Sustaining and sharing: Optimal decisions in product-sharing platforms with green services

Abstract While some researchers consider the traditional product-sharing model in which the platform only focuses on its profits, this study considers a green-sharing mode, where the platform focuses on its profits and provides green services to consumers. We analyze the optimization problems on the pricing scheme under the traditional mode and on the pricing scheme and effort for offering green services under the green mode. We investigate how the green service implementation affects stakeholders and find that providers are always better off under the green mode. When consumers prefer the product-sharing model, the green mode can generate higher profits given that 1) the lower difference and larger cost coefficient or 2) the higher difference and smaller cost coefficient, and the traditional mode increases consumer surplus if the difference is sufficiently high. When consumers prefer the baseline model, whether the green mode brings higher profits depends on the relationship between the sensitivity degree of consumers and discount ratio, and consumers are better off under the traditional mode if the difference and discount ratio are higher. Furthermore, we establish a contract in which all stakeholders are better off under the green mode when consumers have green preferences.


Introduction
The sharing economy has created economic and sustainable values (e.g., the increase in social wellbeing and provision of economic benefits) by prompting intermediaries to easily share their products and provide product-sharing services (Laukkanen & Tura, 2020).However, these emerging business models reveal negative externalities that are at odds with the goals of sustainable economy and are usually ignored by the public (Verboven & Vanherck, 2016).For example, Uber and Lyft were accused of aggravating traffic congestion and environmental pollution (Keating, 2019), and Airbnb was considered to be the cause of rising housing prices and the increase in the local housing stock (Muñoz & Cohen, 2018).Numerous product-sharing platforms have begun to offer green services to support the sustainable economy.Thereinto, ride-hailing service platforms have become a prime candidate for green sharing modes because they started using new energy vehicles (NEVs) to achieve zero emissions; their operating models are relatively mature (Abouee-Mehrizi et al., 2021).These platforms competing with taxi platforms offer both traditional and green services, and introduce NEVs into their fleet (Mo et al., 2020).For example, Lyft brings a "Green Mode" to its app which allows consumers to specifically request a NEV (Price, 2019).Self-operated vehicles owned by Caocao Chuxing are required to be NEVs and cooperative vehicles owned by individuals in Caocao Chuxing can select fuel vehicles.This indicates that Caocao Chuxing needs to make efforts to introduce NEVs from Geely (parent company) to provide green services (Zhao et al., 2023).Uber launches Uber Green to provide green services and Uber itself can use fuel vehicles.Although Uber Green can achieve green travel by restricting drivers to use NEVs, it needs to make some efforts to help drivers pay purchase costs of NEVs (e.g., Uber committed $800 million over the next 5 years to help its drivers switch from gasoline to electric vehicles (Ohnsman, 2020)).Therefore, product-sharing platforms currently have two modes: traditional mode (e.g., cooperative vehicles in Caocao Chuxing and Uber) and green mode (e.g., self-operated vehicles owned by Caocao Chuxing, Uber Green, and Green Mode in Lyft).On the one hand, green service implementation incurs investment costs related to platforms' efforts (e.g., purchasing NEVs, building charging piles for NEVs, and subsidizing providers' losses).For example, in 2018, Zipcar ordered 325 Volkswagen E-Golfs in London for car sharing (Wentworth, 2018).On the other hand, it increases consumers' utility and the probability that consumers select this mode.This is because green products have currently attracted the interest of the public and private sectors, and consumers' environmental awareness has become a crucial factor in product consumption (Hong et al., 2019).Despite the emergence of the green mode in product-sharing platforms, no formal analysis of their operational modes has been conducted, which motivates us to do this research.
Although the OM problems of product-sharing platforms have attracted the attention of academia and industry, the following gaps remains in extant literature, which impels this study.First, the sustainable values of platforms are under-explored despite the gradual increase in the number of studies on matching problems of product-sharing platforms (Tian & Jiang, 2018;Tian et al., 2021).Specifically, some of the studies only focus on economic values and ignore social welfare and the effort for providing green services to reduce carbon emissions.Second, the distinct characteristics of product-sharing platforms (e.g., the self-scheduling capacity and intermediary platform) in sharing economy have not received enough research attention, although scholars consider the competition between traditional platforms and traditional pricing scheme in platforms (Chen et al., 2016).Moreover, we consider a discounted pricing scheme based on Caocao Chuxing's operational mode-consumers can obtain a certain percentage of discounts after services are completed, as shown in Figure 1.Similarly, Uber Green offers discounted green rides for Earth Day (Simphal, 2022) and 10% discount on green trips for members in Uber Pass (Macdonald, 2021); Meituan uses the preferential discount pricing strategy (Zhong et al., 2022).We analyze how the green service adoption of the product-sharing platforms affects stakeholders' decision-making, which has been overlooked in extant literature.To fill these gaps, this study elucidates the operational mode choice of the product-sharing platforms and answers the following research questions: How do productsharing platforms offering green services select the optimal decisions?Which mode can product more profits for product-sharing platforms?How does the green service implementation of the platform affect providers' payoffs and consumer surplus?
To answer the above research questions, we build a product-sharing model where the platform has two modes: traditional and green.In the traditional mode, the platform uses the commission contract and potential providers decide whether to join the product-sharing platform based on the reservation payment.After the total demand is observed by different parties, the platform sets the optimal price and recruitment to maximize its profits.In the green mode, the platform needs to make effort for implementing green services.Thus, the platform needs to design the optimal price, recruitment, and effort for offering green services to maximize its profits.
The contributions of this study are as follows.First, we contribute to the sharing economy literature by considering a product-sharing platform with green mode.Moreover, we enrich the research on green supply chains and apply the green mode of supply chains to product-sharing platforms.Second, this study draws some counterintuitive conclusions by incorporating the characteristics of sharing economy businesses in a competitive model and elucidates the mode choice for product-sharing platforms under different conditions.For example, offering green services is not always optimal for productsharing platforms and a crucial factor to consider is whether product-sharing platforms can bring a better experience to consumers; the price of the green mode is always higher than that of the traditional mode, which is consistent with the practice of Uber Green.Third, we design a contract where all stakeholders are better off under the green mode, which provides an effective tool for industrial practitioners and business owners to motivate consumers to patronize green services.The rest of this work is organized as follows.
Section 2 provides a literature review.Section 3 describes the baseline and product-sharing models.Section 4 analyzes the two models.Section 5 conducts the equilibrium comparison.Section 6 shows the sustainable values of the green mode.Section 7 discusses a contract design.Section 8 concludes this work.All proofs are provided in online supplementary materials.

