key: cord-254272-w7yvp703
authors: Sun, Miao; Chen, Jing; Tian, Ye; Yan, Yufei
title: The impact of online reviews in the presence of customer returns
date: 2020-09-19
journal: Int J Prod Econ
DOI: 10.1016/j.ijpe.2020.107929
sha: 
doc_id: 254272
cord_uid: w7yvp703

We develop a duopoly model to examine how online reviews influence the decisions of two competing online sellers who sell products of differentiated quality under different returns policies. We derive the competing sellers' optimal decisions on price and returns policy with and without online reviews, and we find that online reviews have greater impact on the high-quality seller than on the low-quality seller. If the salvage value of the product is relatively low, the seller has less opportunity to benefit from online reviews when it offers an MBG, as compared to a no-refund policy. The impact of online reviews on the competition between the two sellers has a “symmetric effect area,” where reviews may either weaken or intensify the price competition between the two sellers when they both offer a no-refund policy, but always intensify the competition if they both offer an MBG. We have identified the conditions under which online reviews lead to a win-win, or benefit one seller, or present a prisoner's dilemma for the two online sellers. We also show that MBGs at both sellers help mitigate the prisoner's dilemma if the net salvage value at both sellers is sufficiently high.

Return of products by customers is a common phenomenon in the retailing industry, especially in online retailing. As shown in a National Retail Federation (2018) report, total merchandise returns account for almost $369 billion in lost sales for US retailers alone, and the retail returns rate was as high as 10% in 2018. It has been reported that the returns rate from online sales is two to three times of that of brick-and-mortar retailers (Orendorff, 2019) and is typically between 20% and 40% (Ratcliff, 2014) .

The major reason for the high level of customer returns in online retail is mismatch between customer expectations and the reality of the product (Chen and Chen, 2017a; Ratcliff, 2014) . As the customer cannot physically evaluate and experience the product before purchase, there is a J o u r n a l P r e -p r o o f 2 significant chance that the purchased product will fail to match the customer's expectation and taste.

Online reviews from previous customers reveal additional information about products, enabling customers to adjust their pre-purchase valuations on products and make better purchase decisions, ultimately reducing the rate of customer returns (Dellarocas, 2003; Kostyra et al., 2016; Maslowska et al., 2017) . In practice, BazaarVoice reported that online reviews reduce the number of returned products by 20% (Sahoo et al., 2018) . In an empirical study by Minnema et al. (2016) , online customer reviews were shown to help to form product expectations, and it was suggested that product returns should be considered when examining the effects of online customer reviews.

Although an attractive returns policy can improve customer satisfaction and thus represent a competitive strength, the lost sales and high cost of handling customer returns significantly affects profitability, and online retailers set their returns policy carefully (McWilliams, 2012; Chen and Chen, 2017b) . Furthermore, returns can be managed, and method of handling customers returns may impact the customer's perception and willingness-to-pay (Appriss Retail, 2019; Pei et al., 2014) . To reduce costs associated with customer returns, some retailers tighten their returns policies by offering a no-refund policy (Su, 2009; Choi et al., 2013; Hsiao and Chen, 2015) .Online retailers offer a variety of returns policies (Better Business Bureau; Office of Consumer Affairs (Canada)), ranging from the money-back guarantee (for example, Amazon.com and Walmart.com) to no refund (LCDTVs.com). An MBG returns policy is a widely adopted policy, but no-refund policies can also be observed in practice (especially for digital products like games, music, and software). Some sellers specify no-returns policies under certain conditions; the Camera Store states on its website that any printer in which ink has been installed cannot be returned (https://www.thecamerastore.com). No-returns policies are also common for final sale items.

Online sales have increased from 29.6 billion Canadian dollars in 2015 to 44 billion in 2018 (Clement, 2020) . In the Covid-19 pandemic period, this number has increased to a record $3.9 billion in May 2020 in Canada, with a 99.3% increase over February, according to Statistics Canada (Toneguzzi, 2020) . Many, but not all, online retailers (notably Amazon.com) allow or encourage customers to leave product reviews on their websites, and there are also third-party sites (such as Yelp.com) dedicated to customer reviews. Customers can share their opinions on products or services they have experienced, and seek information from others' experience of products they are J o u r n a l P r e -p r o o f 3 interested in. Furthermore, there are a variety of types of reviews, including star ratings, pictures, and text description of product details and characteristics. Nearly 90% of consumers read online reviews before purchasing (Gilliam, 2017) , and 88% of them trust the online reviews as much as personal recommendations; consumers read reviews as part of their pre-purchase research (Rudolph, 2015) .

Although a number of studies have examined the impact of online reviews on sellers' sales, and several empirical studies have considered the influence of online reviews on customer returns (Sahoo et al., 2018; Minnema et al., 2016) , we are unware of any theoretical study that investigates the impact of online reviews on the decisions of competing sellers on prices and returns policies in the presence of customer returns. To fill this gap, we develop a duopoly model to study how online reviews impact customers' purchases and returns, and how online sellers facing competition can make optimal price and returns policy decisions in the presence of online reviews.

Online reviews provide customers with additional information on products before purchase, and an MBG provides post-sale service; in principle both should reduce the risk of mismatch of the actual product with customer expectations. We are therefore interested in the interactions between online reviews and returns policies, and the influence of online reviews on competing sellers' price and returns policy decisions. In order to analyze the impact of online reviews in a competitive market with customer returns, we build a three-stage game theoretic model, in which two competing online retailers sell a product at different quality levels. Customers are heterogeneous in their valuations on the products, and they make their purchase decisions based on both information provided by the seller and online reviews.

Not surprisingly, we find that online sellers benefit from favorable reviews (with an increase in both price and demand), and can be hurt by negative reviews (with a decrease in price and demand).

Comparable reviews of competing products intensify the competition between the two sellers, so the sellers have to reduce their prices, even at the risk of reduced profits, in order to compete. In addition, not unnaturally, in the presence of online reviews, the seller's price, demand, and profit increase with the value of the reviews of its own product and decrease with the value of the reviews of its rival's product.

