# Advertising Cooperation and Green Technology R&D Strategy in a Platform-Led Stackelberg Game

Authors: Xin Huang; Liangjie Yu
Journal: Mathematical Problems in Engineering
 (2021)

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## Abstract

In this paper, we study a platform-led Stackelberg differential game over an infinite planning period considering an industry with two manufacturers competing in a common platform market. One manufacturer invests in R&D and produces green products, and the other produces nongreen products. Three platform advertising strategies are discussed systematically: the platform supports all advertising expenses for both manufacturers (PB), supports only green advertising expenses (PG), and implements a joint advertising plan (PJ) with the green manufacturer. The results reveal that the equilibrium price, R&D effort, and advertising level of products increase as the current green degree increases, while the green degree shows a monotonic trend over time and finally tends to be a stable value. The results also indicate that, in the three models, the green degree and the profits of all players with the PG strategy are the lowest. Compared with the PB strategy, although the PJ strategy may not maximize the profits of all players, from environmental perspective, the strategy would make the alliance achieve the best environmental performance.


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## Body

## 1. Introduction

With the development of the Internet, the market based on digital platforms is developing rapidly and has occupied a large share of the economy [1, 2]. A digital platform, such as Alibaba, JD, and Tmall, is a virtual trading place that supports the network interactions among multiple participants and facilitates transactions between the supply and demand sides while charging commissions according to sales. From the Ministry of Commerce 2017 China Retail Industry Development Report, the volume of online retail transactions via third-party platforms in China reached 516 million yuan in 2016, 26.2% increase over 2015, accounting for 12.6% of the total retail consumer goods sales [3]. The existence of digital platforms increases the communication channels with customers for merchants who have inconvenient offline communication. It also brings new challenges to traditional supply chain management.Environmental problems have attracted increasingly more attention in recent years. With the publicity of the government and social organizations, people are aware of the importance of environmental protection and pay more attention to the environmental performance of products when purchasing them [4]. Consumers’ awareness of environmental performance is the driving force promoting green supply chain operations. In order to attract consumers to buy products, manufacturers actively conduct R&D to improve the green degree of products. Many large enterprises, such as Haier, P&G, and Siemens, have insisted on environmental protection and sustainable development as their brand orientation and invest much money in R&D and innovation every year [5]. Furthermore, sales platforms, as powerful leaders, can effectively influence the green performance of upstream companies by providing special advertising and transport channels. For example, as one of the largest sales platforms in China, JD provides a convenient and efficient channel for green product circulation to promote the rapid growth of green brands on its platform. In the first half of 2017, the amount of green brand consumption on the JD platform increased by 86%, and the contribution rate to platform sales reached 14% [3].The existence of digital platforms expands the space for consumers to choose products. Various products of the same type, green and nongreen products such as energy-saving refrigerators and common refrigerators, are listed on the same Internet page for consumers to choose. By providing advertising for products, the platform improves product popularity and expands demand, so as to obtain greater commissions. Then, how should a platform determine its advertising strategies? Advertising for green products can effectively improve the R&D enthusiasm of green manufacturers, promote green products, and improve product environmental performance; and the platform can also obtain greater commissions from green manufacturers. Generally, a platform is more willing to provide advertising for products with a high green degree [6]. However, due to the substitutability of products, this would reduce the sales of similar nongreen products, resulting in less commissions from nongreen manufacturers. In addition to green advertising, a platform may advertise all products of the same kind. For example, during the special sales on holidays on Taobao, similar products from different manufacturers are displayed together, and the platform advertises for all brands, including green and nongreen ones. In fact, the advertising strategy of a platform should be related to the type of consumer market. Whether the market is sensitive to environmental performance, advertising effects and the substitutability of two types of products will affect the final advertising decision of a platform. Therefore, it is of great significance to study how a platform customizes advertising strategies for green products and similar nongreen products and how these strategies affect market demand and environmental performance.The objectives of this study inquire about the following questions:(1)
How can a platform choose an advertising strategy in a competitive market of green and nongreen products? Does it only advertise for green products or for both types of products? In addition, does it implement a joint advertising plan with a manufacturer?(2)
When a platform chooses the advertising strategy, what are the optimal prices of green and nongreen products in the price competition marketing systems? What is the optimal R&D effort for green manufacturer?(3)
Technology R&D is long-term work, and the green degree of products depends on the accumulation of R&D experience. Therefore, how does the green degree in turn affect the advertising strategy of the platform?In order to investigate the above problems, we study a platform-led Stackelberg differential game over an infinite planning period considering an industry with two manufacturers competing on a common platform market. One manufacturer produces green products, while the other produces similar nongreen products. The green manufacturer invests in R&D to improve the green degree of products, and the nongreen manufacturer does not invest in this R&D. The platform charges commissions according to sales and adopts an advertising strategy to promote products to consumers. We consider that the advertising strategies in the platform market include three modes: (1) the platform supports all advertising expenses for both manufacturers (PB). (2) The platform only supports green advertising expenses (PG). (3) The platform and green manufacturer implement a joint advertising plan without supporting advertising for nongreen products (PJ).By using optimal control theory, we give the feedback equilibrium decisions of players with different advertising strategies. The results reveal that the green degree of the products shows a monotonic trend over time and finally tends to be a stable value, and the equilibrium prices, advertising level, and R&D effort increase as the green degree increases. From an economic perspective, for the platform and green manufacturer, if two types of products have weak substitutability, and market demand is sensitive to the green degree, a joint green advertising plan is the best choice. Otherwise, it is more suitable for the platform to advertise all products. For the nongreen manufacturer, in most cases, advertising for all products is the best choice. However, in some specific cases, a joint green advertising plan would bring more benefits to nongreen manufacturer. Additionally, although a joint green advertising plan may not maximize the profits of all players, from environmental perspective, it would make the alliance achieve the best environmental performance.The remainder of this paper is organized as follows. Section2 reviews the related research. Section 3 provides our problem characteristics and notations, and the three models with differential advertising strategies are developed and analyzed in Section 4. Section 5 systematically compares and discusses the results of the models. Then, several numerical examples are provided to support the results in Section 6. Finally, we conclude and offer directions for future research and propose directions for future research.


