Pricing Decision Models of Manufacturer-Led Dual-Channel Supply Chain with Free-Rider Problem

Abstract

We study the strategic pricing decision models of manufacture-led dual-channel supply chains with the free-rider problem under the service level and cost. We use the Stackelberg model to study the impact of the degree with the free-rider problem of consumers on the optimal pricing strategy and the optimal service level of the dual-channel supply chain under various decision-making modes and carry out a numerical simulation. The main conclusions are as follows: In the retailer’s dual-channel supply chain, the deepening of consumer free-riding behavior will reduce the enthusiasm of retailers, but the weak position of the channel will lead to improved service levels and reduced prices, as well as to increase the wholesale price to cover costs. In the manufacturer’s dual-channel supply chain, the deepening of consumer free-riding behavior will lead to a decline in the retailers’ service level and enthusiasm, as well as to a decrease in the wholesale prices and retailers’ pricing. In the two types of dual-channel supply chains, the demand of manufacturers’ network channels increases, the price increases first and then decreases, and the profits of all supply chain members decrease with the increase in the free-rider coefficient of consumers. Finally, we use numerical simulation to verify the validity of the above conclusions, which provides a scientific basis to make optimal pricing decisions in the manufacturer-led dual-channel supply chain.

1. Introduction

The current rapid development of many e-commerce models as well as transportation, warehousing, and distribution technology by leaps and bounds has profoundly changed our lives. Under the influence of “Internet plus”, the business model has also begun to transform from the traditional single sales channel to the dual-channel model of “brick + mouse”. In 2010, Proctor & Gamble (P&G) opened an online store called PGestore, which has attracted wide attention from the industry. Esmaeili et al. [1] explored the optimal price and the optimal order quantity decision for different channels of different leaders. The “Internet Plus” online trading mode realizes transtemporal and transregional transactions, which save time, space costs, manpower costs, and so on. However, this model has brought an unprecedented crisis to traditional retailers, with a large number of offline retailers seeing a sharp decline in sales, and the prospect is not optimistic. As a result, traditional retailers choose to open up network channels to increase the market share of products. In the course of cooperation between manufacturers and retailers, the use of quantity discount contracts can achieve the coordination of dual-channel supply chains [2].

By comparing offline channels and online channels, online channels save time, space, and manpower costs and pay lower commodity costs, so it is easier to offer more favorable prices than offline channels, which leads to the price conflict between online and offline channels. In order to attract more consumers and gain greater competitive advantages, traditional retailers have taken a series of measures to ease the channel price conflict. For example, more professional staff, more timely launches, more thoughtful free experience services, and more convenient return and exchange services are provided. However, these measures to attract consumers also directly lead to the increase in the cost of channel services. In addition, some consumers do not directly purchase the relevant services provided by the products through traditional channels but choose the network channels with low prices. Under the premise of considering such free-riding behavior of consumers, if the dual-channel structure is different, the pricing decision of the supply chain should also be made according to the different structure to maximize the benefits. Free-riding behavior is defined as customers who enjoy free and high-quality services in a store and know product information, but they would buy low-priced products from retailers that do not provide services or provide low-quality services. For example, Apple Inc. has developed a fixed-price strategy for the dual-channel supply chain, in other words, the price of the same type of product in physical stores and official websites is exactly identical. However, companies such as Lenovo, Hongda Electric, and Samsung remain focused on the retailers they sign up. Wholesale price contracts have fewer effects on the income of supply chain members than two-step pricing contracts and quantity discount contracts [3]. Shin [4] and Wu et al. [5] studied the impact of dual-channel supply chains on retailer pricing strategies.

The dual-channel supply chain includes manufacturers and retailers, in which the manufacturers are responsible for producing products, part of which are sold wholesale to retailers, and the other part is sold directly to customers through their own online channels. Under the manufacturer-led dual-channel supply chain structure, the generation of consumer free-riding behavior leads to the transfer of supply chain demand, which leads to the conflict between dual-channel supply chains. It is assumed that the upstream and downstream enterprises of the supply chain are rational people who pursue the maximization of their own interests and conduct vertical and horizontal games under different dual-channel structures. The company will be dissatisfied with the cost of investment without the return of sales and will also strive to catch up with the company that gets more customers and revenue. The income loss caused by the free-riding behavior of customers will increasingly aggravate the income disputes between the upstream and downstream enterprises of the supply chain, which will have a negative impact in the long run and bring serious consequences to the market. Therefore, it has become an urgent problem to study and solve the pricing decision under the free-riding behavior of consumers in order to coordinate the benefits of dual-channel supply chains.

The gaps in the former research about manufacturer-led dual-channel supply chains are the lack of in-depth analysis with the free-rider problem on the pricing decision of dual-channel supply chains, and current research is mostly limited to single-type supply chains. This study mainly solves the following problems: (1) we study the optimal pricing strategy and service level in the dual-channel supply chain structure, considering the free-riding behavior of consumers; (2) we design the different structure of channels on the control line of different members under the leadership of the manufacturer and compare the difference of optimal decision and service level under different structure; and (3) the above model is verified by the example analysis, and the influence trend of the free-riding coefficient on the decision parameters is directly embodied.

2. Literature Review

The online retail market has shown abundant vitality, and the demand for goods through online channels has gradually increased. China’s online retail sales totaled CNY 1770.1 billion, an increase of 10.9% over the previous year. Among them, the physical goods online retail sales of CNY 97,590 billion, an increase of 14.8%, accounted for 24.9% of the total retail sales of consumer goods. In general, online channels have a positive growth trend and good prospects for development. The rapid development of online channels has caused fierce competition between the two channels. It has become the main research topic to formulate the corresponding pricing strategy to maximize the benefits of the upstream and downstream players in the dual-channel supply chain. Starting from the outside of the supply chain, some scholars have discussed how external factors such as government subsidies [6,7,8], random demand [9] or supply [10] and disruption demand [11], public preference [12], and consumer channel preference [13,14] determine the decision making of supply chain members. Other scholars have studied the nature of the supply chain [15], the nature of product supply [16], the issue of member fairness [17], sales costs [18], manufacturing cost [19] and sales strategies [20,21,22], and information sharing models [23] from the perspective of the internal member strategy of the supply chain and how member selection affects other members to change the optimal coordination state of the entire supply chain. With the global emphasis on environmental issues and the expanding awareness of eco-sustainability among customers, the question of how to effectively combine green development and supply chain coordination has also become an issue for scholars to consider. Das et al. [24] studied the coordination of a dual-channel supply chain taking into account the level of greening of the items. Barman et al. [25] explored and compared the best pricing strategies with and without government-provided green investment subsidies to maximize the overall profitability of the supply chain.