J o u r n a l P r e -p r o o f 4 We identify the condition for a duopoly to offer MBGs. We show that when the net value of the returns service (shared by the customer and an online seller) is positive, the online seller should offer an MBG, no matter what returns policy is offered by its competitor. We also show that online reviews reduce the customer's need for an MBG, as the reviews can reduce the risk of mismatch that is inherent in an online purchase. As a result, sellers are less likely to offer an MBG when online reviews are available than when they are not.

Online reviews also have several surprising effects. We find that online reviews have greater impact on the high-quality seller than on the low-quality seller. Furthermore, the impact of online reviews on the competition between the two sellers has a "symmetric effect area." If online reviews of the two products fall in this area, they have the same influence direction on both sellers, either positive or negative; otherwise, they benefit one but hurt the other. In the symmetric effect area, online reviews may either weaken or intensify the price competition between the two sellers when both offer a no-refund policy, but always intensify the competition if both offer an MBG. Even so, salvage value matters; when the salvage values of the two products are both sufficiently high, both sellers are more likely to benefit from online reviews when they offer an MBG.

Our contributions to the literature are two-fold. First, we extend the extant studies on the influence of online reviews to include the effect of reviews on competitive online sellers' choice of customer returns policies. Our study suggests that online sellers should respond strategically to reviews, not only in pricing but also in returns policies. We demonstrate that online reviews reduce the motivation of online sellers to provide an MBG; this is a new insight in the literature on customer

returns. Second, we analyze the interactions between online reviews and returns policies in view of the duopoly's competition in prices and returns policies (for products of different qualities). We find that online reviews have greater impact on the high-quality seller than on the low-quality seller, and may have different impacts on the competition.

The rest of this paper is organized as follows. Section 2 briefly reviews the relevant research.

Section 3 describes the setting and game sequence of our duopoly model. Section 4 examines the two online sellers' pricing and returns policy decisions under the influence of online reviews, and presents equilibrium results for returns policies with and without online reviews. Section 5 J o u r n a l P r e -p r o o f 5 examines the impact of online reviews on online sellers' optimal prices and profits, and the duopoly's market when online sellers both offer either a no-refund policy or an MBG. Section 6 concludes the paper and proposes possible extensions for future work. All proofs are presented in the Appendix.

There are two streams of literature related to this study, on online product reviews and customer returns.

Online product reviews have attracted considerable attention recently, as the growing popularity of reviews has potentially important implications for a wide range of management activities (Dellarocas, 2003; Li and Hitt, 2008) . Extensive empirical studies have examined the impact of online reviews and shown that they indeed have an effect on firms' sales (Chevalier and Mayzlin, 2006; Duan et al., 2008; Luca, 2016; Zhou and Duan, 2016) . From an analysis of book reviews at Amazon.com, Chevalier and Mayzlin (2006) find that online reviews have a significant influence on product sales. Similarly, Luca (2011) finds that an increase in ratings on Yelp.com leads to an improvement in the revenues of restaurants. In addition, a large body of detailed work has considered the impact of different characteristics of online reviews, including the association between the variance and volume of product ratings (Clemons et al., 2006; Kostyra et al., 2016; Maslowska et al., 2017) , the review text (Archak et al., 2011) , and professional ratings and sales (Zhou and Duan, 2016) . Differing from those studies, we develop a theoretic model to study the impact of online reviews on customers' purchasing decisions and on competing online retailers' customer returns and pricing strategies.

The existing theoretical studies on online reviews focus on the impact of online reviews on customers' pre-purchase evaluations of products. Online reviews are viewed as an information source and have an effect on customers' purchase behaviors (Chen and Xie, 2008; Li and Hitt, 2008; Markopoulos et al., 2016; Sun, 2012) . Chen and Xie (2008) argue that online reviews can serve as a new element in market communications and as free "sales assistants" to help customers to make purchase decisions. Li and Hitt (2008) model the self-selection bias in early online reviews, which impacts later consumers' purchases and later product reviews. Sun (2012) models both ratings and J o u r n a l P r e -p r o o f 6 variance of product reviews, and examines the impact of the level of variance on products' subsequent price, demand, and profit. Consumers may have different perceptions of either positive or negative reviews (Pekgün et al., 2018) . With the effect of online reviews on customers' utility, Kwark et al. (2014) and Cai et al. (2018) examine the pricing strategies of different players in a supply chain. Some studies show that online reviews can be a promotional device, and provide marketing strategy suggestions to sellers (Chen and Xie 2005; Dellarocas 2006; Mayzlin 2006; Kuksov and Xie 2010) . All these studies focus on the effect of online reviews on customers' behavior before purchase; in the present paper we also consider the effect of online reviews on customer returns after purchase and on online retailers' decisions on returns policies.

Several empirical studies have examined the impact of online reviews on customer returns (Sahoo et al., 2018; Lohse et al., 2017; Minnema et al., 2016) . Sahoo et al. (2018) show that unbiased online reviews help customers make better purchase decisions, leading to fewer product returns. Minnema (2016) and Lohse (2017) find that online reviews affect customers' purchase decisions as well as returns decisions. De et al. (2013) find that the technologies used for customer reviews have different effects on returns. In contrast to these empirical studies, we develop a game theoretical model for two online retailers who sell quality-differentiated products, to examine the impact of online reviews on the sellers' pricing and returns policy decisions in a competitive market. This paper is also related to studies on customer returns. To reduce customers' risk and improve customer satisfaction, many sellers offer a lenient returns policy, even though it may lead to high costs (Che, 1996) . The effect of returns policy on customers and retailers has been extensively studied in the economics and marketing literature. Some studies have found that returns policy can act as a source of product quality information (Moorthy and Srinivasan, 1995; Shieh, 1996) . Moorthy and Srinivasan (1995) use a signaling theory to analyze how an MBG signals a high-quality product. Some studies focus on retailers' strategy in returns policy, and argue that an appropriate returns policy can enhance profits (Chen and Bell, 2012; Davis et al., 2002) . Others studies pay attention to the influence of returns policy on customer purchase decisions (Anderson et al., 2009; Suwelack et al., 2011; Wood, 2003) . Suwelack (2011) argues that MBGs can increase customers' purchase intentions and willingness to pay a price premium. Griffis et al. (2012) examine how customers' returns experiences impact their future purchases. In addition, extensive J o u r n a l P r e -p r o o f 7 studies in operations management have focused on firms' strategies facing customers' returns, including pricing, ordering, and returns strategy decisions in either a monopolistic or a competitive market (McWilliams, 2012; Su, 2009) . The optimal strategies of each player in supply chains with different structures have been discussed and analyzed (Ai et al., 2012; Chen and Chen, 2017a; Liu et al., 2014) . None of these studies have examined the impact of online reviews on retailers' returns policies in a competitive market, as we do in this paper. To fill this gap, in this study we develop a model to analyze the online retailers' optimal decisions in a competitive market in the presence of customer returns and online reviews.

