Impact of Corporate Social Responsibility on Operations of a Live-Streaming Supply Chain

. Corporate social responsibility (CSR) is widely noticed as an essential tool for business operation and sustainable development. Meanwhile, the fercely competitive external environment and unpredictable events prompt enterprises’ cooperation to prevent supply chain collapse. We investigate the cooperative strategy in a live-streaming supply chain (LSC) consisting of a dominant brand owner, a retailer, and a live streamer, where the brand owner considers CSR by considering the welfare of stakeholders. We construct one non-cooperative and three cooperative Stackelberg game models to explore the impact of CSR on cooperative strategy and LSC operations. Te results show the following. (1) When the brand owner considers CSR, LSC members and systems are more proftable in the four models than when the brand owner does not consider CSR. (2) When the fow efect is small, the brand owner tends to cooperate with the retailer; otherwise, the brand owner prefers to cooperate with the live streamer. (3) Te grand coalition C (the brand owner cooperates with the retailer and live streamer) is the consistent strategy for the LSC system, consumers, and society. Tese fndings help enterprises recognize the importance of CSR and collaboration, thus further providing reference opinions on engaging in CSR and how to achieve collaboration.


Introduction
With the upgrade of people's consumption patterns, the livestreaming e-commerce industry has exploded, becoming a "new driver" of economic growth [1,2].According to statistics, more than 50% of the brand owners seized the new trend of Taobao Live, and the full-day live revenue during the "Double 11" was nearly 20 billion RMB.Te total scale of China's live-streaming e-commerce industry reached 1,201.2 billion RMB in 2021 and will reach 2137.3 billion RMB by 2025 [3].As an emerging social marketing method, livestreaming e-commerce has real-time interactivity, social shopping attributes, a fan economy, and a two-way infow of content and e-commerce compared to traditional ecommerce modes [4][5][6].Tis shortens the distance between marketing and trading, improves the shopping experience of consumers [1], and enriches the channels of consumer shopping, attracting more and more enterprises to join the ranks of live-streaming marketing [5,7].In practice, the typical live-streaming shopping mode is where a brand owner hires a live streamer [6].Tus, many brand owners not only started to sell their products through live-streaming channels but also retained their traditional RCs, where brand owners, live streamers, retailers, and consumers constitute the live-streaming supply chains (LSCs) [8].
In the live-streaming supply chain (LSC), the high turnover is inseparable from the "fow" of the live streamer, and the "fow" has a positive impact on the consumers' continued viewing and purchasing desire [9,10].On September 20, 2022, "Lipstick One" Li Jiaqi broadcasted live on Taobao.Without preheating and product previews, the live broadcast had 5 million views in a single half-hour session and 21 million views in a single one-hour session, with 4 products sold out in the mall, and the fnal viewership exceeded 63.5 million (https://www.thepaper.cn/newsDetail_forward_20007107, Accessed on 21 September 2022).Furthermore, we can realize that the competition between traditional retail and live-streaming channels has become increasingly ferce when brand owners hire live streamers to market products.Meanwhile, there is a spillover efect of the "fow" of the live streamers and the product display in the live room on the traditional retail channels [8,11].Positive spillover efects drive consumers to be more interested in the products, thereby expanding the demand for traditional channels.Based on this, this paper focuses on the impact of the live streamers' fow efect and the positive spillover efect on the pricing and operation strategies of LSC.
Enterprises are gradually realizing the importance of cooperation in the context of ferce competition between supply chain channels [12,13].Existing scholars have confrmed that cooperation can eliminate the negative effects of double marginalization, bring huge benefts to enterprises, and improve their competitiveness and supply chain performance [14,15].In practice, a large mobile phone brand, Xiaomi, and Youmi, a Korean smartphone retailer, have allied to expand their mobile phone market in Korea [12].Changhong, a well-known Chinese home appliance brand, has established a partnership with Suning, a famous downstream retailer [16].Several beauty brands, such as Tom Ford, YSL, Dior, Givenchy, Flower West, Perfect Diary, and Ukiss, have cooperated with live streamer Li Jiaqi to market their products with the help of live streamer's professional merchandising ability (https://www.sohu.com/a/355523279_100156659, Accessed on 23 November 2019).A more in-depth study of LSC members' cooperation motivations and strategic choices is relevant and necessary, and thus this paper flls in this work.
