Cooperative and Non-Cooperative Green Advertising in the Low-Carbon Supply Chain under Monopoly or Competitive Market

Abstract

Customers feel a degree of ambiguity associated with low-carbon products, such as remanufactured products, and undervalue them. Although green advertising significantly impacts consumers’ acceptance of remanufactured products and the low-carbon supply chain (LCSC), limited research has been carried out on advertisement decisions for remanufactured products in the LCSC. This study introduces a two-echelon remanufacturing supply chain motivated by the practice of applying green advertising to update consumers’ low-carbon awareness. We use a game-theoretical approach to analyze the remanufacturer’s and retailer’s decisions on the green advertising program (non-coop vs. co-op green advertising) under different competitive scenarios in the LCSC. We find that the LCSC’s and the retailer’s profits are optimal in the non-coop green advertising under the monopoly, but the LCSC’s and the remanufacturer’s profits are optimal in the co-op green advertising under the competition. We suggest that the entry and royalty fees can be applied to coordinate the LCSC under different competitive scenarios.

1. Introduction

Low-carbon products, such as remanufactured products, are a critical component of the low-carbon economy and deliver economic, social, and environmental benefits [1]. Although the benefits of reducing the carbon emission surrounding remanufactured products have attracted much attention from both industry and the academic sector, consumers may have a passive opposition to the consumption of remanufactured goods [2]. Research suggests that consumers feel a degree of ambiguity associated with the level of quality of remanufactured products [3,4]. This may spring from the concern that the product will have poor performance and low reliability. However, Hong et al. [5] suggest informing consumers of the parity in quality and green attributes, such as low-carbon emissions between new and remanufactured products, will increase the value associated with purchasing remanufactured products. A remanufacturing supply chain must build trust actively and arouse consumers’ low-carbon awareness. As green advertising significantly impacts consumers, and it is still unclear how green advertising affects the low-carbon supply chain (LCSC), further research needs to discuss the advertising decisions for remanufactured products in the supply chain.

Ever-increasing consumer low-carbon awareness (CLA), significantly affects consumers’ purchasing behaviors and operational strategies [6]. A complementary way of building green awareness is to clarify the company’s motives on carbon neutrality, e.g., the ambition to produce a product with low-carbon attributes and low-resource consumption by contributing to sustainable development. Research has shown that consumers tend to value remanufactured products less than conventional new products unless they are informed about the respective environmental impacts of each [7]. As the profitability of the entire low-carbon supply chain (LCSC) is contingent upon adequate consumer adoption of remanufactured goods, companies are seeking to promote their sustainable practices to improve the reception of the remanufactured product [8]. These promotional activities include flyers, displays, local advertising, free trials, etc. Traditionally, the remanufacturing research has focused on operational issues from a supply point of view, and the advertising literature mainly discusses the new product promotion. Less attention has been paid to promoting the remanufactured products by advertising their eco-friendly practices as transparent and accountable to the low-carbon supply chain. The effect of green advertising in LCSC has been mostly disregarded in the existing literature and a recent systematic review paper concludes that limited research has been performed on advertising decisions for remanufactured products [9]. Therefore, there is a need to formulate models to investigate LCSC’s optimal green advertising decisions.

Traditionally, manufacturers often delegate local advertising and promotion of their products to their retail partners to sell the product more effectively [10]. Cooperative (Co-op) advertising is a brand or manufacturer sharing (or a subsidy) of local retailer, vendor, or dealer advertising costs. This represents a pool of money in the US that some have estimated to be over $50 billion annually. On the other hand, some retailers choose not to participate in manufacturers’ co-op advertising (Non-coop) programs [11]. Although many studies focus on the co-op advertising mode for the new product, little literature discusses the co-op green advertisement in the low-carbon manufacturing industry where the remanufactured product encounters fierce competition from the new product. Herein, this study models the effect of the green advertising provision on improving consumers’ low carbon awareness of remanufactured products and analyzes the impact of different green advertising modes on the optimal profits of LCSC and its members in different competitive environments.

Manufacturers can pay the slotting allowances or a fixed fee for introducing a new product into a retail store in the traditional market. On the other hand, retailers pay a royalty fee to manufacturers with high brand value and popular products to change the sales rights. The academic explains that these fees transferred between the manufacturers and retailers can coordinate the channel [12]. While considering the vertical competition between the remanufacturer and the retailer, we ask how LCSC and the chain members obtain the optimal profits in co-op or non-coop green advertising programs under different competitive environments.

To answer the above questions, this study introduces a two-echelon LCSC motivated by the non-coop or co-op green advertisement practice of improving consumers’ low carbon awareness to facilitate consumers’ acceptance of the remanufactured product. Considering that green advertising affects customers’ green valuation of remanufactured products, we analyze the impact of the market competition environment on the remanufacturers’ and retailers’ choice of co-op or non-coop green advertising programs. We further explain the entrance or royalty fees’ role in selecting the green advertising modes in different competition scenarios. The study finds that the remanufacturer obtains the optimal profit in the co-op green advertising mode, but the non-coop green advertising mode makes LCSC and retailer optimal under the monopoly. The retailer can transfer part profits such as a royalty fee to the remanufacturer, so the non-coop green advertising mode is optimal for both remanufacturer and retailer. When there is competition, the remanufacturer’s support improves his own and the LCSC’s profits but reduces the retailer’s income. Therefore, the remanufacturer should transfer part profits, such as the entrance fee to his retailer, making the co-op green advertising mode the best choice for them.

The main contributions of this paper to the extant literature are threefold. Firstly, the remanufacturing research has focused on operational issues from a supply point of view and limited research has been done on advertising decisions for remanufactured products. We fill this gap and model that the green advertising provided by the retailer affects the consumers’ low-carbon awareness of the remanufactured product in different green advertising programs. Secondly, the previous advertising literature suggests that co-op advertising increases the advertising level and profits in the traditional supply chain, but we put forward that co-op green advertising is not always optimal for the LCSC. Thirdly, we further stress the significance of the entry and royalty fees to coordinate the LCSC in co-op or non-coop green advertising programs under different competitive environments.

The remainder of this paper proceeds as follows. Section 2 introduces the literature. We present the conceptual model in Section 3. The results are then presented in Section 4, and Section 5 consists of concluding remarks, highlighting the study limitations and the directions for future research.

2. Literature Review

The literature related to our study is mainly based on product information provision affecting consumers’ purchase decisions, remanufacturing supply chain, and marketing management in remanufacturing. This section reviews relevant studies and identifies the research gaps between this work and the current literature.

2.1. Advertising in the Traditional Supply Chain

A large amount of the literature studies the advertising information strategy and its impact on customer purchase decisions. It is proven that, in practice, many retailers usually regard advertising as a key marketing instrument to influence brand switching and channel substitution [13], or/and to establish store image and enhance store traffic [14,15]. Previous research also studies the advertising strategies in the supply chain. For example, Bar-Isaac, etc. [16] noted that customers can constantly collect product information to understand the product, suggesting that retailers can control customers’ difficulty in obtaining product information. Shi etc. [17] considered advertising information addressing customer uncertainty about whether the product matches its own needs, examining the choice of manufacturers’ and retailers’ advertising strategies.

Another stream of research considers the advertisement mode, such as cooperative advertisements in supply chains [18,19]. For example, Huang et al. [20] determine that a manufacturer should bear part of a retailer’s promotional expenditure when a subsidy threshold is exceeded. From the channel integration, the existing literature has widely discussed the bright side of co-op advertising [21]. However, Kennedy et al. [22] consider the competition between the two retailers of the two manufacturers and find that co-op advertising does not benefit the channel if the cooperative advertising model leads to a reduced marginal profit for the channel members. Karray and Amim [23] model the competition between manufacturers selling products through two competing retailers, and find that price levels and advertising competition influence the effectiveness of cooperative advertising model-regulatory channels. Karray et al. [24] study the negative and positive long-term effects of retailer advertising and propose that the co-op advertising model does not exist when the product differences are not significant.

