Journal of the Association for Information Systems (2018) 19(11), 1130-1144 doi: 10.17705/1jais.00522

RESEARCH PAPER

ISSN 1536-9323

Is More Information Better? An Economic Analysis of Group-Buying Platforms

Hong Xu1 1School of Business and Management, University of Science and Technology, Hong Kong, [email protected]

Abstract

Group buying as a new form of e-commerce has experienced rapid development over the past few years. Group-buying platforms offer a new channel for local small- to medium-sized companies to promote themselves, and also provide consumers with the opportunity to experience new products and services at deep discounts. In this paper, we examine merchants’ pricing strategies and consumers’ purchasing decisions when different types of information are available on a group- buying platform. Consumers purchasing deals from group-buying platforms face a high level of quality uncertainty, due to lack of experience with the products and incomplete information about the products and merchants on group-buying platforms. The lack of face-to-face communication between customers and merchants before redeeming the deals also intensifies the uncertainty between the transacting parties. Group-buying platforms seek to alleviate such uncertainty by designing a rich user interface that contains various types of information about the merchants or the deals. We use a game-theoretic model to capture the interactions between merchants and consumers under three cases, contextualized by a simple, moderate, or complex information environment. We show that merchants benefit when the environment moves from a simple to moderate information environment, but further movement from a moderate to a complex information environment leads to a more intriguing effect on merchants’ discount strategies. In particular, very high-quality merchants or very low-quality merchants benefit from larger discounts in the context of complex information versus a moderate information environment; therefore, such merchants are disadvantaged when more than a moderate amount of information is provided. Our analysis shows that providing more information can harm merchants under certain conditions; we offer implications for merchants as well as for the group-buying platforms concerning their information strategies.

Keywords: Group Buying, Online Platforms, Information Asymmetry, Game Theory

Kenny Cheng was the accepting senior editor. This research article was submitted on December 2, 2016 and went through 2 revisions. enormous number of local merchants and consumers. 1 Introduction Local merchants offer products and services at a discounted price through an online group-buying Group buying constitutes an adventurous exploration platform, and consumers purchase vouchers through of the e-commerce world by entrepreneurs who the platform entitling them to consume the product foresee the potential of social commerce. The success later from the merchant directly. The popularity of of , LivingSocial, and many other similar group buying is supported by the multiple benefits it group-buying websites have made group buying a offers to both merchants and consumers. Since popular and sometimes necessary option for an merchants on group-buying websites tend to be small-

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to medium-sized local merchants, group-buying vendor to refer to vendors whose product is of overall platforms offer an economical and efficient promotion high or low quality. Experience quality introduces channel for such merchants to reach new customers. uncertainty into consumers’ purchases because it Merchants share a percentage of their revenue from cannot be evaluated before purchase. Additionally, vouchers sold as a commission to the platform, and merchants may strategically withhold certain there is no up-front cost to join the platform. information from customers in order to influence Consumers, on the other hand, get the opportunity to consumers’ purchasing decisions in favor of the experience previously unfamiliar products and merchants. The incomplete nature of the information services at a discounted price and therefore at lower provided on these sites naturally complicates consumers’ risk. One prominent and common feature on group- purchasing decisions (Dimoka et al., 2012). buying platforms is a rich user interface, which Merchants’ main objective on these platforms is to provides multiple sources of information to facilitate advertise their products to consumers who are consumers’ purchasing decisions, a promotional unaware of their products but who would be willing setting that is scarcely possible offline. Through deal to purchase them at the regular price once acquainted pages, merchants can share information about their with the product quality. The group-buying products, such as the original price, the discount mechanism allows merchants to offer such consumers level, the discounted price, a description of the an opportunity to sample the product at a discount, merchant, a description of the product characteristics, with the anticipation that, after experiencing it, they etc. Along with the above information from the will continue to purchase the product at the regular merchants, platforms also display another important price. Dholakia’s (2012) survey indicates that up to type of information—the number of vouchers sold. 80 percent of customers on group-buying websites are This study analyzes the role of information disclosure first-time customers. However, merchants must on the effectiveness of group-buying promotions. We contend with two challenging categories of develop a game-theoretic model in order to capture customers: Some first-time customers may purchase the interactions between merchants and consumers on the product through the group-buying platform at a a group-buying platform, with the objective of deep discount, but do not value the product enough to developing a theoretical framework for the optimal purchase it at the regular price. As such, this type of information structure that suits different types of consumer will not become a long-term customer. merchants with different market characteristics. This Second, some consumers on the group-buying paper answers two research questions. (1) How does platform are existing customers of the merchants and the information available on the group-buying platform, have already experienced the product quality. such as price, discount level, quantity sold, etc., affect We refer to customers with prior experience about the consumers’ purchasing decisions and merchants’ pricing product as informed customers, while uninformed decisions? And (2) under what information structure can customers indicate customers with no prior merchants most effectively promote themselves in the knowledge of the product. Informed customers have context of a group-buying platform? already experienced the quality attributes of the For this study, we consider an incomplete information product, while uninformed customers are new setting, in which merchants disclose partial quality customers with no prior experience with the product. attributes to consumers. There are several things that Informed customers thus have an information make the information setting incomplete. First, advantage over the uninformed customers. As vendors on group-buying platforms are mostly small- discussed and modeled below, this information to medium-sized local merchants and customers on advantage is reflected in the purchasing decisions of these platforms are mostly first-time shoppers with the informed customers, which can help uninformed the merchants (Dimoka et al., 2012). This thus customers form an expectation about the attributes naturally engenders a high level of uncertainty of the unknown product. between the trading parties, and this uncertainty is Inherent to group-buying websites are some unique difficult to eliminate through the information revealed features that reveal different types of information and on a deal’s webpage. Furthermore, most products are capable of bridging the information gap between contain both search attributes, which are easy to the two types of consumers. The most significant describe through words or pictures, and experience feature is information about the number of vouchers attributes, which customers can evaluate only through sold, which is usually displayed in a prominent consuming the product (Nelson, 1970). The quality of position on a deal’s web page. A high number of a product is determined by the quality of both types of vouchers sold indicates that many customers have attributes, which we refer to as search quality and viewed this product and decided to purchase it. Early experience quality throughout the paper. Both consumer purchasing decisions serve as an important experience quality and search quality can vary among piece of information for later consumers facing the vendors. In this paper, we use high- and low-quality same decision-making process. We argue that the

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early purchasers tend to be informed customers who signals, and (3) a complex information environment are well aware of the product quality; therefore, we with both quantity and discount signals. Our analysis maintain that the quantity sold is a reflection of generated several main findings: First, the informed consumers’ purchasing decisions, which are information environment on a group-buying platform based on their personal knowledge of the true value of has a critical impact on merchants’ decisions to join the product quality. Another feature is the discount level the platform and offer discount promotions. When the displayed on a deal’s page. Although discounts lead to platform provides no information signal to facilitate economic savings for customers, they can also be consumers’ purchases, the platform appeals to a coupled with negative effects on consumer decision- limited group of merchants offering high experience making. Due to their online context, group- buying quality, while the rest of the merchants do not benefit platforms inherently invoke a high degree of uncertainty from discount promotions. When the platform reveals for consumers, which is further elevated by the fact that more information on the platform to guide consumers, most consumers on the websites are new customers it motivates other merchants with low experience (Dholakia, 2012; Tuttle, 2012). As such, a large discount quality to join the platform and offer discount can operate as a negative signal about product quality promotions. Second, information signaling is crucial and hence reduce the number of purchases. for effective discount promotions. The objective of attracting all convertible customers can only be However, it is worth noting that, beyond the unknown achieved when the platform provides quality signals quality attributes, consumers with no prior experience to consumers. Further, more information can also be with the merchants also lack another critical piece of harmful to some merchants because merchants may information—that is, the proportion of existing be forced to offer higher discounts as more customers of a product. In other words, consumers information signals become available. For instance, who are new to the merchants’ products know that vendors with very low or very high experience quality informed customers exist, but they do not know the offer higher discounts in the complex information market coverage—i.e., the ratio of informed versus environment than they do in the moderate information uninformed customers. As a result, consumers are environment. The reason for this is that more unable to assess the true level of quality in the information motivates more merchants to join the price traditional learning context. Therefore, they can promotion, and intensifies the competition among only assume that different types of information merchants to gain customers. We also provide insights influence customers’ belief positively or on the effect of market composition and consumers’ negatively, and we thus investigate the effect of belief formation on merchants’ discounting strategies. different levels of information exposure on the effectiveness of group-buying promotions. This paper makes several contributions. First, we offer a unique focus on the signal structure of group- Merchants determine the price or the corresponding buying platforms, and we assess the effects of discount level with the objective of attracting different signals on merchants’ promotion uninformed customers who would be willing to effectiveness. Our analysis generates the purchase the product at the regular price in the future. counterintuitive result that more information can be We refer to these customers as convertible customers. bad for both merchants and platform owners. Second, A large discount imposes two opposing forces on our findings have important implications for uninformed consumers’ purchasing decisions. On the entrepreneurs about the intricate role of information one hand, it invokes consumers’ suspicions about for merchants’ and consumers’ behaviors. When product quality and negatively affects their intention establishing an online business, entrepreneurs face the to purchase. On the other hand, a large discount not critical decision of how to create an online only leads to high price savings, but also results in a environment with various types of information higher number of vouchers sold from informed displayed across webpages in order to entice consumers; both factors can encourage uninformed consumers to make purchases. Understanding the consumers to purchase from an unfamiliar merchant. consequences of information on consumers is Also, a large discount can induce many informed therefore a critical element in designing an online consumers to purchase, leading to a higher quantity of shopping platform and creating an online consumer vouchers sold. The quantity sold can then positively experience. Finally, our study adds to the growing affect the uninformed consumers’ purchasing decisions. group-buying literature in two ways. To the best of We examine merchants’ pricing strategies, accounting our knowledge, this is the first study that examines for all these potential factors, and analyze the impact of different information structures present on group- various factors on the optimal price decisions. buying platforms and that focuses on the potential We analyze both merchants’ and consumers’ negative effects of information. Also, most existing strategies in scenarios with (1) a simple information studies on group buying are based on the critical environment with no information signal, (2) a assumption that consumers know the market moderate information environment with quantity situations of the products and that they can rationally

