COOPERATION CHOICE IN AN ONLINE LOW-CARBON SUPPLY CHAIN

. This paper considers the cooperation strategies in an Online Selling Low-Carbon Supply Chain (OSLCSC). The manufacturer in OSLCSC establishes an online retailing channel based on a co-operative agency sales format. Three possible online collaboration strategies are considered. We analyze the final cooperative equilibrium and find that cooperation between the platform and manufacturer can promote the dual development of environmental benefit and over-all supply chain profit. But from an individual benefit perspective, the platform and manufacturer do not always have motivation to cooperate with each other, and it related to the revenue-sharing rate and market competition intensity. Furthermore, we reveal that non-cooperation strategy does not always lead to the worst outcome, and in some cases, cooperation between the retailer and platform will result in the lowest entire supply chain performance. Lastly, the results show that each cooperative strategy may be the ultimate equilibrium, and the three players in OSLCSC could achieve a Pareto optimal under the different cooperation strategies.


Introduction
Excessive carbon emissions are accelerating global warming, and the low-carbon economy has become the trend of international economic development [1][2][3][4][5].In the Climate Ambition Summit, China proposed that by 2030, China's carbon dioxide emissions per unit of GDP will decline by more than 65% compared with 2005, and the proportion of non-fossil energy in primary energy consumption will reach about 25% [6][7][8][9].To achievement of low-carbon goals, enterprises gradually attach importance to low-carbon production, and suppliers begin to produce low-carbon raw materials with a precise reduction to achieve low-carbon transformation [10][11][12].In addition, the manufacturer actively invests in reducing research and development costs to achieve low-carbon product manufacturing.For example, China Electric Power is increasing its clean power supply and proposes to become a "world-class green and low-carbon energy supplier" by 2035.Furthermore, Sunning, as a giant of China's home appliance retail industry, actively responds to low-carbon policies through offline energy-saving and low-consumption promotion and advertising [13][14][15][16].achieve alliance equilibrium.This aspect sets our work apart from prior research on integration strategy.Third, our findings demonstrate that in the context of intense channel competition, the alliance decisions made by participants in the low-carbon supply chain can have a beneficial effect on the overall supply chain in the case of alliances between manufacturer and retailer, as well as manufacturer and platform.However, in the case of alliances between retailer and platform, the alliance may have a detrimental impact.This underscores the significance of examining the feasibility and methods of forming alliances, thus contributing to the advancement of platform theory.
This paper is organized as follows.Section 2 provides a review of relevant literature.Section 3 presents the problem assumptions and notations.Section 4 analyzes the three cooperation strategies and the non-cooperation strategy.Section 5 compares the equilibrium decisions and conducts numerical simulation and sensitivity analysis.Section 6 makes some model extensions.Finally, Section 7 summarizes the main findings and concludes the paper by providing some directions for future research.

Literature review
Our study is closely related to three research streams in literature: low-carbon investment of manufacturer, online platform operations and enterprise cooperation.Specifically, our study is the intersection of the above literature streams.To highlight the main contributions of this study, we review the previous literature most related to our research.

Low-carbon investment of manufacturer
Among supply chain managers, product design is particularly important, as it not only involves cost savings and environmental protection issues, but also affects the recycling and reuse of products at the end of the supply chain.Therefore, sufficient attention should be paid to the issue of "energy efficiency" in product design, which is a comprehensive evaluation of the product's environmental friendliness and resource utilization.Thus low-carbon product design is proposed [17,18].Low carbon product design has a significant impact on supply chain management.At present, some scholars have conducted research on green supply chain management, such as Mahato et al. [34] developed a sustainable intelligent manufacturing model to reduce waste and control pollution.Ghosh and Shah [19] studied the impact of channel structure on the greenness of products, prices, and profits of supply chain members.Barman et al. [35] aimed at developing a multi-objective supply chain inventory management, and several carbon reduction policies are considered to mitigate the influence of carbon emission by curbing amount of carbon emission.Vachon and Klassen [36] put forward the concept of green product design, and proposed two types of product design issues, including development intensive products and marginal cost intensive products.They mainly studied the impact of supply chain structure, green product types and product demand competition types on product greenness.Mondal et al. [37] developed a multi-objective mixed integer programming model to analyses the supply chain from both the economic and the environmental.Paul et al. [38] established an Economic Production Quantity (EPQ) model and considered green management.They found that by adopting green operations, the manufacturer can attract more customers to earn more profits.Conrad [39] introduced two homogeneous manufacturers to conduct a game analysis on how consumers' green preferences affect product greenness.Fanelli [22] examined two heterogeneous manufacturers, and consumers also differentiated their environmental requirements, thus conducting a game analysis on product greenness.Liu et al. [23] focused on examining the impact of manufacturers' horizontal competition level on the operation of green supply chains.Sharma and Lyer [24] proposed shortening processes in the innovation process to reduce use less materials to reach green marketing clothes at a lower price to achieve business goals and increase corporate profits.
Our work is different from the above scholars.We examine the environmental responsibility of enterprises, which means that under government carbon emission regulation, enterprises have to invest in emission reduction technologies to manufacture low-carbon products, thereby improving environmental performance.Then, unlike traditional offline channel sales, in the context of the rapid development of e-commerce platforms, we study the manufacturer sells low-carbon products through online channel, and study the two different e-commerce sales models to obtain a game equilibrium between enterprise and e-commerce platforms.