As discussed in the previous sections, researchers have investigated advertisements in the traditional supply chain structures. Different from the above studies, we consider co-op green advertising or non-coop green advertising in a low-carbon supply chain and the impact of the competition on choosing the effective green advertising mode.

2.2. Remanufacturing

The literature on remanufacturing is based on engagement in the remanufacturing process [25,26], inventory considerations [27,28], collection strategy [8,29], and supply chain coordination. For example, the studies on the remanufacturing process consider both the pre-life and end-of-life stages of the product to maximize overall profit along the whole product life cycle [30]. Other studies investigate joint location-inventory problems with the balance of supply and demand by securing adequate stock while avoiding overstocking or shortage [31,32]. Some authors study the choice of collection channels by comparing single and dual channels and suggest the optimal collection channel for remanufacturers due to cost savings associated with collection investment [33]. The research on SC coordination investigates the impact of demand information sharing, revenue-sharing contracts, and other initiatives to improve SC profits in remanufacturing [34,35]. Different from them, we further consider the marketing management of remanufacturing.

2.3. Advertising in the Remanufacturing Supply Chain

Other streams of remanufacturing studies focus on marketing management in remanufacturing, such as the type of market [29,30], pricing decision [36,37], and advertising decision. Authors have considered whether the remanufactured product is sold in the same primary market, as a new product, or in another secondary market in a monopolistic or more competitive market [34]. On another side, most papers investigate the optimal prices of the finished new or remanufactured products [38], and the issues impacting the pricing of end products [39]. Our work is mainly related to the previous research on advertising in the remanufacturing supply chain. A stream of advertising literature has begun, focused on green advertising, putting forward that green advertising is an effective marketing tool that affects customers’ green behaviors and increases a firm’s market share [7,11,40].

An increasing number of studies have focused on the effect of green advertising on the green supply chain and cooperation strategies. For example, Hong et al. [41] determine the optimal pricing, advertising investment, and acquisition to maximize the profits of chain members. Geranmayeh et al. [42] compare two non-coop games with one co-op game. Their results indicate that a manufacturer prefers to partake in a retailer’s advertising expenditure when the difference between new and remanufactured products increases. Jena et al. [43] find that a centralized advertising configuration model is more effective than other models and that advertising can bring increased economic and environmental benefits. Hong and Zhang [8] propose a cross-advertising policy that offers firms initiatives on interactive decisions in the presence of interactive production constraints.

These studies consider that advertising influences consumers’ green behavior and pricing, the optimal profit of the supply chain. However, they do not consider the effect of competition on the optimal decision on green advertising and how to coordinate LCSC in different advertising modes or competition scenarios. We further enrich the growing literature by discussing the transfer of profits between the remanufacturer and the retailer, such as the entrance fee or royalty fee in coordinating the LCSC in co-op or non-coop green advertising mode. We present the related literature in

Table 1. Research directions for decision-making in remanufacturing.

Area	Focus	Issues in the Existing Literature	Research Methods	References
Supply chain related issues	Remanufacture process	This stream of literature focuses on remanufacturing scheduling, process planning disassembly in remanufacturing with uncertainty problems such as the timing, quality, quantity of returns, routing, lead time, and demand in different channel power structures (e.g., centralized; manufacturer-, retailer-, third-party-led decentralized; and vertical).	They set models for considering multi-products and dealing with demand, returns quantity, returns quality, lead time, and quantity uncertainties. Most of their models aim to minimize the environmental effects.	Yang et al., [25]; Ma et al., [26]; Robotis et al., [27]; Kwak and Kim [30];
	Inventory considerations	Inventory management balances supply and demand by securing adequate stock while avoiding overstocking or shortage. This stream of literature promotes joint investigation over inventory control, production control, and disposition with the consideration of uncertainties in returns timing, quantity, quality, and environmental legislation.	Most studies consider economic objectives, i.e., profit maximization and cost minimization. Environmental and social aspects have been emphasized recently.	Robotis et al., [27]; Inderfurth and Kleber [28]; Abdallah er al, [31]; Jonsson and Mattsson [32].
	Collection strategy	The choice of collection channels by comparing single and dual channels has been mostly investigated. For example, 1. Remanufacturer directly collects from customers; 2. Remanufacturer persuades the retailer to collect from customers; 3 Remanufacturer authorizes the third-party to collect from customers; 4. Remanufacturer and retailer; 5. Retailer and the third party; 6. Remanufacturer and third-party.	The main aim of their model is to maximize the collection efficiency and minimize the overall collection effort while keeping a sufficient quantity of cores for meeting the remanufacturing demand. Most studies have formulated collection as a single objective economic rather than multi-objective optimization problem.	Zhang et al., [1]; Hong et al., [5]; Savaskan and Van [29]; Jonsson and Mattsson [32]; Huang et al., [33].
	Coordination	Coordination is essential for resolving conflicts and disagreements between SC members. Researchers have proposed various mechanisms such as information sharing, contracts, trade policy, quantity flexibility, sales rebate, revenue-sharing, and other initiatives to improve SC coordination in remanufacturing.	Game theory modeling is the most popular method to resolve conflicts in SC coordination. Other methods are equilibrium and benchmark models. Regarding model objectives, most studies consider profit maximization.	Li et al., [2]; Huang et al., [33]; Kaya [34]; Govindan and Popiuc [35]; Hong et al., [41];
Marketing management	Type of market	Market type can be looked at from the market structure perspective: monopolistic and competitive markets. Authors have considered whether the remanufactured product gets sold in the same primary market, as a new product, or in another secondary market in a monopolistic or more competitive market.	Most papers have considered a single-period problem with single objectives, such as a cost minimization problem and profits maximization.	Savaskan and Van [29]; Kwak and Kim [30]; Kaya [34]; Ferrer and Swaminathan [38]; Hong et al., [41]; Atasu et al., [44].
	Pricing decision	Authors consider measuring consumers’ willingness-to-switch to remanufactured products by examining the effect of trade-in-related decisions, leasing duration, the degree of disassemblability and interchangeability on the pricing strategies for new and remanufactured products.	Optimization techniques have been used to model the profit/ revenue maximization or cost minimization parts of the solutions on pricing decisions. A mix of papers works in a deterministic or stochastic setting where some parameters are assumed to be random.	Hong et al., [10]; Debo et al., [36]; Macedo et al., [37];Ferrer and Swaminathan [38]; Vorasayan and Ryan [39];
	Advertisement decision (Limited literature on this issue)	Researchers in the existing literature have explained the relationship between purchase intention and advertising activities in the remanufacturing environment that increase consumer awareness of the benefits of remanufactured products, therefore, play a significant role in influencing consumer demand and profitability. They study green advertising encouraging customers to return their used products by increasing their concerns and awareness about environmental issues, and national advertising to create an image about the product and enhance its sale in different cooperative games. We extend this type of research.	Experimental design has been used for surveys to understand consumer behavior. From the other side, theoretical models are established to analyze the proposed problem, such as the Nash, Stackelberg, and the non-cooperative or cooperative game.	Micaud and Llerena [7]; Hazen et al., [3]; Wang and Hazen [4]; Ottman et al., [40]. Hong et al. [5]; Xia et al. [6]; Hong and Zhang [8]; Geranmayeh et al., [42]; Jena et al., [43].