We consider two sellers who compete on an online platform in the presence of online reviews, selling products with differentiated quality. Customers will decide whether or not to buy the product, and from which seller to buy, after reading the online reviews. For example, the customer looking for a blender might consider Vitamix and Oster, which both sell blenders on Amazon.com, but the blender from Vitamix may be of higher quality than the blender from Oster. In the presence of online reviews, we examine how two competing sellers should offer returns policies, and study the impact of online reviews on the sellers' choice of policy. In practice, companies have to make plans based on projections. Our stylized model will allow a company to envision the effects of reviews and returns policies to optimize operations decisions accordingly.

The two online sellers are vertically differentiated in their ability to provide product quality and customer returns service to their customers. As in McWilliams (2012) and Chen and Chen (2017b) , who follow the assumption in Moorthy and Srinivasan (1995) that MBGs can be offered by high-quality firms to signal product quality (where quality is defined as the likelihood of product return) to uninformed consumers (based on signaling theory), high product quality is reflected in a high customer satisfaction rate. We assume that the high-quality retailer has a customer satisfaction rate and the low-quality retailer has a customer satisfaction rate , where

, and satisfaction rate is reflected in returns rate. Therefore, (1 ) reflects the customer returns rate of Seller , if returns are allowed, where , .

The two sellers each set a returns policy ( ), either an MBG ( 1) or a no-refund policy ( J o u r n a l P r e -p r o o f 8 0), where , . With a no-refund policy, the product is worth zero to an unsatisfied customer.

Each seller incurs a unit product acquisition cost ( ), and needs to decide on the selling price ( ).

Without loss of generality, we assume that . Let be the salvage value of a returned product and be the customer's cost of returning the product to retailer (the hassle cost, reflecting shipping cost and/or time spent returning the product). Seller incurs a unit handling cost per returned product (ℎ ).

We assume that the customer's perceived valuation ( ) on a satisfactory product with an MBG policy is between 0 and 1, following a uniform distribution, as in McWilliams (2012) and Chen and Chen (2017a) . If the customer is unsatisfied with the product, its value is 0. As in Chen and Bell (2012) and Chen and Grewal (2013) , we assume that the customer's perceived valuation on a product with a no-refund policy is lower than that with an MBG policy, to account for the risk of having to keep a unsatisfactory product . In practice, a product with a no-refund policy usually has a lower price than one with return service (Camera Store example in Section 1). Both empirical studies (such as, Pei et al., 2014) and theoretical studies (such as Shang et al., 2017) have found that the customer's valuation on the product with a no-refund policy is lower than that with an MBG. To capture the difference in the customer's perceived valuation of products with different returns policies, we assume that the customer has a disutility ( ) on a product purchased under a no-refund policy, and its perceived valuation is ( ≥ 0) (as in Shang et al., 2017) .

In addition to providing the infrastructure to sell the products, an online platform may enable customers to post product reviews and feedback on purchased products. We designate an online platform { , }, where reviews are either enabled ( ) or not enabled ( ). Online reviews provide public information on the product, including quality, fitness, and ease of usage. As pointed out by Sahoo et al. (2018) , it is unclear whether online reviews can help customers in making better purchase decisions that may lead to fewer returns, so we denote the value of online reviews, measured by the star and/or score posted by reviewers, as , where < 1 and , . A potential customer can use this information along with seller-provided information to evaluate the products before purchase. The higher the score or the larger the number of stars, the higher the value of the online review. also depends on additional factors such as the descriptive information on the product provided by the seller and the customer's evaluation of the product after J o u r n a l P r e -p r o o f 9 experiencing the product. The reviewer's valuation on Product with online reviews under an MBG or a no-refund policy becomes ! (1 " and ( " ! (1 " , respectively, where and (1 " are the weights on the customer's own valuation of the product and on the information from online reviews, respectively, and where ∈ (0,1". The online reviews give the customer as second source of information from which to value a product. The assumption that the customer weighs the online reviews the same for both products follows the study of Kwark et al. (2014) , in which the information precision of online reviews on products sold on a given online platform is assumed to be the same.

The main notation that will be used in this paper is summarized in Table 1 . In the presence of online reviews and customer returns, we model the duopoly competition as a three-stage game. Since a seller's decision on returns policy is relatively long term, as compared to its price decision, the returns policy should be set before the price decision is made. The game J o u r n a l P r e -p r o o f 10 sequence is illustrated in Figure 1 . ( 1 ) or no-refund ( 0 ). In Stage 2, both sellers set their optimal selling prices simultaneously. In Stage 3, the customer decides where to buy to maximize utility, based on the returns policy offered (' {00, 01, 10, 11}) and selling price.

We now derive the optimal equilibriums for the duopoly starting with the Stage 3 game.

To examine the impact of online reviews, we consider a benchmark case in which the platform does not enable online reviews (subscript ). The customer evaluates the product based on its own valuation on the product. Given the sellers' returns policies ' and Seller ′ selling price 3 4 , the utility of a customer with valuation ( " on Product is:

where {0, 1}. On the right-hand side of Eq. (1), the first and the second terms are the expected valuation when the customer purchases and keeps the product (if the product is satisfactory), and when the product is unsatisfactory and returned (with an MBG from Seller ) or kept (with a-no-refund policy from Seller ).