While the dual-channel supply chain model is gradually gaining popularity, online channels attract many consumers with their lower sales prices, resulting in fierce pricing competition between upstream and downstream enterprises in the supply chain and between online and offline channels. Among IT companies, Apple has formulated a fixed-price strategy for the dual-channel supply chain: consumers pay the same price from Apple’s physical stores and official website. However, some of its competitors, such as Lenovo, which produces personal computers, HTC in the smartphone industry, and Samsung in the tablet computer industry, still focus on their contracted retailers. In the digital camera industry, Canon continues to operate its online store and offers discounts for almost all types of products in its online store. In the clothing and cosmetics industry, many manufacturers began to operate both physical stores and online stores (such as Levi’s or Clinique). There are similar examples in other industries. As a means of opening up the market, the Internet has increased the market share of enterprises in the dual-channel supply chain model on the one hand, and on the other hand, it has triggered conflicts between channels, exacerbating the double marginalization effect. Therefore, it is of great significance to study how to price in order to coordinate the income of upstream and downstream enterprises in the dual-channel supply chain to achieve win–win results.

Based on the strong position of e-commerce channels through the development of the Internet, retailers have to amplify the advantages of physical sales to compete with them to secure their market position. Among them, providing high-quality physical services is a frequent choice of retailers to provide consumers with services before, during, and after the sale of products, including the product display and experience service, professional explanation, and convenient, fast return and exchange service. Regarding the influence of channel service on supply chain, Ma et al. [26] believe that the reference effect of the consumer will produce the “anchoring mentality”, which has a negative effect on the service level provided by the retailer; Mu et al. [27] found that the decrease in service cost would lead to the increase in consumers’ preference for e-commerce channels and the increase in retailers’ service level. They also proposed a service cost allocation contract which can coordinate the supply chain under decentralized decision making. Zhou et al. [28] proved that contracts can effectively stimulate retailers to provide higher quality services; Li et al. [29] and Ma et al. [30] considered how the “showroom” effect affects the pricing and service level of supply chain members; Wu et al. [31] found that the greater the negative spillover effect of service, the lower the profit and service level of supply chain members; Jiang et al. [32] discussed how consumers’ online channel preference affects the service value of retailers in view of the dual-channel supply chain dominated by retailers; Yao et al. [33] studied the influence of service value on supply chain decision making and the stability region of its decision system; and Yang et al. [34] and Li et al. [35] took retailer innovation service input as a variable to measure how it affected supply chain coordination. Considering the customer value and value-added services provided by online retail platforms, Yi et al. [36] discussed separately each pricing model in decentralized decision-making scenarios and centralized decision-making scenarios; Zhang et al. [37] established a game model with a dual-channel recycling structure based on consumers’ sensitivity to the services of third-party collectors in the reverse supply chain.

However, the channel service often fails to produce the desired effect of retailers, on the contrary, it leads to the “free-riding” behavior of consumers, in other words, customers turn to higher cost-effective online channel purchases after enjoying services in offline channels. In terms of free-riding behavior, Zhang et al. [38] studied the two-level supply chain marketing strategy with the “free-riding” phenomenon and believed that a low degree of “free-riding” was beneficial to stimulate retailers’ market efforts. Ke [39] focused on how the “free-riding” phenomenon affects members’ decision making when differential pricing and nondifferential pricing are used in supply chains; Yan et al. [40] considered the background of online finance and found that the level of members’ sales efforts was directly proportional to the retail price at the same “free-riding” level.

In the research on the influence of consumer behavior on the pricing decision of dual-channel supply chains, the free-riding behavior of consumer service plays a “double-edged sword” role on the dual-channel supply chain. However, few researchers have deeply analyzed the influence of consumer service free-riding behavior on the pricing decisions of dual-channel supply chains, and most of the research involved is limited to single-type supply chains. This study designs supply chains with different structures according to “free-riding” influencing factors to compare the influence trends under different supply chain environments, in order to give more comprehensive practical suggestions.

The main contributions of this study are as follows: (1) The influence analysis of the free-riding coefficient is extended from the traditional single-channel structure to the dual-channel structure, which enriches the research field and application scope. (2) Different from the existing single-structure dual-channel supply chain research, this study designs two channel structures in which the supply chain manufacturer or retailer controls the online channel under the manufacturer’s dominant premise and refines the optimal decision research of the dual-channel supply chain under different environments. (3) In addition to studying the optimal decision and the level of service provision, on this basis, this paper explores the retailer’s enthusiasm to provide service under the degree of free-riding behavior, which is promoted from the objective level to the subjective decision so as to more accurately predict the corresponding changes in the supply chain under the change in the free-riding coefficient.

The remainder of this study is organized as follows. Section 3 presents the Model establishment and solution, and the basic decision models of dual-channel supply chain are described in Section 3. The numerical calculation and analysis of results are presented in Section 4. Section 5 presents the discussion and managerial insights, followed by the conclusions in Section 6.

3. Model Establishment and Solution

3.1. Model Assumptions and Notation Description

The dual-channel supply chain analyzed in this paper is composed of a single manufacturer and a retailer. After the retailer wholesales the products produced by the manufacturer, the mode of selling goods to customers through online channels and offline channels is called the retailer dual-channel supply chain. In addition, after manufacturers produce products, a part of the products is wholesaled to retailers, and the other part is directly sold to customers through their own network channels, which is called manufacturers’ dual-channel supply chain. However, there is a free-riding behavior in the market—consumers turn to online channels after experiencing services in traditional channels, which leads to the transfer of demand, affects the profit distribution between the two channels, and leads to the conflict between channels. Based on this, consider the optimal pricing decisions of dual-channel supply chains with different power structures under consumer free-riding behavior, shown in Figure 1 and Figure 2.

The study background assumptions of this model are shown in

Table 1. List of the study background assumptions.

Study Background Assumptions
1	Upstream and downstream members of the supply chain are perfectly rational, with manufacturers and retailers being rational people seeking to maximize their own interests
2	In the dual-channel supply chain, the attitude of the manufacturer and retailer towards risk is neutral
3	For the convenience of calculation and analysis, it is assumed that the cost per unit product produced by the manufacturer is zero
4	The production capacity of the manufacturer can meet the market demand, and the products of the network channel and the traditional channel are homogeneous
5	The retail price of the commodity is always greater than the wholesale price, and the cost of sales in online and offline channels is not considered
6	The level of service provided by retailers in traditional channels is independent of channel model
7	The companies studied in this research mainly produce electronic and clothing products

.

The symbols used to build the model are shown in

Table 2. List of symbols.

Symbols	Definition
D	The market demand for products
h	The preference coefficient of consumers to offline channels in dual-channel supply chains
Pt, Pd	The sales prices of offline channel and online channel products are represented, respectively, $p_t>p_d$
M, R	M and R represent the manufacturer dual-channel model and the retailer dual-channel model, respectively
Dt	Market demand of offline channel products in dual-channel supply chain
Dd	Market demand of online channel products in dual-channel supply chain
a’, a	Demand price elasticity coefficient—the degree to which the demand function is affected by the price level of the channel
f	When there are both online and offline channels in the dual-channel supply chain, the channel demand is not only affected by the price of the product in the channel but also by the sales price of the product in the competitive channel, which is called cross-price elasticity coefficient, $a^{\prime },a>f>0$
$k$	The service cost coefficient, $k>0$
w	The price per unit product wholesaled by the manufacturer to the retailer
c	Production cost per unit of product
s	The service level provided by traditional channels
r	Demand elasticity coefficient of service, that is, the degree of influence of service level on demand function, $r>0$
e	Consumer free-riding coefficient, $0<e<1$
∏m,∏r,∏	They are, respectively, manufacturer profit, retailer profit, and total supply chain profit
$*$	The optimal pricing decision

.