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learn the true quality of the products in equilibrium be used as a signal that differentiates high-quality (Subramanian and Rao, 2016). We emphasize the fact sellers from low-quality sellers, and, therefore, that consumers have little knowledge about merchants customers tend to rationally perceive that high quality and their products or services on group-buying correlates with a high price tag in equilibrium platforms. We examine these customers’ reactions to (Kirmani and Rao, 2000; Rao, 2005). There is an deals on sites such as groupon.com and we offer extensive literature in information economics suggestions to merchants as well as the platforms to showing that price can be a credible signal of quality better capture these uninformed and valuable customers. in various market settings (Bagwell and Riordan, 1991; Wolinsky, 1983; Daughety and Reinganum, The remainder of the paper is organized as follows. In 2007, 2008; Janssen and Roy, 2010). In particular, Section 2, we survey the related literature. Section 3 Wolinsky (1983) and Bagwell and Riordan (1991) describes the model setup. Section 4 presents the both demonstrate that such signaling effect can result model analysis. Section 5 discusses the implications from the presence of customers who are more of providing more information. We conclude the informed about product quality. In an experimental paper in Section 6. study, Shiv et al. (2005) shows that customers may lower their expectations of product quality when they 2 Related Literature pay a discount price, and later overevaluate the actual performance of the product. Rao (2005) provides Our study is closely related to studies on group- similar evidence showing that consumers are buying platforms. Selling through a platform offers cognitively miserly and are likely to adopt a price- strategic values to online retailers (Kwark et al., quality heuristic. Our paper contributes to this 2016). Yang et al. (2016) study vendors’ decisions to literature by examining the signaling role of join a group-buying platform or not and discover a discounted price in a group-buying setting where the critical range where vendors are better off by joining price is set strategically with the unconventional such a platform. Jing and Xie (2011) compare group objective of effectively promoting the product, selling to conventional single-unit selling and beyond the objective of generating revenue. Our promotion strategies and focused on the information study shows that, in this setting, price continues to gap between the two sales channels. Our current moderate consumers’ purchasing decisions. study further explores the information structure that enables customers to bridge the information gap, and Our study is also related to the vast literature on investigates the effectiveness of group selling in product uncertainty in online commerce. The time different product contexts. Hu et al. (2013) compare and spatial separation between online sellers and simultaneous and sequential group-buying buyers leads to a high level of information asymmetry mechanisms for the categories of necessity and luxury between the trading parties, which in turn leads to goods. Our study examines more generally the high levels of perceived uncertainty in the online impacts of product features on group-buying platform environment (Dewan and Hsu, 2004; Jin and Kato, strategies. Shivendu and Zhang (2013) study the 2006; Ghose, 2009; Li et al., 2009; Dimoka et al., strategic interactions between merchants and the 2012). Studies have shown that consumers’ group-buying platform, and derive the optimal purchasing decisions are significantly affected by the discount strategies. In comparison, we study existence of product uncertainty (Brynjolfsson and merchants’ discount strategies from the perspective of Smith, 2000; Ba and Pavlou, 2002; Overby and Jap, quality signals and customer acquisition. Edelman et 2009; Kim and Krishnan, 2015; Kwark et al., 2016). al. (2014) and Kumar and Rajan (2012) study the Kwark et al. (2014) discovered that product reviews, profitability of selling through group-buying while containing information about product quality, platforms. Subramanian and Rao (2016) examine the can harm the retailer or the manufacturer. Our study signaling effect of discounts and how consumers learn extends this literature to the context of group-buying about product quality through the discount levels. Our websites, where the platforms engage in various study differs from the above literature in that we information structure designs to alleviate the product adopt an incomplete information structure, according uncertainty involved in the transactions, and also to which consumers cannot infer the true quality of demonstrates that releasing more information can the product even in equilibrium. Also, we combine actually harm vendors under certain conditions. two sources of information signals—quantity and discount level—in consumers’ decisions. We take the 3 Model Description unique angle of comparing merchants’ performance when different types of signals are available. We consider a game between a vendor and a mass of 1 consumer. The vendor sells one type of product in Another related stream of research examines the two periods. In the first period, the vendor sells signaling role of prices. Prior studies offer evidence through a group-buying platform (GBP) at a that prices can affect how consumers perceive the discounted price . In the second period, the vendor quality of corresponding products. A high price can 𝑝𝑝1 1133

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sells through his or her own store at the regular price We solve for the cutoffs as = + and of . Let 1 be the discount rate in the context of = + . We denote ( ) as the proportion 𝐼𝐼 0 1 group buying, then = . The product contains of informed consumers who purchase𝜏𝜏̄ 𝑎𝑎 at price𝑎𝑎 − 𝑝𝑝, and 𝑈𝑈𝑈𝑈 0 1 two𝑝𝑝 types of− 𝑑𝑑attributes, search and experience. The 𝜏𝜏̄ ( ) =𝑎𝑎 . 𝑎𝑎We� − denote𝑝𝑝 and 𝑞𝑞 as𝑝𝑝 the proportion of 1 quality of the product𝑝𝑝 therefore𝑑𝑑𝑑𝑑 depends on both types uninformed consumers who purchase in the𝑝𝑝 first 𝐼𝐼 𝑈𝑈𝑈𝑈 of attributes. The vendor reveals information about 𝑞𝑞period𝑝𝑝 at𝜏𝜏 ̄the promotion price,𝑞𝑞 and = . the search attributes through the group-buying website, and we denote the quality related to the The vendor’s profit from selling𝑞𝑞 𝑈𝑈through𝑈𝑈 𝜏𝜏̄𝑈𝑈𝑈𝑈 a group- search attributes as . The experience attributes buying platform in period 1 is cannot be revealed through the website, and can only 0 = ( ( ) + (1 ) ) . be assessed through 𝑎𝑎consumption of the product (3) (Nelson, 1970). We assume that it is public 𝜋𝜋1 𝜆𝜆𝜆𝜆 𝑝𝑝1 − 𝜆𝜆 𝑞𝑞𝑈𝑈𝑈𝑈 𝑝𝑝1 knowledge that the quality of the experience In period 2, some of the uninformed consumers who attributes is uniformly distributed on [ , ]. We use purchased in period 1 may continue to purchase at the to refer to the true value of the experience quality. regular price. The demand from uninformed 1 1 consumers in period 2 is therefore (1 The consumers also differ in their misfit𝑎𝑎 𝑎𝑎 ̄ with the 1 ) min { ( ), }. The vendor’s profit in period 2 is product,𝑎𝑎 and is uniformly distributed on [0, 1]. The − misfit characterizes consumers’ horizontal 𝜏𝜏difference 𝑈𝑈𝑈𝑈 𝜆𝜆 = (𝑞𝑞 𝑝𝑝( )𝑞𝑞+ (1 ) min { ( ), }) in their evaluation𝜏𝜏 of the product, and consumers . (4) know their own misfit. 2 𝑈𝑈𝑈𝑈 𝜋𝜋 𝜆𝜆𝜆𝜆 𝑝𝑝 − 𝜆𝜆 𝑞𝑞 𝑝𝑝 𝑞𝑞 𝑝𝑝 (1 ) ( ) There are two types of consumers. A proportion of Note that, are the uninformed consumers who would have bought under the regular the consumers are informed (I) consumers, who have − 𝜆𝜆 𝑞𝑞 𝑝𝑝 prior experience with the product and know the 𝜆𝜆true price if they knew , and we call these customers the convertible customers. On the other hand, the rest quality of the experience attributes . The rest 1 1 𝑝𝑝 𝑎𝑎 (1 )(1 ( )) are uninformed (UI) consumers, who have no of the uninformed customers, are 1 experience of the product and hold𝑎𝑎 a belief about− 𝜆𝜆 not convertible because their valuation for the product − 𝜆𝜆 − 𝑞𝑞 𝑝𝑝 the quality of the experience attributes. Each consumer is so low that they would not purchase at the regular 1 demands at most one unit of the product 𝑎𝑎�in each price even if they had complete information about < ( ) period1. The utility from the product is = + the product. When , the vendor attracts some 𝑝𝑝of theconvertible customers through group and = + for informed and uninformed 𝑈𝑈𝑈𝑈 0 1 𝑞𝑞 𝑞𝑞 𝑝𝑝( ) consumers respectively. We assume the𝑢𝑢 informed𝑎𝑎 𝑎𝑎 and− selling, and when , all convertible 0 1 customers are attracted through group selling. In the uninformed𝜏𝜏 𝑢𝑢 𝑎𝑎 consumers𝑎𝑎� − 𝜏𝜏 are independently distributed in 𝑈𝑈𝑈𝑈 𝑞𝑞 ≥ 𝑞𝑞 𝑝𝑝 . In other words, captures the characteristics of the following analysis, we focus on the case where the consumers and is independent of one’s prior vendor can attract all convertible customers to 𝜏𝜏experience with the𝜏𝜏 product. purchase in the promotion. This assumption allows us to focus on vendors whose objective for the Given price , there exists a consumer who is promotion is not only to generate revenue, but also to indifferent between buying and not buying the product. promote the product to uninformed customers, We define this𝑝𝑝 consumer as and respectively, particularly the convertible customers. with the subscript indicating whether the consumer is 𝐼𝐼 𝑈𝑈𝑈𝑈 The vendor’s decision is to choose the discount price informed, and they satisfy the following𝜏𝜏̄ 𝜏𝜏̄ conditions: to maximize the overall profit across period 1 and period 1 2. We describe the objective formally as the following.𝑝𝑝 = + , (1)