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3. The Basic Model for Green Advertising in the Low-Carbon Supply Chain

3.1. Modelling Manufacturer and Retailer in Non-Coop or Coop Green Advertising Mode

We consider a low-carbon supply chain consisting of one (independent) remanufacturer (m), and one retailer (r). The remanufacturer produces a remanufactured product and sells the product to the retailer at wholesale price w. The production cost is assumed to be 0. Then the retailer sells the remanufactured product at the price p and provides green advertisements to enhance the consumers’ low-carbon awareness of the remanufactured product. These consist of various promotional activities and can include flyers, displays, local advertising, etc. We will compare two green advertisement modes in the monopoly or competitive scenario that depend on whether the remanufacturer shares the green advertisement cost or not: 1. Non-coop green advertising mode (R), where the retailer undertakes all the green advertising effort; 2. In co-op green advertising mode (MR), the remanufacturer shares the retailer’s promotional costs associated with the remanufactured product at a rate b by offering a co-op green advertising contract. We first study the optimal green advertisement mode of LCSC under the monopoly scenario. This analysis is based on the Hotelling linear city model, where the retail store is located at the linear city’s midpoint. The retail store provides green advertising for the remanufactured product. Then, we analyze the optimal green advertisement mode of the LCSC under the competitive scenario where a competitor (r₂) sells a new product to compete with the retailer (r₁). The retailer and the competitor are located on both ends of the linear city. They sell the two alternative products at prices p₁ and p₂. The green advertising level of the remanufactured product provided by the retailer is s. This paper adopts a quadratic cost function for the advertising level, where the green advertising cost is 1/2 hs² when the green advertising level is s [20,24]. In R mode, the retailer undertakes all the cost of the green advertisement 1/2 hs²; in the MR mode, the remanufacturer and retailer share the cost of the green advertisement, the sharing cost of the remanufacturer is $1/2{ \mathrm{bhs}}^2$ ($0\le \mathrm{b}<1$) and his retailer’s cost is $1/2\left(1-\mathrm{b}\right){\mathrm{hs}}^2$.

3.2. Customers’ Evaluation in Non-Coop or Coop Green Advertising Mode

Atasu et al. [44] indicate that the remanufactured products have the same functions as new products, but consumers have a lower consumption perception of remanufactured products than that of new ones. We assume that the actual consumption value for remanufactured products is $\mathrm{u}$, but consumers undervalue the consumption value and have $\mathrm{au}$ when there is no green advertising provision. Customers are evenly distributed in the interval (0,1) in the Hotelling linear city. Without losing generality, each customer buys one product. The customer’s internal utility of the product is $\mathrm{v}$ and the traveling cost is $\mathrm{t}$.

This article assumes that the customers make a preliminary evaluation of the overall value of the remanufactured product based on the mastered information. After they receive the green advertising information improving their low-carbon awareness in the retail store, they adjust the remanufactured product’s evaluation and finally decide whether to buy the product. The customers evaluate the overall value of the remanufactured product $\left(1-\mathrm{a}\right)\mathrm{u}$ ($0\le \mathrm{a}\le 1$) [45,46], when there is no green advertising. After obtaining the green advertising ($\mathrm{s}$), the customers adjust the evaluation of the product’s overall value. Similar to Kopalle and Lehmann [15], we assume that the impact of the retailing green advertising on the customers’ valuation is $\mathrm{sau}$ ($0\le \mathrm{s}\le 1$, $\mathrm{s}=1$, customer has full information about the remanufactured product and its green attributes, and the valuation is $\mathrm{u}$). This article assumes that the customer evaluates the overall value of the product based on the prior valuation and the adjusted evaluation after obtaining the green advertising information, $\left(1-\mathrm{a}\right)\mathrm{u}+\mathrm{sau}$.

Definitions of the symbols in the model are as follows: $\mathrm{p}$-product sales price; $\mathrm{w}$-product wholesale price; $\mathrm{s}$-green advertising level; $\mathrm{v}$-customer’s internal utility of the product; $\mathrm{t}$-travel cost; $\mathrm{h}$-advertising information cost coefficient; $\mathrm{b}$-the remanufacturer’s sharing coefficient; $\mathrm{a}$-the valuation coefficient of undervaluing the remanufactured product; $\mathrm{u}$-the actual value of the remanufactured product; $\mathrm{V}$-the overall surplus of the product.

4. Results

4.1. The Optimal Green Advertising Mode in LCSC under the Monopoly

This section is divided into two sub-sections belonging to the green advertising effort shared by the remanufacturer or not under the monopoly scenario: 1. Non-coop green advertising mode ($\mathrm{R}$), the retailer undertakes all costs of the green advertisement effort; 2. Co-op green advertising mode ($\mathrm{MR}$): the remanufacturer and the retailer share the cost of the green advertising. We set a baseline model, no green advertising provision ($\mathrm{N}$) to conclude the effect of an advertisement, then compare the two green advertising modes to conclude the optimal choice. As the remanufacturer’s profit increases with the increase of $\mathrm{w},$ and we cannot obtain the optimal solution $\mathrm{w}$ in the full market, we only discuss the uncovered market. We assume $\mathrm{h}>3{\mathrm{u}}^2{\mathrm{a}}^2/2\mathrm{t}$ to guarantee positive results.

From the analysis of the consumers, we can get the surplus of consumers located at $\mathrm{x}$ in $\mathrm{R}$ and $\mathrm{MR}$ modes:

$$\mathrm{V}=\mathrm{v}+\left(1-\mathrm{a}\right)\mathrm{u}+\mathrm{sau}-\mathrm{p}-\left|\mathrm{x}-\frac{1}{2}\right|\mathrm{t}$$

(1)

So we can deduct the demand in $\mathrm{R}$ and $\mathrm{MR}$ mode under the monopoly:

$$\mathrm{q}=2\frac{\mathrm{v}+\mathrm{u}-\mathrm{ua}+\mathrm{sau}-\mathrm{p}}{\mathrm{t}}$$

4.1.1. Non-Coop Green Advertising Mode ($\mathrm{R}$)

In this model, the retailer puts the entire effort into green advertising because of better local knowledge about the customer. Each member tries to maximize their own profit individually, ignoring the impact of their decision on the other member. So the remanufacturer first announces the wholesale prices $\mathrm{w}$. Similar to Iyer [47], the retailer then decides the green advertising level $\mathrm{s}$. In the third stage, the retailer decides the sales price $\mathrm{p}$. Considering the sales revenue and the cost in mode $\mathrm{R}$, the retailer’s or remanufacturer’s optimization is

$${\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{R}}\left(\mathrm{s},\mathrm{p}\right)=\mathrm{pq}-\mathrm{wq}-\frac{1}{2}{\mathrm{hs}}^2$$

(2)

$${\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{R}}\left(\mathrm{w}\right)=\mathrm{wq}$$

(3)

By applying the Stackelberg game, we can get the optimal solutions for the wholesale price, retail price, and advertising level:

$${\mathrm{w}}^{\mathrm{R}}=\frac{1}{2}\mathrm{v}+\frac{1}{2}\mathrm{u}-\frac{1}{2}\mathrm{ua}$$

$${\mathrm{p}}^{\mathrm{R}}=-\frac{1}{4}\frac{\left(-\mathrm{v}-\mathrm{u}+\mathrm{ua}\right)\left(2{\mathrm{u}}^2{\mathrm{a}}^2-3\mathrm{ht}\right)}{{\mathrm{u}}^2{\mathrm{a}}^2-\mathrm{th}}$$

$${\mathrm{s}}^{\mathrm{R}}=\frac{1}{2}\frac{\mathrm{ua}\left(-\mathrm{v}-\mathrm{u}+\mathrm{ua}\right)}{{\mathrm{u}}^2{\mathrm{a}}^2-\mathrm{th}}$$

The remanufacturer’s or retailer’s optimal profit is:

$${\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{R}}=-\frac{1}{4}\frac{{(-\mathrm{v}-\mathrm{u}+\mathrm{ua})}^2\mathrm{h}}{{\mathrm{u}}^2{\mathrm{a}}^2-\mathrm{th}}$$

$${\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{R}}=-\frac{1}{8}\frac{{(-\mathrm{v}-\mathrm{u}+\mathrm{ua})}^2\mathrm{h}}{{\mathrm{u}}^2{\mathrm{a}}^2-\mathrm{th}}$$

See proof in Appendix A.

Proposition 1.