3.2. Decision Model of Retailer Dual-Channel Supply Chain Considering Free-Riding Coefficient

In our study, it is assumed that the network channel does not provide customers with product information services when we study the pricing decision models of different dual-channel supply chain models under the leadership of manufacturers considering consumers’ “free-riding” behavior. Therefore, there is no corresponding service cost for online channels, while the service level provided by offline channels is $s$.

The traditional channel service cost function [41] is set as

$${\mathrm{C}}_t=\frac{k}{2}{s}^2$$

$k$ is the service cost coefficient, $k>0$.

3.2.1. Retailer Dual-Channel Demand Function

While the dual-channel supply chain model brings convenience, consumers’ “free-riding” behavior also causes channel conflicts, leading to the transfer of demand between different channels and between different business entities. In previous studies, the demand of dual-channel supply chains is mainly related to product price. Now, consumers, as rational people who pursue the maximization of their own interests, will experience products or services through traditional channels that provide the best quality services and turn to lower-priced online channels for purchase, resulting in the transfer of demand. Therefore, consumers’ “free-riding” behavior leads to the demand being not only affected by the product sales price but also by the service level and the free-riding coefficient. The introduction of quality service will optimize the product experience of consumers to enhance their purchase intention. Therefore, the demand of traditional channels is positively correlated with the service level, and the increment of demand is $rs$, while the demand of consumers transferred to network channels after “free-riding” behavior is $ers$.

The dual-channel demand functions considering consumers’ “free-riding” behavior are as follows:

$$D_{tR}=(1-h)D-a^{\prime }{p}_{tR}+f(p_{dR}-p_{tR})+(1-e)r{s}_R$$

(1)

$$D_{dR}=hD-a^{\prime }{p}_{dR}+f(p_{tR}-p_{dR})+er{s}_R$$

(2)

For ease of calculation, it is simplified as

$$D_{tR}=(1-h)D-a{p}_{tR}+f{p}_{dR}+(1-e)r{s}_R$$

(3)

$$D_{dR}=hD-a{p}_{dR}+f{p}_{tR}+er{s}_R$$

(4)

3.2.2. Retailer Dual-Channel Profit Function

In a retailer-led dual-channel supply chain, the manufacturer obtains profits by providing products to the retailer, while the retailer obtains profits by selling products online and offline. So, the revenue function of manufacturers and retailers is expressed as follows:

$${\Pi }_{mR}=(w_R-c)(D_{tR}+D_{dR})=(w_R-c)[D-(a-f)(p_{tR}+p_{dR})+r{s}_R]$$

(5)

$$\begin{array}{ll}{\Pi }_{rR}\hfill & =(p_{tR}-w_R)D_{dR}-C_t+(p_{dR}-w_R)D_{dR}\hfill \\ & =(p_{tR}-w_R)[(1-h)D-a{p}_{tR}+f{p}_{dR}+(1-e)r{s}_R]-\frac{k}{2}{s}_R{}^2+(p_{dR}-w_R)[hD-a{p}_{dR}+f{p}_{tR}+er{s}_R]\hfill \end{array}$$

(6)

$${\Pi }_R={\Pi }_{mR}+{\Pi }_{rR}$$

(7)

Compared with centralized decision making, each subject in the supply chain under the decentralized decision-making mode aims at maximizing their own interests. In the manufacturer-dominated retailer dual-channel supply chain pricing Stackelberg game model, the manufacturer takes the dominant position. The manufacturer first sets the wholesale price according to the market situation, and the retailer sets the sales price of the traditional channel, the network channel, and the service level of the traditional channel according to the wholesale price set by the manufacturer. Firstly, the Hessian matrix of dual-channel retailer’s profit function about traditional channel price, online channel price, and traditional channel service level is solved by backward induction.

$$\mathrm{H}=\left[\begin{array}{ccc}\frac{{\partial }^2{\mathsf{\Pi }}_{rR}}{\partial p_{tR}{ }^2}& \frac{{\partial }^2{\mathsf{\Pi }}_{rR}}{\partial p_{tR}\partial p_{dR}}& \frac{{\partial }^2{\mathsf{\Pi }}_{rR}}{\partial p_{tR}\partial s_R}\\ \frac{{\partial }^2{\mathsf{\Pi }}_{rR}}{\partial p_{dR}\partial p_{tR}}& \frac{{\partial }^2{\mathsf{\Pi }}_{rR}}{\partial p_{dR}{ }^2}& \frac{{\partial }^2{\mathsf{\Pi }}_{rR}}{\partial p_{dR}\partial s_R}\\ \frac{{\partial }^2{\mathsf{\Pi }}_{rR}}{\partial s_R\partial p_{tR}}& \frac{{\partial }^2{\mathsf{\Pi }}_{rR}}{\partial s_R\partial p_{dR}}& \frac{{\partial }^2{\mathsf{\Pi }}_{rR}}{\partial s_R^2}\end{array}\right]=\left[\begin{array}{ccc}-2a& 2f& r\left(1-e\right)\\ 2f& -2a& re\\ r\left(1-e\right)& re& -k\end{array}\right]$$

(8)

It can be concluded that the retailer ‘s profit function is not a strictly concave function of the dual-channel price level and the traditional channel service level. Accordingly, the optimal pricing decision for the manufacturer-led retailer dual-channel supply chain is first found when the service level is determined.

3.2.3. Optimal Pricing when Service Level Is Determined

After the service level is determined, the partial derivative of the retailer‘s profit function with respect to the retailer’s dual-channel price is obtained, and it is brought into the profit function to obtain

$${\Pi }_{mR}(s_R,w_R)=\frac{(w_R-c)(D-2a{w}_R+r{s}_R+2f{w}_R)}{2}$$

(9)

$M$ stands for manufacturer-led dual-channel supply chain. It can be seen that the revenue function is a strictly concave function about $w$.

Therefore, the optimal wholesale price can be obtained as follows:

$$w_R(s_R)=\frac{D}{4(\mathrm{a}-f)}+\frac{r{s}_R}{4(a-f)}+\frac{c}{2}$$

(10)

Substituting the optimal wholesale price into the partial derivative of the retailer’s revenue function obtained just about the traditional channel and the network channel price in the retailer’s dual channel, the optimal pricing of the manufacturer-led dual-channel retailer considering the consumer’s “free-riding” behavior is obtained:

$$p_{tR}(s_R)=\frac{(a+5f)D}{8(a^2-f^2)}+\frac{c}{4}+\frac{hD-er{s}_R}{2(a+f)}+\frac{(5a+f)r{s}_R}{8(a^2-f^2)}$$

(11)

$$p_{dR}(s_R)=\frac{(f+5a)D}{8(a^2-f^2)}+\frac{c}{4}-\frac{hD-er{s}_R}{2(a+f)}+\frac{(5f+a)r{s}_R}{8(a^2-f^2)}$$

(12)

By substituting it into the demand function, the demand of the traditional channel and network channel of dual-channel retailers can be written as follows:

$${\mathrm{D}}_{tR}(s_R)=\frac{c(f-a)}{4}+\frac{D(3-4h)}{8}+\frac{(3-4e)r{s}_R}{8}$$

