Green Promotion Service Allocation and Information Sharing Strategy in a Dual-Channel Circumstance

Abstract

Credit purchase enables the manufacturers in the e-commerce environment to provide pre-sales service that consumers can experience first and pay later. This paper considers demand associated with price and green promotion service level and builds four decentralized game models to study two green promotion service allocation strategies and demand forecasting information sharing strategies in a dual-channel environment. The effects of the degree of dual-channel competition and free-riding on the perfect Bayesian Nash equilibrium are studied. The results show that the retailer should actively cooperate with the manufacturer and share private forecasting information if the coefficient of channel substitution is relatively high. Sharing information will aggravate double marginalization and hurt the retailer. In addition, the retailer’s profit is positively influenced by the forecasting accuracy in four models. When the manufacturer invests in the green promotion service, the prediction accuracy hurts the manufacturer’s profit without information sharing and there is a positive impact with information sharing. In particular, when a retailer provides service, we take the consumer’s free-riding behavior into account, and we find that free-riding hurts both parties and the whole supply chain. In addition, the manufacturer’s profit is irrelevant to the prediction accuracy without information sharing and positively influenced by the accuracy with information sharing.

1. Introduction

According to the latest statistical report on Internet development in China, the number of live streaming e-commerce users in China has reached 309 million by June 2020, which is the fastest growing personal Internet application in the first half of the year. The rapid development of live streaming e-commerce enables more traditional manufacturers to open online distribution channels. In a dual-channel environment, manufacturers are not only merely limited to the upstream suppliers of retailers, but also compete with retailers [1,2,3,4]. Suppliers like Haier, Lenovo, Samsung, and IBM sell products through both the traditional distribution channel and online channel. For some high-tech durable products, such as small appliances and digital devices, they may look similar, but the performance of these products can only become known through trial [5].

In the dual-channel operating environment, leading retailers are transforming from traditional retailers to service retailers. In 2019, Gome, a well-known consumer electronics retailer in China, has transformed from a conventional home appliance retailer to a provider of integrated solutions, service solutions, and supply chain suppliers, providing consumers with high-quality goods and services covering home appliances, decoration, and furnishing services. In cooperation with such leading service retailers, green promotion services can be provided by retailers. Their rich offline store scene experience manners and strong supply chain system can maximize the satisfaction of product display and promotion, which provides consumers with a high-quality green promotion service experience [6]. Green promotion services can attract consumers with low-carbon preferences to buy products and increase the turnover of green products and corporate profits, which has important practical significance [7]. However, the Internet allows consumers to learn detailed product information with cost-effective means, which makes it possible for consumers to experience a product in the retail stores and buy from a cheaper online channel [8,9]. Therefore, free-riding behavior should be considered when retailers offer green promotion services. In addition, there are more and more new products in the e-commerce channel. Many consumers worry that they will not find out if a product works well according to photos and videos. To make up for the lack of online shopping experience, T-mall and Sesame Credit (an independent third-party credit investigation agency under Ant Financial Services Group) announced the opening of credit purchase to the whole industry of platform merchants. Merchants with access to credit purchase can allow consumers to enjoy the shopping experience of trial before payment. At the end of the seven-day trial period, consumers can decide whether to buy or return. At present, the credit purchase has covered nearly 50,000 items of T-mall, including 3C digital products, musical instruments, clothing, home furnishing, beauty makeup, and fast-moving consumer goods. Suning, Midea Group, Huawei, and other brands have opened credit purchase channel in T-mall. The multi-channel marketing mode of opening online and offline channels can attract more consumers and alleviate the loss caused by the double marginalization effect [10], as well as encourage manufacturers to increase operations to improve product and service quality. High-quality experience services are conducive to the good reputation of brands and products, to promote consumers’ secondary behavior, i.e., repeat buys or the communication between users [11]. In this paper, this expensive operation is defined as pre-sales promotion service for green products. We assume the level of green promotion service effort positively affects product demand in the direct and retail channels. In addition, green promotion service investment information is private because it involves technologies that are considered proprietary to protect intellectual property [12].

In a highly competitive market for experiential products, products produced by various competitors tend to be homogenized in quality and price. Many companies focus on improving service quality to increase market share [13,14,15]. This marketing strategy is referred to as servitization in the literature [16]. Servitization motivates customers to buy and stimulates demand. For durable experiential products, potential market demand has randomness, which is determined by uncertain consumption preferences. Channel members in the supply chain have different projections of demand based on their data collection capabilities [17]. Because the retailer is located at the end of the supply chain and closer to the consumer, more accurate demand information can be obtained than that by the manufacturer [18]. Thus, it is significant to focus on the retailer having private forecasting demand information. Some large retailers, like Costco and Target, share point-of-sale data with manufacturers. In this paper, we focus only on the retailer to predict an uncertain market. In this case of information asymmetry, the retailer relies solely on its own information to make decisions, including speculating the manufacturer’s information from the endogenous information.

The effect of information sharing on sales service decisions in the experiential consumer goods industry have rarely been studied. The feature of such products is that consumers can enjoy free experience services online, but choose to buy the same product online at a better price [19]. This raises the question of whether the retailer should share information with the manufacturer. If so, when should the retailer share information? Additionally, due to the complexity of data sources and limitations of data analysis techniques, retailers cannot perfectly derive accurate market information in practice. Thus, another question is whether the retailer’s prediction accuracy will influence the decisions of the manufacturer and retailer. If so, how will the accuracy affect their decisions? In addition, this paper also focuses on the consumers’ free-riding behavior, that is, some users are more willing to purchase products through online channels and will not give up the offline service provided by the retailers for free [20]. Thus, what is the impact of the degree of free-riding on the profit of decision-makers? How does this behavior affect the value of information sharing strategies?

Zhang et al. (2019) proposed that after-sales service deployment and information sharing are interactive factors affecting the decision of manufacturers and retailers [20]. However, the current researches mostly discuss the effects of sales service and information sharing separately and pay less attention to their interactive effects. Therefore, it is necessary to explore the interaction between green promotion service deployment and information sharing for solving the practical problems in the business environment. There are two green promotion service allocation strategies: the manufacturer invests in green promotion service or the retailer invests in green promotion service. According to whether the retailer keeps forecasting demand secret, there are two demand forecasting information sharing strategies: no information sharing and information sharing. Thus, if the retailer keeps forecasting demand secret, the manufacturer cannot infer precise market base and updates the belief about the demand only based on the observed retail price and determines online price by this updated belief. According to two green promotion service allocation strategies and two demand forecasting information sharing strategies, there are four cases (shown in

Table 1. Four cases.

Scenarios		Demand Forecasting Information Sharing Strategies
		No Information Sharing	Information Sharing
Green promotion service allocation strategies	Manufacturer invests in green promotion service	CASE 1	CASE 2
	Retailer invests in green promotion service	CASE 3	CASE 4

). Both parties are likely to invest in green promotion service. The retailer is assumed to have ability to forecast uncertain demand information and decide whether to share it independently. Our goal is to identify the green promotion service deployment and the retailer’s information sharing strategy. In addition, the influences of prediction accuracy, the degree of dual-channel competition, and free-rider behavior on the optimal strategy are explored.

