In order to study the dual-channel pricing strategy of clothing manufacturing enterprises under the influence of consumer channel preference, this paper considers the situation that clothing enterprises mainly engaged in online sales sell clothes to consumers on live e-commerce platforms and traditional e-commerce platforms through resale and direct sales modes, and establishes the following two models:

In the resale mode, clothing manufacturing enterprises only act as suppliers and profit by supplying the same clothes to agents on different platforms. At the same time, the influence of consumer channel preference on consumers’ purchasing channels is also considered. Assuming that the potential market demand is q, among which δqconsumers accept both live e-commerce platforms and traditional e-commerce platforms, and the remaining (1−δ)q consumers refuse to buy clothes on live broadcasts and are only willing to buy clothes on traditional platforms (20).

At the same time, in order to describe the competitiveness of the two channels, the variable β is introduced as the channel competition coefficient, and considering the cost differences of the goods purchased on the two platforms, for example, the goods on the live shopping platform have the characteristics of time limit and limited quantity, which require consumers to stay in the live broadcast room to snap up. Missing the sales time or buying too slowly may lead to consumers failing to purchase the goods. Therefore, the cost variable C is introduced to combine with β to measure consumers’ choice of purchasing channels.

Different from offline shopping and live shopping, consumers shopping on the traditional platform means that they can only know the upper body effect and quality of the clothing after the purchase. Usually, in online shopping it is difficult to measure the quality of the goods through pictures. However, due to the anchor explanation and physical display of the live shopping, consumers’ estimation of the value of the goods is more accurate and sufficient. Therefore, the variable t is introduced as the consumer’s trust in the traditional shopping platform (2, 4, 21)so tv is the consumer’s estimation of the value of the goods (22, 23).

Finally, considering the high price competitiveness of the goods on the live-streaming platform, a large number of goods will disturb the market order, and the retailers on the live-streaming platform are willing to adopt the strategy of hunger marketing, so the retailers on the platform will not fully meet the needs of consumers, but only meetγ.

The relevant symbols and their meanings in the study are shown in the following table (18):

The utility function of consumers on the live-streaming e-commerce platform is (16, 18)

The utility function of consumers on traditional e-commerce platforms is:

When U_s1 ≥ U_t1, β≥q⁢(1-t)⁢v+Pt⁢i-Ps⁢i+Ct⁢iCs⁢i+Ct⁢i, and at this time, consumers choose to buy on live-streaming e-commerce platforms. The market demand functions of different platforms are:

Different from the demand composition of live-streaming platforms, the demand composition of traditional e-commerce platforms is also composed of some consumers who are not willing to accept live-streaming shopping.

Therefore, the demand function is as follows:

Under decentralized decision-making, the game model is composed of the relationship between the manufacturer and two retailers, and the Stackelberg game with the manufacturer as the leader and the two retailers as followers. Under this decision-making, only the situation where the manufacturer occupies the dominant position is considered. In the first stage, the manufacturer decides the platform’s unified wholesale pricew₁,and in the second stage, the two retailers decide the optimal retail price P_s1 and P_t1.

The objective function of the clothing manufacturing enterprise is:

The objective function of the live e-commerce platform is:

Considering that the price of the live e-commerce platform is more competitive than that of the traditional platform, the retailer adopts a hunger marketing strategy, which will not fully meet the needs of consumers, but only meet part of the needsγ.

The objective function of the traditional e-commerce platform is:

Theorem 1: In the dual-channel supply chain, there exists a unique optimal equilibrium solution in the game between the clothing enterprise, the traditional platform retailer, and the live e-commerce platform retailer.

Proof

The model is solved by reverse induction.

Given P_t1, the first and second partial derivatives of π_s1 are obtained:

According to ∂2⁡πs⁢1∂⁡Ps⁢12<0, it can be seen that there exists a unique equilibrium optimal pricing for live streaming platform retailers. If ∂⁡πs⁢1∂⁡Ps⁢1=0 is taken, it can be obtained:

At this point, the formula is the strategy of the live platform retailer, that is, if the traditional platform retailer chooses P_t1, the live platform retailer will choose P_s1. In the first stage, when the traditional platform retailer chooses P_t1, it is predicted that the live platform retailer will act according to P_s1(P_t1). Therefore, the optimal solution problem of the traditional platform retailer is to choose P_t1 so that π_t1(P_t1, P_s1 (P_t1)) is maximized.

