Segmented Switchers and Retailer Price Promotion Strategies: Theory and Application to Internet Pricing

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1 Segmented Swtchers and Retaler Prce Promoton Strateges: Theory and Alcaton to Internet Prcng Cenk Koçaş Graduate School of Management Sabanc Unversty Orhanl-Tuzla 4956 Istanbul, Turkey and Jonathan D. Bohlmann El Broad Graduate School of Management Mchgan State Unversty N70 NBC East Lansng, MI FAX: November 005 for submsson to the Journal of Marketng Corresondng author. The authors are assstant rofessors of marketng. They thank Tunga Kyak for excellent research assstance. The authors also thank Roger Calantone, Serdar Sayman, Ruth Bolton, and sear artcants at MSU for ther helful comments on an earler draft. 005 by Cenk Koçaş, East Lansng, Mchgan.

2 Segmented Swtchers and Retaler Prce Promoton Strateges: Theory and Alcaton to Internet Prcng Abstract Emrcal studes reveal a surrsngly wde varety of rce romoton strateges among retalers, even among Internet sellers of undfferentated homogenous goods such as books and musc CD s. Several emrcal fndngs reman uzzlng, artcularly that wthn the same market some small retalers decde to deely dscount, whle other small retalers forgo the rcesenstve swtchers and rce hgh to lay ther nche. We resent theoretcal and emrcal analyses that address these vared rcng strateges. Theoretcal models are usually based on asymmetrc loyalty between two frms that comete for nformed swtchers. Our model of three asymmetrc frms shows that under multle swtcher segments, where dfferent swtchers comare rces at dfferent retalers, frm-secfc loyalty s not suffcent to exlan the varety of retaler rcng strateges. We demonstrate that a retaler s rcng s drven by the rato of the sze of swtcher segments for whch the retaler cometes to ts loyal segment sze. The relatve swtcher-to-loyal ratos among retalers exlan when a frm s more or less nclned to dscount deely or frequently. We thereby dentfy when a small frm fnds t otmal to lay the nche and rce hgh, deste havng few loyals, or to dscount and go for the swtchers. Our analyss reveals several nterestng fndngs, such as a small frm that benefts from a greater number of artally nformed swtchers, even when t cannot sell to them. The emrcal results confrm our model s redctons for vared retaler rcng strateges n a rch set of Internet bookseller rce data. KEYWORDS: Internet Retalng; Prce Promoton; Game Theory; Retaler Loyalty; Swtcher Segments.

3 Introducton Internet retalng offers consumers consderable choce n where to sho and urchase. For examle, a search for several roducts on mysmon.com, a oular rce comarson engne, reveals over three dozen retalers for onlne books, more than 70 retalers offerng rnters, and over 00 dgtal camera retalers. Obvously, many of these retalers are small relatve to the bg layers n the category. Internet book retaler ABooks, for examle, has less than % of the reach number of vewers who vst the ste of Barnes & Noble B&N Onlne. There exst dozens of smlarly small Internet booksellers who comete wth each other and the consderably larger frms Amazon.com and B&N Onlne for a wde assortment of books. What characterzes the rce romoton strateges among these many retalers, both large and small? Frequent dscountng by small frms s generally consstent wth the extant theory e.g., Narasmhan 988; Raju, Srnvasan, and Lal 990. Customers are concetualzed to ossess dfferent nformaton for comarson shong. Customers who know the rce of only one retaler are unnformed or loyal customers, whle customers who know the rces of all retalers are swtchers. Urbany, Dckson, and Kalaurakal 996 reort varous reasons why more than half of grocery customers comare rces across retalers, and cherry-ckng customers tend to beneft gong store to store for secals Fox and Hoch 005 Snce a small frm has relatvely few loyal customers, t generally has more ncentve than a large frm to dscount and attract the swtchers. However, some small retalers decde to rce hgh and sell only to ts loyal or nche segment of customers. Although ths strategy may be aealng for secalzed or hghly dfferentated goods, t s unclear why a small retaler wll rce hgher than a larger rval for a homogenous good such as a book. Clay, Krshnan, and Wolff 00 reort these tyes of uzzlng Internet retalers n ther emrcal analyses, reresentng small and undfferentated frms that, nevertheless, charge relatvely hgh rces. More generally, Internet retalers exhbt consderable rce dserson as frms dscount or rce hgh, often n ways nconsstent wth theoretcal redctons Pan, Ratchford, and Shankar 004.

4 Esecally roblematc for conventonal rce romoton theores s why we observe some small retalers wth heavy dscountng and others wth a hgh-rce strategy n the same homogenous goods market. Prevewng our emrcal study of Internet booksellers, both Worthy and ABooks are small retalers wth smlar Internet reach and ste oularty. They sell many of the same books ABooks carres 90% of the books carred by Worthy n our samle, and also comete wth the larger retalers such as Amazon on a wde varety of books. Deste such smlartes, ABooks dscounts heavly whle Worthy has hgh rces that exceed those of ABooks and Amazon, on average. What exlans these fundamental rcng dfferences among small retalers? How frequently can we exect large retalers to offer shallow or dee dscounts? We resent theoretcal and emrcal analyses that exae a varety of observed rce romoton strateges, such as n Internet retalng. We address two fundamental shortcogs of conventonal rce romoton models: the duooly structure can be lmted n the varety of rce romoton strateges that are consdered, and swtchers are usually assumed homogenous n that they know the rces of all retalers. Retaler rce romoton strateges from the standard duooly aroach small vs. large retalers are drven by dfferent loyal segment szes and homogenous swtchers that comare all rces. We resent a model of an asymmetrc trooly three frms that ncludes multle swtcher segments, where dfferent swtchers comare rces at dfferent retalers. Markets nvolvng several asymmetrc frms may rove more nsghtful and reflectve of actual market condtons than the conventonal duooly. Furthermore, n the context of multle retalers, there may exst multle segments of artally nformed swtchers n addton to the tycal swtchers who comare rces for all retalers. Even n an Internet settng where retalers rolferate and many shoers use rce comarson engnes, not all swtchers wll be exhaustve rce-comarson machnes. For examle, many onlne book customers may comare rces among most of the retalers, but other swtchers are lkely to be unfamlar wth many small Pror models have been aled to both brand and retaler cometton. We model retalers gven our focus on homogenous goods, and to be consstent wth the context of our emrcal settng.