With the increasingly frequent live-streaming overturning incidents, consumers' awareness of environmental protection, and sustainable development concepts, enterprises have found that consumers' motivation to purchase products should include not only economic factors such as price but also social factors such as corporate social responsibility (CSR) (https://zhuanlan.zhihu.com/p/356506325,Accessed on 16 March 2023) [16][17][18].Consequently, more enterprises have released CSR reports gaining consumers' trust and cooperation opportunities with partners [19].For example, the number of CSR reports released by Chinese enterprises from 2009 to 2019 has shown an increasing trend year by year (https://fnance.sina.com.cn/esg/investment/2020-11-12/doc-iiznctke1113520.shtml,Accessed on 11 November 2020).In addition, consumers identify with and are somewhat loyal to companies that undertake CSR and are willing to actively purchase the company's products and pay higher prices [19].But there are some brand owners, such as Nike and Adidas, who have faced consumer resistance and brand reputation damage due to negatively fulflling CSR [16].Tus, brand owners as the dominant players usually implement CSR that benefts stakeholders to improve supply chain performance in LSCs [16].For instance, Hongxing Erke donated 50 million RMB of materials during the rescue of a rainstorm and food in Henan Province.As a result, the sales volume of its livestreaming room exceeded 100 million RMB (https://www.cls.cn/detail/797759, Accessed on 24 July 2021).Terefore, this paper investigates whether brand owners that engage in CSR can gain consumer recognition and greater corporate reputation and improve the operational efciency of LSC.
However, there is little related literature examining enterprises' cooperative motivations and strategic choices under considering enterprises' CSR awareness in an LSC.We consider the live streamers' fow efect and the positive spillover efect, unlike much literature that considers the live streamers' sales eforts.Terefore, this paper aims to explore the brand owner's cooperative strategies in an LSC consisting of a brand owner, a retailer, and a live streamer.In the LSC, we construct four game-theoretic models: the brand owner cooperates with the retailer and live streamer to form a centralized model (Model C), a decentralized model where each member makes their decisions (Model D), the brand owner cooperates with the retailer to form a coalition BR (Model BR), and the brand owner cooperates with the live streamer to form a coalition BL (Model BL).We try to solve the following three questions.(1) When the brand owner has CSR awareness, does the brand owner's CSR beneft each LSC member, coalition BR, coalition BL, and LSC system?(2) For the brand owner, does he prefer to collaborate with the retailer or live streamer under what conditions?(3) What is the impact of CSR on the profts of LSC, consumer surplus, and social welfare?Is there a collaborative strategy to reach a proftable multiparty situation for LSC, consumers, and society?
To solve the above three questions, we frst obtain the equilibrium solutions for four game models and analyze whether the brand owner should consider CSR.Ten, we analyze the relationship between cooperative strategies and game parameters, including the degree of the fow efect spillover efect, and the fow efect of the live streamer.Meanwhile, we compare the optimal decisions and the members' profts to explore the optimal cooperative strategy for the brand owner in the LSC.Furthermore, the impact of CSR on LSC's proft, consumer surplus, and social welfare was verifed through numerical analysis.Finally, we expand the case study to go into more qualitative depth on CSR practices and motivations.We obtain the following fndings: when the brand owner considers CSR, the profts of the brand owner, retailer, live streamer, coalition BR, coalition BL, and LSC system in the four models are higher than those when the brand owner does not consider CSR.Te brand owner tends to cooperate with the retailer when the fow efect is small.On the contrary, the brand owner prefers to cooperate with the live streamer when the fow efect is large.Moreover, when the brand owner cooperates with the retailer (live streamer), the proft of the live streamer (retailer) in coalition BR (BL) is lower than that of decentralized model D. When the brand owner cooperates with the retailer and the live streamer to form a grand coalition C, the coalition C is the consistent strategy for the LSC system, consumers, and society.
Te main contributions are as follows.First, we explore the impact of the live streamers' fow efect and the positive spillover efect considering the brand owner's CSR on the pricing and operation strategies of LSC, which is rarely discussed compared to related literature.Second, we construct four game-theoretic models to enrich the theoretical study of examining the efect of CSR on cooperation strategies for enterprises.Tis can provide suitable cooperation strategies for considering CSR and inform suggestions for live-streaming practice operational decisions.Finally, we propose a partial cooperation strategy for the brand owner.We fnd that the coalition strategy can achieve a win-win-win situation for consumers, LSC, and society.Te fndings of this paper are not only helpful to expanding research on live-streaming operations and CSR but also consistent with examples of platform operational value in practice, such as the beauty industry we expanded on in Section 5.
Te remainder of our work is structured as follows.Section 2 elaborates on the three relevant literature streams: LSC operation, supply chain cooperative strategy, and CSR in supply chains.Section 3 formulates the problem and gives model assumptions.Te equilibrium solutions are obtained for Models C, D, BR, and BL in Section 4. Section 5 analyzes and compares the optimal outcomes of the four scenarios and explores the optimal cooperative strategies of the brand owner.Te section further investigates the impact of CSR on the LSC, consumer surplus, and social welfare.In addition, a case study-the Beauty Industry-is also studied.Finally, Section 6 concludes this paper's main conclusions.