## 2. Literature Review

In recent years, with the increasing attention to environmental issues, many literature have studied the operation of green market and green supply chain [6–8]. There are three streams of research closely related to this study: pricing competition in supply chain, green technology innovation, and platform-based strategic alliance. We review these related research and highlight the differences in our research.The pricing strategy of green and nongreen products is an important link in the decision-making of supply chain. It is an important factor affecting the market demand of products. In green supply chain management, many literatures have studied pricing strategies. For example, Zang et al. [9] focused on the impact of consumer environmental awareness on order quantities and channel coordination, in which the manufacturer produces the green and nongreen products. Zhu and He [10] investigated the green product design issues in supply chains under competition. They analyzed how supply chains’ decisions on the greenness of products are affected by factors such as supply chain structures, the green product types, and the types of competition. Hong et al. [11] focused on pricing competition of green and nongreen products in a green supply chain considering emission constraints and service time. Jamali and Rasti-Barzoki [12] investigated the pricing and determination of the degree of greenness of a product in competition with a nongreen product under two dual-channel supply chains including retail and Internet channels. Sana [13] studied a newsvendor inventory model in light of green product marketing of corporate social responsible firms, where a price contest existed between green and nongreen producer.Technology innovation can help form a benign market environment and promote social development, and technological innovation in green economy is more conducive to the improvement of eco-environmental performance. Scholars have studied the green technology R&D strategies of enterprises under different backgrounds (see [14–16]). Because technology innovation usually takes a long time, some studies use dynamic models to analyze related problems. As for the dynamic product innovation, to our knowledge, the work of Lambertini and Mantovani [17] was the first attempt, which built up a dynamic control model considering the monopolist investing both in process and in product innovation. Yan [18] adopted a system dynamics methodology to study the dynamic price competition and product innovation strategies of the enterprise. In recent studies, as an extension and continuation of Lambertini et al. [19], Li and Ni [20] investigated the dynamic control problem of product and process innovation in a monopoly enterprise under reference quality. Wang et al. [21] used a Stackelberg game structure to investigate the optimal R&D portfolio of a monopolist investment in product and process innovations. The research is conducted using a dynamic game with knowledge accumulation. In these studies, most of them studied the effect of R&D on product quality improvement or cost reduction, and only a few considered the green performance of products in a dynamic setting.Platform-based strategic alliance has attracted much attention recently. In fact, platforms and manufactures constitute a special supply chain, while manufacturers produce goods and sell them through platforms, and platforms provide services and advertising [3]. As the leaders, the platforms formulate advertising strategies to interfere with the manufacturer’s production and sales strategies. In order to discuss how platforms promote and maintain the values of its participants (manufacturers), many scholars have done a lot of research [22–26]. Despite many studies just mentioned above, a few consider green advertising in platform-based strategic alliance. Du et al. [3] and Zhang et al. [25] are exceptions; they studied green advertising in platform-led supply alliance. But different from the dynamic model in this research, they analyze the problems from a static point of view.The new contributions of this research are summarized as follows. First, we study the price competition between the green and nongreen products dominated by a platform, in which the platform can choose three advertising strategies. Second, we describe the dynamic trajectory of products’ green degree, which is determined by the accumulation of the R&D experience of green manufacturer over a period of time. Third, consumers’ awareness of environmental performance affects market demand, which means that the demand function depends on the product price, green degree, and advertising level. Compared with the previous literature, this research provides a new contribution to study the pricing competition between green and nongreen products in a platform-led supply chain by combining the above issues in one model.


## 3. Problem Characteristics and Notation

Suppose that there are two manufacturers competing in a common platform market, producing the similar products with different environmental performance over an infinite planning period. Manufacturer 1 produces green products and determines the green degree of products through technical R&D. The other manufacturer produces nongreen products without R&D. Both manufacturers sell the products directly to customers on the platform, and the platform charges a commission fee (denoted byρ) for each sale. In our research, ρis an exogenous variable. In this system, the platform is the leader, which decides advertising investment for two types of products, and each manufacturer decides its sale price and R&D effort separately.Letukt andpkt be manufacturer k(k = 1, 2)’s advertising level and sale price at time t, respectively, and let yt be products’ green degree produced by green manufacturer (manufacturer 1). Therefore, the demands of the products of manufacturer k(k = 1, 2) are as follows:(1)D1t=a−b1p1t+b2p2t+εyt+cu1t,D2t=a−b1p2t+b2p1t+cu2t,where a is a constant, which indicates the basic market demand of the products. b1 is self-price elasticity of demand, and b2 is cross-price elasticity of demand (substitutability), which means the demand shift between two manufacturers with respect to the price, whereas b1>b2 indicates that one manufacturer’s own price effect is greater than the cross-price effect. ε and c are the expansion effectiveness coefficients of green degree and advertising level to the market demand.In order to improve the green degree of products, green manufacturer invests in green technology R&D. R&D experience accumulates to the stock, which is positively related to the green degree. The dynamics of green degreeyt are governed by the following differential equation:(2)dydt=It−σyt,y0=y0,where It is R&D effort at time t and σ>0 is the rate of depreciation of green technology equipment. Consistent with the setting of many literature, we consider the following quadratic function for the cost of investment in R&D: α/2I2t, where α>0 denotes the coefficient of the marginal cost of investment in R&D. Different from the lag of R&D experience accumulation, the effect of advertisement on product’s goodwill is direct and rapid. Let β/2uk2t denote the platform’s advertising investment on behalf of products in manufacturer k (k = 1, 2), while ukt is manufacturer k’s advertising level. For convenience, the unit fixed production cost is set to zero.


