Sustainable Operation Mode Choices for Second-Hand Inspection Platforms

Abstract

The sale of second-hand goods has formed a complete industrial chain, and second-hand product testing is a crucial part of it. Second-hand inspection platforms (SIPs) have achieved remarkable commercial success by providing inspection services that alleviate consumers’ quality concerns. Different SIPs typically adopt various operation modes, such as consignment, resale, or hybrid modes. Appropriate operation modes not only benefit SIPs in maintaining profitability but also contribute to the sustainable development of the sharing economy. In order to realize the sustainable operation of second-hand inspection platforms, we construct a platform-dominated Stackelberg model to explore the motivations behind SIPs’ choices of different operation modes and investigate the impacts of changes in the inspection service level on the platform’s optimal decisions and market performance. System data analysis results show that the cost of guarantee significantly influences SIPs’ choices of operation modes, specifically; SIPs are inclined to adopt consignment mode or resale mode when the cost of guarantee is relatively high or low, respectively, and choose hybrid mode when the cost of guarantee is moderate. Furthermore, in the presence of inter-channel competition, if the inspection failure loss is relatively high, SIPs may lower the prices of used products as the inspection service level increases. Additionally, although inspection service can disclose the true quality of used products, a higher inspection service level may attract more low-quality sellers into the market when the inspection failure loss is substantial. Finally, under the resale mode, consumer surplus and social welfare will decrease with the inspection service level. Conversely, under the consignment or hybrid mode, both consumer surplus and social welfare will increase with the inspection service level when the inspection failure loss is relatively low.

1. Introduction

In recent years, the global economy is experiencing a downturn due to a complex mix of factors. On the contrary, the online second-hand market is bucking the trend and showing a thriving situation. GlobalData’s report on U.S.-based second-hand e-commerce giant ThredUp shows that total global second-hand clothing sales will increase by 18% in 2023 compared to 2022 to reach USD 197 billion, and the global second-hand clothing market is projected to reach USD 350 billion by 2028 (see globaldata.com). According to the “Used Recycling Insight Report (Q2 2024)” by Zhuanzhuan, a leading platform for second-hand consumer electronics in China, the market for second-hand electronics in China continues to heat up, with the platform’s Q2 sales orders up 35% year-on-year, and recycling orders up 42% year-on-year (see zhuanzhuan.com). eBay noted in its “E-Commerce Report 2024” that young people across the globe are particularly enthusiastic about the circular economy, with over 90% of millennials being particularly interested in recycling enthusiastically, with over 90% of millennial and gen Z sellers saying they value eBay’s ability to keep items out of landfills (see ebayinc.com). There is no doubt that the topic of online second-hand marketplaces will be a constant focus of attention, both now and in the future.

As an important channel for individuals to redeploy their assets, the online second-hand market facilitates sellers to transfer unused products to other people in need, and also enables buyers to save money compared to purchasing new products. However, in the traditional online second-hand market, the non-standardization of used products and information asymmetry often cause buyers to experience a poor purchasing experience when the expected quality of used products deviates from the real quality [1]. In recent years, in order to alleviate buyers’ quality concerns, some second-hand e-commerce platforms have begun to provide customers with inspection services for used products, including setting quality standards for used products as well as testing the authenticity of products [2]. The introduction of inspection services has bolstered buyer confidence in used products and has contributed to significant commercial success for these platforms.

In practice, the operation modes adopted by mainstream SIPs vary significantly, e.g., StockX and RealReal utilize the consignment mode, while ATRnew and PaiPai employ the resale mode, and Zhuanzhuan and Xianyu implement the hybrid mode. We summarize the differences among the three modes as follows: First, the ownership and pricing authority of used products are different. Under the consignment mode, the seller owns the used product and can therefore set its own price. Under the resale mode, the platform makes an offer to the seller to take ownership of the used product, and then sells it to the buyer at the resale price. Under the hybrid mode, the platform operates both the consignment channel and the resale channel, and the ownership and pricing of used products under both channels are similar to those in the consignment and resale modes, respectively. Second, the platform provides different protection services. For used products owned by platforms, platforms often provide guarantees for them, which are not available for products from individual sellers. Therefore, buyers have a higher expected value for the platform’s products. Finally, the degree of competition is different. Under the consignment mode, all individual sellers compete with each other. Under the resale mode, the platform mitigates competition among sellers by setting a recycling price [3]. Under the hybrid mode, sellers in the consignment channel compete with each other while facing competition with products from the platform [4]. Interestingly, we observe that, in addition to different platforms adopting different operation modes, the same platform may also experience shifts in its operation mode over time. For example, Poizon and eBay initially adopted the consignment mode and are now shifting to the hybrid mode. Thus, the motivations behind the platform’s choice among these alternative modes naturally emerge as a significant issue worth exploring.

Platforms need to make trade-offs when it comes to the choice of operation modes. Under the consignment mode, buyers are mainly influenced by the inspection service level when making purchase decisions. On the one hand, the higher inspection service level correlates with increased customer perceived value. On the other hand, the higher inspection service level may lead to supply-side contraction, as low-quality sellers are excluded from the market when they fail to pass the inspection. In the resale mode, platforms provide guarantees for used products, giving buyers a higher perceived value for their products compared to the consignment mode. Additionally, acquiring ownership of the products allows the platform greater flexibility in increasing the unit price of used products. However, the platform must bear the cost of the guarantee, while also potentially facing a decline in buyer demand. Under the hybrid mode, platforms need to consider not only the trade-offs inherent in each individual channel but must also account for competition between channels. Consequently, in order to achieve higher profitability, the platform must exercise greater caution in setting transaction fees within the consignment channel, as well as in determining the recycling price, resale price, and penalty within the resale channel.

The issue of operation mode selection for e-commerce platforms has been widely explored by academics. Scholars have conducted a series of discussions on the impact of different factors (e.g., consumer valuation uncertainty, downstream competition intensity, order fulfillment costs, quality uncertainty, additional services, differentiated products, carbon emissions, and customer returns) on the selection of the optimal operation mode for e-commerce platforms in a variety of business contexts [3,5,6,7,8,9,10,11]. However, these studies mainly focus on manufacturers or new product e-tailers, and relatively few studies have been conducted on second-hand platforms. In addition, the issue of applying emerging technologies (e.g., blockchain and AI technologies) to alleviate consumer quality concerns in online second-hand marketplaces is also addressed by existing studies [2,12,13,14,15,16], which focus on the impact of supply chain structure on the adoption of emerging technologies and the associated pricing issues. However, the inspection service, which has emerged in the online second-hand market in recent years, has received limited attention despite some studies having demonstrated that it can significantly benefit the second-hand marketplace. In order to fill the gap of the existing research, this paper will study the role of inspection services on the decision-making of second-hand platforms’ operation modes from the perspective of SIPs, and explore how the inspection services affect second-hand transactions as well as consumer surplus and social welfare under different operation modes. Specifically, we will try to answer the following questions:

(1) What are the differences between SIPs’ equilibrium results under different operation modes?

(2) What is the optimal operation mode strategy for SIPs?

(3) How do inspection services affect SIPs’ equilibrium strategies and used products sales under different operation modes?

(4) How do SIPs’ operation mode strategy and inspection service level affect consumer surplus and social welfare?

To answer the above questions, we consider a supply chain including an SIP, an individual buyer, and a seller. The goal of the SIP is to maximize its profit, while the buyer and seller decide their buying or selling decisions, respectively, based on the net utilities. We first derive the optimal decisions and maximum profits for the platform under various operation modes through backward induction. Subsequently, we compare the equilibrium results under different modes and explore the platform’s optimal operation mode choices. In addition, we examine the effect of inspection service level on the platform’s optimal decisions and maximum profit. Finally, we investigate the specific impact of inspection service level on consumer surplus and social welfare under different operation modes.

The main findings are as follows:

(1) Despite the inter-channel competition in the hybrid mode, the price of used products may be higher than in the other two modes, depending on the cost of guarantee, which also influences the transaction fee, recycle price, and optimal sales. In addition, penalties charged by platforms vary under different modes. (2) The platform’s choice of optimal operation mode depends on the cost of the guarantee. (3) A higher inspection service level may lead to lower profit, sales, transaction fees, and penalties but increase the recycling price. (4) An increase in the inspection service level may reduce consumer surplus and social welfare.

The rest of this paper is organized as follows. Section 2 briefly reviews the relevant literature. Section 3 develops the analytical model and Section 4 analyzes the equilibrium results. Section 6 examines and analyzes the impact of inspection service level on consumer surplus and social welfare under different operation modes. Section 6 summarizes conclusions and points to future research directions. All proofs are presented in Appendix A.

2. Literature Review

This paper is mainly related to three research directions: (1) online second-hand marketplace, (2) authentication techniques under quality uncertainty, and (3) platform operation modes.