First, the retailer’s information sharing strategy in the context of the manufacturer’s responsibility for green promotion service is studied. We conclude that the precision accuracy has a positive impact on the retailer’s profit and a negative impact on the manufacturer’s profit without information sharing. If the retailer shares information, forecasting accuracy has a positive impact on self-profits, that is, the more accurate the forecast, the greater the benefit. At the same time, the manufacturer can also obtain accurate forecast information and benefit from the retailer’s forecast accuracy. In addition, when the manufacturer provides green promotion service, the optimal information sharing strategy is not to share information, to ensure the retailer’s interests. It is because the manufacturer with shared information can have a more comprehensive grasp of uncertain demand and make decisions on wholesale price and green promotion service more promptly. Raising wholesale price would alleviate the loss caused by the double marginalization effect and be inimical to the interests of the retailer.

This paper also studies the information sharing strategies under the retailer’s responsibility for green promotion service. The manufacturer can speculate the retailer’s private information based on the retailer’s green promotion service decision. In the case of no information sharing, the retailer’s profit increases with more accurate forecasting demand. However, the dominant manufacturer gives priority to the wholesale price and online price decisions and does not have any conjectural behavior; thus, the retailer’s prediction behavior will not have any influence on the manufacturer’s decisions and the manufacturer’s profit is irrelevant to the prediction accuracy. Improving predictive accuracy can enhance the value of information sharing for two parties. In addition, when the manufacturer provides green promotion service, the retailer does not want to share information.

The remainder of this paper is organized as follows. The literature review is shown in Section 2. Section 3 gives the model setting. Four models are discussed in Section 4 and Section 5. The main conclusions and further research are elaborated in Section 6.

2. Literature Review

This research is highly related to information sharing. In recent years, information asymmetry has been widely studied [21,22]. At the same time, many scholars have focused on the problem of asymmetric information sharing [23,24]. Thus, information flows from one channel member to another. In this case, the information receiver relies on both the shared information and their own information, while the sender relies solely on their own information to make decisions. Asymmetric information sharing involves flows from manufacturers to retailers or vice versa [18]. The former is commonly seen in exploiting new markets. Manufacturers have an advantage over retailers in mastering the marketing information. Guo and Iyer (2010) assumed that retailers cannot predict manufacturers’ market demand based on wholesale prices [25]. The same assumption was made in a maritime supply chain [26]. They assumed an upstream port could help the downstream carrier to make decisions by sharing the predictive market information. The influences of the port’s prediction information sharing incentive and carrier’s risk behavior on offshore supply chain sustainability investment decisions were studied. However, retailers serve consumers directly and can get more market information than manufacturers, so information flows from retailers to manufacturers are more common. This paper is different from the previous literature that only studied the impact of demand prediction accuracy on operation management decisions, mainly reflected in more research on green promotion service allocations and information sharing strategies. The results show that if the retailer shares information, forecasting accuracy has a positive impact on self-profits. At the same time, the manufacturer can also obtain accurate forecast information and benefit from the retailer’s forecast accuracy.

This research is also related to the service strategy. The enterprise is committed to improving the service quality of consumers in the durable goods market [27]. They incorporate sales service, i.e., giving free presents, on sales, into business activities to attract more customers. Perdikaki et al. (2016) studied how sales efforts affected the firm’s business strategy [28]. Many researches on sales service focused on after-sales service, such as inventory system of repairable parts in after-sales service management [29,30], after-sales service contract design [31], and after-sales service level design [27]. Li et al. (2014) found that manufacturers’ outsourcing of after-sales service to retailers can not only improve the quality of after-sales service, but also alleviate double marginalization to a certain extent [27]. Kurata and Nam (2013) assumed symmetric market information and explored the design of after-sales service level in uncertain markets [32]. However, realistic marketing information is asymmetric. Some scholars have studied the after-sale service level with asymmetric information and revealed the influence of information asymmetry on the service level decision. Jin et al. (2015), Li et al. (2016), Zhang et al. (2019), and Guan et al. (2020) are relevant to our research. They studied what is the impact on the supply chain when services are provided by different actors. Jin et al. (2015) examined the interaction between contract types and decision-making rights of demand enhancement services [33]. Li et al. (2016) considered that different members could provide demand enhancement services and indicated that both manufacturers and retailers tended to take the risk of serving [34]. Zhang et al. (2019) explored after-sales service deployment and information sharing strategies in a supply chain. The results showed that the retailer preferred to disclose forecasting demand to upstream manufacturer with high cost-efficiency [20]. Guan et al. (2020) considered linear demands related to retail price, and the service level in two competing supply chains was studied. They established a multi-stage game framework to study the influence of information sharing on price and service decision [35]. In the study of dual-channel green supply chains, domestic and foreign scholars mainly focus on the impact of market demand and cost factors on decision-making. Meng and Liang (2024) constructed three channel structures (traditional retail channels, online direct sales dual channels, and online distribution dual channels) and analyzed the pricing decisions of channel preferences, product green levels, and environmental liability costs for the different channel structures [36]. Khorshidvand et al. (2023) examined a multi-level, dual-channel green closed-loop supply chain that integrates circular economy principles [37]. Yan et al. (2022) considered a dual-channel supply chain composed of a manufacturer and a retailer. This investigation is on the influence of consumers’ reference quality under centralized decision-making and decentralized decision-making [38]. Liu and Zhang (2022) considered a dual-channel green supply chain, and noted that chain members pay more attention on the pricing problems considering the inputs of consumer performance information and greening R&D [39].

This paper is most closely related to Zhang et al. (2019) [20], with three major differences. First, a more realistic supply chain structure, i.e., dual-channel supply chain, is considered in our paper. The manufacturer provides wholesale service to the downstream retailer and direct sales to end consumers. There is a dual relationship between competition and cooperation between the two channels. Second, we introduce the sequential game model under uncertain general demand, which replaces the classic high–low demand model in Zhang et al. (2019) [20]. Finally, we study more factors; in addition to the effect of disturbance stochastic demand disturbance, we also study the effects of the degree of dual-channel competition and free-riding behavior on the perfect Bayesian Nash equilibrium. We get some interesting results: the manufacturer’s profit, retailer’s profit, and supply chain’s profit decrease with the degree of free-riding, which indicates that free-riding is not good for enterprises and the whole system.

3. Model Setting

A dual-channel supply chain consisting of a manufacturer (he) and a retailer (she) are considered in this paper. In the retail channel, the manufacturer sells products to the end consumers through the retailer. The wholesale and retail price are $w$ and $p_r$, respectively. In the e-commerce direct-channel, the manufacturer sells at price $p_d$ directly to end users, bypassing the retailer. The manufacturer determines the service provider, i.e., himself or the retailer. Particularly, in the case where the retailer provides green promotion service, the online channel will reduce consumers’ switch costs between channels, which leads to the emergence of free-riding behavior. That is, some users are more willing to purchase products through online channels and will not give up the offline service provided by the retailers for free. The structure of dual-channel supply chain is shown in Figure 1.

We assume that the risk attitudes of the two decision makers are neither risky nor conservative. Thus, the profit utility function of both parties is equal to the mathematical expectation of profit. Therefore, both aim to maximize expected profits. The symbols mentioned in this paper are summarized in

Table 2. Summary of notations.