Online platform operations
With the continuous development of e-commerce, platform operation issues have become a research hotspot.In the past, scholars have conducted a lot of research on e-commerce platforms, mainly focusing on the selection selling format of e-commerce platforms [40][41][42][43] and the channel competition between e-commerce platforms and manufacturers [44,45].For example, Wei et al. [46] studied how two competing manufacturers choose the best-selling model when manufacturers can sell products on e-commerce platforms through the agency selling or reselling model.Abhishek et al. [40] used a programmatic theoretical model to answer a fundamental question faced by online retailers: when should they choose an agency-selling model instead of a more traditional reselling model?Hagiu and Wright [47] considered the role of information in model selection.They found that when marketing activities generate spillover effects between products, e-commerce platforms tend to choose reselling model.Shen et al. [48] studied how manufacturers collaborate with e-commerce platforms and traditional distributors and developed two bargaining models between the manufacturer and e-commerce platform by negotiating franchise fees and revenue sharing.Zhang and Zhang [49] claimed that when the entry cost of a supplier is small or high, the e-tailer shares information under the agency selling format while maintaining information privacy under reselling format.He et al. [41] considered the concerns of third-party platforms regarding consumer surplus in the supply chain, including tourism service providers and third-party platforms.They studied supply chain pricing strategies under three modes: agency selling, reselling, and "agency selling+reselling".Wang et al. [42] explored green logistics investment in e-commerce platforms and studied the choices of manufacturers and e-commerce platforms for agency selling and reselling modes.Liu et al. [43] investigated the sales efforts of e-commerce platforms and studied their preferences for reselling and agency selling models.
Unlike the above literature, we consider the issue of manufacturer's online dual-channel sales.The manufacturer not only sells low-carbon products through an reselling channel but also introduces an online retailer to assist him in selling low-carbon products.In our study, a competitive relationship is formed between the retailer and the platform in the market.In addition, we explore the motivation of stakeholders in the low-carbon supply chain to form partnership with others and obtain the final cooperative equilibrium.

Enterprise cooperation
The cooperation methods of supply chain entities are divided into vertical cooperation and horizontal cooperation, with vertical cooperation directions divided into upward vertical collaboration and downward vertical cooperation [50,51].Ouardighi et al. [52] explored the optimal decision-making problem of the supply chain under vertical and horizontal competition conditions.Yang et al. [53] studied vertical and horizontal cooperation between manufacturers and retailers, and the results showed that vertical cooperation could reduce carbon emissions and retail prices.Zhao [54] first investigated the vertical upward cooperative emission reduction model between manufacturers and suppliers and compared it with the optimal decision in non-cooperative models.He found that manufacturers and suppliers have higher emission reduction efforts and profits under the cooperative emission reduction model than non-cooperative models [55].Li and Chen [56] examined retailers' backward integration strategies and discussed the impact of channel integration on price and quality competition among retailers.He et al. [26] studied how the supplier producing a complementary product cooperates with other members of the supply chain system through repeated interactions.They found that when partners are willing to continue working with others who may deviate from their commitments, as long as the deviating partners accept punishment or compensation, long-term business relationships in the supply chain are more likely to be maintained as a balance.
Cooperation usually requires the collective willingness of two companies, and the studies above mainly analyse the choice of collaborative strategies from the retailer's or manufacturer's perspective.Unlike the scholars men- tioned above, we consider the motivation for cooperation from the perspective of different members and obtain the optimal cooperation strategy between supply chain players.In addition, previous research has shown that cooperation among supply chain members can improve environmental and economic performance.However, the results of this study indicate that collaboration only sometimes achieves an equilibrium between environmental and total profits, which may, in some cases, lead to damage to ecological benefits and supply chain economic performance.