${\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{R}}>{\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{N}}$,${\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{R}}>{\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{N}}$;${\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{R}}+{\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{R}}>{\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{N}}+{\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{N}}$.${\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{N}}$and${\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{N}}$are the profits for the retailer and remanufacturer in the no green advertising provision ($\mathrm{N}$) mode.

Proof. 

The consumers’ surplus in the no green advertising provision ($\mathrm{N}$) mode:

$$\mathrm{V}=\mathrm{v}+\left(1-\mathrm{a}\right)\mathrm{u}-\mathrm{p}-\left|\mathrm{x}-\frac{1}{2}\right|\mathrm{t}$$

(4)

The profit function of the remanufacturer and the retailer are:

$${\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{N}} \left(\mathrm{p}\right)=\mathrm{pq}-\mathrm{wq}$$

(5)

$${\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{N}} \left(\mathrm{w}\right)=\mathrm{wq}$$

(6)

We can deduct the results with the Stackelberg game:

$${\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{N}}=\frac{1}{8}\frac{{(-\mathrm{v}-\mathrm{u}+\mathrm{ua})}^2}{\mathrm{t}}$$

$${\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{N}}=\frac{1}{4}\frac{{(-\mathrm{v}-\mathrm{u}+\mathrm{ua})}^2}{\mathrm{t}}$$

By comparing the results in $\mathrm{N}$ and $\mathrm{R}$ modes, we can obtain the assumption that $\mathrm{h}>3{\mathrm{u}}^2{\mathrm{a}}^2/2\mathrm{t}$:

$${\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{R}}-{\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{N}}=-\frac{1}{4}\frac{{(-\mathrm{v}-\mathrm{u}+\mathrm{ua})}^2{\mathrm{u}}^2{\mathrm{a}}^2}{\left({\mathrm{u}}^2{\mathrm{a}}^2-\mathrm{ht}\right)\mathrm{t}}>0$$

Similarly, ${\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{R}}-{\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{N}}>0$, ${\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{R}}+{\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{R}}-\left({\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{N}}+{\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{N}}\right)>0$. □

Proposition 1 states that the green advertising provision under the monopoly increases both the remanufacturer’s and the retailer’s profits. The retailer is willing to offer green advertising to enhance the consumers’ low-carbon awareness of the remanufactured product, while the remanufacturer does not give any effort to the green advertising and enjoys the benefits as a free rider.

4.1.2. Co-op Green Advertising Mode ($\mathrm{MR}$)

In this case, the retailer puts the effort into the green advertising, while the remanufacturer shares the advertisement cost with the retailer. First, the remanufacturer announces the cost-sharing rate and the wholesale price of the remanufactured product. Then based on the given rate and wholesale price, the retailer decides the green advertising level. The retailer decides the sales price at stage 3. The remanufacturer bears a fraction of the green advertising cost $1/2{\mathrm{bhs}}^2$ ($0\le \mathrm{b}<1$), and the retailer undertakes the green advertising cost of $1/2\left(1-\mathrm{b}\right){\mathrm{hs}}^2$. The profit functions of the remanufacturer and retailer can be written as:

$${\mathsf{\pi }}_{\mathrm{R}}^{\mathrm{MR}}\left(\mathrm{s},\mathrm{p}\right)=\mathrm{pq}-\mathrm{wq}-\frac{1}{2}\mathrm{h}\left(1-\mathrm{b}\right){\mathrm{s}}^2$$

(7)

$${\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{MR}}\left(\mathrm{w},\mathrm{b}\right)=\mathrm{wq}-\frac{1}{2}{\mathrm{hbs}}^2$$

(8)

The optimal solutions of cost-sharing percentage, wholesale price, retail price, and advertising level are obtained under the Stackelberg game.

$$\mathrm{b}=\frac{1}{3}$$

$${\mathrm{w}}^{\mathrm{MR}}=-\frac{\left(-\mathrm{v}-\mathrm{u}+\mathrm{ua}\right)\left(3{\mathrm{u}}^2{\mathrm{a}}^2-4\mathrm{ht}\right)}{9{\mathrm{u}}^2{\mathrm{a}}^2-8\mathrm{ht}}$$

$${\mathrm{p}}^{\mathrm{MR}}=-\frac{3\left(-\mathrm{v}-\mathrm{u}+\mathrm{ua}\right)\left({\mathrm{u}}^2{\mathrm{a}}^2-2\mathrm{ht}\right)}{9{\mathrm{u}}^2{\mathrm{a}}^2-8\mathrm{ht}}$$

$${\mathrm{s}}^{\mathrm{MR}}=\frac{\left(6\left(-\mathrm{v}-\mathrm{u}+\mathrm{ua}\right)\right)\mathrm{ua}}{9{\mathrm{u}}^2{\mathrm{a}}^2-8\mathrm{ht}}$$

The optimal profits of the remanufacturer and retailer are:

$${\mathsf{\pi }}_{\mathrm{R}}^{\mathrm{MR}}=-\frac{4{(-\mathrm{v}-\mathrm{u}+\mathrm{ua})}^2\mathrm{h}\left(-2\mathrm{ht}+3{\mathrm{u}}^2{\mathrm{a}}^2\right)}{{(9{\mathrm{u}}^2{\mathrm{a}}^2-8\mathrm{ht})}^2}$$

$${\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{MR}}=-\frac{2{(-\mathrm{v}-\mathrm{u}+\mathrm{ua})}^2\mathrm{h}}{9{\mathrm{u}}^2{\mathrm{a}}^2-8\mathrm{ht}}$$

Proof. 

See Appendix A. □

Proposition 2.

The remanufacturer sets the cost-sharing percentage as$1/3$in co-op green advertising mode under the monopoly, and his support enables${\mathrm{s}}^{\mathrm{MR}}>{\mathrm{s}}^{\mathrm{R}}$,${\mathrm{w}}^{\mathrm{MR}}>{\mathrm{w}}^{\mathrm{R}}$.

The mathematical expression:

based on the optimal results in$\mathrm{MR}$and$\mathrm{R}$modes under the monopoly, we have the assumption that$\mathrm{h}>3{\mathrm{u}}^2{\mathrm{a}}^2/2\mathrm{t}$:

$${\mathrm{s}}^{\mathrm{MR}}-{\mathrm{s}}^{\mathrm{R}}=\frac{1}{2}\frac{\mathrm{ua}\left(-\mathrm{v}-\mathrm{u}+\mathrm{ua}\right)\left(3{\mathrm{u}}^2{\mathrm{a}}^2-4\mathrm{ht}\right)}{\left(9{\mathrm{u}}^2{\mathrm{a}}^2-8\mathrm{ht}\right)\left({\mathrm{u}}^2{\mathrm{a}}^2-\mathrm{ht}\right)}>0$$

$${\mathrm{w}}^{\mathrm{MR}}-{\mathrm{w}}^{\mathrm{R}}=\frac{3}{2}\frac{{\mathrm{u}}^2{\mathrm{a}}^2\left(-\mathrm{v}-\mathrm{u}+\mathrm{ua}\right)}{9{\mathrm{u}}^2{\mathrm{a}}^2-8\mathrm{ht}}>0$$

Proposition 2 states that the remanufacturer’s support for the retailer’s green advertising effort improves the green advertising level. However, the extra cost resulting from such support makes the remanufacturer raise the wholesale price of the remanufactured product to compensate for the sharing cost.

Proposition 3.

When$3{\mathrm{u}}^2{\mathrm{a}}^2/2\mathrm{t}<\mathrm{h}<27{\mathrm{a}}^2{\mathrm{u}}^2/16\mathrm{t}$,${\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{MR}}<{\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{N}}$;when$\mathrm{h}\ge 27{\mathrm{a}}^2{\mathrm{u}}^2/16\mathrm{t}$,${\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{MR}}\ge {\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{N}}$;${\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{MR}}>{\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{N}}$,${\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{MR}}+{\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{MR}}>{\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{N}}+{\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{N}}$.