With online reviews (subscript ), for {0, 1}, the customer with value ( " on Product has the utility: (1) and (2) capture the impact of the seller's returns policy on the customer's utility.

With Eqs. (1) and (2), for { , }, the customer's utility function (5 9 4 ) can be generalized as:

where Γ < if with online reviews 1 if without online reviews and J 0 with a no refund policy 1 with an MBG policy .

The customer will buy the product if the utility is non-negative. In addition, the customer will select a seller, either Seller or Seller , based on maximizing the utility function. With Eq. (3) 

In the second stage of the game, the two sellers decide their selling prices simultaneously. Given the two sellers' returns policies ' set in the Stage 1 game, for { , }, Seller 's profit function is:

where X : 4 is given by the margin profit multiplied by the demand of Seller .

We define Y :

as the highest net valuation of the customer ( 1) for Product . Then \ : Table A1 in the Appendix. \ : Z [ is referred to as the "maximum net shared value of Seller " in this paper. (See also Chen and Chen (2017b) . Here we are presenting an extension of that work, with consideration of online reviews.) Maximizing the profits of both sellers, the optimal price ( : 4 * )

can be derived, as summarized in the following proposition.

Proposition 1. For { , } and any given returns policies of two sellers ' , the duopoly has unique optimal prices for cases with and without online product reviews, as given by:

We define c 

The optimal profits of the two sellers are: Lemma 1 implies that as long as the efficiency of Seller selling a high-quality product relative to that of Seller selling a low-quality product (p : 4 ) is comparable (between c and f ), the duopoly can coexist. This then implies that when p : 4 < c < 1, Seller will be driven out of the market; when p : 4 f 1, Seller will be driven out of the market. Here we focus on the case when the two online sellers are in sustained competition, that is, they can coexist. Since the boundary values ( c and f ) depend only on the returns rates of the two sellers, they only need to know whether or not their relative efficiency (p : 4 ) falls in the range [ c , f ] to know whether or not they can survive in a competitive market. Obviously, the presence of online reviews affects the efficiencies of both sellers, and thus affects their relative efficiency (p : 4 ), where c , f , p : 4 are listed in Table A1 in the Appendix.

In the first stage of the game, the two online sellers simultaneously decide their own returns policies.

We define r : \ : c \ : s as the net value of offering an MBG for Product . We have:

Notice that Γ for (with online reviews) and Γ 1 for (without online 14 reviews). Γ and t (1 "( ℎ " represent the impact of Seller 's no-refund policy and online reviews, and the expected recovery value of a returned Product on the net value of offering an MBG for Product , respectively. The net salvage of Product (the salvage value after offsetting Seller 's costs of handling the returned product and the customer's cost of returning the product) is ∆ ℎ . With the profits of the duopoly in Eq. (9), we have the first-stage game decisions on returns policy, as summarized in Proposition 2, where t , ∆ , and r : are listed in Table A1 in the Appendix. here Proposition 2 extends this result by considering that the customer's valuation of a product is discounted for a no-refund policy and adjusted by the availability of online reviews. Even more than in a physical store, where the customer can visually inspect the product, in online shopping a no-refund policy will decrease the customer's valuation on the product. The implication of Proposition 2 is that with the customer's disutility on a no-refund policy, the seller's choice of whether or not to offer an MBG policy depends on several factors: the net salvage value of the product (∆ , reflecting the efficiency of Seller in handling the returns product), the quality of the product, the weight the customer assigns to information from online reviews, and the customer's disutility on a no-refund policy ( ). Proposition 2 provides an easy-to-implement mechanism for

Seller 's choice of returns policy, as the decision depends only on the factors/parameters related to its own selling channel and product, independent of the competitor's. The online seller can and should carefully estimate these factors. Proposition 2 also suggests that even when ∆ is negative, Seller may still offer an MBG. The higher the disutility the customer has on a no-refund policy ( ), the more likely the online seller is to offer an MBG.

Comparing r 8 and r 3 (Eq. (11)), we have a direct result as follows. Eq. (11) gives r 8 < r 3 , implying that the value of offering an MBG is reduced (from to " in the presence of online product reviews.

Lemma 2 shows that when the customer can obtain information on the product through online reviews before purchase, the value of an MBG is reduced. This is because online reviews provide a customer with additional information on the products before purchase, and reduce the risk of mismatch with expectations, reducing the risk of a need to return the product. Lemma 2 also suggests that the more information the online reviews provide, the less dependence a customer has on an MBG policy. The implication is that if the members of the duopoly decide not to offer MBGs, they should make efforts to improve the usefulness of their online reviews to reduce the customer's risk of buying an unsatisfactory product. In this way, the sellers can save the cost of returns service while keeping the customer's loyalty.

The Impact of Online Reviews 5.

Eqs. (9)-(10) show that a seller's demand and profit increase with its own maximum net shared value (\ : 4 ", but decrease with the competitor's maximum net shared value, for any returns policy (') of the duopoly and both with and without online reviews. In this section, we first discuss the impact of online reviews on \ : 4 .

Let ∆\

Z [ be the difference in Seller 's efficiency with and without online reviews if it offers a returns policy . We have the following results:

Proposition 3 implies that if online Seller offers an MBG ( 1), online product reviews reduce the seller's efficiency of selling the product. In addition, ∆\ c increases with and , and decreases with . In general, the value of online reviews ( ) reflects the customers' aggregate valuation on Product after experiencing the product. An individual customer's valuation of Product pre-purchase changes after reading online reviews, in view of other customers' experiences with the product. Proposition 3 shows that the presence of online reviews results in a J o u r n a l P r e -p r o o f 16 decrease in the maximum net shared value if an MBG is offered. It is interesting to see that if Seller offers a no-refund policy ( 0), the presence of online product reviews will not always reduce Seller 's efficiency in selling the product; if the value of the online product reviews is sufficiently high, the reviews can increase all customers' expected value on the products, and enhance Seller 's efficiency in selling the product. The implication of Proposition 3 is that online reviews significantly impact a seller's efficiency in selling the product, as they change the customer's valuation and the decision to purchase and/or return the product. In addition, Proposition 3 suggests that sellers with a no refund policy could improve their efficiency in selling products by making efforts to, for example, effectively respond to customers, in order to have favorable reviews on their products.