Literature review
This study is related to the following three aspects: the choice of business model of the platform, product sharing in the operations management, and research on green technology in supply chains.Table 1 shows the differences between the relevant literature and this study.
The first stream involves the studies on the business model choice of the platform.Chen et al. (2016) study the impact of business model choice (advertising and brokerage models) on stakeholders and find dominant regions of brokerage and advertising models.Bellos et al. (2017) study the business model choice of OEM in car sharing and find that OEM can improve the fuel efficiency of cars and the car-sharing program is not always environmentally better for OEMs.Blaettchen et al. (2018) emphasize economic and operational factors and investigate the performance of different business models in durable goods.Abhishek et al. (2021) examine the interaction of the peer-to-peer rental market and OEM and find that when consumers have a lower or higher degree of heterogeneity in usage rates, both OEM and consumers will struggle on the P2P rental market.Although an increasing number of studies in OM are focusing on business model choice, this study focuses on the mode choice of product-sharing platforms and analyzes the impact of the green mode on stakeholders to indicate the optimal mode.
This study contributes to the emerging research literature on peer-to-peer product sharing in sharing economy.Tian and Jiang (2018) study how the consumer-to-consumer product sharing affects the distribution channel and investigate the feasible region of product sharing for each stakeholder.Jiang and Tian (2018) consider the C2C product sharing and investigate the impacts of product sharing on stakeholders.Benjaafar et al. (2019) establish an equilibrium model of peer-to-peer product sharing and investigate the impacts of commission rate and rental price.Tian et al. (2021) consider manufacturers' entry in the product-sharing platform and analyze the optimal entry strategy.Unlike these aforementioned papers, we consider a product-sharing platform with green services using the commission contract and the platform only acts as an intermediary enterprise and connects consumers and self-scheduling providers.Second, we analyze the sustainable values including environmental and social values, and the matching problem of platforms with green mode.
The literature on green technology in the field of supply chains involves two streams.The first is the literature on green technology innovation.Gong and Zhou (2013) focus on the dynamic production problem of a manufacturer who can select a green and regular production technology.Cohen et al. (2016) consider government subsidies for the adoption of green technology and analyze the interaction between government and suppliers in designing consumer subsidy policies.Kong and Yang (2022) study the licensing strategies for green technology under the background of platform selling.Second, this article is related to the literature on green product design.Chen (2001) develops a quality-based model to analyze green product design by considering market segments with green-conscious consumers.Hong et al. (2019) analyze the green product design in a supply chain by considering consumers' reference behaviour.Conversely, we focus more on OM of the productsharing platform instead of supply chains, consider the degree of effort for offering green services, and use a discounted pricing scheme in the green mode.