Literature Review
2.1.LSC Operation.LSC as an emerging business model has received widespread attention from enterprises, consumers, and researchers [6,9,10,20].Many scholars conducted extensive research on whether enterprises establish live-streaming channels [6,9].Zhang and Tang [6] examined the unique factors of live-streaming, such as commission rates and the number of live-streaming fans, that afect manufacturers' opening of live-streaming channels.Chen et al. [20] explored the live-streaming channel strategy for an online retailer.Ji et al. [5] gave decision makers a threshold for adopting live-streaming channels.Zhang et al. [21] studied whether to introduce live-streaming services.Pan et al. [2] found that sellers should only open live-streaming channels when the sales ability of the live streamer exceeds the time cost of consumers.Under the establishment of live-streaming channels, scholars developed a strong interest in the selection of sales models between live-streaming channels and other sales channels [1,22].Xu et al. [23] studied the manufacturer's sales modes of products directly or indirectly through the platform that provides live-streaming functionality.He et al. [24] investigated the optimal contract design for live-streaming shopping by designing three cooperation methods between retailers and live streamers.In addition, some scholars have focused on live-streaming marketing strategies based on the introduction of live-streaming channels [25].Under multichannel sales, Xin et al. [4] analyzed three e-commerce live-streaming product showcasing modes (i.e., brand self-live streaming, infuencer-led live-streaming mixture, and infuencer-led special live-streaming) and explored strategic product showcasing mode.Xie et al. [26] studied the optimal live-streaming service strategy.
Te above-existing research studies mainly focus on whether enterprises establish live-streaming channels and the selection of sales models after building live-streaming channels.Few scholars have focused on the fow efect of live streamers and the impact of spillover efects generated by the fow on the operational strategies of LSCs.Terefore, we incorporate the fow efect of a live streamer and the spillover efect into the LSC (i.e., a brand owner, a retailer, and a live streamer) to consider the operation strategy.

Supply Chain Cooperative
Strategy.Supply chain leaders tend to establish partnerships with others to cope with ferce competition and improve the efciency and competitiveness of the supply chain.Most literature considers cooperative strategies in closed-loop supply chains (CLSCs) [14,15,27].Chen and Chang [28] analyzed under what conditions original equipment manufacturers can adopt cooperative strategies by participating in remanufacturing.Jena and Sarmah [29] indicated that the global cooperative system is the best.Zheng et al. [15] and Zu-Jun et al. [27] found that collaboration can increase alliance profts and supply chain performance.Wei et al. [30] found that the manufacturer's optimal choice is to integrate the retailer and only one collector when the collection competition is intense.In green supply chains, Zhang et al. [13] found that cooperation can help increase the proft of channels or members and improve product greenness.Xie [31] believed that cooperative strategies and parameter adjustments can efectively improve the supply chain's sustainability.In addition to considering cooperative strategies in CLSCs and green supply chains, cooperative strategies in other types of supply chains have attracted scholars' attention.For instance, in a green CLSC, a model of non-cooperation among members and all possible alliance forms among members were examined [32].Leng and Parlar [33] used cooperative game theory to analyze whether there is a unique allocation scheme to save costs.In a sustainable supply chain, Liu et al. [14] studied how a retailer's fairness concerns afect cooperative strategies.
Te research on cooperative strategies for supply chain operation management mainly focuses on CLSCs, green supply chains, sustainable supply chains, etc.However, there is little literature on considering cooperative strategies in LSCs.Accordingly, our research flls this gap and explores the impact of the brand owner's CSR behavior on cooperative strategies and supply chain decisions.

CSR in Supply
Chains.CSR promotes an enterprise's brand image, enhances its social value, and afects the enterprise's supply chain performance [19,34,35].In recent years, many scholars have introduced CSR into supply chain optimization operations and focused on examining the impact of CSR behavior on pricing, collection rate, recycling, member profts, and performance [36][37][38].Panda et al. [17] focused on manufacturer exhibits of CSR to analyze the coordination of the supply chain.A contract-bargaining process was proposed to resolve channel confict and to allocate surplus proft among the channel members.Te manufacturer demonstrates CSR by using reverse channels to recycle used products collected by the retailer [18].Only when the manufacturer's CSR exceeds a certain threshold, the manufacturer's CSR benefts consumers, retailers, and supply chain systems, but it can harm the profts of leading companies [39].Te above research on CSR aims to improve stakeholders' interests (i.e., employees, customers, consumers, government, competitors, upstream and downstream partners, interest groups, etc.) by setting goals that consider maximizing consumer surplus social welfare.In this case, CSR is considered an exogenous variable.Moreover, CSR investment is an endogenous variable.Modak and Kelle [35] and Modak et al. [40] considered social donation activities, as a CSR investment, and further examined the CSR in CLSCs' operations.Liu et al. [41] examined the impact of CSR cost information asymmetry on supply chain decisions.
Te aforementioned literature has examined the impact of CSR on supply chain operations from various aspects, but much literature has not explored the impact of CSR on LSC pricing decisions, profts, and cooperative strategies in the existing literature.Tence, we incorporate the brand owner's CSR into LSC to investigate LSC's cooperative strategies.

