 1848-1868; https://doi.org/10.3390/jtaer19030091
Submission received: 23 April 2024 / Revised: 17 June 2024 / Accepted: 28 June 2024 / Published: 18 July 2024
(This article belongs to the Collection Emerging Topics in Omni-Channel Operations)

Abstract

:
As the e-commerce landscape diversifies, suppliers are faced with the critical decision of how to effectively launch their products through e-commerce channels with varying business models. This study aims to explore the strategic considerations for a supplier launching products through two distinct e-commerce channels: one based on a direct sale model and the other on a reselling model. It builds a theoretical model to examine the supplier’s decision-making across three strategic options: a simultaneous launch through both channels, a sequential launch starting with the direct sale model followed by the reselling model, and vice versa. The equilibria of those options are derived through game analysis and further compared. The results reveal that for suppliers under a non-alliance pricing contract, a simultaneous product launch across both channels is the most advantageous approach. Conversely, in scenarios where an alliance pricing contract is in place, the optimal strategy shifts towards a sequential launch. The decision of which channel to ally with—whether the direct sale or the reselling model—hinges critically on the difference in service efficiency and the intensity of competition between the channels. This nuanced analysis highlights the importance of strategic flexibility and alignment with channel dynamics in maximizing product launch success in the evolving e-commerce environment.

1. Introduction

In recent years, the surge of the Internet economy has transformed e-commerce platforms into prime venues for product launches. Leading the charge in China are e-commerce behemoths like Tmall and JD, which have crafted specialized channels—namely Tmall HeyBox and JD Mofang—to assist suppliers in launching their products. These platforms engage in pre-launch marketing efforts to generate buzz and swiftly introduce new offerings to the market. Notably, products featured on these channels undergo rigorous selection processes, ensuring high quality. The substantial traffic garnered by these e-commerce channels not only boosts purchase rates but also elevates brand reputation. Some suppliers even form strategic alliances with these platforms to amplify their product promotion and sales efforts.
Within the diverse landscape of e-commerce channels, it is crucial to recognize that they operate on distinct business models. Tmall, for instance, primarily generates revenue through commissions charged to suppliers based on sales volume, embodying the direct sale model. Conversely, JD’s revenue primarily stems from purchasing products from suppliers and then reselling them to consumers, exemplifying the reselling model. This variation in business models poses a significant challenge for suppliers when deciding how to launch their products, making the choice of e-commerce platform an essential strategic decision. In this context, there is a crucial need to develop research on suppliers’ strategic options.
The objective of this study is to explore how a supplier launches products through e-commerce platforms with different business models. To achieve this, the study develops a dual-channel product launch model involving a supplier and two distinct e-commerce channels, each based on a different business model. It explores three potential product launch strategies for the supplier: launching products simultaneously across both channels, launching sequentially, starting with the direct sale model channel followed by the reselling model channel, and vice versa. The study focuses on two primary questions: (1) How does the supplier select among these strategies? (2) What factors influence the supplier’s strategic choice?
The theoretical model is solved by game analysis. Based on the contract types in the transactions, the analysis of this study unfolds in two parts: examining transaction equilibria and comparing strategies under non-alliance and alliance pricing contracts. The results reveal that the optimal product launch strategy for the supplier varies with the pricing contract. Under a non-alliance pricing contract, the simultaneous launch across both channels emerges as the best option. Conversely, under an alliance pricing contract, the sequential launch is the optimal strategy.
This study enhances the existing body of literature in three significant ways. Firstly, it contributes to the dual-channel literature by addressing the coordination issues within e-commerce channels. Unlike prior studies in this area, our research delves into the coordination challenges a supplier faces when managing two e-commerce channels that operate under distinct business models. Secondly, this study focuses on the power structure of channels operating under various business models. While much of the existing research has concentrated on power structures within omnichannel environments, our study explores how a supplier navigates strategy selection amidst varying power distributions across two distinct e-commerce channels. Lastly, our research examines suppliers’ product launch strategies, specifically addressing the relatively unexplored aspect of product launch sequencing. Therefore, this study not only fills a gap in the literature but also opens new avenues for understanding strategic decisions in multi-channel retailing.
The remainder of this paper is organized as follows: Section 2 is a review of relevant literature with three streams. Section 3 presents the model setup. In Section 4 and Section 5, we analyze the transaction equilibrium and strategy selection of the supplier under the non-alliance and alliance pricing contracts, respectively. Section 6 presents a numerical analysis. Section 7 concludes the study.

2. Literature Review

This paper is mainly related to three streams of literature. The first steam is about dual-channel operation. The second stream concerns the channel power structure. The last steam pertains to product launch strategy.

2.1. Dual-Channel Operation

With the emergence of Internet commercialization, powerful suppliers began to open online channels to compete with traditional sales channels, resulting in the emergence of the dual-channel sales mode [1,2]. The operation of the online channel has become an interesting research topic [3]. Scholars have examined its pricing strategy [4,5] and its mode selection [6,7]. As outlined above, the online channel can choose between functioning as a marketplace, in which suppliers directly sell their products to buyers, or as a reseller, where the channel purchases products from suppliers and resells them to buyers [8]. The key difference is that in the former mode, the suppliers hold the pricing power of the product and bear the cost of order fulfillment, while in the latter mode, online channels hold the pricing power and are responsible for order fulfillment.
In recent years, this dual-channel operation of the supply chain has attracted increasing attention. Many scholars have studied the pricing and profit strategies of dual channels under non-alliance competition. For example, some scholars studied the impact of a “buy-online-and-pickup-in-store” channel on product quality, prices, and profits [9,10]. They found that both the manufacturer and the retailer can benefit from adding such a channel under certain conditions. Meng et al. [11] analyzed the pricing, demand, and profit of a dual-channel supply chain, with consumers researching online and purchasing offline. Momen and Torabi [12] studied dynamic competition among traditional, online, and dual-channel retailing business models through a Nash-Stackelberg game. Luo and Sun [13] considered the conditions for expanding a dual-channel model from the perspective of product design. Yoo and Lee [14] captured the fundamental difference between both channel types and consumer heterogeneity in preference for Internet channel use. However, when suppliers add online channels through a game-theoretic model, they actually face a new dual-channel model problem, i.e., the choice and coordination between the online direct sale model channel and the online reselling model channel [15,16]. Wang et al. [17] analyzed the e-channel decision of a manufacturer between a direct-sales channel and a third-party consignment channel that complements an existing physical retail channel; they concluded that both the manufacturer’s unit operating cost in the direct e-channel and the e-tailer’s revenue allocation ratio in the consignment e-channel affect the selection of the manufacturer. Chen et al. [18] explored the impact of information sharing on platform optimal channel selection, considering price competition and demand uncertainty. Johnson [19] considered two different revenue models of platforms in the electronic book market: one where platforms set final retail prices and one where suppliers set final retail prices, and found that when prices are set by suppliers instead of platforms, prices may be higher in early periods but lower in later periods.
When exploring the non-alliance competition of the dual-channel supply chain, research showed that under the decentralized pricing decision, using the dual-channel structure may damage the profits of downstream retailers, thus leading to channel conflict. Webb and Hogan [20] indicated that such hybrid channel conflict is an important determinant of both channel performance and satisfaction. They further suggested that the relationship between hybrid channel conflict and channel performance was moderated by the lifecycle stage. Alliance pricing contracts between the supplier and retailer are expected to alleviate these channel conflicts when facing a potential upstream entry, thus achieving a win-win situation for channel members [21]. In the alliance pricing contract, both the Nash negotiation model and the Shapley value distribution method were introduced to allocate the profit among supply chain alliance members. In addition, the horizontal alliance of firms has also been studied. Ren et al. [22] examined how the performance of a firm’s prior alliances influences its propensity to continue using the alliance mode or switch to independent operations in the context of a new product launch. In summary, relevant literature on the online channel selection of suppliers does exist, but most studies focused on the issue of choosing the optimal channel between different channels. The coexistence and coordination between different online channels, as well as the cooperation between suppliers and those channels, remain under-explored.

