The Impact of Cost Sharing on Green Technology Investment in Competing Supply Chains

Chenglin SHEN; Xinxin ZHANG

doi:10.21078/JSSI-2022-216-19

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Journal of Systems Science and Information ›› 2022, Vol. 10 ›› Issue (3) : 216-234. DOI: 10.21078/JSSI-2022-216-19

The Impact of Cost Sharing on Green Technology Investment in Competing Supply Chains

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Abstract

The investment in green technology in the process of product design and production is viewed as a powerful tool for sustainable development and carbon emission reduction. However, the substantial cost and pressure of competition weaken incentives for manufacturers to engage in green technology. In this paper, we consider two competitive manufacturer-retailer supply chains, where each manufacturer sells partially substitutable products through the exclusive retailer, study green technology investment selection by manufacturers, and examine the efficacy of retailer cost sharing scheme. Our analysis shows that a dominant equilibrium strategy for both manufacturers is to invest in green technologies, whether cost sharing is in place or not. Retailer sharing the cost of manufacturer green technology investment can avoid firms' preference confliction over the green technology investment and improve social welfare simultaneously when both the cost-sharing rate and the degree of product/channel competition are relatively low. We also find that green technology investment by manufacturers does not necessarily curb total carbon emission, and the cost sharing can either strengthen or weaken the carbon emission reduction of green technology investment.

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green technology investment / cost sharing / supply chain competition / game theory

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Chenglin SHEN , Xinxin ZHANG. The Impact of Cost Sharing on Green Technology Investment in Competing Supply Chains. Journal of Systems Science and Information, 2022, 10(3): 216-234 https://doi.org/10.21078/JSSI-2022-216-19

1 Introduction

In the past few decades, with the increasingly serious environmental problems, issues on carbon emission reduction and sustainable development have attracted wide attention. The investment of green technology in production process to decline carbon emissions has been regarded as a significant solution to sustainability issues^[1]. The pressure to cut down carbon emissions drives manufacturers to shift to green technologies in the process of product design and production. Take high-tech industry as an example, Apple has invested approximately 1.657 billion dollars in green technologies during 2016–2017, by which it avoided about 454, 200 metric tons of carbon emissions^[2]. Another driver for green investments comes from consumers with environmental consciousness. A global survey by Accenture shows that more than 80% of respondents consider product greenness when make purchasing decisions. Carbon Trust surveys, meanwhile, indicate that approximately 20% of consumers are willing to pay a premium for green products^[3]. Spurred by this market force, an increasing number of manufacturers around various industries make green technology investments in their production process to satisfy the demands of environmentally concerned consumers, gain competitiveness, and strengthen their reputations in terms of social responsibility. Well-known examples include H & M, a famous fast fashion apparel company reduced carbon emissions by investing green technology in production process^[4]; Coca Cola company adopted green technologies aiming to decline its emission one-fourth by 2020^[5]; and Lenovo declined carbon emissions by 35% due to the breakthrough of an innovative low temperature solder manufacturing process^[6].

However, the cost of investment in green technology is usually substantial, which is considered as a main barrier for green production by some scholars^[7]. Thus, manufacturers need an explicit trade-off between the pros and cons resulted from green investment when decide whether to invest in green technology. Particularly, such issues concerning green investment selection become much more complicated in the presence of supply chain competition. As we all know, the modern business competition is changing from firm competition to supply chain competition that is also called chain-to-chain competition^[8]. Take the household appliance industry as an example, a famous household appliance manufacturer Haier and the giant retailer Suning form a strategic alliance to promote energy-saving products¹, while another famous household appliance manufacturer Gree enters into an agreement and works closely with JD.COM to co-develop high quality exclusive custom household appliances². Clearly, there is competition between the two supply chains. When it comes to supply chain competition, a manufacturer's green technology investment will be further affected by the rival manufacturer's decisions, the horizontal competition, and even the downstream retailer's decision. In turn, investment made by a manufacturer will also affect its downstream partner and horizontal competitor. The above discussion leads to our first two research questions: Given these interactive impacts, is it always beneficial for the manufacturers to invest in green technologies in the presence of supply chain competition? And how does the equilibrium investment decision affect the downstream retailers, consumers and supply chain efficiency?

¹http://news.cntv.cn/20120526/115528.shtml.

²https://jd.zol.com.cn/723/7238533.html.

As two different decision-making entities, manufacturers and retailers usually have very different preferences for green technology investments. The resulting channel conflict has reduced overall supply chain efficiency greatly. Generally, manufacturers' green technology investment seems to promise the most potential for the retailers, but is a costly action for the manufacturers. Consequently, retailers usually have incentives to offer their manufacturers some incentive schemes, which can further encourage their manufacturers to invest in green technology. Cost sharing, as an effective channel coordination mechanism has been proved to promote products' green level and improve channel efficiency in one-manufacturer-one-retailer supply chain^[9-11]. However, the impact of cost sharing on manufacturers' green technology investments selections under supply chain competition has not been well understood in the literature. Therefore, some other intriguing research questions arise: Can cost sharing align green investment preferences between manufacturers and retailers as well as enhance overall supply chain efficiency? And if not so, what affect them, and which methods can be taken to improve them?

As noted earlier, green technology is usually viewed as a powerful tool to curb carbon emission. It is unquestionable that a firm's unit carbon emissions reduce when it shifts to green technology. However, it is unclear whether green technology necessarily curb total carbon emissions due to the demand expansion effect of green investment in the presence of environmentally conscious consumers. It is known that retailer cost sharing helps promote manufacturers to invest in green technologies. Thus, the environmental impact of green investment becomes more complicated when chain-to-chain competition and cost sharing coexist. In view of the above phenomena and effects, it is most essential to explore the value of retailer cost sharing on manufacturer green technology investment under chain-to-chain competition deeply.

In this study, we develop a model of two competing supply chains, each of which consists of one manufacturer and one retailer. In each chain, the manufacturer sells its product exclusively through the downstream retailer. The manufacturers have two options. One is to invest in green technology and produce green products, and the other is not to invest in green technology and product ordinary (non-green) products. We first characterize equilibrium green investment decisions of the two manufacturers with and without retailer cost sharing scenarios, and then investigate the impacts of manufacturer green investment and retailer cost sharing on each firm's profit, consumer surplus, supply chain efficiency and environmental performance. The main insights of our research are summarized as follows.

First, a dominant equilibrium strategy for both manufacturers is to make green technology investment; however, they can encounter a Prisoner's Dilemma. That is, while a manufacturer can earn more by introducing green technology regardless of whether its rival invests in green technology, green technology investment can intensify the competition to a point where eventually both manufacturers are worse off. This occurs when the degree of competition between manufacturers is sufficiently high. When the manufacturers invest in green technologies, they tend to increase the wholesale prices to cover some of the investment costs, which in turn raises retail prices and worsens double marginalization. Second, retailer sharing the green investment cost does not change the general preferences of manufacturers on green technology investment. We verify that manufacturers benefit from such behavior as long as the cost-sharing rate is low. We further show that when the cost-sharing rate and the degree of product/channel competition are relatively high, the preference confliction over cost sharing between manufacturers and retailers emerges. When the cost-sharing rate and the degree of product/channel competition are relatively low, however, retailer cost sharing can not only avoid firms' preference confliction over the green technology investment but also improve social welfare (the sum of all firms plus consumer surplus).

Finally, green technology investment by manufacturers does not always reduce total carbon emissions. We find that upstream green technology investment actually increases total carbon emissions when the initial carbon emission per product (i.e., the unit carbon emission before introducing green technology) is sufficiently high. Furthermore, we also find that retailer cost sharing can either enhance or decrease the emission reduction effect of green technology investments, depending on the initial carbon emission per product and the cost-sharing rate. Only when the initial carbon emission per product is sufficiently low or the cost-sharing rate is sufficiently high, can cost sharing lower the total carbon emissions.

The remainder of this paper is organized as follows. In Section 2, we review the most relevant literature. This is followed by the introduction of our model setting in Section 3. Section 4 conducts equilibrium analysis and characterizes equilibrium green technology investment strategies for both manufacturers without and with cost sharing. Sections 5 and 6 shed lights on the impacts of green technology investment and cost sharing on consumer surplus, supply chain efficiency and environmental performance respectively. This study ends with conclusions and directions for future study in Section 7.