2.1. Online Second-Hand Markets

Research on online second-hand markets has primarily focused on two key areas. First, the impact of online second-hand markets on primary markets. For example, Yin et al. [17] explore the product upgrading and retail pricing strategies of durable product manufacturers in the presence of multiple second-hand marketplaces. Feng et al. [18] show that the presence of second-hand platforms usually reduces the total production volume of firms, but the percentage of service fees charged by the platforms has a positive impact. In cases wherein product quality can be determined endogenously, the presence of second-hand marketplaces may be beneficial to firms and ultimately improve product quality. Zhu et al. [19] study the optimal pricing strategy of e-commerce retailers when offering installment services in a competitive environment where P2P (person-to-person) second-hand marketplaces exist. The results show that retailers need to increase the selling price and reduce the installment service fee when facing competition from P2P marketplaces. Zha et al. [20] find that the introduction of a second-hand marketplace affects a manufacturer’s pricing strategy. The introduction of a second-hand market is never optimal when the retail price of used products is very low, but may be beneficial in other cases, depending on the unit production cost of the new product. In these studies, channel competition in the second-hand market is not considered, which is precisely the focus of our research, i.e., the hybrid mode in which used products from the consignment and resale channels compete with each other.

Second, the research has focused on the factors that affect the operational performance of online second-hand markets. For example, Chen et al. [21] designed a text analytics framework to assess the reputation of second-hand sellers. The conclusion shows that helping potential buyers to prejudge the reputation of second-hand sellers when making purchasing decisions can be more effective in developing online second-hand marketplaces. Esenduran et al. [22] investigated the relevant factors affecting consumers’ resale channel choices in the context of tripartite competition among OEMs, independent third parties, and online second-hand platforms, and noted that price, payment time, online ratings, and data security policies influence consumers’ choice of different channels to varying degrees. Hur [23], in an investigation of the UK second-hand clothing market, found that non-consumers have concerns about the consumption of second-hand clothing, including the quality and cleanliness of the product, the constraints on self-improvement and expression of self-identity, and concerns about social image. Moriuchi and Takahashi [24] examine how consumers’ perceived value, trust, and engagement with second-hand products in an electronic second-hand marketplace affect their willingness to repurchase. In contrast to these studies, we investigate how the application of inspection services, from the perspective of online second-hand platforms, affects the platforms’ strategic decisions regarding their operation modes. In addition, we analyze the performance related to second-hand transactions under different operation modes.

2.2. Authentication Techniques Under Quality Uncertainty

Several scholars have investigated the impact of authentication techniques on product sales. For example, Shen et al. [14] explore how permission blockchain technology (PBT) can help brand name companies (BNCs) fight counterfeits in their supply chains and analyze the value of PBT for BNCs. The study shows that, although the implementation of PBT helps primary consumers to recognize the authenticity and quality of products, selling products through PBT retailers can only be effective in combating counterfeits if the number of primary consumers is large enough. Li et al.’s [2] study suggests that inspection services can help to solve the problem of asymmetric information about the authenticity and quality of products on an online C2C (Consumer-to-Consumer) e-commerce platform. Their findings suggest that such services not only modify the structure of signaling games to incentivize sellers of products with a higher probability of authenticity to sell through the platform, but also assist the platform in eliminating seller information rents, thereby generating additional revenue. Our study is similar to that of Li et al. [2], with the difference that, in our study, the inspection service discloses not only the authenticity information of the used products, but also the status information. In addition, unlike the blockchain technology literature which assumes that blockchain can perfectly disclose product information [12,13,14,16], we hypothesize that inspection services cannot disclose information perfectly due to the non-standardized characteristics of used products.

Others scholars focus on the selection of authentication techniques; for example, Basu et al. [25] explore searching and authentication strategies in online matching platforms, where the platform’s optimal pricing strategy suggests that the complementary nature of the searching and authentication services can justify the platform’s use of the authentication service as a loss leader strategy. Pun et al. [26] examine the platform’s use of blockchain technology or pricing strategies to prove product authenticity. The results show that the use of blockchain should be adopted when the quality of the counterfeit product is medium or when consumers have medium level of distrust in the market product. And if the government provides subsidies, blockchain is more effective than differential pricing strategies and better eliminates post-purchase regret. Li et al. [12] explored the use of manual technology authentication and blockchain technology authentication in authentication strategies for luxury e-commerce platforms and indicated that the platforms’ choice of authentication technology depended on the cost of the authentication between manual technology authentication and blockchain technology authentication difference. Xu and He [16] showed that retail platforms are more likely to disclose quality information via blockchain technology when it can significantly increase consumers’ willingness to pay. Basu et al.’s [27] study of online service matching platforms suggests that the platforms’ provision of consulting services and authentication services depends on the market’s overall quality and match seekers’ preferences. When the platform’s counselling capacity is low, increasing counselling capacity can add value to certification services; however, when counselling capacity is high, counselling and certification services may substitute each other. This paper differs from these studies mainly in that we consider the substitution relationship between quality assurance guarantee and inspection service, rather than the selection of authentication techniques. In addition, we focus on the impact of inspection services on choices of operation modes of SIPs, which is not covered in the above literature.

2.3. Platform Operation Modes

The topic of platform operation modes has been widely discussed in academia, and scholars have studied how online platforms choose different operation modes according to the market environment and their own conditions. For example, Tian et al. [3] studied and analyzed the impact of different operation modes on the profits of intermediaries (online retailers) and suppliers (product sellers), and how to choose the optimal model based on the intensity of competition among suppliers and the cost of order fulfilment. Xu et al. [28] analyzed three different operation modes on the profitability of supply chain members. It is found that, under certain conditions, the reselling model and the selling plus service model can generate the most profit for both e-platform owners and used product suppliers. Zhang et al. [11] considered how dominant suppliers and follower e-platforms can choose the optimal online distribution model for two differentiated products, that is, reselling or marketplace. The results show that vendors tend to sell low-cost, high market potential, and highly substitutable products through the marketplace model, while platforms prefer to sell these products through the reselling model. Li et al. [29] investigated how the recycling platform can improve profitability by choosing the optimal online recycling strategy based on heterogeneity of different consumer groups to increase profits. The results show that the recycling strategy depends on the quality depreciation factor of the used and refurbished products and the value of the new product. Hao and Yang [30] explored the selection of sales model and pricing strategy in a live sales supply chain by modelling live sales. They found that the resale mode may become a better choice for platforms and suppliers when considering consumer returns. Zeng et al. [4] developed a two-period model to explore the choices of third-party platforms (TPs) and retailer-established platforms (RPs) in choosing to implement the C2B2C (Customer to Business to Customer) model with their strategies and their impact. The results show that both TPs and RPs implement the C2B2C model when the refurbishment cost of unused products is not high, but TPs prefer to implement the C2B2C model. In addition, when implementing the C2B2C model, RPs may reduce the service level of C2C transactions, while TPs may reduce the C2C transaction fee. Zhang et al. [31] investigated the channel model selection problem of a platform supply chain consisting of a manufacturer and an e-commerce platform in the presence of a second-hand market. They conclude that e-commerce platforms may choose to implement the C2B2C model, depending on refurbishment costs and market conditions. Manufacturers should consider the cost and quality of new and used products when choosing between wholesale and platform models. Xu et al. [10] analyzed the impact of Consumer Returns Windows (CRW) on the optimal operational strategies of manufacturers and platforms in the platform supply chain, and the results showed that manufacturers tend to choose the low MRE (Marketplace Relative Efficiency) in the resale mode and tend to choose marketplace mode at high MRE, but this choice is reversed in the case of endogenous CRW. Wang et al. [8] developed a three-stage game model to analyze the manufacturers’ decision to invest in green technologies to reduce carbon emissions under a carbon trading system and the retail platforms’ choice of sales mode (reseller mode or agent mode) strategy. They found that manufacturers’ investment in green technologies makes platforms more inclined to choose the reseller model, and that such investment mitigates the impact of the carbon trading regime on the platform’s choice of sales model. Liang and Ye [6] analyzed the strategies of online platforms in choosing the way to share information (no sharing or sharing) and the business model (reseller model R or agent Model A) strategies. In the reseller model (RR), online platforms tend not to share information in order to maintain their information advantage. However, under the agency model (AA) and hybrid mode (AR/RA), platforms prefer to share information with manufacturers. Our study distinguishes itself from the above literature in the following ways: first, we study a platform-led supply chain of used products rather than a supply chain of new products, which implies that the quality of the products is uncertain, and in this paper, platforms mitigate this quality uncertainty by providing inspection services. Although Zeng et al. [4] considered the impact of platform services on the expected utility of buyers, they did not consider the impact of inspection services on the expected utility of sellers, specifically, low-quality sellers, which is considered in this paper. Second, this paper simultaneously considers the same platform choosing between consignment mode, resale mode, and hybrid mode, whereas most of the existing literature considers the case of a single platform choosing a single mode, or multiple platforms choosing a single mode each. The most similar to ours is that of Zeng et al. [4], but unlike it, this paper considers the resale mode as a conventional mode rather than a mode that exists under special conditions. Third, none of these studies consider platforms’ strategies regarding penalty, while we examine the optimal penalty strategies of platforms under different operation modes.