Problem Description and Model Assumptions
We consider an LSC consisting of a brand owner (B), a retailer (R), and a live streamer (L), where the brand owner sells products through traditional retail and live-streaming channels.In the retail channel (henceforth RC), the retailer purchases products from the brand owner at a unit wholesale price w and sells products to consumers at a unit retail price p r .In the live-streaming channel (henceforth LC), the brand owner hires a live streamer to market products to consumers at a unit retail price p l .We examine possible coalitions to explore the optimal cooperative strategy based on common examples from reality.Tus, four models are constructed: the brand owner cooperates with the retailer and live streamer to form a centralized model C (Model C), each member makes their decisions to form a decentralized model D (Model D), the band owner cooperates with the retailer to form a coalition BR (Model BR), and the brand owner cooperates with the live streamer to form a coalition BL (Model BL), which are shown in Figure 1.
In Figure 1, we notice that the "pit fee F + unit commission fee m" is the most common cooperation when the brand owner hires a live streamer for product marketing (https://chinae.com.cn/mobile/art_info.php?id=11881, Accessed on 28 December 2022).For instance, Li Jiaqi and some other famous live steamers cooperate with brand owners, such as Jo Malone, MAC, and Proya (https://www.dsb.cn/199178.html,Accessed on 11 October 2022).We summarize the parameters shown in Table 1.
To make the analysis tractable, we introduce the following assumptions.
3.1.Consumer Preference.Following Ji et al. [5], Zheng et al. [15], and Zhang et al. [42], we assume that consumers'willingness to pay for a product from RC is v, which is assumed to be uniformly distributed in [0,1].However, compared to RC, consumers buy products from LC with discount value θ, θ ∈ [0,1], where the parameter θ denotes the consumers' channel acceptance, and the greater θ represents the degree of competition between RC and LC [7].Tis assumption is reasonable because consumers need to participate in the live-streaming show within a fxed time to purchase products [2].Tence, the utility of consumers from RC and LC is U r � v − p r + bf and U l � θv − p l + f, respectively [1,14,42].b represents the positive spillover efect of LC sales on the RC sales, and we assume that b ∈ [0,1], in which b � 0 means no efect, and b > 0 indicates that the LC positively afects the RC [8].
consumers will purchase a product from LC [7].Similar to Zheng et al. [15] and Yan et al. [11], we only pay attention to the coexistence of products in both RC and LC, i.e.,

CSR.
Because manufacturing enterprises usually determine the quality and function of products, fulflling CSR can establish a brand image, enhance brand value, and gain the trust and loyalty of consumers, ultimately forming a brand advantage [18].Terefore, brand owners as the dominant player typically have more initiative to undertake CSR [16].Following Zhang et al. [43], Panda et al. [17], and Panda et al. [18], we assume that brand owner's CSR is refected through their focus on consumer surplus.Consumer surplus can be expressed as CS �  [7].When the brand owner considers CSR, the brand owner's total proft consists of his pure proft and a CSR measure, i.e., V B � π B + rCS.Where r∈[0,1], r�0 implies that the brand owner is the pure proft maximizer, r∈(0,1) means that the brand owner undertakes CSR, but it is not a perfect maximization of social welfare, and r�1 represents that the brand owner is the perfect welfare maximizer [17,18].

Cost Structure.
Since the live streamer or retailer only displays products, we assume that the unit product operating cost of RC and LC is zero [21].Moreover, the production cost of products is assumed to be zero for convenience of analysis [3,6,44].
In the following part, the equilibrium demands in the four models are negative if the fow efect f is sufciently large (i.e., f ≥ f 0 ).Terefore, we focus on the case of f < f 0 throughout our paper to maintain positive equilibrium demands [21,32], where

Te Centralized Model C.
In this model, the brand owner, retailer, and live streamer adopt centralized decision making to maximize the overall benefts of the LSC to decide retail prices (i.e., p r and p l ).At this time, the objective function of the supply chain to pursue social welfare (total proft) maximization is formulated as where i ∈ N, Y { } and model CN and model CY indicate whether the brand owner considers CSR, which means that model CN and model CY, respectively, represent two scenarios: r � 0 and r ∈ (0,1].By frst-order conditions, we obtain the equilibrium results for models CN and CY, which are described in Table 2. Corollary 1 (1) indicates that as the spillover efect increases, it could increase the retail prices of RC, while the equilibrium retail prices of LC remain unchanged whether Discrete Dynamics in Nature and Society 6 Discrete Dynamics in Nature and Society the brand owner has CSR behavioral awareness.Tis means that the fow spillover efect of the live streamer has a positive spillover efect, which has prompted the retailer to increase retail prices.Corollary 1(2) presents that a higher CSR coefcient could decrease the equilibrium retail prices.Tis is because when the dominant brand owner has CSR behavioral awareness, he actively lowers retail prices to better beneft his stakeholders (i.e., retailer and live streamer), thus maximizing social welfare.Corollary 1 (3) shows that when the brand owner considers CSR, the proft of LSC is higher than that of the brand owner as a pure proft earner.

Te Decentralized Model D.
In this model, the brand owner, retailer, and live streamer play a Stackelberg game, and the brand owner considers CSR.Specifcally, the brand owner frst determines the wholesale price w and the retail price p l , and then the retailer and live streamer decide the retail price p r and unit commission fee m, respectively.Te optimal model is formulated as where i ∈ N, Y { } and model DN and model DY indicate whether the brand owner considers CSR.Following Cao et al. [7], we introduce the margin proft d � p − m of the brand owner to solve the game through reverse induction.Te optimal results are given in Table 3. Corollary 2(1) indicates how the equilibrium decisions change with the spillover efect in the decentralized model.Especially, the spillover efect has a positive efect on the wholesale and retail prices of RC, while it hurts the retail prices of LC and unit commission fees.For the RC, the retailer increases the retail prices due to the positive spillover efect of the live streamer.However, the fow overfow of the live streamer improves the competitiveness of RC while weakening the advantages of LC.Tus, in the LC, the brand owner lowers the retail price to further attract consumers.
Corollary 2(2) presents that a higher CSR coefcient could decrease the wholesale and retail prices, while it increases the commission fee in model DY.When the dominant brand owner has CSR behavioral awareness, he aims to better beneft his stakeholders, rather than pursuing proft maximization.On the one hand, the brand owner lowers wholesale prices and retail prices of LC to beneft the retailer and consumers.In this case, the retailer is willing to lower the retail price of RC to beneft consumers due to the decrease in wholesale prices.On the other hand, live streamer charges higher unit commission fee when the brand owner considers CSR, which indicates that the brand owner cares for the benefts of downstream supply chain members.Similar to Corollary 1(3), Corollary 2(3) indicates that when the brand owner considers CSR, the profts of the brand owner, retailer, live streamer, and LSC are higher than those of the brand owner as a pure proft earner.

