The NPV of Bad News. Jacob Goldenberg School of Business Administration Hebrew University of Jerusalem, Jerusalem, Israel

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1 The NPV of Bad News Jacob Goldenberg School of Busness Admnstraton Hebrew Unversty of Jerusalem, Jerusalem, Israel Barak Lba Recanat Graduate School of Busness Admnstraton Tel Avv Unversty, Tel Avv, Israel Sart Moldovan Faculty of Industral Engneerng and Management Technon, Israel Insttute of Technology Etan Muller Stern School of Busness New York Unversty, New York, New York Recanat Graduate School of Busness Admnstraton Tel Avv Unversty, Tel Avv, Israel March 2007 Forthcomng: Internatonal Journal of Research n Marketng We would lke to thank Hubert Gatgnon, Stefan Stremersch, and two anonymous revewers for a number of constructve comments and suggestons. The Insttute for Busness Research n Israel at Tel Avv Unversty; the Kmart Internatonal Center of Marketng and Retalng; the Davdson Center, Hebrew Unversty of Jerusalem; The Horowtz Assocaton and the Center for Complexty Scence; Ths research was supported by the Israel Scence Foundaton (grant No. 1027/06).

2 The NPV of Bad News Abstract We explore the effects of ndvdual- and network-level negatve word-of-mouth on the frm s profts usng an agent-based model and specfcally, an extended small world analyss. We nclude both permanent strong tes wthn the socal network, and changng, often random, weak tes wth other networks. The effect of negatve word-of-mouth on the Net Present Value (NPV) of the frm was found to be substantal, even when the ntal number of dssatsfed customers s relatvely small. We show that the well-known phenomenon of the strength of weak tes has contradctory effects when takng nto account negatve word-ofmouth: Weak tes help to spread harmful nformaton through networks, and can become a negatve force for the product s spread. 2

3 1. Introducton Consder the followng actual case of a consumer electroncs company that recently ntroduced a new audo CD protecton devce. Soon after launch, the company dscovered that the product performed poorly n about 2% of the European market. Fxng the problem was not smple, and the frm s executves debated how much the company should nvest to mtgate the problem. Some argued that 2% of the market would have neglgble economc consequences. Others countered that the dssatsfed customers, who could not be dentfed n advance, would generate negatve word-of-mouth communcatons followng ther poor experence, ultmately harmng the frm s profts. Even though the executves were aware of the conventonal wsdom that bad news travels fast, none of them had a good grasp as to how to assess the possble effects of the antcpated negatve word-of-mouth on ther profts. Unfortunately, there s lttle n the lterature that can help managers n such cases. Marketers do realze that negatve word-of-mouth communcatons can consderably lower a frm s profts. Thus, consderable attenton has been gven n the academc lterature to explore topcs such as the crcumstances under whch consumers spread negatve word-of-mouth (Rchns 1983), the quantty of negatve word-of-mouth that dssatsfed consumers spread (Anderson 1998), and the relatve weght of negatve nformaton receved by consumers as compared to postve nformaton (Mzersk 1982). Smlarly, there are numerous anecdotal stores n the busness lterature about the possble harm caused by a dssatsfed customer s word-of-mouth communcatons (Hart, Heskett, and Sasser 1990). Recently, negatve word-of-mouth has drawn addtonal nterest as marketers have become more aware of the speed at whch negatve product-related nformaton can pass through electronc means such as the Internet (Ward and Ostrom 2006; Rtson 2004).

4 Yet there s scant formal analyss n academc studes that can help managers understand the economc mplcatons of negatve word-of-mouth. Whle consderable lterature has dealt wth negatve word-of-mouth at the ndvdual or network level (see Buttle 1998 for a revew of the word-of-mouth lterature), and some have analyzed negatve word-of-mouth at the aggregate level (Mahajan, Muller, and Kern 1984), lttle s known about how both levels combne to produce market-level results. Tyng both ends together s essental, as managers wll typcally be able to collect nformaton on the determnants and extent of negatve word-of-mouth at the ndvdual level, yet ther nterest n and ablty to justfy frm-level actons wll ultmately le n the analyss of aggregate-level fnancal results. A possble reason for the dearth of formal analyss s that the spread of nformaton n a socal network s a complex system that conssts of a large number of ndvdual enttes nteractng wth each other, n what s sometmes an ndscernble manner, ultmately generatng large-scale, collectve, vsble and quantfable behavor (Anderson 1999; Holland 1995). In other words, negatve word-of-mouth s an nvsble force, leavng no tracks n the sales curves. Unlke the postve nteractons of consumers that lead to adopton and growth of sales, we do not have relable measures of the negatve word-of-mouth that shrnks the market by transformng potental adopters nto non-adopters. In ths study we explore the effect of both ndvdual- and network-level negatve word-ofmouth on aggregate sales usng an agent-based modelng approach, specfcally an extended model of small world analyss (Watts 1999). Utlzng a dynamc small-world approach, we smulate a market n whch nformaton spreads when consumers nteract wth each other, usng both strong tes wthn ther own socal system and weak tes wth other networks (Granovetter 1973). 2