3. Model

We consider a Stackelberg game, in which an SIP links the buyer (she) and seller (he) by providing inspection services for each second-hand product transaction, and only those used products that pass the inspection can be delivered to buyers, while those that do not pass the inspection are returned to sellers (e.g., StockX, Poizon, RealReal, Zhuanzhuan, Paipai). The platform first chooses the optimal operation mode and makes optimal decisions to maximize its profit, which may include the resale price of used products, the recycling price, transaction fees, and penalty. After observing the inspection service level, prices, and penalty, the seller will decide whether to sell or not based on the net utility. If the utility is non-negative, the seller will decide to sell. Similarly, the buyer then observes the price and determines the buying decision based on the net utility. In the following of this section, we first elucidate the inspection process and the different operation modes of the platform, followed by a detailed description of the models for the seller, buyer, and platform.

3.1. Inspection Processes

Assume that there are two types of used products in the market, i.e., high-quality products and low-quality products. Before the used products are delivered to the buyers, the sellers mail the products to the platform for inspection. Referring to the literature [2,32,33], we assume that high-quality products will definitely pass the inspection, while low-quality products will pass the inspection with a probability $1-\mu$, where $\mu$ represents the inspection services level that reflects the probability of identifying low-quality products. $\mu \in [0.5,1)$ reflects the reality that the probability that a set of insubstantial inspection processes can identify a low-quality product is $0.5$, because a used product is either high-quality or low-quality. In addition, the inspection is not perfect, and therefore the probability of identifying a low-quality product is only infinitely close to $1$. This is common in practice, e.g., despite the fact that many SIPs demonstrate the sophistication and rigor of their inspection processes on their homepages, consumers often complain that their purchases of checked products have been found to have quality problems. After inspection processes, if the product passes the inspection, the platform will ship the product to the buyer and remit the portion of the payment to the seller after deducting the transaction fees (in the case of resale, the platform pays the recycling price). If the product fails the inspection, the platform returns the product to the seller and charges a penalty. Figure 1 illustrates the inspection service processes, where the black line represents passing the inspection while the red line represents failing the inspection. The footprint $i\in \left\{c,r,hc,\left.hr\right\}\right.$ represents consignment mode, resale mode, consignment channel, and resale channel in hybrid mode, respectively.

3.2. Operation Modes

Regarding the platform’s operation mode, we classify the platform’s operation mode into consignment mode (e.g., StockX, Poizon, RealReal) and resale mode (e.g., Paipai, ATRnew) based on whether the platform owns the used products, which are labelled C and R, respectively. Under the consignment mode, the seller owns the used products and sells them at the market-clearing price and the platform collects transaction fees from each transaction [34]. In the resale mode, the platform decides the recycling price and resale price, acquires ownership of the used product from the seller, and then sells it to the buyer. In addition to this, we also consider the competition among channels and introduce the third mode, the hybrid mode, labelled H, wherein the platform retains both the consignment channel and the resale channel (e.g., Zhuanzhuan). Figure 2 illustrates the model structure under the three operation modes. The sequences of events under different modes are as follows:

Consignment mode: the platform first sets the transaction fee and penalty, and the seller decides whether to sell based on expected utility. When the seller chooses to sell (the selling price is the market-clearing price), he needs to send the product to the platform for inspection. If the product passes inspection, the buyer will place an order and the platform will mail the product to the buyer and pay the seller the remainder of the purchase price after deducting transaction fees. If the product fails to pass, the platform will return the product to the seller and charge a penalty.

Resale Mode: The platform first sets the recycling price and penalty, and the seller decides whether to sell based on his expected utility. If the seller chooses to sell, the seller sends the product to the platform for inspection. If the product passes inspection, the platform will pay the seller the recycling price, and then the platform will set the resale price and sell it to the buyer. If the product fails to pass, the platform returns the product to the seller and charges a penalty.

Hybrid mode: it is worth mentioning that, in order to ensure the simultaneous existence of the consignment channel and the resale channel under the hybrid mode, the expected utility acquired by the seller through any channel must be equal; otherwise, the channel with the lower expected utility of the seller will not be able to exist because the seller will only choose to join the channel with the higher expected utility [34]. Therefore, the sequence of events under the hybrid mode is that the platform first decides on the transaction fees, recycling prices, and penalty, which will result in sellers acquiring the same expected utility in the consignment channel and the resale channel. Subsequently, sellers decide whether to sell or recycle based on their expected utility (here, we assume that the probability of a seller choosing both channels is equal, i.e., half of the sellers in each channel choose either the consignment channel or the resale channel). When a seller chooses the consignment channel, the subsequent sequence of events is the same as under the consignment mode. When sellers choose the resale channel, the subsequent sequence of events is the same as in the resale mode.

It is worth noting that returns are not permitted under any of the three operation modes, which is a common phenomenon in the second-hand market. There are various reasons for this phenomenon, such as the difficulty for buyers to prove that the quality problems of the used products they purchased were not due to their personal use. Additionally, price volatility of used products has prompted platforms such as StockX and Poizon to ban returns to protect sellers against speculative buyers.

3.3. Seller

Assume that there is a unit number of risk-neutral individual sellers in the market, each holding at most one used product. A proportion $\mathsf{\lambda }\in [0,1]$ of them own high-quality products, which we call the “H-type”, labelled “H”, and a proportion $1-\lambda$ of them own low-quality products, which we call the “L-type”, labelled “L”. Considering the asymmetry of information about the quality of used products, we assume that the quality information is private to the sellers. We capture the heterogeneity of sellers’ salvage value $s$ for used products and assuming $s$ follows a uniform distribution on $[0,1]$ [13,35,36]. As mentioned in the previous section, the seller is paid when the used product passes the inspection and pays the penalty when it fails. A high-quality product must pass the inspection, and the probability that a low-quality product passes the inspection is $1-\mu$. Therefore, we can obtain the expected utility of the “H-type” seller and the “L-type” seller in the consignment, resale, and hybrid modes:

Consignment mode:

$$U_c^H=p_c-t_c-s$$

(1)

$$U_c^L=(1-\mu )(p_c-t_c-s)-\mu {\epsilon }_c$$

(2)

In Equation (1), $p_c-t_c$ is the portion of the purchase price paid by the buyer after deducting the transaction fee charged by the platform. $s$ is the salvage value of the seller. In Equation (2), $(1-\mu )(p_c-t_c-s)$ is the expected gain from passing the inspection of low-quality products, and the expected loss from paying the penalty when the product fails to pass the quality inspection is $\mu {\epsilon }_c$. Then, we can derive the supply of H-type and L-type sellers respectively:

$$n_c^H=\lambda (p_c-t_c)$$

(3)

$$n_c^L=(1-\lambda )\left((1-\mu )(p_c-t_c)-\mu {\epsilon }_c\right)$$

(4)

Resale mode:

$$U_r^H=w_r-s$$

(5)

$$U_r^L=(1-\mu )(w_r-s)-\mu {\epsilon }_r$$

(6)

In Equation (5), $w_r$ is the recycling price paid by the platform to the seller. In Equation (6), $(1-\mu )(w_r-s)$ is the expected gain of the low-quality product passing the inspection, and $\mu {\epsilon }_r$ is the expected loss of failing the inspection. The supply of the two types of sellers is, respectively:

$$n_r^H=\lambda w_r$$

(7)

$$n_r^L=(1-\lambda )\left((1-\mu )w_r-\mu {\epsilon }_r\right)$$

(8)

Hybrid mode:

As mentioned in the previous section, the existence of both the consignment channel and the resale channel under the hybrid mode is conditional on the seller obtaining equal expected utility through both channels, i.e., $p_{hc}-t_{hc}=w_{hr}$. Under this condition, we assume that “H-type” sellers and “L-type” sellers have equal probabilities of choosing the two channels, i.e., half of the “H-type” sellers and half of the “L-type” sellers join the consignment channel, while the other half join the resale channel. In addition to this, the platform’s penalty is the same in both channels, denoted by ${\epsilon }_h$. Therefore, the expected utility of “H-type” sellers and “L-type” sellers under the consignment channel and the resale channel, respectively, is as follows:

Consignment channel:

$$U_{hc}^H=p_{hc}-t_{hc}-s$$

(9)

$$U_{hc}^L=(1-\mu )(p_{hc}-t_{hc}-s)-\mu {\epsilon }_h$$

(10)