## 4. Analytical Models

As shown in the introduction, we compare three models, in which the platform implemented the following advertising strategies: PB, PG, and PJ. In these models, the players use the feedback information structure to conduct a Stackelberg game (manufacturers and platform) and a noncooperative game (two manufacturers) and give the state-dependent prices, R&D investment, and advertisement. By comparing the strategies of these models, we aim to deeply analyze the impact of the platform advertising strategy on the decisions and profits of players.


### 4.1. Model 1: Platform Supports Both Manufactures’ Advertising Expenses (PB)

In this model, the platform promotes the products of two manufactures. As the leader, the platform decides advertising investment and charges two manufacturers’ commission fees. According to the advertising level determined by the platform, two manufacturers determine sale prices, and the green manufacturer determines R&D effort. We use superscriptB or Bk (k = 1,2) to denote the platform that supports all advertising expenses. Assuming that all players are profit maximizers, their optimization problems read as follows:(3)manufacturer1:maxpB1>0,IB>0VB1=∫0∞e−rt1−ρpB1a−b1pB1+b2pB2+εyB+cuB1−α2IB2dt,manufacturer2:maxpB2>0VB2=∫0∞e−rt1−ρpB2a−b1pB2+b2pB1+cuB2dt,platform:maxuB1,uB2VBP=∫0∞e−rtρpB1DB1+pB2DB2−β2uB12+uB22dt,where r is the common discount rate.As usual in autonomous differential games played over an infinite time horizon, we consider that players’ strategies are stationary feedback (see, for example, [27]), which means that pricing, R&D, and advertising strategies, as well as value functions, are time-independent and only depend on the current level of the state variable yB. The next theorem characterizes the Stackelberg equilibrium solution.Theorem 1.
LetVBkyB and VBPyBdenote the manufacturer k (k = 1, 2)’s and the platform’s value functions:(i)
The following expressions satisfy the Hamilton–Jacobi–Bellman (HJB) equations associated with the platform’s and manufacturer’s problems:(4)VB1yB=A12yB2+B1yB+C1,VB2yB=A22yB2+B2yB+C2,VBPyB=A32yB2+B3yB+C3.(ii)
When platform supports all advertising expenses for two manufacturers, the feedback equilibrium solutions are given by(5)uB1∗yB=cb1ρ2a+εyB2b1−b22β−2c2b1ρ+εyB2b1+b22β−2c2b1ρ,uB2∗yB=cb1ρ2a+εyB2b1−b22β−2c2b1ρ−εyB2b1+b22β−2c2b1ρ,(6)pB1∗yB=2b1a+ab2+2b1εyB+2cb1uB1∗+cb2uB2∗4b12−b22,pB2∗yB=2b1a+ab2+b2εyB+2cb1uB2∗+cb2uB1∗4b12−b22,(7)IB∗yB=A1yB+B1α,where Ak,Bk,Ck,k=1,2,3 are shown in Appendix.Proof.
See “Appendix.”
Obviously, the equilibrium price and advertising level of green products are higher than those of nongreen products. This is consistent with the reality. The results also show that, as an important indicator of green products, the green degree, together with advertising effectiveness, greenness effectiveness, platform commission, and other parameters, affects all decisions of players. Through sensitivity analysis, we can further understand these parameters’ impacts on the decision variables.Proposition 1.
Two manufacturers’ equilibrium pricepB1∗,pB2∗, advertising level uB1∗,uB2∗ and green manufacturer’s R&D effort IB∗ increase with the current green degree of the productsyB, green degree effectiveness parameter ε, advertising effectiveness parameter c, and platform commission ρ.Proof.
See “Appendix.”Proposition 2.
LetΔpB∗=pB1∗−pB2∗, which reflects the difference of manufacturers’ pricing decisions, and ΔuB∗=uB1∗−uB2∗, which reflects the difference of platform’s advertising level on two types of products. ΔpB∗ and ΔuB∗ increase with yB,ε,ρ and c and decrease with b2.Proof.
See “Appendix.”
The propositions show that products with a high green degree have a high selling price and large advertising investment on the platform. In addition, if the selling price of green products in the market is high, the selling price of similar nongreen products is also high. This is determined by the spillover effect of price. Therefore, the manufacturer can choose different pricing and R&D effort decisions based on the current green degree and consumers’ awareness of environmental performance. Specifically, in a market with a high green preference, a green manufacturer will improve R&D efforts to obtain a higher green degree, so as to drive an increase in sales prices.
In green market, as the green degree and consumers’ green preference increase, the gaps in the price and advertising level between two types of products increase, resulting in an increase in the profit gap between two manufacturers. Therefore, for the nongreen manufacturer, although the price and advertising level of its products have improved in the green market, its disadvantage is more obvious compared with the green manufacturer.
Taking (7) into dynamic equation (2), the optimal trajectory of the green degree is(8)yBt=yB,∞+y0−yB,∞eA1/α−σt−t0,whereyB,∞=B1σα−A1.
The initial green degree isy0, and it shows a monotonic trend over time and finally stabilizes at yB,∞. Taking (8) into (5)–(7), the optimal strategy trajectories of all players in the whole planning period can be obtained.