5 Our analyss explores the effects of changes n a socal system s nformaton structure, the ntensty of strong and weak tes, and marketng effect, as well as determnants of the negatve word-of-mouth phenomenon, such as the strength of negatve word-of-mouth compared to postve word-of-mouth, or the number of dsapponted customers, on the aggregate sales and net present value of the cash flow that marketers can hope to acheve. An mportant pont to note s that our approach deals wth negatve word-of-mouth more than wth other possble negatve effects of contagon. Whle the nternal nfluence parameter of aggregate dffuson models s often nterpreted to represent word-of-mouth, t can also capture mtaton effects such as socal learnng, socal pressures, or network effects (see Van den Bulte and Stremersch 2004). Based on a meta-analyss of aggregate dffuson models, Van den Bulte and Stremersch even suggest that mtaton effects may be overall stronger than word-of-mouth effects n the growth of markets for new products. Postve contagon effects n aggregate dffuson models may thus nclude both mtaton effects and word-of-mouth. Yet the pcture for negatve word-of-mouth s dfferent. In the modelng approach that we present, negatve word-of-mouth stems from ndvdual customer dssatsfacton, and the effects are manfested at the network level. Negatve contagon effects may not be a product of dssatsfacton, but rather the mere adopton by other consumers, who for example belong to a segment of the populaton whose adopton reduces the socal utlty of the product. For example, Josh, Rebsten, and Zhang (2006) reported a negatve contagon effect of the adopters of the Porsche SUV (Cayenne) on the potental adopters of tradtonal Porsche roadsters. Ths effect requres specfc modelng of segmentaton and contagon that wll capture these segment-based phenomena. For example, unlke word-of-mouth, observatonal learnng does not demand drect contact, so that negatve contagon can draw on the total number 3

6 of adopters n the populaton and operate other than at the network level. Hence we focus on negatve word-of-mouth only, and leave the ntrgung ssue of the negatve effects of observatons and other forms of negatve contagon to future research. The rest of the paper contnues as follows: In the next secton, we dscuss the effects of negatve word-of-mouth at the ndvdual level and ts ntegraton nto a dynamc small world model. In Secton 3, we analyze the adverse economc outcomes of negatve word-of-mouth. In Secton 4, we explore how a socal structure that ncludes negatve word-of-mouth prompts falure, and we offer a model that dscrmnates between falures and successes. Secton 5 presents a structural equatons model that enables us to better understand how network structure affects the consequences of negatve word-of-mouth. The paper concludes wth the manageral mplcatons of the results. 2. A growth process n the presence of negatve word-of-mouth 2.1 Negatve word-of-mouth communcatons Customers respond to dssatsfacton wth a product n a number of ways, ncludng complants, brand swtchng, legal acton, and negatve word-of-mouth. The latter may be partcularly harmful, because t requres lttle effort by consumers, yet t can drectly affect the consumpton habts of would-be adopters. Worse, t s largely nvsble to marketers. One problem n ths regard s that only a mnorty of dssatsfed customers complans to the frm, and so the actual extent of negatve word-of-mouth may be greater than what marketers assess t to be (Charlett, Garland, and Marr 1995). The ndvdual-level effect of negatve word-of-mouth depends on the ndustry and the specfc case. In the fashon ndustry, Rchns (1983) found that most dssatsfed customers 4

7 talked on average to fve others. Examnng mult-product surveys from Sweden and the US, Anderson (1998) found that hghly dssatsfed customers talk to more than ten others. Other numbers have been reported as well (Charlett, Garland, and Marr 1995). Whle the extent may vary, there s general agreement n the lterature that a dssatsfed customer nfluences others more than a satsfed one (Lacznak, Decarlo, and Ramaswam 2001; Herr, Kardes, and Km 1991). Ths consensus s bult both on evdence that dssatsfed customers communcate wth others more than satsfed ones (Anderson 1998; TARP 1986), and that recpents of ths communcaton place more weght on negatve nformaton (Herr, Kardes, and Km 1991). The dsproportonal nfluence of unfavorable nformaton s supported by attrbuton theory (Mzersk 1982), and n general by the fact that such nformaton s more accessble and dagnostc (Herr, Kardes, and Km 1991). Scant formal analyses are avalable as to the aggregaton of negatve word-of-mouth from the ndvdual or network level to the market level, as only recently has agent-based model work tyng ndvdual-level word-of-mouth to aggregate-level response begun to emerge (Goldenberg, Lba, and Muller 2001). One excepton s Moldovan and Goldenberg s (2004) use of Cellular Automata to show how resstance leaders, or opnon leaders wth negatve reactons to a new product, can harm the growth of a new product. The work we present heren does not focus on specfc ndvduals n the market, but rather on the essental mechansms that te ndvdual-level negatve word-of-mouth to the aggregate fnancal results of the frm. 5

8 2.2 Market structure n the presence of negatve word-of-mouth Consder a case n whch a new product grows n a gven socal system. In the presence of negatve word-of-mouth, we can thnk of several pools of market partcpants, as descrbed n Fgure 1. Note that n any gven tme perod, some consumers can stll be potental adopters. They may be stll unaware of the new product, or have not receved enough nformaton yet to adopt. Ths pool naturally s larger at the begnnng of the process and decreases n sze wth tme. Fgure 1: Pools of market partcpants People who leave the potental adopter stage may move to one of the three pools. Some - labeled postve adopters - wll adopt the new product and wll feel postve about the decson. Hence they can be expected to nfluence other potental adopters through future postve wordof-mouth. In the classc dffuson modelng lterature, whch dd not consder negatve word-ofmouth, all adopters are postve adopters. However, n the presence of negatve word-of-mouth, some labeled here dsapponted adopters - wll adopt the new product and wll be dsapponted. Thus, they have the potental to spread negatve word-of-mouth nfluence on potental adopters. Consequently a new pool exsts, 6

9 that of rejecters. Rejecters are ex-potental adopters who receved negatve word-of-mouth such that they wll not consder the product any longer. Ths negatve word-of-mouth can come from dsapponted adopters, as just descrbed, or from other rejecters, who, whle they dd not buy the product, can stll spread negatve nformaton to other potental adopters. The market partcpant pools descrbed above can serve as a basc approach toward modelng a process that ncludes negatve word-of-mouth. An early study by Mdgley (1976) defned a process ncludng negatve word-of-mouth wheren dsapponted consumers nfluence satsfed adopters wth ther negatve word-of-mouth, transformng them to dsapponted as well, nstead of nfluencng potental adopters, as we propose. In a notable aggregate-level dffuson model, whch ncorporated negatve word-of-mouth n the modelng of the growth process, Mahajan, Muller and Kern (1984) used a framework smlar to what we suggest n ths paper. A major lmtaton of ths approach, however, s that t does not consder the dynamcs of the socal system that drve the growth process, as wll be expanded on presently. Dsregard of socal network dynamcs has long been recognzed as one of the prmary lmtatons of aggregate dffuson models (Mahajan and Peterson 1985), and a major challenge for researchers who want to analyze markets n a parsmonous way, yet must take nto account that socal structure has a profound effect on nformaton transfer (Barabás 2003). Whle there have been efforts to model aggregate dffuson processes n the context of a small number of large segments that nteract wth each other (e.g., Tanny and Derzko 1988, Van den Bulte and Josh 2007), dynamcs related to the communcaton processes that occur at the ndvdual network level, have generally been deemed to be too complex to model at the aggregate level. The ncluson of negatve word-of-mouth, whch adds further complexty to the modelng of the growth process, presents aggregate modelers wth a real challenge. Yet t would be hard to truly 7