Problem description
We examine a scenario in which a monopoly manufacturer (M or he) sells low-carbon products to consumers.During the production and manufacturing process, the manufacturer makes an investment in emission reduction to produce low-carbon products with an energy saving level , and sells the low-carbon products through an online platform alongside an online retailing channel operated by a retailer (R or she).The manufacturer wholesales the low-carbon products to the retailer and platform at prices   and   , respectively.By applying a revenue-sharing rate , the platform (P or it) gives the retailer a marketplace for agency selling and competes with the retailer in the market.Then, the online retailer sells the low-carbon products at a retail price   and the platform resells the low-carbon products at a retail price   .
Cooperation strategy.We propose four possible cooperation scenarios, as shown in Figure 1.The first scenario, labeled as N, represents a non-cooperation strategy, where the manufacturer, retailer, and platform independently make decisions without forming any partnership.The second scenario, labeled as MR, involves the manufacturer and retailer forming a partnership, with the entire cooperation acting as the channel leader.In the third scenario, labeled as MP, the manufacturer and platform establish a partnership and engage in a Stackelberg game with the retailer.Finally, the fourth scenario, labeled as RP, involves the retailer and platform forming a partnership and acting as a channel follower [51].
Assumption.Firstly, we assume that the low-carbon investment cost is denoted as (︀  2 )︀ /2.The investment cost function reflects that low-carbon costs increase non-linearly with increasing low-carbon effort, consistent with the law of diminishing returns on investment.Secondly, to simplify the analysis, we assume that the manufacturer's production cost is normalized to zero [57,58].In Section 6.1, we consider a scenario with a positive production cost, demonstrating that our main findings are robust.Thirdly, we assume that all stakeholders in the low-carbon supply chain are risk-neutral and aim to maximize returns [58].
Demand functions.This paper follows the studies of Wang et al. [30], Diamond and Johnson [31], and Vachon and Klassen [36], the demand functions of consumers in different channels are set as: where   represents the demand of consumers in online retailing channel, and   represents the demand of consumers from the platform.In addition,  is the energy-saving level of products, and  ∈ (0, 1) is the channel competition intensity between the platform and the retailer.With the coefficient  improves, the downstream competition will be fierce.Finally,   and   is the retail prices of formulated by the platform and retailer, respectively.
All the notations and descriptions are shown as Table 1.

Models
We proceed by establishing one non-cooperation strategy model and three cooperation strategy models.We formulate strategy model N as a benchmark scenario to contrast with other strategy models and assess the impact on profit of each player in the supply chain when the partnership is formed.The optimal decision variables and profits are then obtained by solving the four strategy models.All proofs and critical values are given in the appendix.
Hereafter, this work attaches superscripts N, MR, MP, and RP to identify the above four different cooperation strategies, "*" represents the optimal decision of low-carbon supply chain players, and subscripts M, R and P represent the manufacturer, retailer and platform, respectively.

Non-cooperation strategy N
Sequence of events in this scenario is as follows: (i) The manufacturer first determines the level of low-carbon investment effort  and the wholesale prices   ,   simultaneously; (ii) The retailer then sets the sales price   ; (iii) The platform finally decides the retail price   .Therefore, the models of strategy N are shown as follows: Proposition 4.1 summarizes the equilibrium outcomes of strategy N, which is obtained by solving the optimization problem using backward induction.Proposition 4.1.In the strategy N with the manufacturer, retailer and platform do not form a partnership: (i) The manufacturer makes the optimal low-carbon investment effort the optimal wholesale price to retailer and the optimal wholesale price to platform The retailer sets the optimal sales price The platform determines the optimal retail price

Manufacturer-retailer collaboration strategy MR
Under this circumstance, the retailer and manufacturer form partnership to determine pricing decisions.The sequence of events unfolds as follows: firstly, the partnership simultaneously determines the low-carbon investment effort level , the wholesale price   and the sales price   .Secondly, the platform decides the retail price   .As such, the optimization problem for the MR strategy can be represented as: Proposition 4.2.In the strategy MR with the manufacturer and retailer form a partnership: (i) The partnership makes the optimal low-carbon investment effort and the optimal wholesale price to platform The partnership decides the optimal sales price The platform sets the optimal retail price

Manufacturer-platform collaboration strategy MP
Under this circumstance, the platform and manufacturer form partnership to determine pricing decisions.The sequence of events unfolds as follows: firstly, the partnership simultaneously determines the low-carbon investment effort level , the wholesale price   , and the retail price   .Secondly, the retailer decides on the sales price   .As such, the models of strategy MP are shown as follows: Proposition 4.3.In the strategy MP with the manufacturer and platform form a partnership: (i) The partnership makes the optimal low-carbon investment effort and the optimal wholesale price to retailer The partnership sets the optimal retail price The retailer determines the optimal sales price

Retailer-platform collaboration strategy RP
Under this circumstance, the platform and retailer form a partnership to determine pricing decisions.The sequence of events unfolds as follows: firstly, the manufacturer simultaneously determines the low-carbon investment effort level  and the wholesale prices   ,   .Secondly, the partnership decides on the retail prices   and   .As such, the models of strategy RP are shown as follows: (i) The manufacturer makes the optimal low-carbon investment effort the optimal wholesale price to retailer and the optimal wholesale price to platform The partnership sets the optimal sales price The partnership determines the optimal retail price •