2 Literature Review

Our paper is closely related to a large body literature on green technology investment of supply chain. Depending on which supply chain party invests in green technology, the research in this area can be divided into two categories: Green technology investment by manufacturers and that by retailers. Our paper belongs to the former category. Some papers in this area focus on the effects of carbon emission regulation and environmental taxes on operational and green technology decisions, e.g., Choi, et al.^[12-15]. Other papers investigate operational and green technology decisions in consideration of consumer environmental awareness, and explore the effects of consumer environmental awareness on manufacturers' incentives to invest, e.g., Liu, et al.^[16] and Zhang, et al.^[17]. All the aforementioned studies do not take the manufacturers' options of not introducing green technology into account. Although, several recent papers, such as Du, et al.^[18], Meng, et al.^[19], Zhang, et al.^{[20, 21]}, investigated manufacturer(s)' green investment choices, they only consider the monopoly setting or competitions between firms or channels but not the chain-to-chain competition. Our study contributes to this stream of research as we investigate manufacturers' green technology investment options in competing supply chains.

Some recent papers analyze the supply chain coordination with green technology investment. For example, Zhang, et al.^[17] explored channel coordination via cost sharing contract in one-manufacturer-one-retailer configuration considering consumer environmental awareness. Wang, et al.^[22] investigated the impact of cost sharing contract and wholesale price premium contract on the chain member's decision and profits in consideration consumer environmental awareness and manufacturer's emission reduction incentive. Yang and Chen^[10] explored the impact of revenue sharing and cost sharing offered by a retailer on a manufacturer's carbon emission reduction efforts and firms' profitability in consideration of consumer environmental consciousness and carbon tax. Different from the above papers that consider a channel composed of one manufacturer and one retailer, we consider two competitive supply chains, each of which consists of one manufacturer and one retailer, and investigate the impact of retailer cost sharing on manufacturer green technology investment.

Our study is also related to the literature considering chain-to-chain competition. An early paper by McGuire and Staelin^[23] considered a price competition between two manufacturers each selling partial substitutable products through an independent retailer, and finds that both manufacturers can benefit from the decentralization of supply chain. Xiao and Yang^[24] extended this research to a demand uncertainty environment, and discuss the effects of the retailers' sensitivity/demand uncertainties, the service investment efficiencies and the charged wholesale prices on supply chain members' decisions. Wu and Chen^[8] studied the structure choice of supply chains under chain-to-chain competition with uncertain demand. Li and Li^[25] developed a model of two competing sustainable supply chains and explore the equilibrium structures for such a two-chain system. Yang, et al.^[26] examined pricing and carbon emission reduction decisions in two competitive supply chains and explore the impacts of vertical and horizontal cooperation on manufacturers' emission reduction behavior, supply chain members and consumers. However, none of the above papers on chain-to-chain competition focuses on whether manufacturers should introduce green technology and its impact on environmental performances. Moreover, we also explore the value of retailer cost sharing on manufacturers' green technology investment decisions, consumer surplus, and overall supply chain efficiency. Hence, our perspective differs from the extant literature.

3 Model Settings

We consider two ex-ante symmetric two-echelon supply chains, indexed by

i = 1, 2

, each consisting of one manufacturer

M_{i}

(e.g., Haier or Gree) and one retailer

R_{i}

(e.g., Suning or JD.COM). The two manufacturers sell substitutable products through their own retailers, and compete in the end-customer market. For example,

M_{1}

and

M_{2}

could be Haier and Gree who sell air conditions through Suning and JD.COM respectively. The manufacturer in each channel has two options for product production: One is to invest in green technology and produce green (eco-friendly) products, and the other is not to invest in technology and produce ordinary products. Similar to Liu, et al.^[16], Zhang, et al.^[17], and Ji, et al.^[27], we assume that consumers are environmentally conscious, and more willing to buy greener products if retail prices are set to be equal. For the remainder of our study, we also use the index

i = 1, 2

to identify the channel and product. For ease of exposition, we use pronouns "he" for manufacturer and "she" for retailer throughout the rest of paper.

To characterize the demand for product i, we adopt a utility function of a representative consumer as follows

\begin{array}{r} U \equiv \sum_{i = 1}^{2} (α_{i} + I_{i} g_{i}) D_{i} - D_{i}^{2} / 2 - λ D_{1} D_{2} - \sum_{i = 1}^{2} p_{i} D_{i}, \end{array}

(1)

where

α_{i}

is supply chain i's initial market size which is normalized to 1 for simplicity;

p_{i}

and

D_{i}

are respectively the retail price and demand of product i;

g_{i}

is the green investment level of Manufacturer i, measuring the green level of product i;

λ \in (0, 1)

is the substitutability between the two products, which can also be interpreted as the competition intensity between two products/chains. As

λ

increases, the product substitutability is stronger and the product/channel competition becomes more intense.

I_{i} = 0

or 1 is the indicator of whether

M_{i}

invests in green technology. Without loss of generality,

I_{i} = 1

represents that

M_{i}

engage in green technology, and

I_{i} = 0

, otherwise.

This utility function was first introduced by Spence^[28], Dixit^[29], Shubik and Levitan^[30], which has been widely used in the economics, marketing, and other related literature (e.g., Cai, et al.^[31]; Wu, et al.^[32]; Liu, et al.^[33]). Maximization of

U

yields the demand for product i as follows.

\begin{array}{r} D_{i} = \frac{1 - λ - p_{i} + λ p_{3 - i} + I_{i} g_{i} - λ I_{3 - i} g_{3 - i}}{1 - λ^{2}}, i = 1, 2. \end{array}

(2)

Notice that our formulation of the decision problems of the channel parties will enforce the logical necessity that a manufacturer i cannot choose no green technology investment (i.e.,

I_{i} = 0

) with a positive green investment level. However, a manufacturer who chooses to invest is free to follow through with virtually zero green investment level. Thus, each manufacturer can strategically commit to making green technology investment or not. Similar to Yang and Chen^[10], we view green technology investment as a one-off investment to reduce the carbon emissions during production process, and adopt a quadratic form function

k_{i} g_{i}^{2}

to denote the green investment cost independent of variable cost, where

k_{i}

is the green investment parameter for

M_{i}

. Specifically, without cost sharing,

M_{i}

bears the investment cost entirely, while with cost sharing,

R_{i}

θ_{i}

(

0 < θ_{i} \leq 1

) proportion of investment cost for

M_{i}

, and thus

M_{i}

incurs investment cost, where

θ_{i}

is the cost sharing rate in supply chain i, articulating how the cost of green investment in supply chain i will be allocated. Without loss of generality, we set

θ_{i} = 0

in the scenario without cost sharing. To enable fair comparison among the various technology investment structures and for simplicity, we assume

k_{i} = 1

. Zhou, et al.^[34] and Li, et al.^[11] also used this assumption in their papers. For parsimony, we further assume that unit production costs and supply chain operational costs are constant and normalized to zero. Our sensitivity analysis shows that the above assumptions do not compromise our findings.

We model the strategic interaction between the two competing supply chains in the scenarios without and with cost sharing for green technology investment as a three-stage game. The game proceeds as follows, depicted in Figure 1. In the first stage, the two manufacturers simultaneously commit to make green technology investments or not. Let

I_{i} = 1

if manufacturer i invests in green technology, and

I_{i} = 0

otherwise. In the second stage, manufacturers simultaneously determine their own wholesale prices and green investment levels if commit to invest in green technology. In the third stage, retailers simultaneously set their own retail prices given the wholesale prices and green investment levels.

Figure 1 Sequence of events

Full size|PPT slide

Note that we assume that manufacturers commit on green technology investment before other decisions because it takes time to invest in green technology, e.g., deploying a certain infrastructure and purchasing new equipment to facilitate green production. Moreover, manufacturers determine wholesale prices and green investment levels simultaneously because a manufacturer cannot commit on these decisions to influence the rival manufacturer's decisions. Actually, sequential decisions on green investment levels and wholesale prices do not affect the qualitative results except for adding complexity to the model analysis.