(13)

$${\mathrm{D}}_{dR}(s_R)=\frac{c(f-a)}{4}+\frac{D(4h-1)}{8}+\frac{(4e-1)r{s}_R}{8}$$

(14)

The corresponding revenue function can be calculated as follows:

$${\Pi }_{\mathrm{mR}}(s_R)=\frac{{(D-2ac+2fc+r{s}_R)}^2}{16(a-f)}$$

(15)

$${\Pi }_{r\mathrm{R}}(s_R)=\frac{{(D+r{s}_R)}^2}{32(a-f)}-\frac{(D+r{s}_R)c-(a-f)c^2}{8}-\frac{k{s}_R{}^2}{2}+\frac{{[(2h-1)D-(1-2e)r{s}_R]}^2}{8(a+f)}$$

(16)

$${\Pi }_R(s_R)=\frac{{(D+r{s}_R)}^2}{32(a-f)}-\frac{c(D+r{s}_R)-(a-f)c^2}{8}-\frac{k{s}_R{}^2}{2}+\frac{{[(2h-1)D-(1-2e)r{s}_R]}^2}{8(a+f)}+\frac{{(D-2ac+2fc+r{s}_R)}^2}{16(a-f)}$$

(17)

3.2.4. Solve for Optimal Service Level

Substitute Equation (10) into the retailer’s profit function to obtain

$${\Pi }_{rR}(s_R)=\frac{(a+f){[D+2c(a-f)+r{s}_R]}^2+4(a-f){[(2h-1)D+r{s}_R(2e-1)]}^2}{32(a^2-f^2)}-\frac{(D+r{s}_R)c+2k{s}_R{}^2}{4}$$

(18)

Only when $\frac{r^2{(1-2e)}^2[(a-f)+r^2(a+f)]}{16(a^2-f^2)}-k<0$, it simplifies to $r^2<16k(a-f)$, ${\Pi }_{rR}(s_R)$ is a strictly concave function of $s_R$.

So the optimal service level can be obtained:

$${\mathrm{s}}_R{}^{*}=\frac{8Dr(a-f)[1-h+e(2h-1)]+Dr(5f-3a)+2c(f^2-a^2)}{r^2[16(a-f)(e-e^2)-5a+3f]+16k(a^2-f^2)}$$

(19)

By substituting it into Equation (19), the optimal price of retailers’ traditional channel and online channel can be obtained as follows:

$$w_R{}^{*}(s_R{}^{*})=\frac{D}{4(\mathrm{a}-f)}+\frac{r{s}_R{}^{*}}{4(a-f)}+\frac{c}{2}$$

(20)

$$p_{tR}{}^{*}=\frac{c}{4}+\frac{(1-h)D-er{s}_R{}^{*}}{2(a+f)}+\frac{(5a+f)r{s}_R{}^{*}+(a+5f)D}{8(a^2-f^2)}$$

(21)

$$p_{\mathrm{d}R}{}^{*}=\frac{c}{4}-\frac{(1-h)D-er{s}_R{}^{*}}{2(a+f)}+\frac{(5f+a)r{s}_R{}^{*}+( f+5a)D}{8(a^2-f^2)}$$

(22)

Similarly:

$${\mathrm{D}}_{tR}{}^{*}(s_R{}^{*})=\frac{c(f-a)}{4}+\frac{D(3-4h)}{8}+\frac{(3-4e)r{s}_R{}^{*}}{8}$$

(23)

$${\mathrm{D}}_{dR}{}^{*}(s_R{}^{*})=\frac{c(f-a)}{4}+\frac{D(4h-1)}{8}+\frac{(4e-1)r{s}_R{}^{*}}{8}$$

(24)

$${\Pi }_{\mathrm{mR}}{}^{*}(s_R{}^{*})=\frac{{(D-2ac+2fc+r{s}_R{}^{*})}^2}{16(a-f)}$$

(25)

$${\Pi }_{r\mathrm{R}}{}^{*}(s_R{}^{*})=\frac{{(D+r{s}_R{}^{*})}^2}{32(a-f)}-\frac{(D+r{s}_R{}^{*})c-(a-f)c^2}{8}-\frac{k{s}_R{{}^{*}}^2}{2}+\frac{{[(2h-1)D-(1-2e)r{s}_R{}^{*}]}^2}{8(a+f)}$$

(26)

$$\begin{array}{l}{\Pi }_R{}^{*}(s_R{}^{*})=\frac{{(D+r{s}_R{}^{*})}^2}{32(a-f)}-\frac{(D+r{s}_R{}^{*})c-(a-f)c^2}{8}-\frac{k{s}_R{{}^{*}}^2}{2}+\frac{{[(2h-1)D-(1-2e)r{s}_R{}^{*}]}^2}{8(a+f)}\\ +\frac{{(D-2ac+2fc+r{s}_R{}^{*})}^2}{16(a-f)}\end{array}$$

(27)

 Theorem 1. 

By calculating the partial derivative of the retailer’s dual-channel price, namely Equations (9) to (11), to the service level, we can obtain that the partial derivatives of retail network channel and traditional channel sales price and manufacturer wholesale price to service level are all greater than zero—in the manufacturer-led retailer dual-channel supply chain, with the improvement of service levels, the retailer’s online channel and offline channel sales prices have increased, and the manufacturer’s wholesale price also increased.

 Proof of Theorem 1. 

$$\begin{gathered} \frac{\partial p_{dR}(s_R)}{\partial s_R}=\frac{[(5-4e)f+(1+4e)a]r}{8(a^2-f^2)} \\ \frac{\partial p_{tR}(s_R)}{\partial s_R}=\frac{[(5-4e)a+(1+4e)f]r}{8(a^2-f^2)} \\ \frac{\partial w_R(s_R)}{\partial s_R}=\frac{r}{4(a-f)} \end{gathered}$$

It can be explained that retailers increase the cost of the channel because of providing services, and the upstream and downstream enterprises in the supply chain are rational individuals who pursue their own interests to maximize them. In order to obtain greater benefits, retailers increase the prices of traditional channels and online channels. Manufacturers dominate the supply chain in the face of retailers to increase sales prices in order to maximize their own interests, based on the original cost to increase the wholesale price. In essence, the cost of retailers in providing quality services is borne by consumers. □

 Theorem 2. 

When the free-riding coefficient is less than 1/2, the partial derivative of the retailer’s traditional channel with respect to the free-riding coefficient is greater than the online channel. When the free-riding coefficient is greater than 1/2, the partial derivative of the retailer’s traditional channel to the free-riding coefficient is less than that of the network channel.