0 1 𝐼𝐼 = max + . =𝑝𝑝 𝑎𝑎+ 𝑎𝑎 − 𝜏𝜏.̄ (2) (5) 1 2 0 1 𝑈𝑈𝑈𝑈 𝜋𝜋 𝑝𝑝1 𝜋𝜋 𝜓𝜓𝜋𝜋 𝑝𝑝 𝑎𝑎 𝑎𝑎� − 𝜏𝜏 ̄ We use to describe the relative importance of the 1 In practice, group-buying websites, such as groupon.com, long-term profit from sales at the regular price and often include a limit on the number of vouchers that a the current𝜓𝜓 profit from group selling. For example, customer is allowed to purchase, which is intended to spas, movie theaters, and restaurants have more prevent repeated purchases by consumers. We believe incentive to attract long-term buyers, and buyers also repeated purchases will not affect our model and findings. tend to go back to the same vendor if they are With the uncertainty that uninformed consumers face, informed consumers would be more likely to purchase satisfied. On the other hand, vendors with low multiple vouchers than uninformed consumers—in either have a high discount factor or expect fewer which case, as discussed below, the quantity sold would repeat purchases due to the nature of the products.𝜓𝜓 be a less accurate signal and could be easily captured Examples include durable goods, such as electronic through a lower , making more of our results robust to devices, hospital services, etc. different levels of . 𝛼𝛼 𝛼𝛼

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In the following, we consider an ideal case where all to make their purchase decision, and the consumers are informed and is public knowledge. 𝑎𝑎1+ 𝑎𝑎1 corresponding cutoff consumer has = + In this special case, the vendor chooses a price to 2 1 ; that is, consumers with will purchase. In the optimize its revenue, without𝑎𝑎 any consideration for 0 1 second period, of the uninformed consumers𝜏𝜏̃ 𝑎𝑎 𝑎𝑎have� − attracting uninformed consumers. Since there is no 1 discovered𝑝𝑝 the true , and𝜏𝜏 consumers≤ 𝜏𝜏̃ with + uncertainty among the consumers, the vendor has no are willing𝜏𝜏̃ to purchase at . Hence, the incentive to offer discounts through the group-buying 1 0 demand from the𝑎𝑎 uninformed consumers𝜏𝜏 ≥ 𝑎𝑎 is platform and will set the same price for both periods. 1 min𝑎𝑎 − {𝑝𝑝 + , }. In other words,𝑝𝑝 an uninformed This benchmark shows the vendor’s and the consumer is convertible, when his or her willingness to consumers’ strategies in the absence of uncertainty. 𝑎𝑎0 𝑎𝑎1 − 𝑝𝑝 𝜏𝜏̃ The optimal price is determined by the following: pay exceeds once becoming informed of . We denote the optimal price in this case with a superscript 1 = max ( ) + ( ) to indicate that𝑝𝑝 it is the simple information scenario.𝑎𝑎 𝑠𝑠 When + < , some of the consumers 𝜋𝜋 = max𝑝𝑝 (𝑝𝑝1𝑞𝑞+𝑝𝑝 ) 𝜓𝜓𝜓𝜓𝜓𝜓 𝑝𝑝 ( ) . attracted by the low price in the first period will not 1 0 1 make further𝑎𝑎 𝑎𝑎 purchases.− 𝑝𝑝 𝜏𝜏̃ The demand in the second 𝑝𝑝 𝜓𝜓 𝑝𝑝 ∫𝑎𝑎1+𝑎𝑎0−𝑝𝑝 𝑓𝑓 𝑥𝑥 𝑑𝑑𝑑𝑑 which leads to = . Consumers with period from both the informed and the uninformed 𝑎𝑎0+𝑎𝑎1 [0, ] purchase ∗the product. consumers is + . The optimal promotion 𝑝𝑝 2 𝜏𝜏 ∈ 𝑎𝑎0+𝑎𝑎1 price can be derived through the first-order 0 1 It is worth2 noting that, if the vendor can successfully condition of 𝑎𝑎 as 𝑎𝑎 − 𝑝𝑝 attract all convertible customers in the first period, their 𝑝𝑝1 1 + + (1 ) second period pricing follows the above strategy. 𝜋𝜋 = . 2 𝑠𝑠 0 1 1 1 𝑎𝑎 𝜆𝜆𝑎𝑎 − 𝜆𝜆 𝑎𝑎� 4 Information Environment In the second𝑝𝑝 period, the demand from both informed and uninformed consumers is + . The Our focus of analysis is on the information optimal regular price can be solved by maximizing 0 1 environment that a group-buying platform designs for (following similar procedures as in𝑎𝑎 the 𝑎𝑎case− 𝑝𝑝with full 2 the vendors and its impact on vendors’ pricing power, information) as = . If we reorganize 𝜋𝜋as as well as the effectiveness in converting all 𝑎𝑎0+𝑎𝑎1 𝑠𝑠 = + (1 ) and denote the discount in 1this convertible customers. We examine three different 𝑝𝑝 2 𝑝𝑝 information environments and compare vendors’ and 𝑠𝑠 𝛥𝛥𝑎𝑎1 ( )( ) 1 = 1 = 𝑝𝑝case as𝑝𝑝 , then− 𝜆𝜆 2 𝑠𝑠 . It is easy customers’ strategies under each of them. The 𝑝𝑝1 1−𝜆𝜆 𝑎𝑎1−𝑎𝑎�1 to see that, only vendors whose quality is below objective is to investigate the role of different 𝑑𝑑𝑠𝑠 𝑑𝑑𝑠𝑠 − 𝑝𝑝 𝑎𝑎0+𝑎𝑎1 information sources, such as different product average will offer discounts when the information properties, as well as different market positions, in environment is simple, i.e., > . inducing effective promotion. In the following, we To ensure that all convertible𝑎𝑎1 consumers𝑎𝑎�1 purchase in assume that the informed consumers move first to the promotion, we need + < , which is make purchases before the uninformed consumers do. equivalent to < . Note that, this condition 0 1 The assumption allows us to focus on the contradicts the earlier result𝑎𝑎 that𝑎𝑎 only− 𝑝𝑝 above𝜏𝜏̃ -average 1 1 informational advantage of the informed consumers. vendors offer discount𝑎𝑎 𝑎𝑎� s. In other words, for a group- In practice, however, it is possible that uninformed buying platform with a simple information consumers purchase right after a deal is posted, environment, only high-quality vendors participate; especially if the price if low enough. We decided to however, they cannot motivate all convertible exclude this scenario from our study because the customers to purchase through the promotion. We information role of the informed consumers is silent present this finding formally in the following. in this case. Lemma 1. For a platform with a simple information 4.1 Simple Information Environment environment, vendors whose experience quality is above consumers’ prior beliefs have incentives to We start with a simple information environment, offer promotions; however, not all convertible where the vendor sells the product at a discount in the consumers purchase during the promotion. first period without providing any additional information for the consumers to learn about the This result states that a platform with no additional product. We observe such promotions in both online information is more favorable to vendors with and offline settings, where consumers cannot see superior quality, but that even these high-quality previous buyers in the promotion. This simple vendors cannot necessarily promote effectively, as information case allows us to focus on the impact of there will always be some valuable consumers the discount itself. With no additional information, who will not purchase at the discounted price. In the consumers use their prior belief, the average â1 = the simple information case, the platform plays a