The mathematical expression:

based on the optimal results in$\mathrm{MR}$and$\mathrm{N}$mode under the monopoly, we have the assumption that$\mathrm{h}>3{\mathrm{u}}^2{\mathrm{a}}^2/2\mathrm{t}$:

$${\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{MR}}-{\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{N}}=-\frac{9}{4}\frac{{(-\mathrm{v}-\mathrm{u}+\mathrm{ua})}^2{\mathrm{u}}^2{\mathrm{a}}^2}{\left(9{\mathrm{u}}^2{\mathrm{a}}^2-8\mathrm{ht}\right)\mathrm{t}}>0$$

Similarly,${\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{MR}}+{\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{MR}}-\left({\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{N}}+{\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{N}}\right)>0$,

${\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{MR}}-{\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{MR}}=-\frac{3}{8}\frac{{(-\mathrm{v}-\mathrm{u}+\mathrm{au})}^2{\mathrm{a}}^2{\mathrm{u}}^2\left(-16\mathrm{ht}+27{\mathrm{a}}^2{\mathrm{u}}^2\right)}{{(9{\mathrm{a}}^2{\mathrm{u}}^2-8\mathrm{ht})}^2\mathrm{t}}$,so when$3{\mathrm{u}}^2{\mathrm{a}}^2/2\mathrm{t}<\mathrm{h}<27{\mathrm{a}}^2{\mathrm{u}}^2/16\mathrm{t}$,${\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{MR}}<{\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{N}}$;when$\mathrm{h}\ge 27{\mathrm{a}}^2{\mathrm{u}}^2/16\mathrm{t}$,${\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{MR}}\ge {\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{N}}$.

Proposition 3 proposes that the green advertising in the co-op green advertising mode improves the LCSC’s and the remanufacturer’s profits under the monopoly, compared with the No-advertising mode. The remanufacturer is willing to support his retailer by providing the green advertising, but the co-op green advertising mode is not always beneficial to the retailer.

Proposition 4.

${\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{MR}}<{\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{R}}$,${\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{MR}}>{\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{R}}$;${\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{R}}+{\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{R}}>{\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{MR}}+{\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{MR}}$.

The mathematical expression:

$${\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{R}}-{\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{MR}}=-\frac{1}{4}\frac{{(-\mathrm{v}-\mathrm{u}+\mathrm{ua})}^2{\mathrm{hu}}^2{\mathrm{a}}^2}{\left(-\mathrm{th}+{\mathrm{u}}^2{\mathrm{a}}^2\right)\left(9{\mathrm{u}}^2{\mathrm{a}}^2-8\mathrm{th}\right)}<0$$

$${\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{R}}-{\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{MR}}=\frac{1}{8}\frac{\mathrm{h}{(-\mathrm{v}-\mathrm{u}+\mathrm{ua})}^2{\mathrm{u}}^2{\mathrm{a}}^2\left(15{\mathrm{u}}^2{\mathrm{a}}^2-16\mathrm{th}\right)}{\left(-\mathrm{th}+{\mathrm{u}}^2{\mathrm{a}}^2\right){(9{\mathrm{u}}^2{\mathrm{a}}^2-8\mathrm{th})}^2}>0$$

$${\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{R}}+{\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{R}}-\left({\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{MR}}+{\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{MR}}\right)=-\frac{{(-\mathrm{v}-\mathrm{u}+\mathrm{ua})}^2{\mathrm{hu}}^4{\mathrm{a}}^4}{\left(-\mathrm{th}+{\mathrm{u}}^2{\mathrm{a}}^2\right){(9{\mathrm{u}}^2{\mathrm{a}}^2-8\mathrm{th})}^2}>0$$

Proposition 4 proposes that the remanufacturer’s support to the retailer by providing the green advertising information improves his profit, but reduces the LCSC’s and the retailer’s profits under the monopoly, compared with the non-coop green advertising mode. The remanufacturer pays the extra cost on the support for the green advertising in $\mathrm{MR}$ mode and raises the wholesale price of the remanufactured product to compensate for the cost. His retailer raises the sale prices accordingly, so the higher price reduces the demand. On the other hand, the increase of the green advertising level because of the support boosts the demand. As the increased demand for the higher green advertising level is greater than the reduced demand caused by the rising price, the total demand in $\mathrm{MR}$ mode is greater than the total demand in $\mathrm{R}$ mode (${\mathrm{q}}^{\mathrm{MR}}>{\mathrm{q}}^{\mathrm{R}}$). In such a case, the income from the higher wholesale price and the increased demand override the support cost, so the remanufacturer obtains the optimal earnings in $\mathrm{MR}$ mode.

However, the retailer and LCSC obtain the optimal profits in $\mathrm{R}$ mode. Although the remanufacturer shares part of the green advertising cost, the wholesale cost of the remanufactured product is higher than that in $\mathrm{MR}$ mode (${\mathrm{w}}^{\mathrm{MR}}>{\mathrm{w}}^{\mathrm{R}}$). Moreover, a higher green advertising level increases the total cost and the retailer bears a large part of the advertising cost. The income from the remanufacturer’s support and the increased demand for higher green advertising levels are insufficient to compensate for the higher wholesale cost and higher advertising cost, so the co-op advertising model is not optimal for the retailer. For the whole channel, the increase of the green advertising level does not only raise the income but also brings the higher cost which dominates the profit of LCSC in $\mathrm{MR}$ mode.

Proposition 5.

When$3{\mathrm{u}}^2{\mathrm{a}}^2/2\mathrm{t}<\mathrm{h}<27{\mathrm{a}}^2{\mathrm{u}}^2/16\mathrm{t}$,${\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{R}}>{\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{N}}>{\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{MR}}$; when$\mathrm{h}\ge 27{\mathrm{a}}^2{\mathrm{u}}^2/16\mathrm{t}$,${\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{R}}>{\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{MR}}\ge {\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{N}}$;${\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{MR}}>{\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{R}}>{\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{N}}$,${\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{R}}+{\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{R}}>{\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{MR}}+{\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{MR}}>{\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{N}}+{\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{N}}$.

Proposition 5 indicates that the non-coop green advertising mode makes the whole LCSC’s and the retailer’s profits optimal under the monopoly, but the remanufacturer’s profit is lower than that in the coop green advertising mode (See Figure 1). To make $\mathrm{R}$ mode become both remanufacturer’s and retailer’s best choice, the retailer can coordinate the channel by transferring part of the profit, for example paying the royalty fees, to the remanufacturer in $\mathrm{R}$ mode.

4.2. The Optimal Green Advertising Mode for LCSC under the Competitive Scenario

This section will study the effect of the competition on the optimal green advertising mode for the LCSC, so we will compare the co-op green advertising mode with the non-cooperative green advertising mode under the competitive scenario. The remanufacturer (${\mathrm{m}}_1$) produces a remanufactured product to compete with a common product. The remanufacturer wholesales the remanufactured product to his retailer (${\mathrm{r}}_1$) at a wholesale price $\mathrm{w}$, then the retailer delivers to the market at price ${\mathrm{p}}_1$ to compete with the current competitor (${\mathrm{r}}_2$) selling the common category of alternative products. Customers have full information about the current competitor’s product but undervalue the remanufactured product. The retailer and competitor are located at both ends of the linear city. They sell the two alternative products at price ${\mathrm{p}}_1$ and ${\mathrm{p}}_2$, respectively. To increase the consumers’ low-carbon awareness of the remanufactured product, the retailer provides green advertising and its level is $\mathrm{s}$. The added valuation increased by the green advertising is $\mathrm{sau}$. As we assume that the actual value of the retailer’s and competitor’s products have the same intrinsic utility, we assume that both products have the same production cost and are set to 0. This paper assumes that the current competitor as the whole channel decides the retail price (we can assume that the current competitor sells products through the direct channel). This assumption enables us to focus on studying the impact of competition on the optimal green advertising strategies for LCSC. We also assume that $\mathrm{t}>1/3\mathrm{au}$ and $\mathrm{h}>2{\mathrm{u}}^2{\mathrm{a}}^2/9$ to keep the positive results.