The first and second partial derivatives of π_t1 are obtained:

According to ∂2⁡πt⁢1∂⁡Pt⁢12<0, it can be seen that there is a unique optimal pricing equilibrium for the traditional platform retailer. Taking ∂⁡πt⁢1∂⁡Pt⁢1=0:

Substituting P_s1 into P_t1 The optimal wholesale price at this time is:

Simultaneously, the equilibrium optimal pricing for retailers on the live streaming platform is:

Similarly, taking the second partial derivative of manufacturer profit with respect to wholesale price w₁ results in:

Therefore, the optimal wholesale price at this point is:

Substituting w1* into P_s1 and P_t1 yields Pt⁢1* and Ps⁢1*, which proves Theorem 1.

Theorem 2: As consumer trust t in traditional shopping platforms increases, the optimal equilibrium wholesale price w1* also increases, leading to higher profits π₁ for apparel manufacturing enterprises. Simultaneously, the pricing Pt⁢1* by traditional platform retailers increases, with profits π_t1 initially decreasing and then increasing. In contrast, the pricing Ps⁢1* on live shopping platforms decreases, resulting in lower profits π_s1.

Proof

To simplify the proof, let’s represent the three optimal equilibrium prices as follows:

where φ_t1, φ_s1, φ₁ denote the parts of the functions unrelated tot

Here, v-∂⁡Pt⁢1*∂⁡t=2⁢v⁢Ct⁢1⁢(δ-1)-2⁢v⁢Cs⁢14⁢Cs⁢1⁢δ-4⁢Ct⁢1-4⁢Cs⁢1+Ct⁢1⁢δ>0, hence ∂⁡π1∂⁡t>0

Also, -v+∂⁡Pt⁢1*∂⁡t-∂⁡Ps⁢1*∂⁡t=v⁢Ct⁢1+v⁢Cs⁢1⁢(1-δ)4⁢Cs⁢1⁢δ-4⁢Ct⁢1-4⁢Cs⁢1+Ct⁢1⁢δ<0, leading to ∂⁡πs⁢1∂⁡t<0

In conclusion, ∂⁡w1*∂⁡t>0,∂⁡Pt⁢1*∂⁡t>0,∂⁡Ps⁢1*∂⁡t<0,∂⁡π1∂⁡t>0,∂⁡πs⁢1∂⁡t<0,and ∂⁡πt⁢1∂⁡t initially decreases, becoming positive when \(t\) reaches a certain point. Thus, the second theorem is proved.

This proposition elucidates the relationship between the optimal equilibrium game solution of supply chain members and consumer trust in traditional shopping platforms. Higher trust brings higher pricing and profits for apparel manufacturing enterprises and traditional platform retailers. However, for live platform retailers, it suggests avoiding high trust product competition with traditional platform retailers, instead focusing on promoting and selling low-trust products.

Theorem 3: Reasonable secondary pricing by live shopping platform retailers is advantageous for market share capture.

Proof

As the pricing by live shopping platform retailers is a secondary pricing after the completion of primary pricing on traditional platforms, the game between them can be considered a complete information dynamic game with the following relationship:

At this point, the profit for live shopping platform retailers is:

Taking partial derivatives:

As the discount intensity increases, the profit of live shopping platform retailers initially rises and then falls. The optimal discount rate is:

Thus, within a certain range, offering discounts is beneficial for the revenue of retailers.

For traditional platform retailers, aware that live shopping platform retailers will perform secondary pricing based on their primary pricing, the profit function is:

To illustrate the impact of live platform discounts on traditional platform retailer profits:

Since traditional platform retailers set prices P_t1 higher than the wholesale price w₁, live platform discounts are bound to reduce traditional platform retailer profits.