Model
We develop two platforms with multiple providers on one side and multiple consumers on the other, as shown in Figure 2. One platform, such as a taxi platform, is a baseline model in which the price is set by the government, and providers have already been hired; thus, all members will not make any decisions.The other platform is the product-sharing platform that can select two operational modes with self-scheduling providers: traditional mode, such as Uber and Lyft, which adopts the fixed commission contract (e.g., 20% commission in Uber (Zhong et al., 2022)) and offers traditional sharing services; green mode, such as Caocao Chuxing and Uber Green, which uses the discounted pricing scheme in which the platform provides consumers with a certain percentage of discounts and adopts the commission contract to connect with providers (e.g., 23% commission in Caocao Chuxing (caocao.fr/en/driver-terms-conditions/)).The platform must offer green services to attract environmentally conscious consumers to patronize green services.For convenience, we use the subscript T and N as the traditional and green modes, respectively.We explain the parameters from three perspectives: platform, consumers, and providers.Regarding the platform, k denotes the commission ratio in which some percentage of fees will be deducted from the finished services as the commission (Lin & Zhou, 2019) and p i denotes the price.Thus, a provider's payoff is w i ¼ ð1 À kÞp i : For the green mode, the platform provides a certain percentage of discount u for consumers after services are completed.We assume u þ k ! 1 for the profit function to be well behaved because p N À ð1 À uÞp N À ð1 À kÞp N !0: Moreover, the platform must determine the effort degree e and incur the corresponding cost be 2 , where b is the cost coefficient.A larger b means additional costs for the platform to be engaged in green sharing services.We can also interpret be 2 as the green investment cost.The cost function indicates that the green cost non-linearly increases in the green effort, which is consistent with the law of diminishing returns on investment (Cheng et al., 2022).A similar form of cost function is also adopted by Xu et al. (2021), Kong andYang (2022), andCheng et al. (2022).We also consider another form of the cost function in online supplementary materials and find that most of the qualitative results continue to hold.
For providers in the product-sharing model, they can only decide whether to join based on the reservation price r i that is captured by the distribution function GðÁÞ: K i denotes the mass of providers participating in the platform, i.e., the number of potential providers.Thus, in the product-sharing model, each provider will join the platform if and only if the payoff is greater than the reservation price.For providers in the baseline model, their payoffs are w 0 that will be ignored in the rest because we do not consider the competition between providers in different models; their wages are relatively fixed and their salaries are not determined by the platform (ChinaDaily, 2015).
For consumers, v 0 and v denote the perceived service value offered by the baseline and product-sharing models, respectively.We consider heterogeneous consumer valuation in the product-sharing model in online supplementary materials and find that all results remain robust.v 0 follows a uniform distribution function U½0, 1 and this type of distribution has been used in some studies (e.g., Chen et al., 2022;Yu et al., 2020b).We denote 1 as the mass of consumers patronizing the platform.Equation (1) shows consumers' utility function in the baseline model.
where p 0 is the fixed price and is not determined by the baseline platform.This setting is reasonable because, in other countries, the government regulates the taxi industry by designing a price rate (p 0 per kilometre) and the number of taxicabs (Yu et al., 2020a).Thus, we assume that p 0 is "exogenously given."Consumers' utility functions in the product-sharing model are: where c measures the sensitivity of consumers to green services and ce represents that consumers' expected utility linearly increases in the platform's effort for implementing green services.The similar practice appears in Hong et al. ( 2019) and Xu et al. (2021).When the platform does not offer green services and use the discounted pricing scheme, e ¼ 0 and u ¼ 1 in Eq. ( 3), which suggests that consumers' expected utility function is the same as that in Eq. ( 2).We model the sequence of decisions as shown in Figure 3. First, the product-sharing platform determines the price, degree of effort for offering green services under the green mode, and maximal potential capacity of providers.Second, the consumer with valuation v selects the platform and thus, the demand in each model is achieved.Third, providers decide whether to participate based on reservation payments after observing consumer demand.Consumers pay the fares and providers receive wages when services are completed.

Equilibrium analysis
For convenience, let v v 0 ¼ s: s captures the extent to which consumers prefer the product-sharing model to the baseline model.Specifically, consumers prefer the baseline model when s 2 ð0, 1Þ and the productsharing model when s !1: Similar practice is used in some literature (Lin & Zhou, 2019;Yu et al., 2020a).We consider independent consumer valuation in online supplementary materials and find that the key results remain robust.