10 understand the role of negatve word-of-mouth n the growth process wthout takng these dynamcs nto account. An mportant ssue n ths regard relates to the fundamental effect of socal network structure on the way agents nfluence each other. Researchers have been ncreasngly aware of the need to dstngush between the two knds of avenues of socal nfluence: strong tes and weak tes (Wuyts et al. 2004; Sh 2003; Goldenberg, Lba, and Muller 2001; Brown and Rengen 1987; Granovetter 1982, 1973). In typcal settngs, ndvduals may nteract wth ther close vcnty. However, the more mportant nteractons wth others are not necessarly wth ndvduals mmedate personal network; ndvduals are also nfluenced by contacts wth others wth whom they have tenuous or random relatonshps. Such nfluences are labeled weak tes to dstngush them from the more stable, frequent, and ntmate strong te nteractons that characterze ndvduals personal networks. If the mportance of weak tes for the transfer of postve nformaton has been acknowledged (Granovetter 1973) and quantfed (Goldenberg, Lba, and Muller 2001), there has been practcally no research on the effect of both weak and strong tes n the presence of both postve and negatve nformaton. An nterestng queston, for example, s whether the strength of weak tes remans n effect n the presence of negatve word-of-mouth. Our nterest n ths paper s n ganng an understandng of how the nterplay between postve and negatve nformaton, as well as weak and strong tes, affects the growth of new products and the consequent economc results, whch are of prmary manageral nterest. To do so, we present our model n the next secton. 8

11 2.3 A model of growth n the presence of negatve word-of-mouth Only a decade ago, Easton and Håkansson (1996) reported that dynamc network research n general gnores the dosyncratc relatonshp between ndvdual consumers n the market. However, n recent years, socal scence researchers have become nterested n the effects of ndvdual- or network-level parameters on market-level factors. In ths context, they have ncreasngly used agent-based models, or complex system methods, n ther analyses, wth applcatons to felds such as economcs (Rosser 1999), management (Anderson 1999), and marketng (Lba, Muller, and Peres 2005; Shakh, Rangaswamy, and Balakrshnan 2005; Goldenberg, Lba, and Muller 2001; Krder and Wenberg 1997). These approaches are especally sutable for cases n whch a larger number of agents nteract n a way that may be smple to model on the ndvdual level, yet may be too complex to track usng smple aggregate approaches. Essentally, researchers buld an ndvdual- or network-level model of behavor, and use a smulaton to examne how ndvdual-level behavor aggregates to market-level aggregate consequences. Followng ths tradton, we start wth an ndvdual-level model. We look at a socal system composed of potental adopters,.e., at the begnnng of the process, no member has adopted. Ths socal system s composed of dscrete, smaller socal networks. People can communcate wth ther socal network counterparts- these are strong tes communcatons. They can also engage n more random communcaton wth ndvduals outsde ther network,.e., weak tes. See Fgure 2 for an extended model of consumer pools that ncludes both strong and weak tes. In each perod, potental adopters may adopt the product nfluenced by ether marketng actons such as advertsng (parameter p n the followng model), or word-of-mouth that can 9

12 ether follow a strong te nteracton (q s ) or a weak te nteracton (q w ). Many of these adopters wll be satsfed wth the product and wll supply postve word-of-mouth of ther own va ether strong- or weak-te nteractons. However, a certan percentage of the buyers e.g., d, wll be dsapponted and spread negatve word-of-mouth va both strong and weak tes. Fgure 2: Pools of market partcpants: An extended vew Followng the above dscusson, we can assume that negatve word-of-mouth effect s stronger than postve. Hence, the effect of negatve word-of-mouth may be m tmes as strong as that of postve word-of-mouth (for both strong and weak tes). Followng negatve word-ofmouth, some potental adopters turn nto rejecters,.e., those who wll not consder the product n the future. 10

13 Are rejecters also a source of negatve word-of-mouth? It s commonly suggested n the popular busness lterature that negatve word-of-mouth can be passed on by those who dd not even purchase the product. However, not much s known on the extent of ths phenomenon, or how t changes (weakens) as we move away from the person who actually had the bad experence. It s hard to beleve however, that effects are the same for dsapponted customers and for people who heard about the product from a far away source. To take nto account the dfference, our model allows negatve word-of-mouth to pass through one layer n an ndvdual s socal network. Rejecters affected by a dsapponted adopter wll not only reject the nnovaton, but mght also spread negatve word-of-mouth themselves; thrd-hand negatve word-of-mouth s not consdered. Ths restrcton s somewhat conservatve regardng negatve word-of-mouth s effect. 2.4 Dynamc Small World To examne product growth n the envronment descrbed above, we use an agent-based approach that s an extenson of the Small World, a tool that has receved much attenton followng Mlgram s well-known studes about the low degrees of separaton between ndvduals n large socal systems (Watts 1999). Small World was demonstrated as relevant to a varety of socal systems through whch word-of-mouth nformaton passes on a new product (see Shakh, Balakrshnan, and Rangaswam 2005 and Garber et al for recent marketng mplcatons). The orgnal small world approach descrbed a socal system composed of ndvduals n rather solated socal networks (or caves ) wth some communcaton between caves (Watts 1999; Watts and Strogatz 1998). We use a dynamc generalzaton of the small world approach 11