Resale channel:

$$U_{hr}^H=w_{hr}-s$$

(11)

$$U_{hr}^L=(1-\mu )(w_{hr}-s)-\mu {\epsilon }_h$$

(12)

The meanings of the components in Equations (9)–(12) are similar to those of Equations (1), (2), (5) and (6) and will not be repeated. The supply of different types of sellers in different channels is as follows:

Consignment channel:

$$n_{hc}^H={\displaystyle \frac{1}{2}}\lambda (p_{hc}-t_{hc})$$

(13)

$$n_{hc}^L={\displaystyle \frac{1}{2}}(1-\lambda )\left((1-\mu )(p_{hc}-t_{hc})-\mu {\epsilon }_h\right)$$

(14)

Resale channel:

$$n_{hr}^H={\displaystyle \frac{1}{2}}\lambda w_{hr}$$

(15)

$$n_{hr}^L={\displaystyle \frac{1}{2}}(1-\lambda )\left((1-\mu )w_{hr}-\mu {\epsilon }_{hr}\right)$$

(16)

3.4. Buyer

Assume that there exist potential buyers, labelled B. In practice, buyers are only willing to pay the price for used products of a certain standard of quality, and therefore many platforms set thresholds for the quality of used products, e.g., RealReal only accepts products with minor wear and tear; Poizon only accepts brand new, unused products; Zhuanzhuan does not accept disassembled of electronic products. Therefore, in our model, we assume that buyers’ valuations of low-quality products are $0$, and valuations of high-quality products are $v$, which is heterogeneous and follows a uniform distribution on $[0,1]$. In addition, buyers’ valuation of used products is also affected by the different operation modes adopted by the platform, as follows:

Under the consignment mode, the buyer’s valuation of the used product is affected by the platform’s inspection service level $\mu$, and the higher $\mu$ means that the buyer is able to buy a high-quality product with a higher probability. The expected utility of the buyer is as follows:

$$U_c^B=\mu (v-p_c)-(1-\mu )p_c=\mu v-p_c$$

(17)

When the expected utility is non-negative, the buyer will choose to buy and hence the buyer’s demand can be obtained as follows:

$$n_c^B=1-{\displaystyle \frac{p_c}{\mu }}$$

(18)

Under the resale mode, the ownership of the used product will be transferred from the seller to the platform, and when selling to the buyer, the platform usually provides a quality guarantee for its products to boost buyers’ confidence. Therefore, when a buyer buys a low-quality product through the platform, the platform can make up for it through measures such as guarantee or replacement. We assume that the quality guarantee can fully compensate for the buyer’s valuation loss due to the purchase of a low-quality product. The expected utility of the buyer is as follows:

$$U_r^B=v-p_r$$

(19)

When the expected utility is non-negative, the buyer will choose to buy and hence the buyer’s demand can be obtained as follows:

$$n_r^B=1-p_r$$

(20)

Under the hybrid mode, buyers decide their purchasing channel based on the level of their expected utility. Therefore, there exists a threshold $v_1$ such that the expected utility of a buyer who buys a used product from both channels is equal, i.e., $\mu v_1-p_{hc}=v_1-p_{hr}$. And there exists a threshold $v_2$ such that the expected utility of buying from the consignment channel is equal to the expected utility of not buying enough, i.e., $\mu v_2-p_{hc}=0$. And the buyer’s demand for each of the two channels is as follows:

$$n_{hc}^B=1-{\displaystyle \frac{p_{hr}-p_{hc}}{1-\mu }}$$

(21)

$$n_{hr}^B={\displaystyle \frac{p_{hr}-p_{hc}}{1-\mu }}-{\displaystyle \frac{p_{hc}}{\mu }}$$

(22)

3.5. Platforms

The platform provides a trading place for buyers and sellers and exerts influence on both sides through inspection services. We assume that the platform’s cost of providing inspection services is a sunk cost, e.g., the purchase of testing equipment and the training cost of inspection personnel. For simplicity, sunk costs are assumed to be $0$, because positive costs do not essentially change our results except by increasing the complexity of the computation. The profitability of platforms varies depending on their mode of operation. Under the consignment mode, platforms profit by charging transaction fees for each transaction. Under the resale mode, the platform acquires used products from sellers and sells them to buyers to earn the difference in price. Under the hybrid mode, the platform makes profits in both ways, charging transaction fees in the consignment channel and earning the difference in price in the resale channel. We present the profit function of the platform under each of the three operation modes below:

Consignment mode:

Under the consignment mode, the platform generates revenue from transaction fees and penalties charged for products that fail the inspection. Since the buyer’s demand equals the seller’s supply, the platform charges a transaction fee of $t_c{n}_c^B$. The number of products that do not pass the inspection is $(1-\lambda )\mu \left(p_c-t_c-\mu {\epsilon }_c/(1-\mu )\right)$, so the revenue from penalties is ${\epsilon }_c(1-\lambda )\mu \left(p_c-t_c-\mu {\epsilon }_c/(1-\mu )\right)$. When a low-quality product passes the inspection, we assume that buyers will eventually find out and become dissatisfied, resulting in a loss $\beta$ to the platform, e.g., it is common for platforms to issue coupons to buyers in response to consumer dissatisfaction. In practice, we observe that such compensation generally does not exceed the $50\%$ total price of the products (see Poizon.com), so we assume that $\beta \in [0,0.5]$. Therefore, the profit function of the platform is as follows:

$${\pi }_c=t_c{n}_c^B+{\epsilon }_c(1-\lambda )\mu \left(p_c-t_c-\mu {\epsilon }_c/(1-\mu )\right)-\beta n_c^L$$

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Resale mode:

Under the resale mode, the platform’s revenue comes from the price difference between the resale price and the recycling price, and from penalty charged for products that do not pass the inspection. Since the platform can decide the recycling price and resale price, its optimal price decision must make supply and demand equal, because when there is an imbalance between supply and demand, the platform can adjust the recycling price or resale price to bring supply and demand into equilibrium. Therefore, the platform’s resale revenue is $(p_r-w_r)n_r^B$. Similar to the consignment mode, the platform’s penalty revenue is ${\epsilon }_r(1-\lambda )\mu \left(w_r-\mu {\epsilon }_r/(1-\mu )\right)$. In addition, the platform will incur a marginal cost $c_g$ when providing guarantees. Motived by the practice in the insurance industry, we assume that the cost of the guarantee does not exceed $50\%$ of the total price of the products, e.g., $c_g\in [0,0.5]$, and the total guarantee cost is $c_g{n}_r^B$. The profit function of the platform is as follows:

$${\pi }_r=(p_r-w_r)n_r^B+{\epsilon }_r(1-\lambda )\mu \left(w_r-\mu {\epsilon }_r/(1-\mu )\right)-c_g{n}_r^B$$

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Hybrid mode:

Under the hybrid mode, the platform’s revenues include transaction fees from the consignment channel, sales revenues from the resale channel, and penalty revenues from both channels. The platform’s expenses, on the other hand, include the consignment channel’s expenses in response to buyer dissatisfaction and the resale channel’s guarantee cost. As a result, the platform profit function for each of the two channels is as follows:

$${\pi }_{hc}=t_{hc}{n}_{hc}^B+{\epsilon }_h(1-\lambda )\mu \left(p_{hc}-t_{hc}-\mu {\epsilon }_h/(1-\mu )\right)-\beta n_{hc}^L$$

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$${\pi }_{hr}=(p_{hr}-w_{hr})n_{hr}^B+{\epsilon }_h(1-\lambda )\mu \left(w_{hr}-\mu {\epsilon }_h/(1-\mu )\right)-c_g{n}_{hr}^B$$

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Table 1. List of decision variables and parameters.

Decision Variables
$t_j$	Transaction fee, $j=c,hc$
$p_k$	Resale price, $k=r,hr$
$w_k$	Recycle price, $k=r,hr$
${\epsilon }_i$	Penalty, $i=c,r,h$
Parameters
$\lambda$	Portion of “H-type” seller
$\mu$	The service level of inspection
$p_j$	Market cleaning price in C or H mode, $j=c,hc$
$\beta$	Inspection failure loss
$c_g$	Cost of providing guarantee
$s$	Seller’s reservation price
$v$	Buyer’s valuation

summarizes the decision variables and parameters.

4. Equilibrium Analysis

Lemma 1.

The equilibrium results of the platform under different modes are summarized in 

Table 2. Equilibrium results under different strategy modes.