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weak role in assisting consumers’ purchasing The vendor chooses the optimal discount price to decisions, and consumers face high uncertainty in maximize the following objective 𝑚𝑚 1 making their purchasing decisions. 𝑝𝑝 = ( ( ) + (1 ) ) . Our finding points to two drawbacks of a platform 𝑚𝑚 𝑚𝑚 First order1 condition1 leads𝑈𝑈 𝑈𝑈 1to = with a simple information environment. On the one ( 𝜋𝜋) 𝜆𝜆𝜆𝜆 𝑝𝑝( )( −) 𝜆𝜆 𝑞𝑞 𝑝𝑝 , with = 𝑚𝑚 hand, such a platform is suitable only to high-quality ( ( )) 1 𝑎𝑎0+𝜆𝜆𝑎𝑎1+ 1−𝜆𝜆 𝑎𝑎�1−𝛥𝛥𝑎𝑎1𝛼𝛼𝛼𝛼 1−𝜆𝜆 𝑎𝑎0+𝑎𝑎1 𝑝𝑝 vendors, who have a large proportion of consumers . The second period price is derived by optimizing 2 1−𝛥𝛥𝑎𝑎1𝛼𝛼𝛼𝛼 1−𝜆𝜆 Δ𝑎𝑎1 𝑎𝑎�1 − who are convertible. Low-quality vendors will not in a similar fashion as in the full information benefit from price promotion because the benefit from 1 benchmark,𝑎𝑎 and = . We rearrange the discount their low proportion of convertible consumers is 2 𝜋𝜋 𝑎𝑎0(+𝑎𝑎1) price as = + . outweighed by the high cost of offering discounts. On 𝑝𝑝 ( 2 ( )) the other hand, high-quality vendors who indeed offer 𝑚𝑚 1−𝜆𝜆 𝛥𝛥𝑎𝑎1 1 discounts may fail to attract all valuable customers The vendor𝑝𝑝 has𝑝𝑝 2an1− 𝛥𝛥𝑎𝑎incentive1𝛼𝛼𝛼𝛼 1−𝜆𝜆 to offer a price ( ) through the promotion. Customers with very low misfit promotion when < , i.e., < 0 . ( ( )) cost will purchase through the promotion, but those with 𝑚𝑚 1−𝜆𝜆 𝛥𝛥𝑎𝑎1 We derive the condition1 as > 1 or < 0. relatively high misfit cost will find it not worthwhile to 𝑝𝑝 𝑝𝑝 2 1−(𝛥𝛥𝑎𝑎 𝛼𝛼) 𝛼𝛼 1−𝜆𝜆 1 purchase the deal, due to the high uncertainty they face In other words, vendors offer discounts when their Δ𝑎𝑎1 𝛼𝛼𝛼𝛼 1−𝜆𝜆 Δ𝑎𝑎1 regarding the vendor’s experience quality. Overall, the experience quality is above average or significantly above result highlights the necessity of enhancing the below average. We summarize the result formally in information environment and we discuss two such cases the following. in the following subsections. Lemma 2. When the group-buying platform provides 4.2 Moderate Information Environment moderate information environment, vendors offer discounts when < < We now turn to a more sophisticated information ( ) 1 environment, where the platform discloses to < < or when . 1 1 1 𝛼𝛼𝛼𝛼 1−𝜆𝜆 consumers the number of vouchers sold. When an 𝑎𝑎 𝑎𝑎 𝑎𝑎� − uninformed consumer comes to the platform, the This result𝑎𝑎�1 states𝑎𝑎1 that𝑎𝑎̄1 when consumers can update quantity sold (which is provided and often updated on their beliefs through the observed quantity of sales, websites like Groupon, LivingSocial, etc.) is an not only vendors with above average experience indicator of how previous buyers perceive the quality quality join the promotion, but also those with very of the underlying products/services. The higher the low experience quality. Recall that in the case with quantity sold, the more popular the deal is, i.e., the simple information, price promotion is only favorable more people perceive the deal as worthwhile. We for high-quality vendors. This shows that by hence assume an updating rule of = + facilitating consumers’ purchasing decisions, group- (1 ) , where = ( ). buying platforms provide an additional opportunity 𝑎𝑎�1 𝜇𝜇𝑎𝑎1 to low-quality vendors. We− interpret𝜇𝜇 𝑎𝑎�1 this𝜇𝜇 updating𝛼𝛼𝛼𝛼𝛼𝛼 𝑝𝑝1 rule as follows. The demand from informed consumers, ( ), contains We next verify that all convertible customers are + < information about the true quality . However, attracted through the promotion, i.e., 1 + . We introduce = as the solution consumers cannot infer the true quality𝜆𝜆𝜆𝜆 𝑝𝑝 accurately 0 1 1 𝑚𝑚 𝑎𝑎 𝑎𝑎 − 𝑝𝑝 since they lack information about the𝑎𝑎 proportion of to0 =1 1 1 . We1 summarize the 1 𝑎𝑎 𝑎𝑎� − 𝑝𝑝 [ ( ) ] 𝑎𝑎 𝐴𝐴 existing consumers, . Instead, they find𝑎𝑎 out the true 1 1 result0 formally in 1the following proposition.1 quality with a probability , and with probability 𝑎𝑎 𝛼𝛼𝛼𝛼 − 𝛼𝛼 𝛥𝛥𝑎𝑎 𝛼𝛼𝛼𝛼 1−𝜆𝜆 −1 − 𝑎𝑎 1 , they continue𝜆𝜆 to use their prior belief . The Proposition 1. When the group-buying platform 1 probability𝑎𝑎 is increasing in𝜇𝜇 the observed demand provides a moderate information environment, 1 from− 𝜇𝜇 the informed consumers, and is a scalar𝑎𝑎� to vendors can attract all convertible customers if ensure [𝜇𝜇0,1], and we let [0, ]. In other (1) their experience quality is above average, i.e., ( ) 𝛼𝛼 1 max { , } < < , or words, the observed demand determines the accuracy 1 𝜇𝜇 ∈ 𝛼𝛼 ∈ 𝜆𝜆 𝑎𝑎0+𝑎𝑎̄ 1 𝑎𝑎 of consumers’ updated beliefs. (2) when𝑎𝑎�1 𝐴𝐴1 is significantly𝑎𝑎1 𝑎𝑎̄1 below average quality, i.e., < < min { , }. We next analyze consumers’ purchasing decisions 1 ( ) 𝑎𝑎 1 based on the above updating rule. We focus on the 1 1 1 1 case where all convertible customers purchase during With𝑎𝑎 moderate𝑎𝑎 information,𝑎𝑎� − 𝛼𝛼𝛼𝛼 1−the𝜆𝜆 𝐴𝐴platform is more the promotion. We use the superscript to indicate suitable for vendors with either very high or very low the optimal decision from the case of the moderate experience quality. Vendors with very high information environment, as the consumers𝑚𝑚 update experience quality can easily attract a high number of their beliefs based on the number of vouchers sold. informed consumers to purchase their deals. The resulting high quantity of sales can in turn encourage