### 4.2. Model 2: Platform Supports Green Advertising Expenses (PG)

In this model, the platform focuses its advertising effort to invest in green brand, so there isu2=0. Here, we use superscript G or Gk (k = 1, 2) to denote the platform only supports green advertising. The optimization problems of two manufacturers and platform can be expressed as(9)manufacturer1:maxpG1>0,IG>0VG1=∫0∞e−rt1−ρpG1a−b1pG1+b2pG2+εyG+cuG1−α2IG2dt,manufacturer2:maxpG2>0VG2=∫0∞e−rt1−ρpG2a−b1pG2+b2pG1dt,platform:maxuG1>0VGP=∫0∞e−rtρpG1DG1+pG2DG2−β2uG12dt.Theorem 2.
LetVGkyG and VGPyG denote the manufacturer k (k = 1, 2)’s and the platform’s value functions:(i)
The following expressions satisfy the HJB equations associated with the platform’s and manufacturer’s problems:(10)VG1yG=A42yG2+B4yG+C4,VG2yG=A52yG2+B5yG+C5,VGPyG=A62yG2+B6yG+C6.(ii)
When the platform supports green advertising expenses, the feedback equilibrium solutions are given by(11)uG1∗yG=2b1ρca2b1+b22+4b12+b22εyGβ4b12−b222−2b1ρc24b12+b22,(12)pG1∗yG=2b1a+ab2+2b1εyG+2b1cuG1∗4b12−b22,pG2∗yG=2b1a+ab2+b2εyG+b2cuG1∗4b12−b22,(13)IG∗yG=A4yG+B4α,where Ak,Bk,Ck,k=4,5,6 are shown in Appendix.Proof.
See “Appendix.”
The influence of parameters on the decision-making of players is similar to that of Model 1. We will not repeat it here.
Taking (13) into dynamic equation (2), the optimal trajectory of green degree is(14)yGt=yG,∞+y0−yG,∞eA1/α−σt−t0,whereyG,∞=B4σα−A4.


### 4.3. Model 3: Platform Supports Joint Advertising with the Green Manufacturer (PJ)

In order to attract more high-quality manufactures to enter the platform and enhance user stickiness, the platform launches a joint advertising marketing plan, and green manufacturer chooses to cooperate with the platform, that is, bear part of the advertising costs. For example, in March 2018, Nike launched Air Max globally on Tmall and put outdoor posters on the streets and subways of Shanghai. During this period, Tmall customized promotional videos and offline flash stores for Nike, sharing a certain advertising expenses of the brand.Denoteμ0<μ<1 as advertising cost sharing rate. The other assumptions are the same as those in Model 2, which means that the platform would not support advertising for nongreen products. Superscripts Jk (k = 1, 2) and J are used to denote joint advertising investment. We give the optimization problems of two manufacturers and platform:(15)manufacturer1:maxpJ1>0,IJ>0VJ1=∫0∞e−rt1−ρpJ1a−b1pJ1+b2pJ2+εyJ+cuJ1−α2IJ2−μβ2uJ12dt,manufacturer2:maxpJ2>0VJ2=∫0∞e−rt1−ρpJ2a−b1pJ2+b2pJ1dt,platform:maxuJ1>0VJP=∫0∞e−rtρpJ1DJ1+pJ2DJ2−1−μβ2uJ12dt.Theorem 3 characterizes the feedback equilibrium strategies of two manufacturers and platform.Theorem 3.
LetVJkyJ and VJPyJ denote the manufacturer k (k = 1, 2)’s and the platform’s value functions:(i)
The following expressions satisfy the HJB equations associated with the platform’s and manufacturer’s problems:(16)VJ1yJ=A72yJ2+B7yJ+C7,VJ2yJ=A82yJ2+B8yJ+C8,VJPyJ=A92yJ2+B9yJ+C9.(ii)
When the green manufacturer and platform cooperate in advertising, the feedback-Nash equilibrium solutions are given by(17)uJ1∗yJ=2b1ρca2b1+b22+4b12+b22εyJ1−μβ4b12−b222−2b1ρc24b12+b22,(18)pJ1∗yJ=2b1a+ab2+2b1εyJ+2b1cuJ1∗4b12−b22,pJ2∗yJ=2b1a+ab2+b2εyJ+b2cuJ1∗4b12−b22,(19)IJ∗yJ=A7yJ+B7α,where Ak,Bk,Ck,k=7,8,9 are shown in Appendix.Proof.
See “Appendix.”
Taking (19) into dynamic equation (2), the optimal trajectory of green degree is(20)yJt=yJ,∞+y0−yJ,∞eA7/α−σt−t0,whereyJ,∞=B7σα−A7.
Next, we analyze the impact of advertising cost sharing rate on strategies.Proposition 3.
For a given green degree, the prices of two types of products,pJ1∗,pJ2∗, and green products’ advertising level, uJ1∗, increase with advertising cost sharing rate μ.Proof.
Taking partial derivatives ofpJ1∗,pJ2∗ and uJ1∗, the result is obtained.
Proposition3 indicates that if a green manufacturer shares more advertising costs for the platform, it will promote the platform to increase advertising investment, so as to increase the prices of the two types of products. However, because the price increase is usually accompanied by a rise in the green degree, if the manufacturer’s R&D investment is not followed up, consumers may not be willing to spend more money on products. Therefore, it is important to choose the appropriate cost sharing ratio for the platform. While the platform increases advertising investment, the improvement of R&D effort should also be followed up to ensure that both the platform and manufacturers can obtain greater benefits.