Value	C-Mode	R-Mode	H-Mode
$p_j^{*}$	${\displaystyle \frac{\mu \left(2+\mu \Delta +\beta (\Delta -\lambda )\right)}{2(1+\mu \Delta )}}$	$-$	${\displaystyle \frac{\mu \left(4+\Delta (c_g+\beta +2\mu )-\beta \lambda \right)}{5+\mu (3\Delta +\lambda -1)}}$
$p_k^{*}$	$-$	${\displaystyle \frac{2+(1+c_g)\Delta }{2(1+\Delta )}}$	${\displaystyle \frac{9+c_g(1+\mu )\Delta +\mu \left((4-\mu )\Delta +\lambda -1\right)+\beta (\Delta -\lambda )(1+\mu )}{10+2\mu (3\Delta +\lambda -1)}}$
$w_k^{*}$	$-$	${\displaystyle \frac{1-c_g}{2(1+\Delta )}}$	${\displaystyle \frac{4(1+\mu )+\beta (\Delta -\lambda )(1+3\mu )-4c_g}{4\left(5+\mu (3\Delta +\lambda -1)\right)}}$
$t_j^{*}$	${\displaystyle \frac{\mu }{2}}$	$-$	${\displaystyle \frac{\beta (\Delta -\lambda )(1-\mu )+4c_g(1+\mu \Delta )+4\mu (3+2\mu \Delta )-4}{4\left(5+\mu (3\Delta +\lambda -1)\right)}}$
${\epsilon }_i^{*}$	${\displaystyle \frac{\beta (1-\mu )}{2\mu }}$	$0$	${\displaystyle \frac{\beta (1-\mu )}{4\mu }}$
$d_i^{*}$	${\displaystyle \frac{\mu \Delta -\beta (\Delta -\lambda )}{2(1+\mu \Delta )}}$	${\displaystyle \frac{(1-c_g)\Delta }{2(1+\Delta )}}$	${\displaystyle \frac{1-c_g-\beta (1-\lambda )+\left((c_g+\beta )(1-\lambda )+\lambda \right)\mu -(1-\lambda ){\mu }^2}{5+\mu (3\Delta +\lambda -1)}}$
${\pi }_i^{*}$	${\displaystyle \frac{(\Delta -\lambda ){(\mu -\beta )}^2+\lambda \mu \left(\mu +(\Delta -\lambda ){\beta }^2\right)}{4(1+\mu \Delta )}}$	${\displaystyle \frac{{(1-c_g)}^2\Delta }{4(1+\Delta )}}$	${\displaystyle \frac{4\Delta {(1+\mu -c_g)}^2+\beta (\Delta -\lambda )\left(\beta (4+\lambda +3\lambda \mu )-8(1+\mu -c_g)\right)}{16\left(5+\mu (3\Delta +\lambda -1)\right)}}$

For the sake of presentation, let $\Delta =1-(1-\lambda )\mu$.

.

According to Lemma 1, we find that optimal prices (including equilibrium market clearing prices, resale prices, and recycling prices), transaction fee, penalty, sales, and profits differ when platforms adopt different operation modes. This is because these outcomes are subject to the combined effects of seller structure ($\lambda$), inspection service level ($\mu$), guarantee cost ($c_g$), and inspection failure loss ($\beta$), which in turn vary depending on the platform’s adoption of different operation modes. Some of these differences are more intuitive; e.g., in terms of penalty decisions, the platform does not charge penalties in the resale mode while it charges higher penalties under the consignment mode than under the hybrid mode. The penalty decreases with the inspection service level but increases with the inspection failure loss. There are also differences that are relatively complex, such as the platform’s profit, which make it necessary for platforms to carefully consider the interplay of relevant factors when making operation mode decisions.

Proposition 1.

For the platform under different operation modes, the trends of the equilibrium results change with the cost of guarantee $c_g$ as follows:

(a) Profit: ${\displaystyle \frac{\partial {\pi }_r^{*}}{\partial c_g}}<{\displaystyle \frac{\partial {\pi }_h^{*}}{\partial c_g}}<{\displaystyle \frac{\partial {\pi }_c^{*}}{\partial c_g}}=0$;

(b) Price: ${\displaystyle \frac{\partial p_r^{*}}{\partial c_g}}>{\displaystyle \frac{\partial p_{hr}^{*}}{\partial c_g}}>{\displaystyle \frac{\partial p_{hc}^{*}}{\partial c_g}}>{\displaystyle \frac{\partial p_c^{*}}{\partial c_g}}=0$;

(c) Transaction fee: ${\displaystyle \frac{\partial t_h^{*}}{\partial c_g}}>{\displaystyle \frac{\partial t_c^{*}}{\partial c_g}}=0$;

(d) Sales: ${\displaystyle \frac{\partial d_r^{*}}{\partial c_g}}<{\displaystyle \frac{\partial d_h^{*}}{\partial c_g}}<{\displaystyle \frac{\partial d_c^{*}}{\partial c_g}}=0$;

(e) Recycling price: ${\displaystyle \frac{\partial w_r^{*}}{\partial c_g}}<{\displaystyle \frac{\partial w_h^{*}}{\partial c_g}}<0$;

(f) Penalty: ${\displaystyle \frac{\partial {\epsilon }_c^{*}}{\partial c_g}}={\displaystyle \frac{\partial {\epsilon }_r^{*}}{\partial c_g}}={\displaystyle \frac{\partial {\epsilon }_h^{*}}{\partial c_g}}=0$.

Proposition 1 suggests that the guarantee cost may have different effects on the platform’s optimal profits and decisions under different operation modes. The optimal profit of the consignment mode is independent of the guarantee cost, the optimal profit of the resale mode and the hybrid mode both decrease with the guarantee cost, and the optimal profit of the resale mode decreases faster than that of the hybrid mode (see Proposition 1(a)). With respect to the price, the equilibrium price of the consignment mode is independent of the guarantee cost, the optimal price of the resale mode, the equilibrium price in the consignment channel and the optimal price of the resale channel under the hybrid mode all increase with the guarantee cost, and the rate of the rise is shown to be the fastest in the resale mode, the second fastest in the resale channel, and the slowest in the consignment channel (see Proposition 1(b)). The optimal transaction fee of the consignment mode is independent of the guarantee cost, while the optimal transaction fee of the consignment channel under the hybrid mode increases with the guarantee cost (see Proposition 1(c)). The optimal sales under the consignment mode are independent of the guarantee cost, whereas the optimal sales in both the resale mode and the hybrid mode decrease with the guarantee cost, and the optimal sales in the resale mode decline more rapidly (see Proposition 1(d)). In terms of recycling price, the optimal recycling price decreases with the guarantee cost in both the resale mode and the resale channel under the hybrid mode, and in the resale mode, the optimal recycling price declines faster (see Proposition 1(e)). The optimal penalty in all modes is independent of the guarantee cost (see Proposition 1(f)).

Proposition 2.

For the prices of used products $p_j^{*}$ and $p_k^{*}$ under different operation modes, the following hold ($c_g$: the cost of guarantee):

(a) $p_c^{*}<p_r^{*}$, $p_{hc}^{*}<p_{hr}^{*}$;

(b) When $c_g\in (0,min\{c_1,0.5\})$, $p_c^{*}>p_{hc}^{*}$; when $c_g\in (min\{c_1,0.5\},0.5)$, $p_c^{*}<p_{hc}^{*}$;

(c) When $c_g\in (min\{c_2,0.5\},0.5)$, $p_r^{*}>p_{hr}^{*}$; when $c_g\in (0,min\{c_2,0.5\})$, $p_r^{*}<p_{hr}^{*}$.

Proposition 2 indicates that the prices of used products vary under different operation modes. According to Proposition 2(a), the price under the resale mode is higher than that under the consignment mode, and the price in the resale channel is also higher than that in the consignment channel under the hybrid mode. This is because the platform can maximize buyers’ trust by providing them with quality guarantee, whether in the resale mode or in the resale channel under the hybrid mode, which allows buyers to accept higher selling prices because they perceive a higher value for the platform’s own products compared to those of individual sellers (e.g., used products from the consignment mode or the consignment channel under the hybrid mode). According to Proposition 2(b), when the cost of guarantee is low, the price under the consignment mode is higher than that in the consignment channel under the hybrid mode. When the cost of guarantee is high, the price under the consignment mode is lower than that in the consignment channel under the hybrid mode. This is because the price under the consignment mode is independent of the cost of guarantee, while the price in the consignment channel under the hybrid mode increases with the cost of guarantee (see Proposition 1(b)). The price in the consignment channel under the hybrid mode is lower than that under the consignment mode when the cost of guarantee tends to converge, and as the cost of guarantee increases, the gap between the two prices gradually narrows, and the magnitude relationship is likely to be reversed eventually (see Figure 3a). According to Proposition 2(c), when the cost of guarantee is high, the price under the resale mode is higher than that in the resale channel under the hybrid mode. When the cost of guarantee is low, the price under the resale mode is lower than that in the resale channel under the hybrid mode. This is because the price in the resale channel under the hybrid mode is higher than that under the resale mode when the cost of guarantee is close to $0$. While both the price under the resale mode and the price in the resale channel under the hybrid mode tend to increase with the cost of guarantee, the former rises faster with the cost of guarantee than the latter (see Proposition 1(b)), and thus the situation may eventually reverse (see Figure 3a).

