Abstract

The progress of communication technology and the Internet has made the dual-channel supply chain have great development. Supply chain members have to compete and cooperate with other enterprises on the chain in order to obtain greater self-benefit. In the competitive-cooperative relationship among enterprises, price discrimination and sales effort are common tools of operation, and Nash equilibrium theory is a common strategy in the process of supply chain game. Whether manufacturers can promote retailers to implement sales efforts through price discrimination and ensure that the overall revenue of the supply chain is improved at the Nash equilibrium is great significance to both the supply chain and individual enterprises. This paper constructs a decentralized dual-channel supply chain mathematical model composed of an independent manufacturer, an offline retailer, and an online retailer, taking into account the impact of the offline retailer’s sales efforts on his demand and its positive external for the other channel. The revenue matrix of retailers’ decisions about whether or not to pay their sales efforts is built under the condition that manufacturers charge different wholesale prices to different retailers and solves the condition of every decision combination becoming the Nash equilibrium using the Nash equilibrium game theory. Finally, the optimal pricing strategy of the manufacturers is analysed to get the constraints of this dual-channel supply chain achieving Pareto improvement when manufacturer uses wholesale price discrimination strategy.

1. Introduction

The increase in the number of personal computers and smartphones, combined with the rapid popularization of the Internet and the increasing perfection of logistics networks, has resulted in a significant shift in consumer behaviour patterns. The penetration rate of online shopping has increased significantly due to the fact that it provides customers with a wealth of information and reduces various restrictions on shopping. Because it effectively reduces the operating costs of sellers, it has greater price competitiveness and is preferred by merchants. To seize the market and gain more benefits, enterprises begin to replan distribution channels, and the dual-channel supply chain system with the coexistence of online and offline sales channels has become a hot spot in theoretical research and enterprise practice.

Supply chain management aims to meet the needs of consumers while maximizing overall benefits by coordinating enterprises’ internal and external resources. As an independent economic and decision-making entity, each enterprise comprising the supply chain pursues profit as its primary objective, and supply chain management must solve the issue of how to effectively coordinate the relationships between enterprises. Sales is the only way for enterprises to obtain profits, and price, as the most sensitive factor affecting sales, is crucial to the impact of corporate profits. Due to the fact that the same product is sold through both channels of the dual-channel supply chain, there is intense competition between bricks and mortar and online retailers. To compete for market share and increase profits, sales efforts, such as increasing publicity and enhancing service quality, have become essential. Zhang et al. [1] confirmed the important impact of sales efforts on the profits for supply chain enterprises. However, sales effort has significant positive externalities, and consumers are likely to free ride, enjoying the sales effort of one channel while consuming through another. For example, consumers accept the services provided by offline channels to learn about product information and then choose online channels with lower price for purchase (this phenomenon is especially common in the sale processes of clothing and small household appliances). The free-riding behaviour of consumers and retailers has a significant impact on the willingness to pay for sales efforts, which will eventually lead to the loss of the overall efficiency of supply chain. Therefore, it is of great theoretical and practical value to investigate how to use price to motivate retailers of different channels to make sales efforts and to coordinate the dual-channel supply chain.

2. Literature Review

As a classic game theory, Nash equilibrium was widely used to analyse the behaviour of supply chain members. Lu et al. [2] used a progressive hedging algorithm to find Nash equilibrium of a two-stage supply-chain model constituted by multimanufacturers and multisuppliers. Liu et al. [3] analysed dual-channel supply chain decision making in the presence of market volatility and risk aversion and compared the differences in decision making in centralized, manufacturers or retailers as dominant player and Nash equilibrium. The study by Pal et al. [4] researched the dual-channel supply chain that the sale price set by every player and vertical Nash and manufacturer Stackelberg models were discussed in the decentralized structure. Gou et al. [5] focused on the cooperative advertising program of supply chain that manufacturers help retailers bear the corresponding advertising costs and derived Nash equilibrium advertising investments of manufacturers and retailers. Clempner and Poznyak [6] used Nash equilibrium to maintain the decentralization of departments and used strong Nash equilibrium to achieve the optimal effect of centralized decision-making. Considering two competing supply chains, Mahmoodi [7] transformed internal and external competition of supply chain into a bilevel programming problem by game theory and solved Stackelberg-Nash equilibrium of this problem at the same time. Liu et al. [8] developed a numerical scheme for computation of Nash equilibrium and extended the method to set distributional robust Stackelberg model to study hierarchical competition of supply chain. Rofin and Mahanty [9] studied how the speed of price adjustment affects the Bertrand Nash equilibrium under the dual-channel supply chain environment and how retailers use the speed of price adjustment to maximize their profits. The research by Qian et al. [10] showed that the prisoner’s dilemma in technology investment can be avoided effectively and the interest of the social welfare system composed of consumers, manufacturers, and technology suppliers can be maximized by asymmetric Nash equilibrium.