5 retalers such as ABooks and comare rces at only the larger frms lke Amazon and B&N. Recent studes ndcate that onlne shoers vst only. to.4 booksellers on average Johnson et al. 004; Montgomery et al Even the use of rce-comarson shobots remans relatvely low, gven the varous cogntve costs of evaluatng many alternatves Montgomery et al Consumers are more lkely to vst Internet retalers they trust based on an assortment of factors e.g., Bart et al If some customers refer to rce comare only among trusted stores, whle other customers comare rces from all lsted retalers, swtcher segments wth dfferent tyes of rce-comarson behavor wll occur. The realstc assumton, therefore, s that swtchers are segmented snce they are nformed about a subset of retaler rces. By ncludng segmented swtchers n an asymmetrc trooly, our model derves a more comlete set of romoton strateges that are not redcted under asymmetrc duooles. Pror theoretcal models, based largely on Varan 980 and Narasmhan 988, sometmes reort vared results for romotonal actvty. Raju et al 990 conclude that the average dscount offered by the stronger brand greater loyalty s larger than the average dscount offered by the weaker brand less loyalty, but Rajv, Dutta, and Dhar 00 reach a dfferent concluson. Fndngs also dffer about rce romoton frequency. Narasmhan 988 and Raju et al 990 conclude that the romotonal frequency of the stronger brand s less than that of the weaker brand. Rajv et al 00 conclude that hgh-servce stores as an analogue to a strong brand romote more frequently under romotonal advertsng. Small retalers seem to romote wth less ntensty, although dscount rces may have a hgher exected ayout to smaller stores Hoch, Drèze, and Purk 994; Shankar and Bolton 004. The hgh versus low rcng dchotomy does not often ft the rch romotonal strateges observed emrcally e.g., Bolton and Shankar 00. The need clearly exsts for research to address these rce romoton varatons, artcularly for the rcng strateges of small retalers. Narasmhan 988 consders several cases where the frequency and deth of dscount change, accordng to swtchers brand references. For homogenous goods we comare to Narasmhan s 988 basc results. 4

6 By consderng a homogenous good market wth three frms asymmetrc n loyals and swtchers, our results clarfy the vared rce romoton strateges n equlbrum. For examle, we show that a frm can adot a arttoned rcng strategy that combnes frequent shallow dscounts to comete wth one frm wth nfrequent dee dscounts to comete wth another frm. Our results also exlan when a small frm s better off rcng hgh wth lttle dscountng, deste ossessng few loyals. Our analyss reveals several nterestng fndngs, such as a small frm that benefts from a greater number of artally nformed swtchers, even when t cannot sell to them. In general our model not only encomasses a three-frm extenson of ror duooly models, but also exlans revously ambguous stuatons, such as when a retaler has both few loyals and few swtchers. Our secfc research questons nclude: How do multle asymmetrc frms comete for multle swtcher and loyal segments? How do frms dffer n ther rce dserson, ncludng the frequency and deth of ther romotons, based on ther loyal and swtcher customer bases? Why do some small retalers rce hgh, whle others offer dee dscounts? Our results demonstrate that a retaler s rcng s drven by the rato of swtchers for whch the retaler cometes to ts loyal segment sze. The retalers relatve swtcher-to-loyal ratos exlan when a large or small frm s more or less nclned to dscount deely or frequently, or when a small frm wth few loyals s better off rcng hgh. Our emrcal results for Internet bookseller rcng confrm the model s redctons based on the swtcher-to-loyal rato, addng a new ersectve to revous studes of dsersed rces Baye and Morgan 00; Burdett and Judd 98; Raju et al 990; Salo and Stgltz 977. The remander of ths aer s organzed as follows. We frst resent our model, hghlghtng the strategc ntuton n detal and contrastng our results wth ror models. We also formulate several hyotheses from the model s results. We then descrbe our emrcal results for Internet booksellers. We conclude wth manageral mlcatons and future research. 5

7 Model and Analyss Our model bulds uon Narasmhan 988 and Varan 980. Whereas Varan 980 consders many symmetrc frms and Narasmhan 988 studes two asymmetrc frms, we analyze a market wth three asymmetrc frms and multle swtcher segments. Swtcher segments among multle asymmetrc frms are not comonents of ror models, makng our research unque. For conventonal retalers, t s easy to magne that not all customers wll be nformed of all rces because of the hgh cost assocated wth searchng rces. In an Internet settng, however, search costs are generally low. We can reasonably assume that at least some customers are hghly nformed about onlne rces, even for low-cost tems Carlton and Chevaler 00; Kocas 00; Smth and Brynjolfsson 00. However, ths assumton does not reclude multle segments of artally nformed swtchers who do not comare rces among every retaler. Even when dealng wth rce-comarson engnes, not all retalers are lsted, and not all customers utlze rce-comarson stes Iyer and Pazgal 00; Montgomery et al 005. Asymmetrc awareness of retalers by rce senstve swtchers may lead to dfferent rcng strateges Pan et al 004. The fundamental ntuton behnd our model s that multle swtcher segments can lessen rce cometton among frms see Lal and Sarvary 999 for a model of rce comettveness n the context of consumer search costs. Frms wth greater motvaton to dscount, because of a smaller loyal segment sze and/or a greater number of swtchers to otentally serve, wll more actvely comete for the fully nformed swtchers. Ths leaves frms wth fewer relevant swtchers for a gven loyalty sze to focus on ther loyals and the subset of swtchers who consder them n ther rce-comarson search. In such nstances, rces wll generally be hgher than they would be were the frm to comete for all swtchers. Other frms dscount less n reacton to these hgher rces, and so the severty of rce cometton becomes less overall. Under some condtons, the frm wth the fewest loyals can be the hghest-rced frm, a result that asymmetrc loyalty by tself cannot mlement. Our model redctons reflect a wde varance n retalers rce dsersons, consstent wth emrcal observatons. 6