Proposition 3.

For the optimal sales $d_i^{*}$ under different operation modes, the following hold ($c_g$: the cost of guarantee):

(a) When $c_g\in (0,min\{c_3,0.5\})$, $d_r^{*}>d_h^{*}>d_c^{*}$;

(b) When $c_g\in (min\{0.5,c_3\},min\{0.5,c_4\})$, $d_h^{*}>d_r^{*}>d_c^{*}$;

(c) When $c_g\in (min\{0.5,c_4\},min\{0.5,c_5\})$, $d_h^{*}>d_c^{*}>d_r^{*}$;

(d) When $c_g\in (min\{0.5,c_5\},0.5)$, $d_c^{*}>d_h^{*}>d_r^{*}$.

Proposition 3 shows that there are various cases of size relationships between optimal sales under different operation modes. Specifically, the resale mode has the highest optimal sales when the cost of guarantee is low (see Proposition 3(a)). The hybrid mode has the highest optimal sales when the cost of guarantee is moderate (see Proposition 3(b)(c)). Optimal sales are highest under the consignment mode when the cost of guarantee is high (see Proposition 3(d)). This is because the optimal sales are highest in the resale mode, second highest in the hybrid mode, and lowest in the consignment mode when the cost of guarantee converges to $0$. In addition, the optimal sales under the resale and hybrid modes decrease with the cost of guarantee, and the optimal sales under the consignment mode decrease faster than that under the hybrid mode, while the optimal sales under the consignment mode are independent of the cost of guarantee (see Proposition 1(d)). As the cost of guarantee increases, the optimal sales under the consignment mode and the hybrid mode decrease, and the optimal sales under the consignment mode are highest before the cost of guarantee reaches the threshold $min\{c_3,0.5\}$. The hybrid mode has the highest optimal sales when the cost of guarantee crosses the threshold $min\{c_3,0.5\}$, but before it reaches the threshold $min\{c_5,0.5\}$. The consignment mode has the highest optimal sales when the cost of guarantee crosses the threshold $min\{c_5,0.5\}$.

Proposition 4.

For the optimal transaction fee $t_j^{*}$ , recycling price $w_k^{*}$, and penalty ${\epsilon }_i^{*}$ under different operation modes, the following hold ($c_g$: the cost of guarantee):

(a) When $c_g\in (0,c_6)$, $t_c^{*}>t_h^{*}$; when $c_g\in (c_6,0.5)$, $t_c^{*}<t_h^{*}$;

(b) When $c_g\in (0,c_7)$, $w_r^{*}>w_h^{*}$; when $c_g\in (c_7,0.5)$, $w_r^{*}<w_h^{*}$;

(c) ${\epsilon }_c^{*}>{\epsilon }_h^{*}>{\epsilon }_r^{*}=0$.

Proposition 4 suggests that the relative sizes of optimal transaction fee, recycling price, and penalty may be related to the cost of guarantee under different operation modes. In terms of optimal transaction fee, when the cost of guarantee is low, the optimal transaction fee under the consignment mode is higher than that in the consignment channel under the hybrid mode (see Proposition 4(a)). This is because the optimal transaction fee under the consignment mode is higher than that in the consignment channel under the hybrid mode when the cost of guarantee tends to be $0$, and the optimal transaction fee in the consignment channel under the hybrid mode increases with the increase in the cost of guarantee, whereas the optimal transaction fee under the consignment mode is not affected by the change in the cost of guarantee (see Proposition 1(c)); thus, the optimal transaction fee in the consignment channel under the hybrid mode will be higher than that under the consignment mode when the cost of guarantee is higher than the threshold $c_6$ (see Figure 3c). Furthermore, when the cost of guarantee is low, the optimal recycling price under the resale mode is higher than that in the resale channel under the hybrid mode. When the cost of guarantee is high, the optimal recycling price under the resale mode is lower than that in the consignment channel under the hybrid mode (see Proposition 4(b)). This is because the optimal recycling price under the resale mode is higher than that in the consignment channel under the hybrid mode when the cost of guarantee tends to be $0$; at the same time, the optimal recycling price of the resale mode decreases faster with the cost of guarantee than that in the resale channel under the hybrid mode (see Proposition 1(e)), and the magnitude of the relationship is reversed as the cost of guarantee exceeds the threshold $c_7$ (see Figure 3d). In addition, the optimal penalty under the consignment mode is higher than that in the consignment channel under the hybrid mode, and the optimal penalty under the resale mode is $0$ (see Proposition 4(c)).

Proposition 5.

For the platform’s optimal choice among different operation modes, the following hold ($c_g$: the cost of guarantee):

(a) When $c_g\in (min\left\{0.5,max\{c_8,c_9\}\right\},0.5)$, the preferred mode is consignment mode;

(b) When $c_g\in (max\left\{min\{c_8,c_9\},0\right\},min\left\{max\{c_8,c_9\},0.5\right\})$, the preferred mode is hybrid mode;

(c) When $c_g\in (0,max\left\{min\{c_8,c_9\},0\right\})$, the preferred mode is resale mode.

For SIPs, the optimal operation mode means that they can maximize their profits when they adopt this mode strategy. According to Proposition 5, the cost of guarantee has a significant impact on the platform in making operation mode decisions. Specifically, when the cost of guarantee is high, the consignment mode is preferred (see Proposition 5(a)). When the cost of guarantee is moderate, the hybrid mode is preferred (see Proposition 5(b)). When the cost of guarantee is low, the resale mode is preferred (see Proposition 5(c)). This is because the optimal profit of the resale mode is the largest, the optimal profit of the hybrid model is the second largest, and the optimal profit of the consignment mode is the smallest when the cost of guarantee tends to be $0$. According to Proposition 1(a), when the cost of guarantee increases, the optimal profits of both the resale and hybrid modes decrease, and the optimal profit of the resale mode decreases faster than that of the hybrid mode, while the optimal profit of the consignment mode does not change. Specifically, the optimal profit of the resale mode is largest when the cost of guarantee is below the threshold $min\{c_1,c_2\}$. The optimal profit of the hybrid mode is greatest when the cost of guarantee exceeds the threshold $min\{c_1,c_2\}$, but does not reach $max\{c_1,c_2\}$. The optimal profit for the consignment mode is greatest when the cost of guarantee exceeds the threshold $max\{c_1,c_2\}$. Figure 4 illustrates the impact of the cost of guarantee and the inspection failure loss on the SIP’s optimal mode choices.

Proposition 6.

Under different operation modes, the trends of equilibrium results change with the inspection service level $\mu$ are as follows ($\beta$: inspection failure loss):

(a) Profits: Under the C-mode, when $\beta \in (min\left\{0.5,max\{0,{\beta }_1\}\right\},0.5)$, ${\displaystyle \frac{\partial {\pi }_c^{*}}{\partial \mu }}>0$, and when $\beta \in (0,min\left\{max\{0,{\beta }_1\},0.5\right\})$, ${\displaystyle \frac{\partial {\pi }_c^{*}}{\partial \mu }}<0$; Under the R-mode, ${\displaystyle \frac{\partial {\pi }_r^{*}}{\partial \mu }}<0$; Under the H-mode, when $\beta \in (min\left\{0.5,max\{0,{\beta }_2\}\right\},0.5)$, ${\displaystyle \frac{\partial {\pi }_h^{*}}{\partial \mu }}>0$ and when $\beta \in (0,min\left\{max\{0,{\beta }_2\},0.5\right\})$, ${\displaystyle \frac{\partial {\pi }_h^{*}}{\partial \mu }}<0$;

(b) Price: Under the C-mode, ${\displaystyle \frac{\partial p_c^{*}}{\partial \mu }}>0$; Under the R-mode, ${\displaystyle \frac{\partial p_r^{*}}{\partial \mu }}>0$; Under the H-mode, in the consignment channel, ${\displaystyle \frac{\partial p_{hc}^{*}}{\partial \mu }}>0$; in the resale channel, when $\beta \in (min\left\{0.5,max\{0,{\beta }_3\}\right\},0.5)$, ${\displaystyle \frac{\partial p_{hr}^{*}}{\partial \mu }}<0$ and when $\beta \in (0,min\left\{max\{0,{\beta }_3\},0.5\right\})$, ${\displaystyle \frac{\partial p_{hr}^{*}}{\partial \mu }}>0$;

(c) Transaction fee: Under the C-mode, ${\displaystyle \frac{\partial t_c^{*}}{\partial \mu }}>0$; Under the H-mode, ${\displaystyle \frac{\partial t_{hc}^{*}}{\partial \mu }}>0$;