Te Brand Owner and Retailer Form a Coalition BR.
In this model, the brand owner cooperates with the retailer to form a coalition BR, which frst decides retail prices p r and maximizes its proft.Ten, the live streamer sets its unit commission m.Te coalition model is given as Discrete Dynamics in Nature and Society )) Discrete Dynamics in Nature and Society where i ∈ N, Y { } and model BRN and model BRY indicate whether the brand owner considers the CSR.We obtain the equilibrium results for models BRN and BRY through reverse induction.We have the optimal outcomes described in Table 4. , and Corollary 3 (1) indicates how the equilibrium decisions change with the spillover efect in coalition of the brand owner and the retailer.When the brand owner cooperates with the retailer, the retail prices of RC increase with the increase of the spillover efect, while the retail prices of LC and unit commission fees decrease.Corollary 3(2) presents that a higher CSR coefcient could decrease the equilibrium retail prices, while it increases the commission fee in model BRY.When the brand owners collaborate with the retailer, the alliance BR, as the leading decision maker, has a CSR behavioral awareness that benefts stakeholders, thereby providing higher unit commissions and reducing retail prices.Corollary 3 (3) shows that when the brand owner considers CSR, the profts of coalition BR, live streamer, and LSC are higher than those of the brand owner as a pure proft earner.

Te Brand Owner and Live Streamer Form a Coalition BL.
In this model, the brand owner cooperates with the live streamer to form a coalition BL, which frst decides the wholesale price w and retail price p l to maximize its proft.Ten, the retailer determines the retail price p r .Te coalition optimal model is given as where i ∈ N, Y { } and model BLN and model BLY indicate whether the brand owner considers CSR.We obtain the equilibrium results for models BLN and BLY through reverse induction.Te optimal results are described in Table 5. ).
Corollary 4(1) indicates how the equilibrium decisions change with the spillover efect in coalition BL.When the brand owner cooperates with the live streamer, the retail prices of RC increase with the increase of the spillover efect, while the retail prices of LC and unit commission fees decrease.Corollary 4(2) presents that a higher CSR coefcient could decrease the equilibrium wholesale and retail prices, while it increases the commission fee in model BLY.When the dominant decision maker coalition BL has CSR behavioral awareness, he aims to better beneft his stakeholders, rather than pursuing proft maximization.Corollary 4 (3) shows that when the brand owner considers CSR, the profts of coalition BL, retailer, and LSC are higher than those of the brand owner as a pure proft earner.
Corollaries 1(3)-4(3) mean that in both non-cooperative strategy and three cooperative strategies, the profts of LSC members and the system are greater than those when the brand owner does not consider CSR.Tat is to say, whether the brand owner has formed a new coalition with other LSC members, LSC members and the system can always beneft from the brand owner considering CSR.Terefore, we further examine our research in the context of the brand owner's CSR behavioral awareness in the following text.For further analysis, we simplify models CY, DY, BRY, and BLY as C, D, BR, and BL, respectively.
When the brand owner considers CSR, to ensure that the brand owner's profts in models D and BR are all nonnegative, we assume that Discrete Dynamics in Nature and Society Discrete Dynamics in Nature and Society (1 + bf)/2 Discrete Dynamics in Nature and Society Tis shows that when the pit fee is too high, the profts of the brand owner are negative.Against the backdrop of ferce competition from the world, many brand owners are pinning their hopes on live-streaming shopping to increase sales.However, the high pit fees are eroding the profts of enterprises, as they need to pay the pit fees in advance, and it is unknown whether the live streamers can achieve a certain number of sales, which means that the risk is entirely borne by the enterprise.Terefore, to better expand LCs, live streamers should control their pit fees and collaborate with brand owners [24].

Comparison Analysis. In this section, by defning
and , we compare the optimal solutions of four models and obtain the following conclusions.4) Te unit commission fee in model D is higher than that in model BR, i.e., m D * > m BR * .Proposition 5 (1) indicates that in LSC, when the brand owner adopts a non-cooperative strategy, the wholesale price is higher than that when the brand owner cooperates with the live streamer (i.e., w D * > w ML * ).When the brand owner collaborates with the live streamer, they no longer need to pay a unit commission fee to the live streamer, thus increasing the brand owner's marginal proft in the LC.In this case, the brand owner strategically reduces wholesale prices in the RC, meaning that the costs saved by the brand owner in livestreaming channels will be used for the RC to stabilize its market dominance and increase its total profts.On the other hand, when the brand owner adopts a non-cooperative strategy, the brand owner, retailer, and live streamer aim to maximize their benefts, and thus the brand owner sets higher wholesale prices to strive for more profts.Similarly, when the brand owner collaborates with the retailer, from Proposition 5(4), we can fnd that the unit commission fee is lower than that when the brand owner adopts a non-cooperative strategy.