The customers’ surplus to the remanufactured or the common product when the retailer 1 provides the green advertising:

$$\mathrm{V}\left({\mathrm{r}}_1\right)=\mathrm{v}+\left(1-\mathrm{a}\right)\mathrm{u}+\mathrm{sau}-{\mathrm{p}}_1-\mathrm{xt}$$

(9)

$$\mathrm{V}\left({\mathrm{r}}_2\right)=\mathrm{v}+\mathrm{u}-{\mathrm{p}}_2-\left(1-\mathrm{x}\right)\mathrm{t}$$

(10)

So we can obtain the demand for the retailer (${\mathrm{r}}_1$) and the competitor (${\mathrm{r}}_2$) in $\mathrm{R}$ or $\mathrm{MR}$ mode:

$${\mathrm{q}}_{\mathrm{r}1}=\frac{1}{2}\frac{-{\mathrm{au}+\mathrm{sau}-\mathrm{p}}_1+{\mathrm{p}}_2+\mathrm{t}}{\mathrm{t}}$$

$${\mathrm{q}}_{\mathrm{r}2}=1-\frac{1}{2}\frac{-{\mathrm{au}+\mathrm{sau}-\mathrm{p}}_1+{\mathrm{p}}_2+\mathrm{t}}{\mathrm{t}}$$

4.2.1. Non-Coop Advertising Mode ($\mathrm{R}$)

As retailer 1 undertakes all green advertising costs, the profit functions for retailer 1, the competitor, and the remanufacturer are respectively:

$${\mathsf{\pi }}_{\mathrm{r}1}^{\mathrm{R}}\left(\mathrm{s},{\mathrm{p}}_1\right)={\mathrm{p}}_1{\mathrm{q}}_1-{\mathrm{wq}}_1-\frac{1}{2}{\mathrm{hs}}^2$$

(11)

$${\mathsf{\pi }}_{\mathrm{r}2}^{\mathrm{R}}\left({\mathrm{p}}_2\right)={\mathrm{p}}_2{\mathrm{q}}_2$$

(12)

$${\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{R}}\left(\mathrm{w}\right)={\mathrm{wq}}_1$$

(13)

In this case, the remanufacturer first announces the wholesale price of the remanufactured product, and then his retailer chooses the green advertising level. In the third stage, the retailer and the competitor choose their respective sale prices ${\mathrm{p}}_1$ and ${\mathrm{p}}_2$.

According to the Stackelberg model, we can obtain the optimal sale prices and the advertising level, and the optimal profits of the remanufacturer and his retailer:

$${\mathrm{p}}_{\mathrm{r}1}^{\mathrm{R}}=-\frac{1}{2}\frac{\left(\mathrm{ua}-3\mathrm{t}\right)\left({\mathrm{a}}^2{\mathrm{u}}^2-12\mathrm{ht}\right)}{{\mathrm{a}}^2{\mathrm{u}}^2-9\mathrm{ht}}$$

$$\mathrm{s}=\frac{1}{2}\frac{\mathrm{au}\left(\mathrm{ua}-3\mathrm{t}\right)}{{\mathrm{a}}^2{\mathrm{u}}^2-9\mathrm{ht}}$$

$${\mathsf{\pi }}_{\mathrm{r}1}^{\mathrm{R}}=-\frac{1}{8}\frac{\mathrm{h}{(\mathrm{ua}-3\mathrm{t})}^2}{{\mathrm{a}}^2{\mathrm{u}}^2-9\mathrm{ht}}$$

$${\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{R}}=-\frac{3}{8}\frac{\mathrm{h}{(\mathrm{ua}-3\mathrm{t})}^2}{{\mathrm{a}}^2{\mathrm{u}}^2-9\mathrm{ht}}$$

Proof. 

See Appendix A. □

4.2.2. Co-op Green Advertising Mode ($\mathrm{MR}$)

In such a case, the remanufacturer bears a fraction of the green advertising cost $1/2{\mathrm{bhs}}^2$ ($0\le \mathrm{b}<1$), and the retailer undertakes the green advertising cost of $1/2\left(1-\mathrm{b}\right){\mathrm{hs}}^2$. So the remanufacturer’s, the retailer’s, and the competitor’s profit functions are:

$${\mathsf{\pi }}_{\mathrm{r}1}^{\mathrm{MR}}\left(\mathrm{s},{\mathrm{p}}_1\right)=\left({\mathrm{p}}_1-\mathrm{w}\right){\mathrm{q}}_1-\frac{1}{2}\left(1-\mathrm{b}\right){\mathrm{hs}}^2$$

(14)

$${\mathsf{\pi }}_{\mathrm{r}2}^{\mathrm{MR}}\left({\mathrm{p}}_2\right)={\mathrm{p}}_2{\mathrm{q}}_2$$

(15)

$${\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{MR}}\left(\mathrm{w},\mathrm{b}\right)={\mathrm{wq}}_1-\frac{1}{2}{\mathrm{bhs}}^2$$

(16)

In this case, the remanufacturer first announces the wholesale price $\mathrm{w}$ of the remanufactured product and the support percentage $\mathrm{b}$, then his retailer chooses the green advertising level. Finally, the retailer and the competitor decide their sale prices ${\mathrm{p}}_1$ and ${\mathrm{p}}_2$.

According to the Stackelberg model, we obtain the optimal sale prices, the green advertising level, the support percentage, and the optimal profits of the remanufacturer and his retailer:

$${\mathrm{b}}^{\mathrm{MR}}=\frac{1}{2}$$

$${\mathrm{p}}_{\mathrm{r}1}^{\mathrm{MR}}=\frac{\left(\mathrm{au}-3\mathrm{t}\right)\left(2{\mathrm{a}}^2{\mathrm{u}}^2-27\mathrm{ht}\right)}{4{\mathrm{a}}^2{\mathrm{u}}^2-27\mathrm{ht}}$$

$${\mathrm{w}}^{\mathrm{MR}}=-\frac{1}{2}\frac{\left(\mathrm{au}-3\mathrm{t}\right)\left(2{\mathrm{a}}^2{\mathrm{u}}^2-27\mathrm{ht}\right)}{4{\mathrm{a}}^2{\mathrm{u}}^2-27\mathrm{ht}}$$

$${\mathrm{s}}^{\mathrm{MR}}=\frac{3(\mathrm{au}-3\mathrm{t})\mathrm{au}}{4{\mathrm{a}}^2{\mathrm{u}}^2-27\mathrm{ht}}$$

$${\mathsf{\pi }}_{\mathrm{r}1}^{\mathrm{MR}}=-\frac{9}{8}\frac{{(\mathrm{au}-3\mathrm{t})}^2\mathrm{h}\left(-9\mathrm{ht}+2{\mathrm{a}}^2{\mathrm{u}}^2\right)}{{(4{\mathrm{a}}^2{\mathrm{u}}^2-27\mathrm{ht})}^2}$$

$${\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{MR}}=-\frac{9}{8}\frac{{(\mathrm{au}-3\mathrm{t})}^2\mathrm{h}}{4{\mathrm{a}}^2{\mathrm{u}}^2-27\mathrm{ht}}$$

Proof. 

See Appendix A. □

Proposition 6.

When there is competition,${\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{R}}>{\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{MR}}$, but${\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{MR}}>{\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{R}}$,${\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{MR}}+{\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{MR}}>{\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{R}}+{\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{R}}$.