This theorem highlights discount promotions as a common marketing strategy, emphasizing that, to a certain extent, lowering prices can enhance retailer revenue. However, excessive price reduction may lead to a price war, causing market disruption and harm to both sides.

Theorem 4: If live shopping platform retailers aim to attract more potential consumers by reducing profits through increased discount intensity while ensuring non-negative profits, the discount intensity should satisfy θ∈(max⁡(w1Pt⁢1,(1-t)⁢v+Pt⁢1-Cs⁢1Pt⁢1),1).

Proof

The function related to the discount intensity θ for live shopping platform retailers is:

When consumers prefer both platforms and choose the live shopping platform when both are willing, we have:

When the profit of live shopping platform is zero:

Thus, θ∈(max⁡(w1Pt⁢1,(1-t)⁢v+Pt⁢1-Cs⁢1Pt⁢1),1) proving the fourth theorem.

This theorem indicates that live shopping platform retailers managing multiple categories of products can attract more potential consumers by lowering prices for certain categories, even at the cost of reduced profits. Combining with the second theorem, live platform retailers can strategically lower prices for traditional e-commerce platform products with high consumer trust, avoiding excessive investment in high-trust products and potentially gaining a larger market with minimal losses.

Theorem 5: Based on the cost differences for consumers purchasing goods from different platforms, when w1>v⁢(2+t)3, for traditional platform retailers, changes in consumer shopping costs have a smaller impact on their own channel retail price than on the opposite side’s retail price. If, at this point, consumer channel preference (\(\delta\)) is within δ∈(0,23), then live shopping platform retailers also adhere to this theorem.

Proof

For Rt=∂⁡Pt⁢1∂⁡Ct⁢1-∂⁡Ps⁢1∂⁡Ct⁢1,

when δ∈(0,23), 12δ²−20δ + 8 > 0,

and when δ ∈ (0,1),8δ²−24δ + 16 > 0, δ²−6δ + 8 > 0

Thus, when w1<v⁢(2+t)3, Rt=∂⁡Pt⁢1∂⁡Ct⁢1-∂⁡Ps⁢1∂⁡Ct⁢1<0

For traditional platform retailers, when w1=v⁢(2+t)3 and δ∈(0,23), Rt=∂⁡Pt⁢1∂⁡Ct⁢1-∂⁡Ps⁢1∂⁡Ct⁢1<0. This implies that P_t1 changes at a slower rate with C_t1 than P_s1 changes withC_t1. For live shopping platform retailers, when w1<v⁢(2+t)3, Rs=∂⁡Ps⁢1∂⁡Cs⁢1-∂⁡Pt⁢1∂⁡Cs⁢1<0, indicating that P_s1 changes at a slower rate with C_s1 than P_t1 changes with C_s1. Thus, the fifth theorem is proved.

This theorem elucidates the relationship between the costs consumers incur when purchasing goods through traditional and live shopping platforms and the retail prices of goods on different platforms. In specific circumstances, both live platform retailers and traditional platform retailers experience a smaller impact on their own channel prices from changes in the cost consumers bear when purchasing goods through their channels compared to the impact on the opposite channel’s price.

In this decision-making model, apparel manufacturers directly join both live e-commerce platforms and traditional e-commerce platforms for sales. Therefore, in this model, the objective function for apparel manufacturers is given by:

which can be expressed as:

Under this decision-making mode, only the optimal equilibrium discount rate for live e-commerce platforms is considered to maximize the total profit for the apparel manufacturing enterprise without further distinguishing the profit differences between the two channels.

Theorem 6: Under centralized decision-making, there exists a unique optimal equilibrium discount rate θ and optimal equilibrium pricing P_t2, maximizing the overall profit for the apparel manufacturing enterprise.

Proof

The profitπ₂ for the apparel manufacturing enterprise with respect to the discount rate θ has first- and second-order partial derivatives:

This indicates the existence of an optimal equilibrium discount rate that maximizes the profit for the apparel manufacturing enterprise. When ∂⁡π2∂⁡θ=0, the optimal equilibrium discount rate is obtained:

Based on the Stackelberg game model, the secondary pricing behavior of the apparel manufacturing enterprise on the live e-commerce platform transforms the overall optimization problem into π₂(P_t2, θP_t2(θ)).