Demand for each model
Consumers will patronize the traditional mode platform if and only if u T !0 and u T !u 0 , and they will patronize the green mode platform if and only if u N !0 and u N !u 0 : Thus, we can determine consumers' demand for each platform as follows.
Theorem 1.Given p i and e, the demand for the baseline model is D 0 ¼ m 0 ðp 0 , p i Þ and that for the product-sharing model is D i ¼ m i ðp i , p 0 Þ, where the market shares m 0 ðp 0 , p i Þ and m i ðp i , p 0 Þ satisfy: From Theorem 1, the demand for traditional mode decreases in p T but increases in p 0 , and the demand for green mode decreases in p N but increases in p 0 .This shows the substitution effect and captures the underlying competition among different models.Theorem 1 shows that zero demand may appear under these conditions, which indicates that consumers in these cases are out of the market.
To avoid the trivial cases, we do not consider these situations; therefore, we have D 0 þ D i 1: From Theorem 1 (a) and (b), some market shares remain because of D 0 þ D i < 1, which suggests that some consumers can select other channels.

Actual number of providers in each model
Let the actual number of providers in the productsharing model be k i .From Theorem 1, the demand for each mode is D i .Consequently, the actual transaction quantity Q i ¼ min k i , D i f g: Here, we do not consider the case that a provider can serve multiple times given k i < D i because we assume that consumers cannot wait; they will select other services when all providers are occupied.Thus, when k i < D i , the demand of D i À k i will be lost and the actual transaction quantity is k i ¼ D i (Yu et al., 2020a).The probability of a provider to serve a consumer is and the wage rate is w i Thus, the number of participating providers

Equilibrium strategies in each mode
First, we analyze the traditional mode and the platform's objective is to set the price and the recruitment to maximize its expected profit.Thus, we can formulate the problem as follows.s.t.
When s 2 ð0, 1Þ and p T sp 0 , and From Model (i), the equilibrium price can be derived after solving the second constraint, specific- We consider that the distribution of reservation payment r i is uniformly distributed over the range ½0, 1 to obtain the closed-form solutions.This makes us establish the following lemma.
Lemma 1.There are always equilibrium solutions that can balance the market demand and actual number of participating providers in the productsharing platform in Model (i).
Lemma 1 suggests that the equilibrium price exists under the condition of k T ¼ D T when r i , v 0 $ U½0, 1 and we must not loose the constraint in Model (i).Based on the constraint of k T ¼ D T , we can obtain the optimal price that satisfies the following theorem.max When s 2 ð0, 1Þ and p T sp 0 , : From the constraints in Model (ii), the platform can balance the demand and supply by adjusting the number of potential providers K T .Thus, K T is uniquely determined by solving the above constraints.By substituting K T back into Model (ii), we obtain the optimal price that satisfies the following theorem.
Theorem 2. Given p 0 , we have p T ¼ p 0 s 2 , p T sp 0 , From Theorem 2, the optimal price increases in the difference of consumer valuation between the two models.This is because the increase in differences suggests that more providers join the platform given s 2 ð0, 1Þ because consumers can treat different models differently with lower probability.The consumer pool advantage of the product-sharing platform has gradually increased, which can be reflected in dw T ds !0: Therefore, the platform can increase the price when the difference is gradually increasing.When s ! 1, the advantages of consumer and provider pools occupied by the product-sharing platform increase in the difference of consumer valuation between the two models.Thus, the platform can increase the price to obtain higher profits.Furthermore, we find that dK T dk !0: This is because higher payoffs will attract more providers to register on the platform.
Theorem 2 suggests that the optimal expected profit increases in the difference.This tells decision-makers to strive to reduce the difference when consumers prefer the baseline model or increase the difference when consumers prefer the product-sharing model.This is the only method for improving the profits.Theorem 2 is consistent with the fact that Uber currently pays more for consumers as the platform increases fares and commission ratio (Abiodun, 2021) when better service experience is provided.This is because consumers increasingly prefer Uber and Didi Chuxing in terms of price, efficiency, service quality, and convenience (Muoio, 2016).
Subsequently, we analyze the green mode, and the platform's objective is to select the price, effort for offering green services, and recruitment to maximize its expected profit.Thus, we can write the problem as follows.
Similar to Lemma 1, r i , v 0 $ U½0, 1 enables us to establish the following property.
Lemma 2. The green mode platform can achieve maximal profits under the condition of supply and demand balance such that k N ¼ D N .
From Lemma 2, we can obtain After verifying the Hessian matrix of the profit function Hðp N Þ, we can obtain Theorem 3. Theorem 3. Given p 0 , the equilibrium strategies in the green mode platform are: , s 2 ð0, 1Þ, > > : and From Theorem 3, we find that dp N db 0, dp N dc !0, de db !0, de dc !0, dp N db 0, and dp N dc !0 when s 2 ð0, 1Þ and s !1: dp N db 0 and de db !0 because implementing green services will incur additional costs for the product-sharing platforms as b increases.This causes a decrease in consumers' utility from the green attribute service and the loss of consumer resources.Thus, the platform with this mode has to lower the price and improve the effort degree to attract consumers to patronize.In some start-ups, although their initial move incurs a larger cost when providing green services, they increase consumers' green awareness by reducing prices and making more efforts.Theorem 3 demonstrates that consumers' green awareness positively influences services' greenness degree.If consumers are green-sensitive, the platform will increase the investment in green services to promote green consumption, which improves consumers' utility, optimal price, and platform's expected profits.We also find that de du !0 and dp N du !0 when s 2 ð0, 1Þ and s !1: This is because as the discount ratio increases, platforms will obtain more revenue; thus, they can raise more capital for offering green services.Notably, we find that p N is non-monotonic in u: 4 and b 2 c 2 4sÀ4 , 1 , otherwise, dp N du !0: When s 2 ð0, 1Þ, whether dp N du 0 or dp N du !0 depends on the relationships between u, k, s, and b.This tells decision-makers that they must consider the relationship between parameters when setting the optimal price and dynamically adjust it based on the consumers' sensitivity degree and commission ratio.