Symbol	Notations
Parameters
$\mu$	The degree of free-riding, $0<\mu <1$
$b$	Coefficient of substitution effect, $0<b<1$
$k$	Consumers’ sensitivity to green promotion service level, $k>0$
$h$	Investment coefficient of green promotion service, $h>0$
$A$	Potential market size, $A=a+{\epsilon }_0$, $a$ is a positive constant and the mean of $A$
$Y$	Demand information predicted by the retailer
$\eta$	Manufacturer’s investment efficiency, $\eta =k^2/h$
${\epsilon }_0$	A random variable obeying a normal distribution with mean zero and variance ${\sigma }_0^2$
${\epsilon }_1$	A random variable obeying a normal distribution with mean zero and variance ${\sigma }_1^2$
${\sigma }_0$	Standard deviation of ${\epsilon }_0$,${\sigma }_0>0$, we define $\tau ={{\sigma }_0}^2$
${\sigma }_1$	Standard deviation of ${\epsilon }_1$, ${\sigma }_1>0$
$\gamma$	Forecast accuracy of the e-retailer, $0<\gamma ={{\sigma }_0}^2/({{\sigma }_0}^2+{{\sigma }_1}^2)<1$
$\pi$	Net profit
$V$	The value of information sharing
Decision Variables
$p_r$	Retail price for unit product, $p_r>0$
$p_d$	Direct channel for unit product, $p_d>0$
$s$	Green promotion service level, $s>0$
$w$	Wholesale price for unit product, $w>0$

Note. Superscript denotes the optimal solutions.

.

The investment subject choice of green promotion service affects the value of information sharing, the retailer’s predictive accuracy, and the profits of the two members. According to whether green promotion service is invested by the manufacturer or the retailer, and whether the retailer shares demand forecasting information, four possible equilibrium outcomes exist in this dual-channel supply chain. Figure 2 shows the unique equilibrium outcomes in four cases. The shaded areas represent the feasible regions where the positive equilibriums exist.

To ensure the practical significance of the model in this paper, the subsequent models’ solutions and analyses are developed in these feasible regions. All equilibrium solutions are derived by Bayes formula, mathematical expectation, and backward induction. Figure 3 shows the sequence of the events.

Firstly, the manufacturer decides who should invest in the sales service (himself or the retailer). In the second phase, the retailer decides whether share forecasting information and observes the forecast signal $Y$. In the third stage, if the manufacturer provides green promotion service, the retailer decides the retail price after the manufacturer determines the optimal wholesale price and green promotion service level. Finally, the manufacturer determines the direct price. If the retailer provides green promotion service, the manufacturer needs to make decisions on the wholesale price and direct price before the retailer makes the optimal service level and retail price decisions. In the fourth stage, consumer demand and the enterprise profit are achieved.

4. Manufacturer Invests in Green Promotion Service

Firstly, we focus on the manufacturer provides the green promotion service. Thus, in the direct online channel, the manufacturer offers the consumers free trials before payment and undertakes all green promotion service investments. Demand in the direct channel is related to green promotion service. Thus, the manufacturer’s high-quality green promotion service can promote the sales volume of the direct channel. On the contrary, poor green promotion service will lead to customer loss and sales decline. According to the sequence of events in Figure 3, the manufacturer determines the wholesale price $w$ and green promotion service level $s$ at first. Then, the follower decides retail price $p_r$. In the end, the manufacturer decides online price $p_d$.

Demand functions of the direct channel and retail channel are separately expressed as: $A-p_d+b{p}_r+ks$ and $A-p_r+b{p}_d$. $0<b<1$ denotes that own-channel effects are greater than competition channel effects. $k$ is referred to as the sensitivity of consumers to service level. As the green promotion service is provided by the manufacturer, the service level will have an impact on the direct channel sales volume of the manufacturer. In this paper, market demand $A$ is stochastic; we assume $A=a+{\epsilon }_0$, where $a>0$, ${\epsilon }_0$ obeys normal distribution. We then derive $E\left(A\right)=a,Var\left(A\right)={{\sigma }_0}^2$. In addition, we assume $a$ is much larger than ${\sigma }_0$ to make sure that the optimal solution makes sense [18]. These linear demand functions widely exist in the literature, like marketing, operations, and economics [40]. Similar examples are common in reality. For example, Huawei joined the T-mall ‘enjoy first, pay later’ service and sold smartphones in the online official flagship store. Meanwhile, Huawei also cooperated with large offline retailers, i.e., Suning and Gome, to synchronously sell phones. This indicates there is fierce competition between manufacturers and retailers.

4.1. CASE 1: No Information Sharing

In this case, the retailer keeps forecasting demand secret. Thus, the manufacturer cannot infer precise market base and updates the belief about the demand only based on the observed retail price and determines online price by this updated belief. Considering diseconomies of scale exist in service cost [35], we assume that the variable cost of green promotion service is zero and there is no difference between the services provided by the manufacturer and retailer, that is, the coefficient of demand and profit on the service level is the same regardless of whether the manufacturer provides service or the retailer provides service. The service cost function is $h{s}^2/2$, where $h>0$ denotes the investment coefficient of green promotion service. This function is commonly found in many researches [41]. We index this case by superscript ‘1*’. The two parties’ ex-ante expected profits are described as:

$$\mathrm{E}\left[\left.{\mathsf{\pi }}_{\mathrm{M}}\right|{\mathrm{p}}_{\mathrm{r}}\right]=\mathrm{w}(\mathrm{a}-{\mathrm{p}}_{\mathrm{r}}+\mathrm{b}{\mathrm{p}}_{\mathrm{d}})+{\mathrm{p}}_{\mathrm{d}}(\mathrm{a}-{\mathrm{p}}_{\mathrm{d}}+\mathrm{b}{\mathrm{p}}_{\mathrm{r}}+\mathrm{k}\mathrm{s})-\mathrm{h}{\mathrm{s}}^2/2,$$

(1)

$$\mathrm{E}\left[\left.{\mathsf{\pi }}_{\mathrm{R}}\right|\mathrm{Y}\right]=({\mathrm{p}}_{\mathrm{r}}-\mathrm{w})\left(\mathrm{E}\right[\left.\mathrm{A}\right|\mathrm{Y}]-{\mathrm{p}}_{\mathrm{r}}+\mathrm{b}{\mathrm{p}}_{\mathrm{d}}).$$

(2)

The two parties are aiming to maximize their own expected profits. Equation (1) denotes the manufacturer’s expected profit. He infers retailer’s information by observed retail price $p_r$.$Y=A+{\epsilon }_1$ is the demand information predicted by the retailer, where ${\epsilon }_1$ is normal distributed, i.e., $E\left({\epsilon }_1\right)=0$ and $Var\left({\epsilon }_1\right)={{\sigma }_1}^2$. The manufacturer cannot get accurate uncertain demand information unless it is leaked or the retailer is willing to share it. We derive $E\left[A\right]=E\left[Y\right]=E\left[E\left[\left.A\right|Y\right]\right]=E\left[\left.Y\right|A\right]=a$, $E\left[\left.A\right|Y\right]=\left(1-\gamma \right)a+\gamma Y$, where$\gamma ={\sigma }_0^2/({\sigma }_0^2+{\sigma }_1^2)$ denotes retailer’s forecasting accuracy. In CASE 1, the retailer, who infers uncertain demand as $E\left[\left.A\right|Y\right]$, does not share demand information with the manufacturer. Thus, he infers market base as $E\left[A\right]$ (i.e.,$a$).