Therefore, taking the first and second partial derivatives of the profit function of the apparel manufacturing firm (denoted as π₂) with respect to the pricing set by the traditional e-commerce platform (P_t2):

Hence, there exists an optimal equilibrium price, P_t2, that maximizes the profit of the apparel manufacturing firm. Setting ∂⁡π2∂⁡Pt⁢2=0 yields:

Due to the marketing strategy of apparel manufacturers on live e-commerce platforms, not all consumers opting to purchase goods on these platforms will be satisfied. Only a proportion represented by γwill be catered to. However, the previously described model assumes that the quantity δq of consumers will inevitably choose to buy goods, overlooking the market demand changes due to discount pricing on live e-commerce platforms. For ease of calculation, we assume the price sensitivity function of market demand is given by:

Theorem 7: There exists an optimal equilibrium demand fulfillment, maximizing the profit for the apparel manufacturing enterprise.

Proof

In this model assumption, the profit function for the apparel manufacturing enterprise is given by:

Taking the first and second derivatives with respect to γ:

Thus, there exists an optimal equilibrium demand fulfillment, maximizing the profit for the apparel manufacturing enterprise. Setting ∂⁡π2∂⁡γ=0:

As the chosen price sensitivity function is a linear function, and real-world market demand and prices often exhibit a non-linear relationship, this model may not perfectly reflect the impact of demand fulfillment on the profit of the apparel manufacturing enterprise. However, it generally suggests that an appropriate level of demand fulfillment can enhance the profit of the apparel manufacturing enterprise.

Consumer trust in traditional e-commerce platforms positively influences the wholesale prices and profits of apparel manufacturers, as well as the retail prices of live e-commerce platform retailers. Conversely, it negatively impacts the retail prices and profits of traditional platform retailers. In other words, an increase in consumer trust in traditional e-commerce platforms leads to higher wholesale prices for apparel manufacturers and higher retail prices for traditional e-commerce platform retailers, while the retail prices of live e-commerce platform retailers will decrease. For live e-commerce platform retailers, products with low trust on traditional e-commerce platforms are typically those with stronger consumer desires, high-end fabric, or sophisticated designs. Retailers should capitalize on this characteristic of certain apparel products, reinforce consumer attitudes toward products with low trust on traditional e-commerce platforms, and leverage live shopping interactions and displays to highlight the features of live e-commerce platforms, making it easier to enhance overall company profits. Simultaneously, for high-trust products, live platform retailers can adopt a strategy of small profits and high sales. Under the premise of no losses, they can set appropriate discount levels to exchange minimal profits for higher consumer popularity and customer loyalty. For manufacturers and traditional platform retailers, brand promotion and increasing product stickiness can continuously build and enhance consumer trust in products, serving as an additional growth point for seeking business development.

If there are differences in the costs incurred by consumers when purchasing goods from traditional e-commerce platforms and live e-commerce platforms, changes in consumer shopping costs will directly impact the pricing of goods on both platforms. For traditional e-commerce platforms, when wi=v⁢(2+t)3 and δ∈(0,23) with the shopping costs of live e-commerce platforms remaining constant, the increase in shopping costs for traditional e-commerce platforms has a smaller impact on the retail prices of traditional platform retailers than on those of live platform retailers. Similarly, when wi=v⁢(2+t)3 and the shopping costs of traditional e-commerce platforms remain constant, the increase in shopping costs for live e-commerce platforms has a smaller impact on the retail prices of live platform retailers than on those of traditional platform retailers. Therefore, regardless of which channel’s retailer is setting retail prices, they should not only consider changes in the shopping costs of the other channel but also pay close attention to changes in their own channel’s shopping costs. In other words, for a dual-channel supply chain game, it is crucial not only to consider changes in one’s own channel value but also, more importantly, to focus on subtle improvements in the competitive channel. Changes in the prices and shopping costs of the competitive channel are closely related to consumer purchasing decisions. Timely insight into these changes and quicker formulation of response strategies are effective ways to address the consumer market in the game of dual-channel supply chains.