1136 Journal of the Association for Information Systems

the uninformed consumers to purchase. Similarly, product. With these two opposing forces in place, we vendors with very low experience quality also benefit find it interesting to examine the overall effect of because they have a very small proportion of discounts on consumers’ purchasing decisions, as well as convertible customers. Despite their low quality, these to compare consumers’ behavior under this updating rule vendors can offer very deep discounts to boost the sales to that of the previous case. We use superscript to refer from the informed consumers, and in turn attract all to this case with the complex information environment. convertible customers. It is worth noting that, without 𝑐𝑐 We first derive the optimal price under this case. The quantity information, neither the high-quality nor the first-order condition of vendors’ profit function leads low-quality vendors can attract their convertible ( ) ( ) ( ) to = , which can customers, even if they offer deep discounts. [ ( ) ( ) ( ) ] 𝑎𝑎0+𝑎𝑎1+ 1−𝜆𝜆 𝛥𝛥𝑎𝑎1−𝑚𝑚𝑚𝑚𝑚𝑚 1−𝜆𝜆 𝛥𝛥𝑎𝑎1 𝑎𝑎0+𝑎𝑎1 𝑐𝑐 = + be 1 2 1reorganized+ 1−𝜆𝜆 𝛥𝛥𝑎𝑎1 1− 𝑚𝑚 𝛽𝛽−𝑚𝑚𝑚𝑚𝑚𝑚 as1− 𝜆𝜆 𝛥𝛥𝑎𝑎1 We also compare the discount level in this case with ( 𝑝𝑝 ) [ ( ) ( )] the simple promotion case. Since the simple . 𝑐𝑐 [ ( )( ( ) )] 𝑝𝑝1 𝑝𝑝 promotion only applies to vendors with above 1−𝜆𝜆 𝛥𝛥𝑎𝑎1 1− 1−𝑚𝑚 𝛽𝛽 𝑎𝑎0+𝑎𝑎1 average experience quality, we restrict our We2 1− 𝛥𝛥have𝑎𝑎1 1− the𝜆𝜆 𝑚𝑚 following𝑚𝑚𝑚𝑚− 1−𝑚𝑚 𝛽𝛽 result on vendors’ incentives comparison to < 0 .The following corollary for participating in group buying. Recall that in our summarizes the result. previous analysis, we discovered that certain vendors Δ𝑎𝑎1 of below average quality may not benefit from Corollary 1. When the group-buying platform provides offering discounts through a group-buying platform. a moderate information environment, vendors with the same experience quality choose to offer smaller Lemma 3. When the group-buying platform provides discounts in comparison to the simple information case. complex information environment, vendors offer discounts under the following two sets of conditions: 4.3 Complex Information Environment (1) when > , and < < or < < We now turn to the case where more complex 𝑚𝑚 𝛽𝛽 , or 1 1 1 1 1 ( )[1−𝑚𝑚 ( 𝛼𝛼𝛼𝛼 ) ] 𝑎𝑎� 𝑎𝑎 𝑎𝑎̄ 𝑎𝑎 𝑎𝑎 information is provided to consumers. Besides 1 observing the quantity sold, the platform also 𝑎𝑎�1 − 1−𝜆𝜆 𝑚𝑚𝑚𝑚𝑚𝑚− 1−𝑚𝑚 𝛽𝛽 emphasizes the role of discount (price) information in (2) when < , < < min { 𝑚𝑚 𝛽𝛽 consumers’ decision-making. We assume the < < 0, }1. 1 1 ( )[ ( )1−]𝑚𝑚 𝛼𝛼𝛼𝛼 𝑎𝑎� 𝑎𝑎 𝑎𝑎� − following updating rule: 1 The1−𝜆𝜆 above𝑚𝑚𝑚𝑚𝑚𝑚− 1result−𝑚𝑚 𝛽𝛽 statesΔ𝑎𝑎 1that when𝑎𝑎̄1 multiple sources of = + (1 ) , information are provided, and when the platform is where = 𝑎𝑎�1( )𝜇𝜇𝑎𝑎+1(1 −)𝜇𝜇 𝑎𝑎�1. able to engageconsumers to put a relatively high weight on the observed number of vouchers sold, In the above𝜇𝜇 𝑚𝑚 updating𝑚𝑚𝑚𝑚𝑚𝑚 𝑝𝑝1 rule, both− 𝑚𝑚 𝛽𝛽 and𝑝𝑝1 are scalars to vendors are willing to participate as long as their ensure that ( ) [0,1] and [0,1]. To be quality is not too low, i.e., below . The more specific, we let [0𝛼𝛼, 𝛽𝛽 ] and ( ) 1 ( 1 ) 1 𝛼𝛼𝛼𝛼𝛼𝛼 𝑝𝑝 ∈ 𝛽𝛽𝑝𝑝 1∈ platform is therefore able to exclude very low- 𝑎𝑎�1 − 𝛼𝛼𝛼𝛼 1−𝜆𝜆 [1, ]. The term reflects𝛼𝛼 ∈ the𝜆𝜆 relative𝑎𝑎0+𝑎𝑎̄ 1 weight𝛽𝛽 of∈ quality vendors from joining the platform. We next 1 the two sources of information. A higher means analyze whether the participating vendors can 𝑎𝑎0+𝑎𝑎̄ 1 𝑚𝑚 that consumers put more weight on the observed attract all convertible consumers. 𝑚𝑚 number of vouchers sold, and vice versa. To see this, we check if this condition holds: + < + . Note that this updating rule captures the effect of the 0 discount in two opposing directions. As the discount 𝑐𝑐 𝑎𝑎 We𝑎𝑎1 − 𝑝𝑝denote𝑎𝑎0 𝑎𝑎�1 as− 𝑝𝑝such1 that when = the level increases, meaning that decreases, on the one following equation holds: hand it has the direct effect of lowering consumers’ 𝐴𝐴2 𝑎𝑎1 𝐴𝐴2 𝑝𝑝1 ( ) (( ) ) belief about the unobserved quality. It is worth noting = ( ) . Also that this direct effect of the discount has been [ 𝜆𝜆+1+ 1−𝜆𝜆 (𝛥𝛥𝑎𝑎1 ) 1−𝑚𝑚(( 𝛽𝛽−𝑚𝑚)𝑚𝑚𝑚𝑚 )] 0 1−𝑚𝑚 𝛽𝛽 ( ) 1 established in the prior literature on price as a signal denote𝑎𝑎 𝜆𝜆 𝜆𝜆𝜆𝜆 𝑚𝑚𝑚𝑚as +the1+ 1−solution𝜆𝜆 𝛥𝛥𝑎𝑎1 1 −𝑚𝑚to 𝛽𝛽−𝑚𝑚𝑚𝑚𝑚𝑚 −+𝑎𝑎1 + (1 for quality—i.e., it has been discovered that low ) ((1 ) ) = 0 . 1We−𝑚𝑚 𝛽𝛽 state the 𝑚𝑚𝑚𝑚 prices (i.e., a large discount) may operate as a conditions𝑚𝑚̄ for converting all convertible customers in− 1 negative signal for quality, leading consumers to below.𝜆𝜆 Δ𝑎𝑎 − 𝑚𝑚 𝛽𝛽 − 𝑚𝑚𝑚𝑚𝑚𝑚 think negatively about the product quality (Bagwell and Riordan, 1991; Daughety and Reinganum, 2007; Proposition 2. When the group-buying platform Janssen and Roy, 2010). On the other hand, large provides a complex information environment, discounts may lead to a higher number of vouchers vendors can attract all convertible customers under sold, and therefore can indirectly lead to an increase any of the following three cases: in consumers’ beliefs in the unobserved quality of the

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(1) the vendor’s experience quality is above average, the complex information environment, low-quality i.e., max { , } < < , or vendors face the challenge of further increasing the number of vouchers sold in order to entice (2) customers1 2put significant1 1 weight on quantity 𝑎𝑎� 𝐴𝐴 𝑎𝑎 𝑎𝑎̄ uninformed consumers to purchase, which requires information and the vendor’s experience quality is ( ) them to further lower their prices. Some high-quality low, i.e., < < 1 and < < ( ) ( ) vendors benefit from the complex information 1+𝜆𝜆+ 1−𝜆𝜆 𝛥𝛥𝑎𝑎1𝛽𝛽 environment, particularly those of very high min { , }, or 1 1 1 1−𝜆𝜆 𝛥𝛥𝑎𝑎 𝛽𝛽+𝛼𝛼𝛼𝛼 𝑚𝑚 𝑎𝑎 𝑎𝑎 experience quality. The reason for this is that a large (3) when𝑎𝑎�1 𝐴𝐴 2customers put significant weight on the discount, while increasing the quantity sold, can also discount information and the vendor’s experience lead to a negative perception by consumers about quality is not much lower than the average, i.e., 0 < product quality, and vice versa for a small discount. < and < < . The trade-off between these two forces determines ( ) vendors’ optimal discounting strategy. It is easy to 2 show1 that1 < . This 𝑚𝑚 𝑚𝑚̄ 𝐴𝐴 𝑎𝑎 𝑎𝑎� ( ) ( ) 1+𝜆𝜆+ 1 − 𝜆𝜆 ∆𝑎𝑎1𝛽𝛽 result describes three different sets of conditions, 𝑚𝑚̄ 1 − 𝜆𝜆 ∆𝑎𝑎1 𝛽𝛽+𝛼𝛼𝛼𝛼 under which the vendor can attract all convertible 5 Implications of More Information customers through a group-buying promotion. One Is more information beneficial to vendors? We direct observation is that under the complex discovered that there exists a trade-off between the information condition, vendors with any level of two types of information, which leads to different experience quality can effectively promote through a discounting strategies by vendors with different levels group-buying platform, as long as the platform can of experience quality. Both quantity and discount guide customers to update their beliefs properly. In carry useful information about the vendors’ other words, under complex information experience quality, and they reduce the uncertainty environments, the platform can cater to vendors with and risk faced by uninformed consumers. Vendors different experience qualities, through adjusting the with high quality therefore do not need to engage in parameter . Recall that measures the relative deep discounting, as informed customers who are importance of quantity information for consumers’ aware of their product and quality will “advertise” for decisions. One𝑚𝑚 potential way𝑚𝑚 of influencing is by them through the quantity sold. In the meantime, varying the accuracy or timeliness of quantity reducing their discount level also prevents information. For example, if the platform updates𝑚𝑚 the uninformed consumers from thinking negatively quantity information every ten minutes, instead of in about their high experience quality. On the other real time, the customers may rely less on the quantity hand, vendors with low experience quality offer information and hence adopt a lower . higher discounts than in the simple promotion case, because they need to encourage more informed We next compare to and summarize the results 𝑚𝑚 customers to purchase by using high discounts, and in below. We define𝑐𝑐 𝑚𝑚 ( ) as ( ) = ( ) 1 1 turn attract uninformed customers. 𝑝𝑝 , and𝑝𝑝 as = + ( ). ( )( ( )) 1 1 𝛽𝛽 𝑎𝑎0+𝑎𝑎1 𝑁𝑁 𝑎𝑎 𝑁𝑁 𝑎𝑎 Combining findings from Corollary 2 and Corollary Corollary1−𝜆𝜆 𝛽𝛽+𝛼𝛼𝛼𝛼− 𝛼𝛼2𝛼𝛼𝛼𝛼. 𝑎𝑎When0+𝑎𝑎1 the 𝐴𝐴3group𝐴𝐴3-buying𝑎𝑎�1 𝑁𝑁platform𝐴𝐴3 1, we draw comparisons about vendors’ discounting provides complex information environment, strategies under the three levels of information. (1) vendors of below-average experience quality, i.e., Proposition 3. Comparing the vendor’s discounting < < , always offer larger discounts compared strategy under all three cases, to the moderate information environment scenarios; (1) when a vendor’s experience quality is below 𝑎𝑎1 𝑎𝑎1 𝑎𝑎�1 (2) vendors of above-average quality offer larger average, i.e., < < , the vendor offers lower discounts compared to the moderate information case discounts under the moderate information environment 𝑎𝑎1 𝑎𝑎1 𝑎𝑎�1 if < < and > + ( ) ; otherwise, than under the complex information environment, that they offer lower discounts. is > , and the vendor has no incentive to offer 𝐴𝐴3 𝑎𝑎1 𝑎𝑎̄1 𝑎𝑎̄1 𝑎𝑎�1 𝑁𝑁 𝑎𝑎̄1 discount𝑚𝑚 s in𝑐𝑐 the simple information environment; When the platform provides a complex information 𝑝𝑝1 𝑝𝑝1 environment, vendors with low experience quality (2) when a vendor’s experience quality is much must offer larger discounts compared to the moderate higher than the average, i.e., < < , and < + ( ), the vendor offers the lowest discount information case in order to effectively promote 3 1 1 1 under the moderate information𝐴𝐴 𝑎𝑎environment,𝑎𝑎̄ 𝑎𝑎̄and themselves. Platforms may have incentives to provide 1 1 more information in order to reduce the uncertainties 𝑎𝑎offers� 𝑁𝑁 the𝑎𝑎̄ highest discount under the simple faced by consumers and facilitate transactions. information environment, i.e., < < ; However, we discovered that in the setting of group- 𝑠𝑠 𝑐𝑐 𝑚𝑚 (3) in all other cases, the vendor𝑝𝑝1 s𝑝𝑝 offer1 𝑝𝑝 1the lowest buying promotions, some vendors were worse off discount under the complex information environment, when more information was provided to customers. In