Comparative analysis
The purpose of this section is to reach a final equilibrium outcome by comparing three different cooperation strategies against strategy N, and examining the optimal cooperation strategy for each player.We are going to start by analyzing the relationships between the deciding variables in the different models of collaborating strategies.Following this, we will investigate whether the two players are motivated to form a partnership, and determine which player in the low-carbon supply chain is more inclined to cooperate from each player's perspective.Once the final equilibrium is reached, we will assess how the equilibrium affects consumer surplus and profit of low-carbon supply chain system.By comparing decision variables, we can establish Theorems 5.1 and 5.2.
Theorem 5.1.The level of low-carbon investment effort for the various strategies meets following relationships: Theorem 5.1 indicates that in strategic MP, the manufacturer will make the highest low-carbon investment effort.In this scenario, the collaborate between manufacturer and platform to sell low-carbon products can reduce the double-marginalization effect in the selling process.Therefore, the manufacturer will have a motivation to make greater emissions reduction investment, thus to promote environmental benefits.Compared to the cooperation strategy MR, the partial revenue-sharing fee paid by the partnership to the platform enables manufacturer to make a low-carbon effort lower than the cooperation strategy MP.Then, when the retailer cooperates with the platform, it can better promote the retailer's revenue level due to platform cost savings.Finally, under the non-cooperation case, each stakeholder aims to maximize their own benefits, thereby enabling the manufacturer to make the lowest emission reduction efforts, which will be detrimental to environmental and economic performances.
Theorem 5.2.The following relationships hold for the prices in different strategy models: , and , and Theorem 5.2 indicates that the manufacturer will charge retailer a higher wholesale price under strategy RP, and set a higher wholesale price for the platform under strategy MR.This is because when the retailer collaborates with platform to sell low-carbon products, they do not need to pay additional platform fees.In this case, the manufacturer sets a higher wholesale price for retailer to obtain more profits.Interestingly, although there is a high wholesale price under the strategy RP, the retailer will not increase the sales price of their products in the retail market.This is because the savings in revenue sharing expenses in cooperation with the platform can cover the wholesale cost of retailer, resulting in a lower retail price.In the strategy MP, considering the additional platform expenses and costs, the retailer will attract consumers through higher product energy efficiency levels and take the opportunity to increase prices to obtain more benefits.
In addition, from Theorem 5.2, we can see that compared to strategy RP, when manufacturer and retailer form a cooperative group, the wholesale price of the product reaches its highest.This is because in this case, the manufacturer needs to pay a portion of the platform fees, which increases his operating costs.Therefore, the manufacturer will increase the wholesale price of the platform to obtain more surplus revenue.Under the strategy MP, cooperation between manufacturers and platform can reduce the double-marginalization effect, thereby improving the sales efficiency of the channel.So, the manufacturer will make a minimum wholesale price.With the increase in wholesale prices, the retail prices of products set by the platform will also improve.