2.2. Channel Power Structure

The existence of dual channels inevitably leads to the issue of the channel power structure [23,24]. Dennis, Cheong, and Sun [24] examined the impacts of channel power structure and retail channel dominance on a manufacturer’s optimal distribution channel strategy. Shen et al. [25] focused on the interaction between a retailer’s selling format decision and a manufacturer’s channel selection decision. They found that demand substitution between the dominant retailer and the weak retailer influences the manufacturer’s channel selection. Chen and Wang [26] examined the impact of power structures on pricing and channel selection decisions between a free channel and a bundled channel. Agi and Yan [27] focused on the equilibrium among centralized systems, manufacturer-led decentralized systems, and retailer-led decentralized systems under different product launch structures. Kumar and Purushottam [28] studied the closed-loop supply chain, considering omnichannel retailing under different channel power structures. They concluded that omnichannel retailing affects supply chain relationships and channel power structures by changing value creation processes. Jafari et al. [29] studied pricing and ordering decisions in a dual-channel supply chain consisting of a monopolistic manufacturer and duopolistic retailers. They found that under the collusion game, the manufacturer and retailers receive the lowest and highest profits, respectively. In addition, other scholars studied the influence of different channel power structures on supply chain pricing and profit from the perspectives of altruistic preference [30], information asymmetry [31], demand disruptions [32], price sensitivity [33], utility perception [34], and alliance selection [35]. In general, the power structure of channels plays an important role in supply chain performance. However, most prior studies focused on comparisons between traditional supply chains and dual-channel supply chains, while the influence of the power structure of channels with different business models on the marketing decisions of suppliers has not been well explored to date.

2.3. Product Launch Strategy

The existing research showed that product launch strategies and tactics affect the profitability of products as well as product acceptance by target consumers [36]. These product launch strategies could be relevant for product launch timing [37,38], consumer sensitivity [39], product preannouncement [40,41,42], demand uncertainty [43], trade-in [44], digital advertising spillover [45], information asymmetry among different channels [46], and launch locations [47]. Wu and Lai [38] studied the impact of the timing of new product launches and promotions on a firm’s profits. Chellappa and Mukherjee [40] presented a game-theoretic analysis of three different product preannouncement strategies (i.e., formal, informal, and no-preannouncement) in a duopoly and found a clear relationship between equilibrium preannouncement strategies and agents’ strength of taste preferences. Gruner et al. [48] used the reactance theory to analyze the extent to which investments in social media communication and online advertising are related to both the sales volume and profits of new products launched. In summary, most existing studies have discussed the influence of product launch strategies on the change of supply and demand as well as the profits of suppliers in a single online channel; however, a comparison and selection of product launch strategies among multiple channels have not been presented so far.

3. The Model

The method of this study is game analysis through the development of a theoretical model. The model introduces a scenario where supplier S launches a product into the market via two distinct e-commerce channels: channel D and channel R. Both channels, as major players in the Internet space, attract massive user traffic and play pivotal roles in the product launch process. The two channels operate under different business models: channel D adopts the direct sale model, similar to Tmall, whereas channel R adopts the reselling model, similar to JD. Supplier S is presented with three strategic options for launching the product through channels: a simultaneous launch across both, a sequential launch starting with channel D and followed by channel R, and an alternate sequential launch beginning with channel R and followed by channel D. The available product launch strategies of the supplier are shown in Figure 1.
To describe the transactions between supplier S and channels D and R, we rely on assumptions that capture the characteristics of each channel’s business model. The basic assumptions of the model are listed in the following:
Assumption 1. For the product launch, channel D leverages its significant user traffic and imposes a transaction commission rate r on supplier S. Subsequently, supplier S determines the final retail price p D for consumers and incurs a per-unit service cost m, which encompasses expenses related to logistics or after-sales support.
Assumption 2. During the product launch process, channel R acquires the product from supplier S and determines the final retail price p R for consumers by leveraging its significant user traffic. It incurs a per-unit service cost of tm, where t signifies the service efficiency differential between channel D and channel R. The wholesale price levied by supplier S on channel R is denoted as w R . The variable d represents channel R’s markup, defined as d = p R w R t m .
Assumption 3. Consumers can access both e-commerce channels to buy the product. The utility function of consumers is as follows [49,50]:
U = q D + q R 1 2 q D 2 + q R 2 + 2 γ q D q R p D q D p R q R ,
where q D and q R are the quantity of product sold through channel D and channel R, respectively, and γ is the competition degree between the two channels on the consumer market, where γ ( 0 , 1 ) . Consumer demand for products from each channel is obtained by the first-order conditions of Equation (1), which is:
q D = γ 1 + p D γ p R γ 2 1 , q R = γ 1 + p R γ p D γ 2 1 .
Assumption 4. It is assumed that 0 < m 1 + γ γ 2 2 and 0 < t < 1 m + γ ( 1 m ) γ 2 2 m to guarantee the existence of equilibria in the analysis.
In this paper, we explore two types of pricing contracts that the supplier may adopt: the non-alliance pricing contract and the alliance pricing contract. The equilibrium of the supplier’s three strategic options under the non-alliance pricing contract is analyzed in Section 4, and the optimal product launch strategy is derived by comparing these equilibria. Similarly, the equilibrium of the supplier’s three strategic options under the alliance pricing contract is analyzed in Section 5, and the optimal product launch strategy is derived by comparing these equilibria.
All parameters used in the model are standardized; the notation is shown in Table 1.