The backward induction is applied to solve this dynamic game. Firstly, we derive the optimal online price $p_d^{*}\left(p_r\right)={\displaystyle \frac{1}{2}}(a+ks+bw+b{p}_r)$ by the first-order condition of Equation (1). Then, substituting $p_d^{*}\left(p_r\right)$ into Equation (2), we can derive the optimal reaction functions in the second stage $p_r^{*}\left(\left.w,s\right|Y\right)={\displaystyle \frac{-ab-2E\left[\left.A\right|Y\right]-bks-2w}{2(-2+b^2)}}$,$p_d^{*}\left(\left.w,s\right|Y\right)={\displaystyle \frac{1}{2}}(a+ks+bw-{\displaystyle \frac{b(ab+2E[\left.A\right|Y]+bks+2w)}{2(-2+b^2)}})$. Finally, substituting $p_r^{*}\left(\left.w,s\right|Y\right)$ and $p_d^{*}\left(\left.w,s\right|Y\right)$ into Equation (1), the optimal wholesale price and green promotion service level in the first stage are derived and shown in Proposition 1.

Proposition 1. 

In the case where the manufacturer invests in green promotion service and the retailer does not share information, the optimal solutions exist and are expressed as:

$$\begin{array}{c}{w}^{1*}={\displaystyle \frac{(b^2-4)\left(a\right(b^2-4)+2E[\left.A\right|Y\left]\right)}{2(8-5b^2+b^4)}}-{\displaystyle \frac{ab(1+b)h}{2(-1+b^2)h+k^2}}\mathit{,}\\ s^{1*}={\displaystyle \frac{-a(1+b)k}{2(-1+b^2)h+k^2}}\mathit{,}\\ p_r^{1*}={\displaystyle \frac{-2\left(b^2-2\right)E\left[\left.A\right|Y\right]\left(2\right(b^2-1)h+k^2)+a(-2(8+8b-4b^2-5b^3+b^5)h+(8-4b^2+b^4\left)k^2\right)}{2(8-5b^2+b^4)\left(2\right(-1+b^2)h+k^2)}}\mathit{,}\\ p_d^{1*}={\displaystyle \frac{-\left(2bE\right[\left.A\right|Y\left]\right(2(-1+b^2)h+k^2)+a(2(8+12b-5b^2-10b^3+b^4+2b^5)h+b(-4+b^2)k^2\left)\right)}{2(8-5b^2+b^4)\left(2\right(-1+b^2)h+k^2)}}\mathit{.}\end{array}$$

According to the optimal solutions in Proposition 1, the ex-ante expected profits are derived as $E\left[{\pi }_R^{1*}\right]=F_R^{1*}+T_R^{1*}$ and $E\left[{\pi }_M^{1*}\right]=F_M^{1*}+T_M^{1*}$, where $F_R^{1*}$ and $F_M^{1*}$ denote fixed profits of the retailer’s and manufacturer’s ex-ante expected profits, respectively. $T_R^{1*}$ and $T_M^{1*}$ denote their variable profits. Detailed profit expressions in this paper are shown in

Table 3. The equilibrium conditions and optimal ex-ante expected profits.

CASES		Optimal Expected Profits	Fixed Profits	Variable Profits
Manufacturer invests in green promotion service	No information sharing	$E\left[{\pi }_R^{1*}\right]=F_R^{1*}+T_R^{1*}$, $E\left[{\pi }_M^{1*}\right]=F_M^{1*}+T_M^{1*}$.	$F_R^{1*}=2\left(2-b^2\right)a^2/{(8-5b^2+b^4)}^2$, $F_M^{1*}={\displaystyle \frac{a^2(-2(12+16b-5b^2-10b^3+b^4+2b^5)h+{(b^2-2)}^2{k}^2)}{4(8-5b^2+b^4)\left(2\right(b^2-1)h+k^2)}}$.	$T_R^{1*}={\displaystyle \frac{2(2-b^2){(b^2-3)}^2{\sigma }_0^2\gamma }{{(8-5b^2+b^4)}^2}}>0$, $T_M^{1*}={\displaystyle \frac{(b^2-3-b){\sigma }_0^2\gamma }{(8-5b^2+b^4)}}<0$.
	Information sharing	$E\left[{\pi }_R^{2*}\right]=F_R^{2*}+T_R^{2*}$, $E\left[{\pi }_M^{2*}\right]=F_M^{2*}+T_M^{2*}$.	$F_R^{2*}=F_R^{1*}$, $F_M^{2*}=F_M^{1*}$.	$T_R^{2*}=2\left(2-b^2\right){\sigma }_0^2\gamma /{\left(8-5b^2+b^4\right)}^2>0$, $T_M^{2*}={\displaystyle \frac{\left(2\left(12+16b-5b^2-10b^3+b^4+2b^5\right)h-{\left(b^2-2\right)}^2{k}^2\right){\sigma }_0^2\gamma }{-4\left(8-5b^2+b^4\right)\left(2\left(-1+b^2\right)h+k^2\right)}}>0$.
	The unique equilibrium outcomes: $\eta <2(1-b^2)$. The value of information sharing under the manufacturer undertakes the pre-sale service: $V_R^{2*}=E\left[{\pi }_R^{2*}\right]-E\left[{\pi }_R^{1*}\right]={\displaystyle \frac{2\left(b^2-4\right){\left(b^2-2\right)}^2{\sigma }_0^2\gamma }{{\left(8-5b^2+b^4\right)}^2}}<0$; $V_M^{2*}=E\left[{\pi }_M^{2*}\right]-E\left[{\pi }_M^{1*}\right]={\displaystyle \frac{\left(-2\left(1+b\right)\left(2b-3\right)\left(-8+\left(b-1\right)b\left(4+b\right)\right)h+\left(16+b\left(4-8b+b^3\right)\right)k^2\right){\sigma }_0^2\gamma }{4\left(8-5b^2+b^4\right)\left(2\left(-1+b^2\right)h+k^2\right)}}>0$.
Retailer invests in green promotion service	No information sharing	$E\left[{\pi }_R^{3*}\right]=F_R^{3*}+T_R^{3*}$, $E\left[{\pi }_M^{3*}\right]=F_M^{3*}+T_M^{3*}$.	$F_R^{3*}={\displaystyle \frac{a^2{(1+b)}^{2}h{(-2(b-1)h+k^2(b(\mu -1)-\mu \left)\right(\mu -1\left)\right)}^2{(k^2{(\mu -1)}^2-2h)}^2}{2(2h-k^2{(\mu -1)}^2){\left(8\right(b^2-1)h^2-4(b^2-1)h{k}^2{(\mu -1)}^2+k^4{(\mu -1)}^2{(b+\mu -b\mu )}^2)}^2}}$, $F_M^{3*}={\displaystyle \frac{-a^2(1+b)h\left(\right(3+b)h+k^2(3\mu -1-2{\mu }^2\left)\right)}{8(b^2-1)h^2-4(b^2-1)h{k}^2{(\mu -1)}^2+k^4{(\mu -1)}^2{(b+\mu -b\mu )}^2}}$.	$T_R^{3*}={\displaystyle \frac{h{\sigma }_0^2\gamma }{2(2h-k^2{(\mu -1)}^2)}}>0$, $T_M^{3*}=0$.
	Information sharing	$E\left[{\pi }_R^{4*}\right]=F_R^{4*}+T_R^{4*}$, $E\left[{\pi }_M^{4*}\right]=F_M^{4*}+T_M^{4*}$.	$F_R^{4*}=F_R^{3*}$, $F_M^{4*}=F_M^{3*}$.	$T_R^{4*}={\sigma }_0^2\gamma F_R^{4*}/a^2>0$, $T_M^{4*}={\sigma }_0^2\gamma F_M^{4*}/a^2>0$.
	The unique equilibrium outcomes: $\eta <2/{(-1+\mu )}^2$ and $-8+b^2(8+\eta (-4+\eta {(\mu -1)}^2\left){(\mu -1)}^2\right)-2b{\eta }^2{(\mu -1)}^3\mu +\eta {(\mu -1)}^2(4+\eta {\mu }^2)<0$. The value of information sharing under the retailer undertakes the pre-sale service: $V_R^{4*}=E\left[{\pi }_R^{4*}\right]-E\left[{\pi }_R^{3*}\right]={\displaystyle \frac{h\left(12\left(b^2-1\right)h^2-2\left(1+b\right)h{k}^2\left(3+4b\left(\mu -1\right)-4\mu \right)\left(\mu -1\right)+k^4\left(2b\left(\mu -1\right)-1\right)\left(b\left(\mu -1\right)-\mu \right){\left(\mu -1\right)}^2\right)\left(4\left(b^2-1\right)h^2-2\left(1+b\right)h{k}^2\left(\mu -1\right)-k^4\left(b\left(\mu -1\right)-\mu \right){\left(\mu -1\right)}^2\left(2\mu -1\right)\right){\sigma }_0^2\gamma }{-\left(2\left(2h-k^2{\left(-1+\mu \right)}^2\right){\left(8\left(-1+b^2\right)h^2-4\left(-1+b^2\right)h{k}^2{\left(-1+\mu \right)}^2+k^4{\left(-1+\mu \right)}^2{\left(b+\mu -b\mu \right)}^2\right)}^2\right)}}<0$; $V_M^{4*}=T_M^{4*}={\sigma }_0^2\gamma F_M^{4*}/a^2>0$.