## 4.1. Model 1: Platform Supports Both Manufactures’ Advertising Expenses (PB)

In this model, the platform promotes the products of two manufactures. As the leader, the platform decides advertising investment and charges two manufacturers’ commission fees. According to the advertising level determined by the platform, two manufacturers determine sale prices, and the green manufacturer determines R&D effort. We use superscriptB or Bk (k = 1,2) to denote the platform that supports all advertising expenses. Assuming that all players are profit maximizers, their optimization problems read as follows:(3)manufacturer1:maxpB1>0,IB>0VB1=∫0∞e−rt1−ρpB1a−b1pB1+b2pB2+εyB+cuB1−α2IB2dt,manufacturer2:maxpB2>0VB2=∫0∞e−rt1−ρpB2a−b1pB2+b2pB1+cuB2dt,platform:maxuB1,uB2VBP=∫0∞e−rtρpB1DB1+pB2DB2−β2uB12+uB22dt,where r is the common discount rate.As usual in autonomous differential games played over an infinite time horizon, we consider that players’ strategies are stationary feedback (see, for example, [27]), which means that pricing, R&D, and advertising strategies, as well as value functions, are time-independent and only depend on the current level of the state variable yB. The next theorem characterizes the Stackelberg equilibrium solution.Theorem 1.
LetVBkyB and VBPyBdenote the manufacturer k (k = 1, 2)’s and the platform’s value functions:(i)
The following expressions satisfy the Hamilton–Jacobi–Bellman (HJB) equations associated with the platform’s and manufacturer’s problems:(4)VB1yB=A12yB2+B1yB+C1,VB2yB=A22yB2+B2yB+C2,VBPyB=A32yB2+B3yB+C3.(ii)
When platform supports all advertising expenses for two manufacturers, the feedback equilibrium solutions are given by(5)uB1∗yB=cb1ρ2a+εyB2b1−b22β−2c2b1ρ+εyB2b1+b22β−2c2b1ρ,uB2∗yB=cb1ρ2a+εyB2b1−b22β−2c2b1ρ−εyB2b1+b22β−2c2b1ρ,(6)pB1∗yB=2b1a+ab2+2b1εyB+2cb1uB1∗+cb2uB2∗4b12−b22,pB2∗yB=2b1a+ab2+b2εyB+2cb1uB2∗+cb2uB1∗4b12−b22,(7)IB∗yB=A1yB+B1α,where Ak,Bk,Ck,k=1,2,3 are shown in Appendix.Proof.
See “Appendix.”
Obviously, the equilibrium price and advertising level of green products are higher than those of nongreen products. This is consistent with the reality. The results also show that, as an important indicator of green products, the green degree, together with advertising effectiveness, greenness effectiveness, platform commission, and other parameters, affects all decisions of players. Through sensitivity analysis, we can further understand these parameters’ impacts on the decision variables.Proposition 1.
Two manufacturers’ equilibrium pricepB1∗,pB2∗, advertising level uB1∗,uB2∗ and green manufacturer’s R&D effort IB∗ increase with the current green degree of the productsyB, green degree effectiveness parameter ε, advertising effectiveness parameter c, and platform commission ρ.Proof.
See “Appendix.”Proposition 2.
LetΔpB∗=pB1∗−pB2∗, which reflects the difference of manufacturers’ pricing decisions, and ΔuB∗=uB1∗−uB2∗, which reflects the difference of platform’s advertising level on two types of products. ΔpB∗ and ΔuB∗ increase with yB,ε,ρ and c and decrease with b2.Proof.
See “Appendix.”
The propositions show that products with a high green degree have a high selling price and large advertising investment on the platform. In addition, if the selling price of green products in the market is high, the selling price of similar nongreen products is also high. This is determined by the spillover effect of price. Therefore, the manufacturer can choose different pricing and R&D effort decisions based on the current green degree and consumers’ awareness of environmental performance. Specifically, in a market with a high green preference, a green manufacturer will improve R&D efforts to obtain a higher green degree, so as to drive an increase in sales prices.
In green market, as the green degree and consumers’ green preference increase, the gaps in the price and advertising level between two types of products increase, resulting in an increase in the profit gap between two manufacturers. Therefore, for the nongreen manufacturer, although the price and advertising level of its products have improved in the green market, its disadvantage is more obvious compared with the green manufacturer.
Taking (7) into dynamic equation (2), the optimal trajectory of the green degree is(8)yBt=yB,∞+y0−yB,∞eA1/α−σt−t0,whereyB,∞=B1σα−A1.
The initial green degree isy0, and it shows a monotonic trend over time and finally stabilizes at yB,∞. Taking (8) into (5)–(7), the optimal strategy trajectories of all players in the whole planning period can be obtained.


## 4.2. Model 2: Platform Supports Green Advertising Expenses (PG)

In this model, the platform focuses its advertising effort to invest in green brand, so there isu2=0. Here, we use superscript G or Gk (k = 1, 2) to denote the platform only supports green advertising. The optimization problems of two manufacturers and platform can be expressed as(9)manufacturer1:maxpG1>0,IG>0VG1=∫0∞e−rt1−ρpG1a−b1pG1+b2pG2+εyG+cuG1−α2IG2dt,manufacturer2:maxpG2>0VG2=∫0∞e−rt1−ρpG2a−b1pG2+b2pG1dt,platform:maxuG1>0VGP=∫0∞e−rtρpG1DG1+pG2DG2−β2uG12dt.Theorem 2.
LetVGkyG and VGPyG denote the manufacturer k (k = 1, 2)’s and the platform’s value functions:(i)
The following expressions satisfy the HJB equations associated with the platform’s and manufacturer’s problems:(10)VG1yG=A42yG2+B4yG+C4,VG2yG=A52yG2+B5yG+C5,VGPyG=A62yG2+B6yG+C6.(ii)
When the platform supports green advertising expenses, the feedback equilibrium solutions are given by(11)uG1∗yG=2b1ρca2b1+b22+4b12+b22εyGβ4b12−b222−2b1ρc24b12+b22,(12)pG1∗yG=2b1a+ab2+2b1εyG+2b1cuG1∗4b12−b22,pG2∗yG=2b1a+ab2+b2εyG+b2cuG1∗4b12−b22,(13)IG∗yG=A4yG+B4α,where Ak,Bk,Ck,k=4,5,6 are shown in Appendix.Proof.
See “Appendix.”
The influence of parameters on the decision-making of players is similar to that of Model 1. We will not repeat it here.
Taking (13) into dynamic equation (2), the optimal trajectory of green degree is(14)yGt=yG,∞+y0−yG,∞eA1/α−σt−t0,whereyG,∞=B4σα−A4.