4. Equilibrium Analysis

Based on the assumptions presented above, the profit of the supplier π S , and the profits of the two channels π D and π R under the non-alliance pricing contract are calculated as follows:
π S = ( p D r m ) q D + w R q R ;
π R = d q R ,   π D = r q D

4.1. Simultaneous Product Launch across Both Channels

When employing the simultaneous product launch strategy, the supplier launches the product to the market through both channel D and channel R at the same time, initiating a two-stage game. In the first stage, channels D and R decide r ,   d at the same time. In the second stage, the supplier decides w R , p D . The game is solved by backward induction. The optimal retail price p D * of the supplier through channel D and the optimal wholesale price w R * of the supplier through channel R are derived from the maximization problem of Equation (3). By substituting p D * and w R * into Equations (4) the optimal transaction commission rate r * of channel D and the optimal markup d * of channel R can be derived from the profit maximization. By this derivation, the following equilibrium is obtained.
Proposition 1.
In the context of the simultaneous product launch strategy, the optimal prices of the supplier through the two channels are as follows:
p D * = 1 2 ( 1 m ) + γ ( 1 t m ) 2 4 γ 2 ,   w R * = 2 ( 1 t m ) + γ ( 1 m ) 2 4 γ 2 ;
The optimal transaction commission rate of channel D and the optimal markup of channel R are as follows:
r * = γ ( 1 t m ) + ( γ 2 2 ) ( 1 m ) γ 2 4 ,   d * = γ ( 1 m ) + ( 1 t m ) ( γ 2 2 ) γ 2 4 .
The proof of Proposition 1 is shown in Appendix A.
Based on Proposition 1, the profits of the supplier and both channels can be derived as follows:
π S = 2   ( 1 γ ) ( 2 + γ ) 2 ( 1 m t m ) m 2 [ ( 1 + t 2 ) ( 3 γ 2 4 ) + 2 t γ 3 ] 4 ( 4 γ 2 ) 2 ( 1 γ 2 ) ,
π R = [ γ ( 1 m ) + ( 1 t m ) ( γ 2 2 ) ] 2 2 ( 4 γ 2 ) 2 ( 1 γ 2 ) .

4.2. Sequential Product Launch from Channel D to Channel R

When employing the sequential product launch strategy in this case, the supplier launches the product starting with channel D, followed by channel R. This sequential product launch leads to a four-stage game. In the first stage, channel D decides r D R ; in the second stage, the supplier decides p D D R ; in the third stage, channel R decides d D R ; and in the fourth stage, the supplier decides w R D R . By backward induction, the optimal wholesale price w R D R * of the supplier through channel R is derived from the maximization problem of Equation (3) By substituting w R D R * into Equation (3), the optimal markup d D R * can be derived from the profit maximization of channel R. By substituting w R D R * and d D R * into Equations (3), the optimal retail price p D D R * through channel D can be derived from profit maximization. Finally, the optimal transaction commission rate r D R * of channel D can be derived from the maximization problem of Equation (4). By this derivation, the following equilibrium is obtained.
Proposition 2.
In the context of the sequential product launch strategy from channel D to channel R, the optimal prices of the supplier through the two channels are as follows:
p D D R * = γ ( 1 t m ) + ( 3 + m ) ( γ 2 2 ) 4 ( γ 2 2 ) ,   w R D R * = γ ( m 2 ) + γ 3 ( 1 m ) + ( 1 t m ) ( γ 2 4 ) 8 ( γ 2 2 ) ;
The optimal transaction commission rate of channel D and the optimal markup of channel R are as follows:
r D R * = γ ( 1 t m ) + ( γ 2 2 ) ( 1 m ) 2 ( γ 2 2 ) ,   d D R * = ( t m 1 ) ( 3 γ 2 4 ) + γ ( γ 2 2 ) ( 1 m ) 4 ( 2 γ 2 ) .
The proof of Proposition 2 is shown in Appendix A.
Based on Proposition 2, the profits of the supplier and the two channels can be derived as follows:
π S D R =   4 γ 2 [ 12 2 m ( 7 + 5 t ) + m 2 ( 7 + 5 t 2 ) ] + γ 4 [ m ( 32 + 10 t m ( 16 + 5 t 2 ) ) 21 ] 16 [ 2 + m ( m 2 2 t + m t 2 ) ] 2 γ 3 ( γ 2 2 ) ( t m 1 ) ( m 1 ) + 3 γ 6 ( m 1 ) 2 64 ( γ 2 2 ) ( γ 2 1 ) ,
π D D R = [ γ ( 1 t m ) + ( γ 2 2 ) ( 1 m ) ] 2 16 ( γ 2 2 ) ( γ 2 1 ) ,   π R D R = [ ( t m 1 ) ( 3 γ 2 4 ) + γ ( 2 + γ 2 ) ( 1 m ) ] 2 32 ( 2 γ 2 ) 2 ( 1 γ 2 ) .

4.3. Sequential Product Launch from Channel R to Channel D

When employing the sequential product launch strategy in this case, the supplier launches the product starting with channel R followed by channel D. This sequential product launch also leads to a four-stage game. In the first stage, channel R decides d R D ; in the second stage, the supplier decides w R R D ; in the third stage, channel D decides r R D ; and in the fourth stage, the supplier decides p D R D . By backward induction, the optimal retail price p D R D * of the supplier through channel D can be derived from the maximization problem of Equation (3). Then, p D R D * is substituted into Equation (4) to derive the optimal transaction commission rate r R D * from the profit maximization of channel D. By substituting p D R D * and r R D * into Equation (3), the optimal wholesale price w R R D * of the supplier through channel R can be derived from profit maximization. Finally, the above equilibrium is substituted into Equation (3) to derive the optimal markup d R D * of channel R from profit maximization. Therefore, the following equilibrium is derived.
Proposition 3.
In the context of the sequential product launch strategy from channel R to channel D, the optimal prices of the supplier through the two channels are as follows:
p D R D * = ( 7 + m ) γ 2 + γ ( 2 γ 2 ) ( 1 t m ) 4 ( 3 + m ) 8 ( γ 2 2 ) ,   w R R D * = γ ( 1 m ) + ( 1 t m ) ( γ 2 2 ) 4 ( γ 2 2 ) ;
The optimal transaction commission rate of channel D and the optimal markup of channel R are as follows:
r R D * = γ ( 2 γ 2 ) ( t m 1 ) + ( 1 m ) ( 4 3 γ 2 ) 4 ( 2 γ 2 ) ,   d R D * = γ ( 1 m ) + ( 1 t m ) ( γ 2 2 ) 2 ( γ 2 2 ) .
The proof of Proposition 3 is shown in Appendix A.
Based on Proposition 3, the profits of the supplier and the two channels can be derived as follows:
π S R D =   4 γ 2 [ 12 2 m ( 5 + 7 t ) + m 2 ( 5 + 7 t 2 ) ] + γ 4 [ m ( 10 + 32 t m ( 5 + 16 t 2 ) ) 21 ] 16 [ 2 + m ( m 2 2 t + m t 2 ) ] 2 γ 3 ( γ 2 2 ) ( t m 1 ) ( m 1 ) + 3 γ 6 ( m 1 ) 2 64 ( γ 2 2 ) ( γ 2 1 ) ,
π D R D = [ γ ( 2 γ 2 ) ( t m 1 ) + ( 1 m ) ( 4 3 γ 2 ) ] 2 32 ( 2 γ 2 ) 2 ( 1 γ 2 ) ,   π R R D = [ γ ( 1 m ) + ( 1 t m ) ( γ 2 2 ) ] 2 16 ( 2 γ 2 ) ( 1 γ 2 ) .