Equilibrium comparison
In this section, we compare the platform's profits, optimal price, providers' payoffs, and consumer surplus under two modes, and analyze the conditions under which the modes can generate more profits to indicate the economic value of the green mode.

Platform's profit
First, we analyze the platform's profits under the two operational modes.Proposition 1 shows the results of comparing the optimal profits.Proposition 1.The green mode generates more profits for the platform compared with the traditional mode if the following conditions hold.
When s 2 ð0, 1Þ, we can obtain the regions as shown in Figure 4(b).
Please see s 1 , s 1 , and b 1 in online supplementary materials.From Proposition 1 (a), when consumers prefer the product-sharing model, whether the platform should offer green services largely depends on the relationship between the cost coefficient and difference in consumer valuation between the two models.Figure 4(a) shows that, if the cost coefficient is larger and the difference in consumer valuation is higher, using the traditional mode is optimal.This is because the platform will incur larger costs for offering green services and make less effort when the difference is larger, decreasing the market demand and reducing the platform's profit.Therefore, the regions where the platform offering green services will always be better off when s ! 1 are ‹ the lower difference and larger cost coefficient, or › the higher difference and smaller cost coefficient.Proposition 1 (a) can effectively explain why the "Qingshan Plan" launched by Meituan has been successful.Meituan invested 500 million yuan (larger cost coefficient) to implement the "Qingshan Plan" in 2017 to solve environmental protection issues in the food delivery industry (ChinaDaily, 2020) because consumers pay more attention to green products (higher sensitivity degree of consumers) and prefer on-demand product-sharing services (Yu et al., 2020a) (lower difference between the two models).
We can consider Proposition 1 (a) as the differentiated service offered by the product-sharing platform to consumers.s 2 ðs 1 , s 1 Þ represents the car-pooling service or common chauffeur service.Although consumers enjoy better services, cheap cars will not provide them with a significant difference in service.Thus, the platform must improve effort and incur higher operating costs because this type of service has a high proportion in the market and occupies more resources.s !s 1 represents the chauffeur service for luxury cars, where consumers can enjoy exquisite services.Therefore, the platform does not need to improve its effort degree to offer green services and invest more capital to purchase luxury cars.Selecting the traditional mode is optimal when the platform with green mode must invest more money in luxury cars to improve user experience.
Proposition 1 (b) shows that when consumers prefer the baseline model, the sensitivity degree of consumers and the discount ratio will determine which mode can generate higher profits.From Figure 4(b), when both u and c are larger, the platform should select the green mode because more consumers are sensitive to green products, and setting a higher discount ratio results in fewer discounts for consumers.This tells decision-makers that when consumers prefer the baseline model, implementing green services is not always optimal.However, from Proposition 1 (b), one of the conditions under which the green mode can create higher profits is the higher discount ratio, lower sensitivity degree of consumers, and larger cost coefficient.This is counterintuitive because the green mode remains optimal when consumers are insensitive to green services and the cost of green service implementation is larger.This is because when consumers' sensitivity degree is lower, the platform must increase investment in green services in the initial move to increase their green awareness.Meanwhile, the platform can offset the excessive cost of implementing green services by setting a higher discount ratio.This is consistent with the practice that Caocao Chuxing's initial move provides cross-ruff coupons and establishes Caocao Caixuan where consumers can use these coupons to buy some goods to increase consumers' awareness of low-carbon behaviour (ChinaDaily, 2021b).