(d) Sales: Under the C-mode, when $\beta \in (min\left\{0.5,max\{0,{\beta }_4\}\right\},0.5)$, ${\displaystyle \frac{\partial d_c^{*}}{\partial \mu }}>0$ and when $\beta \in (0,min\left\{max\{0,{\beta }_4\},0.5\right\})$, ${\displaystyle \frac{\partial d_c^{*}}{\partial \mu }}<0$; Under the R-mode, ${\displaystyle \frac{\partial d_r^{*}}{\partial \mu }}<0$; Under the H-mode, when $\beta \in (min\left\{0.5,max\{0,{\beta }_5\}\right\},0.5)$, ${\displaystyle \frac{\partial d_h^{*}}{\partial \mu }}>0$ and when $\beta \in (0,min\left\{max\{0,{\beta }_5\},0.5\right\})$, ${\displaystyle \frac{\partial d_h^{*}}{\partial \mu }}<0$, and:

(1) Supply of high-quality sellers: Under the C-mode, ${\displaystyle \frac{\partial d_c^{H*}}{\partial \mu }}>0$; Under the R-mode, ${\displaystyle \frac{\partial d_r^{H*}}{\partial \mu }}>0$; Under the H-mode, ${\displaystyle \frac{\partial d_h^{H*}}{\partial \mu }}>0$;

(2) Supply of low-quality sellers: Under the C-mode, when $\beta \in (min\{0.5,{\beta }_6\},0.5)$, ${\displaystyle \frac{\partial d_c^{L*}}{\partial \mu }}>0$ and when $\beta \in (0,min\{0.5,{\beta }_6\})$, ${\displaystyle \frac{\partial d_c^{L*}}{\partial \mu }}<0$; Under the R-mode, ${\displaystyle \frac{\partial d_r^{L*}}{\partial \mu }}<0$; Under the H-mode, when $\beta \in (min\{0.5,{\beta }_7\},0.5)$, ${\displaystyle \frac{\partial d_h^{L*}}{\partial \mu }}>0$ and when $\beta \in (0,min\{0.5,{\beta }_7\})$, ${\displaystyle \frac{\partial d_h^{L*}}{\partial \mu }}<0$.

(e) Recycling price: Under the R-mode, ${\displaystyle \frac{\partial w_r^{*}}{\partial \mu }}>0$; Under the H-mode, ${\displaystyle \frac{\partial w_h^{*}}{\partial \mu }}>0$;

(f) Penalty: Under the C-mode, ${\displaystyle \frac{\partial {\epsilon }_c^{*}}{\partial \mu }}<0$; Under the H-mode, ${\displaystyle \frac{\partial {\epsilon }_h^{*}}{\partial \mu }}<0$.

According to Proposition 6, we find that the platform’s profit, price, sales, recycling price, and penalty may show different trends as the inspection service level changes under different operation modes. We elucidate the underlying mechanism of such changes below.

Under the consignment mode, when the inspection failure loss is large, the platform’s profit increases with the inspection service level. When the inspection failure loss is small, the platform’s profit decreases with the inspection service level (see Proposition 6(a)). This result is somewhat counter-intuitive, i.e., an increase in the inspection service level favors the platform because it implies greater competitiveness, enabling the platform to attract more buyers and thus allowing the platform to capture more profits. However, the situation is further complicated by the fact that the platform’s profit under the consignment mode is mainly composed of transaction fees, penalty, and the inspection failure loss (see Equation (23)). The equilibrium price is allowed to rise as the inspection service level increases (see Proposition 6(b)). Higher equilibrium price provides space for the platform to charge higher transaction fees (see Proposition 6(c)). At the same time, a rise in the equilibrium price raises the expected utility of high-quality sellers and increases their supply. In contrast, the expected utility of low-quality sellers decreases with the inspection service level and increases with the equilibrium price, leading to an uncertain change in their supply, which ultimately leads to a different trend in sales with the inspection service level (see Proposition 6(d)). Therefore, an increase in the inspection service level does not necessarily increase the platform’s transaction fee revenue. In addition to this, the platform’s penalty decreases with the inspection service level (see Proposition 6(f)), which, combined with the uncertainty of how the supply of low-quality sellers varies with the inspection service level, makes it likely that the platform’s penalty revenues decrease with the inspection service level. Finally, an increase in the inspection service level does not necessarily reduce the losses suffered by the platform due to inspection failures. This is because, while an increase in the inspection service level reduces the probability of inspection failures, it may also lead to an influx of more low-quality sellers into the marketplace, increasing rather than decreasing the number of low-quality products that pass the inspection, and ultimately resulting in the platform facing more losses.

Under the resale mode, the platform’s profit decreases with the inspection service level (see Proposition 6(a)). This is because, on the demand side, the guarantee offered by the platform is able to completely dispel the buyer’s quality concerns, although the platform pays an additional cost as a result. On the supply side, while the resale price rises with the inspection service level (see Proposition 6(b)), this does not lead to a rise in their unit profit because the price of recycling rises with the inspection service level (see Proposition 6(e)), which offsets the effect of the rise in resale price on the marginal profit ($\partial (p_r^{*}-w_r^{*})/\partial \mu =0$), and with the inspection service level increases, more low-quality sellers are excluded from the market, which makes the supply of sellers lower (see Proposition 6(d)), which ultimately leads to the platform’s profit shrinking with the inspection service level.

Under the hybrid mode, the trend of the platform’s profit with inspection service level is similar to that in the consignment mode (see Proposition 6(a)). In addition, the equilibrium results of the consignment channel under the hybrid mode change with the inspection service level in a similar way as those under the consignment mode (see Proposition 6(b–d,f)). Furthermore, the trend of the recycling price of the resale channel under the hybrid mode changes with the inspection service level is similar to that under the resale mode (see Proposition 6(e)), whereas the trend of the resale price changes with the inspection service level is different from that under the resale mode. Specifically, the resale price of the resale channel under the hybrid mode decreases with the inspection service level when the inspection failure loss is large and increases with the inspection service level when the inspection failure loss is small (see Proposition 6(b)). This is because the resale channel faces competition from the consignment channel under the hybrid mode, and competition for customers between channels becomes fierce as the inspection service level increases.

5. Welfare Analysis

In this section, we investigate the impact of the platform’s operation mode choices and the inspection service level on consumer surplus and social welfare. Following the general definition, consumer surplus is the difference between the consumer’s willingness to pay and the price of the product, and social welfare is the sum of the benefits to all participants in the supply chain. We represent consumer surplus as $C{S}_i(i=c,r,h)$ and social welfare as $S{W}_i(i=c,r,h)$, which specifically includes consumer surplus, seller revenue ($S{R}_i(i=c,r,h)$), and platform’s profit. Consumer surplus, seller revenue, and social welfare under different operation modes are as follows:

Consignment mode:

$$C{S}_c={{\displaystyle \int }}_{({\displaystyle \frac{p_c^{*}}{\mu }})}^1(\mu v-p_c^{*})f(v)dv$$

(27)

$$S{R}_c=\lambda {{\displaystyle \int }}_0^{p_c^{*}-t_c^{*}}(p_c^{*}-t_c^{*}-s)f(s)ds+(1-\lambda ){{\displaystyle \int }}_0^{p_c^{*}-t_c^{*}-{\displaystyle \frac{\mu {\epsilon }_c^{*}}{1-\mu }}}\left((1-\mu )(p_c^{*}-t_c^{*}-s)-\mu {\epsilon }_c^{*}\right)f(s)ds$$

(28)

$$S{W}_c=C{S}_c+S{R}_c+{\pi }_c^{*}$$

(29)

Resale mode:

$$C{S}_r={{\displaystyle \int }}_{p_r^{*}}^1(v-p_r^{*})f(v)dv$$

(30)

$$S{R}_r={{\displaystyle \int }}_0^{w_r^{*}}\left((2-\mu )(w_r^{*}-s)\right)f(s)ds$$

(31)

$$S{W}_r=C{S}_r+S{R}_r+{\pi }_r^{*}$$

(32)

Hybrid mode:

$$C{S}_h{{\displaystyle =\int }}_{({\displaystyle \frac{p_{hc}^{*}}{\mu }})}^{p_{hc}^{*}}(\mu v-p_{hc}^{*})f(v)dv+{{\displaystyle \int }}_{p_{hr}^{*}}^1(v-p_{hr}^{*})f(v)dv$$

(33)

$$S{R}_h=\lambda {{\displaystyle \int }}_0^{p_{hc}^{*}-t_h^{*}}(p_{hc}^{*}-t_h^{*}-s)f(s)ds+(1-\lambda ){{\displaystyle \int }}_0^{p_{hc}^{*}-t_h^{*}-{\displaystyle \frac{\mu {\epsilon }_h^{*}}{1-\mu }}}\left((1-\mu )(p_c^{*}-t_c^{*}-s)-\mu {\epsilon }_h^{*}\right)f(s)ds$$

(34)

$$S{W}_h=C{S}_h+S{R}_h+{\pi }_h^{*}$$

(35)

Proposition 7.