Proposition 2 provides a simple condition for a seller when it offers an MBG (r : ≥ 0) with and without online reviews. A seller needs to evaluate r : in deciding its optimal returns policies.

To examine the impact of online reviews on sellers' decisions with and without an MBG, we first compare the equilibrium prices, demands, and profits of both sellers for the cases with and without reviews, and for both sellers with an MBG (' {11}" and with a no-refund policy 

Let w Z [ t be Seller 's unit acquisition cost (if 0) or unit net acquisition cost after offsetting the recovery value of a returned product (if 1), where t (1 "( ℎ ".

We also define x 4 , y 4 , and z 4 as boundary values for Δ 4 0, ΔS 4 0, and ΔX 4 0, respectively, where we can obtain y 4 < z 4 < x 4 , and x 4 , y 4 , and z 4 are listed in Table A1 in the Appendix. Table   A2 in the Appendix. Comparing the optimal prices, demands, and profits with online reviews to J o u r n a l P r e -p r o o f 17 those without online reviews in Eq. (8) to (10), Proposition 4 presents the impact of the values of online reviews on Seller i's price, demand, and profit, where , .

Proposition 4. For ' {00, 11}, the impact of the online reviews on the optimal prices, demands, and profits of the two sellers are summarized in Table 2 and illustrated in Figure 3 . Figure 3 . The impact of the value of online reviews ( ) on Seller 's price, demand, and profit Note that in Figure 3 , the changes due to online reviews vary with the value of the reviews. y 4 , z 4 , and x 4 are threshold values of online reviews by comparing with the results of Seller 's demand, profit, and price without online reviews.

Proposition 4 shows that as compared to the case without online reviews, if the online reviews heavily favor Product (

x 4 ), the profit of Seller increases as both the optimal price and market size of Product increase. The intuition is that favorable reviews improve the average customer valuation on the product and thus increase the customer's willingness-to-pay, which allows Seller to increase its price (positive price effect). In addition, positive online reviews make Product more competitive than its competitor. As a result, Seller attracts more customers J o u r n a l P r e -p r o o f 18 (positive market share effect). Both positive price and market size effects enhance Seller 's profit.

On the other extreme, when the value of online reviews on Product is low ( < y 4 ), the online reviews negatively affect product , due to a decrease in both the optimal price and the demand of Product , leading to a reduction in Seller 's profit. If the value of online product reviews on Product is moderate ( y 4 < < x 4 ), the presence of online reviews has a negative price effect and a positive demand effect. Online product reviews will enhance Seller 's profit when z 4 < < x 4 (and decrease it when y 4 < < z 4 ) if the positive demand effect can outweigh (not outweigh) the negative price effect.

For a given returns policy, in the absence of online reviews, the customer's valuation on the product is only based on its valuation on the product itself and the MBG if offered; with online reviews, the valuation depends on both information provided by the seller and information from online reviews.

As a result, the online seller benefits from higher value reviews (high stars/scores), but it is hurt by relatively negative reviews.

The implication of Proposition 4 is that in the presence of competition and online reviews, when the value of online reviews is moderately low, an online seller can expand its market share by reducing its price. This expansion, however, may not enhance its profit. If expansion of market share is a target for an online seller, this seller should put efforts into improving the value of online reviews by asking reviewers specific questions and enhancing other customer experience operations (online interactions with customers on products and quick delivery). The seller should, however, carefully evaluate when such market expansion can be profitable.

The impacts of the value of online reviews of Product ( ) on the prices, demands, and profits of the two products are summarized in the following proposition.

Lemma 3 shows that in the presence of online reviews, for given returns policies of the two sellers ('), positively impacts Seller 's own selling price, market share, and profit, and negatively J o u r n a l P r e -p r o o f 19 impacts the competitor's price, market share, and profit. Furthermore, the valuation of online reviews on a seller's own product has a larger effect on price, demand, and profit than that of online reviews of the competitor's product. Lemma 3 implies that in a market with competition, an online seller should consider customer reviews on both its own and its rival's products.

Comparing the impact of the value of online reviews ( ) on the price, demand, and profit of Product with and without an MBG policy, we summarize the results in Lemma 4.

Lemma 4 shows that in the presence of online reviews, the impact of review value on the price of Product with an MBG is higher than that with a no-refund policy. This suggests that the price with an MBG might be more sensitive to the change of review value than the price with a no-refund policy. The impact of review value on demand, however, is independent of the returns policy, and its impact on the profit of a seller with an MBG depends on the net shared value of the returns service of the seller relative to that of its competitor. When the net shared value of the returns service of Seller is relatively higher than that of its competitor, its profit with an MBG is more sensitive to change of online review value than with a no-refund policy. This suggests that as the value of its online reviews increases, whether a seller with an MBG can be more profitable depends on the net shared value of its returns service relative to that of its competitor; furthermore, Seller 's net shared value of returns service should be high relative to that of Seller for Seller L to be more profitable with an MBG.

These results suggest that when the two sellers decide to offer MBGs (improving the efficiency of handling customer returns), they can benefit more from an increase in the value of online reviews.

Let t … y | f t , t … y | c t , t … z | f 6t ! 2 √ ( "7 , and t … z | c 6t ! √ ( ss , if t < t … y ; y cc < y ss and z cc z ss , if t … y < t < t … z ; y cc < y ss and z cc < z ss , if t t … z .

Proposition 5 shows that when it offers an MBG, online Seller should have a higher value of online reviews, such that it can set a higher price than with a no-refund policy. Without online reviews, the customer evaluates a product based on its own valuation only, and valuation is lower without returns service than with an MBG (because the returns service reduces the customer's risk of mismatch). Online reviews may improve the customer's expected value of the product, if they are favorable enough ( 1 ), and reduce the value of the returns service. In such a case, the seller offering a produce with good reviews and a no-refund policy has more space to increase the retail price. In other words, the more customers value the returns service, the lower the valuation on a no-refund product, and the more likely that price can be increased in the presence of favorable online reviews. Favorable online reviews have a higher impact on the price of a no-returns product.