Motivate to collaborate
Next, we compare the basic model with three cooperative strategy models to investigate whether stakeholders have motivation to cooperate with other members of the low carbon supply chain.In addition, we analyse the impact of collaboration on the benefits to third party supply chain members in the low carbon supply chain.The findings of this analysis are presented in Theorems 5.3-5.5.
Theorem 5.3.Upon comparing strategy model N with strategy model MR, we observed that: (1) The manufacturer is motivated to co-operate with retailer (i.e., The following relationship holds for the profit of platform:  MR * P >  N * P .
Theorem 5.3 shows that the manufacturer always has the motivation to collaborate with the retailer to sell low-carbon products.In addition, the platform's revenue under cooperative strategy MR is also higher than that under non-cooperative strategy N.This is because cooperation can reduce the double-marginalization effect of retailing channel, allowing retailer to set the lowest market sales price and manufacturer to make a high low-carbon effort to attract potential consumers.As demand increases, the revenue of the partnership also increases.Therefore, compared to non-cooperative strategy, the manufacturer always has the motivation to reach cooperation agreements with retailer.Furthermore, we find from the results of Theorem 5.3 that cooperative strategies can not only enhance the utility of manufacturer and retailer, but also promote the performance of third-party members.The reason for this result is that under the premise of manufacturer producing products with higher energy-saving level, the increasing demand in the market promotes the profits of retailer while increasing the revenue sharing costs that the platform receives from the retailer.Despite the high prices set by the platform under the cooperation strategy MR, revenue sharing expenses from the retailer dominate and promote the platform's performance.
Theorem 5.4.In the comparison of strategy N with strategy MP, we find that: (1) The manufacturer is motivated to co-operate with platform to sell low-carbon products (i.e.,  MP * M+P >  N * M +  N * P ); (2) The following relationship holds for the profit of retailer: ). Theorem 5.4 indicates that manufacturer always chooses to collaborate with platform to sell low-carbon products.In this cooperation model, the energy efficiency of the product reaches the highest level and the retail price set by the platform is the lowest.These two factors play positive roles in consumer demand and the profits of stakeholders.The reason is that the cooperation between manufacturer and platform has improved the operational efficiency of the low-carbon supply chain, gradually weakening the dual-marginalization effect.Therefore, the manufacturer always has the motivation to form a cooperative group with the platform.
Compared to strategy N, whether the retailer can benefit from cooperation strategy MP depends on the revenue-sharing rate and channel competition intensity.Specifically, cooperation can ham the retailer's interests when the revenue-sharing rate is low and the channel competition is fierce, while collaboration helps the retailer when channel competition is weak, or the revenue-sharing rate is high and channel competition is fierce.This is easy to understand because, compared to strategy N, the price of the product is high under the cooperation strategy MP, which will put the group at a disadvantage in the sales market.However, as shown in Theorem 5.1, in this cooperative model, manufacturer makes the largest emission reduction investment and achieve the best environmental protection of their products, which will drive consumer purchasing power and promote retailer profits.With a higher platform fee, the retailer has to increase product prices to reduce operating costs.Under this collaborative strategy MP, the positive effects of higher product energy efficiency outweigh the negative effects of price increases, thereby making retailer more profitable.
However, when channel competition is fierce and revenue-sharing costs are high, the retailer prefers a state where the manufacturer and platform do not cooperate.Because in this situation, despite the high environmental pollution level of the product, the retailer can attract consumers by setting lower sales prices, thereby maximizing her profits.Obviously, this is detrimental to the development of the environment.Our research results show that companies typically sacrifice environmental benefits to achieve optimal economic benefits.The results indicate that when the revenue-sharing rate is high, a Pareto improvement (see shaded area in Fig. 2) can be achieved by all stakeholders in the low-carbon supply chain.
Theorem 5.5.Comparing strategy N and strategy RP, we find that: (1) When  ∈ (0,  2 ), the retailer lacks motivation to collaborate with the platform to sell the low-carbon product (i.e.,  RP * R+P <  N * R +  N * P ); when  ∈ ( 2 , 1), the retailer is motivated to co-operate with platform (i.e.,  RP * R+P >  N * R +  N * P ); (2) The following relationships hold for the total profit of manufacturer: ).The cooperation between the retailer and platform depends on the revenue-sharing rate.When the revenuesharing rate is high, the retailer has the motivation to cooperate with the platform.However, when the revenue sharing-rate is low, the retailer will choose the non-cooperative sales model.Obviously, when the revenue-sharing rate is high, it is wise for retailer to choose to cooperate with the platform because it can save a higher proportion of additional expenses, thereby promoting the improvement of revenue.Compared to non-cooperative strategy N, although the retail prices under cooperative strategy RP are higher, the attractiveness of higher product energy efficiency to consumers and higher platform expense costs can fully compensate for the loss of revenue caused by price increases.Therefore, cooperative marketing models will be developed between the retailer and platform.Compared to strategy N, the manufacturer's profit is also decided by the revenue-sharing rate.When the revenue-sharing rate is low, forming a partnership between retailer and platform can harm the manufacturer's total revenue.If the revenue-sharing rate is high, the manufacturer's profit can be increased through cooperation.As described above, when the retailer collaborates with platforms at a high revenue-sharing ratio, the cooperating group will achieve a higher level of revenue.With an objective return, the retailer and platform have the motivation to order more products from manufacturer.More importantly, from Theorems 5.1 and 5.2, we can see that compared to the non-cooperative model, the manufacturer charges higher wholesale prices to both retailer and platform, and makes a high emission reduction effort in the cooperation model between the retailer and platform.Therefore, the manufacturer is always profitable.When the revenue-sharing rate is low, the retailer and platform will order more products under a non-cooperative strategy.Although the manufacturer sets lower wholesale prices under cooperative strategies, due to his significant reduction in low-carbon investment costs, the manufacturer can still obtain an objective benefit.However, in this case, environmental benefits are compromised.In summary, when the revenue-sharing rate meet certain conditions, the total yield of supply chain stakeholders under the RP strategy is higher than strategy N.With this setting, a Pareto improvement can be achieved by all players in the low-carbon supply chain, as indicated by the shaded area in Figure 3.