Note. In this paper, we assume $0<b<1$, $0\le \mu \le 1$, $\eta =k^2/h$.

. Obviously, only their variable profits are related to the manufacturer’s forecasting accuracy $\gamma$. Thus, we just need to pay close attention to $T_R^{1*}$ and $T_M^{1*}$ for analyzing the impacts of prediction accuracy. By $T_R^{1*}>0$, $T_M^{1*}<0$, we derive that the manufacturer’s profit is negatively impacted by forecasting accuracy. This is the result of decision makers’ conjectural behavior caused by their information asymmetry.

The manufacturer making the decision in the last stage of the game can infer market information from observed retail price. Meanwhile, the retailer will adopt new marketing methods, i.e., price-off promotions, to cope with the manufacturer’s conjecture. This will result in a decrease of the demand in the direct channel and falling of the manufacturer’s profit. The forecasting behavior of the retailer helps her adjust her retail price timely after observing the wholesale price of the manufacturer, so as to reduce the double marginalization effect caused by the change of wholesale price. Therefore, the profit of the retailer will increase with forecasting accuracy. In real business cases, the retailer’s pricing information is always being passed to the manufacturer through network or advertising. These signal costs are undertaken by the retailer to promote the manufacturer’s conjecture. Importantly, if the profit increment brought by increasing the retail price is greater than the increment of signal cost, the forecasting accuracy will positively affect the retailer’s profit.

4.2. CASE 2: Information Sharing

Since the retailer’s private forecast information is shared, the information in this supply chain is completely symmetrical. Thus, two parties update beliefs at the same time. This case is superscripted by ‘2*’. Their ex-ante expected profits are described as:

$$\mathrm{E}\left[\left.{\mathsf{\pi }}_{\mathrm{M}}\right|\mathrm{Y}\right]=\mathrm{w}\left(\mathrm{E}\right[\left.\mathrm{A}\right|\mathrm{Y}]-{\mathrm{p}}_{\mathrm{r}}+\mathrm{b}{\mathrm{p}}_{\mathrm{d}})+{\mathrm{p}}_{\mathrm{d}}\left(\mathrm{E}\right[\left.\mathrm{A}\right|\mathrm{Y}]-{\mathrm{p}}_{\mathrm{d}}+\mathrm{b}{\mathrm{p}}_{\mathrm{r}}+\mathrm{k}\mathrm{s})-\mathrm{h}{\mathrm{s}}^2/2,$$

(3)

$$\mathrm{E}\left[\left.{\mathsf{\pi }}_{\mathrm{R}}\right|\mathrm{Y}\right]=({\mathrm{p}}_{\mathrm{r}}-\mathrm{w})\left(\mathrm{E}\right[\left.\mathrm{A}\right|\mathrm{Y}]-{\mathrm{p}}_{\mathrm{r}}+\mathrm{b}{\mathrm{p}}_{\mathrm{d}}).$$

(4)

Equation (3) denotes the manufacturer’s ex-ante expected profit. Both parties have retailer’s prediction demand $Y$, so they infer market base as $E\left[\left.A\right|Y\right]$. Same as CASE 1, the backward induction method is used to solve this Stackelberg game model. The optimal solutions are shown in Proposition 2.

Proposition 2. 

In the case of the manufacturer invests in green promotion service and the retailer shares information, the optimal solutions exist and are expressed as:

$$\begin{array}{c}{w}^{2*}={\displaystyle \frac{(-4+b^2)\left(E\right[\left.A\right|Y\left]\right(-4+b^2)+2B)}{2(8-5b^2+b^4)}}-{\displaystyle \frac{E\left[\left.A\right|Y\right]b(1+b)h}{2(-1+b^2)h+k^2}}\mathit{,}\\ s^{2*}={\displaystyle \frac{-E\left[\left.A\right|Y\right](1+b)k}{2(-1+b^2)h+k^2}}\mathit{,}\\ p_r^{2*}={\displaystyle \frac{-2(-2+b^2)E\left[\left.A\right|Y\right]\left(2\right(-1+b^2)h+k^2)+E\left[\left.A\right|Y\right](-2(8+8b-4b^2-5b^3+b^5)h+(8-4b^2+b^4\left)k^2\right)}{2(8-5b^2+b^4)\left(2\right(-1+b^2)h+k^2)}}\mathit{,}\\ p_d^{2*}={\displaystyle \frac{2bE\left[\left.A\right|Y\right]\left(2\right(-1+b^2)h+k^2)+E\left[\left.A\right|Y\right]\left(2\right(8+12b-5b^2-10b^3+b^4+2b^5)h+b(-4+b^2\left)k^2\right)}{-2(8-5b^2+b^4)\left(2\right(-1+b^2)h+k^2)}}\mathit{.}\end{array}$$

Substituting the optimal solutions in Proposition 2 into Equations (3) and (4), the optimal expected profits in CASE 2 are:$E\left[{\pi }_R^{2*}\right]=F_R^{2*}+T_R^{2*}$ and $E\left[{\pi }_M^{2*}\right]=F_M^{2*}+T_M^{2*}$, where $F_R^{2*}=F_R^{1*}$ and $F_M^{2*}=F_M^{1*}$. Interestingly, we derive$T_R^{1*}={(b^2-3)}^2{T}_R^{2*}$. Thus, $T_R^{2*}$ is also positive. This indicates that even if the retailer shares information, her forecasting behavior has a positive impact on her profit; specifically, the more accurate the forecast, the greater the benefit. In addition, we derive $T_M^{2*}>0$, which is completely different from the result $T_M^{1*}<0$ in Proposition 1. It indicates that once a manufacturer gets an accurate forecast, he can profit from more accurate demand information. When the manufacturer invests in green promotion service, the value of information sharing information brings to the manufacturer and retailer are $V_M^{2*}$ and $V_R^{2*}$. By $V_M^{2*}>0$ and $V_R^{2*}<0$, we derive that the retailer, to maintain her interest, prefers not to share information. It is because the manufacturer with shared information can have a more comprehensive grasp of uncertain demand and make decisions on wholesale price and green promotion service more promptly. Adjusting wholesale price would exacerbate double marginalization and damage the retailer’s profit. If the retailer keeps her forecast information secret, the manufacturer’s speculative behavior will bring the signal cost to the retailer. On the contrary, the retailer’s sharing strategy can eliminate the manufacturer’s speculation, which will reduce the signal cost, but exacerbate the double marginalization, which will increase the wholesale cost. In CASE 2, the retailer refuses to share private information because incremental wholesale cost outweighs decreasing signal cost.