On the other hand, as the main means of competition and cooperation are among supply chain members, price had been widely studied by many scholars. Liu et al. [11] derived the method to reflect the impact of consumer overconfidence on market demand, pricing strategies, and profits of supply chain members based on the analysis of centralized and decentralized pricing strategies in dual-channel supply chain. Liu and Zhang [12] analysed the profits models and its pricing rules of dual-channel green supply chain in the big data environment and verified only when retailers are willing to bear some cost of green production technology, the optimal wholesale price is affected by the cost-sharing parameter. Sun et al. [13] studied optimal decisions in a dual-channel supply chain composed of single supplier and two different duopolistic retailers for three competitive behaviour patterns (Cournot, Collusion, and Stackelberg) and found that supplier can achieve more profit by raising maximum retail price or holding down self-price sensitivity factor. The study by Yang et al. [14] analysed how the innovation input of retailers affects the supply chain operation using Stackelberg game model based on consumer utility theory and drew the conclusion that the optimal efficiency of supply chain is affected by retail prices, wholesale prices, and innovation input levels. The research by Zhang et al. [15] showed that the dual-channel supply chain under decentralized decision-making can get the same optimal benefits as centralized decision-making using price discount and compensation strategy. Hu et al. [16] found that facing to the uncertain market demand, manufacturers and retailers in the dual-channel supply chain are able to achieve higher profits by cooperating than competing, so they have a stronger willingness to make sales efforts. On the basis of analysing the pricing strategy of dual-channel supply chain in different decision models, Sha and Zheng [17] applied modified Shapley value with cost to realize the reasonable distribution of individual benefits under the premise of maximizing the overall revenue of supply chain. Yan et al. [18] incorporated reference price to the design of product line to reflect the influence of reference price on the company and the consumer and it is concluded that the optimal range of quality in product line will decrease with the increasing importance of price comparison. Li et al. [19] developed a duopoly game considering the free-riding cost based on the Hotelling model to discuss the effectiveness of the reference price mechanism and the results showed that the brick-and-mortar/online retailers can benefit from implementing the reference price mechanism separately. Yan et al. [20] demonstrated that manufacturers are more likely to choose a uniform wholesale price strategy rather than price discrimination due to the role of innovation incentives and the optimal pricing level depends on fluctuations in market demand. Wang et al. [21] looked at which is the better choice manufacturers or channels rebate and formulated different rebate strategies using game theory on the premise of considering rebate sensitivity. Yang and Wang [22] took a supply chain consisting of a single manufacturer and duopoly retailers as the target studied information access and three-level price discrimination and analysed how the price strategies of supply chain members are affected by the proportion of high price sensitive consumers and the different price sensitivities of consumers. The research by Zhou et al. [23] investigated the manufacturer’s behaviour-based price discrimination strategy with the retailer’s information disclosure service in dual-channel supply chain. Chen et al. [24] indicated that the robustness of the business model will enhance with the development of the trade-in program. Cai et al. [25] showed that when cost saving and demand growth are large enough or acceptance of online channel of consumer reaches a certain level, the uniform pricing strategy will be superior to the price discrimination strategy. Matsui [26] investigated the supply chain system consisting of traditional retailers and manufacturers integrating online channels and obtained the optimal wholesale and retail prices using non-cooperative game theory.