As compared to a no-refund returns policy, whether or not online reviews will enable a seller to attract more customers and be more profitable with an MBG depends on t (the expected recovery value of a returned product). If t is low relative to that of its competitor (t < t … y ), online Seller needs better online reviews for its product, such that it can attract more demand and be more profitable with an MBG. This means that online reviews have less positive effect on Seller 's demand in the case with an MBG ( y cc y ss ). Since the lower net salvage value may suggest a higher cost in handling customer returns, the Seller who offers an MBG may lose the advantage in competition to gain market share if the reviews are not favorable enough; with the impact on price, it is obvious that Seller is less likely to benefit from online reviews with an MBG ( z cc z ss ). This is because Seller has less space to raise the selling price in view of positive online reviews, and less chance of expanding the market, due to the high cost of offering an MBG.

If t t … y , a seller is likely to expand its demand by offering an MBG in the presence of online reviews. This furthermore suggests that the higher t , the more value the seller can recover from a J o u r n a l P r e -p r o o f 21 returned product and the lower the cost of offering an MBG, which provides more space for the seller to reduce its price to compete with its rival in the presence of online reviews. Therefore, by providing a good returns service (an MBG), online Seller can attract even more demand.

Whether or not Seller is likely to be more profitable from online reviews with an MBG depends on the strength of the positive effect of the demand increase and the negative effect of the price increase. If and only if t t … z can the advantage due to a higher net expected salvage value offset the lower expected value of an MBG resulting from online reviews, and allow the seller to be more profitable from online reviews with an MBG.

The interactions between the impact of online reviews and customer returns in Proposition 5 provide some guidance for online sellers in deciding their returns policies. In the presence of online reviews, if the efficiency of handling customer returns is relatively low, they benefit less by offering an MBG; this benefit can be enhanced if the salvage value of a returned product sufficiently high.

This result may explain the practice of online sellers in some platforms (such as Tmall.com and Amazon.com) in setting restrictions on returns (requiring intact tags and/or original packaging) to ensure a high salvage value of the returned product.

We now discuss the impact of online reviews on the competition of the duopoly. We define ˆx 4 1 (1 " (where ‰ 4 ‰ 4 0 when ˆx 4 , see in Figure 4 Proposition 6: For ' {00, 11} and ~ , S, X, the impacts of online product reviews on the two competing sellers' prices, demands, and profits are summarized in Table 3 . Proposition 6 and Figure 4 show that if • { ∈ ( c , f ", where ~ , S, X, the presence of online reviews has the same influence trend (either positive or negative) on both sellers' prices, demands, and profits, respectively; otherwise, online reviews positively influence one seller, but negatively influence the other seller. We refer to the range ( c , f " as the "symmetric effect range." Now, we discuss the impact of online reviews on both sellers when the ratio of changes due to online reviews is in the symmetric effect range. no-returns case. Proposition 6 shows that the impacts of online reviews on sellers' optimal prices, demands, and profits depend on the relative difference in value of the online reviews of the two products. Both online sellers will mark down their prices if the values of the online reviews (the scores) of the two products are comparable (in Region V) and low ( < ˆx 4 ), leading to intensified price competition (negative price effect on the competition). The intuition is that low values of online reviews for both products reduce the difference in the customer's valuation on the two products, and at the same time reduce the customer's utility overall, resulting in intensified price competition between the two sellers. On the other hand, when the values of online reviews are high for both products ( ˆx 4 in Region I), the presence of online reviews softens the price competition (positive price effect on the competition). When the value of online reviews of one product is significantly higher than that of the competitor's product, the online reviews have a positive impact on the seller's price and a negative impact on the competitor's price (Figure 4(a) ).

The implication of the result is that collaboration between the sellers in improving the value of online reviews could soften the price competition. Notice that the dash-lines and solid lines are for the cases ' {1,1} and ' {0,0}, respectively, implying that an MBG at both sellers will always intensify the price competition of the duopoly.

The impact on the demands of the two products (Figure 4(b) ) depends on whether the value of J o u r n a l P r e -p r o o f 24 product 's online reviews is higher or lower than the net shared cost of the product divided by the customer's satisfaction ( ˆy 4

, "net unit cost"). If the review values of both products are higher than their net unit costs ( ˆy 4 in Region I), online reviews can serve as free advertisement for the products, attracting more customers and improving the demand for both sellers. Conversely, if the value of online reviews is low ( < ˆy 4 in Region V) for both products, both sellers will risk losing customers, and the total market demand will decrease (positive demand effect on the competition). Negative reviews may imply that the product is not as good as advertised, and both sellers will lose demand (negative demand effect on the competition).

Both sellers benefit in terms of profit from extremely positive reviews ( 61 (1 " 7)

( Figure 4 (c)), as good reviews provide an opportunity for them to raise their prices and expand market size (positive effects in both price and demand). They both suffer from very negative reviews ( < ˆy 4 ), due to both negative price and negative demand effects. When online reviews are moderate ( ˆx 4 ˆy 4 ), both sellers will reduce prices due to the lower customer valuation on the products and the intensified market competition, but demands will increase due to the price reduction. If the online reviews are favorable enough ( ˆz 4 in Region I), they will enhance both sellers' profits, since the positive effect of online reviews (demand expansion effect) outweighs the negative effect of lower customer valuations and intensified market competition.

Proposition 6 suggests that under market competition, when the values of the reviews for the two products are comparable and relatively high, online reviews can benefit both sellers; when the values of the reviews are unbalanced only the high value seller will benefit. In addition, when the values are comparable and relatively low, both sellers are worse off, leading to a "prisoner's dilemma." The results suggest that a collaborative effort between the two sellers to improve the quality of online reviews (such as by encouraging answers to questions that customers care most about and rewarding informative reviews), might benefit both sellers.