4.4. Comparison of Product Launch Strategies

Based on Propositions 1, 2, and 3, we further compare the profits of the supplier under the three product launch strategies. The differences between the profits of the supplier under the three product launch strategies are derived as follows:
Δ π 1 = π S π S D R = γ 2 ( ( 240 γ 2 3 γ 8 128 ) ( m 1 ) 2 + ( 2 γ 7 + 12 γ 5 64 γ 3 + 64 γ ) ( m 1 ) ( t m 1 ) + 5 γ 6 ( 9 2 m ( 8 + t ) + m 2 ( 8 + t 2 ) ) 12 γ 4 ( 14 2 m ( 13 + t ) + m 2 ( 13 + t 2 ) ) ) 64 ( γ 2 1 ) ( 8 6 γ 2 + γ 4 ) 2 Δ π 2 = π S π S R D = γ 2 ( ( 64 γ 64 γ 3 + 12 γ 5 + 2 γ 7 ) ( m 1 ) ( t m 1 ) + ( 240 γ 2 3 γ 8 128 ) t m 1 2 + 5 γ 6 ( 9 2 m ( 1 + 8 t ) + m 2 ( 1 + 8 t 2 ) ) 12 γ 4 ( 14 2 m ( 1 + 13 t ) + m 2 ( 1 + 13 t 2 ) ) ) 64 ( γ 2 1 ) ( 8 6 γ 2 + γ 4 ) 2 Δ π 3 = π S D R π S R D = γ 2 m ( 3 γ 2 8 ) ( t 1 ) ( 2 m t m ) 64 ( γ 2 2 ) 2
Under Assumption 4, there are Δ π 1 > 0 and Δ π 2 > 0 but Δ π 3 > 0 only when 0 < t < 1 . Based on the above comparison, the following can be concluded:
Proposition 4.
It is optimal for the supplier to launch the product simultaneously through both e-commerce channels. The second-best choice is sequential product launch from channel D to channel R if  0 < t < 1 ; otherwise, sequential launch from channel R to channel D is the second-best choice.
Proposition 4 suggests that the supplier gains more benefits by launching products to the market simultaneously across channels rather than in a sequential manner, independent of the level of competition among the channels. A sequential launch strategy endows the initially chosen channel with a first-mover advantage, inadvertently disadvantaging the subsequent channel and significantly diminishing the supplier’s profits from it. Thus, equitably distributing the first-mover advantage by launching products simultaneously across channels emerges as the optimal strategy for the supplier. However, the second-best option for the supplier hinges on the disparity in service efficiency between channels. Specifically, initiating a product launch through the channel with higher service costs proves more advantageous than starting with the channel with lower service costs. This implies a strategic incentive for suppliers to equalize the competitive edge across channels. By allocating the first-mover advantage to the channel at a service efficiency disadvantage, suppliers can enhance the collective profit derived from both channels.

5. Product Launch Strategy by Alliance

In this section, we further consider the case that the supplier allies with channels and employs an alliance pricing contract for product launches.
When supplier S allies with both channels to launch the product, it initiates the product launch simultaneously through both channels under an alliance pricing contract. The profit of the alliance { S R D } is as follows:
π S R D = ( p D S R D m ) q D S R D + ( p R S R D t m ) q R S R D .
When supplier S only allies with channel D to launch the product, it initiates the product launch through channel D under an alliance pricing contract, followed by a subsequent launch through channel R. The profit of the alliance { S D } is as follows:
π S D = ( p D S D m ) q D S D + w R S D q R S D .
When supplier S only allies with channel R to launch the product, it initiates the product launch through channel R under an alliance pricing contract, followed by a subsequent launch through channel D. The profit of the alliance { S R } is as follows:
π S R = ( p D S R r S R m ) q D S R + ( p R S R t m ) q R S R .
In the alliances mentioned above, we consider that the supplier and its allied channel distribute the alliance profits according to the Shapley value method. This approach ensures a fair allocation based on each party’s contribution to the collective success.

5.1. Simultaneous Product Launch by the SRD Alliance

When supplier S allies with both channels to launch the product through alliance pricing, the alliance { S R D } decides p D S R D , p R S R D jointly to maximize the alliance profit. The optimal retail price p D S D R * of the supplier through channel D and the optimal retail price p R S D R * of channel R are derived from the maximization problem of Equation (11). By backward induction, the following equilibrium can be derived.
Proposition 5.
In the context of the simultaneous product launch by the SRD alliance, the optimal prices of the supplier through the two channels are
p D S R D * = 1 + m 2 ,   p R S R D * = 1 + t m 2 .
Based on the Shapley value method, the profits of the supplier and the two channels can be derived as follows:
π S S R D = 2 ( 1 γ ) [ 1 m ( 1 + t ) ] + m 2 ( t 2 + 1 2 t γ ) 16 ( 1 γ 2 ) ,
π D S R D = π R S R D = 3 [ 2 ( 1 γ ) ( 1 m ( 1 + t ) ) + m 2 ( t 2 + 1 2 t γ ) ] 32 ( 1 γ 2 ) .
The proof of Proposition 5 is shown in Appendix A.

5.2. Sequential Product Launch by the SD Alliance

When supplier S only allies with channel D through alliance pricing, the product launch is sequential and builds on three stages. In the first stage, the alliance { S D } decides p D S D ; in the second stage, channel R decides d S D ; and in the third stage, the alliance { S D } decides w R S D . By backward induction, the optimal wholesale price w R S D * of the supplier through channel R is derived from maximizing the alliance profit as Equation (12). By substituting w R S D * into Equation (4), the optimal markup d S D * can be derived from the profit maximization of channel R. By substituting w R S D * and d S D * into Equations (12), the optimal retail price p D S D * through channel D can be derived from the profit maximization of the alliance. Through this derivation, the following equilibrium can be derived.
Proposition 6.
In the context of the sequential product launch strategy by the SD alliance, the optimal prices of the supplier through the two channels are as follows:
p D S D * = 1 + m 2 ,   w R S D * = 1 + γ m ( t + γ ) 4 ;
The optimal markup of channel R is as follows:
d S D * = 1 t m + ( m 1 ) γ 2 .
Based on the Shapley value method, the profits of the supplier and the two channels can be derived as follows:
π S S D = ( m 1 ) 2 16 ( t m 1 ) 2 16 ( γ 2 2 ) +   4 γ 2 [ 12 2 m ( 7 + 5 t ) + m 2 ( 7 + 5 t 2 ) ] + γ 4 [ m ( 32 + 10 t m ( 16 + 5 t 2 ) ) 21 ] 16 [ 2 + m ( m 2 2 t + t 2 m ) ] 2 γ 3 ( γ 2 2 ) ( t m 1 ) ( m 1 ) + 3 γ 6 ( m 1 ) 2 128 ( γ 2 2 ) ( γ 2 1 ) ,
π D S D = [ γ ( 1 t m ) + ( γ 2 2 ) ( 1 m ) ] [ ( t m 1 ) γ ( 5 γ 2 12 ) + ( m 1 ) ( 13 γ 4 46 γ 2 + 40 ) ] 128 ( γ 2 2 ) 2 ( 1 γ 2 ) ,   π R S D = [ 1 γ m ( t γ ) ] 2 8 ( 1 γ 2 ) .
The proof of Proposition 6 is shown in Appendix A.