8 Assume a market for a homogenous good, such as a secfc book or musc CD, sold by three retalers. On the demand sde, each customer urchases a sngle unt of the good f t s offered at or below the reservaton rce r, whch s assumed to be homogenous for all customers and across all retalers. We model dfferent segments of loyal customers, who buy from ther referred retaler as long as the rce does not exceed r, and swtchers who comarson sho. The loyal customers are fathful to only one frm, wth the number of customers loyal to Frm gven as n. Wthout loss of generalty, we assume that n > n > n.e., the retalers can be ranked n terms of ther loyal segment szes. We also assume the exstence of two swtcher segment szes, s and s, whose members are not loyal to any frm but rather buy from the lowest rced retaler among those they comare. Swtcher segment s s fully nformed, meanng ts members comare rces quoted by all three frms. Swtcher segment s comares rces quoted only by the larger Frms and. Although these artally nformed swtchers are not arsed of all retaler rces, they stll comare the rces from the best-recognzed retalers, whch may have the bggest reach and the most actve communcaton channels. Frms and would be lke B&N and Amazon the two bggest onlne booksellers, whle Frm would be lke ABooks. Although some swtchers wll rce comare all three retalers s, ABooks has less than % of B&N s reach, so there are lkely other swtchers who are unfamlar wth ABooks and only comare Amazon and B&N s. A more general consderaton of segmented swtchers addng s and s swtcher segments does not change the model s ntuton or conclusons. We also note that generalzng to more than three asymmetrc retalers gves results very smlar to a trooly detals avalable from the authors. Hence, our model focuses on three frms and two swtcher segments for relatve tractablty. We make several other customary assumtons that do not alter the nature of our results. The market sze s normalzed to one n + n + n + s + s, wthout loss of generalty. = Whle the segment szes and the reservaton rce are common knowledge, because of merfect A common reservaton rce s a tycal assumton Iyer and Pazgal 00; Narasmhan 988; Raju et al 990; Varan 980. Narasmhan 988 consders a case where consumers have dfferent reservaton rces for brands. 7

9 addressablty and targetablty retalers cannot rce dscrately Blattberg and Deghton 99; Chen, Narasmhan, and Zhang 00. All frms face constant fxed and margnal costs, whch are assumed to be zero, wthout loss of generalty Iyer and Pazgal 00; Narasmhan 988; Raju et al Overall, the model and ts assumtons are smlar to Narasmhan 988 and other related models, excet for analyzng three frms and two swtcher segments. In an effort to cature ts swtcher segments, frms have an ncentve to undercut the rce of other frms cometng for those swtchers, a tendency that results n a downward ush n rces. Motvaton also exsts to rce at the reservaton rce, n case the swtchers cannot be served wth a lower rce. A retaler s mum rce makes the frm ndfferent between sellng only to ts nche of loyal customers at the reservaton rce and sellng to ts swtcher segments gven t s the lowest-rced frm at the mum rce. A frm wll never dscount below ts mum rce snce t could then do better by focusng on ts loyal customers. A frm s smaller loyal segment sze and/or larger swtcher segment sze gves more ncentve to forgo sellng only to the loyals. We defne a frm s rato of swtcher-to-loyal segment szes, φ, as φ = s n, φ = s + s n, and φ = s + s n. Under segments s and s, Frms and comete for the same swtchers, so Frm always has a hgher swtcher-to-loyal rato SLR or φ than Frm gven Frm s smaller loyal segment. However, Frm can only cature swtcher segment s, so ts SLR may be hgher or lower than that of both frms. Thus, Frm may dscount deely to cature the swtchers, or lay only ts nche loyal segment and charge hgher rces. Absent multle swtcher segments, the relatve order of φ for these frms would strctly be a functon of the loyal segment szes, as seen n ror models. Our addton of segmented swtchers thus changes the nature of a retaler s ncentve to dscount. Equlbrum Prce Promoton Strateges The tenson of sellng to swtchers and loyals results n a lack of ure strateges tycal of such models. Therefore, we solve for a mxed strategy equlbrum that deends uon the relatve szes of the loyal and swtcher segments. A mxed strategy can be nterreted as arsng from a retaler s uncertanty about the rcng decsons of cometng retalers Gbbons 99. 8

10 Equlbrum rces are defned by a robablty densty functon ndcatng the range of rces a retaler may charge the retaler s rce suort. We fnd that the retalers equlbrum rce romoton strateges fundamentally deend on the frms relatve swtcher-to-loyal ratos. In Prooston, we resent the mxed strategy equlbrum for the case that s more tycal of ror models, where the large Frm has the lowest φ. PROPOSITION : When φ > φ, Frms and have mutually exclusve rce ranges that, when combned, form Frm s rce range. Frm cometes wth Frm n the lower art of ts rce range and wth Frm n the uer art of ts rce range. PROOF: See Aendx. The robablty and cumulatve dstrbuton functons for the equlbrum rces are shown n Fgure. Frm has more motvaton to comete for s than Frm, and because Frm can only cature s, the cometton between Frms and s farly ntense. The low rces Frm quotes whle tryng to cature s make t easer for Frm to also sell to s. Thus, there s no guarantee that Frm wll cature any swtchers, even at ts mum rce, snce the other two frms already comete for s at lower rces. Frm s, therefore, less nclned to dscount. The more ntense cometton between Frms and makes the lower bound of Frm s rce range move u, to the ont n equlbrum where Frm no longer drectly cometes for s. Thus, Frms and s equlbrum rce ranges do not overla. Moreover, note that when Frm rces below Frm and cometes wth Frm to cature segment s, t also always serves segment s. That s, n the rce regon where only Frms and comete, s effectvely becomes a comonent of Frm s loyal segment. Because an effectvely larger loyal segment means that Frm now has more to lose from rce cuts, the lowest rce that Frm can roftably quote ncreases, whch lessens the severty of the rce cometton wth Frm. The lowest rce suort for Frms and thus rses above the mum rces of both frms Insert Fgure here

