Group Buying via Social Network ∗ Fei Shi† Yong Sui‡ Jianxia Yang§ May, 2014 Abstract This paper studies a special selling strategy, group buying, under which consumers enjoy a discounted group price if the committed purchases exceeds the specified minimum size within a certain time period. Introducing social network among consumers, we analyze group buying from social advertising perspective. We characterize the optimal group buying strategy for a firm and investigate the effect of social network on group buying strategies. We provide suffi- cient conditions under which group buying strategy is more profitable than traditional private selling strategies and more effective than traditional advertising. Keywords: Group Buying, Advertising, Social Network JEL Classification: D85, L12, D83 ∗We are grateful to Cheng-Zhong Qin for helpful comments. Yang gratefully acknowledges financial support from National Natural Science Foundation of China (Grant No. 71103065), 2011 Shanghai Young College Teacher Training Subsidy Scheme, the Humanities and Social Sciences Campus Fund of East China University of Science and Technology (Grant No. YN0157129), and the Fundamental Research Funds for the Central Universities (Grant No. WN1122003). †Antai College of Economics and Management, Shanghai Jiao Tong University. E-mail: [email protected] ‡Antai College of Economics and Management, Shanghai Jiao Tong University. E-mail: [email protected] §School of Business, East China University of Science and Technology. E-mail: [email protected] 1 1 Introduction Group Buying, as a new selling mechanism, has generated increasing attention in both online busi- ness industry and academia. While group buying has long existed in certain industries1, the Internet and recent emergence of social media dramatically reduced the transaction cost for different buyers to form a purchase group so as to qualify the discount price. In a typical group buying mechanism, a good or service is offered for sale under a discount for group purchase if the committed purchases exceeds the specified minimum size within a certain time period. In recent years, many Internet sites have emerged that allow sellers to offer group buying campaigns, where consumers purchas- ing with group coupons receive substantial discounts when the minimum group size is reached. Launched in November 2008, Groupon was a pioneer in this industry and has grown into a major public company.2 The existing literature mainly considers group buying to be an efficient selling mechanism un- der either demand uncertainty (Chen and Zhang, 2012) or demand certainty (Jing and Xie, 2011). In this paper, we investigate group buying from the perspective of social advertising. Many firms, es- pecially small business, launch group buying campaign in order to advertise their goods or services through social interactions among consumers. On the one hand, the minimum size requirement for group discount will provide an incentive for the informed consumers to transmit the information about the sale in their social networks, thus stimulating the dissemination of product information and expanding market demand. On the other hand, after the committed buyers consume the prod- ucts or services, they may further diffuse among their social networks the product information, including price, quality, evaluation, and so on. The ex post network diffusion works again as ad- vertising for new products or services. In essence, group buying serves as a marketing strategy to attract an ideal number of consumers to purchase by discount for further social advertising. The advertising channels may vary in many ways such as word-of-mouth communication and online 1In a Business to business context, groups of independent grocers, convenience stores, or retail hardware stores have long existed in the United States as well as in Europe. In some industries, such as food services and health care, group purchasing organizations have a dominant presence. See Chen and Roma (2011) for more examples. 2There are many group buying sites around the world, including Lashou, Meituan in China, MyCityDeal in Europe and Spreets in Australia. 2 referral.3 In this study, we investigate the optimal group buying strategy for a monopolistic seller and how the optimal strategy is affected as the consumer network structure changes. Moreover, we examine under what conditions group buying strategy is more effective than traditional advertising strategy. Assuming consumers may value the product or service either high or low, we focus our discussion on the minimum group size: how the optimal minimum size is determined, whether the seller announces or conceals it, and how it varies with the changes of consumers’ network structure. The optimal minimum group size results from the balance of two effects: group sale effect and social advertising effect. When the informed or committed consumers communicate with sufficiently large number of their social neighbors about the product or service, the social advertising effect tends to dominate, leading to a relatively smaller minimum group size. Otherwise, the seller would set a relatively larger minimum group size. Moreover, we show that it is weakly dominant for the seller to conceal the minimum group size in order to take better advantage of social advertising effect. This result provides a rationale for the stylized fact of most practice of group buying strategy. We also examine how the change of consumers’ network structure affects the optimal minimum group size. When consumers’ network turns less dispersed, the social advertising effect of group buying becomes strengthened, resulting in a smaller optimal minimum group size. In addition, we show that group buying is more profitable than traditional advertising strategy with higher ratio of high-value consumers or larger mean of conditional degree distribution. 1.1 Related Literature In the presence of demand uncertainty, the group buying is shown to outperform posted pricing or other pricing schemes under demand heterogeneity, economies of scale and risk-seeking sellers. For instance, Anand and Aron (2003) study group buying as a a menu of quantity discounts in markets with demand uncertainty. They show that group buying outperforms posted price under heterogeneous demand. Chen et al. (2007) analyze an optimal pricing strategy when the firm adopts 3On LivingSocial, a consumer receives a free deal if she gets three persons to buy the product. 3 a group-buying auction. They show that group buying outperforms a fixed-price mechanism when there are economies of scale or the firm is risk-seeking. Chen et al. (2010) compare the uniform group buying price with nonuniform-price group buying mechanisms and show that buyers may over purchase in exchange for a lower unit price. Assuming the firm has adopted group buying mechanism, Hu et al. (2013) focus on the deal’s success rate under distinct information disclosure schemes. In a dynamic game where consumers are engaged in sequential decisions, they investigate the benefit of revealing the cumulative number of sign-ups in increasing deal success rates. Reveal- ing the sign-up information can reduce consumer’s reluctance to sign up to deals for fear that the deals fail in reaching the thresholds. To isolate the impact of information disclosure, they assume that the group buying price and the minimum size for the deal to be valid are exogenously deter- mined, whereas we assume that that prices and the minimum size are optimized by the seller. Wu et al. (2013) empirically identify two threshold effects in online group buying diffusion, induced by the minimum sign-up quantity of a deal. All of these studies do not address the perspective of social interaction or advertising effect among consumers. Group buying’s function of social advertising has been investigated in the following literature. Jing and Xie (2011) study group buying as a mechanism for selling through social interactions. They explore the role of group buying in facilitating social interaction among consumers with different levels of product information. They show that group buying can dominate traditional promotional schemes as it can motivate informed consumers to market products to less-informed consumers. Chen and Zhang (2012) consider group buying as interpersonal bundling and com- pare it with traditional bundling. They characterize the conditions to show that group buying is a profitable strategy in the presence of demand uncertainty, and how it may further boost profits by stimulating product information dissemination. Subramanian (2012) studies when and why (or why not) the firm finds profitable to prescribe a minimum group size for the deal to be valid. His find- ings provide a rationale for the observed trends that more and more firms no longer set minimum limits. Edelman et al. (2014) examine how the firms can potentially use group buying as a mecha- nism for price discrimination and advertising. The profitability of group buying generally depends 4 on the heterogeneity of consumers’ valuation and the level of firms’ recognition. In addition, they analyze certain challenges facing group buying in various business environment and characterize the narrow conditions in which group buying is likely to increase firm profits. However, the afore- mentioned studies do not explicitly investigate the effect of consumers’ social network. Our study contributes to the literature by explicitly analyzing consumers’ social network and its influence on firms’ optimal group buying strategy. There are quite