5.3. Sequential Product Launch by the SR Alliance

When the supplier only allies with channel R through alliance pricing, the sequential product launch leads to a three-stage game. In the first stage, the alliance { S R } decides p R S R ; in the second stage, channel D decides r S R ; and in the third stage, the alliance { S R } decides p D S R . By backward induction, the optimal retail price p D S R * of the supplier through channel D can be derived from the maximization problem of Equation (13). Then, p D S R * is substituted into Equation (4) to derive the optimal transaction commission rate r S R * of channel D from the profit maximization. By substituting p D S R * and r S R * into Equation (13) the optimal retail price p R S R * of channel R can be derived from the profit maximization of the alliance. Through this derivation, the following equilibrium can be derived.
Proposition 7.
In the context of the sequential product launch strategy by the SR alliance, the optimal prices of the supplier through the two channels are as follows:
p D S R * = 3 γ + m ( 1 t γ ) 4 ,   p R S R * = 1 + t m 2 ;
the optimal commission rate of channel D is as follows:
r S R * = 1 γ + m ( t γ 1 ) 2 .
Based on the Shapley value method, the profits of the supplier and the two channels can be derived as follows:
π S S R = ( t m 1 ) 2 16 ( m 1 ) 2 16 ( γ 2 2 ) +   4 γ 2 [ 12 2 m ( 5 + 7 t ) + m 2 ( 5 + 7 t 2 ) ] + γ 4 [ m ( 10 + 32 t m ( 5 + 16 t 2 ) ) 21 ] 16 [ 2 + m ( m 2 2 t + t 2 m ) ] 2 γ 3 ( γ 2 2 ) ( t m 1 ) ( m 1 ) + 3 γ 6 ( m 1 ) 2 64 ( γ 2 2 ) ( γ 2 1 ) ,
π R S R = [ γ ( 1 m ) + ( 1 t m ) ( γ 2 2 ) ] [ ( m 1 ) γ ( 5 γ 2 12 ) + ( t m 1 ) ( 13 γ 4 46 γ 2 + 40 ) ] 128 ( γ 2 2 ) 2 ( 1 γ 2 ) ,   π D S R = [ 1 γ m ( 1 t γ ) ] 2 8 ( 1 γ 2 ) .
The proof of Proposition 7 is shown in Appendix A.

5.4. Comparison of Product Launch Strategies by Alliance

Based on Propositions 5, 6, and 7, we further compare the profits of the supplier under the three product launch strategies. The differences between the profits of the supplier under the three product launch strategies are derived as follows:
Δ π 4 = π S S R D π S S D = 2 ( 1 γ ) ( 1 m ( 1 + t ) ) + m 2 ( t 2 + 1 2 t γ ) 16 ( 1 γ 2 ) 1 16 [ ( m 1 ) 2 ( t m 1 ) 2 γ 2 2 ] 4 γ 2 [ 12 2 m ( 7 + 5 t ) + m 2 ( 7 + 5 t 2 ) ] + γ 4 [ m ( 32 + 10 t m ( 16 + 5 t 2 ) ) 21 ] 16 [ 2 + m ( m 2 2 t + t 2 m ) ] 2 γ 3 ( γ 2 2 ) ( t m 1 ) ( m 1 ) + 3 γ 6 ( m 1 ) 2 128 ( γ 2 2 ) ( γ 2 1 ) Δ π 5 = π S S R D π S S R = 2 ( 1 γ ) ( 1 m ( 1 + t ) ) + m 2 ( t 2 + 1 2 t γ ) 16 ( 1 γ 2 ) 1 16 [ ( t m 1 ) 2 ( m 1 ) 2 γ 2 2 ] 4 γ 2 [ 12 2 m ( 5 + 7 t ) + m 2 ( 5 + 7 t 2 ) ] + γ 4 [ m ( 10 + 32 t m ( 5 + 16 t 2 ) ) 21 ] 16 [ 2 + m ( m 2 2 t + t 2 m ) ] 2 γ 3 ( γ 2 2 ) ( t m 1 ) ( m 1 ) + 3 γ 6 ( m 1 ) 2 128 ( γ 2 2 ) ( γ 2 1 ) Δ π 6 = π S S D π S S R = m ( 1 t ) ( m t + m 2 ) ( 11 γ 4 32 γ 2 + 16 ) 128 ( γ 2 2 ) 2
Under Assumption 4, there are Δ π 4 < 0 and Δ π 5 < 0 ; but the sign of Δ π 6 depends on both γ and t . Based on the comparison, the following can be concluded:
Proposition 8.
The simultaneous product launch by the SRD alliance is the worst choice for the supplier. The optimal choice for the supplier is sequential product launch by the SD alliance if    0 < γ < 2 1 11 4 5  and   t > 1 , or   2 1 11 4 5 < γ < 1  and   0 < t < 1 ; the sequential product launch by the SR alliance is optimal if   0 < γ < 2 1 11 4 5  and   0 < t < 1  , or   2 1 11 4 5 < γ < 1  and   t > 1 .
Proposition 8 suggests that for the supplier, a sequential product launch strategy outperforms a simultaneous launch strategy when the launch is conducted through an alliance. Launching in alliance not only secures a first-mover advantage but also a joint pricing advantage for the allied channel, creating an advantage gap between the channels. This gap allows the supplier to generate sufficient profit from the allied channel to compensate for any losses incurred through the non-allied channel, rendering the sequential launch via an alliance the superior strategy for the supplier.
Moreover, the supplier’s decision on which channel to ally with for the sequential launch hinges on the degree of competition and the difference in service efficiency between the channels. Specifically, in circumstances of low (or high) inter-channel competition, it is advantageous for the supplier to ally with the channel exhibiting lower (or higher) service costs. This strategy implies that the supplier is motivated to amplify the advantage gap between channels by bestowing both first-mover and joint pricing advantages to the channel with a service efficiency edge in scenarios of mild competition, thereby maximizing benefits from the alliance. Conversely, in highly competitive scenarios, the supplier aims to narrow this gap by allying with the channel at a service efficiency disadvantage, a move that equitably distributes advantages and leads to an increase in the supplier’s overall profits from both channels.

6. Numerical Analysis

In this section, we conduct a numerical analysis to elucidate the findings derived from the equilibrium analysis. The subsequent figures depict the supplier’s profit when launching the product under the non-alliance pricing contract (Figure 2) and the alliance pricing contract (Figure 3).
We first outline the profits of the supplier under different product launch strategies by letting γ = 0.4 when the competition level between channels is low, followed by letting γ = 0.9 when the competition level between channels is high. Figure 2 shows that the profit of the supplier is the largest when the product is launched simultaneously, regardless of γ . The profit of the supplier when launching sequentially from channel D to channel R is the second-largest only if 0 < t < 1 ; while its profit when launching sequentially from channel R to channel D is the second-largest if t > 1 . The findings corroborate Proposition 4, suggesting that simultaneous product launches outperform sequential product launches when the supplier employs a non-alliance pricing contract.
Figure 3 shows that the profit of the supplier is always lower when launching the product simultaneously than sequentially, regardless of both t and γ . The profit of the supplier is the largest when launching the product sequentially by allying with channel D either if 0 < t < 1 and γ is large ( γ = 0.9 ) or if t > 1 and γ is small ( γ = 0.4 ); the profit of the supplier is the largest when launching the product sequentially by allying with channel R either if 0 < t < 1 and γ is small ( γ = 0.4 ) or if t > 1 and γ is large ( γ = 0.9 ). The findings align with Proposition 8, indicating that simultaneous product launches are less effective than sequential ones when the supplier adopts an alliance pricing contract. The optimal product launch strategy for the supplier hinges on both the level of competition and the variance in service efficiency across channels.