11 These results emerge manly because of asymmetry n both the swtcher and loyal segment szes. The lowest rces are hgher n our model than n Varan 980, Narasmhan 988, and other models whch lack multle swtcher segments. The exstence of s as a swtcher segment that omts Frm leads to hgher average rces for Frms and, whle ther cometton for segment s leads to hgher average rces for Frm. At the extreme of s = 0 where φ > φ, the results reresent a three-frm extenson to Narasmhan 988. We fnd that the equlbrum of Pro. does not change regardless of whether or not Frm s swtcher-to-loyal rato SLR exceeds that of Frm. The ntuton s straghtforward, notng that the lower rce suort for Frms and rses above ther resectve mum rces. Therefore, the equlbrum s unaffected by whether the mum rces of Frms and swtch order, snce nether s art of the equlbrum rce ranges for those two frms. Furthermore, even though Frm may have the hghest SLR, t stll sets ts lower rce suort artally n resonse to Frm s hgher suort as Frm forgoes cometton for s. Frm s man ssue s that both Frms and have hgher SLRs, mmateral of whose s greater. Prooston contrasts remarkably wth the case where Frm has the weakly lowest SLR, or φ φ recall φ > φ. In ths stuaton, Frm lacks suffcent dscount motvaton to cature ts swtcher segment, and so becomes a hgh-rced nche retaler focusng on ts loyal segment. Snce Frm s SLR s not the lowest, t fnds t worthwhle to lay for s. Segments s and s mlctly combne nto a sngle swtcher segment that s served only by Frms and. The resultng equlbrum s defned n Prooston : PROPOSITION : When φ φ, only Frms and dscount whle Frm s rce s set at the reservaton rce r. PROOF: See Aendx. The densty and cumulatve robablty functons for the equlbrum rces are resented n Fgure. The lower rce suort s defned by Frm s mum rce, snce Frm never needs to dscount below ths to comete for the swtchers. Frm s content to be a nche layer, rcng hgh to serve only ts relatvely small loyal segment. Gven that n > n, the Prooston 0

12 condton that φ φ essentally reresents the case where s s small n comarson to s s 0 wll always meet the condton of Prooston. Frm recognzes that most of the = swtchers comare rces only between Frms and, so Frm becomes a hgh-rced retaler for ts small loyal nche. Model Dscusson Insert Fgure here Before turnng to the emrcal valdaton of our model, we descrbe the frms rofts and rces n more detal, focusng on key asects of segmented swtchers. A summary of the frms rofts and lowest rces s gven n Table. The ncluson of a artally nformed segment of swtchers reduces the comettve ressure on the frms. The frms lowest rce suorts are hgher than ther resectve mum rces. Wth the artally nformed swtcher segment s ncluded, average rces and rofts are generally hgher, snce the rce suorts ncrease as Frm abandons s under Prooston. Multle swtcher segments thus tend to reduce cometton, snce not all frms are able to cature all swtchers. The relatve szes of the fully and artally nformed segments shae the nature of cometton between the frms. Under Prooston, as Fgure a dects, Frm s dscount deeens as s exceeds s holdng the total number of swtchers constant. However, when the sze of the fully nformed segment ncreases, so does the severty of cometton between Frms and. As shown n Fgure b, ths ncreased cometton for segment s ushes Frms and s dscounts deeer. At the same tme, t forces Frm to offer shallower dscounts, snce Frm already serves more of segment s n exectaton wth ts deeer dscounts. The comoston of swtchers thus fundamentally affects when retalers should offer frequent or nfrequent, dee or shallow dscounts Insert Table and Fgure here When we comare frms rofts as the comoston of swtcher segments vares, we frst observe that Frm s ndfferent, snce t always receves the guaranteed roft n r. Frm s rofts ncrease when s ncreases at the exense of s, gven that segment s acts as a

13 second-degree loyal segment to Frm. Frm acheves more than ts guaranteed roft at s = 0, but t can gan even more roft f at least some swtchers dsregard Frm. A more nterestng result ertans to the rofts of Frm under Prooston. Frm can beneft from a ostve s customer base as long as the hgher rce suort more than comensates for the loss of some s customers as s ncreases. Frm s rofts generally do not reach a maxmum when all swtchers belong to s. 4 Frm may thus refer to lose some of ts s customers, the only swtchers to whom t can sell, and convert them nto s to make Frm focus more on ts cometton wth Frm. That s, Frm benefts from a more balanced dstrbuton of swtchers, a condton that laces Frm n a more balanced consderaton for both swtcher segments. Our model thus comlements the results of Iyer and Pazgal 00 and Baye and Morgan 00 that ertan to retalers belongng or not to Internet agents that allow rce comarsons among multle frms. By consderng varous-szed swtcher segments, our model onts to a small retaler otentally beneftng from some degree of rce comarson strctly between the larger or better-known frms. Ths result further hghlghts the comettve nature of the asymmetrc trooly. Frm s rces and rofts deend crtcally uon how Frms and comete wth each other for ts swtcher segment. When the relatve sze of the fully nformed swtcher segment s sgnfcantly small, Frm may refer to gnore the swtchers comletely and offer no dscounts at all Pro.. Ths result reresents an mortant dstncton between our segmented-swtcher model and other models of asymmetrc loyalty. When multle swtcher segments exst, loyal segment szes are not suffcent to descrbe the nature of cometton among the varous frms. The relatve szes of the swtcher segments must also be consdered as they affect the swtcher-to-loyal ratos φ among the frms. A small frm may thus dscount or rce hgh to lay the nche, deendng on ts relatve SLR. 4 Frm s rofts for at least some ostve regon of s are hgher than ts rofts at s =0. More secfcally, as long as the total number of swtchers remans above a modest threshold, Frm s roft has a ostve sloe at s =0 +, such that there s at least some ostve s where Frm s better off.