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and offer the highest discount under the simple both high- and low-quality vendors can promote information environment, i.e., < < ; effectively and attract all convertible customers, under 𝑠𝑠 𝑚𝑚 𝑐𝑐 certain conditions. Third, not all vendors prefer One main finding from the above1 1 analysis1 is that 𝑝𝑝 𝑝𝑝 𝑝𝑝 complex information to moderate information, additional information leads to different effects for although all of them prefer either complex or different types of vendors. On the one hand, high- moderate information to simple information. In other quality vendors always prefer either moderate or words, more information is not necessarily better for complex information to simple information; on the the vendors or the platform. other hand, some of them would choose moderate information over complex information. In other These results highlight the importance of information words, more information can harm high-quality structure to group-buying platforms. By offering vendors. In contrast, for low-quality vendors, the different types of information to customers, the finding is more unanimous in that all low-quality platform may become popular with vendors of vendors prefer moderate information to complex different qualities. For instance, to cater to low- information. Our explanation for this intriguing quality vendors, the platform should provide a very finding is that in the complex information rich information environment to facilitate customers’ environment, vendors’ discount choices have opposite purchasing decisions. This can be done by placing the effects on customers’ purchasing decisions. This discount and quantity information at prominent places complexity is particularly harmful for low-quality on a deal’s web page. The platform can also educate vendors, because they must offer very deep discounts consumers on how to make more informed decisions in order to increase the quantity sold and hence by using not only quantity information, but also influence convertible customers’ decisions. However, discount information. In contrast, to attract high- complex information can also harm vendors with very quality vendors, the platform should be cautious and high quality, i.e., < < . As the platform not provide too much information to customers. It is switches from a moderate information to a complex worth highlighting that more information is not 3 1 1 information environment𝐴𝐴 ,𝑎𝑎 these𝑎𝑎 ̄ high-quality vendors necessarily better for group-buying platforms, must offer even larger discounts because they have a depending on the type of information. very high proportion of convertible customers. In other This study can be potentially extended in a few words, as more information becomes available to directions. First, future studies may look at the case customers, vendors must adjust their discounting scenario of vendors promoting through group-buying strategy in order to influence customers’ updated beliefs, platforms who do not attract all convertible and hence their purchasing decisions. Our analysis customers. In the current study, we chose to focus on highlights an aspect that is very important and yet the scenario in which vendors experience effective different from previous studies. Information, while promotion, meaning that all customers who are alleviating the quality uncertainty concerning interested in buying at regular prices are attracted by consumers’ purchasing decisions in the online the promotion. While we believe our focus fits the environment, can also harm vendors through the indirect objectives of most vendors promoting on group- effects of their discount strategies on their customers. buying platforms, examining other case scenarios may provide complementary insights. Second, the 6 Conclusion current model assumes a uniform distribution of consumers, and this distribution can be extended to In this paper, we analyzed the information structure other more complex formats to potentially capture on group-buying platforms and its impact on other consumer characteristics. It would also be customers’ and vendors’ strategies. We focus on three interesting to examine other types of information on types of information contexts: simple, moderate, and group-buying platforms, such as social information. complex information environments. We have several Groupon.com now displays social information such as main findings. First, only high-quality vendors join “likes” and Yelp review excerpts on deal the platform under the simple information case pages. Although this information is selected by the scenario. As more information is provided to vendors themselves, social information like this may customers, low-quality vendors also have incentives nevertheless influence consumers’ purchasing decisions. to promote on the platform. Second, in both the moderate and complex information environments, .

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Appendix

Proof to Proposition 2 The condition is equivalent to < ( + ) , and can be reorganized as (1 ( ) ( ) ) < + (1 ( + )) . Substituting in , the condition𝑚𝑚 𝑚𝑚 becomes < 𝑚𝑚(1 1 1 1 0 1 1 1 ( ( )) 1 𝑎𝑎 − 𝑝𝑝 𝑎𝑎� − Δ𝑎𝑎 𝛼𝛼𝛼𝛼 𝑎𝑎 𝑚𝑚 𝑎𝑎 − 𝑝𝑝 − 𝑝𝑝 1−𝜆𝜆 𝛥𝛥𝑎𝑎1 1−𝛥𝛥𝑎𝑎1𝛼𝛼𝛼𝛼 𝑝𝑝 − 1 ). Note that,1 to ensure0 1< , we already know1 that < 0. Therefore,1 if we multiple1 both Δ𝑎𝑎 𝛼𝛼𝛼𝛼 𝑝𝑝 Δ𝑎𝑎 − 𝛼𝛼𝛼𝛼 𝑎𝑎 𝑎𝑎 𝑝𝑝 ( ( )) 2 1−𝛥𝛥𝑎𝑎 𝛼𝛼𝛼𝛼 1−𝜆𝜆 Δ𝑎𝑎 − 0 1 1 𝑎𝑎 +𝑎𝑎 ( 𝑚𝑚 ( )) 𝛥𝛥𝑎𝑎 sides𝛼𝛼𝛼𝛼 2of the condition with 𝑝𝑝1 𝑝𝑝 , the condition becomes2 1−𝛥𝛥𝑎𝑎1𝛼𝛼𝛼𝛼 (11−𝜆𝜆 )(1 ) > 2(1 (1 2 1−𝛥𝛥𝑎𝑎1𝛼𝛼𝛼𝛼 1−𝜆𝜆 ))(1 ) , which can be simplified as [ (1 ) 1][1 ( + )] >1 . When >1 , 𝛥𝛥𝑎𝑎1 − 𝜆𝜆 − Δ𝑎𝑎 𝛼𝛼𝛼𝛼 − Δ𝑎𝑎 𝛼𝛼𝛼𝛼( −) 𝑎𝑎0+𝑎𝑎1 1 the condition is solved as < 1 . When < 0, the0 condition1 is solved as1 > 𝜆𝜆 − 𝛼𝛼𝜆𝜆 2 [ ( )Δ𝑎𝑎] 𝛼𝛼𝛼𝛼 − 𝜆𝜆 − − 𝛼𝛼𝛼𝛼 𝑎𝑎 𝑎𝑎 𝜆𝜆 Δ𝑎𝑎 𝛼𝛼𝛼𝛼 1−𝜆𝜆 1 1 1 . We introduce0 as1 such that when1 = 1, the following equation holds: 0 = [ ( ) ] 𝑎𝑎 𝛼𝛼𝛼𝛼 − 𝛼𝛼 𝛥𝛥𝑎𝑎 𝛼𝛼𝛼𝛼 1−𝜆𝜆 −1 − 𝑎𝑎 Δ𝑎𝑎 𝑎𝑎 𝛼𝛼𝛼𝛼 − 1 1 1 1. It is easy to see that1 the right side of the equation1 1 in decreasing in . Therefore, when 0 > , 𝛼𝛼[𝛥𝛥𝑎𝑎 𝛼𝛼𝛼𝛼(1−𝜆𝜆)−1] − 𝑎𝑎 𝐴𝐴 𝑎𝑎 𝐴𝐴 𝑎𝑎 𝛼𝛼𝛼𝛼 − 1 > , and vice versa. Therefore, the condition for + < + can be summarized as > 𝛼𝛼 𝛥𝛥𝑎𝑎1𝛼𝛼𝛼𝛼 1−𝜆𝜆 −1 − 𝑎𝑎1 𝑎𝑎1 𝑎𝑎1 𝐴𝐴1 max { , } or < min { , }. 𝑚𝑚 ( ) 0 1 0 1 1 1 𝐿𝐿𝐿𝐿𝐿𝐿 𝑅𝑅𝑅𝑅𝑅𝑅 1 𝑎𝑎 𝑎𝑎 − 𝑝𝑝 𝑎𝑎 𝑎𝑎� − 𝑝𝑝 𝑎𝑎 𝑎𝑎�1 𝐴𝐴1 𝑎𝑎1 𝑎𝑎�1 − 𝛼𝛼𝛼𝛼 1−𝜆𝜆 𝐴𝐴1 Proof to Corollary 1 ( ) ( ) Compare with is equivalent to comparing with . Since < 0, this can be ( ( )) ( ( )) 1−𝜆𝜆 𝛥𝛥𝑎𝑎1 1−𝜆𝜆 𝛥𝛥𝑎𝑎1 𝛥𝛥𝑎𝑎1 reorganized𝑠𝑠 as comparing𝑚𝑚 1 with 1 (1 ). It is easy to see that < when < 0, meaning 𝑝𝑝1 𝑝𝑝1 2 2 1−𝛥𝛥𝑎𝑎1𝛼𝛼𝛼𝛼 1−𝜆𝜆 2 1−𝛥𝛥𝑎𝑎1𝛼𝛼𝛼𝛼 1−𝜆𝜆 vendors with the same quality offer lower discount when quantity is observable to consumers. − Δ𝑎𝑎1𝛼𝛼𝛼𝛼 − 𝜆𝜆 𝐿𝐿𝐿𝐿𝐿𝐿 𝑅𝑅𝑅𝑅𝑅𝑅 Δ𝑎𝑎1 Proof to Lemma 3 ( ) [ ( ) ( )] Vendors offer a discount if < , meaning < 0 . It is easy to see that 1 (1 [ ( )(( ) )] 𝑐𝑐 1−𝜆𝜆 𝛥𝛥𝑎𝑎1 1− 1−𝑚𝑚 𝛽𝛽 𝑎𝑎0+𝑎𝑎1 ) ( + ) > 0 >1 0 1 + (1 )((1 ) ) < 0 > . When 𝑝𝑝 , 𝑝𝑝the condition2 1becomes+𝛥𝛥𝑎𝑎1 1−𝜆𝜆 1−𝑚𝑚 𝛽𝛽−𝑚𝑚𝑚𝑚𝑚𝑚 . When− − 𝑚𝑚 , this0 condition1 holds when 1 > . When <1 , the condition cannot hold. When < 0, 𝑚𝑚 𝛽𝛽 𝑎𝑎 𝑎𝑎 Δ𝑎𝑎 ( )[ ( ) ] Δ𝑎𝑎 − 𝜆𝜆 − 𝑚𝑚 𝛽𝛽 − 𝑚𝑚𝑚𝑚𝑚𝑚 1−𝑚𝑚 𝛽𝛽 1 𝑚𝑚 𝛽𝛽 the𝛼𝛼𝛼𝛼 condition becomes 1 + Δ(𝑎𝑎11 )1(−(𝜆𝜆1 𝑚𝑚𝑚𝑚𝑚𝑚−)1−𝑚𝑚 𝛽𝛽 ) > 01.− When𝑚𝑚 𝛼𝛼 𝛼𝛼 > , this condition always holds.Δ𝑎𝑎 1When 𝑚𝑚 𝛽𝛽 < , the condition can be1 simplified as < < 0. Δ𝑎𝑎 − 𝜆𝜆 −(𝑚𝑚 𝛽𝛽)[ − 𝑚𝑚(𝑚𝑚𝑚𝑚 ) ] 1−𝑚𝑚 𝛼𝛼𝛼𝛼 𝑚𝑚 𝛽𝛽 1 1−𝑚𝑚 𝛼𝛼𝛼𝛼 1−𝜆𝜆 𝑚𝑚𝑚𝑚𝑚𝑚− 1−𝑚𝑚 𝛽𝛽 Δ𝑎𝑎1