To directly indicate the value of information sharing, a numerical example is illustrated in Figure 4. By $V_M^{2*}+V_R^{2*}>0$, we derive that the positive impact of information sharing on the manufacturer’s profit is greater than the negative impact on the retailer’s profit. Thus, information sharing can be lucrative for the entire supply chain. These conclusions contribute to expanding the literature on the interaction between information sharing and green promotion service.

5. Retailer Invests in Green Promotion Service

The green promotion service undertaken by the retailer is considered. Thus, the retailer bears all the investment costs of the green promotion service. Service-provided retailers have many offline stores where consumers are given free trials. For example, consumers can try out the goods on display in Suning’s stores. They can experience the cooling of air conditioners, the new features of mobile phones, the wind of hair dryers, the cleaning power of vacuum cleaners, etc. In this case, the retailer has to provide a variety of green promotion services (i.e., shopping guide, product advertising) before consumers buy products. Therefore, service quality (or service level) will affect consumer satisfaction and their purchase intention.

However, the openness of information and the convenience of online shopping channels result in lower free-riding cost. Thus, the actual demand is not only affected by the price and service level, but also the degree of free-riding behavior. In order to reflect the influence of free-rider behavior in the dual-channel environment, demand functions of direct channel and retail channel are separately expressed as: $A-p_d+b{p}_r+\mu ks$ and $A-p_r+b{p}_d+\left(1-\mu \right)ks$. $\mu$ denotes the degree of free-riding. In reality, free-riding behavior is affected by many factors, such as income level, cost of free-riding, and service level [8]. This paper focus on the influence of free-riding on the management decisions in a dual-channel supply chain, rather than how individual free-riding behavior is affected by various factors. Thus, the degree of free-riding is assumed as an exogenous parameter to avoid the intervention of these factors. These demand functions exist in the available literature [42].

5.1. CASE 3: No Information Sharing

The retailer takes on all green promotion service cost and keeps forecasting demand secret. The manufacturer cannot infer precise market base and first determines the wholesale price $w$ and online price. Then, the retailer decides retail price and green promotion service level. Because retail price is determined in the last stage of the game, the manufacturer needs to rely on ex-ante belief to determine the wholesale price and online price if he cannot obtain accurate marketing information. The retailer determines the retail price based on the forecast information and the manufacturer’s decisions in the previous stage. This case is superscripted by ‘3*’. The ex-ante expected profits are described as:

$$\mathrm{E}\left[{\mathsf{\pi }}_{\mathrm{M}}\right]=\left(\mathrm{w}\right(\mathrm{a}-\mathrm{E}\left[{\mathrm{p}}_{\mathrm{r}}\right]+\mathrm{b}{\mathrm{p}}_{\mathrm{d}}+\left(1-\mathsf{\mu }\right)\mathrm{k}\mathrm{E}\left[\mathrm{s}\right])+{\mathrm{p}}_{\mathrm{d}}(\mathrm{a}-{\mathrm{p}}_{\mathrm{d}}+\mathrm{b}\mathrm{E}\left[{\mathrm{p}}_{\mathrm{r}}\right]+\mathsf{\mu }\mathrm{k}\mathrm{E}\left[\mathrm{s}\right]\left)\right),$$

(5)

$$\mathrm{E}\left[\left.{\mathsf{\pi }}_{\mathrm{R}}\right|\mathrm{Y}\right]=({\mathrm{p}}_{\mathrm{r}}-\mathrm{w})\left(\mathrm{E}\right[\left.\mathrm{A}\right|\mathrm{Y}]-{\mathrm{p}}_{\mathrm{r}}+\mathrm{b}{\mathrm{p}}_{\mathrm{d}}+(1-\mathsf{\mu }\left)\mathrm{k}\mathrm{s}\right)-\mathrm{h}{\mathrm{s}}^2/2.$$

(6)

Since the retailer keeps the forecasting demand secret, he deduces the market base to be $E\left[A\right]$ (i.e., $a$). Because the retailer makes decisions behind the manufacturer, he cannot infer the exact random variables (i.e., retail price and service level). Thus, the manufacturer’s expected ex-ante profit should contain $E\left[p_r\right]$ and $E\left[s\right]$. In addition, since the retailer has access to information about the market, she deduced the market base as $E\left[\left.A\right|Y\right]$. The optimal solutions in CASE 3 are shown in Proposition 3.

Proposition 3. 

In the case of the retailer invests in green promotion service and the retailer does not share information, the optimal solutions exist and are expressed as:

$$\begin{array}{c}{w}^{3*}={\displaystyle \frac{a(-4(1+b)h^2-k^4(b(\mu -1)-\mu \left){\left(\mu -1\right)}^2\right(2\mu -1)+h{k}^2(\mu -1\left)\right(b(3+b)\mu -2-b(4+b)\left)\right)}{8(b^2-1)h^2-4(b^2-1)h{k}^2{(-1+\mu )}^2+k^4{(-1+\mu )}^2{(b+\mu -b\mu )}^2}}\mathit{,}\\ s^{3*}={\displaystyle \frac{k(\mu -1)(-E[\left.A\right|Y]+w-b{p}_2)}{2h-k^2+2k^2\mu -k^2{\mu }^2}}\mathit{,}\\ p_r^{3*}=-{\displaystyle \frac{k^{2}w{(1-\mu )}^2-h\left(E\right[\left.A\right|Y]+w+b{p}_2)}{2h-k^2{(1-\mu )}^2}}\mathit{,}\\ p_d^{3*}={\displaystyle \frac{-ah\left(4\right(1+b)h-k^2(-1+\mu \left)\right(-2+b(-1+\mu )+3\mu \left)\right)}{8(b^2-1)h^2-4(b^2-1)h{k}^2{(\mu -1)}^2+k^4{(\mu -1)}^2{(b+\mu -b\mu )}^2}}\mathit{.}\end{array}$$

Substituting the optimal solutions in Proposition 3 into Equations (5) and (6), the optimal expected profits in case 3 are:$E\left[{\pi }_R^{3*}\right]=F_R^{3*}+T_R^{3*}$ and $E\left[{\pi }_M^{3*}\right]=F_M^{3*}+T_M^{3*}$. Interestingly, by $T_M^{3*}=0$, we find that $E\left[{\pi }_M^{3*}\right]$ is irrelevant to forecast accuracy. This is because the manufacturer gives priority to the wholesale price and the online price. Thus, he does not have conjectural behavior. This means that the retailer’s prediction behavior will not have any influence on the manufacturer’s decisions. In addition, $T_R^{3*}>0$ shows that when green promotion service undertaken by the retailer without information sharing, the retailer’s forecasting behavior has an impact on her profit, and the more accurate the forecast, the greater the benefit.