Proposition . (1) Te wholesale price in model
From Propositions 5(2) and 5(3), we fnd that the brand owner's cooperation with LSC members is benefcial for consumers because of the lower retail prices.Especially, the retail price in the grand coalition C is the lowest.When the brand owner does not cooperate with the retailer and live streamer, the retail price is the highest.In addition, compared to the coalition between the brand owner and the live streamer (retailer), when the brand owner cooperates with the retailer (live streamer), it is more conducive to reducing the retail price of the RC (LC).Tis is because when the m brand owner collaborates with a retailer or live streamer, or with both of them, he saves the retailer's unit proft or the anchor's unit commission fee.Tus, coalition BR, coalition BL, and grand coalition C lower the retail price of the RC to attract consumers, and coalition BR lowers the retail price more signifcantly, due to the coalition directly deciding on the retail price.Similarly, in the LC, coalition BL lowers the retail price more signifcantly, as coalition BL saves the commission fee.Proposition 6. (1) In the RC, the demand in coalition BR is the highest, while that in coalition BL is the lowest, i.e., Proposition 6 indicates that in LSC, cooperation between the brand owner and retailer or live streamer, as well as third-party cooperation, does not always improve market demand.Especially, when the brand owner cooperates with the retailer (live streamer), the demand of RC (LC) is highest; otherwise, the demand is lowest when the brand owner and live streamer (retailer) form a coalition.Tis means that for the RC (LC), the cooperation between the brand owner and the retailer (live streamer) is the best because the cooperation between the two parties improves the competitiveness of the channel.
From Proposition 6, when the brand owner, retailer, and live streamer form a grand coalition C, we also fnd an interesting phenomenon that the market demand is lower than that when the brand owner adopts a non-cooperative strategy.Specifcally, the collaboration among LSC members cannot attract more consumers to purchase products, and the fow efect afects the relationship between model C and model D. For the RC, when the fow efect threshold f 1 is less than the threshold f 0 and the fow efect is relatively large, the demand of RC in grand coalition C is higher than that in non-cooperative model D. If the three party members cooperate to attract more consumers to purchase products, brand owners should evaluate whether the live streamers' fow efect is within a certain range when selecting live streamers.Similar to the RC, the demand of LC has a threshold between model C and model D.

Optimal Coalition Strategy for the Brand Owner.
In this section, we frst analyze whether the brand owner has a motivation to coalition with the retailer or live streamer and how the coalition afects the profts of third-party supply chain members by comparing coalitions BR and BL with non-cooperative model D.

(2) Te third-party supply chain member (i.e., member outside the coalition group) prefers a non-cooperative model
Proposition 7 indicates that the cooperative strategy increases the proft of coalition BR or BL but is disadvantageous for enterprises that do not participate in LSC cooperation.Specifcally, when the brand owner collaborates with the retailer or live streamer, the proft and social welfare of coalition BR or BL are higher than when they do not cooperate.But the retailer or live streamer cannot beneft from a cooperative strategy.Tis is because when the brand owner and retailer or live streamer cooperate, they weaken the double marginal utility but increase the intensity of competition between retail and LCs, which cannot efectively increase the demand of the whole market.Tus, the proft of enterprises not involved in cooperation is lower than that of the non-cooperative strategy.
Next, we explore from the perspective of the brand owner who is more inclined to cooperate.Here, L represent the cooperation additional proft when the brand owner and retailer or live streamer form a coalition, respectively.

Proposition 8. For the brand owner: if
Proposition 8 indicates that the brand owner always has the motivation to ally with the retailer or live streamer.From Proposition 8, we can know that the value of this incentive is related to the spillover efect.When the fow efect threshold f 3 is less than the threshold f 0 and the fow efect is relatively small or large, the brand owner and live streamer have stronger motivation to cooperate due to achieving higher profts and social welfare; otherwise, the brand owner is more inclined to collaborate with retailer.As a result, it is clear that whether the brand owner allies with a retailer or a live streamer, coalition BR or BL reduces retail prices and drives consumers to the coalition channel, resulting in higher market demand and profts.Figure 2 intuitively illustrates the decision of whom the brand owner tends to cooperate with.
It can be seen that the brand owner always tends to cooperate with the retailer or live streamer, but the coalition is unfavorable for the third-party member, and the three parties cannot achieve a win-win-win situation.Terefore, we further compare the profts of LSC in the four models.

Proposition 9. In the LSC, we have
Proposition 9 indicates that in LSC, the brand owner's grand cooperative strategy is benefcial for increasing consumer surplus compared to the decentralized model D, coalition cooperative strategy BR, and coalition cooperative strategy BL, which improves the proft of LSC.Specifcally, when the brand owner, retailer, and live streamer form a grand coalition C, the proft of LSC is the largest.In addition, when the brand owner collaborates with the retailer or live streamer, we can draw the same conclusion as the brand owner's cooperative strategy.When the fow efect threshold f 3 is less than the threshold f 0 and the fow efect is relatively large, the proft of the LSC under coalition BL is higher than that in coalition BR; otherwise, the proft of the LSC under coalition BR is higher than that in coalition BL.Based on Proposition 7, the brand owner and retailer or live streamer have the motivation to form coalitions to increase profts and social welfare, but only through tripartite cooperation among LSC members can the benefts of the LSC be maximized.Tence, the government can formulate some incentive measures to promote tripartite cooperation, thereby achieving a win-win situation in both economic and social benefts.