Providers' payoffs
Subsequently, we compare the optimal prices and examine providers' payoffs under the two operational modes.The result is summarized in the following proposition.
Proposition 2. The optimal price of the green mode is higher than that of the traditional mode and thus, providers are always better off under the green mode.
Proposition 2 shows that, when s 2 ð0, 1Þ, the green mode platform will have the incentive to set a price that is higher than that of the traditional mode platform.The reasons are as follows.First, the product-sharing platform has to design a higher price to compensate for the cost incurred by offering green services and strive to implement green services because consumers prefer a baseline model.Second, the platform attracts consumers by offering green services rather than a lower price.When s ! 1, the product-sharing model can bring higher consumer valuation compared with the baseline model.Thus, more providers must be hired and efforts must be increased.This enables the green mode platform to design a higher price.Proposition 2 is in line with the practice that consumers receive 15% higher rates (compared to UberX) on all Uber Green trips in London because of the "Clean Air Plan" in Uber Green (Drake, 2022).Furthermore, Proposition 2 states that providers can obtain higher payoffs when joining the green mode platform because of the commission contract.This indicates that the productsharing platforms can achieve a win-win outcome when providing green services.This result is consistent with the practice that the consumer in Uber Green must pay a $1 surcharge (sufficiently low discount ratio) and Uber Green will give drivers an extra $0.5 directly for every completed Uber Green trip, which encourages drivers to join (Berry, 2022).
According to the characteristics of the two-sided markets, consumers arrive after providers (Hagiu, 2006), which indicates that compared with the traditional mode, the green mode can easily gather providers to form a service resource pool when the platform explores a new market.Therefore, this mode enables the platform to match more consumers to rapidly occupy the market and gain a competitive advantage.This result might explain why Caocao Chuxing's expansion speed and the number of drivers on it are increasing yearly.

Consumer surplus
We investigate consumer surplus under the two modes; CS represents consumer surplus.The comparison results are summarized in Proposition 3.
Proposition 3. When s 2 ð0, 1Þ, the traditional mode can produce higher consumer surplus if the difference and discount ratio are higher.When s ! 1, the traditional mode can produce higher consumer surplus if the difference is sufficiently high.
Consumer surplus under the two modes is affected by two aspects: provider resources and service price.Because the green mode platform has more provider resources and the matching probability that consumers can be serviced is higher (positive aspect), whether CS N À CS T !0 largely depends on consumers' sensitivity to the price.From Figure 5(a), when s ! 1, consumers are always better off in the traditional mode platform if the perceived value of consumers is sufficiently high (i.e., s ! 5) and the cost coefficient is larger.This is because the larger s implies that consumers must pay higher fees ( dp N ds !0 if s is larger).Additionally, offering green services will incur high costs, which enables the platform to set higher prices and results in lower consumer surplus (negative aspect).The negative aspect dominates the positive aspect; therefore, the green mode decreases consumer surplus.We provide the relationship between consumer surplus under two models when s 2 ð0, 1Þ as shown in Figure 5(b).We find that both the larger u and s may increase consumer surplus under the traditional mode.This is because dp N ds !0 and dp N du !0 if s is larger, which may result in lower consumer surplus (negative aspect).Because the negative aspect dominates the positive aspect, the traditional mode increases consumer surplus.Proposition 3 may explain the phenomenon that Caocao Chuxing in the early stage of operation often provided better services and offered medium discount ratio to consumers to attract them to select the green service platform when settling in some cities.
Proposition 3 tells decision-makers that because the public focuses on product sharing (s !1), they should appropriately increase the perceived value of consumers when providing green services; excessive improvement of consumers' service experience may result in the loss of demand resources.We explain this result using the practice of Caocao Chuxing.Caocao Chuxing uses Maple Leaf 80 V instead of some luxury cars (e.g., Tesla and Mercedes Benz in Didi Premium) to provide green services (medium s).This makes significant differences to consumers and brings lower service prices.Thus, this practice has attracted more passengers to patronize (ChinaDaily, 2022).When product sharing is in its infancy (s 2 ð0, 1Þ), decision-makers should set appropriate discounts to subsidize consumers' fares when providing green services.The higher discount ratio may affect consumers because of higher service prices, which is consistent with the fact that Caocao Chuxing's initial move sets the medium discount ratio (e.g., u ¼ 0:1 or 0.15 in peak periods).Additionally, as the commission ratio increases, the dominant regions of both modes gradually decrease.This is because the higher commission ratio means lower payoffs of providers and providers' motivation to join the platform is weakened, thus affecting consumer surplus (Gurvich et al., 2019).

Sustainable values of the green mode
In this section, we analyze the sustainable values of the green mode by extending it to two aspects to generalize the results and seek new insights.