The impact of online reviews on the two sellers is different, however, under different returns policies. We summarize in Proposition 7.

Proposition 7. For ~ , S, X and , , J o u r n a l P r e -p r o o f 25 (b) ˆx cc ˆx ss , ˆy cc < ˆy ss , and ˆz cc ˆz ss , if 0 < t < √ ;

(c) ˆx cc ˆx ss , ˆy cc < ˆy ss , and ˆz cc < ˆz ss , if t √ .

When both sellers offer an MBG, they have to mark down their prices because online reviews reduce the customers' highest valuation on the product (see dash lines in Figure 4 (a); recall that good online reviews reduce the risk of product/expectation mismatch and thus reduce the value of the MBG). When both sellers offer a no-refund policy, the customer's valuation on the product is low, and if reviews of both products are favorable enough ( 1 ) the reviews may improve the customer's highest valuation on both products and allow price increases. In other words, online reviews only intensify the competition between two sellers with an MBG, but high value online reviews may soften the price competition between two sellers with a no-refund policy. The results

in Proposition 7 imply that as compared to offering a no-refund policy at both sellers, offering an MBG at both sellers intensifies the price competition in the market. This result differs from the study of Chen and Chen (2017b) , which shows (without considering online reviews) that offering an MBG at both sellers softens the price competition, as both sellers can raise prices in view of good post-sales service. We show that online reviews mitigate the advantages of an MBG, as they reduce the risk of mismatch before purchase. Seller H and L, respectively; solid and dotted lines are for MBG and no-returns cases, respectively.

As compared to the case of a no-refund policy (shown in Figure 5 ), when the value recovered from a returned product (t ) is negative (t < 0), ˆ{ 4 for both demand and profit with an MBG is high ( Figures 5(a) and 5(c)). The implication of this result is that if Seller cannot efficiently handle customer returns, its price and demand, and therefore profit, are more likely to decrease with online reviews. When t is moderate (0 V t V √ ), ˆy 4 is low ( Figure 5 (b)) while ˆz 4 is high ( Figure 5(c) ). This implies that the overall market is more likely to expand with online reviews. The positive t reduces the net unit cost of the products, leading to more space for the sellers to expand their market. However, since the online reviews cannot improve prices in the market, the revenue due to online reviews decreases, and the reviews are less likely to benefit the sellers. When t is sufficiently high (t ≥ √ ", ˆ{ 4 for both demand and profit are lower (Figures 5(b) and 5(d)).

This suggests that online reviews can have stronger positive impact on the demands and profits of both products. With a high salvage value, the unit cost of a product is lower, and this provides more space for online sellers to overcome the negative effect of online reviews on their prices and thus benefit from the reviews. This implies that a prisoner's dilemma is less likely to happen if both sellers offer an MBG returns policy.

J o u r n a l P r e -p r o o f 27 Note that the two sellers coexist in the range c V p 8 4 V f , where p 8 4 g`€ • g i€

• is the efficiency of Seller relative to Seller in selling products in the presence of online reviews. Interestingly, this range is exactly the "symmetric effect range." In general, online product reviews reduce the customers' highest valuation and then reduce the maximum net shared value of the product with an MBG. When the relative changes of both sellers' efficiencies due to the presence of online reviews is in the relative efficiency range where the two sellers coexist, the customer perception of the difference in value between the two products is affected significantly by the additional information from online reviews. Both sellers can either benefit or suffer.

Online shopping offers customers flexibility and convenience, but the lack of hands-on pre-purchase experience with products increases the risk of dissatisfaction, and causes high rates of customer returns. Customers thus rely heavily on online product reviews when they make purchase decisions. Online reviews may significantly affect the customer's valuation on products, and online sellers should consider the impact of reviews in their pricing and returns policies decisions. This paper examines the impact of online reviews in a competitive market with customer returns, and provides new insights into online sellers' optimal pricing strategies and returns policies. Our research shows that ignoring the effects of reviews on online sellers' strategic responses to customer returns may lead sellers to misunderstand the processes and outcomes of online shopping and sales.

We generate several managerial implications for online retailing.

We identify the conditions under which both sellers should offer an MBG in the presence of online reviews. We find that this decision depends not only on the net salvage value of a returned product, as previously noted in the literature, but also on the degree to which the customer relies on online reviews. This implies that it is important for online sellers to consider the impact of product reviews when they choose a returns policy. Our research also shows that the customer is less likely to rely on an MBG in the presence of online reviews, as online reviews provide additional pre-purchase information and reduce the risk of dissatisfaction. Our results suggest that online reviews with comments that contain a lot of information and small variance may be most useful to customers, so the online seller with useful reviews and small variance can reduce the likelihood of customer J o u r n a l P r e -p r o o f 28 returns and reduce the costs (to customer and seller) of returns service.

Our study also suggests that an online seller who sells a high-quality product is more motivated to generate reviews, and will benefit from relatively favorable reviews, as those reviews have more effect on the high-quality seller than on the low-quality seller. For a competing duopoly, online reviews may present the same trend of influence (either positive or negative) on both sellers, when the reviews of the two products are within a symmetric effect region. It is interesting that price competition is intensified between the two sellers if both offer an MBG. Nevertheless, if the salvage value of the product is sufficiently high (for example, durable products), both online retailers are more likely to benefit from online reviews when they offer an MBG.

Our research provides new insights into the behavior of competitive online sellers facing customer returns and online reviews. In setting its returns policy, an online retailer must of course estimate the cost of handling the returned product, the customer's cost of returning the product, and the salvage value of the returned product. Our results emphasize, however, that the online retailer must also evaluate the online reviews posted by customers who have purchased and experienced the products.

Our study can be extended in several ways. Here we consider the impact of online reviews on the customer's valuation on product, but it would be interesting to examine how online reviews can affect the customer's satisfaction rate. The study could also be extended to examine how online reviews impact the decisions of the retailers and manufacturers in a supply chain facing customer returns. Finally, the multi-period case, in which both sellers offer an MBG policy for a certain period of time, but a no-refund policy afterwards (final sale), might shed new light on all of the conditions and results discussed here.