 Proof of Theorem 2. 

$$\begin{gathered} \frac{\partial p_{tR}(s_R)}{\partial s_R}-\frac{\partial p_{dR}(s_R)}{\partial s_R}=\frac{r(1-2e)}{2a+2f} \\ \mathrm{When} \frac{\partial p_{tR}(s_R)}{\partial s_R}-\frac{\partial p_{dR}(s_R)}{\partial s_R}>0,1-2e>0,\mathrm{this} \mathrm{is}, e<1/2 \\ \mathrm{When} \frac{\partial p_{tR}(s_R)}{\partial s_R}-\frac{\partial p_{dR}(s_R)}{\partial s_R}<0,1-2e<0,\mathrm{this} \mathrm{is}, e>1/2 \end{gathered}$$

When there is less free riding, consumers buy more products in traditional channels, and the price of traditional channels increases faster with the increase in the free-riding coefficient, which indicates that the transaction costs brought by retailers providing high-quality services are shared by customers in traditional channels. When the free-riding situation is greater, consumers buy more products in the network channel, and the price of the network channel increases faster with the increase in the free-riding coefficient, indicating that the price of the network channel is higher, and the service cost of the network channel is also greater. □

 Theorem 3. 

When the free-riding coefficient is in the range of$\left(0,1/4\right)$, the partial derivative of the retailer’s traditional channel demand to the service level is greater than zero, and the partial derivative of the retailer’s network channel demand to the service level is less than zero. When the free-riding coefficient is in the range of $\left(1/4,3/4\right)$, the partial derivative of the retailer’s traditional channel and online channel demand to the service level is greater than zero. When the free-riding coefficient is in the higher range of$\left(3/4,1\right)$, the partial derivative of the retailer’s traditional channel demand to the service level is less than zero, and the partial derivative of the retailer’s network channel demand to the service level is greater than zero.

 Proof of Theorem 3. 

$$\begin{gathered} \frac{\partial {\mathrm{D}}_{\mathrm{t}R}(s_R)}{\partial s_R}=\frac{r(3-4e)}{8}\frac{\partial {\mathrm{D}}_{\mathrm{d}R}(s_R)}{\partial s_R}=\frac{r(4e-1)}{8} \\ \mathrm{When} \frac{\partial {\mathrm{D}}_{\mathrm{tR}}(s_R)}{\partial s_R}>0,3-4e>0,0<e<3/4 \\ \mathrm{When} \frac{\partial {\mathrm{D}}_{\mathrm{tR}}(s_R)}{\partial s_R}<0,3-4e<0,3/4<e<1 \\ \mathrm{When} \frac{\partial {\mathrm{D}}_{\mathrm{d}R}(s_R)}{\partial s_R}>0,4e-1>0,1/4<e<1 \\ \mathrm{When} \frac{\partial {\mathrm{D}}_{\mathrm{d}R}(s_R)}{\partial s_R}<0,4e-1<0,0<e<1/4 \end{gathered}$$

When the free-riding coefficient is in the range of $\left(0,1/4\right)$, with the improvement of service level, the retailer’s traditional channel demand increases and the network channel demand decreases. When the free-riding coefficient is in the range of $\left(1/4,3/4\right)$, the demand of traditional channels and network channels increases with the increase in service level. When the free-riding coefficient is in the higher range of $\left(3/4,1\right)$, the retailer’s traditional channel demand decreases, while the network channel demand increases. Only when the free-riding factor is at $\left(1/4,3/4\right)$ does the retailer’s dual-channel demand increase as the service level increases. That is to say, no matter how the service level is improved, the demand of retailers’ dual-channel supply chain will not continue to increase, which is closely related to the “free-riding” coefficient of consumers. □

 Theorem 4. 

The partial derivatives of the sales price and demand of the traditional channel of the retailer to the free-riding coefficient are less than zero, while the partial derivatives of the sales price and demand of the network channel to the free-riding coefficient are greater than zero, and the manufacturer’s wholesale price to the free-riding coefficient is zero. In the manufacturer-led dual-channel supply chain, as the free-riding coefficient increases, the sales price and demand of the retailer’s traditional channel decrease, and the sales price and demand of the network channel increase, while the manufacturer’s wholesale price has nothing to do with it.

 Proof of Theorem 4. 

$$\begin{gathered} \frac{\partial p_{tR}(s_R)}{\partial e}=-\frac{rs}{2a+2f} \frac{\partial {\mathrm{D}}_{\mathrm{t}R}(s_R)}{\partial e}=-\frac{r{s}_R}{2} \\ \frac{\partial {\mathrm{D}}_{d\mathrm{R}}(s_R)}{\partial e}=\frac{r{s}_R}{2} \frac{\partial {\mathrm{w}}_R(s_R)}{\partial e}=0 \end{gathered}$$

This conclusion explains the following: With the increase in the free-riding coefficient, the demand of traditional channels decreases, while the demand of network channels increases. In order to further attract customers, the price of traditional channel products decreases, while the price of network channel products increases in order to improve profits, and the balance is realized. The free-riding coefficient of consumers has no effect on the balance of manufacturers. □

3.3. A Dual-Channel Supply Chain Decision Model for Manufacturers Considering the Free-Riding Factor

With the development of the Internet, manufacturers not only rely on offline channels to wholesale products to retailers but also gradually add online channels to close the distance between them and consumers so as to facilitate better understanding of consumers’ individual needs, as well as to also greatly meet the requirements of manufacturing enterprises to achieve flat development, such as Haier, Huawei, Xiaomi, etc. The demand functions for the manufacturer’s traditional retail channel and the network direct sales channel are as follows:

$$D_{tM}=(1-h)D-a{p}_{tM}+f{p}_{dM}+(1-e)r{s}_M$$

(28)

$$D_{\mathrm{d}M}=hD-a{p}_{dM}+f{p}_{tM}+er{s}_M$$

(29)

The profit functions of the manufacturer and the retailer are, respectively, as follows:

$${\Pi }_{mM}=(w_M-c)D_{tM}+(p_{dM}-c)D_{dM}$$

(30)

$${\Pi }_{rM}=(p_{tM}-w_M)D_{tM}-C_t$$

(31)

3.3.1. Optimal Pricing When Service Levels Are Determined

The manufacturer dominates in the manufacturer’s dual-channel supply chain. In the first stage of the game, the manufacturer prioritizes the offline channel wholesale price and the online channel retail price according to the competitive market situation and the demand forecast. In the second stage of the game, the retailer sets the offline channel retail price based on the manufacturer’s pricing strategy. Solved by backward induction, both the manufacturer and the retailer pursue the goal of revenue maximization. First, substitute Equation (28) into Equation (30), the retailer’s profit on the traditional channel retail price, to find the first-order partial derivative, and making the derivative zero can be solved for the response function as:

$$p_{tM}=\frac{(1-h)D+a{w}_M+f{p}_{dM}+(1-e)r{s}_M}{2a}$$

(32)

Substituting Equations (28), (29), (32) into Equation (30), the first-order partial derivative of the manufacturer’s profit function with respect to the wholesale price of the traditional channel and the retail price of the direct network sales channel can be obtained:

$$\frac{\partial {\Pi }_{mM}}{\partial w_M}=f{p}_{dM}-a{w}_M+\frac{(1-h)D+(a-f)c+(1-e)r{s}_M}{2}$$

(33)

$$\frac{\partial {\Pi }_{mM}}{\partial p_{dM}}=-\frac{cf}{2}+hD+a(c-2p_{dM})+er{s}_M+\frac{f[(1-h)D-cf+2f{p}_{dM}+(1-e)r{s}_M]}{2a}+f{w}_M$$