Social value
When product-sharing platforms have conflicts of interest with some groups, such as self-scheduling drivers, consumer rights organizations, and some government agencies, they may focus on their expected revenues and on the maximization of social welfare for sustainable development.Thus, we analyze social welfare under the two operational modes; W represents social welfare.
Under the green mode, social welfare is Similarly, we can formulate the equilibrium solutions in the traditional mode platform based on the first-order condition of By comparing W T and W N , we can obtain the following proposition.
Proposition 4. The green mode generates more social welfare compared with the traditional mode.
Proposition 4 shows that W N !W T when s 2 ð0, 1Þ and s !1: Selecting green mode can always generate positive external effects, which shows that the green mode platform can obtain higher sustainable values compared with the traditional mode (Abouee-Mehrizi et al., 2021).The intuition is as follows.First, more providers join the trading platform under the green mode compared with the traditional mode, as explained in Proposition 2.More consumers participating in the green mode platform will be matched by providers with a higher probability.Because of the greater participation by providers and the higher matching probability, more transactions that increases social welfare occur.Second, green sharing increases consumers' perceived value and attracts them.Thus, consumers are more likely to select this service, which increases the volume of transactions and social welfare.According to the 6thanniversary green development data report, Caocao Chuxing saved 534 million litres of fuel resources and reduced 1.0835 million tons of carbon emissions, which achieves positive external effects (ChinaDaily, 2021a).This practice indirectly verifies Proposition 4.

Environmental value
In this subsection, we estimate the quantity of carbon emission a consumer can save under the green mode to indicate the environmental value.Here, we take Caocao Chuxing as an example.From Caocao's website, a consumer taking NEV will reduce carbon emissions by 142 grams per kilometre, as shown in Figure 6.Because the carbon emission has a linear relationship with the distance, we consider the consumer's destination distance s 2 ð0, 1Þ and use 0.142 as the basis of calculation, i.e., C ¼ 0:142s, where C denotes the carbon emission reduction.
The fares paid by consumers include two terms: base fare F that is independent of the distance s and distance fee p N that is related to the destination (Yu et al., 2020a).For convenience, let F ¼ gp N and g !1: Under the green mode, consumers must pay p N s þ F: Therefore, the platform's objective function is By solving Model (iv), we can easily obtain the relationship between C and p N s, as shown in Figure 7. From Figure 7, although p N s increases in C, the growth rate is different in cases of s 2 ð0, 1Þ and s !1: Thus, the mileage fee will be higher in the case of s ! 1 if the carbon emissions are the same.This is because the platform incurs higher costs because of more efforts for offering green services, and setting a higher mileage fee can compensate for the excessive losses.Region 1 shows that, consumers must pay higher mileage fees under the green mode when the carbon emissions are the same to obtain a better service experience in the product-sharing platform.Based on functions of market demand, we can estimate the carbon emissions saved by the green mode after substituting p N and e into demand functions.Therefore, the total reduction in carbon emission per unit distance is C ¼ 0:284buðp 0 þsÀ1Þ 4bðsÀ1ÞuÀc 2 ðkþuÀ1Þ when s 2 ð0, 1Þ and C ¼ 0:284bp 0 su 4bðsÀ1Þsuþc 2 ð1ÀkÀuÞ when s !1:

Discussion: Contract design
Previous analysis shows that compared with the traditional mode, it is not always optimal for consumers to patronize the green mode platform.This indicates that the existing green mode might not effectively motivate consumers.A natural question is whether the product-sharing platform can establish a mechanism to enable all stakeholders to thrive under the green mode.This discussion can help platform enterprises to improve the existing business model.Here, we assume that p T is given under the green mode because the traditional mode is older than the green mode.Thus, the green mode platform can build its business model based on the traditional mode.
We consider a contract T ð, n, eÞ where the platform can slightly lower the service price to obtain more capital toward the greening efforts.Specifically, the service price is p T þ p N , where 2 ð0, 1Þ, which indicates that providers are always better off under the green mode.Because the provider's payoff is ð1 À kÞðp T þ Þ, the platform can save ð1 À kÞðp N À p T À Þ when a provider serves one consumer.For convenience, let p N À p T À ¼ n: The platform can save ð1 À kÞn, where n ¼ p T þ u À p T À : We assume that the platform will use ð1 À kÞn to subsidize the input of green services, i.e., ð1 À kÞne, and the cost of implementing green services becomes be 2 À ð1 À kÞne: The consumer's perceived value becomes u The platform's objective function is to set , e, and K N to maximize p N , which is expressed as follows. max By solving Model (v), we can derive the equilibrium solutions as follows When s 2 ð0, 1Þ, (5) Please see A 1 and A 2 in online supplementary materials.By comparing the equilibrium solutions  Proposition 5 shows that when consumers prefer the baseline model, the platform, providers, and consumers are always better off under the green mode, which indicates that using the contract T ð, n, eÞ can achieve the win-win-win outcome.When consumers prefer the product-sharing model, the green mode can generate higher profits for the platform and higher payoffs for providers.Figure 8 shows the relationship of consumer surplus between the two modes.From Figure 8, if consumers are more sensitive to green services, using the contract T ð, n, eÞ can achieve the winwin-win solution.This is because the service price increases in the consumers' sensitivity degree and the higher sensitivity degree will boost a higher price, which results in lower consumer surplus.Additionally, the effort degree increases in the consumers' sensitivity degree, which suggests that consumers with higher green sensitivity will perceive the higher value, increasing consumer surplus.Because the positive aspect dominates the negative aspect, the green mode increases consumer surplus if the sensitivity degree is higher.Proposition 5 demonstrates that the contract T ð, n, eÞ can attract more providers and consumers with higher preferences for green services regardless of which model consumers prefer.Particularly, all stakeholders are better off under the green mode when consumers have green preferences, which motivates consumers to select green services.