Based on the demand function in (2) and the above assumptions, the general profit functions of the manufacturers and the retailers in the scenarios without and with cost sharing for green technology investment are given as

\begin{array}{rcl} Π_{M_{i}}^{} = w_{i} (\frac{1 - λ - p_{i} + λ p_{3 - i} + I_{i} g_{i} - λ I_{3 - i} g_{3 - i}}{1 - λ^{2}}) - I_{i} (1 - θ_{i}) {g_{i}}^{2}, \end{array}

(3)

\begin{array}{rcl} Π_{R_{i}}^{} = (p_{i} - w_{i}) (\frac{1 - λ - p_{i} + λ p_{3 - i} + I_{i} g_{i} - λ I_{3 - i} g_{3 - i}}{1 - λ^{2}}) - I_{i} θ_{i} {g_{i}}^{2} . \end{array}

(4)

4 Equilibrium Analysis

In this section, we first characterize manufacturers' equilibrium green technology investment decisions in scenarios without and with cost sharing, and then explore the preferences of manufacturers and retailers towards cost sharing.

4.1 Scenario Without Cost Sharing

We first consider the setting of no cost sharing as a benchmark. Based on the analysis in Section 3, manufacturers' green technology investment decisions without cost sharing lead to four possible portfolios, that is, both manufacturers invest in green technology (GG), only Manufacturer 1 invests (GN), only Manufacturer 2 invests (NG), or neither manufacturer invests (NN). By symmetry, GN is the same as NG, and without loss of generality we consider GN hereafter.

We identify each subgame with a two-character string in which the first character describes the manufacture's investment in the first supply chain (G for investing in green technology, and N for not investing in green technology), and likewise for the second character and the second supply chain. For each portfolio, we solve for the equilibrium retail prices, wholesale prices, and green investment levels (if green technology investment is in place) by backward. Based on that, we get each firm's profit in any given portfolio. Note that the individual firm's profit functions are concave with respect to the corresponding decision variables at each stage of the game, when the feasible region for

λ

satisfies

λ \in (0, 0.94]

. This condition also guarantees the non-negative prices and green investment levels decisions as well as market demands. Thus, the optimal solutions are unique, forming the unique Nash equilibrium for the given subgame, summarized in Lemma 1.

Lemma 1 Without cost sharing, the equilibrium outcomes among portfolios GG, GN and NN are summarized in the following Table 1.

Table 1 The equilibrium results across subgames GG, GN and NN without cost sharing

	GG	GN	NN
$p_{1}$	$\frac{4 (1 - λ^{2}) (3 - λ^{2})}{4 λ^{4} - 2 λ^{3} - 17 λ^{2} + 4 λ + 14}$	$\frac{4 (3 - λ^{2}) (1 - λ^{2}) (8 - 2 λ - 9 λ^{2} + λ^{3} + 2 λ^{4})}{112 - 270 λ^{2} + 221 λ^{4} - 72 λ^{6} + 8 λ^{^{8}}}$	$\frac{2 (3 - λ^{2}) (1 - λ)}{(4 - 4 λ - 2 λ^{2}) (2 - λ)}$
$p_{2}$	$\frac{4 (1 - λ^{2}) (3 - λ^{2})}{4 λ^{4} - 2 λ^{3} - 17 λ^{2} + 4 λ + 14}$	$\frac{2 (3 - λ^{2}) (1 - λ^{2}) (14 - 4 λ - 17 λ^{2} + 2 λ^{3} + 4 λ^{4})}{112 - 270 λ^{2} + 221 λ^{4} - 72 λ^{6} + 8 λ^{^{8}}}$	$\frac{2 (3 - λ^{2}) (1 - λ)}{(4 - 4 λ - 2 λ^{2}) (2 - λ)}$
$w_{1}$	$\frac{2 (1 - λ^{2}) (4 - λ^{2})}{4 λ^{4} - 2 λ^{3} - 17 λ^{2} + 4 λ + 14}$	$\frac{2 (4 - λ^{2}) (1 - λ^{2}) (8 - 2 λ - 9 λ^{2} + λ^{3} + 2 λ^{4})}{112 - 270 λ^{2} + 221 λ^{4} - 72 λ^{6} + 8 λ^{^{8}}}$	$\frac{2 - λ - λ^{2}}{4 - 4 λ - 2 λ^{2}}$
$w_{2}$	$\frac{2 (1 - λ^{2}) (4 - λ^{2})}{4 λ^{4} - 2 λ^{3} - 17 λ^{2} + 4 λ + 14}$	$\frac{(4 - λ^{2}) (1 - λ^{2}) (14 - 4 λ - 17 λ^{2} + 2 λ^{3} + 4 λ^{4})}{112 - 270 λ^{2} + 221 λ^{4} - 72 λ^{6} + 8 λ^{^{8}}}$	$\frac{2 - λ - λ^{2}}{4 - 4 λ - 2 λ^{2}}$
$g_{1}$	$\frac{2 - λ^{2}}{4 λ^{4} - 2 λ^{3} - 17 λ^{2} + 4 λ + 14}$	$\frac{(2 - λ^{2}) (8 - 2 λ - 9 λ^{2} + λ^{3} + 2 λ^{4})}{112 - 270 λ^{2} + 221 λ^{4} - 72 λ^{6} + 8 λ^{^{8}}}$
$g_{2}$	$\frac{2 - λ^{2}}{4 λ^{4} - 2 λ^{3} - 17 λ^{2} + 4 λ + 14}$
$D_{1}$	$\frac{2 (2 - λ^{2})}{4 λ^{4} - 2 λ^{3} - 17 λ^{2} + 4 λ + 14}$	$\frac{2 (2 - λ^{2}) (8 - 2 λ - 9 λ^{2} + λ^{3} + 2 λ^{4})}{112 - 270 λ^{2} + 221 λ^{4} - 72 λ^{6} + 8 λ^{^{8}}}$	$\frac{2 - λ^{2}}{(1 + λ) (2 - λ) (4 - λ - 2 λ^{2})}$
$D_{2}$	$\frac{2 (2 - λ^{2})}{4 λ^{4} - 2 λ^{3} - 17 λ^{2} + 4 λ + 14}$	$\frac{(2 - λ^{2}) (14 - 4 λ - 17 λ^{2} + 2 λ^{3} + 4 λ^{4})}{112 - 270 λ^{2} + 221 λ^{4} - 72 λ^{6} + 8 λ^{^{8}}}$	$\frac{2 - λ^{2}}{(1 + λ) (2 - λ) (4 - λ - 2 λ^{2})}$
$Π_{M_{1}}$	$\frac{(2 - λ^{2}) (4 λ^{4} - 19 λ^{2} + 14)}{{(4 λ^{4} - 2 λ^{3} - 17 λ^{2} + 4 λ + 14)}^{2}}$	$\frac{(2 - λ^{2}) (14 - 19 λ^{2} + 4 λ^{4}) {(8 - 2 λ - 9 λ^{2} + λ^{3} + 2 λ^{4})}^{2}}{{(112 - 270 λ^{2} + 221 λ^{4} - 72 λ^{6} + 8 λ^{^{8}})}^{2}}$	$\frac{(2 - λ^{2}) (2 + λ - λ^{2})}{(2 - λ - λ^{2}) {(4 - λ - 2 λ^{2})}^{2}}$
$Π_{M_{2}}$	$\frac{(2 - λ^{2}) (4 λ^{4} - 19 λ^{2} + 14)}{{(4 λ^{4} - 2 λ^{3} - 17 λ^{2} + 4 λ + 14)}^{2}}$	$\frac{(4 - λ^{2}) (2 - 3 λ^{2} + λ^{4}) {(14 - 4 λ - 17 λ^{2} + 2 λ^{3} + 4 λ^{4})}^{2}}{{(112 - 270 λ^{2} + 221 λ^{4} - 72 λ^{6} + 8 λ^{^{8}})}^{2}}$	$\frac{(2 - λ^{2}) (2 + λ - λ^{2})}{(2 - λ - λ^{2}) {(4 - λ - 2 λ^{2})}^{2}}$
$Π_{R_{1}}$	$\frac{{(2 - λ^{2})}^{2} (1 - λ^{2})}{{(4 λ^{4} - 2 λ^{3} - 17 λ^{2} + 4 λ + 14)}^{2}}$	$\frac{4 (1 - λ^{2}) {(64 - 16 λ - 104 λ^{2} + 16 λ^{3} + 52 λ^{4} - 4 λ^{5} + 8 λ^{6})}^{2}}{{(112 - 270 λ^{2} + 221 λ^{4} - 72 λ^{6} + 8 λ^{^{8}})}^{2}}$	$\frac{(1 - λ) {(2 - λ^{2})}^{2}}{{(4 - 3 λ^{2} + λ^{3})}^{2} {(4 - λ - 2 λ^{2})}^{2}}$
$Π_{R_{2}}$	$\frac{{(2 - λ^{2})}^{2} (1 - λ^{2})}{{(4 λ^{4} - 2 λ^{3} - 17 λ^{2} + 4 λ + 14)}^{2}}$	$\frac{(1 - λ^{2}) {(28 - 8 λ - 48 λ^{2} + 8 λ^{3} + 25 λ^{4} - 2 λ^{5} + 4 λ^{6})}^{2}}{{(112 - 270 λ^{2} + 221 λ^{4} - 72 λ^{6} + 8 λ^{^{8}})}^{2}}$	$\frac{(1 - λ) {(2 - λ^{2})}^{2}}{{(4 - 3 λ^{2} + λ^{3})}^{2} {(4 - λ - 2 λ^{2})}^{2}}$