5.2. CASE 4: Information Sharing

In this case, the information in this supply chain is completely symmetrical, and two parties update beliefs simultaneously. This case is indexed by superscript ‘2*’. The ex-ante expected profits are expressed as:

$$\mathrm{E}\left[\left.{\mathsf{\pi }}_{\mathrm{M}}\right|\mathrm{Y}\right]=\mathrm{w}\left(\mathrm{E}\right[\left.\mathrm{A}\right|\mathrm{Y}]-{\mathrm{p}}_{\mathrm{r}}+\mathrm{b}{\mathrm{p}}_{\mathrm{d}}+(1-\mathsf{\mu }\left)\mathrm{k}\mathrm{s}\right)+{\mathrm{p}}_{\mathrm{d}}\left(\mathrm{E}\right[\left.\mathrm{A}\right|\mathrm{Y}]-{\mathrm{p}}_{\mathrm{d}}+\mathrm{b}{\mathrm{p}}_{\mathrm{r}}+\mathsf{\mu }\mathrm{k}\mathrm{s}),$$

(7)

$$\mathrm{E}\left[\left.{\mathsf{\pi }}_{\mathrm{R}}\right|\mathrm{Y}\right]=({\mathrm{p}}_{\mathrm{r}}-\mathrm{w})\left(\mathrm{E}\right[\left.\mathrm{A}\right|\mathrm{Y}]-{\mathrm{p}}_{\mathrm{r}}+\mathrm{b}{\mathrm{p}}_{\mathrm{d}}+(1-\mathsf{\mu }\left)\mathrm{k}\mathrm{s}\right)-\mathrm{h}{\mathrm{s}}^2/2.$$

(8)

Both parties have retailer’s prediction demand $Y$, so they infer market base as $E\left[\left.A\right|Y\right]$. The optimal solutions are shown in Proposition 4.

Proposition 4. 

In the case of the retailer invests in green promotion service and shares information, the optimal reaction functions in the first-stage of backward induction are:

$$p_r^{4*}={\displaystyle \frac{k^2{w}^{4*}{(1-\mu )}^2-h\left(E\right[\left.A\right|Y]+w+b{p}_d^{4*})}{-(2h-k^2{\left(1-\mu \right)}^2)}},s^{4*}={\displaystyle \frac{k(\mu -1)(-E[\left.A\right|Y]+w^{4*}-b{p}_d^{4*})}{2h-k^2+2k^2\mu -k^2{\mu }^2}}$$

The optimal online price and wholesale price in the second-stage of backward induction are:

$$\begin{array}{c}{p}_d^{4*}={\displaystyle \frac{E\left[\left.A\right|Y\right]h(-4(1+b)h+k^2(\mu -1\left)\right(-2+b(-1+\mu )+3\mu \left)\right)}{8(b^2-1)h^2-4(b^2-1)h{k}^2{(\mu -1)}^2+k^4{(\mu -1)}^2{(b+\mu -b\mu )}^2}}\mathit{,}\\ w^{4*}={\displaystyle \frac{E\left[\left.A\right|Y\right](-4(1+b)h^2-k^4(b(\mu -1)-\mu \left){\left(\mu -1\right)}^2\right(2\mu -1)+h{k}^2(\mu -1\left)\right(b(3+b)\mu -2-b(4+b)\left)\right)}{\left(8\right(b^2-1)h^2-4(b^2-1)h{k}^2{(-1+\mu )}^2+k^4{(-1+\mu )}^2{(b+\mu -b\mu )}^2)}}\mathit{.}\end{array}$$

Substituting the optimal solutions in Proposition 4 into Equations (7) and (8), we get the optimal expected profits in CASE 4 are:$E\left[{\pi }_R^{4*}\right]=F_R^{4*}+T_R^{4*}$ and $E\left[{\pi }_M^{4*}\right]=F_M^{4*}+T_M^{4*}$, where $F_R^{4*}=F_R^{3*}$, $T_R^{4*}={\sigma }_0^2\gamma F_R^{4*}/a^2$, $F_M^{4*}=F_M^{3*}$, and $T_M^{4*}=V_M^{4*}={\sigma }_0^2\gamma F_M^{4*}/a^2$. By $F_R^{3*}>0$, we derive $F_M^{4*}>0$,$T_M^{4*}>0$. By $T_M^{4*}>0$ and $T_R^{4*}>0$, we derive that the retailer’s predictive behavior has a positive impact on her own and manufacturer’s profits. This means improving predictive accuracy can enhance the values that information sharing brings to the manufacturer and retailer. When green promotion service is undertaken by the retailer, the value of information sharing information brought to the manufacturer and retailer are $V_M^{4*}$ and $V_R^{4*}$. By $V_M^{4*}>0$ and $V_R^{4*}<0$, we derive the retailer is reluctant to share private forecasting market when she undertakes green promotion service. This is because the manufacturer has access to capture uncertain demand fluctuation and improve his agility to make a pricing decision. The increase in the wholesale price will aggravate double marginalization and be harmful to the retailer’s profit. Moreover, by $d{V}_M^{4*}/d{\sigma }_1^2=-V_M^{4*}/({\sigma }_1^2+{\sigma }_0^2)$, we derive if the manufacturer can benefit from the sharing strategy, the prediction accuracy will affect his value. Thus, the higher the prediction accuracy, the greater the value that information sharing brings to the manufacturer.

5.3. Analysis of Channel Substitution Effect and Free-Riding Effect

In this part, numerical examples are given to further analyze the effect of channel substitution and free-riding behavior on the profits of both parties. The value of information sharing and the optimal ex-ante expected profits in four equilibrium strategies are depicted in Figure 4 and Figure 5, respectively. The results in Figure 4 show that the manufacturer’s profit, retailer’s profit, supply chain’s profit, and the values of information sharing increase with the channel’s substitution effect. Their growth rates are gradually accelerating. This is because the stronger the channel substitution effect is, the more sensitive consumers are to the competitive channel’s price. It is easy to explain this phenomenon. As information becomes more transparent and spreads faster, consumers can quickly and efficiently obtain the price information of products in different channels and make the optimal purchasing decisions. Therefore, compared with the traditional single channel, price changes in two competitive channels will have a more obvious impact on the market demand under the dual-channel environment. In addition, the information open enables the manufacturer to obtain more accurate market information. Even if the retailer’s private prediction information is not shared, it is easy for the manufacturer in the big data environment to speculate. Therefore, the retailer’s optimal information sharing strategy is more beneficial to her own interests. To sum up, the greater the channel substitution effect, the more the retailer should take the initiative to cooperate with the manufacturer and share her private forecasting information.

To intuitively observe the influence of free-rider behavior, we present the profit and information sharing values in

Table 4. The optimal ex-ante expected profits when green promotion service undertaken by the retailer.