Numerical Analysis of LSC, Consumer Surplus, and Social
Welfare.In this section, we further examine the impact of CSR on the proft of LSC and consumer surplus to provide a reference for enterprises and consumers by using numerical analysis.Following Cao et al. [7], Zhang et al. [21], and Zhang et al. [45], we set θ � 0.7, β � 0.5, F � 0, and f < f 0 � 0.6.Under the above parameters' settings, r varied with the range of [0,1], and the profts of LSC are shown in Figure 3.
Figure 3 shows that as the brand owner's CSR awareness increases, the profts of LSC in the four models increase.Figure 3(a) indicates that the LSC's proft in grand coalition C is always highest, followed by coalition BR when the fow efect is relatively small (i.e., f � 0.2).When the fow efect is relatively large (i.e., f � 0.4), Figure 3(b) implies that the LSC's proft in grand coalition C is always highest, followed by coalition BL.Tis means that the brand owner should form a grand coalition with the retailer and live streamer to maximize profts for LSC, followed by forming a coalition BR with the retailer when the fow efect is small or a coalition BL with the live streamer when the fow efect is large.In summary, as the leader in the LSC, brand owners should pay attention to the interests of other members of the LSC and enhance their CSR awareness.Moreover, they should establish cooperative relationships with retailers and live streamers to maximize supply chain profts.Te consumer surpluses are shown in Figure 4.
Figure 4 shows that as the brand owner's CSR awareness increases, the consumer surpluses in the four models increase.From Figure 4(a), we can fnd that the consumer surplus in model C is always highest, followed by coalition BR and then the coalition BL, and it is lowest in model D when the fow efect is relatively small (i.e., f � 0.2).When the fow efect is relatively large (i.e., f � 0.4), Figure 4(b) implies that the consumer surplus in model C is always highest, followed by coalition BL and then the coalition BR, and it is lowest in model D. Te reasons are as follows.Te CSR behavior of the brand owner lowers the retail prices to stimulate consumers to purchase products, which in turn increases the market demand.Additionally, by combining Proposition 8, we can fnd that the demands for retail and LCS and consumer surpluses in grand coalition C are highest and lowest in model D. In summary, the LSC tripartite cooperation is benefcial for consumers.
Figures 3 and 4 indicate that when the brand owner considers CSR, he cooperates with the retailer and live streamer to form a grand coalition C which is benefcial for the LSC system and consumers.Following et al. [42] and Liu and Xiao [37], social welfare can be calculated as SW � V T + CS.From Figures 3 and 4, we can fnd that social welfare is highest in grand coalition C. Terefore, it is recommended that LSC members actively cooperate in the face of ferce external environments to achieve a multiparty win-win situation for the supply chain system, consumers, and society.