The mathematical expression:

$${\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{MR}}-{\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{R}}=-\frac{1}{8}\frac{\mathrm{h}{(\mathrm{au}-3\mathrm{t})}^2{\mathrm{u}}^2{\mathrm{a}}^2\left(-27\mathrm{ht}+2{\mathrm{a}}^2{\mathrm{u}}^2\right)}{{(4{\mathrm{a}}^2{\mathrm{u}}^2-27\mathrm{ht})}^2\left({\mathrm{a}}^2{\mathrm{u}}^2-9\mathrm{ht}\right)}<0$$

$${\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{MR}}-{\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{R}}=\frac{3}{8}\frac{\mathrm{h}{(\mathrm{au}-3\mathrm{t})}^2{\mathrm{u}}^2{\mathrm{a}}^2}{\left(4{\mathrm{a}}^2{\mathrm{u}}^2-27\mathrm{ht}\right)\left({\mathrm{a}}^2{\mathrm{u}}^2-9\mathrm{ht}\right)}>0$$

$${ \mathsf{\pi }}_{\mathrm{m}}^{\mathrm{MR}}+{\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{MR}}-\left({\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{R}}+{\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{R}}\right)=\frac{1}{4}\frac{\mathrm{h}{(\mathrm{ua}-3\mathrm{t})}^2{\mathrm{u}}^2{\mathrm{a}}^2\left(5{\mathrm{u}}^2{\mathrm{a}}^2-27\mathrm{th}\right)}{{(4{\mathrm{u}}^2{\mathrm{a}}^2-27\mathrm{th})}^2\left({\mathrm{u}}^2{\mathrm{a}}^2-9\mathrm{th}\right)}>0$$

Proposition 6 indicates that similar to the monopoly scenario, the remanufacturer’s support increases his profits and reduces his retailer’s profit, but contrary to the conclusion of the whole channel’s profit in monopoly, the remanufacturer’s support improves the LCSC’s profit in the presence of the competitor (See Figure 2). The results of the LCSC’s profit in the monopoly scenario (optimal in R mode) are contrary to the competitive scenario (optimal in MR mode). We will explain how the change in the advertising level affects the results in $\mathrm{R}$ and $\mathrm{MR}$ modes under a different competitive environment.

The two figures show that the remanufacturer’s support increases the green advertising level under the monopoly (See Figure 3) or competitive scenario (See Figure 4). We also have that the green advertising level set by the retailer under the monopoly is much higher than that under the competitive environment, whether in $\mathrm{R}$ or $\mathrm{MR}$ mode.

Under the same green advertising level, the green advertising provided by the retailer under the monopoly can serve more customers, so the retailer sets a higher green advertising level than that in the competitive case. It also can be seen that under the monopoly, the increased green advertising level due to the remanufacturer’s support is much higher than that in the competitive scenario. As the marginal cost of the green advertising level increases, the higher advertising level in $\mathrm{MR}$ mode means that the whole LCSC undertakes the higher green advertising cost under the monopoly. Compared with the competitive scenario, the remanufacturer’s support under the monopoly raises the green advertising level from a relatively higher level to a much higher level, causing a huge cost. Therefore, the cost incurred by the remanufacturer’s support to improve the green advertising level under the monopoly is far greater than that in the competitive scenario. From the perspective of the whole LCSC, compared with the non-coop advertising mode, the benefits brought by the co-op advertising model under the monopoly can not compensate for the added cost of the increased green advertising level, leading to the reduction of the overall profit of the channel; however, the increased revenue in the co-op green advertising mode under the competitive scenario can compensate for the increased cost of the rising green advertising level, increasing the LCSC’s profit.

Proposition 6 proposes that the green advertising support favors the remanufacturer and the whole LCSC under the competitive scenario, so the remanufacturer has a great willingness to provide support to his retailer. However, the retailer suffers from the support and does not accept it, so the remanufacturer needs to coordinate the channel through entry fees, then the retailer obtains a higher profit and accepts the co-op green advertising program.

4.3. Profit Coordination Mechanism in $MR$ Mode under the Competitive Scenario

We will discuss the coordination of LCSC through the generalized Nash Bargaining Game. According to Harsanyi etc. [48], we define the condition in which both remanufacturer and his retailer accept the coordination mechanism in the co-op advertising mode under the competition. That is when the profit coordination results can make the remanufacturer and his retailer’s profits higher than the profits obtained in the non-coop green advertising mode, so the remanufacturer and his retailer will accept the profit coordination mechanism.

We apply ${\mathrm{y}}_1$, ${\mathrm{y}}_2$ to represent the amount of profit allocated to the manufacturer and retailer after the profit coordination; the allocated profit is the increased profit of the whole channel, compared with the non-cooperative green advertising mode, represented by ${\Delta \mathsf{\pi }}_{\mathrm{r}}^{\mathrm{MR}}+{\Delta \mathsf{\pi }}_{\mathrm{m}}^{\mathrm{MR}}$. The bargaining power of the remanufacturer or retailer is, respectively, ${\mathrm{r}}_{\mathrm{m}}$, ${\mathrm{r}}_{\mathrm{r}}$ (we assume ${\mathrm{r}}_{\mathrm{m}}>{\mathrm{r}}_{\mathrm{r}}$ because the remanufacturer is in the dominant position). We have the profit coordination between the remanufacturer and his retailer, to address the following problem:

$$\max :\mathrm{g}\left({\mathrm{y}}_1,{\mathrm{y}}_2\right)={\mathrm{y}}_1{}^{{\mathrm{r}}_{\mathrm{m}}}{\mathrm{y}}_2{}^{{\mathrm{r}}_{\mathrm{r}}}\left({\mathrm{y}}_1\ge 0,{\mathrm{y}}_2\ge 0\right)$$

$$\mathrm{s}.\mathrm{t}.\mathrm{P}=\left\{\left({\mathrm{y}}_1,{\mathrm{y}}_2\right):{\mathrm{y}}_1+{\mathrm{y}}_2={\Delta \mathsf{\pi }}_{\mathrm{r}}^{\mathrm{MR}}+{\Delta \mathsf{\pi }}_{\mathrm{m}}^{\mathrm{MR}}\right\}$$

$$\begin{array}{cc}{\Delta \mathsf{\pi }}_{\mathrm{r}}^{\mathrm{MR}}+{\Delta \mathsf{\pi }}_{\mathrm{m}}^{\mathrm{MR}}& ={ \mathsf{\pi }}_{\mathrm{r}}^{\mathrm{MR}}+{\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{MR}}-\left({\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{R}}+{\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{R}}\right)\\ & =\frac{1}{4}\frac{\mathrm{h}{(\mathrm{ua}-3\mathrm{t})}^2{\mathrm{u}}^2{\mathrm{a}}^2\left(5{\mathrm{u}}^2{\mathrm{a}}^2-27\mathrm{th}\right)}{{(4{\mathrm{u}}^2{\mathrm{a}}^2-27\mathrm{th})}^2\left({\mathrm{u}}^2{\mathrm{a}}^2-9\mathrm{th}\right)}\end{array}$$

We put ${\mathrm{y}}_2={\Delta \mathsf{\pi }}_{\mathrm{r}}^{\mathrm{MR}}+{\Delta \mathsf{\pi }}_{\mathrm{m}}^{\mathrm{MR}}-{\mathrm{y}}_1$ into the objective function and transfer it to:

$$\ln (\mathrm{g}\left({\mathrm{y}}_1\right))=\ln ({\mathrm{y}}_1{}^{{\mathrm{r}}_{\mathrm{m}}}\left({\Delta \mathsf{\pi }}_{\mathrm{Sr}}+{\Delta \mathsf{\pi }}_{\mathrm{Sm}}-{\mathrm{y}}_1{)}^{{\mathrm{r}}_{\mathrm{r}}}\right)$$

We solve the first condition of $\ln (\mathrm{g}\left({\mathrm{y}}_1\right))$ on ${\mathrm{y}}_1$, and obtain the optimal solution of ${\mathrm{y}}_1$:

$${\mathrm{y}}_1=\frac{{\mathrm{r}}_{\mathrm{r}}\left({\Delta \mathsf{\pi }}_{\mathrm{r}}^{\mathrm{MR}}+{\Delta \mathsf{\pi }}_{\mathrm{m}}^{\mathrm{MR}}\right)}{{\mathrm{r}}_{\mathrm{m}}+{\mathrm{r}}_{\mathrm{r}}}$$