(34)

The Hessian matrix of ${\Pi }_{mM}$ on point $(w_M,p_{dM})$ is

$$\mathrm{H}=\left|\begin{array}{cc}\frac{{\partial }^2{\Pi }_{mM}}{\partial w_M{}^2}& \frac{{\partial }^2{\Pi }_{mM}}{\partial w_M\partial p_{dM}}\\ \frac{{\partial }^2{\Pi }_{mM}}{\partial p_{dM}\partial w_M}& \frac{{\partial }^2{\Pi }_{mM}}{\partial p_{dM}{}^2}\end{array}\right|=\left|\begin{array}{cc}-a& f\\ f& -2a+\frac{f^2}{a}\end{array}\right|=2(a^2-f^2)$$

(35)

Because $\mathrm{H}>0$,and $\frac{{\partial }^2{\Pi }_{mM}}{\partial w_M{}^2}<0$,the Hessian matrix is negative definite, and ${\Pi }_{mM}$ is a strictly concave function about $w_M,p_{dM}$,in which ${\Pi }_{mM}$ are local maximum at $(w_M,p_{dM})$. Then, the manufacturer’s optimal wholesale price and the sales price of the direct network sales channel can be solved as

$$w_M=\frac{a^{2}c+a[(1-h)D+(1-e)r{s}_M]+f(hD-cf+er{s}_M)}{2(a^2-f^2)}$$

(36)

$$p_{dM}=\frac{a^{2}c+f[(1-h)D-cf+(1-e)r{s}_M]+a(hD+er{s}_M)}{2(a^2-f^2)}$$

(37)

Substituting the above two equations gives

$$p_{tM}=\frac{a^{3}c+a^2[cf+3D(1-h)+3(1-e)r{s}_M]-f^2[(1-h)D+cf+(1-e)r{s}_M]+af(2hD-cf+2er{s}_M)}{4(a^3-a{f}^2)}$$

(38)

$${\mathrm{D}}_{tM}=\frac{(f-a)c+(1-h){\mathrm{D}+(1-\mathrm{e})\mathrm{rs}}_M}{4}$$

(39)

$$D_{dM}=\frac{-2a^{2}c+f[(1-h)D+cf+(1-e)r{s}_M]+a(2hD+cf+2er{s}_M)}{4a}$$

(40)

$${\Pi }_{mM}=\frac{\begin{array}{l}3a^4{c}^2+f^2{[(1-h)D+cf+(1-e)r{s}_M]}^2-2a^{3}c[cf+(1+h)D+(1+e)r{s}_M]+\\ 2af\{c^2{f}^2-2d^2(h-1)h+2d(e+h-2eh)r{s}_M{+2(1-\mathrm{e})\mathrm{er}}^2{s}_M{}^2+\\ cf[(1+h)D+(1+e)r{s}_M]\}+a^2\{-4c^2{f}^2+d^2(1-2h+3h^2)+\\ 2c(e-1)fr{s}_M+(1-2e+3e^2)r^2{s}_M{}^2+2d[cf(h-1)+(1-e-h+3eh)r{s}_M\left]\right\}\end{array}}{8a(a^2-f^2)}$$

(41)

3.3.2. Solving for the Optimal Service Level

By substituting Equations (28), (32) and (36) into Equation (31), the profit function of retailers in manufacturer-dominated manufacturer dual-channel supply chain can be written:

$${\Pi }_{rM}=\frac{a^2{c}^2+{[(1-h)D+cf+(1-e)r{s}_M]}^2-2a\{4k{s}_M{}^2+c[(1-h)d+cf+(1-e)r{s}_M\}}{16a}$$

(42)

Taking the second-order partial derivative of the profit function with respect to the level of service provided by the retailer’s traditional channels yields $\frac{{\partial }^2{\Pi }_{rM}}{\partial s_M{}^2}=\frac{-8ak+{(1-e)}^2{r}^2}{8a}$, when $r^2<\frac{8ak}{{(1-e)}^2}$, the profit function is strictly concave with respect to the service level, and the optimal service level in the manufacturer-led manufacturer dual-channel supply chain is found to be

$$s_M{}^{*}=\frac{(e-1)[(a-f)c+(h-1)D]r}{8ak-{(1-e)}^2{r}^2}$$

(43)

Similarly, the optimal wholesale price, selling price, and demand and profit function for a manufacturer-led manufacturer dual-channel supply chain considering consumer free-riding behavior can be obtained as follows:

$$w_M{}^{*}=\frac{a^{2}c+a[(1-h)D+(1-e)r{s}_M{}^{*}]+f(hD-cf+er{s}_M{}^{*})}{2(a^2-f^2)}$$

(44)

$$p_{dM}{}^{*}=\frac{a^{2}c+f[(1-h)D-cf+(1-e)r{s}_M{}^{*}]+a(hD+er{s}_M{}^{*})}{2(a^2-f^2)}$$

(45)

$$p_{tM}{}^{*}=\frac{a^{3}c+a^2[cf+3(1-h)D+3(1-e)r{s}_M{}^{*}]-f^2[(1-h)D+cf+(1-e)r{s}_M{}^{*}]+af(2hD-cf+2er{s}_M{}^{*})}{4a(a^2-f^2)}$$

(46)

$${\mathrm{D}}_{tM}{}^{*}=\frac{(f-a)c+(1-h){\mathrm{D}+(1-\mathrm{e})\mathrm{rs}}_M{}^{*}}{4}$$

(47)

$$D_{dM}{}^{*}=\frac{-2a^{2}c+f[(1-h)D+cf+(1-e)r{s}_M{}^{*}]+a(2hD+cf+2er{s}_M{}^{*})}{4a}$$

(48)

$${\Pi }_{rM}{}^{*}=\frac{a^2{c}^2+{[(1-h)D+cf+(1-e)r{s}_M{}^{*}]}^2-2a\{4k{s}_M{{}^{*}}^2+c[(1-h)D+cf+(1-e)r{s}_M{}^{*}\}}{16a}$$

(49)

$${\Pi }_{mM}{}^{*}=\frac{\begin{array}{l}3a^4{c}^2+f^2{[(1-h)D+cf+(1-e)r{s}_M{}^{*}]}^2-2a^{3}c[cf+(1+h)D+(1+e)r{s}_M{}^{*}]+\\ 2af\{c^2{f}^2-2h(h-1)D^2+2(e+h-2eh)r{s}_M{}^{*}D{+2(1-\mathrm{e})\mathrm{er}}^2{s}_M{{}^{*}}^2+\\ cf[(1+h)D+(1+e)r{s}_M{}^{*}]\}+a^2\{[-4c^2{f}^2+D^2(1-2h+3h^2)+\\ 2c(e-1)fr{s}_M{}^{*}+(1-2e+3e^2)r^2{s}_M{{}^{*}}^2+2D[cf(h-1)+(1-e-h+3eh)r{s}_M{}^{*}]\}\end{array}}{8a(a^2-f^2)}$$

(50)

 Theorem 5. 