Case Study.
In the 21st century, the Chinese government began to promote the CSR, and Article 5 of the new Company Law implemented in 2006 clearly stipulates that companies should "fulfll social responsibility."Tus, numerous companies started to publish CSR report under the promotion of society and government.Figure 5 shows the number of CSR reports released by Chinese enterprises.Te "green line" and "blue line" represent the number of CSR reports released in each year and linear prediction, respectively.It can be seen that the number of CSR reports by Chinese enterprises is gradually increasing.Meanwhile, the epidemic afected the sales of ofine channels of multiple categories but opened up e-commerce sales with the help of live-streaming, an online channel with strong experience and interactivity.It is worth noting that the beauty industry with strong seeding attributes has been developing rapidly by utilizing live-streaming e-commerce.Along with the rise of social e-commerce such as Xiaohongshu and TikTok, many beauty brands carry out content marketing through short videos, graphics, and other forms to efectively enhance brand awareness and trafc conversion rate.According to the Net Society, the transaction scale of China's beauty industry was around 27.8 billion RMB in 2021, with a compound annual growth rate of about 40.3%, and it is estimated that by 2027, the transaction scale will exceed 200 billion RMB (https://bg.qianzhan.com/trends/detail/506/220629-e05a3ef2.html,Accessed on 29 June 2020).Tese  Live-streaming e-commerce brings great success to beauty brands, and the reasons are divided into the following two aspects.On the one hand, a successful beauty brand pays attention to corporate CSR, such as focusing on the product itself, adhering to the concept of serving consumers frst, and paying attention to the interests of employees, the environment, society, etc.In practice, beauty brands participate in CSR strategies, as shown in Table 6.In addition, against the backdrop of global climate change, sustainable consumption and green products are gradually deepening consumer awareness.According to a survey report conducted in November 2021 by First Insight and the Baker Retail Center at the Wharton School of Business at the University of Pennsylvania, approximately 73% of Generation Z (born in 1995-2009) consumers are willing to pay a premium of over 10% for sustainable products.Te representative track of sustainable beauty, "pure beauty," is gradually moving from niche to mainstream.Moreover, the main focus of consumers on "pure beauty" is on safety and risk-free, environmental protection and low-carbon, and humanitarianism, with a proportion of 89.3%, 59.7%, and 41.1%, respectively.According to Brand Essence Market Research, the compound annual growth rate of "pure beauty" from 2020 to 2027 will reach 12%, far higher than the global beauty market growth rate.In addition, top beauty companies are increasingly paying attention to the disclosure of Environmental, Social, and Governance-related reports.From a longitudinal historical perspective, the CSR report disclosure rate of A-share beauty companies has rapidly increased from 27% in 2015 to 73% in 2021, consistently higher than the  Te brand image bonus brought by the CSR strategy continuously enhances the brand's appeal.In the process of carrying out CSR projects that deeply align with the brand image, beauty brands have achieved their public welfare aspirations while winning the emotional recognition of consumers.Tis emotional identifcation has also been transformed into stickiness towards various brands, ultimately achieving the sustainable development of the enterprises.On the other hand, beauty brands seize the opportunity of livestreaming and actively collaborate with major retailers and anchors to market products in a ferce environment.Numerous beauty brands (i.e., Estée Lauder, Lamer, 3CE, Sulwhasoo, SK-II, Elixir, Girlcult, Nars, etc.) actively cooperate with retailers, such as JD, Tmall, Taobao, and Pinduoduo, to sell products.In addition, these beauty brands would hire a live streamer to promote products.Te live streamers not only describe the characteristics and advantages of each product to consumers but also interact with viewers in the live-streaming room, thus conveying the value of the product and increasing consumers' willingness to purchase beauty products.Te beauty brands formed a coalition with live streamers, greatly increasing the brands' profts.In summary, the success of beauty brands stems from their attention to CSR and collaboration with other supply chain members, which fully demonstrates the rationality of this paper.
Overall, the focus of enterprises on CSR has become the mainstream in promoting the sustainable development of live-streaming supply chains and meeting consumers' social responsibility awareness.For example, L'Oreal's 2030 Sustainable Development Commitment proposes a strategy based on three pillars to achieve its vision of corporate social responsibility.First, it proposes self-transformation to respect the boundaries of the earth, aimed at limiting the impact of company operations on climate, water resources, biodiversity, and natural resources.Second, an empowered business ecosystem helps customers, suppliers, and consumers participate in completing the transformation, developing a labeling system for the environmental and social impact of products and allowing consumers to make purchasing choices that align with their values with sufcient information.Finally, it is necessary to provide support for the urgent needs of society and the environment, such as allocating 100 million euros for innovative investment, restoring ecosystems, developing a circular economy, and creating a 50-million-euro charity and donation fund to support vulnerable women.As we can see, many beauty brands are transforming to create more sustainable business models while contributing to addressing the challenges facing the world.To meet consumers' needs and face the transformation of consumers' shopping methods, live-streaming e-commerce is highly favored by enterprises and consumers.In the process of interacting with live streamers, consumers are more likely to recognize products with CSR attributes.In addition, it is inevitable for enterprises to actively cooperate with upstream and downstream members of the supply chain to adapt to the ferce competition context.Terefore, the CSR awareness and cooperation strategies of enterprises have become a powerful tool to achieve economic and social benefts.

Conclusions
6.1.Main Findings.In the fercely competitive environment, strengthening cooperation between enterprises and incorporating CSR into the supply chain has become an important means for enterprises to obtain high profts and improve the environment and social welfare.Tence, we consider an LSC composed of a brand owner, retailer, and live streamer.In the LSC, we build a non-cooperative strategy and three diferent cooperative strategies, i.e., the brand owner and retailer form a coalition BR, the brand owner and live streamer form a coalition BL, and LSC tripartite members form a grand coalition C. Ten we solve the four models, analyze how the fow efect and CSR parameters afect the LSC members' decisions and demands, and explore the brand owner's cooperative strategies.Te results show the following.(1) Te brand owner considers CSR to be benefcial to each LSC member, coalition BR, coalition BL, and LSC in the four models.(2) Te brand owner tends to cooperate with the retailer when the fow efect is small.Otherwise, the brand owner prefers to cooperate with the live streamer.(3) When the brand owner cooperates with the retailer and the live streamer to form a grand coalition C, coalition C is the consistent strategy for the LSC system, consumers, and society.

E. Proof of Corollary 3
From the assumptions 0 , by examining the equilibrium results, we can verify that

Table 1 :Figure 1 :
Figure 1: Te non-cooperative and cooperative models of the LSC.

Figure 5 :
Figure 5: Number of CSR reports released from 2009 to 2022.

Table 2 :
Equilibrium results for models CN and CY.

Table 3 :
Equilibrium results for models DN and DY.

Table 4 :
Equilibrium results for models BRN and BRY.

Table 5 :
Equilibrium results for models BLN and BLY.
D is higher than that in model BL, i.e., w D * > w BL * .(2)Te retail price of the RC in model D is the highest, followed by model BL, and then those under models BR and C are the lowest, i.e., l > p BL * l � p C * l .(

Table 6 :
CSR strategies of several beauty brands.