Choosing the collaborative strategy
In this subsection, we analyze the preference of each low-carbon supply chain player towards cooperation with the other two players.Specifically, we define as the additional profit gained from a partnership between the manufacturer and retailer, while  MP * M+P =  MP * M+P −  N * M −  N * P represent the additional profit gained from cooperation between the manufacturer and platform, and  RP * R+P =  RP * R+P −  N * R −  N * P denotes the additional profit gained from a partnership between the retailer and platform.Based on this, we present the following observations.Theorem 5.6.For the manufacturer: (1) When  ∈ (0,  4 ),  MP * M+P <  MR * M+R , the manufacturer shows a stronger preference for forming a partnership with the retailer; (2) When  ∈ ( 4 , 1),  MP * M+P >  MR * M+R , the manufacturer shows a stronger preference for forming a partnership with the platform.Theorem 5.6 reveals that the incentive value is associated with the revenue-sharing rate.When the revenuesharing cost is low, the manufacturer prefers to cooperate with the retailer rather than platform.Otherwise, the manufacturer should chosen to collaborate with the platform.This is because for the manufacturer, when the revenue-sharing rate is low, he cannot receive many revenue-sharing fees when forming a cooperative group with the platform.In addition, under the cooperation strategy MP, the manufacturer has the highest lowcarbon investment cost.Therefore, the manufacturer will choose to collaborate with the retailer to reduce costs.Under the cooperative strategy MP, the product has the highest environmental friendliness, which will stimulate potential market demand.In addition, in this cooperative situation, the partnership sets a minimum retail price, which will further promote consumer utility.With the increase of revenue sharing rate, if the manufacturer chooses to cooperate with the retailer, he will have to pay a high platform fee, which is detrimental to his optimal efficiency.Therefore, the manufacturer will determine to collaborate with platforms to obtain higher revenue-sharing fees from the retailer.In summary, when the revenue share is high, the manufacturer always prefer to form a partnership with platform.Otherwise, the manufacturer prefers to collaborate with retailer to sell low-carbon products.
From Theorem 5.7, we can see that which supply chain member the retailer chooses to cooperate with depends on the intensity of channel competition and the proportion of revenue-sharing.When channel competition is fierce and the proportion of revenue-sharing is high, the retailer is more willing to cooperate with the platform to sell low-carbon products.Otherwise, the retailer is more inclined to form a cooperative group with manufacturer.This is because when the platform charges high fees to the retailer, cooperation between the retailer and the platform can save a significant amount of expenses, which is beneficial for retailer's profits.Furthermore, when the revenue-sharing ratio is low and there is strong competition between the platform and retailer, the retailer will determine to cooperate with manufacturer.The reason is that under the cooperation strategy MR, the retail channel has the lowest price and is accompanied by a higher product environmental friendliness compared to the cooperation strategy RP.For the platform, the sales price of the product under the cooperation strategy and the environmental pollution level of the product are both high, so the retailer will not have the motivation to cooperate with the platform, because this is not conducive to the retailer occupying more market share and achieving optimal returns.Similarly, when channel competition is relatively low, cooperative strategy MR is still the best choice for the retailer.In this case, the retailer can attract more consumers with lower retail prices and higher product energy efficiency.
Theorem 5.8.For the platform: (1) When  ∈ ( 3 , 1), and  ∈ (0,  6 ),  MP * M+P >  RP * R+P , the platform shows a stronger preference for forming a partnership with the manufacturer; (2) When  ∈ ( 3 , 1), and  ∈ ( 6 , 1),  MP * M+P <  RP * R+P , the platform shows a stronger preference for forming a partnership with the retailer; (3) When  ∈ (0,  3 ),  MP * M+P >  RP * R+P , the platform shows a stronger preference for forming a partnership with the manufacturer.Theorem 5.8 shows that the platform's incentive to collaborate with the manufacturer or retailer depends on both the channel competition intensity and revenue-sharing rate.When the channel competition intensity is low, the platform is more willing to cooperate with the manufacturer to alleviate the double marginalization effect and maximize the total profit.Similarly, as indicated by Theorem 5.7, Theorem 5.8 also shows that when the channel competition intensity is high while the revenue-sharing rate is low, the platform prefers to collaborate with the manufacturer to promote low-carbon products in the market, which leads to an increase in profits due to the positive effect of the relief in the strategy MP.But this positive effect of the relief weakens as the revenue share increases, causing a decrease in the platform's motivation to collaborate with the manufacturer.In conclusion, a higher revenue share is not facilitating the formation of cooperation with manufacturer, because in this situo cooperate with the retailer.

Cooperation equilibrium
Building on the aforementioned analysis, we proceed to describe the cooperation equilibrium in Theorem 5.9.
Theorem 5.9.The cooperation equilibrium is: (1) Strategy MR if and only if  ∈ (0, max(0,  4 )); (2) Strategy MP if and only if  ∈ (max(0,  4 ),  5 ); (3) Strategy RP if and only if  ∈ ( 5 , 1).Theorem 5.9 indicates that a cooperation strategy is always superior to a non-cooperation approach for all stakeholders in the low-carbon supply chain.Every cooperation strategy may be the ultimate equilibrium.In general, if the channel competition intensity is very low or very high, and if the revenue-sharing rate is low, the final cooperation equilibrium is typically the MR strategy.This retailer and manufacturer cooperative approach helps to mitigate channel competition and bolster their control over the sale of the terminal.However, if the channel competition intensity and revenue-sharing rate fall within moderate ranges, the cooperation equilibrium shifts to the MP strategy.When the channel competition intensity is high and the revenue-sharing fee is high, cooperate with the platform is the strongest incentive for retailer.The reason is that in this situation, the retailer does not have to bear higher platform expenses, which will improve her operational efficiency.Thus, the ultimate cooperation equilibrium is achieved through the collaboration between the platform and the retailer, which is illustrated in Figure 4.