In the manufacturer’s dual-channel model, the retailer’s traditional channel sales price and the manufacturer’s direct sales channel price have increased as the traditional channel service level has improved. In the Stackelberg game decision, the manufacturer raises the wholesale price to the retailer in order to gain greater revenue. The increase in the sales price of the manufacturer’s direct sales channel and the retailer’s traditional channel sales price are closely related to the coefficient of consumer free riding, with the increase in the number of consumers free riding, the price increase slope of the traditional channel decreases, while the price increase slope of the network direct sales channel increases.

 Proof of Theorem 5. 

$$\begin{gathered} \frac{\partial p_{tM}}{\partial s_M}=\frac{3a^2(1-e)r+2afer-(1-e)f^{2}r}{4a(a^2-f^2)}=\frac{2afer+(3a^2-f^2)(1-e)r}{4a(a^2-f^2)} \\ \frac{\partial p_{dM}}{\partial s_M}=\frac{(ae+f-ef)r}{2(a^2-f^2)}=\frac{fr+(a-f)er}{2(a^2-f^2)} \\ \frac{\partial w_M}{\partial s_M}=\frac{(a-ae+ef)r}{2(a^2-f^2)}=\frac{a(1-e)r+efr}{2(a^2-f^2)} \\ \mathrm{Due} \mathrm{to} a>f,\frac{\partial p_{tM}}{\partial s_M}>0,\frac{\partial p_{dM}}{\partial s_M}>0,\frac{\partial w_M}{\partial s_M}>0; \\ \mathrm{Let} {\beta }_1=\frac{\partial p_{tM}}{\partial s_M}, \mathrm{then} \frac{\partial {\beta }_1}{\partial e}=-\frac{(3a+f)r}{4a(a+f)}<0 \\ \mathrm{Let} {\beta }_2=\frac{\partial p_{\mathrm{d}M}}{\partial s_M}, \mathrm{then} \frac{\partial {\beta }_2}{\partial e}=\frac{r}{2(a+f)}>0 \end{gathered}$$

Description: After traditional channel retailers upgraded their service levels, both manufacturers and retailers increased their selling and wholesale prices to varying degrees, suggesting that the increased supply chain costs and promotional costs of upgrading service levels were indirectly borne by consumers. With the increase in the free-riding coefficient, consumers buy more products online after experiencing the service and traditional channels reduce the increase in sales price to avoid losing a large number of customers, while online direct sales channels increase the increase in sales price to gain more profit. □

 Theorem 6. 

In the manufacturer’s dual-channel supply chain model, demand in both the offline and online channels is positively correlated with service levels. When$e\in [0,1-\frac{2a}{3a-f})$, service level has a greater positive impact on the offline channel than on the online channel. When$e\in [1-\frac{2a}{3a-f},1)$, service level has a smaller positive impact on the offline channel than on the online channel.

 Proof of Theorem 6. 

$$\frac{\partial {\mathrm{D}}_{tM}}{\partial s_M}=\frac{(1-e)r}{4}>0$$

$$\frac{\partial {\mathrm{D}}_{dM}}{\partial s_M}=\frac{[2ae+(1-e)f]r}{4a}>0$$

$$\mathrm{When} \frac{\partial {\mathrm{D}}_{\mathrm{t}M}}{\partial s_M}-\frac{\partial {\mathrm{D}}_{\mathrm{d}M}}{\partial s_M}>0, \mathrm{there} \mathrm{is} e<1-\frac{2a}{3a-f}$$

$$\mathrm{When} \frac{\partial {\mathrm{D}}_{\mathrm{t}M}}{\partial s_M}-\frac{\partial {\mathrm{D}}_{\mathrm{d}M}}{\partial s_M}<0, \mathrm{there} \mathrm{is} e>1-\frac{2a}{3a-f}$$

The quality of service provided by the retailer’s offline channel will increase the attractiveness of the channel and customer stickiness, thus attracting consumers to experience and purchase, which enhances the demand of the offline channel. In addition, there is an increase in demand for online channels as some consumers turn to lower-cost online channels to purchase products after experiencing the service. Additionally, the degree of increase in demand in both channels is closely related to the free-riding coefficient: consumers buy more in offline channels when the free-riding coefficient is less than $1-\frac{2a}{3a-f}$, and consumers buy more in online channels when the free-riding coefficient is more than $1-\frac{2a}{3a-f}$. □

 Theorem 7. 

In a manufacturer-led dual-channel supply chain model, as the free-riding coefficient increases, both price and demand decrease in the retailer’s traditional channel, while both price and demand increase in the manufacturer’s direct sales channel.

 Proof of Theorem 7. 

$$\frac{\partial p_{tM}}{\partial e}=-\frac{(3a+f)r{s}_M}{4a(a+f)}<0$$

$$\frac{\partial p_{dM}}{\partial e}=\frac{r{s}_M}{2(a+f)}>0$$

$$\frac{\partial {\mathrm{D}}_{\mathrm{t}M}}{\partial e}=-\frac{r{s}_M}{4}<0$$

$$\frac{\partial {\mathrm{D}}_{dM}}{\partial e}=\frac{(2a-f)r{s}_M}{4a}>0$$

Description: After retailers implement certain promotional measures in traditional channels with the increase in the free-riding coefficient, that is, consumers turn more to online channels to buy after experiencing services in traditional channels, the demand of online channels increases and the cost of services in traditional channels increases while the demand decreases; in order to retain customers and increase revenue, retailers have to reduce the sales price of traditional channels to increase customer stickiness. In addition, as the demand of the online channel increases, the manufacturer raises the sales price of the online channel in order to get more profit. □

4. Numerical Calculation and Analysis of Results

When considering free-riding behavior, manufacturers dominate different channel structures, which correspond to different optimal service levels and pricing decisions; let D = 100, a = 5, f = 2, c = 2.5, l = 0.4, r = 2, and k = 5. $e$ varies in the $(0,1)$ range. Numerical simulations were performed by Matlab to analyze more visually the impact of the free-riding coefficient on service level, sales price, demand, and profit under different channel structures dominated by manufacturers in pictorial form.

4.1. Impact of Consumer Free-Riding Coefficient on Service Level

The relationship between the value change in consumer free-riding coefficient and service level is shown in Figure 3.

The circle in Figure 3 represents the retailer dual-channel supply chain, and the rhombus represents the manufacturer dual-channel supply chain. As seen in the figure, the level of service provided by the manufacturer-led manufacturer dual-channel supply chain tends to decrease as the free-riding coefficient increases. After customers experience the quality service of traditional channels, they turn to online channels to buy, and the cost of traditional channels increases while attracting a smaller group of consumers, which seriously affects the enthusiasm of traditional channels to provide services, thus showing a decreasing trend. When the free-ride coefficient is less than 0.9817, the service level of manufacturer-dominated retailers’ dual channel shows a decreasing trend, while when the free-ride coefficient is greater than 0.9817, the service level shows an increasing trend. This suggests that, in the manufacturer-led retailer dual-channel model, the increase in the number of consumer free ridings first acts as a disincentive to service levels, and when the number of consumer free ridings gradually becomes excessive, it instead leads to an increase in service levels. However, the level of service provided by the manufacturer-led retailer dual-channel supply chain is always higher than that of the manufacturer dual-channel supply chain, regardless of the variation of the free-riding coefficient within $(0,1)$.