For consumer surplus under different operation modes, the following hold ($\beta$: inspection failure loss; $\mu$: the service level of inspection):

(a) When $\beta \in (min\{0.5,{\beta }_8\},0.5)$, ${\displaystyle \frac{\partial C{S}_c}{\partial \mu }}<0$; When $\beta \in (max\{0,{\beta }_8\},min\{{\beta }_8,0.5\})$, ${\displaystyle \frac{\partial C{S}_c}{\partial \mu }}>0$;

(b) ${\displaystyle \frac{\partial C{S}_r}{\partial \mu }}<0$;

(c) When $\beta \in (min\{0.5,{\beta }_9\},0.5)$, ${\displaystyle \frac{\partial C{S}_h}{\partial \mu }}<0$; When $\beta \in (max\{0,{\beta }_9\},min\{{\beta }_9,0.5\})$, ${\displaystyle \frac{\partial C{S}_h}{\partial \mu }}>0$.

Proposition 7 suggests that the inspection failure loss and the inspection service level will have different effects on consumer surplus for buyers in the market under different operation modes (see Figure 5a). Specifically, under the consignment mode, consumer surplus decreases with the inspection service level when the inspection failure loss is large, and increases with the inspection service level when the inspection failure loss is small (see Proposition 7(a)). Under the resale mode, consumer surplus decreases with the inspection service level (see Proposition 7(b)). Under the hybrid mode, consumer surplus follows a similar trend with the increasing inspection service level as under the consignment mode (see Proposition 7(c)).

Proposition 8.

For social welfare under different operation modes, the following hold ($\beta$: inspection failure loss; $\mu$: the service level of inspection):

(a) When $\beta \in (min\{0.5,{\beta }_{10}\},0.5)$, ${\displaystyle \frac{\partial S{W}_c}{\partial \mu }}<0$; When $\beta \in (max\{0,{\beta }_{10}\},min\{{\beta }_{10},0.5\})$, ${\displaystyle \frac{\partial S{W}_c}{\partial \mu }}>0$;

(b) ${\displaystyle \frac{\partial S{W}_r}{\partial \mu }}<0$;

(c) When $\beta \in (min\{0.5,{\beta }_{11}\},0.5)$, ${\displaystyle \frac{\partial S{W}_h}{\partial \mu }}<0$; When $\beta \in (max\{0,{\beta }_{11}\},min\{{\beta }_{11},0.5\})$, ${\displaystyle \frac{\partial S{W}_h}{\partial \mu }}>0$.

Proposition 8 suggests that the inspection failure loss and the inspection service level will have different impacts on social welfare under different operation modes (see Figure 5b). Specifically, under the consignment mode, social welfare decreases with the inspection service level when the inspection failure loss is high, and increases with the inspection service level when the inspection failure loss is low (see Proposition 8(a)). In the resale mode, social welfare declines with the inspection service level (see Proposition 8(b)). Under the hybrid mode, the trend of social welfare with the increasing inspection service level is similar to that under the consignment mode (see Proposition 8(c)).

6. Results and Discussion

The main results of this paper are as follows:

(1) Compared to the consignment and resale modes, the price of used products is not necessarily lower, despite the fact that there exists the inter-channel competition under the hybrid mode. Specifically, when the cost of guarantee is relatively high, the price in the consignment channel will be higher than that under the consignment mode and the price in the resale channel will be higher than that in the resale mode. Similarly, when the cost of guarantee is relatively low, the platform under the hybrid mode charges lower transaction fees than under the consignment mode and pays a lower recycle price for used products than in the resale mode. In addition, the platform charges lower penalty under the hybrid mode than under the consignment mode, while no penalty is charged under the resale mode. Furthermore, when the cost of guarantee is low, the used product sales under the resale mode are the highest. When the cost of guarantee is moderate, the sales under the hybrid mode are the highest. When the cost of guarantee is high, the sales under the consignment mode are the highest. (2) The platform’s choice of the optimal operation mode depends on the cost of guarantee, and when it is high, low, or moderate, the platform will choose the consignment mode, resale mode, or hybrid mode, respectively. (3) As the inspection service level increases, the optimal profit and sales may decrease when the inspection failure loss is relatively low. Moreover, a higher inspection service level will incentivize the platform to reduce the transaction fee and penalty, while simultaneously enhancing the recycling price. (4) Consumer surplus and social welfare decline with the inspection service level under the resale mode and increase with the inspection service level only if the inspection failure loss is relatively low.

Our main contributions are summarized follow: First, we consider the application of inspection technologies within the online second-hand market. Unlike the literature related to the application of blockchain technology in the supply chain, which argues that blockchain technology can deliver perfect product information [12,13,14,16], we hypothesize that the inspection services are not perfect, especially when it comes to disclosing product quality information, which coincides with the practical realities in the second-hand market. Second, we analyze the influence of inspection services on the operation mode selection of SIPs, thereby filling a gap in the existing research. Our study also provides guidance for SIPs in establishing penalty frameworks. While the previous literature indicates that platforms should waive penalties when the inspection service is perfect [2], we demonstrate that, even with imperfect inspection services, penalties can be waived in the absence of inspection failure loss. Lastly, we reveal the dual nature of the value of inspection services in second-hand transactions, where the used product sales, consumer surplus, and social welfare are negatively correlated with the inspection service level in the resale mode, and the used product sales are positively related to the inspection service level in the consignment and hybrid modes if and only if the inspection failure loss is large enough, but consumer surplus and social welfare are positively related to the inspection service level if and only if the inspection failure loss is sufficiently small.

7. Conclusions

7.1. Summary and Managerial Insight

SIPs are rapidly gaining popularity in online marketplaces, which offer product quality inspection services for second-hand transactions to alleviate buyers’ quality concerns. Meanwhile, different SIPs often link buyers and sellers with different operation modes, such as consignment, resale, and hybrid modes. This study aims to investigate how SIPs maximize their profits by choosing different operation modes, and how inspection services affect the platforms’ equilibrium strategies and used products sales under different operation modes. In addition, what are the effects of inspection services on consumer surplus and social welfare? We first develop a Stackelberg model to derive the optimal strategies and maximum profits of platforms under different operation modes through backward induction. Subsequently, we examine how factors such as the cost of guarantee and inspection service level influence the platform’s optimal strategies and sales. A comparative analysis of these results allows us to assess how various factors, such as the cost of guarantee and inspection failure loss, affect the platform’s choice of optimal operation modes. Finally, we investigate the impact of the inspection service level on consumer surplus and social welfare. Our results show that the platform’s optimal operation mode choice depends on the relative magnitudes of the cost of guarantee and inspection failure loss. The consignment mode is the optimal when the cost of guarantee is relatively high; the hybrid mode is optimal when the cost of guarantee is relatively moderate; and the resale model is optimal when the cost of guarantee is relatively low. In addition, an increase in inspection service level does not always increase the platform’s profit. The platforms’ equilibrium strategies, sales, prices, and profits show significant differences under different operation modes. Finally, an increase in the inspection service level may hurt consumer surplus or social welfare. The results of our study can bring the following managerial insights: (1) Operation mode selection: SIPs should regularly monitor market dynamics, including seller composition, guarantee costs, and consumer sentiment. Based on these changes, timely adjustments to the operation mode are essential to optimize profitability and adapt to market demand variations. (2) Inspection service strategy: SIPs must accurately assess the trade-off between the enhancement of the inspection service level and profitability based on the operation mode and the actual situation of the inspection failure loss. When the inspection failure loss is relatively low, the platform should avoid blindly increasing the inspection service level to prevent unnecessary cost increases, which could adversely affect overall profits. (3) Consumer surplus and social welfare: In formulating strategic decisions, SIPs should rigorously quantify the specific impacts of their actions on consumer surplus and social welfare. By employing differentiated pricing strategies or regulating the inspection service level, the platform can optimize consumer welfare, while concurrently aligning its strategies with long-term social value and sustainable development objectives.

7.2. Limitations and Future Research

This study has several limitations that can be addressed in future work. Firstly, this paper considers a scenario involving a monopolistic platform. However, in reality, the introduction of competitive platforms may yield more intriguing findings. Secondly, while we have assumed that consumers are unable to return products based on platform practices, recent changes in regulations and policies have compelled certain platforms to allow consumers to return products after receipt and evaluation. Thirdly, we do not consider the impact of the SIP brand (reputation), which may change the SIP’s equilibrium strategy in providing the inspection service, just like the compliance with certain (strict) quality rules (ISO, etc.). Due to space constraints, we will consider consumer return behavior and investigate the effects of various (independent or co-) branding options for these platforms in future research.