1142 Journal of the Association for Information Systems

Proof to Proposition 2 The condition + < + is equivalent to [1 + ((1 ) )] < + 𝑐𝑐 𝑐𝑐 ( ) ( + ) 0 1. Substituting0 in1 , 1we can further simplify the condition1 as ( + ) 1[ 0 + 11 + 𝑎𝑎 0 𝑎𝑎1 − 𝑝𝑝 𝑎𝑎 𝑎𝑎� − 𝑝𝑝 Δ𝑎𝑎 − 𝑚𝑚 𝛽𝛽 − 𝑚𝑚𝑚𝑚𝑚𝑚 𝑝𝑝 𝑎𝑎 𝑎𝑎� − (1 ) ((1 )𝑎𝑎 +𝑎𝑎 )] > + 1 +𝑐𝑐(1 ) ((1 ) ). We already know that, 1−𝑚𝑚 and𝛽𝛽 1 + 1 0 1 2 1 0 1 𝑚𝑚𝑚𝑚 (Δ1𝑎𝑎 𝑚𝑚𝑚𝑚) 𝑎𝑎 ((1𝑎𝑎 −) ) must hold 𝑝𝑝different signs in order for vendors to participate𝑎𝑎 in𝑎𝑎 discount𝜆𝜆𝜆𝜆𝜆𝜆 promotion. − 𝜆𝜆 Δ𝑎𝑎1 − 𝑚𝑚 𝛽𝛽 − 𝑚𝑚𝑚𝑚𝑚𝑚 𝜆𝜆 − 𝜆𝜆 Δ𝑎𝑎1 − 𝑚𝑚 𝛽𝛽 − 𝑚𝑚𝑚𝑚𝑚𝑚( ) (( ) ) Δ𝑎𝑎1 Therefore, 1when < 0, the condition becomes + > ( ) . When > 0, − 𝜆𝜆 Δ𝑎𝑎 − 𝑚𝑚 𝛽𝛽 − 𝑚𝑚𝑚𝑚𝑚𝑚 [ 𝜆𝜆+1+ 1−𝜆𝜆 (𝛥𝛥𝑎𝑎1 ) 1−𝑚𝑚(( 𝛽𝛽−𝑚𝑚)𝑚𝑚𝑚𝑚 )] 1 +1 (1 ) ((1 ) )0< 0 1 +1−1𝑚𝑚 +𝛽𝛽 (1 ) ((1 ) ) < 01 we know that Δ𝑎𝑎 𝑎𝑎 𝑎𝑎 . If𝜆𝜆 𝜆𝜆𝜆𝜆 𝑚𝑚𝑚𝑚 +1+ 1−𝜆𝜆 𝛥𝛥𝑎𝑎1 1−𝑚𝑚 𝛽𝛽−𝑚𝑚𝑚𝑚𝑚𝑚 Δ𝑎𝑎 , or ( ) ( ) (( ) ) equivalently, > , then the condition becomes + < . If ( ) ( )1 ( 1) 1+𝜆𝜆+ 1−−𝜆𝜆𝜆𝜆𝛥𝛥𝑎𝑎Δ1𝑎𝑎𝛽𝛽 − 𝑚𝑚 𝛽𝛽 − 𝑚𝑚𝑚𝑚𝑚𝑚 𝜆𝜆 − 𝜆𝜆[ 𝜆𝜆Δ+𝑎𝑎1+ 1−𝜆𝜆−(𝛥𝛥𝑚𝑚𝑎𝑎1 )𝛽𝛽1−−𝑚𝑚((𝑚𝑚𝛽𝛽−𝑚𝑚𝑚𝑚𝑚𝑚)𝑚𝑚𝑚𝑚 )] ( ) 1−𝑚𝑚 𝛽𝛽 1−𝜆𝜆 𝛥𝛥𝑎𝑎1 𝛽𝛽+𝛼𝛼𝛼𝛼 0 1 + 1 + 𝑚𝑚(1 ) ((1 ) ) > 0 , then 𝑎𝑎 the𝑎𝑎 𝜆𝜆condition𝜆𝜆𝜆𝜆 𝑚𝑚𝑚𝑚 +1+ 1becomes−𝜆𝜆 𝛥𝛥𝑎𝑎1 1 −𝑚𝑚 𝛽𝛽−𝑚𝑚𝑚𝑚𝑚𝑚+ > 1−𝑚𝑚 𝛽𝛽 ( ) (( ) ) 𝑚𝑚𝑚𝑚( ) − 𝜆𝜆 Δ𝑎𝑎1 − 𝑚𝑚 𝛽𝛽. − 𝑚𝑚𝑚𝑚𝑚𝑚 𝑎𝑎0 𝑎𝑎1 [ 𝜆𝜆+1+ 1−𝜆𝜆 (𝛥𝛥𝑎𝑎1 ) 1−𝑚𝑚(( 𝛽𝛽−𝑚𝑚)𝑚𝑚𝑚𝑚 )] 1−𝑚𝑚 𝛽𝛽 𝜆𝜆𝜆𝜆𝜆𝜆 +1+ 1−𝜆𝜆 Δ𝑎𝑎1 1−𝑚𝑚 𝛽𝛽(−𝑚𝑚𝑚𝑚𝑚𝑚) Denote𝑚𝑚𝑚𝑚 as the solution to + 1 + (1 ) ((1 ) ) = 0. It is easy to see that the left side in 1−(𝑚𝑚 𝛽𝛽 ) + 1 + (1 ) 1 ((1 ) ) > 0 < decreasing𝑚𝑚̄ in . As a result, 𝑚𝑚𝑚𝑚 − 𝜆𝜆 Δ𝑎𝑎 − 𝑚𝑚 𝛽𝛽 − 𝑚𝑚𝑚𝑚𝑚𝑚 holds when . In any other cases, the condition cannot hold.1 − 𝑚𝑚 𝛽𝛽 𝑚𝑚 𝑚𝑚𝑚𝑚 − 𝜆𝜆 Δ𝑎𝑎1 − 𝑚𝑚 𝛽𝛽 − 𝑚𝑚𝑚𝑚𝑚𝑚 𝑚𝑚 𝑚𝑚̄ ( ) (( ) ) Denote as such that when = the following equation holds: = ( ) . [ 𝜆𝜆+1+ 1−𝜆𝜆 (𝛥𝛥𝑎𝑎1 ) 1−𝑚𝑚(( 𝛽𝛽−𝑚𝑚)𝑚𝑚𝑚𝑚 )] 2 1 2 0 1−𝑚𝑚 𝛽𝛽 1 𝐴𝐴 𝑎𝑎 𝐴𝐴 ( ) 𝑎𝑎 𝜆𝜆𝜆𝜆𝜆𝜆 𝑚𝑚𝑚𝑚 +1+ 1−𝜆𝜆 𝛥𝛥𝑎𝑎1 1−𝑚𝑚 𝛽𝛽−𝑚𝑚𝑚𝑚𝑚𝑚 − 𝑎𝑎