Concluding remarks
In this study, we consider the product-sharing platform with different modes and study the impact of green service adoption on all stakeholders.The analysis shows some relevant results: When consumers prefer the baseline model, whether the platform should offer green services largely depends on the relationship between the sensitivity degree of consumers and discount ratio.Specifically, using the green mode is optimal for the platform if the discount ratio is higher, the sensitivity degree of consumers is lower, and the cost coefficient is larger.The traditional mode can bring higher consumer surplus if the difference and discount ratio are higher.When consumers prefer the product-sharing model, the platform offering the green service will always be better off if 1) the difference is lower and the cost coefficient is larger, or 2) the difference is higher and the cost coefficient is smaller.Consumers are better off under the traditional mode if the difference is sufficiently high.Moreover, we find that the optimal price of the green mode is higher than that of the traditional mode, which indicates that providers are always better off under the green mode.This result is consistent with the practice that consumers in Uber Green must pay a surcharge.Additionally, we verify the social value of the original models and find that the green mode can bring more social welfare compared with the traditional mode.We estimate the carbon emission a consumer can save under the green mode to demonstrate the environmental value.Moreover, we establish a contract in which all stakeholders are better off under the green mode when consumers have green preferences, which motivates stakeholders to select green services.
This study has several implications.When consumers begin to prefer product-sharing platforms, decision-makers should appropriately improve the perceived value of consumers if offering green services, and an excessive increase in consumer value may result in the loss of demand resources.Because the public prefers product sharing, decision-makers should set an appropriate discount ratio to subsidize consumers' fares when conducting the discounted pricing.This is consistent with the fact that Caocao Chuxing's initial move sets the medium discount ratio.Furthermore, decision-makers should improve the green degree of the service even if larger costs might be incurred.This is because it positively influences consumers' green awareness, which can increase profits.This result is consistent with what we observe in product-sharing industries.For example, the increasing environmental awareness of consumers is driving Caocao Chuxing to upgrade the service quality of green travel to obtain more profits.
For other stakeholders, providers should join the green mode platform to seek higher payoffs.Consumers should realize that although the green mode has more provider resources and thus may increase consumer surplus, whether they are better off under this mode depends on service prices that may bring a negative effect.The above results suggest that the choice of a product-sharing platform owner may be aligned with that of other stakeholders within some thresholds, and thus a win-win-win outcome might be achieved.However, misalignment might occur in some regions where consumers struggle under the green mode.Thus, product-sharing platforms might need to subsidize consumers' fares to induce optimal operational mode participation.This insight explains why some ride-hailing platforms subsidize passengers' fares at irregular intervals to encourage them to patronize green services.
The following are some caveats about the model and some directions for future research.First, we assume that the product-sharing platform needs to make some efforts to provide green services and simplify the parameter related to the effort to e without defining it in detail.The implementation of green services can increase the expected utility of consumers and encourage consumers to buy products from some firms.Thus, the platform's effort may need to be redefined as cross-ruff coupons or subsidies.One can potentially extend our core model to analyze the joint promotion problem of cross-market by redefining the effort offered by the product-sharing platform with green services.
Second, this study focuses on a scenario where the product-sharing platform offers the green services and is responsible for matching consumers with single-homing providers.Specifically, providers on the supply side of the market can join one platform.Service providers on the supply side of the market can simultaneously join some platforms, termed multi-homing.Consequently, providers on the supply side have two options when they make decisions on joining a product-sharing platform.This results in different platform structures: both sides partially single-homing, and single-homing consumers and multi-homing providers.Therefore, another direction is to extend this study to incorporate the multihoming providers and systematically investigate the changes in equilibrium outcomes.

Figure 2 .
Figure 2. Structure of the product-sharing platform with two modes.

Figure 7 .
Figure 7. Impact of C on p N s under the green mode.

Table 1 .
Comparison of previous works with the current study.