Proof of Proposition 2: With profits of two online sellers in Eq. (9), for { , } and r : ≥ 0, X : cZ i X : sZ i <(fe`de i "g`a m de`g ia b i h(fe`de i "g`a ƒ de`g ia b i -(fe`de i ""`a (e`de i "(je`de i " o n ≥ 0 and X : Z`c X :

Z`s e`<(fe`de i "g ia m de i g`a b`h (fe`de i "g ia ƒ de i g`a b`-(fe`de i "" ia e i (e`de i "(je`de i " o n ≥ 0.

Proof of Lemma 2: For < 1, we have r 8 r 3 ( 1" < 0.

For < fi (f-`di " o (cd‹"(" i€ d" o "`€" (je`de i " o (e`de i "‹ 0.

For | c < | f < 1 , we have x

Pricing strategies in a supply chain with multi-manufacturer and a common retailer under online reviews

Canada retail e-commerce sales

Customer return policies for experience goods

Implementing market segmentation using full-refund and no-refund customer returns policies in a dual-channel supply chain structure

When to introduce an online channel, and offer money back guarantees and personalized pricing?

Compete in price or service? -A Study of personalized pricing and money-back guarantees

Competing in a supply chain via full-refund and no-refund customer returns policies

Third-party product review and firm marketing strategy

Online consumer review: Word-of-mouth as a new element of marketing communication mix

The effect of word of mouth on sales: Online book reviews

When online reviews meet hyperdifferentiation: A study of the craft beer industry

No refund or full refund: When should a fashion brand offer full refund consumer return service for mass customization products?

Return policies and the optimal level of "hassle

Product-oriented web technologies and product returns: an exploratory study

The digitization of word of mouth: promise and challenges of online feedback mechanisms

Strategic manipulation of internet opinion forums: Implications for consumers and firms

The dynamics of online word-of-mouth and product sales-An empirical investigation of the movie industry

Demonstrations and money-back guarantees: Market mechanisms to reduce uncertainty

Retailer's rationale to refuse consumer returns in supply chains

Top 14 ecommerce rating and review tools: An overview

Decomposing the effects of online customer reviews on brand, price, and product attributes

Pricing, frills, and customer ratings

Online product reviews : Implications for retailers and competing manufacturers

Self-selection and information role of online product reviews

Supply chain coordination with customer returns and refund-dependent demand

How online customer reviews affect sales and return behavior -An empirical analysis in fashion e-commerce

Reviews, reputation, and revenue: The case of Yelp

Product information websites: Are they good for consumers?

Too good to be true: The role of online reviews' features in probability to buy

Promotional chat on the internet

Money-back guarantees: Helping the low-quality retailer

To keep or not to keep: effects of online customer reviews on product returns

Signaling quality with a money-back guarantee: The role of transaction costs

Consumer returns in the retail industry. National Retail Federation

The plague of ecommerce return rates and how to maintain profitability

Office of Consumer Affairs. Innovation, science and economic development Canada

E-tailer's return policy, consumer's perception of return policy fairness and purchase intention

How unequal perceptions of user reviews impact price competition

Retail returns specialist optoro raises $75 million in new funding

How fashion ecommerce retailers can reduce online returns

The impact of online reviews on customers' buying decisions

The impact of online product reviews on product returns

How much do online consumers really value free product returns? Evidence from eBay

Price and money-back guarantees as signals of product quality

Consumer returns policies and supply chain performance

How does the variance of product ratings matter?

Understanding money-back guarantees: Cognitive, affective, and behavioral outcomes

Retail e-commerce explodes in Canada amid COVID-19 pandemic

Remote purchase environments: The influence of return policy leniency on two-stage decision processes

Do professional reviews affect online user choices through user reviews? An empirical study

The authors gratefully acknowledge financial support from the Fundamental Research Funds for the Central Universities (China) (Grant No. JBK1805005), and the Social Sciences and HumanitiesResearch Council and the Natural Sciences and Engineering Research Council of Canada.

Ai, X., Chen, J., Zhao, H., & Tang, X. (2012) . Competition among supply chains: Implications of J o u r n a l P r e -p r o o f 29 full returns policy. International Journal of Production Economics, 139(1) , 257-265.

Retail (2019) . Consumer Returns in the Retail Industry 2019, https://appriss.com/retail/wp-content/uploads/sites/4/2020/01/AR3019-2019-Customer-Returns-in-t he-Retail-Industry.pdf (Accessed on August 9, 2020).Anderson, E.T., Hansen, K., & Simester, D. (2009) . The option value of returns: Theory and empirical evidence. Marketing Science, 28(3) , 405-423. Archak, N., Ghose, A., & Ipeirotis, P. G. (2011) . Deriving the pricing power of product features by mining consumer reviews. Management Science, 57(8) , 1485-1509.

Business Bureau. Your refund rights with retailers. https://www.bbb.org/new-york-city/get-consumer-help/articles/your-refund-rights-with-retailers/ (Accessed on August 9, 2020). The boundary values of for Δ 4 0, ΔS 4 0, and ΔX 4 0, respectively. ˆx 4 , ˆy 4 , and ˆz 4

The boundary values of for ‰ 4 ‰ 4 0 , ‰S 4 ‰S 4 0 , ‰X 4 ‰X 4 0, respectively.The impact of the value of online reviews on Seller 's price, demand, and profit relative to that of Seller , where ~ , S, X. fe`e i (e`de i "n < 0, and 

For ' {00, 11}, with prices, demands and profits of two online sellers in (8) (je`de i " o (e`de i " ‹ < 0;In addition, , then ˆy cc ˆy ss 0 and ˆz cc ˆz ss 0. J o u r n a l P r e -p r o o f Highlights • We consider two online sellers selling quality-differentiated products on a platform;• The online platform may enable customers to post and search product reviews;• The online seller's returns policy strategy under the impact of reviews is examined;• Reviews impact the duopoly's decisions differently under different returns policies;• Interactions between online reviews and returns policy are discussed for the duopoly.J o u r n a l P r e -p r o o f