## 4.3. Model 3: Platform Supports Joint Advertising with the Green Manufacturer (PJ)

In order to attract more high-quality manufactures to enter the platform and enhance user stickiness, the platform launches a joint advertising marketing plan, and green manufacturer chooses to cooperate with the platform, that is, bear part of the advertising costs. For example, in March 2018, Nike launched Air Max globally on Tmall and put outdoor posters on the streets and subways of Shanghai. During this period, Tmall customized promotional videos and offline flash stores for Nike, sharing a certain advertising expenses of the brand.Denoteμ0<μ<1 as advertising cost sharing rate. The other assumptions are the same as those in Model 2, which means that the platform would not support advertising for nongreen products. Superscripts Jk (k = 1, 2) and J are used to denote joint advertising investment. We give the optimization problems of two manufacturers and platform:(15)manufacturer1:maxpJ1>0,IJ>0VJ1=∫0∞e−rt1−ρpJ1a−b1pJ1+b2pJ2+εyJ+cuJ1−α2IJ2−μβ2uJ12dt,manufacturer2:maxpJ2>0VJ2=∫0∞e−rt1−ρpJ2a−b1pJ2+b2pJ1dt,platform:maxuJ1>0VJP=∫0∞e−rtρpJ1DJ1+pJ2DJ2−1−μβ2uJ12dt.Theorem 3 characterizes the feedback equilibrium strategies of two manufacturers and platform.Theorem 3.
LetVJkyJ and VJPyJ denote the manufacturer k (k = 1, 2)’s and the platform’s value functions:(i)
The following expressions satisfy the HJB equations associated with the platform’s and manufacturer’s problems:(16)VJ1yJ=A72yJ2+B7yJ+C7,VJ2yJ=A82yJ2+B8yJ+C8,VJPyJ=A92yJ2+B9yJ+C9.(ii)
When the green manufacturer and platform cooperate in advertising, the feedback-Nash equilibrium solutions are given by(17)uJ1∗yJ=2b1ρca2b1+b22+4b12+b22εyJ1−μβ4b12−b222−2b1ρc24b12+b22,(18)pJ1∗yJ=2b1a+ab2+2b1εyJ+2b1cuJ1∗4b12−b22,pJ2∗yJ=2b1a+ab2+b2εyJ+b2cuJ1∗4b12−b22,(19)IJ∗yJ=A7yJ+B7α,where Ak,Bk,Ck,k=7,8,9 are shown in Appendix.Proof.
See “Appendix.”
Taking (19) into dynamic equation (2), the optimal trajectory of green degree is(20)yJt=yJ,∞+y0−yJ,∞eA7/α−σt−t0,whereyJ,∞=B7σα−A7.
Next, we analyze the impact of advertising cost sharing rate on strategies.Proposition 3.
For a given green degree, the prices of two types of products,pJ1∗,pJ2∗, and green products’ advertising level, uJ1∗, increase with advertising cost sharing rate μ.Proof.
Taking partial derivatives ofpJ1∗,pJ2∗ and uJ1∗, the result is obtained.
Proposition3 indicates that if a green manufacturer shares more advertising costs for the platform, it will promote the platform to increase advertising investment, so as to increase the prices of the two types of products. However, because the price increase is usually accompanied by a rise in the green degree, if the manufacturer’s R&D investment is not followed up, consumers may not be willing to spend more money on products. Therefore, it is important to choose the appropriate cost sharing ratio for the platform. While the platform increases advertising investment, the improvement of R&D effort should also be followed up to ensure that both the platform and manufacturers can obtain greater benefits.


## 5. Analysis and Discussion

Based on the above results, we further compare the decisions among the models, including greenness degree, advertising levels, and the prices of two types of products. The following propositions are provided to show the comparisons.Proposition 4.
For a given green degreey, the optimal advertising level and prices in PB and PG models satisfied the following:(1)
A thresholdy1>0 exists, where if y>y1, there is uB1∗>uG1∗; if y≤y1, there is uB1∗≤uG1∗, where the expression of y1 can be seen in Appendix(2)
pB1∗≥pG1∗ andpB2∗≥pG2∗Proof.
See “Appendix.”
Because of the complexity of the forms of (8) and (14), it is difficult to compare the steady-state green degree in the PB model and in the PG model. However, Proposition 4 shows that if the green degree is given, the advertising levels and prices in the two models can be compared. Compared with advertising only for green products (PG), the platform’s choice to advertise for all products (PB) can increase the prices of all products. However, for green products, the advertising level may not increase. In fact, we know that the green degree represents the degree of energy saving of green products, and a higher green degree indicates that the products are more competitive than nongreen products. Therefore, compared with nongreen products, products with a higher green degree will obtain more advertising resources and attract more consumers. If the green degree of the products is low, green products have little advantage over nongreen products, and the platform may not pay special attention to green products when advertising for all products. In this way, manufacturers make their own decisions by observing the advertising strategy of the platform: if the platform only supports green advertising, both manufacturers use a low-price strategy; and if the platform supports both manufacturers’ advertising, they use a high-price strategy.
Next we compare the manufacturer’s and platform’s steady-state strategies between the PG and PJ models and analyze the impact of joint advertising plan on the green degree, advertising level, and price. Taking the steady-state green degreeyJ,∞,yG,∞ into (11)–(13), (17)–(19), the steady-state strategies in the PG and PJ models are given. Mark them with ∞ in the lower right corner. The following proposition is provided to show the comparisons.Proposition 5.
The steady-state green degree, prices, advertising level, and R&D effort in PG and PJ models satisfyyJ,∞>yG,∞,uJ1,∞∗>uG1,∞∗,pJ1,∞∗>pG1,∞∗,pJ2,∞∗>pG2,∞∗,IJ,∞∗>IG,∞∗.Proof.
See “Appendix.”
Proposition5 reveals that if a green manufacturer and platform implement the joint advertising plan (PJ), all players can achieve strategy improvement compared to the situation, where no joint advertising plan occurs (PG). This is because the joint advertising plan requires green manufacturer to share advertising expenses for platform, so as to promote platform to increase the advertising investment and improve the advertising level of green products. This leads to an increase in the market demands and prices of all products. Therefore, the green manufacturer’s profits increase, and it has more funds to invest in technology R&D, which results in the improvement of products’ green degree, so that the economic and environmental performance of the alliance are improved. In this way, if the green manufacturer intends to participate in the platform joint advertising plan, it will increase its product sales price and R&D efforts and improve the green degree of products, so as to follow up on the improvement of green products’ advertising level.
To summarize, we characterize the feedback equilibrium in each model and compare some of them. Due to the complexity of the form, it is difficult to compare the profits of the players in each model; therefore, we will use numerical methods to study the equilibrium profits in the next section.