A comprehensive analysis of the existing literature reveals that research on the price coordination mechanism of dual-channel supply chains primarily lacks in the following three areas: First, the selection of research objects typically focuses on vertical and partially centralized dual-channel supply chains (i.e., manufacturer-owned network channels) in four typical dual-channel supply chains [27–29], whereas there are few studies on decentralized and horizontally centralized dual-channel supply chains (i.e., manufacturers and network channels are independent of one another). Second, few studies have examined the effect of retailers’ sales efforts on the dual-channel supply chain, and even fewer have examined the interaction between channels of positive externalities of sales efforts. Third, most studies focus on the formulation of optimal strategies and the acquisition of optimal values, which minimizes the harshness of the conditions required to achieve the optimal and ignores the possibility of Pareto improvement even if adequate coordination of the dual-channel supply chain is not possible. In light of the aforementioned flaws, this paper selects the distributed dual-channel supply chain in which manufacturers, traditional retailers, and online retailers are independent of one another as the research object, fully considering the sales efforts of each channel and the impact of positive externalities on the supply chain, and employs Nash equilibrium theory to analyse the conditions for manufacturers to ensure the Pareto improvement of dual-channel supply chain through positive externalities.

3. Materials and Methods

3.1. Assumptions and Parameter Settings

This paper constructs a distributed dual-channel supply chain consisting of a single manufacturer, traditional retailers, and online retailers and considers only the sales of a single commodity. Manufacturers adopt the wholesale price discrimination strategy, selling products to various retail channels at varying wholesale prices. Traditional retailers only sell through physical stores, while online retailers only sell through direct online channels. There is no subordination between members of the supply chain, and they make decisions independently and risk-neutral. In order to preserve generality, the manufacturers determine the wholesale price first, followed by the two retailers, who each determine the retail price of the channel.

The key mathematical notations used in this paper are listed in Table 1.

Considering that consumers of network channels are often more sensitive to price in reality, it is assumed that .

Based on reference [30], fully considering the impact of sales efforts on the demand of this channel and the impact of its positive externalities on the demand of other channels, the demand function of each channel of the dual-channel supply chain is set as follows:

3.2. Model Establishment and Analysis

According to the above hypothesis, the respective profits of traditional retailers and online retailers in the dual-channel supply chain are obtained as follows:

Because of the Cournot game between traditional retailers and online retailers, judge and . It is known that and exist to maximize and .

Simultaneous and solve equations:

It can be known that

Substituting equations (6) and (7) into equations (1) and (2), we obtain

To ensure that the market demand of each channel is greater than zero, it is required that and , and the inequality set is solved as follows:

Substituting equations (6) and (7) into equations (3) and (4), we obtain

4. Results and Discussion

4.1. Nash Equilibrium Analysis of Traditional Retailers and Online Retailers

As shown in Table 2, the income matrix for each retailer in the dual-channel supply chain with and without sales investment was constructed.

When traditional retailers invest sales efforts, , and vice versa, , and the same is true for online retailers. The superscript “I” is used to represent the investment strategy, and the superscript “N” is used to represent the noninvestment strategy. For instance, the superscript (I, N) represents the strategy combination parameters when traditional retailers invest in sales efforts, but online retailers do not. Using equations (11) and (12), we can obtain

When [A > E] ∩ [B > D], the (investment, investment) strategy combination is a Nash equilibrium solution, that is, all channel retailers expand sales efforts. Combining and solving this set of inequalities, we obtain

When [G > C] ∩ [H > F], the (noninvestment, noninvestment) strategy combination is the Nash equilibrium solution, that is, neither retailer in the two channels expends sales effort. The result of combining and solving this set of inequalities is

When [C > G] ∩ [D > B], the (investment, noninvestment) strategy combination is a Nash equilibrium solution, i.e., traditional retailers expand sales efforts while online retailers do not. The result of combining and solving this set of inequalities is

When [E > A] ∩ [F > H], the (noninvestment, investment) strategy combination is Nash equilibrium solution, i.e., traditional retailers do not invest in sales efforts, while online retailers invest in sales efforts. The result of combining and solving this set of inequalities is

Because [A > E] ∩ [B > D], [G > C] ∩ [H > F], [C > G] ∩ [D > B], and [E > A] ∩ [F > H] are all strategy combinations, (investment, investment), (noninvestment, noninvestment), (investment, noninvestment), and (noninvestment, investment) are sufficient conditions for the Nash equilibrium solution. For this purpose, consider the following situation: