Flirting with the Enemy: Online Competitor Referral and Entry-Deterrence

Transcription

1 Flirting with the Enemy: Online Cometitor Referral and Entry-Deterrence January 11, 2016 Abstract Internet retailers often comete fiercely for consumers through exensive efforts like search engine advertising, online couons and a variety of secial deals. Against this background, it is somewhat uzzling that many online retailers have recently begun referring their website visitors to their direct cometitors. In this aer, using an analytical model, we examine this counterintuitive ractice and osit that an entry deterrence motive can otentially exlain this marketlace uzzle. Secifically, we develo a model where two incumbents comete for consumers business while facing a otential entrant who is deciding whether to enter the market. In addition to setting rice, each incumbent firm could otentially dislay a referral link to its direct cometitor. We find that when confronted with a otential entry, an incumbent may refer consumers to its cometitor, intensifying the market cometition and resulting in shutting off the entrant. Only one incumbent may refer its cometitor (i.e., one-way referral) when no loyal consumers exist for either incumbent whereas both incumbents may refer each other (i.e, two-way referral) when each incumbent has a set of loyal consumers. As long as a one-way referral can deter entry, a two-way referral is always sub-otimal. Interestingly, we find that a relatively weak incumbent may refer the consumers to a strong incumbent even when the strong incumbent does not recirocate. Surrisingly, our analysis shows that the ractice of online cometitor referral which imroves the rice transarency could end u hurting aggregate consumer welfare. Overall, our results indicate that firms may be motivated by entry deterrence to voluntarily refer consumers to their direct cometitors even when they are aid nothing for the referral. Keywords: Online Referral, Cometitor Referral, Entry-Deterrence, Game Theory

2 1 Introduction Online retailers often devote considerable financial resources in acquiring new customers either organically or via oaching from cometition. Online brokerages like E*Trade and TD Ameritrade offer cash offers as high as USD 600 to customers to oen a new IRA account (Tergesen, 2015). To induce switching, cellular comanies like T-Mobile and Srint rominently advertise on their websites their willingness to ay early termination fees and the ayments remaining on the hone obtained through cometing service roviders (Bonnington, 2014). Such significant investments towards acquisition of new customers are not surrising given that marketers have often advocated firms to invest into ufront marketing activities with an eye on customer lifetime value. In other words, even when a firm might be seen losing money in the short term while acquiring a customer, long term future income streams from this customer might add u and be rofitable for the firm over a longer horizon (Guta et al., 2004; Shin and Sudhir, 2010). This logic rings esecially true when consumers might face switching costs when moving to cometition. Against this background, a curious new henomenon has emerged recently whereby many online retailers have started dislaying links for their customers and visitors to click to find the rice and other information for a similar roduct at a cometing retailer(s) s website. This henomenon which we call online cometitor referral refers to the ractice wherein firms refer consumers to their direct cometitors on their websites. For examle, RetailMeNot.com, the largest online couon site in the US, dislays referral links to its cometitors web-ages where similar couons might be found (see Macy s couon examle in Fig.1). Grouon.com and chameleonjohn.com also follow a similar ractice to kee consumers informed of couons offered by their cometitors. This ractice is observed in many other online contexts ranging from large national retail chains to small local retailers. As an examle, Greenville Ballet School (greenvilleballet.com) lists all its major cometitors online along with referral links. K9Caers (k9caersdaycenter.com), a day center for dogs, encourages consumers to check out its cometitors by roviding names, addresses, hone numbers and links to their websites. ProfitWell (home.rofitwell.com), a technology firm, dislays cometitors logos with referral links and allows consumers to confirm whether ProfitWell is the best. On Esurance.com (see Fig.2), an online insurance comany, when consumers request a quote, they can also view real-time comarison quotes, visit cometitors websites and buy a cometitor s olicy (Esurance.com, 2006). Zaos.com is well known for referring consumers to its cometitors for consumers best interest (Zaos.com, 2008). Online travel agencies such as Orbitz, Priceline and Exedia also actively 1

3 dislay links to a host of cometitors. Figure 1: Cometitor Referral Page at RetailMeNot.com Figure 2: Cometitor Referral Page at Esurance.com This ractice seems truly uzzling at a first glance because in industries like insurance, travel and online e-tailing, firms comete very fiercely for consumers business for roducts that are largely homogeneous and consumers are very likely to urchase from an e-tailer that offers the lowest rice. Consider a consumer intending to buy an airline ticket between Boston and Atlanta on Exedia.com. This customer has her credit card details and other ersonal information on Exedia and can seamlessly book a ticket there. By referring consumers to cometition, Exedia is lowering consumers search costs and ossibly roviding incentives for them to make their 2

4 booking elsewhere (if they can find a sufficiently attractive rice). While such referrals aear to be getting ubiquitous, neither ractitioners nor researchers seem to gras the underlying mechanism and tradeoffs involved in the ractice. For examle, in a ost on the MOZ Q&A forum (The Moz Q&A Forum, 2013) and in a follow-u ost on the SEO Chat forum (SEO Chat Forum, 2015), ractitioners were debating whether they should offer consumers links to their cometitors. While they desire to kee consumers informed, they worry more about the intensified cometition after dislaying referral links. As ointed out in the comments (SEO Chat Forum, 2015), no one is interested in sending consumers to their cometitors. However, this concern contradicts the fact that many firms across multile industries are doing so online. To the best of our knowledge, the revious research has not investigated the mechanisms for voluntarily referring cometitors online. We seek to address this ga in the resent aer. Secifically, we examine the following questions: (1) What is the rationale behind cometitor referrals? Why do firms refer consumers to their cometitors even though they are aarently worse off by doing so? (2) Under what conditions would firms refer each other and under what conditions would one firm refer other firms but not be referred? (3) When would stronger firms refer weaker firms and when would weaker firms refer stronger firms? These questions are esecially intriguing when we consider that the ractice of referring cometitors seems common in markets where firms comete intensively for business. On a broader level, online sales are steadily accounting for higher fraction of US retail sales, surassing a figure of USD 300 billion dollars for the first time in the year An enhanced understanding of the online retail ractices has clear managerial and ublic olicy imlications. Our study fits within the academic literature researching referral rograms. Consumer referral rograms in which firms reward existing customers for bringing in new customers is a secific ractice of word-of-mouth marketing. As an examle, Schmitt et al. (2011) examined the rofitability and loyalty of the customers acquired through consumer referral rograms and found that they are more rofitable, loyal and valuable than other customers. Research on firm referrals has mostly focused on the imlementation and imact of online referral services. For examle, Chen et al. (2002) studied the otimal contracts of online referral infomediaries that rovide consumers with rice quotes from enrolled brick-and-mortar retailers and direct consumer traffic to articiating retailers. Garicano and Santos (2004) treated referrals as matching oortunities with talent and roosed contracts that can lead to efficient referrals. Ghose et al. (2007) examined the imact of indeendent third-arty and manufacturer-owned internet re- 3

5 ferral services on a suly chain. On the other hand, little research has studied the underlying motivations for firms engaged in referring cometitors. One excetion is Arbatskaya and Konishi (2012) where a firm may refer to its cometitors only when the firm knows that a consumer will not urchase its roduct. Different from such ex-ost referrals, we focus on ex-ante referrals where firms refer to cometitors regardless whether consumers will urchase from them. The other related work is Cai and Chen (2011), who looked at cometitor referral, wherein one retailer could dislay links to a cometing retailer directly (e.g., direct referral) or indirectly through an advertising agency (e.g., third-arty referral). However, direct referral in their context is essentially latform selling: a large latform owner, such as Amazon.com, acts both as a retailer and as a host for many small retailers and makes money by charging commission for sales haening on the latform. Jiang et al. (2011) suggested an alternative exlanation for such a latform selling latform owner can learn from indeendent sellers which of the roducts are worthwhile for direct selling. Another strand of literature studies third-arty referral which refers to the henomenon wherein firms monetize their consumer traffic through a third-arty ad ublisher (Kenny and Marshall, 2000). Recall that both the direct and third-arty referrals include a revenue-sharing contract, which drives retailers referrals to their cometitors. In contrast, we consider the context where a seller directly refers its cometitor online comletely for free. For examle, RetailMeNot.com voluntarily refers Couon.com on its website. In this study, we show that even when a firm does not earn any revenue by referring a consumer to cometitor, it might willingly do so from the ersective of entry-deterrence. This rovides an alternative exlanation for online firm referral in industries where in site of fierce cometition, the entry deterrence might be an imortant force leading to the increasing emergence of this ractice. We develo a model where two incumbents comete for consumers business in the same market. Each incumbent makes a decision on whether to dislay a referral link to its rival while an entrant decides whether to enter the market. We osit that when confronted with a otential entry, an incumbent may refer consumers to its cometitor, intensifying the market cometition to scare off the entrant from entering the market a more severe threat to the incumbents. When no consumers are loyal to a articular incumbent, only one incumbent may refer its cometitor (i.e., one-way referral). In contrast, when a fraction of consumers are loyal to a articular incumbent, both incumbents may refer each other (i.e, two-way referral). As long as a one-way referral can deter entry, a two-way referral is always sub-otimal. In addition, a stronger incumbent may refer its weaker cometitor and, more interestingly, the weaker incumbent may also refer the strong incumbent even when the strong incumbent does 4

6 not recirocate. Surrisingly, our analysis shows that online cometitor referral which imroves the rice transarency in an existing market could end u hurting aggregate consumer welfare. Overall, our results indicate that firms may be motivated by entry-deterrence to voluntarily refer consumers to their direct cometitors comletely for free. To the best of our knowledge, we are among the first in the literature to rovide an unifying exlanation for online cometitor referral shedding light on the underlying motivations for firms seemingly irrational referral behavior. The rest of this aer is organized as follows. In Section 2, we develo a base model where two cometing incumbents make referral decisions while one entrant decides whether to enter the market. In Section 3, we extend the base model to the context where a fraction of consumers are loyal to a articular incumbent. In Section 4, we extend the base model to the case where one incumbent is stronger than the other. We examine the consumer welfare in the base model and two extensions in Section 5. In Section 6, we conclude with a discussion of our findings, alternative modeling ossibilities and future research directions. 2 The Base Model Consider a market for a homogeneous roduct served by two incumbent online sellers, 1 and 2. On the demand side, there is a unit mass of consumers who desire at most one unit of good with a common reservation rice v. Consumers may be aware of only one incumbent. Assume that each incumbent has a fraction α (0, 1 2 ) of customers who visit only its own website. These customers are artially informed and are aware of the existence of one of the incumbent sellers; hence they are loyal to the incumbent they are aware of (referred as loyalist henceforth) and urchase the roduct from this seller as long as the rice is below the reservation rice v. The remaining fraction 1 2α are fully informed consumers who are aware of both sellers. These customers are rice sensitive and always buy the roduct with the lowest rice (referred as switchers henceforth). Online cometitor referral can hel artially informed customers (loyalists) become fully informed (switchers). For examle, if seller 1 rovides a referral link to seller 2, customers who used to visit seller 1 only now are informed of both sellers. The third layer, seller 3 is considering entering the same market to comete with sellers 1 and 2. The entry cost (e.g., the cost of oening an online store) is G > 0. We assume that if seller 3 enters the market a fraction β (0, 1) of consumers will become aware of its existence. β and α are indeendent of each other. 5

7 The sequence of events roceeds as follows. In the first stage, the two incumbents simultaneously decide whether to dislay a referral link to their cometitor. Denote seller i s referral and non-referral strategy by R i and R i (i = 1, 2), resectively. The cost of online referral is normalized to zero. In the second stage, the otential entrant decides whether or not to enter the market, denoted as strategy E and Ē resectively. In the third stage, the two firms (if no entry occurs) or the three firms (if entry occurs) set rices simultaneously. Denote seller i s rice as i, where i = 1, 2, 3. Given these rices, consumers decide whether and where to urchase, if they are aware of more than one seller. In this section, we analyze the case where only one incumbent is considering referring its cometitor (one-way referral). Although we allow both the incumbents to deloy referral strategy simultaneously (two-way referral), as will be shown shortly in subsection 2.5, a two-way referral never occurs under equilibrium in the base model. Without loss of generality, we assume that seller 1 decides whether to refer its cometitor whereas seller 2 does not do so. We examine the following 2 2 subgames: seller 1 alies or does not aly a referral while seller 3 enters or does not enter the market. 2.1 Benchmark: No Referral and No Entry First consider the benchmark case where there is no otential entry or referral ( R 1 Ē). The two incumbents comete for both the loyalists and switchers. Under this setu, analogous to the arguments made in Varian (1980) and Narasimhan (1988), it can easily be shown that no ure strategy equilibrium in rices exists, and only a mixed strategy Nash equilibrium is feasible (see Aendix A for a reca of these arguments). Denote the CDF of i as F i (), which is the robability that seller i charges a rice no higher than. Let F i () = 1 F i (), the robability that layer i charges a rice higher than. When seller i chooses rice while seller j (j i) uses a mixed strategy, the exected rofit of seller i is π i = [α + (1 2α) F j ()]. (1) Sellers 1 and 2 simultaneously set rices to maximize individual rofits. Solving the firms otimization roblem, we obtain the equilibrium rices as below (see Aendix A for the derivation of equilibria): 0 if < α ( ) v, F 1 () = F 2 () = 1 2 α v α if v v, 1 if > v. 6

8 The equilibrium rofit of each seller is equal to the rofit when the two sellers charge the maximum rice = v and serve only their monooly segment; that is, π R 1 Ē 1 = π R 1 Ē 2 = αv, (2) where the suerscrit denotes the corresonding subgame equilibrium. In other words, the rofits that each incumbent can realize deend on the the extent of consumer ignorance the higher the number of loyalists (or non-searchers), the higher the rofits realized by each incumbent in equilibrium. 2.2 Online Referral without Entry When seller 1 refers seller 2 and there is no otential entry (R 1 Ē), seller 1 s customers become aware of seller 2. Therefore, a fraction α of consumers remain loyal to seller 2 and the fraction 1 α are the remaining switchers in the market. The exected rofits of the two sellers (at rice ) are: π 1 = (1 α) F 2 (), π 2 = [α + (1 α) F 1 ()]. (3) Following Narasimhan (1988), we obtain the asymmetric mixed ricing strategies as follows (see Aendix A for derivation): 0 if < αv, ( ) F 1 () = 1 1 αv if αv v, 1 if > v, where seller 2 has a mass α at = v. 0 if < αv, F 2 () = 1 αv if αv v, 1 if > v, The equilibrium rofit of seller 2 (who has a larger base of loyal customers) equals to the rofit when it serves only its monooly segment by quoting the maximum rice = v. contrast, the equilibrium rofit of seller 1 (who has a smaller base of loyal customers) equals the rofit when it charges the minimum rice = αv, oaching all of the consumers who are aware of seller 1; that is, π R1Ē 1 = α(1 α)v, π R1Ē 2 = αv. (4) By comaring subgames R 1 Ē and R 1 Ē, we have the following roosition: In 7

9 Proosition 1 Online referral makes the referring firm worse off but does not affect the rofit of the referred firm. Without otential entry, seller 1 would never refer its cometitor. Proosition 1 shows that online referral makes the referring firm worse off; that is, π R1Ē 1 < π R 1 Ē 1, which confirms the intuition that no firm should be willing to undercut its monooly ower by roviding consumers easy access to the information about its cometitor. Somewhat surrisingly, online cometitor referral does not hel the referred firm; that is, π R1Ē 2 = π R 1 Ē 2. This result is due to the fact that seller 2 cannot benefit from a larger customer base without discounting its rice. As long as the size of its loyal consumer segment remains unchanged, seller 2 always has to trade off attracting switchers with a lower rice against serving loyalists at a higher rice. Figure 3: Equilibrium Prices under R 1 Ē and R 1 Ē (v = 1, α = 1 4 ) Fig.3 resents the mixed rices under R 1 Ē and R 1 Ē. It shows that seller 1 charges a lower rice on average when referring its cometitor, imlying that seller 1 loses its monooly ower because of referral. However, seller 2 may raise or cut its rice on average in resonse to seller 1 s referral. 1 1 As can be calculated, E( R 1 Ē 1 ) = E( R 1 Ē 2 ) = αv 1 2α ln, α E(R 1Ē 1 ) = αv ln 1, and α E(R 1Ē 2 ) = αv(1 + ln 1 ). α By algebra, E( R 1Ē 1 ) < E( R 1 Ē 1 ), E( R 1Ē 2 ) < E( R 1 Ē 2 ) α > 0.34, and E( R 1Ē 1 ) < E( R 1Ē 2 ). 8

10 Table 1: Market Segmentation for R 1 E Segment Fraction of consumers Notation Loyal to 1 α(1 β) n 1 Loyal to 2 α(1 β) n 2 Switch between 1 and 3 αβ s 13 Switch between 2 and 3 αβ s 23 Switch between 1 and 2 (1 2α)(1 β) s 12 Switch among 1, 2 and 3 (1 2α)β s Entry without Online Referral In this section, we analyze a scenario where a third entrant could otentially enter the market (and the layers cannot engage in cometitive referral). As noted before, if seller 3 enters the market a fraction β (0, 1) of consumers will be aware of its existence. β and α are indeendent of each other and the consumers who are aware of layer 3 are drawn from all the existing segments of loyalists and switchers. If the entry indeed haens then this subgame without online referral ( R 1 E) involves three layers and six market segments as shown in Table 1. Relying on the arguments made in Varian (1980), Vives (2001) and Xu et al. (2011), it can be shown that the ure ricing strategies do not exist. We follow oligooly ricing techniques to arrive at the equilibrium outcomes (see Aendix A for derivation). Denote the fraction of customers who are loyal to seller i as n i, the fraction of switchers between sellers i and j as s ij, and let s 123 be the fraction of customers who switch among the three sellers. The values of n i, s ij and s 123 are listed in Table 1 (n 3 = 0). The exected rofits of sellers 1, 2 and 3 (at rice ) are given by, resectively, π 1 = [n 1 + s 12 F2 () + s 13 F3 () + s 123 F2 () F 3 ()], (5) π 2 = [n 2 + s 12 F1 () + s 23 F3 () + s 123 F1 () F 3 ()], (6) π 3 = [s 13 F1 () + s 23 F2 () + s 123 F1 () F 2 ()] G, (7) where seller 3 has an entry cost of G. The three sellers simultaneously choose rices to maximize 9

11 their own rofits. The equilibrium rice strategies are 0 if < min, ( 1 2 α h() ) if min max, F 1 () = F 2 () = ( ) 1 2 α v if max v, 1 if > v, 0 if < min, F 3 () = 1 β 1 β v β h() if min max, 1 if > max, where we define min = α(1 β) v, (1 β)2 (1 2α) max = 2 +4α 2 () 2 (1 β)(1 2α) 2α() v, and h() = 2 + (1 β)(1 2α)v α(). The exressions of F 1 (), F 2 () and F 3 () indicate that sellers 1 and 2 set rices over the entire interval [ min, v] whereas seller 3 sets the uer bound max lower than v. The rationale is that seller 3 has the smallest (zero) loyal segment and the weakest ower in setting rice. The mixed ricing strategy of the three-layer game is similar to that in Koçaş and Bohlmann (2008) and Xu et al. (2011). We show in Aendix A that when β aroaches zero, F 1 () and F 2 () reduce to the exressions derived under R 1 Ē. The equilibrium rofits of the three sellers are π R 1E 1 = π R 1E 2 = α(1 β)v, π R 1E 3 = αβ(1 β) v G. (8) 1 α Similar to the equilibrium rices, the equilibrium rofits of sellers 1 and 2 also aroach those under R 1 Ē when β 0. Comaring subgames R 1 Ē and R 1 E, we have π R 1E 1 < π R 1 Ē 1 and π R 1E 2 < π R 1 Ē 2. This makes intuitive sense since the entry of a third layer now reduces the ricing ower of the two incumbents and makes them worse off. resented in the roosition below: This outcome is formally Proosition 2 Absent online referral, seller 3 enters the market as long as G αβ(1 β) v. The entry of the third layer makes the two incumbents worse off. Proosition 2 is very intuitive because no incumbent wants higher cometition in the market. Fig.4 illustrates the mixed rices under R 1 Ē and R 1 E. When seller 3 enters the market, both sellers 1 and 2 discount rices more heavily. In other words, the new entry intensifies the market cometition making the incumbents worse off. 2.4 Online Referral with Entry Now we consider the outcomes in a scenario where online referrals are a ossibility. In the subgame R 1 E where seller 3 enters the market and seller 1 refers seller 2, the market segments 10

12 Figure 4: Equilibrium Prices under R 1 Ē and R 1 E (v = 1, α = 1 4, β = 1 2 ) Table 2: Market Segmentation for R 1 E Segment Fraction of consumers Notation Loyal to 2 α(1 β) n 2 Switch between 2 and 3 αβ s 23 Switch between 1 and 2 (1 α)(1 β) s 12 Switch among 1, 2 and 3 (1 α)β s 123 are shown in Table 2. Note that since the seller 1 refers seller 2 through an online referral link, this seller now does not retain any loyal customers. The exected rofits of sellers 1, 2 and 3 (at rice ) are given by, resectively, π 1 = F 2 ()[s 12 + s 123 F3 ()], (9) π 2 = [n 2 + s 12 F1 () + s 23 F3 () + s 123 F1 () F 3 ()], (10) π 3 = F 2 ()[s 23 + s 123 F1 ()] G. (11) The attern of mixed rices is similar to that under R 1 E: Two sellers set high rices on average and they set rices over the entire interval, while one seller may set the uer bound lower than other two. R 1 E differs from R 1 E in the following: Since n 2 > n 1 = n 3 = 0, whether seller 1 or seller 3 sets the lowest rice deends on whether s 23 exceeds s 12 (see Aendix A for derivation). 11

13 If s 12 > s 23, i.e., α + β < 1, seller 3 has the weakest ower in setting rice. The equilibrium rices of sellers 1, 2 and 3 are, resectively, 0 if < α(1 β)v, 1 F 1 () = 1 α(1 β)v if α(1 β)v α 1 β v, 1 α(v ) α () if 1 β v v, 1 if > v, 0 if < α(1 β)v, 1 F 2 () = 1 αv α if 1 β v v, α(1 β)v if α(1 β)v α 1 β v, 1 if > v, 0 if < α(1 β)v, F 3 () = 1 β 1 β 1 if > α 1 β v, where seller 2 has a mass α at = v. α(1 β)v if α(1 β)v α 1 β v, If s 12 s 23, i.e., α + β 1, seller 1 has the weakest ower in setting rice. In this case, the equilibrium rices of sellers 1, 2 and 3 are, resectively, 0 if < α(1 β)v, F 1 () = 1 1 α(1 β)v if α(1 β)v 1 β α v, 1 if > 1 β α v, 0 if < α(1 β)v, 1 α(1 β)v if α(1 β)v 1 β α F 2 () = v, 1 (1 β)v if 1 β α v v, 1 if > v, F 3 () = 0 if < α(1 β)v, 1 β 1 β α(1 β)v 1 (1 β)(v ) β where seller 2 has a mass 1 β at = v. if α(1 β)v 1 β α v, if 1 β α v v, 1 if > v, No matter which firm charges the lowest rice, seller 2, who has n 2 fraction of loyalists, always earns the rofit equal to n 2 v; while sellers 1 and 3, both of whom have zero loyalist, earn rofits equal to (s 12 + s 123 ) min and (s 23 + s 123 ) min G, resectively; that is, π R1E 1 = α(1 α)(1 β)v, π R1E 2 = α(1 β)v, π R1E 3 = αβ(1 β)v G. (12) 12

14 Note that when β 0, the equilibrium rices and rofits of R 1 E aroach the form under R 1 Ē. Next roosition is obtained by comaring results from R 1 E and R 1 E. Proosition 3 In the resence of online cometitor referral dislayed by seller 1, seller 3 enters the market as long as G αβ(1 β)v. The referral strategy makes seller 1 and seller 3 worse off without affecting seller 2 s rofit. Online referral is detrimental to the referring firm, i.e., π R1E 1 < π R 1E 1. Therefor, no incumbent has an incentive to refer its cometitor conditional on the entry of the third layer. In addition, online referral does not influence the rofit of the referred firm, i.e., π R1E 2 = π R 1E 2. These results are consistent with the case with no entry (see Proosition 1). It is noteworthy that π R1E 3 < π R 1E 3 ; that is, seller 3 is also hurt by seller 1 s referral strategy because of the intensified cometition. This finding suggests that seller 3, who could originally earn ositive rofits through entry, may be blocked out of the market when an incumbent refers his cometitor. This key insight exlains why at equilibrium seller 1 could refer its cometitor even when its rofit is attenuated because this is comensated via non-entry of the third firm, as will be shown later. Fig.5 illustrates the equilibrium rices under R 1 E and R 1 E, showing the influence of online referral on rices under the case with new entry. Figure 5: Equilibrium Prices under R 1 E and R 1 E (v = 1, α = 1 3, β = 1 4 ) 13

15 2.5 Equilibrium Referral Strategy Subsections have discussed one-way referral dislayed by seller 1. Considering that sellers 1 and 2 are symmetric with each other, the referral dislayed by seller 2 will result in similar subgame equilibrium rofits as shown in Eqs.(2, 4, 8, 12). In case of two-way referral where sellers 1 and 2 refer each other, all consumers will be fully informed. The market oerates under Bertrand rice cometition, which drives the equilibrium rices and rofits of both incumbents to zero. Therefore, two-way referral is never adoted in the equilibrium. This leads to our equilibrium referral strategy outcome stated as follows: Proosition 4 The equilibrium referral and entry strategies are as follows: (i) If G αβ(1 β)v, or αβ(1 β)v < G αβ(1 β) v and β α, there is no referral by incumbents and seller 3 enters the market; (ii) If αβ(1 β)v < G αβ(1 β) v and β > α, one incumbent seller refers its consumers to the other incumbent while the other does not recirocate, and seller 3 does not enter the market; (iii) If G > αβ(1 β) v, no incumbent ractices referral, and seller 3 does not enter the market. Proosition 4 shows that the equilibrium referral and entry strategies are (i) R 1 R2 E if the entry cost G or the fraction of customers who are aware of the entrant β is sufficiently small, (ii) R 1 R2 Ē or R 1 R 2 Ē if G is medium and β is sufficiently large, and (iii) R 1 R2 Ē if G is sufficiently large (see Fig.6). Figure 6: Equilibrium under Base Model Part (i) and art (iii) of Proosition 4 are consistent with our intuition: If the entry cost is 14

16 small, seller 3 always enters the market regardless whether seller 1 (2) refers seller 2 (1). In this case, online cometitor referral lays no other role besides romoting cometition. Thus, seller 1 (2) has no reason to refer seller 2 (1). On the other hand, if the fraction of customers who are aware of the entrant s roduct is small, seller 1 (2) can tolerate the influence of the new entry and therefore does not refer its cometitor. However, if the entry cost is too high, seller 3 never enters the market, which is indeendent of referral decisions of the two incumbents. In this case too, seller 1 (2) has no incentive to refer seller 2 (1). Part (ii) of Proosition 4 is the core interesting insight gleaned from our analysis. It shows that if G is medium and β is large, counter-intuitively, online referral occurs in equilibrium even though it makes the referring firm worse off (see Proosition 1 for π R1Ē 1 < π R 1 Ē 1 ). Why does this seller might self-cut its rofit by referring its cometitor? The rationale behind this counterintuitive behavior lies in the entry-deterrence motive. In a market with weak cometition, otential entrant has high incentives to enter for a share of the ie. In contrast, if firms comete intensely in the market, the entrant would rather stay outside of the market. Therefore, online cometitor referral can serve as an entry-deterrence strategy via intensifying the cometition. Although the referral hurts the referring firm, it is the lesser of two evils and can discourage the entrant from entry, a more severe threat to the incumbents (π R1Ē 1 > π R 1E 1 β > α). Part (ii) of the roosition also indicates that in equilibrium either seller 1 or seller 2 has to shoulder the cost of referral since the act hurts the referring firm. Note that sellers 1 and 2 make referral decisions simultaneously and non-cooeratively. Therefore, each incumbent is better off if the other incumbent does the referral. There exist two Nash equilibria: seller 1 refers seller 2, or seller 2 refers seller 1. Additionally, it can be easily shown that if the incumbents use mixed referral strategy, in equilibrium each seller will aly referral with robability τ and does not aly referral with robability 1 τ, where τ = β α 1+β α (see Aendix B3). Irresective of whether firms used ure or mixed strategies, the key insight is that the referral will emerge as a voluntary ractice under certain conditions even when firms are not being aid for rendering this service. 3 Imerfect Referral In the base model, we assume that all of the loyalists of the referring firm become switchers once it refers its customers to a cometitor. In this section, we relax this assumtion and allow a fraction of consumers to remain loyal to the referring firm even when it ractices online referral. In reality, some consumers may stick to a website like RetailMeNot or Esurance because of 15

17 switching costs, inattention or brand loyalty, even when they are rovided with easy access to cometition. For examle, consumers may already have a social network and be very familiar with how to find good couons on RetailMeNot, but they have to start from scratch and learn how to find couons on RetailMeNot s cometitors. In addition, sellers aly online cometitor referral with varying details and on varying ositions on their websites. For instance, Greenville Ballet School laces cometitors links at the center of the webage which facilitates customers clicking on the links. In contrast, cometitors links on RetailMeNot are located at the bottom of the webage where a large fraction of consumers may never reach. We assume that when one incumbent refers the other, only a fraction ϕ (0, 1) of consumers who visit the referring incumbent comare shoing at the two firms. The remaining fraction 1 ϕ stays loyal to the referring firm. 3.1 One-way Referral Suose that only seller 1 could otentially ractice referral whilst seller 2 could not. scenario is similar to the base model, with a minor difference where the referring firm owns a ositive roortion of loyalists. The equilibrium rofits of the 2 2 subgames are (see Aendix B1 for derivation): π R1E 1 = This π R 1 Ē 1 = π R 1 Ē 2 = αv, (13) π R1Ē α(1 α) 1 = v, πr1ē 2 = αv, (14) 1 α + αϕ π R 1E 1 = π R 1E 2 = α(1 β)v, π R 1E 3 = α(1 α)(1 β) v, πr1e 2 = α(1 β)v, π R1E 3 = 1 α + αϕ αβ(1 β) v G, (15) 1 α αβ(1 β) v G. (16) 1 α + αϕ By comaring, we find that π R1Ē 1 < π R 1 Ē 1 and π R1E 1 < π R 1E 1, imlying that seller 1 has no incentive to refer seller 2 on conditional that seller 3 enters or does not enter the market. Furthermore, π R1E 3 < π R 1E 3 ; that is, seller 3 is worse off resulting from the incumbent s online referral. αβ(1 β) This indicates that seller 1 is able to deloy referral to deter otential entry when +αϕ v < G αβ(1 β) v. Seller 1 is willing to embrace this strategy if it earns a higher rofit under R 1 Ē than under R 1 E which requires that β should be sufficiently large, i.e., π R1Ē 1 > π R 1E 1 β > αϕ +αϕ. The comarisons above yield the following roosition. Proosition 5 One-way imerfect referral can be used to deter entry and imrove rofit if αβ(1 β) +αϕ v < G αβ(1 β) αϕ v and β > +αϕ. 16

18 Table 3: Market Segmentation for R 1 R 2 E with Imerfect Referral Segment Fraction of Consumers Notation Loyal to 1 α(1 ϕ)(1 β) n 1 Loyal to 2 α(1 ϕ)(1 β) n 2 Switch between 1 and 3 α(1 ϕ)β s 13 Switch between 2 and 3 α(1 ϕ)β s 23 Switch between 1 and 2 [1 2α(1 ϕ)](1 β) s 12 Switch among 1, 2 and 3 [1 2α(1 ϕ)]β s 123 The intuition for Proosition 5 is similar to that for the base model: Although online referrals intensify market cometition and thereby hurt the referring firm, the referring firm may still rovide one to its cometitor. This is because the fiercer cometition induced by online referral could be a credible threat to the entrant scaring it out of the market. If entry is more detrimental than losing loyal customers, the incumbent seller will refer its cometitor. 3.2 Two-way Referral In this subsection, we discuss two-way referral where both sellers 1 and 2 simultaneously decide whether to refer their cometitor. imerfect two-way referral may benefit the incumbents. As will be shown shortly, unlike under the base model, The subgames R 1 R2 Ē and R 1 R2 E are the same as the subgames R 1 Ē and R 1 E in the base model, and thus π R 1 R2 Ē 1 = π R 1 R2 Ē 2 = αv, (17) π R 1 R2E 1 = π R 1 R2E 2 = α(1 β)v, π R 1 R2E 3 = αβ(1 β) v G. (18) 1 α When the two incumbents refer each other and seller 3 does not enter the market (R 1 R 2 Ē), the size of each market segment is n 1 = n 2 = α(1 ϕ). This subgame is similar to R 1 Ē in the base model. We easily obtain the equilibrium rofits as follows (see Aendix B1 for derivation): π R1R2Ē 1 = π R1R2Ē 2 = α(1 ϕ)v. (19) When the two incumbents refer each other and seller 3 enters the market (R 1 R 2 E), the size of each market segment is resented in Table 3. 17

19 Table 3 is very similar to Table 1, and the equilibrium rices and rofits can be obtained directly from the subgame R 1 E of the base model. The equilibrium rofits are as follows (the equilibrium rices are listed in the Aendix B1): π R1R2E 1 = π R1R2E 2 = α(1 ϕ)(1 β)v, π R1R2E 3 = αβ(1 β)(1 ϕ) v G. (20) 1 α(1 ϕ) Based on the 2 2 subgames analyzed above, we can investigate whether two-way referral still has an effect of entry deterrence, as shown in the next roosition. Proosition 6 If the two incumbents simultaneously decide whether to aly a referral strategy and the referral is imerfect in affecting the loyalists, then a two-way referral will be used to deter entry if αβ(1 β)(1 ϕ) (1 ϕ) v < G αβ(1 β) v and β > ϕ. Proosition 6 shows that two-way referral can be an effective entry-deterrence tool. Although the incumbents may be hurt by two-way referral because of more intense cometition, in equilibrium they still deloy it to avoid more serious consequences from entry (the market will not oerate under Bertrand cometition when ϕ < 1). The rationale here is similar to one-way referral where the referring firm is always worse off when referring a cometitor. However, two-way referral differs from one-way referral in the following two ways: First, two-way referral imlies more intense cometition relative to one-way referral, so as long as one-way referral can deter entry, two-way referral will be sub-otimal. Second, two-way referral may be referred over one-way referral. In articular, by comaring Proositions 5 and 6 we see that when αβ(1 β)(1 ϕ) (1 ϕ) v < G αβ(1 β) (1 ϕ) v and β > ϕ, two-way referral can discourage entry while one-way referral is no longer effective. This rovides an intuition of the situations in which two-way referral might be more effective than one-way referral A two-way referral is more effective under a lower range of fixed cost (G) and under the resence of a stronger entrant (higher β) relative to the the region where one-way referral works. In other words, when the threat of an entrant is higher for incumbents (due to lower fixed cost of entry and a higher otential of the entrant luring existing customers), a one-way referral might not suffice and incumbents will need to resort to two-way referrals to intensify the cometition and shut off the entrant. 3.3 Equilibrium Referral Strategy Based on the subgames of one-way and two-way referrals, we summarize equilibrium outcome of the three-stage game next in roosition 7, where we define G 1 = αβ(1 β) v, G 2 = αβ(1 β) (1 ϕ) v, G 3 = αβ(1 β)(1 ϕ) (1 ϕ) v, β 1 = ϕ, and β 2 = αϕ +αϕ. 18

20 Proosition 7 With imerfect referral, the equilibrium referral and entry strategies are: (i) If G G 3, or G 3 < G G 2 and β β 1, or G 2 < G G 1 and β β 2, there is no referral by incumbents and seller 3 enters the market; (ii) If G 3 < G G 2 and β > β 1, there is either no referral or two-way referral by incumbents, and seller 3 enters the market if there is no referral while does not enter if there is two-way referral; (iii) If G 2 < G G 1 and β > β 2, one incumbent seller refers its consumers to the other incumbent while the other does not recirocate, and seller 3 does not enter the market; (iv) If G > G 1, no incumbent ractices referral, and seller 3 does not enter the market. Figure 7: Equilibrium under Imerfect Referral Model Fig.7 deicts the equilibrium referral and entry strategies shown in Proosition 7, which carries the intuition similar to the base model but also brings forth additional nuances. First, within the region G 2 < G G 1 and β > β 2, both one-way and two-way referrals can deter entry. In this case, two-way referral is sub-otimal and could never be an equilibrium. Second, within the region G 3 < G G 2 and β > β 1, one-way referral can no longer deter entry. In this case, only when the two incumbents refer each other can the otential seller be scared off. However, no incumbent knows its cometitor s referral choice and any incumbent will lose more rofits if it refers its cometitor while the cometitor does not do the same. Therefore, the equilibrium in this region might be R 1 R 2 Ē or R 1 R2 E. In addition to this ure strategy equilibrium, a mixed equilibrium also exists wherein each incumbent refers the cometitor with robability τ and does not refer the cometitor with robability 1 τ, where τ = α(1 β)ϕ ()β ϕ(1 2α+αϕ) (see 19

21 Aendix B3). 4 Asymmetric Incumbents In this section we extend the base model to examine the case where sellers 1 and 2 differ in their number of loyalists. This is a natural extension since we do often see online retailers vary in their reach and loyalty due to differential brand strengths. We assume that seller i has a fraction α i (i = 1, 2) of loyal segment, where > α 2. Without loss of generality, we label seller 1 as the strong brand whilst labeling seller 2 as the weak brand. For simlicity, we kee ϕ = Strong-Brand Referral In this subsection, we analyze the strong-brand referral; that is, only seller 1 decides whether to aly referral whereas seller 2 does not. When there is no otential entry and no referral is adoted ( R 1 Ē), the sizes of the loyal consumer segment and the switcher segment are n 1 =, n 2 = α 2 and s 12 = 1 α 2. Following the same logic as the base model, we obtain equilibrium rofits of the incumbents as follows (see Aendix B2 for the equilibrium rices): π R 1 Ē 1 = v, π R 1 Ē 2 = (1 ) 1 α 2 v. (21) When there is no otential entry and seller 1 refers seller 2 (R 1 Ē), seller 1 ends u with zero loyalist and seller 2 has a fraction α 2 of loyalists. The remaining fraction 1 α 2 are switchers. Analogue to Eq.(4), we obtain the equilibrium rofits as follows: π R1Ē 1 = α 2 (1 α 2 )v, π R1Ē 2 = α 2 v. (22) In the case that seller 3 enters the market and seller 1 does not aly referral ( R 1 E), the market will be segmented as shown in Table 4. The exected rofit of seller i is π i = [n i + s i,i+1 Fi+1 () + s i,i+2 Fi+2 () + s 123 Fi+1 () F i+2 ()], (23) where n 1 > n 2 > n 3 = 0, and seller i and seller i + 3 denote the same entity (i = 1, 2, 3). Analogue to the base model, we can obtain the equilibrium rofits of the three sellers as follows (see Aendix B2 for derivation): π R 1E 1 = (1 β)v, π R 1E 2 = (1 )(1 β) 1 α 2 v, π R 1E 3 = β(1 β) 1 α 2 v G. (24) 20

22 Table 4: Market Segmentation for R 1 E under Strong-Brand Referral Segment Fraction of Consumers Notation Loyal to 1 (1 β) n 1 Loyal to 2 α 2 (1 β) n 2 Switch between 1 and 3 β s 13 Switch between 2 and 3 α 2 β s 23 Switch between 1 and 2 (1 α 2 )(1 β) s 12 Switch among 1, 2 and 3 (1 α 2 )β s 123 Table 5: Market Segmentation for R 1 E under Strong-Brand Referral Segment Fraction of Consumers Notation Loyal to 2 α 2 (1 β) n 2 Switch between 2 and 3 α 2 β s 23 Switch between 1 and 2 (1 α 2 )(1 β) s 12 Switch among 1, 2 and 3 (1 α 2 )β s 123 Finally, when seller 3 enters the market and seller 1 refers seller 2 (R 1 E), the market is segmented as shown in Table 5. Table 5 is very similar to Table 2. We just need to relace α with α 2 to get the equilibrium. Therefore, the equilibrium rofits of sellers 1, 2 and 3 are, resectively, π R1E 1 = α 2 (1 α 2 )(1 β)v, π R1E 2 = α 2 (1 β)v, π R1E 3 = α 2 β(1 β)v G. (25) Based on the four subgames analyzed above, we have the following roosition. Proosition 8 Under the strong-brand referral format, (i) online referral is always harmful to the referring firm as well as to the referred firm regardless of whether seller 3 enters the market or not; that is, π R1Ē 1 < π R 1 Ē 1, π R1Ē 2 < π R 1 Ē 2, π R1E 1 < π R 1E 1 and π R1E 2 < π R 1E 2 ; and (ii) seller 1 will deloy referral to deter entry if α 2 β(1 β)v < G α1β(1 β) 2 v and β > 1 α2(2). Proosition 8 shows that strong-brand referral can be used to deter entry when G is medium and β is large enough. This result is consistent with the base model. However, strong-brand 21

23 Table 6: Market Segmentation for R 2 E under Week-Brand Referral Segment Fraction of Consumers Notation Loyal to 1 (1 β) n 1 Switch between 1 and 3 β s 13 Switch between 1 and 2 (1 )(1 β) s 12 Switch among 1, 2 and 3 (1 )β s 123 referral differs from the base model in that it not only hurts the referring firm but also makes the referred firm worse off. The main reason lies in that seller 2 is a small firm (with fewer loyalists) without seller 1 s referral and can earn rofits from its loyalists as well as switchers since seller 1 is interested largely (with a larger share of loyalists) on earning higher rofits from its loyalists and kees its rice relatively higher. After referral, seller 1 (strong brand) has access only to switchers and hence rices aggressively to ta into this ool leading to aggressive rice cometition and seller 2 rofiting mainly from its (smaller) share of loyalists. 4.2 Weak-Brand Referral In this subsection, we analyze the weak-brand referral format; that is, only seller 2 decides whether to refer seller 1. The results of subgames R 2 Ē and R 2 E stay the same as those under strong-brand referral. So we discuss only the subgames R 2 Ē and R 2 E. When there is no otential entry and seller 2 refers seller 1 (R 2 Ē), the sizes of loyal segments of sellers 1 and 2 are and 0, resectively. The equilibrium rofits of the two sellers are as follows (see Aendix B2 for derivation): π R2Ē 1 = v, π R2Ē 2 = (1 )v. (26) When otential entry exists and seller 2 refers seller 1 (R 2 E), the size of each segment will be that in Table 6. The equilibrium rofits of the three sellers are as follows (see Aendix B2 for derivation): π R2E 1 = (1 β)v, π R2E 2 = (1 )(1 β)v, π R2E 3 = β(1 β)v G. (27) Based on the above analysis, we have the following roosition. Proosition 9 Under the weak-brand referral format, (i) online referral is harmful to the referring firm but has no influence on the referred firm regardless of whether seller 3 enters the 22

24 market; that is, π R2Ē 1 = π R 2 Ē 1, π R2Ē 2 < π R 2 Ē 2, π R2E 1 = π R 2E 1 and π R2E 2 < π R 2E 2 ; and (ii) seller 2 will deloy referral to deter entry if β(1 β)v < G α1β(1 β) 2 v and β > α 2. Proosition 9 shows that under the weak-brand referral format, the referring firm is always worse off whereas the referred firm is not affected. This is different from the strong-brand format because here the referring firm is always the relatively weak brand either before or after referral; hence the strong seller always receives the rofit that is equal to that when it serves only the loyalists by charging the monooly rice. In addition, the conditions for strong-brand referral to be effective differ from those for weak-brand referral. As shown in Proositions 8 and 9, the strong-brand referral format is used to deter entry when α 2 β(1 β)v < G α1β(1 β) 2 v and β > 1 α2(2), whereas the weak-brand referral is adoted when β(1 β)v < G α1β(1 β) 2 v and β > α 2. Obviously, strong-brand referral may be effective while weak-brand referral is not (when α 2 β(1 β)v < G β(1 β)v), and weak-brand referral is effective while strong-brand referral is not (when α 2 < β 1 α2(2) ). It conforms to our intuition that the strong-brand referral format is more effective in entrydeterrence than the weak-brand referral because the stronger seller earns more rofits without entry and is hurt more when an entry occurs. Therefore, the stronger seller has a stronger incentive to block otential entry. It seems uzzling that weak-brand referral may become more effective under certain conditions. In fact, the stronger seller has to ay a higher rice for referral than the weaker seller (referral hurts the stronger seller more since it loses more loyal customers when referring cometitor; on the contrary, the weaker seller loses less since it has fewer loyal consumers). Therefore, under certain circumstances (α 2 < β 1 α2(2) ), the stronger seller may find it unrofitable to deter entry via referral whereas the weaker seller finds it worthwhile to do so. 4.3 Equilibrium Referral Strategy Analogous to the base model, two-way referral results in zero rofit for sellers 1 and 2. Based on the strong-brand referral, weak-brand referral and two-way referral formats analyzed above, we have the following roosition that summarizes our analysis, where we define G a = α1β(1 β) 2 v, G b = β(1 β)v, G c = α 2 β(1 β)v, β a = 1 α2(2), and β b = α 2. Proosition 10 When the incumbents are asymmetric, the equilibrium referral and entry strategies are as follows: 23

25 (i) If G G c, or G c < G G b and β β a, or G b < G G a and β β b, there is no referral by incumbents and seller 3 enters the market; (ii) If G c < G G b and β > β a, the strong brand refers the weak brand whilst the weak brand does not refer the strong brand, and seller 3 does not enter the market; (iii) If G b < G G a and β b < β β a, the weak brand refers the strong brand whilst the strong brand does not refer the weak brand, and seller 3 does not enter the market; (iv) If G b < G G a and β > β a, no incumbent refers its cometitor or both incumbents ractice referrals, and seller 3 enters the market if there is no referral while does not enter if two-way referral is resented; (v) If G > G a, no incumbent ractices referral, and seller 3 does not enter the market. Figure 8: Equilibrium under Asymmetric Incumbent Model Proosition 10 is roughly sketched by Fig.8. The main finding from Proosition 10 is that the weaker seller may refer the stronger seller even when the stronger seller does not do so, as shown in arts (iii) and (iv) of the roosition. As exlained after Proosition 9 earlier, the stronger seller has a higher incentive to rotect its share but under certain conditions referral strategy may be not efficient because the seller might lose more loyal customers resulting in loss of its monooly ower. On the other hand, the weaker seller has less incentive to rotect its market share but under certain conditions may be efficient in using referral to deter entry. Therefore, Proosition 10 can exlain why a relatively weak incumbent like chameleonjohn.com refers the relatively strong cometitor like RetailMeNot. Note that when G b < G G a and β > β a, as shown in art (iv) of Proosition 10, 24

26 either strong or weak-brand referral could shut off the otential entrant. In this case, each incumbent may choose to shoulder the cost of referral or just wait for the rival s referral and thus take a free ride. In this case, there also exists a mixed referral strategy equilibrium wherein seller 1 refers seller 2 with robability τ 1 and seller 2 refers seller 1 with robability τ 2, where τ 1 = ( 1)(β α 2) α and τ 1( 1)(β α 2)+α 2( 2) 2 = α2(2) (1 β)α1 α 2( 2)+β (see Aendix B3). 5 Consumer Welfare Analysis In this section, we investigate how the use of online cometitor referral influences consumer welfare. From the analysis in the revious sections, if online referral is used, then in equilibrium, seller 3 is always blocked out of the market. It is not clear a riori what the effects of referral would be on consumer welfare. This is because, on the one hand, the referral is eroding the monooly ower of a layer since it brings higher rice transarency in the marketlace whereby more consumers are able to comare rices and buy the good available at a lower rate. On the other hand, consumers may be worse off because referring cometitors imlies less market cometition since an additional layer is blocked out of the market. Denote consumer welfare by w. If we treat the sellers and customers as an integrated system, the market rices cannot influence the total welfare (i.e., firm rofits lus consumer welfare) but only affect the surlus division among different entities. Obviously, if seller 3 does not enter the market, the total welfare is equal to consumers aggregate utilities obtained from consuming roducts, v. If seller 3 enters the market with a cost of G, the total welfare will be v G. Thus, the consumer welfare is given by w = v G 3 i=1 π i if seller 3 enters the market, or w = v 2 i=1 π i if seller 3 does not. 5.1 Consumer Welfare under Base Model We first discuss the base model. As shown in Proosition 4, online referral (one-way) will be used at the equilibrium to deter entry only if αβ(1 β)v < G αβ(1 β) v and β > α. In this case, the referring firm earns a rofit of α(1 α)v and the referred firm s rofit equals to αv. Therefore, consumer welfare under referral, denoted by w R, is equal to v α(1 α)v αv; that is, w R = (1 α) 2 v. (28) However, if online referral is not alied, seller 3 will enter the market and the rofits of the three sellers are given by Eq.(8); that is, π 1 = π 2 = α(1 β)v and π 3 = αβ(1 β) v G. 25