Analyzing the entire low-carbon supply chain and utilities of consumers
After analyzing, it is evident the three cooperation strategies could yield profits to all low-carbon supply chain players in some cases.There is a win-win-win scenario for all stakeholders.Furthermore, any cooperation strategy could represent the ultimate equilibrium.However, firms often take into account social responsibility or fairness concerns, making it crucial to investigate effects of the ultimate balance.Consequently, we extend our examination to the effects of different cooperation strategy models on the overall low-carbon supply chain profit and consumer surplus, with the aim of offering insight and guidance to the entire industry and consumers.
Theorem 5.10.The following relationships hold for the profit of the entire low-carbon supply chain: (1) When  ∈ (0,  4 ), and  ∈ (0,  7 ), Theorem 5.10 indicates that when both the channel competition intensity and the revenue-sharing fee are low, the retailer and platform cooperate strategy will result in the lowest profit for the entire low-carbon supply chain system.When the channel competition intensity is low and the revenue-sharing cost are high, the noncooperation strategy will result in the lowest profit of the entire low-carbon supply chain system.The reason is that when channel competition intensity is low, the consumers are more inclined to purchase high energysaving products in the market, thus the demand for low greenness products will be divided.Additionally, the decentralized decision-making of stakeholders in the low-carbon supply chain will lead to an increase of double marginalization effect and a lower product's environmental friendliness, and eventually cause a loss of total benefits.On the contrary, when the revenue-sharing rate is high and channel competition is weak, the higher operational efficiency under the cooperative strategy MP enables supply chain members to make decisions that promote both economic and environmental performance.In this situation of high revenue sharing, although retailer can save a significant portion of platform fees by collaborating with platforms, her higher product prices will result in a loss of market demand.
When the channel competition intensity is high, the profit of the entire low-carbon supply chain is the highest under the cooperation strategy MP, followed by strategy MR, then strategy N, and finally, strategy RP.In this case, cooperation among stakeholders in the low-carbon supply chain is not always better than decentralized decision-making.Compared to the non-cooperative strategy N, the retail price of the product is higher under the cooperative strategy RP, which is not conducive to stimulating market demand.Moreover, when competition between channels is more intense, the lower energy efficiency of products under cooperation between retailer and platform will put the cooperating group at a disadvantage.However, under the cooperative strategy MP, the manufacturer makes the greatest efforts to reduce emissions and the platform sets the most favorable sales prices, which is beneficial for the cooperative group to occupy more markets in the fierce competition.At this point, as consumer utility increases, market demand and revenue will also increase.The relationships among the profits of the entire low-carbon supply chain system under the four strategy models are represented in Figure 5.
Theorem 5.11.The following relationship holds for the consumers' utilities in different cooperation strategy models: Theorem 5.11 shows that when the manufacturer and platform form a partnership, the consumer's utility reaches a maximum, while it will achieve a minimum when there is no cooperation between each stakeholder.As shown in Theorem 5.1, the energy efficiency of products is highest under cooperation strategy MP and achieves lowest under non-cooperation strategy N. Higher product energy-saving levels can lead to higher consumer satisfaction.In addition, the retailer and platform make the lowest selling price under cooperation strategies MP and MR, which are beneficial for improving consumer's utility.Compared to non-cooperation, the cooperation between stakeholders could reduce the double-marginalization effect in selling channel and make the partnership more efficient.However, the collaboration between the platform and retailer alleviates horizontal channel conflicts by increasing the retail prices and reducing product energy efficiency, which exacerbates the vertical double-marginalization effect and serious damages the interests of the consumers.Thus, the consumer surplus under this case is lower than the cooperation strategies MP and MR.

Extensions
In this section, we aim to gain additional insights by relaxing the assumption made in our main model.We have provided a detailed analysis of these assumptions in the follows.

A positive cost of production for the manufacturer
In the models above, we previously assumed that the manufacturer's cost of production was zero.However, this assumption is relaxed and positive production costs are considered in this section.Assume that a cost incurred by manufacturer is  in the production of a product, and denoted by the superscript "C".Accordingly, we can formulate the corresponding problems as follows, with further details presented in the subsequent sections.
The profit functions in the strategy non-cooperation (referred to as strategy N-C) can be expressed as: (6.1) Proposition 6.1 summarizes the equilibrium outcomes of strategy N-C, which is obtained by solving the optimization problem using backward induction.Proposition 6.1.In the strategy N-C with the manufacturer, retailer and platform do not form a partnership: (i) The manufacturer makes the optimal low-carbon investment effort the optimal wholesale price to retailer and the optimal wholesale price to platform The retailer sets the optimal sales price The platform determines the optimal retail price where )︂  6 − 4 2 ( − 1) )︂ Under the strategy retailer-manufacturer cooperation (referred to as strategy MR-C),the profit functions can be expressed as: and the optimal wholesale price to platform The partnership decides the optimal sales price The platform sets the optimal retail price • Under the strategy platform-manufacturer cooperation (referred to as strategy MP-C), the profit functions can be expressed as: Proposition 6.3.In the strategy MP-C with the manufacturer and platform form a partnership: (i) The partnership makes the optimal low-carbon investment effort and the optimal wholesale price to retailer The partnership sets the optimal retail price The retailer determines the optimal sales price Under the strategy retailer-platform cooperation (referred to as strategy RP-C), the profit functions can be expressed as: Proposition 6.4.In the strategy RP-C with the retailer and platform form a partnership: (i) The manufacturer makes the optimal low-carbon investment effort the optimal wholesale price to retailer and the optimal wholesale price to platform The partnership sets the optimal sales price The partnership determines the optimal retail price We present the optimal solutions for the four models.Through comparing the profits obtained from these solutions, we obtain the cooperation equilibrium, as stated in Theorem 6.1.Theorem 6.1.The cooperative equilibrium is: (1) Strategy MR if and only if  ∈ (0, max(0,  9 )); (2) Strategy MP if and only if  ∈ (max(0,  9 ),  10 ); (3) Strategy RP if and only if  ∈ ( 10 , 1).From Theorem 6.1, it can be seen that when the production cost of the manufacturer is positive, the final cooperation equilibrium is consistent with the result of Theorem 5.9, indicating that our basic model is robust.The equilibrium cooperation strategies between the manufacturer, retailer, and platform are determined by different factors.Firstly, when the revenue-sharing rate is low, the equilibrium is a cooperation strategy between the manufacturer and retailer.Secondly, when channel competition is fierce and the revenue-sharing rate is high, the equilibrium is a cooperation strategy between the retailer and platform.Thirdly, when the revenuesharing rate is at a moderate level but the channel competition is weak, the cooperation strategy between the manufacturer and platform is optimal.Theorem 6.1 suggests that non-cooperation is never the ultimate equilibrium as the cooperation strategies generate added value to the low-carbon supply chain players.The quantitative analysis reveals this equilibrium region of MR and MP gradually decreases as the manufacturer's production cost increases.When production costs are relatively high, the manufacturer loses market sales advantage, and the retailer and platform do not cooperate with the manufacturer.Moreover, due to high production costs, the manufacturer sets high wholesale and retail prices in the market.Figure 6 shows the cooperation equilibrium with  = 0.4 [40,58].