7. Conclusions

This research builds a theoretical model to examine a supplier’s strategic decision-making for product launches across two e-commerce channels with distinct business models: the direct sale and the reselling models, under both alliance and non-alliance pricing contracts. It analyzes the supplier’s choice among simultaneous launches across both channels: a sequential launch starting with the direct sale model, then the reselling model, and a sequential launch starting with the reselling model, followed by the direct sale model.
By equilibrium analysis, the study concludes that: (1) With a non-alliance pricing contract, the optimal strategy is a simultaneous launch across both channels, with the sequential launch from the higher to the lower service cost channel being the second-best strategy. (2) With an alliance pricing contract, the simultaneous launch is the least optimal strategy. The best strategy depends on the service efficiency difference and the competitive intensity between channels. The sequential launch, starting with the lower service cost channel, is most advantageous when channel competition is low, while starting with the higher service cost channel is preferable when channel competition is high.

7.1. Theoretical Implications

This study makes three significant contributions to the field. First, it delineates a new perspective within the dual-channel operation literature by analyzing the coordination challenges a supplier encounters when managing two e-commerce channels [3,8], each operating under distinct business models [6]. This exploration diverges from prior research, offering a novel viewpoint on navigating dual-channel complexities [1,16]. Second, this study deepens the understanding of channel power dynamics by exploring how a supplier strategically navigates power distribution between two disparate e-commerce channels. Previous studies have explored the influence of different channel power structures on supply chain pricing and profit from the perspectives of altruistic preference [30], demand disruptions [32], and alliance selection [35]. This study contrasts with the existing focus on omnichannel power structures [23], introducing a fresh angle on channel strategy formulation. Lastly, this study broadens the scope of knowledge on suppliers’ product launch strategies [36,40]. By addressing the under-explored area of product launch sequencing, this study fills a notable gap in the literature, shedding light on strategic considerations that have yet to be thoroughly examined.

7.2. Managerial Implications

This study unveils key managerial insights for suppliers aiming to launch products on e-commerce platforms, emphasizing the strategic adaptation of diverse channel business models and pricing contracts. The optimal product launch strategy for suppliers hinges on their selected pricing contracts, necessitating tailored approaches for different e-commerce partnerships. In scenarios where a non-alliance pricing contract is utilized, a simultaneous launch across channels proves more effective than a sequential approach, advocating for a balanced engagement strategy that does not favor one channel over another. Conversely, under an alliance pricing contract, a sequential launch strategy emerges as superior. This necessitates a careful evaluation of service efficiency and competitive dynamics across channels, guiding the supplier towards forming an alliance with the channel that aligns with the prevailing market conditions—opting for the channel with lower service costs in less competitive environments or the one with higher costs when competition intensifies.

7.3. Limitations and Future Research

This study identifies several limitations that suggest potential avenues for future research. First, we do not consider the network effect of products in the model. Due to consumer behaviors such as sharing and reviewing, product sales through e-commerce channels experience significant network effects. These effects amplify the product’s visibility and appeal among potential buyers, leveraging the interconnectedness of consumers online. Understanding the impact of network effects on consumer decisions is crucial for suppliers planning e-commerce product launches. Future research can incorporate network effects into the model to underscore their importance.
Second, our study operates under the assumption that the pricing contract adopted by the supplier is exogenous. However, the pricing contract decision could be endogenous. Future work could explore the decision-making process of suppliers when determining contract types, providing a more comprehensive understanding of how these decisions impact product launch strategies.

Author Contributions

Conceptualization and methodology, Z.L., B.W., and Y.W.; writing, Z.L., B.W. and Y.W.; supervision, Z.L.; numerical simulation, B.W. and Y.W.; investigation and visualization, Y.W. Project administration and writing—review and editing, Z.L.; Supervision and writing—review and editing, Z.L. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the National Social Science Foundation of China (grant number 19BGL263).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.

Acknowledgments

The authors would like to thank the editors and the anonymous reviewers for their insightful suggestions to improve the quality of this paper.

Conflicts of Interest

The authors declare no conflicts of interest.