14 that takes nto account the exstence of varous levels of communcaton. Frst, as dscussed above, we dfferentate between the strong tes wthn the network and the weak tes outsde the network. An ndvdual strong-te connecton conveys more relable nformaton and so has more chance of convncng a potental adopter. Second, whle the strong-te structure nsde each socal system s fxed, the weak-te structure s dynamc: In each perod, weak tes are randomly reassgned, so that the new structure of the weak-te network dffers from that of the prevous perod. For example, a study on onlne groups found that more group nteractons and a stronger sense of belongng to the group are related to group dentty. Whle small fxed groups were hghly focused on group benefts, large random groups partcpatng were more focused on ndvdual beneft (Dholaka, Bagozz, and Klen Pearo 2004). The latter assumpton reflects the dynamc character of weak tes as descrbed n the orgnal work of Granovetter (1973) and n subsequent lterature. The unqueness of weak tes les n ther randomness from one perod to another. In the orgnal example of Granovetter, weak tes effect followed a random meetng n a tax. Because they are more random, and wth people wth whom the word-of-mouth recpent nteracts less, the nformaton may be less convncng as compared wth a smlar dscusson wth someone n the strong-te network. Yet t s the varous people meetng from perod to perod that allows them to be exposed to varous knds of nformaton from other parts of the socal system, and hence for weak tes to be nfluental. Also note that we could have modeled the nteractons as fxed,.e., as f they always exst between some members n varous caves, nstead of randomly actvated n each perod. In a fnte perod game such as ours, from a practcal pont of vew, the result s exactly the same as ours. What one observes s that an agent has some random contact wth members outsde hs/her 12

15 own cave. Because the number of perods s lmted, t follows that the number of contacts s lmted as well, and thus one cannot dstngush between the two processes. Ether an ndvdual has a fxed number of weak contacts, some of whch are actvated perodcally; or s/he has random contacts wth the same subgroup. Hence, we can vew ths network as composed of tme-ndependent caves wth strong tes between them, and vbratng sets of weak tes that each perod connect varous nodes and therefore (possbly) varous caves. Formally, the network can be descrbed as follows: 1) Nodes: Each cell, representng a potental consumer, can accept one of four states: 1) A value of 0 denotes a potental consumer who has not yet adopted the nnovaton; 2) a consumer who has adopted the product can ether be a satsfed consumer (+1), or 3) a dssatsfed consumer (-1); 4) a consumer affected by a dssatsfed adopter who does not adopt the product, and spreads negatve word-of-mouth thereabout, s denoted a rejecter, and takes the value of -2. Note that other than 0, the states are absorbng,.e., once consumers have adopted or rejected the nnovaton, they reman n ther respectve states. 2) Lnks: The ndvdual mantans relatonshps wth all ndvduals n hs / her network, denoted as strong tes, n addton to random tes wth ndvduals outsde ths network, denoted as weak tes. The weak tes are tme-dependent and connect varous pars of nodes each perod. 3) Dynamcs: The rules that defne transtons of potental adopters from state to state are classfed nto two types: Global factors, such as advertsng, where a probablty p exsts that an ndvdual wll be nfluenced by these factors to adopt the nnovatve product; and Local factors, where a probablty q exsts that durng a gven tme perod, an ndvdual wll be nfluenced by an nteracton wth another ndvdual (n hs / her strong- or weak-te relatonshps) who has already adopted the product. In addton, the structure of the network s dynamc n that the weak tes of ndvduals change randomly each perod. Note that the somewhat more famlar nomenclature would denote the global and local factors as external and nternal factors, respectvely (Mahajan, Muller, and Wnd 2000). In addton, consstent wth the epdemology lterature, we have mplctly assumed that these two forces are ndependent. Ths assumpton s also consstent wth nnovaton dffuson modelng, begnnng wth the Bass (1969) model, whch has an epdemology framework as ts foundaton 13