Note: GN is the same as NG by symmetry, and thus we only list the equilibrium outcomes under GN in this table.

As indicated in Lemma 1, a manufacturer benefits from his own green technology investment but is hurt by his rival's. Take Manufacturer 1 as an example, GN outperforms NN, and GG outperforms NG, while the opposite is true for Manufacture 2 due to symmetry. This occurs because, a manufacturer's green technology investment generates more demand for his own product, it also encroaches on his rival's existing market, and thereby reducing the demand of the rival manufacturer.

We now proceed to solve for the manufacturers' equilibrium green technology investment decisions at the first stage. Based on the results in Lemma 1, by comparing the manufacturers' profits among subgames NN, GN and GG, we obtain the manufacturers' (pure-strategy) equilibrium green technology investment decisions in the following proposition.

Proposition 1 In the scenario without cost sharing, GG arises as the unique equilibrium.

Proposition 1 shows that without cost sharing, the focal manufacturer always chooses to invest in green technology regardless of the rival manufacturer's choice. As we previously discussed, green technology investment stimulates the base demand for the focal manufacturer, and it also encroaches on his rival's existing market. This intensifies chain-to-chain competition. To stay in competition, the rival manufacturer then has no choice but to step up his own green investment effort, if the focal manufacturer chooses to invest in green technology. Hence, the investment in green technology is a dominant equilibrium strategy for both manufacturers.

In view of the strong incentive for manufacturers to invest in green technology, an immediate question arises: Does green investment lead to a win-win outcome for every firm? For that we compare the firms' profits under GG to those under NN, and obtain the following theorem.

Theorem 1 There exists a threshold

\hat{λ}

(\approx 0.824)

, such that

Π_{M_{i}}^{G G} > (<) Π_{M_{i}}^{N N}

when

λ < (>) \hat{λ}

; while

Π_{R_{i}}^{G G} > Π_{R_{i}}^{N N}

in the whole feasible region.

Theorem 1 indicates that if the product substitutability

λ

is low (i.e.,

λ < \hat{λ}

), both manufacturers would benefit from introducing green technology investment, whereas if

λ

sufficiently high (i.e.,

λ > \hat{λ}

), both manufacturers would be worse off by green technology investment. The reason can be explained as follows. When

λ

is lower, each manufacturer behaves more like a monopolist. Here, green technology investment significantly increases each manufacturer's own demand without encroaching on the other's market share too much. Besides, double marginalization is softened by the intensified channel/product competition caused by bilateral green investment (i.e., both manufacturers make green technology investments). Thus, both manufacturers gain more in GG than NN. As

λ

grows, green technology investment intensifies the horizontal competition between manufacturers. The retailers must cut retail prices, pressuring their manufacturers to lower the wholesale prices and thereby the profit margins. With a sufficiently high

λ

(i.e.,

λ > \hat{λ}

), the chain-to-chain competition is so intense that outweighs the benefit of the accompanying reduction in double marginalization. At this time, manufacturers trap into the Prisoner's Dilemma, that is, each manufacturer actually can benefit more when both do not introduce green investment, but under the competitive pressure each one would choose green investment rather than without green investment. From the perspective of retailers, manufacturers' green investments intensify the channel/product competition, pushing down the wholesale prices, and thereby increasing retailers' profit margins. This implies that each retailer always benefits from the green technology investment by his own manufacturer.

Take both upstream and downstream into account together, we observe that green investments by manufacturers, compared to no green investment, may lead to either a win-lose situation with the manufacturers being worse off and the retailers being better off, or a win-win situation with both manufacturers and retailers being better off, depending on

λ

. If

λ

is below threshold

\hat{λ}

, the win-win outcome emerges; otherwise, the win-lose outcome arises.

Given that retailers always benefit from their manufacturers' green technology investments, while manufacturers would be hurt when both invest in green technology, retailers have strong incentives, such as sharing a proportion of green technology investment cost with their manufacturers, to motivate their manufacturers to invest. Then, several intriguing and important questions arise: Can both manufacturers and retailers necessarily benefit from cost sharing? Are the preferences of the manufacturers and retailers toward cost sharing aligned? In the following sub-section, we set out to address these questions.

4.2 Scenario with Cost Sharing

When each retailer shares green investment cost with each own manufacturer (henceforth, we call this cost sharing for brevity), each retailer i shares a

θ_{i}

proportion of total green technology investment cost with the corresponding manufacturer. Thus, each manufacturer i incurs only

1 - θ_{i}

proportion of investment cost. To investigate the value of cost sharing, we assume that a retailer shares a fixed portion of the total cost incurred by the green technology investment for her manufacturer if the manufacturer chooses to invest in green technology. Furthermore, to focus purely on the impact of any given cost-sharing rate on firms' preferences, we assume that the cost sharing rate

θ_{i}

is exogenous, and the two chains have a common cost sharing rate, that is,

θ_{i} = θ

. In reality,

θ_{i}

would result endogenously from the balance of power between the manufacturer and the retailer, which falls beyond the scope of our model.

We use the superscript "CS" to denote the scenario of cost sharing. Hence, the two manufacturers' decisions also lead to four possible portfolios: Both manufacturers invest in green technology (CSGG), only Manufacturer 1 invests in green technology (CSGN), only Manufacturer 2 invests in green technology (CSNG), and neither invests in green technology (CSNN). Notice that cost sharing has no impact when neither manufacturer introduces green investment, CSNN is equivalent to NN. For parsimony, we use NN to represent the case where neither manufacturer invests in the scenarios without and with cost sharing. Recall that CSGN is the same as CSNG owing to symmetry, and thus we use CSGN to stand for the case where only one manufacturer makes green technology investment in the scenario of cost sharing.

In each subgame, the manufacturers first determine the wholesale prices and green investment level(s) simultaneously if applicable, and then the retailers set their respective retail prices. The equilibrium solutions as well as the firms' profits given the technology investment decisions in the scenario with cost sharing are summarized in Lemma 2.

Lemma 2 With cost sharing, the equilibrium outcomes under portfolios CSGG and CSGN are summarized in Table 2.