Similarly:

$${\mathrm{y}}_2=\frac{{\mathrm{r}}_{\mathrm{m}}\left({\Delta \mathsf{\pi }}_{\mathrm{r}}^{\mathrm{MR}}+{\Delta \mathsf{\pi }}_{\mathrm{m}}^{\mathrm{MR}}\right)}{{\mathrm{r}}_{\mathrm{m}}+{\mathrm{r}}_{\mathrm{r}}}$$

According to the previous analysis, the remanufacturer’s profit increases in $\mathrm{MR}$ mode by comparing it to $\mathrm{R}$ mode. Assume that the increased profit is ${\Delta \mathsf{\pi }}_{\mathrm{m}}^{\mathrm{MR}}$, so the remanufacturer gets the profit ${\Delta \mathsf{\pi }}_{\mathrm{m}}^{\mathrm{MR}}$ of the increased profit of the whole channel before the profit coordination. After the profit coordination, the remanufacturer obtains the profit ${\mathrm{y}}_1$, so the remanufacturer should transfer the profits ${\Delta \mathsf{\pi }}_{\mathrm{m}}^{\mathrm{MR}}-{\mathrm{y}}_1$ to the retailer, to ensure that his own and the retailer’s profit are better than their profits in $\mathrm{R}$ mode.

Proposition 7.

Under the competition, the remanufacturer transfers${\mathrm{T}}_{\mathrm{m}}^{\mathrm{MR}}$to his retailer while providing support to his retailer with the green advertising.

${\mathrm{T}}_{\mathrm{m}}^{\mathrm{MR}}=\frac{1}{8}\frac{\left(\mathrm{au}-3\mathrm{t}{)}^2{\mathrm{hu}}^2{\mathrm{a}}^2{\mathrm{r}}_{\mathrm{r}}\right)}{{(4{\mathrm{u}}^2{\mathrm{a}}^2-27\mathrm{ht})}^2\left({\mathrm{u}}^2{\mathrm{a}}^2-9\mathrm{ht}\right)\left({\mathrm{r}}_{\mathrm{m}}+{\mathrm{r}}_{\mathrm{r}}\right)} (12{\mathrm{u}}^2{\mathrm{a}}^2{\mathrm{r}}_{\mathrm{m}}+2{\mathrm{u}}^2{\mathrm{a}}^2{\mathrm{r}}_{\mathrm{r}}-81{\mathrm{htr}}_{\mathrm{m}}-27\mathrm{ht}$, so${\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{MR}}\left({\mathrm{T}}_{\mathrm{m}}^{\mathrm{MR}}\right)>{ \mathsf{\pi }}_{\mathrm{r}}^{\mathrm{MR}}$,${\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{MR}}\left({\mathrm{T}}_{\mathrm{m}}^{\mathrm{MR}}\right)>{\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{R}}$.${\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{MR}}\left({\mathrm{T}}_{\mathrm{m}}^{\mathrm{MR}}\right)$,${\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{MR}}\left({\mathrm{T}}_{\mathrm{m}}^{\mathrm{MR}}\right)$is the remanufacturer’s and retailer’s profit after the coordination.

The mathematical expression:

$${\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{MR}}\left({\mathrm{T}}_{\mathrm{m}}^{\mathrm{MR}}\right)-{\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{R}}=\frac{1}{4}\frac{\mathrm{h}{(\mathrm{au}-3\mathrm{t})}^2{\mathrm{u}}^2{\mathrm{a}}^2{\mathrm{r}}_1\left(5{\mathrm{u}}^2{\mathrm{a}}^2-27\mathrm{ht}\right)}{{(4{\mathrm{u}}^2{\mathrm{a}}^2-27\mathrm{ht})}^2\left({\mathrm{u}}^2{\mathrm{a}}^2-9\mathrm{ht}\right)\left({\mathrm{r}}_1+{\mathrm{r}}_2\right)}>0$$

$${\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{MR}}\left({\mathrm{T}}_{\mathrm{m}}^{\mathrm{MR}}\right)-{\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{R}}=\frac{1}{4}\frac{\mathrm{h}{(\mathrm{au}-3\mathrm{t})}^2{\mathrm{u}}^2{\mathrm{a}}^2{\mathrm{r}}_2\left(5{\mathrm{u}}^2{\mathrm{a}}^2-27\mathrm{ht}\right)}{{(4{\mathrm{u}}^2{\mathrm{a}}^2-27\mathrm{ht})}^2\left({\mathrm{u}}^2{\mathrm{a}}^2-9\mathrm{ht}\right)\left({\mathrm{r}}_1+{\mathrm{r}}_2\right)}>0$$

Proposition 7 shows that in the competitive market, the remanufacturer should actively provide support to his retailer by providing green advertising, and transferring part of the profits, such as the entry fee to his retailer, the remanufacturer’s and retailer’s profits are better than the non-coop green advertising mode. As a result, his retailer accepts the co-op green advertising program to improve the advertising level of the LCSC competition edge.

5. Conclusions

5.1. Findings

Customers have a low valuation of the low-carbon product, such as the remanufactured product, so the green advertising disclosed by retail stores will significantly affect customers’ low-carbon awareness. Considering that the remanufacturer can support his retailer by providing green advertising to improve the advertising level, this paper compares the optimal decision-making between non-coop and co-op green advertising modes under the monopoly and competitive scenario. We find that the low-carbon supply chain benefits from the co-op green advertising mode under the competitive scenario, but obtains the optimal profit in non-coop green advertising under the monopoly. We further explain the coordination of LCSC by analyzing the transfer of the profits between the remanufacturer and his retailer, such as the entry and royalty fees in non-coop and co-op green advertising mode under different competitive scenarios.

5.2. Implications

This study makes two significant theoretical implications. First, limited remanufacturing research has focused on the effect of green advertising on the pricing and optimal profit from a supply point of view and does not consider the impact of different advertising modes on the supply chain. This paper fills this gap and sheds light on the impact of non-cooperative or cooperative advertisements on the low-carbon supply chain. Our result brings new insights to the ever-growing literature on green advertising for remanufactured products. Second, the past literature has considered the bright side of the cooperative advertisement mode. We suggest that co-op green advertising is not always optimal for LCSC and contribute to the literature by offering the significance of the entry and royalty fees to coordinate LCSC in co-op or non-coop green advertising programs under different competitive environments.

This study has important practical implications for the retailers and manufacturers in LCSC making green advertising decisions on choosing the advertisement modes (non-coop or co-op) and taking strategies to coordinate the supply chain. We have two suggestions for the remanufacturer and the retailer. First, both the remanufacturer and the retailer should have an agreement on the non-coop green advertising program in which the LCSC’s profit is optimal under the monopoly. In the contract, the remanufacturer sets a relatively low wholesale price and allows the retailer to provide the green advertisement independently to reduce the wholesale and advertising cost. The remanufacturer also can charge a royalty fee in the contract to enjoy the benefits of the lower cost brought by the non-coop green advertising program. Second, the remanufacturer should provide the co-op green advertising program to increase the advertising level under the competitive scenario. In the contract, the remanufacturer chooses a relatively higher wholesale price and promises support for the retailer’s green advertising effort. The remanufacturer can pay the entrance fee to gain the retailer’s agreement on this mode, so both of them obtain optimal profits.

5.3. Limitation and Future Research

Our findings point to several promising avenues for further research on managing green advertising in the low-carbon supply chain, but this paper only focuses on the optimal green advertising information strategy in LCSC and does not discuss the strategies applied by the competitor or another LCSC. It is interesting to further study the Nash game on the green advertising strategies between two LCSCs. Secondly, we consider the game in a single-period setting in this paper. It is exciting and worth noting to study a multi-period game. Admittedly, any thorough analysis of these issues would be complicated. However, we hope that this paper has laid the groundwork for future research.