16 (see for example Mahajan, Muller, and Wnd 2000 or the meta-analyss of Sultan, Farley, and Lehmann 1990). Note that other approaches could also be taken to model agent-based dffuson. For example, Bell and Song (2005) ntroduced a utlty-based approach wth the nteracton appearng as thresholds, whle ours s a more classc, dffuson-based approach that vews the nteracton as uncertanty reducton n the form of word-of-mouth. Yet another approach was taken by Shakh, Rangaswamy, and Balakrshnan (2005) who modeled a classc small world model that begns wth close neghbors fully connected by strong lnks, wth each lnk beng replaced by some rewrng probablty wth a weak lnk to another randomly selected ndvdual. Thus they can control the connectedness of ther network by the rewrng probablty that determnes the quantty of weak tes that replace strong tes. In our model, we begn as they dd, wth close neghbors fully connected, and then add (rather than replace) weak tes. We thus control the connectedness by drectly varyng the quantty of strong and weak tes. The probablty of transton s computed next: Central to an agent-based approach s the constructon of the probablty of an agent s transton from one state to another, for example movng from potental adopter to postve or negatve adopter. For that, we have to frst understand the probablty of beng affected by each knd of nformaton. To do so, we defne a number of ntermedate measures that wll help us to examne these probabltes: S (t) the cumulatve number of adopters at tme t n ndvdual s strong-te personal +1 1 networks; of these, S are satsfed wth the product, and S are dssatsfed. We also defne S 2 ( t) as the cumulatve number of rejecters at tme t n ndvdual s strong-te personal networks. W (t) the cumulatve number of adopters at tme t n an ndvdual s weak-te network; of these, W are satsfed wth the product and, W are dssatsfed. We also defne W 2 ( t) as the cumulatve number of rejecters at tme t n ndvdual s weak-te networks. 14

17 Gven the above, the probablty of ndvdual s beng nfluenced by ether postve wordof-mouth or by advertsng at tme perod t s gven by the followng: p pos ( t) + 1 S ( t) W ( t) = 1 (1 p) (1 qs ) (1 qw) (1) Negatve word-of-mouth s spread by dssatsfed consumers, and by rejecters, the latter whom were affected by the negatve word-of-mouth of the former (and ther state s commensurately changed from 0 to -2). Thus, the probablty of ndvdual s beng nfluenced by negatve word-of-mouth durng tme perod t s gven by the followng: + 1 p neg ( t) 1 1 S ( t) W ( t) S ( t) W ( t) = 1 (1 mqs ) (1 mqw) (1 mqs ) (1 mqw) (2) We now turn to the calculaton of the transton probabltes. Note that an ndvdual may be exposed to postve nformaton, negatve nformaton, both postve and negatve, or nether. Thus the probablty of beng nfluenced by only postve word-of-mouth s gven 2 2 neg pos by ( 1 p ) p, and smlarly for only negatve word-of-mouth: ( 1 p ) p. Lastly, the pos neg probablty of beng nfluenced by both postve and negatve word-of-mouth s gven pos neg by p p. We dvded the last group so that a proporton of α adopts the product, and (1- α ) pos pos neg rejects, accordng to ther respectve sze ( α = P /( P + P ) ). The fnal equatons for the probablty of ndvdual adoptng or rejectng, or not beng nfected at tme t, are therefore gven by: neg pos P ( adopt) = (1 p ) p + α p p (3) pos neg pos P ( reject) = (1 p ) p + (1 α ) p p (4) neg pos neg pos neg P ( none) = (1 p )(1 p ) (5) 15

18 Clearly, the three equatons add up to 1. Thus, a non-adopter (wth a value of 0) has three avenues va whch s/he can be affected: wth probablty d P (adopt), s/he adopts and becomes satsfed, recevng the value of +1; wth probablty ( 1 d) P ( adopt), s/he adopts and becomes dssatsfed, recevng the value of -1; wth probablty P (reject), after recevng negatve wordof-mouth, s/he becomes a rejecter, recevng the value of Parameter ranges When basng a decson on parameter ranges, our man focus s to examne ranges that correspond reasonably wth market realty ranges. We reled on prevous research on the dffuson of nnovatons and socal networks and the use of agent-based models to create the parameter set for our analyss. The dffuson parameters (p and q) were chosen to comply wth fndngs on values of aggregate dffuson, transformed to an ndvdual-level grd. The dea s to choose ndvduallevel parameters n a range that wll create aggregate dffuson processes of the type actually wtnessed n markets. See Sultan, Farley, and Lehmann (1990) and Jang, Bass, and Bass (2006) for aggregate dffuson modelng results and standard dffuson parameters; and Goldenberg, Lba, and Muller (2001) for a dscusson of the transformaton of parameters to ndvdual-level cellular automata and small world. For example, f one takes the average word-of-mouth parameter of q s and q w (0.025), and the average strong and weak tes of an ndvdual (36), then the average probablty that ths person wll be affected by nternal nfluence s gven 36 by (1 ( ) ) = 0. 59, a number that s comparable to the nternal nfluence parameter n the growth of durables such as record players or color televson sets n the USA (Sultan, Farley, 16