## 6. Numerical Analysis

To obtain the equilibrium solution and compare the profits of all players in three models, the following parameter values will be substituted into the model:(21)a=100,b1=2,b2=1,c=0.5,ε=0.4,ρ=0.2,α=4,β=1,σ=0.1,r=0.05,y0=0.Taking the above setting as the base, we vary related parameters within a range of ±25% to ±50% to check whether the qualitative results on the strategies and trajectories are robust to model calibration. (Beyond this range, the optimal solution may not exist, such that the advertising level is less than 0.)DefineΔVBGP∗=VBP,∞∗−VGP,∞∗,ΔVBG1∗=VB1,∞∗−VG1,∞∗ and ΔVBG2∗=VB2,∞∗−VG2,∞∗, where VBP,∞∗ and VGP,∞∗ denote platform’s profits at the steady state in PB and PG models, and VB1,∞∗,VG1,∞∗,VB2,∞∗ and VG2,∞∗ denote manufacturer 1 (green manufacturer) and manufacturer 2 (nongreen manufacturer) profits at the steady state in PB and PG models. Similarly, we can also define the profits difference of platform, manufacturer 1, and manufacturer 2 at the steady state in PJ model and PG model or in PB model and PJ model: ΔVGJP∗=VGP,∞∗−VJP,∞∗,ΔVGJ1∗=VG1,∞∗−VJ1,∞∗ and ΔVGJ2∗=VG2,∞∗−VJ2,∞∗; ΔVBJP∗=VBP,∞∗−VJP,∞∗,ΔVBJ1∗=VB1,∞∗−VJ1,∞∗ and ΔVBJ2∗=VB2,∞∗−VJ2,∞∗. In the table below, we judge the sign of the above profits difference for different parameter changes and determine in which scenario the platform and manufacturer’s profits are higher (+means that the result is greater than 0,−means that it is less than 0).Table1 shows that the signs of the differences of profits in PB and PG models, and those in PG and PJ models, remain the same and are independent of the calibration that is used in the set of interior solutions. That means no matter how the parameters change, there is always ΔVBGP∗>0, ΔVBG1∗>0,ΔVBG2∗>0 and ΔVGJP∗<0,ΔVGJ1∗<0,ΔVGJ2∗<0.Table 1
Comparison of profits in PB, PG, and PJ models.
ParametersΔVBGP∗ΔVBG1∗ΔVBG2∗ΔVGJP∗ΔVGJ1∗ΔVGJ2∗ΔVBJP∗ΔVBJ1∗ΔVBJ2∗b1+50%+++−−−−−++25%+++−−−−−+2+++−−−−−+−15%+++−−−−−+−25%+++−−−−−−b2+50%+++−−−++++25%+++−−−−−+1+++−−−−−+−25%+++−−−−−+−50%+++−−−−−+c+50%+++−−−−−−+25%+++−−−−−+1+++−−−−−+−25%+++−−−−−+−50%+++−−−−−+ε+25%+++−−−−−−+15%+++−−−−−+0.4+++−−−−−+−25%+++−−−+−+−50%+++−−−+++ρ+50%+++−−−−−++25%+++−−−−−+0.2+++−−−−−+−25%+++−−−−−+−50%+++−−−−−+α+50%+++−−−−−++25%+++−−−−−+4+++−−−−−+−15%+++−−−−−+−25%+++−−−−−+β+50%+++−−−−−++25%+++−−−−−+3+++−−−−−+−25%+++−−−−−+−50%+++−−−−−+μ+25%+++−−−−−++15%+++−−−−−+0.2+++−−−−−+−25%+++−−−+++−50%+++−−−+++Accordingly, we can make the following conjecture on players’ profits.Conjecture 1.
If the platform supports both manufactures’ advertising, all players can achieve profit improvement compared to the case where only green manufacturer’s advertising occurs.Conjecture 2.
All players can benefit more from advertising cooperation than from the platform’s full support for green advertising.The results of Conjectures1 and 2 indicate that, in three models, the profits in PG model are lowest. That is, if the platform only supports green advertising and does not cooperate with green manufacturer in advertising, all players will achieve lowest profits.However, if we compare the profits of the players in PG and PJ models, we will find that the profit trends of the three parties are different. As shown in Table1, although ΔVBJP∗<0,ΔVBJ1∗<0 and ΔVBJ2∗>0 in most cases, ΔVBJP∗>0,ΔVBJ1∗>0 and ΔVBJ2∗<0 can be found in a few cases. This shows that in which model players’ profits are highest is uncertain, and it is affected by the values of some parameters. We can see the following conjecture for details.Conjecture 3.
From an economic perspective, (i) for the platform and green manufacturer, ifb2 is not too large, ε and μ are not too small, and cooperating in advertising is the best choice. Otherwise, it is more suitable for platform to advertise for all products. (ii) For nongreen manufacturer, in most cases, it will be more willing to let the platform advertise for it. Only in a few cases (b1 is too small or c and ε are too large), advertising cooperation between the platform and green manufacturer will bring more benefits to nongreen manufacturer.The result of Conjecture3 indicates that if two types of products have weak substitutability, and market demand is sensitive to the green degree, the platform will publish a joint green advertising plan, and the green manufacturer will participate in it. Otherwise, a joint advertising plan is not suitable, and the optimal strategy for the platform should be to advertise for all products without joint green advertising. Additionally, an advertising cost sharing proportion that is too low will also reduce the profits of green manufacturers and platforms. Therefore, we need to choose the appropriate proportion to ensure that advertising cooperation between the platform and manufacturer can continue. For the nongreen manufacturer, in most cases, it hopes that the platform can also provide advertising for its products. However, it is surprising that, in some special cases, the platform’s implementation of the green joint advertising plan is more beneficial to the nongreen manufacturer.Next, we consider the difference of stable state green degrees in models within the variation range of different parameters. DefineΔyBG=yB,∞−yG,∞,ΔyGJ=yG,∞−yJ,∞ and ΔyBJ=yB,∞−yJ,∞. Proposition 5 shows that no matter how the parameters change, there is always ΔyGJ<0. Then, how do the sign of other two differences (ΔyBG and ΔyBJ) change? In the table below, we judge it and determine which platform advertising strategy will lead to the highest green degree (+means that the result is greater than 0, − means that it is less than 0).Table2 shows that the signs of the differences of the green degree remain the same and are independent of the calibration; i.e., there is always ΔyBG>0, ΔyGJ<0,ΔyBJ<0. Then, we obtain the following conjecture.Table 2
Comparison of green degree in PB, PG, and PJ models.
ParametersΔyBGΔyGJΔyBJb1+50%+−−+25%+−−2+−−−15%+−−−25%+−−b2+50%+−−+25%+−−1+−−−25%+−−−50%+−−c+50%+−−+25%+−−1+−−−25%+−−−50%+−−ε+25%+−−+15%+−−0.4+−−−25%+−−−50%+−−ρ+50%+−−+25%+−−0.2+−−−25%+−−−50%+−−α+50%+−−+25%+−−4+−−−15%+−−−25%+−−β+50%+−−+25%+−−3+−−−25%+−−−50%+−−μ+25%+−−+15%+−−0.2+−−−25%+−−−50%+−−Conjecture 4.
The steady-state green degree of products with the PG strategy is lowest, and that with the PJ strategy is highest.The result of Conjecture4 indicates that although the implementation of the joint advertising plan may not be able to maximize the profits of all players, it can promote green manufacturer to conduct R&D and improve the green degree of products. Therefore, from environmental perspective, the PJ strategy would allow the alliance achieve the best environmental performance.Figure1 shows the change trends of green degrees in the entire planning period under the benchmark parameters when the platform applies three advertising strategies. The initial green degree is set to 0. The figure indicates that the green degree shows an upward trend over time and finally tends to a stable state. In the entire planning period, the green degree under the PJ strategy is always the highest, and that under the PG strategy is always the lowest.Figure 1
Green degree over time with three advertising strategies.