$\mathit{\mu }$	$\mathit{E}\left[{\mathit{\pi }}_{\mathit{M}}^{3\mathit{*}}\right]$	$\mathit{E}\left[{\mathit{\pi }}_{\mathit{M}}^{4\mathit{*}}\right]$	${\mathit{V}}_{\mathit{M}}^{4\mathit{*}}$	$\mathit{E}\left[{\mathit{\pi }}_{\mathit{R}}^{3\mathit{*}}\right]$	$\mathit{E}\left[{\mathit{\pi }}_{\mathit{R}}^{4\mathit{*}}\right]$	${\mathit{V}}_{\mathit{R}}^{4\mathit{*}}$	$\mathit{E}\left[{\mathit{\pi }}_{\mathit{S}\mathit{C}}^{3\mathit{*}}\right]$	$\mathit{E}\left[{\mathit{\pi }}_{\mathit{S}\mathit{C}}^{4\mathit{*}}\right]$	${\mathit{V}}_{\mathit{S}\mathit{C}}^{4\mathit{*}}$
0	89.6576	90.2852	0.6276	7.5173	7.3838	−0.1335	97.1749	97.669	0.4941
0.1	89.4874	90.1138	0.6264	7.4301	7.298	−0.1321	96.9175	97.4118	0.4943
0.2	89.3074	89.9325	0.6251	7.3381	7.207	−0.1311	96.6455	97.1395	0.4940
0.3	89.1172	89.7411	0.6239	7.2412	7.1109	−0.1303	96.3584	96.852	0.4936
0.4	88.9169	89.5394	0.6198	7.1393	7.0096	−0.1297	96.0562	96.549	0.4928
0.5	88.7064	89.3259	0.6195	7.0324	6.903	−0.1294	95.7388	96.2304	0.4916
0.6	88.4856	89.105	0.6194	6.9206	6.7913	−0.1293	95.4062	95.8963	0.4901
0.7	88.2545	88.8723	0.6178	6.8039	6.6745	−0.1294	95.0584	95.5468	0.4884
0.8	88.0132	88.6293	0.6161	6.6824	6.5525	−0.1299	94.6956	95.1818	0.4862
0.9	87.7616	88.376	0.6144	6.556	6.4256	−0.1304	94.3176	94.8016	0.4840
1.0	87.5	88.1125	0.6125	6.425	6.2938	−0.1312	93.925	94.4063	0.4813

Note. In this example, $a=10$, $h=1.5$, $k=0.4$, ${{\sigma }_0}^2=1$, $b=0.5$ and $\rho =0.7$.

by changing the free-riding ratio $\mu$ over $(0,1)$ with the step of $0.1$. Especially, $\mu =0$ means the free-riding phenomenon does not exist. Thus, consumers who have enjoyed the green promotion services in offline retailing stores will not buy online. For expensive goods, like jewelry and cars, or durable goods with complex installation, like air conditioners, consumers are more willing to buy in offline stores to ensure the quality of products and services. $\mu =1$ denotes all the consumers will choose to experience offline and buy online. In practice, it could happen if online prices are cheaper than offline ones. For example, price-sensitive consumers may choose to hitchhike if they can get a better price for online coupons than offline ones.

The results in Table 3 show that the value that information sharing brings to the manufacturers is positive and decreases with the free-rider ratio. However, with the increase of free-rider ratio, the value of information sharing for the retailer is negative, and its negative value increases firstly and then decreases. This indicates that information sharing is bad for the retailer. But with the increase of the degree, the negative impact of information sharing becomes smaller and smaller, and with the continuous increase of free-riding, the negative impact of information sharing becomes larger and larger.

When the retailer undertakes green promotion service, the manufacturer’s profit, retailer’s profit, and supply chain’s profit decrease with the degree of free-riding, which indicates that free-riding is not good for enterprises and the whole system. This is because as more consumers experience products offline for free and buy products online, which leads to the retailer’s green promotion service investment not to promote the growth of demand in the retail channel, but to stimulate the growth of competitor’s demand in the direct channel. For the manufacturer, providing offline pre-sales experience service is a good means of promotion, but he cannot blindly rely on the free-rider tendency to make profits, because it is bad for the whole supply chain. In practice, retailers will also take some measures to reduce the losses caused by free riders, such as signing service cost sharing contracts with manufacturers [43]. Therefore, to better profit from such cooperation and competition, the manufacturer should provide appropriate offline experience services. This is also consistent with the reality. For example, Huawei and Apple have opened many free offline experience stores to encourage consumers to buy online.

6. Conclusions and Limitations

The rapid development of e-commerce creates the conditions for manufacturers, i.e., MI and Huawei, to provide green promotion service for consumers through the way of ‘consumption in advance and repayment after’. Consumers can choose free experience products within the credit limit, and pay if satisfied with the product, or elect to return if not. In a dual-channel environment, green promotion service may be undertaken by the manufacturer providing credit purchase service, or by offline retailer. This paper focuses on four equilibrium outcomes according to whether green promotion services are provided by the manufacturer or the retailer, and whether the retailer shares demand forecasting information. In addition, the effects of the degree of dual-channel competition and free-riding behavior on the perfect Bayesian Nash equilibrium are studied. All equilibrium solutions are derived by Bayes formula, mathematical expectation, and backward induction.

The main conclusion of this paper is summarized into three aspects: (1) In the case of the manufacturer undertakes the service investment, we find that the forecasting accuracy has a positive impact on the retailer’s profit and a negative impact on the manufacturer’s profit without information sharing. If the retailer shares information, forecasting accuracy has a positive impact on self-profits. At the same time, the manufacturer can also obtain accurate forecast information and benefit from the retailer’s forecast accuracy. In addition, the optimal information sharing strategy of the retailer is not sharing information. This is because the manufacturer with shared information can have a more comprehensive grasp of uncertain demand and make decisions on wholesale price and green promotion service more promptly. Raising wholesale price would alleviate the loss caused by the double marginalization effect and be inimical to the interests of the retailer. (2) When the green promotion service is offered by the retailer, the results show that her profit increases with forecasting accuracy without information sharing. However, the dominant manufacturer gives priority to the wholesale price and online price decisions and does not have any conjectural behavior, so the retailer’s prediction behavior will not have any influence on his decisions and his profit is irrelevant to the prediction accuracy. If the retailer shares information, forecasting behavior will positively affect two parties’ profits. Thus, improving predictive accuracy can enhance the value of information sharing for both parties. Moreover, the manufacturer’s profit, retailer’s profit, and supply chain’s profit decrease with the degree of free-riding, which indicates that free-riding is not good for enterprises and the whole system. (3) The retailer’s profit, supply chain’s profit, and the values of information sharing increase with the channel’s substitution effect. Thus, the retailer should take the initiative to cooperate with the manufacturer and share her private forecasting information in a relatively high coefficient of channel substitution. In addition, the manufacturer should provide appropriate offline experience services to make profits.

The conclusion of this paper has important management implications. First of all, for green manufacturing enterprises, retailers should be encouraged to participate in green emission reduction actions, and strengthen cooperation with their downstream retailers to achieve win–win cooperation through demand information sharing behavior. At the same time, effective measures should be taken in the cooperation process to reduce consumers’ free-riding behavior, so as to reduce the adverse impact of free-riding behavior on supply chain profits. Then, for policymakers and regulators, strengthening pricing controls in the e-commerce environment is critical to the key role that companies along the green manufacturing supply chain play in achieving sustainable practices. The government should continue to improve the macro policy framework for enterprises’ digital transformation, including increasing special fund support, providing credit incentives, facilitating financing, and implementing tax incentives, so as to promote enterprises to improve the accuracy of market demand forecasting.

This paper also has the limitation that we only consider two decision makers; however, there are many participants (i.e., e-retailer, third-party logistics companies) in reality. We will further explore free-riding and information sharing in the e-commerce dual-channel environment to overcome this limitation.