19 and Lehmann 1990). These parameters also create dffuson processes compatble n length wth the above aggregate fndngs on USA durables. Consstent wth prevous research, the effect of a sngle weak-te word-of-mouth nteracton (q w ) was chosen for a range that s less than that of a sngle strong-te conversaton (q s ). Ths choce of course does not mply that the aggregate effects behave smlarly, as we examne presently. There s no consensus n the relevant research on what mght be a typcal network sze for weak and strong tes. Classc Cellular Automata research typcally uses a strong-te network of eght ndvduals around each agent. We enable larger networks as well, yet the range covered (8-28) stll reflects a reasonable range for a product-related personal network, whch s small compared wth socal system sze, and s generally consstent wth ranges used n prevous smlar research (Goldenberg, Lba, and Muller 2001), and wth emprcal results (Brown and Rengen 1987; see also Secton 2.6 n ths study). Also, network sze remans the same for all agents. Note that we are less nterested n the absolute value of network sze, and more n the effect of a change on that sze, as well as the rato of the szes of strong- to weak-te networks, and hence the exact absolute values may matter less here. Fnally, as the percentage of dssatsfed consumers (d) and the multpler m that descrbes the relatve power of negatve word-of-mouth are expected to be hghly correlated, we fxed m at a reasonable level of 2, consstent wth accepted ndustry practce (Hart, Heskett, and Sasser 1990 and TARP 1986), and changed the parameter d. However, we ran the basc analyss on varous values of ths parameter (m) wth no dscernable dfference n the results that follow. We substtuted the values of these parameters, performng a total of fve runs per parameter (done n order to allow a wde enough varance n the parameter analyss) wth the followng 17

20 ncrements: the szes of strong tes and weak tes from 8 to 28 n ncrements of 5; percentage of dsapponted consumers n ncrements of 5%; advertsng n ncrements of ; q s n ncrements of 0.015; q w n ncrements of The range of parameter values s gven n Table 1. One ssue that should be noted n Table 1 s that of network sze. To smplfy the followng analyss, and snce our analyss focuses on the dfference between weak- and small-te effects and not on ther absolute network sze, n the followng analyses we used a sze rato varable r, whch s the rato of the sze of each ndvdual strong-te personal network dvded by sze of the ndvdual s weak-te personal network. Gven the network ranges above (the szes of strong tes and weak tes, varyng from 8 to 28), the range of the sze rato s between 8/28 = 0.29 to 28/8 = 3.5, reflectng cases n whch there are more strong tes than weak tes per perod, and vce versa. Parameter Table 1: Range of parameters used n our analyses Range of values r rato of sze of each ndvdual strong-te personal network dvded by sze of weak-te personal networks d percentage of dsapponted adopters 5% - 25% p global marketng nfluence parameter (such as advertsng) q s postve strong-te word-of-mouth communcatons parameter q w postve weak-te word-of-mouth communcatons parameter Emprcal support for some assumptons Rogers (1995) has noted the dffcultes of collectng word-of-mouth-related data from consumers as a major obstacle to emprcal dffuson-of-nnovatons research. Indeed, obtanng n-depth data on the spread of postve and negatve nformaton over tme n a gven socal system s not trval, and beyond the scope of ths paper. Stll, whle our assumptons and parameter range are generally based on emprcal fndngs n ths area, we wshed to see f we 18