Appendix A

Proof of Proposition 1.
In the second stage, the first-order conditions of the supplier’s profit π S with respect to p D and w R are calculated.
π S p D = 1 + m 2 p D + r + γ d 1 + t m + 2 w R γ 2 1 = 0 π S w R = d 1 + γ 1 + m 2 p D + r + t m + 2 w R γ 2 1 = 0 .
This yields that
p D * = 1 + m + r 2 ,   w R * = 1 d t m 2 .
In the first stage, the first-order condition of channel D’ s profit π D with respect to r and the first-order condition of channel R’s profit π R with respect to d are calculated.
d π D d r = m 1 + 2 r γ d + t m 1 2 γ 2 1 = 0 d π R d d = 2 d 1 γ m + r 1 + t m 2 γ 2 1 = 0 .
This yields that
r * = γ ( 1 t m ) + ( γ 2 2 ) ( 1 m ) γ 2 4 ,   d * = γ ( 1 m ) + ( 1 t m ) ( γ 2 2 ) γ 2 4 .
By replacement, following equilibrium are derived:
p D * = 1 + 2 ( 1 m ) + γ ( 1 t m ) 2 γ 2 4 ,   w R * = 2 ( 1 t m ) + γ ( 1 m ) 2 γ 2 4 .
Proof of Proposition 2.
In the fourth stage, the first-order condition of the supplier’s profit π S D R with respect to w R D R is calculated.
π S D R w R D R = d D R + γ 1 + m 2 p D D R + r D R + t m + 2 w R D R 1 γ 2 1 = 0 .
This yields that
w R D R = 1 d D R γ 1 + m 2 p D D R + r D R t m 2 .
In the third stage, the first-order condition of channel R’s profit π R D R with respect to d D R is calculated.
d π R D R d d D R = 2 d D R 1 γ m + r D R 1 + t m 2 γ 2 1 = 0 .
This yields that
d D R = 1 + γ m + r D R 1 t m 2 .
In the second stage, the first-order condition of the supplier’s profit π S D R with respect to p D D R is calculated.
π S D R p D D R = 1 + m 2 p D D R + r D R = 0 .
This yields that
p D D R = 1 2 1 + m + r D R .
In the first stage, the first-order condition of channel D’s profit π D D R with respect to r D R is calculated.
d π D D R d r D R = γ + 2 m + 2 r D R 1 γ 2 m + 2 r D R 1 γ t m 4 γ 2 1 = 0 .
This yields that
r D R = 2 γ γ 2 2 m + γ 2 m + γ t m 2 γ 2 2 .
By replacement, the following equilibrium are derived:
p D D R * = γ ( 1 t m ) + ( 3 + m ) ( γ 2 2 ) 4 ( 2 + γ 2 ) ,   w R D R * = γ ( m 2 ) + γ 3 ( 1 m ) + ( 1 t m ) ( γ 2 4 ) 8 ( 2 + γ 2 ) ;
r D R * = γ ( 1 t m ) + ( γ 2 2 ) ( 1 m ) 2 ( γ 2 2 ) ,   d D R * = ( t m 1 ) ( 3 γ 2 4 ) + γ ( 2 + γ 2 ) ( 1 m ) 4 ( 2 γ 2 ) .
Proof of Proposition 3.
In the fourth stage, the first-order condition of the supplier’s profit π S R D with respect to p D R D is calculated.
π S R D p D R D = 2 p D R D 1 m r R D γ w R R D γ d R D + t m + w R R D 1 γ 2 1 = 0 .
This yields that
p D R D = 1 + m + r R D + γ d R D + t m + 2 w R R D 1 2 .
In the third stage, the first-order condition of channel D s profit π D R D with respect to r R D is calculated.
d π D R D d r R D = 2 r R D 1 + m γ d R D + t m 1 2 γ 2 1 = 0 .
This yields that
r R D = 1 m + γ d R D + t m 1 2 .
In the second stage, the first-order condition of the supplier’s profit π S R D with respect to w R R D is calculated.
π S R D w R R D = 1 d t m 2 w R R D = 0 .
This yields that
w R R D = 1 d t m 2 .
In the first stage, the first-order condition of channel R’s profit π R R D with respect to d R D is calculated.
d π R R D d d R D = γ 2 2 d R D γ 2 2 γ m + 2 t m + γ 2 1 t m 4 γ 2 1 = 0 .
This yields that
d = 1 2 γ + γ 2 2 γ m γ 2 2 t m .
By replacement, the following equilibrium is derived:
p D R D * = 4 ( 3 + m ) + ( 7 + m ) γ 2 + γ ( 2 γ 2 ) ( 1 t m ) 8 ( γ 2 2 ) ,   w R R D * = γ ( 1 m ) + ( 1 t m ) ( γ 2 2 ) 4 ( γ 2 2 ) ;
r R D * = γ ( 2 γ 2 ) ( t m 1 ) + ( 1 m ) ( 4 3 γ 2 ) 4 ( 2 γ 2 ) ,   d R D * = γ ( 1 m ) + ( 1 t m ) ( γ 2 2 ) 2 ( γ 2 2 ) .
Proof of Proposition 5.
The principle of allocating the alliance profit based on the Shapley value method is that when supplier S allies with channel D or channel R, they will jointly face market demand and risk, and share cost and profit. That is, the profit that each member gains from the alliance is equal to the average of its marginal contribution to each alliance in which it participates in.
There are three members in the product launch: supplier S, channel D and channel R. When the supplier adopts the alliance pricing contract with both channels to launch product simultaneously, the profits of alliance members according to the Shapley value are as follows:
ψ i ( v ) = s N i w ( s ) [ v ( s ) v ( s \ i ) ] ,   i = S ,   D ,   R w ( s ) = ( s 1 ) ! ( n s ) ! n ! ,   N i = { S R D } .
ψ i ( v ) represents the profit of the member i, and N i represents the grand alliance of all members; s represents sub-alliances, and s is the number of members in the sub-alliances; w ( | s | ) is the weighting factor; v ( s ) is the profits of sub-alliances; v ( s \ i ) represents the profits of sub-alliances after excluding member i; [ v ( s ) v ( s \ i ) ] represents the marginal contribution of member i to the sub-alliance s .
The first-order condition of the profit of the alliance { S R D }   π S R D with respect to p D S R D and p R S R D are calculated.
π S R D p D S R D = γ m + 2 p D S R D 2 γ p R S R D + γ t m 1 γ 2 1 = 0 π S R D p R S R D = γ 1 + m 2 p D S R D + 2 p R S R D t m 1 γ 2 1 = 0 .
This yields that
p D S R D * = 1 + m 2 , p R S R D * = 1 + t m 2 .
By substituting p D S R D and p R S R D into π S R D , the profit of the grand alliance is derived as follows:
π S R D = 2 m 1 + t + 2 γ m 1 t m 1 m 2 1 + t 2 2 4 γ 2 1 .
Then the profits π S D 0 R 0 and π D 0 R 0 when channel D and channel R form an alliance are calculated. The first-order conditions of the supplier’s profit π S D 0 R 0 with respect to p D D 0 R 0 and w R D 0 R 0 are as follows:
π S D 0 R 0 p D D 0 R 0 = 1 + m 2 p D D 0 R 0 + r D 0 R 0 + γ d D 0 R 0 1 + t m + 2 w R D 0 R 0 1 γ 2 = 0 π S D 0 R 0 w R D 0 R 0 = d D 0 R 0 + γ 1 + m 2 p D D 0 R 0 + r + t m + 2 w R D 0 R 0 1 γ 2 1 = 0 .
This yields that
p D D 0 R 0 = 1 + m + r D 0 R 0 2 , w R D 0 R 0 = 1 d D 0 R 0 t m 2 .
The first-order conditions of the profit of the alliance { D 0 R 0 }   π D 0 R 0 with respect to r D 0 R 0 and d D 0 R 0 are calculated.
π D 0 R 0 r D 0 R 0 = γ 1 2 d D 0 R 0 γ + m + 2 r D 0 R 0 γ t m 2 γ 2 1 = 0 π D 0 R 0 d D 0 R 0 = 2 d D 0 R 0 1 γ m + 2 r D 0 R 0 1 + t m 2 γ 2 1 = 0 .
This yields that
r D 0 R 0 * = 1 m 2 ,   d D 0 R 0 * = 1 t m 2
By replacement, the following equilibrium is derived:
p D D 0 R 0 * = 3 + m 4 , w R D 0 R 0 * = 1 t m 4 .
Based on the above, the profit of the sub-alliance formed by channel D and channel R is derived as follows:
π S D 0 R 0 = 2 m 1 + t + 2 γ m 1 t m 1 m 2 1 + t 2 2 16 γ 2 1 , π D 0 R 0 = 2 m 1 + t + 2 γ m 1 t m 1 m 2 1 + t 2 2 8 γ 2 1 .
According to the Shapley value, the profits of the members are as follows:
ψ S S R D = 1 6 [ 2 v ( { S R D } ) + 2 v ( { S } ) 2 v ( { D 0 R 0 } ) ] = 2 ( 1 γ ) ( 1 m ( 1 + t ) ) + m 2 ( t 2 + 1 2 t γ ) 16 ( γ 2 1 ) , ψ D S R D = ψ R S R D = 1 6 [ 2 v ( { S R D } ) + v ( { D 0 R 0 } ) v ( { S } ) ] = 3 [ 2 ( 1 γ ) ( 1 m ( 1 + t ) ) + m 2 ( t 2 + 1 2 t γ ) ] 32 ( γ 2 1 ) .
Proof of Proposition 6.
In the third stage, the first-order condition of the profit of the alliance { S D }   π S D with respect to w R S D is calculated.
π S D w R S D = d S D + γ 2 γ p D S D + m γ + t + 2 w R S D 1 γ 2 1 = 0 .
This yields that
w R S D = 1 d γ γ m + 2 γ p D S D t m 2 .
In the second stage, the first-order condition of channel R’s profit π R S D with respect to d S D is calculated.
d π R S D d d S D = 2 d S D + γ γ m + t m 1 2 γ 2 1 = 0 .
This yields that
d D R * = 1 γ + γ m t m 2 .
In the first stage, the first-order condition of the profit of the alliance { S D }   π S D with respect to p D S D is calculated.
π S S D p D S D = 1 + m 2 p D S D = 0 .
This yields that
p D S D * = 1 + m 2 .
By replacement, the following equilibrium is derived as follows:
p D S D * = 1 + m 2 , w R S D * = 1 + γ m ( t + γ ) 4 ,   d S D * = 1 t m + ( m 1 ) γ 2 .
π S D = 3 γ 2 m 1 2 + 2 m 4 + t + 2 γ m 1 t m 1 m 2 4 + t 2 5 16 γ 2 1 .
According to the Shapley value, the profits of the members are as follows:
ψ S S D = 1 2 [ v ( { S D } ) + v ( { S } ) v ( { D } ) ] = 1 16 [ ( m 1 ) 2 ( t m 1 ) 2 γ 2 2 ] + 4 γ 2 [ 12 2 m ( 7 + 5 t ) + m 2 ( 7 + 5 t 2 ) ] + γ 4 [ m ( 32 + 10 t m ( 16 + 5 t 2 ) ) 21 ] 16 [ 2 + m ( m 2 2 t + t 2 m ) ] 2 γ 3 ( γ 2 2 ) ( t m 1 ) ( m 1 ) + 3 γ 6 ( m 1 ) 2 128 ( γ 2 2 ) ( γ 2 1 ) , ψ D S D = 1 2 [ v ( { S D } ) + v ( { D } ) v ( { S } ) ] = [ γ ( 1 t m ) + ( γ 2 2 ) ( 1 m ) ] [ ( t m 1 ) γ ( 5 γ 2 12 ) + ( m 1 ) ( 13 γ 4 46 γ 2 + 40 ) ] 128 ( γ 2 2 ) 2 ( 1 γ 2 ) .
Proof of Proposition 7.
In the third stage, the first-order condition of the profit of the alliance { S R }   π S R with respect to p D S R is calculated.
π S R p D S R = 1 γ + m 2 p D S R + 2 γ p R S R + r S R γ t m 1 γ 2 = 0 .
This yields that
p D S R = 1 γ + m + 2 γ p R S R + r S R γ t m 2 .
In the second stage, the first-order condition of channel D’s profit π D S R with respect to r S R is calculated.
d π D S R d r S R = γ + m + 2 r S R γ t m 1 2 γ 2 1 = 0 .
This yields that
r S R * = 1 γ m + γ t m 2 .
In the first stage, the first-order condition of the profit of the alliance { S R }   π S R with respect to p R S R is calculated.
π S R p R S R = 1 2 p R S R + t m = 0 .
This yields that
p R S R * = 1 + t m 2 .
By replacement, the following equilibrium is derived:
p D S R * = 3 γ + m ( 1 t γ ) 4 ,   r S R * = 1 γ + m ( t γ 1 ) 2 ,   p R S R * = 1 + t m 2 .
π S R = 2 γ m 1 m t 1 + 3 γ 2 m t 1 2 m m 8 t + 4 m t 2 2 5 16 γ 2 1 .
According to the Shapley value, the profits of the members are as follows:
ψ S S R = 1 2 [ v ( { S R } ) + v ( { S } ) v ( { R } ) ] = 1 16 [ ( t m 1 ) 2 ( m 1 ) 2 γ 2 2 ] + 4 γ 2 [ 12 2 m ( 5 + 7 t ) + m 2 ( 5 + 7 t 2 ) ] + γ 4 [ m ( 10 + 32 t m ( 5 + 16 t 2 ) ) 21 ] 16 [ 2 + m ( m 2 2 t + t 2 m ) ] 2 γ 3 ( γ 2 2 ) ( t m 1 ) ( m 1 ) + 3 γ 6 ( m 1 ) 2 64 ( γ 2 2 ) ( γ 2 1 ) , ψ R S R = 1 2 [ v ( { S R } ) + v ( { R } ) v ( { S } ) ] = [ γ ( 1 m ) + ( 1 t m ) ( γ 2 2 ) ] [ ( m 1 ) γ ( 5 γ 2 12 ) + ( t m 1 ) ( 13 γ 4 46 γ 2 + 40 ) ] 128 ( γ 2 2 ) 2 ( 1 γ 2 ) .