**Table 2 The equilibrium outcomes under CSGG and CSGN portfolios**

	CSGG	CSGN
$p_{1}$	$\frac{4 (1 - θ) (3 - 4 λ^{2} + λ^{4})}{14 - 2 θ (2 - λ) (1 + λ) (4 - λ - 2 λ^{2}) + λ (4 - λ (17 + 2 λ - 4 λ^{2}))}$	$\frac{4 (1 - θ) {(1 - λ)}^{2} (1 + λ) (2 + λ) (3 - λ^{2}) (4 + λ - 2 λ^{2})}{16 (7 - 8 θ) - 2 (135 - 148 θ) λ^{2} + 13 (17 - 18 θ) λ^{4} - 2 (36 - 37 θ) λ^{6} + 8 (1 - θ) λ^{8}}$
$p_{2}$	$\frac{4 (1 - θ) (3 - 4 λ^{2} + λ^{4})}{14 - 2 θ (2 - λ) (1 + λ) (4 - λ - 2 λ^{2}) + λ (4 - λ (17 + 2 λ - 4 λ^{2}))}$	$\frac{2 (3 - 4 λ^{2} + λ^{4}) (14 - 2 θ (1 - λ) (2 + λ) (4 + λ - 2 λ^{2}) - λ (4 + λ (17 - 2 λ - 4 λ^{2})))}{16 (7 - 8 θ) - 2 (135 - 148 θ) λ^{2} + 13 (17 - 18 θ) λ^{4} - 2 (36 - 37 θ) λ^{6} + 8 (1 - θ) λ^{8}}$
$w_{1}$	$\frac{2 (1 - θ) (4 - 5 λ^{2} + λ^{4})}{14 - 2 θ (2 - λ) (1 + λ) (4 - λ - 2 λ^{2}) + λ (4 - λ (17 + 2 λ - 4 λ^{2}))}$	$\frac{2 (1 - θ) (2 + λ - λ^{2}) {(2 - λ - λ^{2})}^{2} (4 + λ - 2 λ^{2})}{16 (7 - 8 θ) - 2 (135 - 148 θ) λ^{2} + 13 (17 - 18 θ) λ^{4} - 2 (36 - 37 θ) λ^{6} + 8 (1 - θ) λ^{8}}$
$w_{2}$	$\frac{2 (1 - θ) (4 - 5 λ^{2} + λ^{4})}{14 - 2 θ (2 - λ) (1 + λ) (4 - λ - 2 λ^{2}) + λ (4 - λ (17 + 2 λ - 4 λ^{2}))}$	$\frac{(4 - 5 λ^{2} + λ^{4}) (14 - 2 θ (1 - λ) (2 + λ) (4 + λ - 2 λ^{2}) - λ (4 + λ (17 - 2 λ + 4 λ^{2}))}{16 (7 - 8 θ) - 2 (135 - 148 θ) λ^{2} + 13 (17 - 18 θ) λ^{4} - 2 (36 - 37 θ) λ^{6} + 8 (1 - θ) λ^{8}}$
$g_{1}$	$\frac{2 - θ^{2}}{14 - 2 θ (2 - λ) (1 + λ) (4 - λ - 2 λ^{2}) + λ (4 - λ (17 + 2 λ - 4 λ^{2}))}$	$\frac{(2 - λ^{2}) (2 - λ - λ^{2}) (4 + λ - 2 λ^{2})}{16 (7 - 8 θ) - 2 (135 - 148 θ) λ^{2} + 13 (17 - 18 θ) λ^{4} - 2 (36 - 37 θ) λ^{6} + 8 (1 - θ) λ^{8}}$
$g_{2}$	$\frac{2 - θ^{2}}{14 - 2 θ (2 - λ) (1 + λ) (4 - λ - 2 λ^{2}) + λ (4 - λ (17 + 2 λ - 4 λ^{2}))}$
$D_{1}$	$\frac{2 (1 - θ) (2 - λ^{2})}{14 - 2 θ (2 - λ) (1 + λ) (4 - λ - 2 λ^{2}) + λ (4 - λ (17 + 2 λ - 4 λ^{2}))}$	$\frac{2 (1 - θ) (1 - λ) (2 + λ) (2 - λ^{2}) (4 + λ - 2 λ^{2})}{16 (7 - 8 θ) - 2 (135 - 148 θ) λ^{2} + 13 (17 - 18 θ) λ^{4} - 2 (36 - 37 θ) λ^{6} + 8 (1 - θ) λ^{8}}$
$D_{2}$	$\frac{2 (1 - θ) (2 - λ^{2})}{14 - 2 θ (2 - λ) (1 + λ) (4 - λ - 2 λ^{2}) + λ (4 - λ (17 + 2 λ - 4 λ^{2}))}$	$\frac{(2 - θ^{2}) (14 - 2 θ (1 - λ) (2 + λ) (4 + λ - 2 λ^{2}) - λ (4 + λ (17 - 2 λ - 4 λ^{2})))}{16 (7 - 8 θ) - 2 (135 - 148 θ) λ^{2} + 13 (17 - 18 θ) λ^{4} - 2 (36 - 37 θ) λ^{6} + 8 (1 - θ) λ^{8}}$
$Π_{M_{1}}$	$\frac{(1 - θ) (2 - λ^{2}) (14 - 19 λ^{2} + 4 λ^{4} - 4 θ (4 - 5 λ^{2} + λ^{4}))}{{(14 - 2 θ (2 - λ) (1 + λ) (4 - λ - 2 λ^{2}) + λ (4 - λ (17 + 2 λ - 4 λ^{2})))}^{2}}$	$\frac{(1 - θ) {(1 - λ)}^{2} {(2 + λ)}^{2} (2 - λ^{2}) {(4 + λ - 2 λ^{2})}^{2} (14 - 19 λ^{2} + 4 λ^{4} - 4 θ (4 - 5 λ^{2} + λ^{4}))}{{(16 (7 - 8 θ) - 2 (135 - 148 θ) λ^{2} + 13 (17 - 18 θ) λ^{4} - 2 (36 - 37 θ) λ^{6} + 8 (1 - θ) λ^{8})}^{2}}$
$Π_{M_{2}}$	$\frac{(1 - θ) (2 - λ^{2}) (14 - 19 λ^{2} + 4 λ^{4} - 4 θ (4 - 5 λ^{2} + λ^{4}))}{{(14 - 2 θ (2 - λ) (1 + λ) (4 - λ - 2 λ^{2}) + λ (4 - λ (17 + 2 λ - 4 λ^{2})))}^{2}}$	$\frac{(4 - λ^{2}) (2 - 3 λ^{2} + λ^{4}) {(14 - 2 θ (1 - λ) (2 + λ) (4 + λ - 2 λ^{2}) - λ (4 + λ (17 - 2 λ - 4 λ^{2})))}^{2}}{{(16 (7 - 8 θ) - 2 (135 - 148 θ) λ^{2} + 13 (17 - 18 θ) λ^{4} - 2 (36 - 37 θ) λ^{6} + 8 (1 - θ) λ^{8})}^{2}}$
$Π_{R_{1}}$	$\frac{{(2 - λ^{2})}^{2} (4 - 9 θ + 4 θ^{2} - 4 {(1 - θ)}^{2} λ^{2})}{{(14 - 2 θ (2 - λ) (1 + λ) (4 - λ - 2 λ^{2}) + λ (4 - λ (17 + 2 λ - 4 λ^{2})))}^{2}}$	$\frac{{(1 - λ)}^{2} {(2 + λ)}^{2} {(2 - λ^{2})}^{2} (4 - 9 θ + 4 θ^{2} - 4 {(1 - θ)}^{2} λ^{2}) {(4 + λ - 2 λ^{2})}^{2}}{{(16 (7 - 8 θ) - 2 (135 - 148 θ) λ^{2} + 13 (17 - 18 θ) λ^{4} - 2 (36 - 37 θ) λ^{6} + 8 (1 - θ) λ^{8})}^{2}}$
$Π_{R_{2}}$	$\frac{{(2 - λ^{2})}^{2} (4 - 9 θ + 4 θ^{2} - 4 {(1 - θ)}^{2} λ^{2})}{{(14 - 2 θ (2 - λ) (1 + λ) (4 - λ - 2 λ^{2}) + λ (4 - λ (17 + 2 λ - 4 λ^{2})))}^{2}}$	$\frac{{(2 - λ^{2})}^{2} (1 - λ^{2}) {(14 - 2 θ (1 - λ) (2 + λ) (4 + λ - 2 λ^{2}) - λ (4 + λ (17 - 2 λ - 4 λ^{2})))}^{2}}{{(16 (7 - 8 θ) - 2 (135 - 148 θ) λ^{2} + 13 (17 - 18 θ) λ^{4} - 2 (36 - 37 θ) λ^{6} + 8 (1 - θ) λ^{8})}^{2}}$

Note: CSNN is equivalent to NN, and thus we omit the equilibrium outcomes in this table.

With the results in Lemma 2, we characterize the equilibrium portfolio of the two manufacturers by comparing their profits among subgames CSGG, CSGN and NN. To ensure a meaningful comparison, we assume that

θ < θ^{C S G G} (λ)

, which enforce the common feasible domain for all cases. This condition also guarantees the concavity of the profit functions and the non-negative prices, green investment level and demands in all cases.