Findings of this paper
This paper investigates cooperation strategies in OSLCSC under the context of rapid development of ecommerce platforms.We examine the motivation of stakeholders to cooperate with each other by establishing game models under four types of collaborations, with the non-cooperation strategy as the benchmark case.Based on the possibility of forming partnerships between any two stakeholders, we further explore the incentive value of partnerships from each stakeholder's perspective and derive the optimal cooperation strategy.Expanding on the primary models, we examine the case of positive manufacturing costs.Our findings indicate that from an environmental perspective, cooperative strategies can always promote the improvement of environmental benefits compared to non-cooperative strategy.However, from the perspective of benefits of entire supply chain system, cooperation strategies are not always optimal, especially when channel competition is fierce, or when the channel competition is weak and the profit sharing rate is low, cooperation between retailer and platform will result in the lowest profit for the supply chain system.Furthermore, compared to the other three strategies, cooperate between the manufacturer and platform will achieve optimal environmental benefits, overall supply chain performance, and consumer utility, while from the perspective of individual profit of manufacturer, only when the proportion of revenue-sharing is high, can he have a motivation to cooperate with the platform, and from the perspective of individual profit of platform, the platform will not choose to cooperate with manufacturer, but rather prefer to cooperate with retailer under the cases of fierce channel competition and high proportion of revenue-sharing.Finally, the results show that compared to the non-cooperative strategy N, the manufacturer always willing to cooperate with the retailer and platform, and whether a partnership will be formed between the retailer and platform mainly depends on the proportion of revenue-sharing.Specifically, when platform fees are high, the retailer and platform have the motivation to cooperate with each other.Otherwise, the non-cooperative strategy will make both stakeholders more profitable.

Theoretical and managerial implications
This study offers valuable insights for managers to improve the environmental performance and selling strategies of low-carbon supply chain.Firstly, stakeholder cooperation is crucial and can create win-win-win solutions that improve profitability.However, it is important to note that cooperation does not always positively impact the environment, and cooperation strategies may harm the environment if the minimum carbon reduction investment effort is not met.Additionally, although cooperation between the retailer and platform can generate high environmental benefits compared to non-cooperation strategy, it only benefits entire profit of low-carbon when the channel competition is weak and the revenue-sharing rate is high.Therefore, balancing environmental and economic development is necessary when implementing cooperation promotions among stake-holders.Secondly, online platform managers should not always partner with the online retailer to sell low-carbon products in the market.This strategy is only effective when the revenue-sharing rate is high.Thirdly, the revenue-sharing rate is an essential factor for cooperation equilibrium.Although it can alleviate channel conflicts between the platform and retailer, it may enhance dual-marginalization effect.Thus, platform administrators need to adjust this revenue share proportion promptly based on their situation to guide other players in the low-carbon supply chain to form partnerships.Lastly, a positive production cost of manufacturer will not affect the optimal cooperation strategy selection.Therefore, enterprises can establish stable cooperative relationships and seek long-term benefits in OSLCSC.

Limitations of the research and future research directions
Future research can explore several limitations to our model.Firstly, the current assumption is that the supply chain players are risk-neutral, while future research can consider that each interest subject is risk-averse.Secondly, the manufacturer mainly sells low-carbon products through online reselling format, but future scholars can focus on agency/direct selling formats to study how the manufacturer can formulate optimal emission

Figure 1 .
Figure 1.Cooperation structures.(a) Non-cooperation strategy N. (b) The cooperation strategy MR.(c) The cooperation strategy MP.(d) The cooperation strategy RP.

( 4 . 8 )
Proposition 4.4.In the strategy RP with the retailer and platform form a partnership:

Figure 2 .
Figure 2. Pareto region of cooperation strategy MP.

Figure 3 .
Figure 3. Pareto region of cooperation strategy RP.

Figure 5 .
Figure 5. Orders of profit for the entire low-carbon supply chain.

Figure 6 .
Figure 6.Cooperation equilibrium with a positive cost.

Table 1 .
List of notations.