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Figure 1. Supplier’s product launch strategy through two e-commerce channels.
Figure 1. Supplier’s product launch strategy through two e-commerce channels.
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Figure 2. Profit of the supplier under the non-alliance pricing contract ( m = 0.4 ).
Figure 2. Profit of the supplier under the non-alliance pricing contract ( m = 0.4 ).
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Figure 3. Profit of the supplier under the alliance pricing contract ( m = 0.4 ).
Figure 3. Profit of the supplier under the alliance pricing contract ( m = 0.4 ).
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Table 1. Notation.
Table 1. Notation.
NotationDefinition
r Transaction commission rate charged by channel D
p Retail price on the consumer market
m Service cost of channel D
q Quantity of products sold
w Wholesale price charged by supplier S
d Markup of channel R
t Difference in service efficiency between channels
γ Competition degree between channels
π Profit
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MDPI and ACS Style

Li, Z.; Wang, B.; Wu, Y. Simultaneous or Sequential? Supplier Product Launch Strategy through E-Commerce Channels with Different Models. J. Theor. Appl. Electron. Commer. Res. 2024, 19, 1848-1868. https://doi.org/10.3390/jtaer19030091

AMA Style

Li Z, Wang B, Wu Y. Simultaneous or Sequential? Supplier Product Launch Strategy through E-Commerce Channels with Different Models. Journal of Theoretical and Applied Electronic Commerce Research. 2024; 19(3):1848-1868. https://doi.org/10.3390/jtaer19030091

Chicago/Turabian Style

Li, Zhiwen, Baojiao Wang, and Yeting Wu. 2024. "Simultaneous or Sequential? Supplier Product Launch Strategy through E-Commerce Channels with Different Models" Journal of Theoretical and Applied Electronic Commerce Research 19, no. 3: 1848-1868. https://doi.org/10.3390/jtaer19030091

APA Style

Li, Z., Wang, B., & Wu, Y. (2024). Simultaneous or Sequential? Supplier Product Launch Strategy through E-Commerce Channels with Different Models. Journal of Theoretical and Applied Electronic Commerce Research, 19(3), 1848-1868. https://doi.org/10.3390/jtaer19030091

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