Proposition 2 With cost sharing, CSGG arises as the unique equilibrium.

Clearly, retailer sharing the green investment cost does not change the manufactures' options for green technology investment. This implies that investing in green technology continues to be a dominant strategy for the two manufacturers under cost sharing scheme. This occurs because, cost sharing has no impact on the manufacturers other than to promote them to increase green technology investment levels.

Given that the two manufacturers always prefer green technology investments regardless of with and without cost sharing, two comparative concerns arise: (ⅰ) Would manufacturers and retailers always benefit from manufacturer green investment in scenario of cost sharing? (ⅱ) Would manufacturers and retailers always prefer cost sharing over no cost sharing? We compare the profits of the manufacturers and retailers in CSGG with those in NN, as well as the corresponding profits in CSGG and those in GG, and obtain Theorem 2.

Theorem 2

(i)

There exists a threshold

θ_{M}^{C S G G - N N} (λ)

, such that

Π_{M_{i}}^{C S G G} > (<) Π_{M_{i}}^{N N}

, if

θ < (>) θ_{M}^{C S G G - N N} (λ)

, and (ⅱ) there exists a threshold

θ_{R}^{C S G G - N N} (λ)

, such that

Π_{R_{i}}^{C S G G} > (<) Π_{R_{i}}^{N N}

, if

θ < (>) θ_{R}^{C S G G - N N} (λ)

Consistent with the scenario without cost sharing, the manufacturers may be either better off or worse off under cost sharing scheme, depending on the cost-sharing rate

θ

. Specifically, when

θ

is relatively low (i.e.,

θ < θ_{M}^{C S G G - N N} (λ)

), introducing green technology investment is mutually beneficial to both manufacturers. That is to say, CSGG leads to a win-win outcome for the two manufacturers. However, when

θ

is sufficiently high (i.e.,

θ > θ_{M}^{C S G G - N N} (λ)

), the manufacturers also encounter a Prisoner's Dilemma. This is because a higher cost sharing rate boosts more green investments; this further worsens the double marginalization and thereby reducing the manufacturers' gains from green technology investment. Recall that the retailers are always better off by upstream green technology investment in the scenario without cost sharing, then what would happen in the scenario of cost sharing? From Part (ii) of Theorem 2, we find that retailers can be actually hurt by manufacturer green investment, if

θ

is too high (i.e.,

θ > θ_{R}^{C S G G - N N} (λ)

). This stems from two opposing effects of

θ

. On one hand, a higher

θ

stimulates heavier green technology investment and hence the demand (the market expansion effect). On the other hand, a higher

θ

increases the retailers' costs and in turn driving up the retail prices, which worsens the double marginalization (the cost incurring effect). When

θ

is low, the former effect dominates, and thus the advantage of upstream green investment for retailers outweighs its drawback. However, as

θ

grows, the latter effect becomes more significant, and eventually when

θ

surpasses

θ_{R}^{C S G G - N N} (λ)

, the retailers are hurt by the upstream green investment. To better understand Theorem 2, we plot Figure 2.

**Figure 2 Comparison with respect to profits between CSGG and NN**

Full size|PPT slide

It is shown that all firms benefit from upstream green technology investment, if

θ

and

λ

are relatively low. Thus, a win-win outcome for both the manufacturers and the retailers emerges (a Pareto Zone, Zone R1 in Figure 2). However, as

θ

increases (Zone R4), the win-win situation is disturbed: The retailers prefer NN here, not CSGG. Thus, a win-lose outcome emerges with manufacturers being better off but retailers worse off. On the other hand, as

θ

grows (Zone R2), the manufacturers benefit from NN while are hurt by CSGG. Hence, another win-lose situation occurs, where manufacturers are worse off but the retailers are better off. Note that if

θ

and

λ

are both really high (Zone R3), both manufacturers and retailers can benefit if they deviate from CSGG, but they would not do so unilaterally due to the competitive pressure. This means both manufacturers and retailers encounter Prisoner's Dilemma. We also observe that the two thresholds,

θ_{R}^{C S G G - N N} (λ)

and

θ_{M}^{C S G G - N N} (λ)

are both decreasing in

θ

, which corroborates the mechanism described earlier: The lower the

θ_{R}^{C S G G - N N} (λ)

(

θ_{M}^{C S G G - N N} (λ)

), the larger the set of circumstances for which the Prisoner's Dilemma for the retailers (manufacturers) arises, and the higher

θ

, the lower the

θ_{R}^{C S G G - N N} (λ)

and

θ_{M}^{C S G G - N N} (λ)

We are now in position to answer the second question by comparing firms' profits under cost sharing to those without cost sharing. The result is summarized as follows.

Theorem 3 There exist two thresholds

θ_{R}^{C S G G - G G} (λ)

and

θ_{M}^{C S G G - G G} (λ)

(θ_{R}^{C S G G - G G} (λ) < θ_{M}^{C S G G - G G} (λ))

, such that the manufacturers prefer CSGG over GG, if and only if

θ < θ_{M}^{C S G G - G G} (λ)

, while the retailers prefer CSGG to GG, if and only if

θ < θ_{R}^{C S G G - G G} (λ)

Theorem 3 catalogs a divergence between manufacturers and retailers in preferences towards cost sharing. It is found that cost sharing becomes undesirable for the manufacturers, if the cost-sharing rate

θ

is sufficiently high (i.e.,

θ > θ_{M}^{C S G G - G G} (λ)

). However, retailers prefer cost sharing if and only if

θ

is not high (i.e.,

θ < θ_{R}^{C S G G - G G} (λ)

). Figure 3 and Table 3 summarize all firms' preferences towards cost sharing. As indicated in Figure 3 and Table 3, all firms prefer cost sharing when

θ

and

λ

are relatively small (Zone 1 in Figure 3). As

θ

and

λ

grow (Zone 2), conflict over cost sharing preferences among all firms becomes more apparent: the retailers prefer no cost sharing, while the manufacturers prefer cost sharing. However, if

θ

and

λ

are both very high (Zone 3), cost sharing becomes undesirable for both manufacturers and retailers. Note that when

θ

and

λ

are both very high, the manufacturers are motivated to increase green technology investment, which intensifies the product/channel competition; the accompanying increased wholesale prices and in turn the retail prices put downward pressure on demand and profits for all firms. In this sense, the best cost sharing rate is somewhere in between, so as to strike a balance among these forces.

Figure 3 Manufacturers' and retailers' preferences towards cost sharing

Full size|PPT slide

Table 3 The firms' preferences over cost sharing

Zone	$M_{i}$ prefers	$R_{i}$ prefers
1	CSGG	CSGG
2	CSGG	GG
3	GG	GG

We have so far shown that manufacturer(s)' green technology investment option(s) without and with cost sharing as well as the value of cost sharing on both the manufacturers and the retailers. In the next section, we compare the equilibrium solutions for different settings with a view to providing managerial insights.

5 Welfare Analysis

In this section, we conduct welfare analysis, and further explore the impact of manufacturer green technology investment and cost sharing on supply chain efficiency and consumer surplus.

5.1 Scenario Without Cost Sharing

In this subsection, we focus on the impacts of manufacturer green investment and cost sharing on supply chain efficiency. Here, similar to Liu, et al^[33], we define supply chain efficiency as the sum of all firms' profits. To capture the impact of green technology investment on supply chain efficiency, we compare the sum of manufacturers' and retailers' profits under GG and those under NN. The results are summarized in the following theorem.

Theorem 4 Without cost sharing, manufacturers' green technology investments increase supply chain efficiency, if and only if

λ \leq \overset{}{λ} \approx 0.8959

The direct implication of Theorem 4 is that manufacturers' green technology investments may either improve or worsen overall supply chain efficiency, depending on the product substitutability

λ

. Specifically, when

λ

is relatively low (i.e.,

λ \leq \overset{}{λ}

), GG performs better than NN. Otherwise, GG performs worse than NN due to the intensified channel/product competition. This property is reminiscent of the Prisoner's Dilemma, which confirms that upstream green technology investment worsens supply chain efficiency. This result is in line with intuition, because fierce channel/product competition drives up the wholesale and retail prices, which worsens the double marginalization and thereby reducing supply chain efficiency.