## 7. Concluding Remarks and Future Research

This study compares platform-led advertising strategies in three models, in which two manufacturers compete in a common platform market. The essential difference among these strategies in the three models lies in the allocation of platform advertising investment. In the PB model, the platform invests in advertising for all products, while in the PG model, only green products can obtain advertising. In the PJ model, the platform only provides advertising services for green products, and the manufacturer shares part of the advertising costs for the platform.The results reveal that the equilibrium price and advertising level of products increase as the current green degree increases, while the green degree shows a monotonic trend over time and finally tends to be a stable value.In three models, the green degree and the profits of all players with the PG strategy are lowest, while the green degree with the PJ strategy is highest. This means that the implementation of a joint green advertising plan can maximize the green manufacturer’s R&D enthusiasm and improve the R&D level. Compared with only supporting green advertising, manufacturers will adopt the strategy of a high price and high R&D investment when the platform supports both manufacturers’ advertising. Additionally, in a market with a high green preference, if two types of products have weak substitutability, the platform will publish a joint advertising plan. The green manufacturer participates in the plan and adopts the strategy of a high price and high R&D investment to improve the green degree of products. In a market with a low green preference, if two types of products have strong substitutability, a joint advertising plan is not suitable. The optimal strategy for the platform is to advertise for all products without joint green advertising. In this way, all players can obtain the most profits, but the green degree of the products may not reach the optimal level. To summarize, from an economic point of view, the platform will not advertise only for green products. It will choose to advertise for all products or cooperate with the green manufacturer in advertising. Although a joint advertising plan may not maximize the profits of all players, from environmental perspective, it would make the alliance achieve the best environmental performance.This study provides a new idea for platform green advertising and platform-based alliance management, which is of constructive and practical significance. However, this study has some limitations. In this paper, we only consider the mode in which enterprises sell goods through the platform and pay commissions to the platform; other sales modes have not been mentioned. For example, a platform can exist as a retailer that purchases products from manufacturers and then sells them to consumers. This mode is called the wholesale mode. Typical examples of wholesale modes are the Tmall supermarket and JD self-support. It is interesting to study the competition between green products and nongreen products under these two modes. In addition, in our model, the supply chain only involves one platform, and the model can be expanded to explore the problem of green advertising in multiplatform market sharing competition. These interesting topics can be the directions of our future research.



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*Source: 4873032-2021-10-06.xml*