The right side can be reorganized as ( ) 1−𝑚𝑚 𝛽𝛽 , and it is easy to verify that it [ ( ) (( ) )] 1 𝜆𝜆− 𝑚𝑚𝑚𝑚 1−𝑚𝑚 𝛽𝛽 1 decreases in . We can therefore restate𝜆𝜆𝜆𝜆𝜆𝜆 the conditions𝑚𝑚𝑚𝑚 +1+ 1− 𝜆𝜆above𝛥𝛥𝑎𝑎1 1as−𝑚𝑚 follows.𝛽𝛽−𝑚𝑚𝑚𝑚𝑚𝑚 To− 𝑎𝑎ensure + < + , ( ) we need (1) > max { , }, or (2) when < < 1, and < min { , }, or (3) when 0 < <𝑐𝑐 1 ( ) ( ) 0 1 0 1 1 𝑎𝑎 1+𝜆𝜆+ 1−𝜆𝜆 𝛥𝛥𝑎𝑎1𝛽𝛽 𝑎𝑎 𝑎𝑎 − 𝑝𝑝 𝑎𝑎 𝑎𝑎� − 𝑝𝑝 , < < . 𝑎𝑎1 𝑎𝑎�1 𝐴𝐴2 1−𝜆𝜆 𝛥𝛥𝑎𝑎1 𝛽𝛽+𝛼𝛼𝛼𝛼 𝑚𝑚 𝑎𝑎1 𝑎𝑎�1 𝐴𝐴2 𝑚𝑚 2 1 1 Proof𝑚𝑚̄ 𝐴𝐴 to𝑎𝑎 Corollary𝑎𝑎� 2 ( ) ( ) [ ( ) ( )] Note that is equivalent to , which can be simplified as [1 ( ( )) [ ( )(( ) )] 1−𝜆𝜆 𝛥𝛥𝑎𝑎1 1−𝜆𝜆 𝛥𝛥𝑎𝑎1 1− 1−𝑚𝑚 𝛽𝛽 𝑎𝑎0+𝑎𝑎1 (1 )𝑚𝑚( 𝑐𝑐 (1 ) )] [1 (1 ) ( + )][1 (1 )] , or equivalently (1 𝑝𝑝1 − 𝑝𝑝1 2 1−𝛥𝛥𝑎𝑎1𝛼𝛼𝛼𝛼 1−𝜆𝜆 − 2 1+𝛥𝛥𝑎𝑎1 1−𝜆𝜆 1−𝑚𝑚 𝛽𝛽−𝑚𝑚𝑚𝑚𝑚𝑚 𝑎𝑎𝑎𝑎1 − )[ ( + ) + (1 )( + ( + ))]. We denote this expression as . When > 0, it is 1 1 0 1 1 1 Δeasy𝑎𝑎 to− see𝜆𝜆 𝑚𝑚that𝑚𝑚𝑚𝑚 − > 0−, 𝑚𝑚and𝛽𝛽 consequently− Δ𝑎𝑎 − −>𝑚𝑚 𝛽𝛽. 𝑎𝑎When𝑎𝑎 <−0Δ,𝑎𝑎 or𝛼𝛼 𝛼𝛼 >− 𝜆𝜆 , we have < 0 if Δ<𝑎𝑎 +− 0( 1) 1 0 1 ( ) 1 𝑚𝑚 𝛽𝛽 𝑎𝑎 𝑎𝑎 Δ𝑎𝑎 , and− 𝜆𝜆vice𝛽𝛽 versa.𝛼𝛼𝛼𝛼 − Denote𝛼𝛼𝛼𝛼𝛼𝛼 𝑚𝑚𝑎𝑎 ( 𝑎𝑎𝑐𝑐) = . It is easy𝑀𝑀 to verifyΔ that𝑎𝑎 ( ) is ( )( ( )) 1 1 ( )( 1 ( 1 )) 1 1 1 𝛽𝛽 𝑎𝑎0+𝑎𝑎1 𝑀𝑀 𝑝𝑝 𝑝𝑝 Δ𝑎𝑎𝛽𝛽 𝑎𝑎0+𝑎𝑎1 𝑎𝑎 𝑎𝑎� 𝑀𝑀 𝑎𝑎 𝑎𝑎� strictly positive and increases in , and < + ( ). Therefore, if < + ( ), then < 0 and < 1−𝜆𝜆 𝛽𝛽+𝛼𝛼𝛼𝛼−α𝜆𝜆𝜆𝜆 𝑎𝑎0+𝑎𝑎1 𝑁𝑁 𝑎𝑎1 1−𝜆𝜆 𝛽𝛽+𝛼𝛼𝛼𝛼−𝛼𝛼𝛼𝛼𝛼𝛼 𝑎𝑎0+𝑎𝑎1 𝑁𝑁 𝑎𝑎1 as long as > . If > + ( ), then there exist such that < 0 and < when < <𝑚𝑚 and𝑐𝑐 1 1 1 1 1 1 1 1 1 > 0 and > when < 𝑎𝑎 < 𝑎𝑎�, where𝑎𝑎� 𝑁𝑁=𝑎𝑎 + ( ). 𝑎𝑎̄ 𝑎𝑎� 𝑁𝑁𝑚𝑚 𝑎𝑎̄ 𝑐𝑐 𝑀𝑀 𝑝𝑝 𝑝𝑝 1 1 1 1 1 3 1 1 1 1 3 𝑎𝑎 𝑚𝑚 𝑎𝑎� 𝑐𝑐 𝑎𝑎̄ 𝑎𝑎� 𝑁𝑁 𝑎𝑎̄ 𝐴𝐴 𝑀𝑀 𝑝𝑝 𝑝𝑝 𝑎𝑎� 𝑎𝑎 𝐴𝐴 1 1 3 1 1 3 1 3 Proof𝑀𝑀 to𝑝𝑝 Proposition𝑝𝑝 𝐴𝐴 3 𝑎𝑎 𝑎𝑎̄ 𝐴𝐴 𝑎𝑎� 𝑁𝑁 𝐴𝐴 We also need to compare with under < 0, which is equivalent to comparing = [ ( + ) + (1 ) + (1 𝑠𝑠)] with 𝑐𝑐 = ( + ) + (1 ) . Note that ( + ) + (1 ) = 1 1 1 0 1 ( + + (1 )( 𝑝𝑝 )) is 𝑝𝑝positive, Δ𝑎𝑎and [ ( + ) + (1 ) + (1𝐿𝐿𝐿𝐿𝐿𝐿 )]𝑚𝑚< 𝛽𝛽(𝑎𝑎 + 𝑎𝑎 ) + 1 1 0 1 1 0 1 1 𝛽𝛽Δ𝑎𝑎 (1 − 𝜆𝜆). WhenΔ𝑎𝑎 𝛼𝛼 [𝛼𝛼 ( −+𝜆𝜆 ) + 𝑅𝑅𝑅𝑅𝑅𝑅(1 𝛽𝛽 )𝑎𝑎+ 𝑎𝑎 (1𝛽𝛽Δ𝑎𝑎 )] >− 0𝜆𝜆, we have 𝛽𝛽<𝑎𝑎 𝑎𝑎 due to𝛽𝛽 Δ𝑎𝑎< 1−. When𝜆𝜆 0 1 1 1 0 1 1 1 0 1 [𝛽𝛽 (𝑎𝑎 +𝑎𝑎 ) + − 𝜆𝜆 (1𝑎𝑎� − )𝑎𝑎+ (1 )] < 0, we𝛽𝛽 also𝑎𝑎 have𝑎𝑎 𝛽𝛽Δ𝑎𝑎< − 𝜆𝜆due toΔ 𝑎𝑎 𝛼𝛼𝛼𝛼< 0− and𝜆𝜆 𝛽𝛽 >𝑎𝑎 0. 𝑎𝑎 𝛽𝛽Δ𝑎𝑎1 − 𝜆𝜆 𝛽𝛽 𝑎𝑎0 𝑎𝑎1 βΔ𝑎𝑎1 − 𝜆𝜆 Δ𝑎𝑎1𝛼𝛼𝛼𝛼 − 𝜆𝜆 𝐿𝐿𝐿𝐿𝐿𝐿 𝑅𝑅𝑅𝑅𝑅𝑅 𝑚𝑚 𝛽𝛽 𝑎𝑎0 𝑎𝑎1 𝛽𝛽Δ𝑎𝑎1 − 𝜆𝜆 Δ𝑎𝑎1𝛼𝛼𝛼𝛼 − 𝜆𝜆 𝐿𝐿𝐿𝐿𝐿𝐿 𝑅𝑅𝑅𝑅𝑅𝑅 𝐿𝐿𝐿𝐿𝐿𝐿 𝑅𝑅𝑅𝑅𝑅𝑅

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Is More Information Better?

About the Authors Hong Xu is an associate professor of information systems in the School of Business and Management at Hong Kong University of Science and Technology. Her general research interests are in social media and user-generated content, e-commerce, online privacy, and economics of information systems. Her papers have been published in academic journals, including Information Systems Research, MIS Quarterly, Journal of Management Information Systems, and Economics Letters. She received her PhD from McCombs School of Business at the University of Texas at Austin in 2010.

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