14 Comarson wth Pror Models The fner comettve detals rovded by our model hel exlan some of the varety n ror fndngs for romoton frequency and deth. In terms of romoton frequency, our Pro. results generally follow Narasmhan 988 and Raju et al 990 n that they redct that the strong retaler one wth greater loyalty romotes less frequently. However, our model also redcts that a strong retaler can romote more frequently f t has relatvely more nterest n the swtchers than the weaker retalers do e.g., Frm romotes more often than Frm under Pro.. Ths concluson s consstent wth Rajv et al 00, where a hgh-servce.e., strong store offers advertsed sales more frequently, albet due to traffc buldng. Our model condtons for Prooston concur wth the redctons of Rajv et al 00, even n the absence of traffc consderatons, suggestng that a relatvely larger sze of swtchers targeted by hgh-servce stores can exlan a hgher frequency of advertsed sales. In the case of romoton deth, recall that Narasmhan 988, Raju et al 990, and Rajv et al 00 all deal wth asymmetrc duooles. Under ther resectve models, Narasmhan 988 suggests that the two stores offer the same deth of dscounts for ndfferent swtchers, Raju et al 990 redct that the stronger or larger store should offer deeer dscounts, and Rajv et al 00 redct that the stronger store should offer shallower dscounts. Our model of segmented swtchers redcts the condtons under whch a store may offer deeer or shallower dscounts. More secfcally, a strong store may ndeed offer shallower dscounts f t has the least motvaton to romote, as characterzed by ts smaller swtcher-to-loyal rato Pro.. A strong store may also offer the same dscount deth as a smaller store f no other weak frms comete for swtchers Pro., Frms and. A strong store may even offer deeer dscounts than a weak store f ts share of swtchers s relatvely larger than that of the weak store Pro., Frms and comared to Frm. Our three-frm model wth segmented swtchers thus encomasses the varous cases of ror duooly models. Iyer and Pazgal 00 resent a model of many frms as n Varan 980 wth swtchers and asymmetrc loyalty, but they nclude at most two tyes of frms. Iyer and Pazgal 00 also

15 consder artal loyals who behave as loyals wth a lower reservaton rce. In contrast, we model three asymmetrc frms wth multle swtcher segments. Some of our results, therefore, dffer from Iyer and Pazgal 00 and other models that lack segmented swtchers. In artcular, we redct the exstence of a hgh-rced nche strategy for a small retaler, whch we emrcally observe. Other models do not make such redctons for homogenous goods. Our model also offers some unque nsghts nto rce strateges when a retaler cometes on multle fronts. The novel dscountng behavor of Frm n Pro. comletely draws from the three-frm asymmetry wth segmented swtchers. Frm offers two tyes of dscounts: dee dscounts to comete wth Frm and shallow dscounts to comete wth Frm. Furthermore, as Fgure dects, deendng on the relatve szes of the swtcher segments, the frequency of dee and shallow dscounts vares. Cometng wth dfferent frms for dfferent swtcher segments allows a retaler to develo a arttoned rcng strategy, where the deth and frequency of dscounts vary on each comettve front. Ths tye of rce-romoton strategy s unque to our model of asymmetry n an olgooly. Model Predctons To demonstrate that our model can exlan rcng behavor n a rch emrcal context, we resent testable model redctons and exae them wth rcng data from Internet book retalers. Our model yelds rce dstrbutons as equlbrum strateges that deend uon the relatve swtcher-to-loyal ratos of the frms. 5 Whle summary statstcs that descrbe the romoton strateges can be used to generally test the ft of rcng data, a more robust method s to comare the emrcal and theoretcal rce dstrbutons themselves. We resent hyotheses based on summary statstcs n H. Hyotheses H and H are based on the rce dstrbutons. 5 Mxed strateges n rcng are usually assumed to be observable through temoral rce dserson Narasmhan 988; Varan 980 that s ooled across multle roducts and retalers e.g., Iyer and Pazgal 00; Raju et al 990. Data for multle roducts books, n our case reresent reeated observatons of a mxed rcng strategy over tme. Our analyss s consstent wth ths vew n that we defne dscount n terms of temoral rce changes, and we consder a retaler s average dscountng behavor across books. The hyotheses, therefore, reflect what should be observed for a retaler on average, accordng to both model roostons taken n tandem. In ts most general form, a mxed strategy s a robablty dstrbuton over ure strateges such that rce dserson may be reflected across books as well as tme. See Gbbons 99 for a dscusson of mxed strategy nterretatons. 4

16 The equlbrum rce suorts and dstrbutons make mmedate the followng: H: Retalers wth a hgher swtcher-to-loyal rato wll, on average, have: a lower average rces, b hgher standard devatons n rces, c more frequent dscounts, d a hgher maxmum dscount frequency, e greater dscount deth, and f a hgher maxmum dscount deth. Under the model s roostons, frms wth a hgher SLR wll have lower average rces Ha and a hgher standard devaton n rces Hb n relaton to rce devaton from the reservaton regular rce. The frequency of rce dscounts relates to the lkelhood that a retaler wll rce below the maxmum retal rce. Under Pro., Frms and wll dscount more frequently than Frm, and under Pro., a frm wth a hgher SLR wll romote more frequently than a frm wth a lower SLR. Overall, a frm wth a hgher SLR wll dscount at least as often as a frm wth a lower SLR, and wll therefore dscount more frequently Hc and have a hgher maxmum dscount frequency Hd, on average. The dscount deth relates to the rce suorts and cumulatve dstrbuton functons CDF. From our model, a frm wth a lower rce suort wll tend to have a greater deth of dscount. Under Pro., for examle, Frm has a greater robablty of dscountng at a lower rce than Frm, as evdenced n the CDF lot of Fgure b. From the model s roostons, n most cases, a frm wth a hgher SLR wll be more lkely to dscount wth greater deth. Across all ossble condtons, we exect to observe that retalers wth hgher SLRs wll, on average, have greater dscount deth He and hgher maxmum dscount deth Hf. The rcng relatonshs redcted by H move beyond the tycal loyalty ersectve to a broader vew that ncludes segmented swtchers. For examle, a frm wth a hgh SLR wll dscount more frequently Hc due to havng relatvely few loyals as n tycal models and/or havng fewer swtchers who consder ts rces. By combnng loyalty and swtcher asymmetres, we can redct rcng behavor under revously ambguous stuatons, such as when a frm has both few loyals and few swtchers. 5

17 Whle summary statstcs of retalers rces can ndcate whether the swtcher-to-loyal rato exlans rce romotons, a more rgorous test would consder the entre rce dserson curve. Theoretcally, we have very clear redctons about how equlbrum rce dstrbutons should aear Fgures and. We test whether the emrcal rce dstrbutons vary as redcted by analyzng stochastc doance. For any two CDF functons, F j x frst-order stochastcally doates F x ff F x F x, x. Put dfferently, f Frm j s rce CDF les j nowhere above and somewhere below Frm s dstrbuton, then Frm j frst-order doates. In Fgure b, for examle, Frm frst-order stochastcally doates Frms and, whle Frm doates Frm. Frst-order doance s a farly strct standard when consderng emrcal rce dstrbutons that may nclude shocks or random error. Second-order stochastc doance s smlar excet t consders the defct functons, or the ntegral of the CDF. Second-order stochastc doance holds under frst-order doance, but not vce-versa. Our model redcts that a frm wth a lower SLR should stochastcally doate a frm wth a hgher SLR the sole exceton beng Frms and when φ > φ under Pro.. On average, we should observe: H: The rce dstrbutons of retalers wth a lower swtcher-to-loyal rato wll frst- and second-order stochastcally doate frms wth a hgher swtcher-to-loyal rato. The model s roostons also make very secfc redctons concernng dfferent rcng strateges for small frms wth a small loyal segment sze Frm. For a hgher SLR, the small frm wll be stochastcally doated by the large frm, whle the reverse s true f the small frm has a lower SLR. Ha: The rce dstrbutons of small retalers wth a hgh swtcher-to-loyal rato wll be frst- and second-order stochastcally doated by large frms wth a lower swtcher-to-loyal rato. Hb: The rce dstrbutons of small retalers wth a low swtcher-to-loyal rato wll frst- and second-order stochastcally doate large frms wth a hgher swtcherto-loyal rato. 6

18 Emrcal Evdence We test the redctons of our modelng effort by usng rcng data we collected from onlne book retalers. A book s a homogenous roduct that s unquely dentfed by an ISBN number, a classfcaton that s wdely used and recognzed by customers as well as sellers. To ensure that the onlne retalers n our data set share at least a common swtcher segment, we collected daly data on book rces from all the retalers lsted on the rce comarson ste mysmon.com. In the erod durng whch our data were collected, mysmon was the leadng rce-comarson engne, wth 80% of the rce-comarson ste vst market share Medametrx and Nelsen Netratngs; see also Allen and Wu 00, Kocas 00. Our consderaton of booksellers lsted on mysmon establshes the exstence of a fully nformed swtcher segment s n our model, wthout recludng the exstence of other swtcher segments. Prces reorted from mysmon are taken drectly from each retaler s web ste, reflectng the book s offered rce to all shoers at that ont n tme, net of shng and handlng costs. Data Collecton Methodology We comled a samle of,07 books from varous sources. 6 From June 00 to August 00, we collected daly rce data on these books from all the bookstores returned by a search on mysmon. We refer that rce changes n the data reflect the mxed strategy dscountng of retalers rather than systematc changes from rce shocks e.g., net rce changes due to a swtchover to free shng or reservaton rce changes. Prce data collected over longer erods of tme have more rsk of beng contaated by systematc rce adjustments. To allevate ths roblem, we use only data on non-bestseller books collected durng a relatvely short wndow of tme. Bestsellers have more rce dserson than non-bestsellers and are more lkely to have reservaton rce adjustments and be traffc generators comared to non-bestsellers Clay et al 00. Elatng bestsellers, dulcates, and books not carred by any of the 6 These sources conssted of four booklsts that were ublcly avalable on the Internet: 40 books from Publsher's Weekly bestsellers lst on 6/4/0; 70 books from One Book Lst: Collaboratve Books to Read, a lst comled by the Usenet newsgrou rec.arts.books; 60 books from Latest Acqustons by Government Envronmental Lbrary 00; and 4,77 books bought by Sdney Sussex Unversty Lbrary n 00. 7

19 mysmon bookstores left a total of,640 books. For our emrcal analyss, we used the daly rcng data on these,640 books for a erod of 6 days n June 00. Ths month reresents the most recent tme erod for whch we have comlete data from all the retalers and no systematc rce adjustments. Ths 6-day wndow also sans a relatvely short erod of tme n an effort to mze reservaton rce adjustments. 7 In our June 00 samle erod, 8 unque mysmon retalers carred at least one of the,640 books. All books n the samle were offered by multle retalers. To comare retalers that carry a smlar assortment of books, we ranked the booksellers wth resect to the ercentage of books they carred from the total lst of,640. We observed a ga between the to 4 retalers, who carred at least 40% of the books, and the bottom 4 retalers who carred at most only 9% of the,640 books. Based on ths observaton, we lmted our analyss to the 4 retalers that carred at least 40% of the books. The fnal samle had 9,45 total observatons, or nearly 8,000 er retaler on average. Loyal and Swtcher Measures as Predctor Varables Our objectve s to observe how the relatve swtcher-to-loyal ratos of these 4 retalers affect ther rcng strateges. In order to form an emrcal roxy of the swtcher-to-loyal rato, we need ndcators of loyal and swtcher segment szes for these 4 frms. Wth ths objectve n d, we collected data on several measures for each retaler n our samle. Reach and Lnk Poularty. Reach measures the number of users who vst a gven ste and therefore reresents the sum of both loyal and swtcher customer vsts. Reach data are obtaned from Alexa, an Amazon.com comany that collects data on the browsng behavor of several mllon customers who use Alexa s toolbar. Lnk oularty refers to the total number of lnks that a ste has across the Internet. Book-lnk oularty s detered as the number of stes that lnk to a book retaler and whch contan the word book on the same age where the lnk 7 Emrcal studes strve to use a large enough number of erods to cature temoral realzatons of the mxed strategy. Our number of tme erods s smlar to others e.g., Clay et al 00; Raju et al 990, although we use daly nstead of weekly data to mze systematc rce adjustments. We dd exae three- and sx-month versons of the data set 87 and 84 days, resectvely, and the overall results and conclusons are the same. 8

20 aears. Book-lnk oularty and lnk oularty may ndcate the sum of swtcher and loyal customers, although the resultng conclusons may correlate more wth loyalty retalers wth a large number of loyals may be lnked more often. We detere lnk oularty as the sum of all lnks found by the search engnes Alltheweb, AltaVsta, Google/AOL, HotBot/Inktom, and MSN. Book-lnk oularty s detered usng AltaVsta. Page Vews er User. Page vews er user, also obtaned from Alexa, are the average number of unque ages vewed er user by ste vstors each day. The age vews er user can be used as an ndcator of loyalty, because loyal customers tend to send sgnfcantly more tme on a sngle ste when comared to swtchers. Page vews er user have been a referred measure of onlne loyalty n recent studes Demers and Lev 00; Goldfarb 00. Research has exaed the drvers of trust and loyalty n onlne shong, and webste navgaton ssues arse as mortant factors e.g., Bart et al. 005; Shankar, Smth, and Rangaswamy 00; Srnvasan, Anderson, and Ponnavolu 00. Navgatng webste nformaton for n-deth content ncreases satsfacton and loyalty Shankar et al. 00. Demers and Lev 00 fnd age vews er user to be hghly correlated to the number of vsts and average tme sent at the webste. Greater Internet loyalty s also assocated wth greater wllngness to ay Srnvasan et al. 00. The age vews er user metrc thus reresent a good roxy for loyalty gven ts assocaton wth ndeth navgaton and loyalty behavors generally absent from rce-senstve swtchers. Search Share. Search share s an ndcator of the relatve swtcher generaton otental of the retalers. A bookstore desrng to attract more swtchers may become lsted more often n a rce-comarson query. For a artcular set of rce-comarson stes, we formulate a retaler s search share as the roorton of rce comarson stes that return rces for that retaler. We use the nne to-ranked book rce-comarson stes as well as mysmon to formulate a lst of rce-comarson stes for books. 8 Greater search share means the retaler s lsted on more book 8 These book rce-comarson stes are the to nne stes that dentfy the booksellers from whch they quote rces, as ranked by google.com. These stes are bookfnder.com, addall.com, bestbookdeal.com, allbookstores.com, textbookland.com, aaabooksearch.com, camusbooks.com, comareshobooks.com and anybooksforless.com. Other general rce-comarson stes beyond mysmon were not ncluded, snce mysmon reresents over 80% of all rce-comarson actvty conducted on the Internet. 9

21 rce-comarson stes, and may thus attract more swtchers from varous segments. Although search share does not dfferentate swtcher segment szes, t does gve a frm-secfc ndcaton of relevant swtcher ntensty. The swtcher-to-loyal rato of our model, n general form, reresents the sum of ts swtcher segment szes relatve to loyal segment sze. Hence, t s suffcent to form a roxy of a retaler s relatve frm-secfc swtcher sze, wthout needng to know recsely the sze of each artcular swtcher segment. We note that there are several reasons why a frm mght be lsted n a rce-comarson engne. Sometmes a retaler s rces are used by the rce-comarson ste wthout secfc acton on the art of the retaler. In addton, relatvely hgh-cost retalers are not necessarly absent from rce-comarson stes. A frm wth comarably hgher rces may want greater access to all otental buyers and, therefore, may share ts rcng data wth the search engne Iyer and Pazgal 00. Whether hgh-rced or low-rced, retalers lsted wthn rcecomarson stes have access to a hgher number of swtchers. Therefore, the degree of artcaton n rce-comarson engnes serves as an ndcator of the retaler s access to swtchers who become nformed of ts rces. Swtcher-to-Loyal Rato. Gven the above measures, we notce that whle reach and oularty could rovde measures of the sum of swtcher and loyal segment szes, we can use age vews er user normalzed across retalers as a roxy for relatve loyal segment szes, and search share as a roxy for the relatve swtcher segment sze. Snce φ s defned as the rato of the frm s swtcher-to-loyal segment szes, we form a roxy measure of φ as the rato of search share the relatve exected number of swtcher customers to the normalzed age vews er user the relatve exected number of loyal customers. Descrtve statstcs for the 4 retalers are resented n Table. The retalers are ordered by decreasng swtcher-to-loyal rato SLR. In terms of lnk oularty and reach, Amazon, B&N, and BooksAMllon are the to three frms. Gven the overwhelg szes of Amazon and B&N, oularty measures are too skewed to be of much use n deterng the retalers rcng strateges. Both of the to two retalers lkely have very large loyal segments, 0

22 but they also lkely aeal to many swtchers. It s hard to ascertan from oularty measures alone whether Amazon and B&N wll rce more accordng to ther loyals or swtchers. However, SLR allows us to assess the relatve dscountng behavor of frms that loyalty or swtcher szes alone cannot accomlsh. For the smaller frms, the SLR clearly searates those wth a hgh SLR e.g., ecamus from those wth low SLR e.g., Varsty. For examle, deste ecamus and Varsty havng nearly the same oularty and age vews er user, the SLR s clearly hgher for ecamus than Varsty. We now show emrcally that the relatve SLRs exlan the dscountng behavor of the retalers consstent wth our model redctons Insert Table here Prce Promoton Measures For each retaler, we calculate varous measures of rce-dscountng actvty. We do so wth the vew toward rce dscounts reflectng rce changes over tme. Durng June 00, each book had a sequence of daly retaler rces. Average rce for any retaler s the average of all normalzed rces for that retaler, where normalzed rces are calculated by dvdng any gven book rce by the hghest rce quoted for that book by any one of the 4 retalers n the samle erod. The standard devaton of the normalzed rces n each sequence, averaged over all the books carred by the retaler, gves the average standard devaton. For each retaler we also count the number of rce changes n our daly data. We then average that fgure across all the books sold by the retaler to calculate the average number of rce changes dscount frequency. The maxmum s found by takng the hghest number of rce changes for the retaler across books. We calculate the retaler s absolute changes n normalzed rces, averaged across all books, to obtan the average and maxmum deth of dscounts across books for that retaler. Analyss of Prcng Strateges The summary statstcs for retaler rces are gven n Table, where the retalers are ordered by ther swtcher-to-loyal rato. To test the exected rce relatonshs under H, we use the frms SLRs along wth the rcng data from Table. In regresson analyses for the 4 retalers studed, we use a rce statstc as the deendent varable and SLR as the ndeendent

23 varable. The resultng standardzed coeffcent of the SLR and ts sgnfcance are, by defnton, dentcal to the Pearson correlaton coeffcent and ts sgnfcance. We reort these correlatons n Table 4. We observe that the SLR s sgnfcantly correlated wth the frms rce dscountng. The results suort H, demonstratng that retalers wth a hgher SLR have lower rces Ha and a hgher standard devaton Hb on average. They also dscount more often Hc and Hd wth greater deth He and Hf. We conclude that a frm s swtcher-to-loyal rato s a sgnfcant redctor of ts romotonal actvty. Further nvestgaton of Table 4 reveals that only search share and SLR have any sgnfcant correlaton wth the rce-dscount statstcs. Note that the roxy loyalty measure age vews er user does not correlate well wth the rcng statstcs. 9 Ths result echoes our model s mlcaton that asymmetry n loyalty alone s not adequate to assess rcng strateges. Emrcally, we should demonstrate that the swtcher-to-loyal rato s a better exlanatory varable than other retaler varables. The correlatons of Table 4 suggest search share as a ossble alternatve. Comarng SLR to search share as an ndeendent varable, we generate F- statstcs from regressons usng both SLR and search share and comare them to restrcted regressons wth ether varable alone. The results show that search share never sgnfcantly adds to the regresson ft beyond SLR for any rce varable. Conversely, SLR does sgnfcantly add beyond search share alone for all but the standard devaton and maxmum frequency analyses. Our SLR roxy s, therefore, able to cature the average dscountng behavor of the retalers studed. Furthermore, t does so better than the other retaler descrtve varables. Tests of Retaler Prce Dstrbutons Insert Tables and 4 here Hyotheses and relate our model redctons to measures of stochastc doance. Fgure 4 resents the emrcal cumulatve dstrbuton functons CDF of normalzed rces for 9 We also analyzed the correlatons of the rcng statstcs wth reach and lnk oularty after omttng Amazon and B&N due to ther hgh values. The correlatons reman nsgnfcant, excet for a ostve correlaton of 0.59 <0.05 between reach and maxmum dscount frequency. The age vew measures for Amazon.com and Sam Goody may reflect more than book searches by consumers. Deletng these two retalers does not change the nsgnfcance of the age vew correlatons n Table 4, whle the SLR correlatons reman hghly sgnfcant.

24 the 4 retalers. The numbers n arentheses next to each retaler n the fgure refer to that retaler s rank accordng to decreasng SLR the same orderng as n Tables and. 0 The fgure makes clear that at the lower rce levels, most frms have a small ercentage of observed rces. Ths observaton makes a strct test of stochastc doance roblematc, snce a retaler who may have hghly dscounted a few books on a few days out of 8,000 rces quoted by the average retaler dstorts the fact that the same retaler may have relatvely hgh rces for all other books across all days. Furthermore, the retalers CDF functons may cross n closelysaced rce regons, meanng nether frm stochastcally doates the other. For a gven ar of retalers, our model redcts that the retaler wth a lower SLR should stochastcally doate the other. However, we cannot make general statements about multle frms of the same tye e.g., a Frm should doate a Frm, but multle Frm s may not exhbt any doance attern among themselves. Therefore, we elate the 5% lowest rces quoted by each retaler and exae stochastc doance by consderng retaler ars n whch stochastc doance s evdent. Wth 4 retalers, there are a total of 9 combnatons of two that we can exae for stochastc doance. Out of the 9 ars, there are combnatons 5% whose CDF s ntersect at least once, such that nether retaler can frst-order stochastcally doate the other. Of the remanng 68 combnatons, 4 6% are classfed correctly when we use SLR as the redctor. The ch-square statstc of.77 shows that the classfcaton guded by the SLR measure roduces sgnfcantly better results = 0.05 than by chance alone Insert Fgure 4 here We use the defct functons the ntegral of the CDF to test for second-order stochastc doance. Of the 9 ars of defct functons, 5 ars 6% have functons that ntersect at least once. Of the remanng 76 ars, 5 70% are classfed correctly accordng to SLR. The 0 The fgure shows normalzed rces for all books across all days. From our model, a retaler that stochastcally doates another retaler for one book should do so for all books only the reservaton rce vares across books. We thus exae rce dstrbutons across both books and tme to test for stochastc doance. The lowest 5% of a retaler s rces reresent rces that are at least eght standard devatons n nter-temoral terms below the average rce for each retaler. Ths rocedure reflects the concet of almost stochastc doance see Leshno and Levy 00.