Next, we investigate the impact of retailer cost sharing, for which we compare the sum of all firms' profits in CSGG to that in GG. The results are provided in the following theorem.

Theorem 5 The supply chain efficiency can be improved under retailer cost sharing, if and only if

θ < θ_{S C}^{D} (λ)

One might expect that cost sharing would improve supply chain efficiency because double marginalization can be reduced. However, our analysis shows this is not necessarily the case. It would be true if the cost sharing rate

θ

is relatively low. However, if

θ

is too much high, cost sharing actually leads to a poor supply chain efficiency.

Figure 4 graphically depicts the impact of cost sharing on supply chain efficiency. When

θ

is relatively low (Zone R1 and R2), CSGG performs better than GG, indicating that the overall supply chains benefit from cost sharing due to the reduction double marginalization. It is worth noting that when

θ

and

λ

are both relatively small (Zone R1), all firms benefit from cost sharing. However, as

θ

and

λ

grow (Zone R2), an inconsistent preference over cost sharing emerges: The retailers are worse off and the manufacturer are better off. This indicates that attaining a better supply chain performance might require additional side payments from the manufacturers to the retailers. Or put differently, with a medium

θ

(i.e.,

θ_{R}^{C S G G - G G} (λ) < θ < θ_{S C}^{D} (λ)

), side payments from the manufacturers to the retailers could enable a Pareto improvement. With the further increase in

θ

, in Zone R3, total channel profit is lower in CSGG than GG, although the manufacturers still benefit from cost sharing. Finally, when both

θ

and

λ

are sufficiently high (Zone R4), all firms prefer no cost sharing, and cost sharing certainly leads to a poor supply chain efficiency.

Figure 4 Comparison with respect to supply chain efficiency with and without cost sharing

Full size|PPT slide

5.2 Consumer Surplus

Consumer surplus, denoted as

U

is based on the utility of the representative consumer in (1). Specifically, we use

U

subscripted CSGG, GG and NN to represent consumer surplus under scenarios CSGG, GG and NN, respectively. Table 4 summarizes consumer surplus under CSGG, GG and NN.

**Table 4 Consumer surplus among CSGG, GG and NN**

Scenario	Consumer surplus
NN	$\frac{{(2 - λ^{2})}^{2}}{(1 + λ) {(2 - λ)}^{2} {(4 - λ - 2 λ^{2})}^{2}}$
GG	$\frac{4 (1 + λ) {(2 - λ^{2})}^{2}}{{(4 λ^{4} - 2 λ^{3} - 17 λ^{2} + 4 λ + 14)}^{2}}$
CSGG	$\frac{4 (1 + λ) {(2 - λ^{2})}^{2} {(1 - θ)}^{2}}{{(4 θ λ^{4} - 2 θ λ^{3} - 4 λ^{4} - 18 θ λ^{2} + 2 λ^{3} + 4 θ λ + 17 λ^{2} + 16 θ - 4 λ - 14)}^{2}}$

A comparison of the results in Table 4 yields Theorem 6, which depicts the ranking of consumer surplus among scenarios CSGG, GG and NN.

Theorem 6 Consumer surplus is lower in GG than CSGG, but higher than NN.

According to Theorem 6, manufacturer green technology investment generates a higher consumer surplus than does not invest in green technology, and cost sharing strengthens the positive effect of green technology investment on consumer surplus. This is because, green technology investments by manufacturers increase the representative consumer's product evaluation (raising purchases), and thereby intensifying channel/product competition; the fierce competition keeps the prices from too much. Cost sharing, as we previously discussed, benefits to motivate more green technology investment, and thereby further intensifying channel/product competition, which unsurprisingly leads to more utility for consumers.

6 Environmental Impact

Given that the aim of adopting green technology is to reduce carbon emissions, in this section, we take the environmental perspective to explore whether green technology investment and cost sharing benefit the environment. Following Agrawal, et al.^[35] and Örsdemir, et al.^[36], we take the amount of carbon emissions as a measure of the environmental impact. Given the carbon emissions reduction effect of green technology, we assume that the carbon emissions of each product i before green technology adoption is

e

, and that of each product i after green technology adoption (i.e., with green investment) is (

e - g_{i}

). Recall that

g_{i}

measures the greenness of product i. Thus, a product with a higher green level means that the unit emissions level is lower, and hence a consumer can get a higher utility by consuming such a product.

Recall that GG and CSGG are dominant technology investment strategies of manufacturers in the scenarios without and with cost sharing. The general formula of total carbon emissions under GG and CSGG are

C E^{X} = \sum_{i = 1}^{2} (e - g_{i}^{X}) D_{i}^{X},

(5)

where

X = G G, C S G G

, and

D_{i} (i = 1, 2)

as in (2) with

I_{i} = 1

As a benchmark, we also consider the total carbon emissions under NN as follows.

C E^{N N} = \sum_{i = 1}^{2} e D_{i} .

(6)

In (6),

D_{i} (i = 1, 2)

as in (2) with

I_{i} = 0

We summarize the total carbon emissions under NN, GG and CSGG in Table 5.

Table 5 Total carbon emissions among NN, GG and CSGG

Scenario	Total carbon emissions (CE)
NN	$\frac{2 (2 - λ^{2}) e}{(1 + λ) (2 - λ) (4 - λ - 2 λ^{2})}$
GG	$\frac{4 (2 - λ^{2}) (4 e λ^{4} - 2 e λ^{3} - 17 e λ^{2} + 4 e λ + 14 e + λ^{2} - 2)}{{(4 λ^{4} - 2 λ^{3} - 17 λ^{2} + 4 λ + 14)}^{2}}$
CSGG	$\frac{4 (2 - λ^{2}) (1 - θ) (- 4 e θ λ^{4} + 2 e θ λ^{3} + 4 e λ^{4} + 18 e θ λ^{2} - 2 e λ^{3} - 4 e θ λ - 17 e λ^{2} - 16 e θ + 4 e λ + λ^{2} + 14 e - 2)}{{(4 θ λ^{4} - 2 θ λ^{3} - 4 λ^{4} - 18 θ λ^{2} + 2 λ^{3} + 4 θ λ + 17 λ^{2} + 16 θ - 4 λ - 14)}^{2}}$

To capture the value of green investment in carbon abatement, we compare the total carbon emissions under GG and NN. The result is summarized in the following theorem.

Theorem 7 There exists a threshold

e_{0} (λ)

, such that

C E^{G G} < C E^{N N}

e < e_{0} (λ)

, and

C E^{G G} > C E^{N N}

, otherwise.

Theorem 7 suggests that green technology investments by manufacturers do not necessarily reduce carbon emissions unless the initial carbon emission per product

e

is sufficiently low (i.e.,

e < e_{0}

). This result stems from two effects caused by upstream green technology investment. Note that upstream green technology investment reduces carbon emissions per unit of product (the per unit emission reduction effect), but it also enhances consumers' utility and thereby stimulating the base demand (the base demand expanding effect). When

e

is low (below

e_{0}

), for a given green technology investment level, the per unit emission reduction effect dominates. However, as

e

grows, the per unit emission reduction effect diminishes, and eventually when

e

surpasses

e_{0}

, the base demand expanding effect outweighs the per unit emission reduction effect.

The expression of

e_{0} (λ)

further reveals that as

λ

grows, green technology investment by manufacturers can either increase or decrease total carbon emissions depending on the value of

λ

. More specifically, when

λ

is relatively low, the higher the value of

λ

is, the more likely green technology investment by manufacturers is to exacerbate total carbon emissions. However, when

λ

is high enough, as

λ

grows, manufacturers' green technology investment is more likely to reduce total carbon emissions. An interesting driving force behind this observation stems from the two opposing effects of

λ

. It is well known that a higher

λ

means a fierce channel competition. To stay in competition, each manufacturer has to reduce individual wholesale price and thereby stimulating the demand. We call this the demand-stimulating effect. On the other hand, recall that below the demand function in (2), as

λ

increases, the size of the total potential market shrinks. For easy reference, we call this the market shrinkage effect. For a given

e

, when

λ

is below the threshold, the demand-stimulating effect dominants, and thus green technology investment by manufacturers increases total carbon emissions. Otherwise, the market shrinkage effect takes over the lead, and thus manufacturers' green technology investment reduces total carbon emissions.