4.2. Impact of Consumer Free-Riding Coefficient on Price Level

The numerical relationship of the impact of the free-riding coefficient on the price level is shown in Figure 4.

The circle in Figure 4 represents the retailer dual-channel supply chain, and the fork represents the manufacturer dual-channel supply chain; blue refers to the wholesale price, red refers to the traditional channel sales price, and green refers to the online channel sales price. Thus, it can be seen from the figure that the free-riding coefficient is negatively correlated with the manufacturer-led retailer dual-channel offline price and the manufacturer dual-channel wholesale price and offline price, and as the free-riding coefficient increases, the retailer dual-channel wholesale price and online price and the manufacturer dual-channel online price both tend to increase and then decrease. First, when the free-riding coefficient is less than 0.9817, the retailer’s dual-channel wholesale price decreases monotonically, and when the free-riding coefficient is greater than 0.9817, the retailer’s dual-channel wholesale price increases monotonically. Second, when the free-riding coefficient is less than 0.2211, the retailer’s dual-channel online price increases monotonically, and when the free-riding coefficient is greater than 0.2211, the retailer’s dual-channel offline price decreases monotonically. In addition, the manufacturer dual-channel online price tends to increase when the free-riding coefficient is less than 0.1547 and decreases when the free-riding coefficient is greater than 0.1547. As the consumer free-riding coefficient increases, the retailer’s traditional channel reduces the sales price of the traditional channel in order to retain customers and increase revenue. In the manufacturer’s dual-channel supply chain, the manufacturer also adopts the strategy of reducing the wholesale price in order to protect the traditional channel, while in the retailer’s dual-channel supply chain, when the free-riding coefficient is greater than a certain value, the level of service provided by the retailer begins to increase and the cost rises, so the wholesale price also rises. In the manufacturer-led manufacturer dual-channel supply chain and retailer dual-channel supply chain model, both upstream and downstream companies in the supply chain are rational people pursuing their own interest maximization. As the free-riding coefficient increases, the price of the online channel rises in order to obtain higher revenue, however, when the consumer free-riding coefficient exceeds a certain range, the offline channel starts to adopt a price reduction strategy, and the sales price of the online channel starts to fall in order to increase customer stickiness, attract more customers, and thus obtain greater profits.

4.3. Impact of Consumer Free-Riding Coefficient on Demand

The numerical change in the free-riding coefficient on demand is shown in Figure 5.

The circle in Figure 5 represents the retailer dual-channel supply chain, and the fork represents the manufacturer dual-channel supply chain; the blue refers to the traditional channel demand, and the red refers to the online channel demand. Therefore, it can be seen from the above figure that with the increase in the free-riding coefficient, the traditional channel demand in both the manufacturer-led retailer dual-channel supply chain and the manufacturer dual-channel supply chain model shows a monotonically decreasing trend, and the demand in the network direct sales channel shows a monotonically increasing trend, achieving a balance within the supply chain. When the offline channel’s quality service experience attracts new consumers to the online channel to buy more cost-effective products, the flow and transfer of demand is realized, which naturally leads to the decreasing demand of traditional channels and increasing demand of online channels.

4.4. Impact of Consumer Free-Riding Coefficient on Profit Level

The numerical change in the free-riding coefficient on profit level is shown in Figure 6.

The circle in Figure 6 represents the retailer dual-channel supply chain, and the fork represents the manufacturer dual-channel supply chain; the blue refers to the profit made by the retailer, and the red refers to the profit made by the manufacturer. It can be seen that with the increasing coefficient of consumer free-riding behavior, the profits obtained by manufacturers and retailers in the manufacturer-led manufacturer dual-channel supply chain tends to decrease, as does the profit level in the manufacturer-led retailer dual-channel supply chain. It is clear that the profit earned by the whole supply chain is also negatively correlated with the free-riding coefficient. This suggests that consumer free-riding behavior is detrimental to the proper functioning of the supply chain, both in the manufacturer-led retailer dual-channel model and in the manufacturer-led manufacturer dual-channel model.

5. Discussion and Managerial Insights

The findings of our study have important implications for the different pricing and service-level decisions of the various actors in the supply chain under different channel structures.

In a manufacturer-led retailer dual-channel supply chain with the presence of consumer free-rider behavior, retailers should align prices or use differential pricing strategies when setting prices for products in both online and offline dual-channel supply chains. This helps to reduce the extent of consumer free-riding, thereby reducing conflict between the two channels in the supply chain and therefore preventing manufacturers from raising the wholesale price of their products to maximize their own profit.

The emergence of consumer free-riding behavior in manufacturer-led manufacturer dual-channel supply chains has led to conflicts in the dual-channel supply chain that have become increasingly acute as the degree of free-riding has increased. Retailers should enhance the level of quality service in offline sales in order to increase demand in traditional channels and make consumers prefer to buy products from traditional channels. This reduces the impact of the increase in the consumer free-riding factor on the various actors in the supply chain and on overall development.

6. Conclusions

In this paper, we study a manufacturer-led dual-channel supply chain pricing game model considering free-riding behavior, and we also analyze the optimal service level and pricing decisions under two models of manufacturer-led manufacturer and supplier dual-channel supply chains. The research results and contributions are as follows:

• In a manufacturer-led retailer dual-channel supply chain, after consumers enjoy offline services in traditional channels, the motivation of retailers to provide good multisensory experience services such as visual, auditory, and tactile will be inhibited to a certain extent as the degree of their subsequent free-riding behavior deepens. When the free-riding coefficient is large enough, it stimulates retailers to offer better buying services instead, due to a sharp decrease in demand from traditional channels. The increase in the number of free ridings caused price competition between traditional and online channels, with decreasing sales prices in the traditional channels, and when the free-riding coefficient increased to a certain range, the level of service provided began to increase, costs rose, and so did the wholesale prices.
• In the manufacturer-led manufacturer dual-channel supply chain, as the free-riding coefficient increases, the less motivated the retailers are to provide services; the demand decreases, and the service level decreases, which also has an impact on the pricing decisions of each member of the supply chain. The manufacturer’s wholesale price and the retailer’s traditional channel sales price decrease, and the manufacturer’s network channel has an incremental increase in demand and a rising and then decreasing sales price trend. Consumer free-riding behavior adversely affects the development of each player in the supply chain and the whole, resulting in a downward trend in the profits earned by each player. Due to the increase in the number of free ridings and the incremental demand in the online channel, the manufacturer first raised the price in the online channel to maximize revenue, but as retailers also started to compete for the market, the manufacturer lowered the selling price to increase customer stickiness. The consumers’ free-riding behavior has led to channel conflict, resulting in reduced revenue for both upstream and downstream companies in the supply chain, as well as for the supply chain as a whole.

We study the pricing decision problems of manufacturer-led manufacturer and retailer dual-channel supply chain under free-riding behavior and propose the optimal service level and pricing strategy under two models, which provides a theoretical basis for the pricing decision of upstream and downstream enterprises in dual-channel supply chains under the influence of free riding, but this paper does not consider the pricing strategy when consumers have return of goods behavior, which will be the direction of further research.