Next, we consider the impact of cost sharing, for which we compare the total carbon emissions under CSGG and GG. The result of our analysis is summarized in Theorem 8.

Theorem 8 There exists a threshold

e_{1} (λ) (> e_{0} (λ))

, such that

C E^{C S G G} < C E^{G G}

when

e < e_{1} (λ)

. Otherwise,

C E^{C S G G} < C E^{G G}

θ > θ^{*}

, and

C E^{C S G G} > C E^{G G}

, if

θ < θ^{*}

Theorem 8 demonstrates that cost sharing can either strengthen or weaken the carbon emission reduction effect of green technology investment, depending on the initial carbon emission per product

e

and the cost-sharing rate

θ

. Specifically, when

e

is relatively low (i.e.,

e < e_{1} (λ)

), cost sharing strictly promotes the carbon emission reduction effect of green technology investment regardless of the cost sharing rate. Recall that cost sharing motivates green technology investment. As explained after Theorem 8, with a low

e

, the per unit emission reduction effect dominates the base demand expanding effect, such that cost sharing, compared to no cost sharing, will lower carbon emissions. However, when

e

is sufficiently high (i.e.,

e > e_{1} (λ)

), whether cost sharing strengthens or weakens the carbon emissions reduction effect of green technology investment depends on the cost-sharing rate

θ

. Specifically, with a high

θ

(i.e.,

θ > θ^{*}

), cost sharing leads to more carbon emissions than no cost sharing, while with a low

θ

, cost sharing leads to less carbon emission than no cost sharing. Note that with a sufficiently high

θ

, the carbon emission reduction effect of green technology investment diminishes because the per unit emission reduction effect is defeated by the base demand expanding effect. Meanwhile, a higher

θ

generates more green technology investments, which further intensifies the base demand expanding effect, and thereby resulting in more carbon emissions.

7 Conclusions

Motivated by the fact that manufacturers often face the choice of whether to invest in green technology in practice, this paper investigates manufacturers' green technology investment decisions as well as the impacts of green technology investment and retailer cost sharing on each firm's profit, consumer surplus, supply chain efficiency and environmental performance in two competing supply chains, each consisting of one manufacturer and one retailer. Our results offer managerial insights to better understand the value of cost sharing on manufacturer green technology investment under competition in practice.

First, we show that a dominant strategy for both manufacturers is to invest in green technology at a positive investment level, although a Prisoner's Dilemma occurs under a sufficiently fierce channel/product competition. Meanwhile we verify that preference conflict of firms for manufacturer green technology investment also arises, if the channel/product competition is sufficiently high. Given that Prisoner's Dilemma and channel conflict damage supply chain efficiency greatly, our results stress the necessity between supply chain members, such as forming industry alliance, and (or) joint green technology investment between upstream and downstream via some contracts.

Second, if the channel/product competition is not too fierce, then both supply chain efficiency and consumer surplus will benefit from manufacturer green technology investment since it yields a greater market expansion effect; further, more intense chain-to-chain competition results from both investing. We also demonstrate that retailer cost sharing for upstream green technology investment benefits to improve consumer surplus, but it does not necessarily lessen firms' preference confliction or improve supply chain efficiency unless the cost-sharing rate is not high. These findings highlight the significance of a proper cost-sharing rate in the real world. With a proper cost-sharing rate, the retailer cost sharing can not only avoid channel conflict, but also improve the social welfare (consumer surplus plus all firms profits).

Another practical implication of our findings is that green technology investments by manufacturers do not always benefit the environment, although such actions might be beneficial to both firms and consumers. In the real world, many countries induce manufacturers to invest in green technology to curb carbon emission, but our analysis shows such an action might lead to a poor environment performance especially when the intensity of market competition is low. We also find that retailer cost sharing might deteriorate environment if the cost-sharing rate is relatively high. Recall that retailer cost sharing scheme has a negative effect on firms under a sufficiently high cost-sharing rate. This finding indicates that excessive cost-sharing rate not only hurts total channel profit, but also exacerbates carbon emission.

We note several limitations of our research and provide promising directions for future research. First, the cost-sharing rate in our model is exogenous for tractability. This rate could be decided endogenously by the retailers or by negotiating within a Nash bargaining framework in future research. Second, this study has focused on cost sharing mechanism. Other cooperation mechanisms, such as profit redistribution, revenue-sharing, or other effective incentive mechanisms, are necessary to be examined in future studies. Finally, due to computational complexity, we have limited our discussion to deterministic demand. In the following study, it will be interesting and more challenging to explore the impact of uncertain demand on manufacturers' green technology choices.

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Acknowledgements

The authors gratefully acknowledge the Editor and anonymous refereefor their insightful comments and helpful suggestions that led to a marked improvement of the article.

Funding

the National Social Science Fund of China(16BGL079)

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Abstract
Key words
Cite this article
1 Introduction
2 Literature Review
3 Model Settings
Figure 1 Sequence of events
4 Equilibrium Analysis
4.1 Scenario Without Cost Sharing
Table 1 The equilibrium results across subgames GG, GN and NN without cost sharing
4.2 Scenario with Cost Sharing
Table 2 The equilibrium outcomes under CSGG and CSGN portfolios
Figure 2 Comparison with respect to profits between CSGG and NN
Figure 3 Manufacturers' and retailers' preferences towards cost sharing
Table 3 The firms' preferences over cost sharing
5 Welfare Analysis
5.1 Scenario Without Cost Sharing
Figure 4 Comparison with respect to supply chain efficiency with and without cost sharing
5.2 Consumer Surplus
Table 4 Consumer surplus among CSGG, GG and NN
6 Environmental Impact
Table 5 Total carbon emissions among NN, GG and CSGG
7 Conclusions
References
Acknowledgements
Funding

Received	Accepted	Published
2021-02-20	2021-09-15	2022-06-25
Issue Date
2022-06-22

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Abstract

Key words

Cite this article

1 Introduction

2 Literature Review

3 Model Settings

Figure 1 Sequence of events

4 Equilibrium Analysis

4.1 Scenario Without Cost Sharing

Table 1 The equilibrium results across subgames GG, GN and NN without cost sharing

4.2 Scenario with Cost Sharing

**Table 2 The equilibrium outcomes under CSGG and CSGN portfolios**

**Figure 2 Comparison with respect to profits between CSGG and NN**

Figure 3 Manufacturers' and retailers' preferences towards cost sharing

Table 3 The firms' preferences over cost sharing

5 Welfare Analysis

5.1 Scenario Without Cost Sharing

Figure 4 Comparison with respect to supply chain efficiency with and without cost sharing

5.2 Consumer Surplus

**Table 4 Consumer surplus among CSGG, GG and NN**

6 Environmental Impact

Table 5 Total carbon emissions among NN, GG and CSGG

7 Conclusions

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References

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Footnotes

Acknowledgements

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Content to export

Abstract

Key words

Cite this article

1 Introduction

2 Literature Review

3 Model Settings

Figure 1 Sequence of events

4 Equilibrium Analysis

4.1 Scenario Without Cost Sharing

Table 1 The equilibrium results across subgames GG, GN and NN without cost sharing

4.2 Scenario with Cost Sharing

Table 2 The equilibrium outcomes under CSGG and CSGN portfolios

Figure 2 Comparison with respect to profits between CSGG and NN

Figure 3 Manufacturers' and retailers' preferences towards cost sharing

Table 3 The firms' preferences over cost sharing

5 Welfare Analysis

5.1 Scenario Without Cost Sharing

Figure 4 Comparison with respect to supply chain efficiency with and without cost sharing

5.2 Consumer Surplus

Table 4 Consumer surplus among CSGG, GG and NN

6 Environmental Impact

Table 5 Total carbon emissions among NN, GG and CSGG

7 Conclusions

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{{custom_sec.title}}

References

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Footnotes

Acknowledgements

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Funding

**Table 2 The equilibrium outcomes under CSGG and CSGN portfolios**

**Figure 2 Comparison with respect to profits between CSGG and NN**

**Table 4 Consumer surplus among CSGG, GG and NN**