21 can fnd support for some of our basc assumptons that relate to the extent of strong- and weakte nformaton upon whch consumers mght rely. Specfcally, we wanted to examne the followng two ponts: What s the expected relatonshp between the szes of the strong- and weak-te networks for a gven product? Are consumers wllng to accept second-hand negatve word-of-mouth as suggested n our model? Would t change among weak and strong tes? In order to obtan reasonable ranges, we tested these questons n a 2x2 between-subjects setup n whch we manpulated the valence of the word-of-mouth (as postve or negatve), as well as ts source of word-of-mouth (as drectly from adopter or second-hand word-of-mouth). For each respondent, we examned the dfferental response for varous strengths of tes (strong or weak). Partcpants were MBA students, randomly assgned to one of four condtons when they agreed to fll out a questonnare. As ncentve for partcpaton, they were elgble to enter a drawng for an MP3 player. 84 partcpants answered the questonnare, of whch three outlers who reported over 100 tes were removed from the analyss. The questonnare started wth questons about the number of strong and weak tes. To estmate the number of strong tes, we asked partcpants to count the number of people n ther address books wth whom they have frequent nteractons. Then we asked them to estmate the number of people wth whom they had randomly met and talked n the past week. Ths was the estmate of the number of weak tes. Next, we explaned the concepts of strong and weak tes, and gave them a scenaro wheren they consult wth a frend about a new product that they are consderng adoptng. Scenaros for varous condtons ncluded a postve recommendaton from an acquantance, a dsapponted acquantance, and second-hand nformaton. Respondents were asked about the nfluence on 19

22 ther decson-makng n cases where the source of nformaton s strong and weak tes respectvely. We used an analyss of varance combnng between- and wthn-subject measures to analyze the above data. In general, the results provde support for the basc assumptons of the lterature (and our model) on the effect of word-of-mouth. Respondents reported a stronger effect of word-of-mouth spread by a strong te than word-of-mouth that spread by a weak te ( x strong = 5.8, x weak = 3.9, F = 217, p <.01), and beleved that they would be more affected by negatve as compared to postve word-of-mouth ( x postve = 4.6, x negatve = 5.1, F = 7.4, p <.01) regardless of the source. Regardng the number of tes, the results supported our use of roughly equvalent ranges of weak- and strong-te networks. The mean number of strong tes was 11.9 (the medan was 10), and 95% of the answers ranged between 3 and 28. The mean number of weak tes was 13.1 (medan 8.5), and 95% of the answers ranged between 1 and 40. We see that the results and specfcally the smlar magntudes of the word-of-mouth networks are consstent wth the parameter range used n our model. Partcpants were also more affected by negatve word-ofmouth spread by an adopter than by second-hand word-of-mouth ( x drect = 5.2, x ndrect = 4.6, F = 6.7, p <.02). However, as can be seen, the dfference was not very great. In fact, for strong tes the numbers were smlar, and most of the dfference stemmed from weak tes, (for weak tes: x drect = 4.3, x ndrect = 3.5). Gven the smlartes between the two, we beleve that our assumpton of a second layer of rejecters that affect others n the same magntude s reasonable. 20

23 3. The NPV of Bad News The objectve of the frst analyss was to study the aggregate response to negatve word-ofmouth. We want to compare processes across the range of parameters wth and wthout negatve word-of-mouth, as well as examne the economc damage the frm suffers due to negatve wordof-mouth. Hence, we frst defne a one-dmensonal measure that wll summarze the dfference between the processes. Snce any change n a growth pattern can have major economc consequences for the ndustry, we have chosen to express our measure n the rato of the NPV of the growth process between two cases: a process wth negatve word-of-mouth dvded by the same process, yet wth an artfcal removal of ths negatve word-of-mouth. Thus we compute the NPV for the negatve word-of-mouth case and for the non-negatve word-of-mouth case, usng a 10% dscount rate per perod, whch s a reasonable yearly rate for many markets; ther percentage rato (called NPV Rato) wll serve as a proxy for the economc dfference n the product growth process. For example, f the result of the NPV Rato s 50% for a certan set of parameters, then the monetary value of the growth process wth negatve word-of-mouth would be half that wthout negatve word-of-mouth wth the same parameters. Note that the NPV analyss we use assumes that each unt sold supples one unt of monetary proft based on the revenues and the varable costs of the product. We do not consder losng products, nor the full range of cost allocaton to the ndvdual product. We ran the small world process descrbed earler usng a C++ applcaton specfcally desgned for our purpose. Intally, the entre market s unexposed to the product, and thus everyone begns n zero state. The weak tes are randomly assgned at each perod, ncludng the frst perod. The network contans a fxed number of consumers (3,000). We also ran the analyss wth a sze that s larger by an order of magntude (30,000), wth no sgnfcant dfferences n the 21

24 result. All combnatons were consdered n a full factoral desgn to produce a total of 5 6 = 15,625 smulatons. We termnated a smulaton when the percentage that had made a decson (adopt or reject) reached 95% of the market potental (3,000). In order to understand the role of network and socal structure and frm actons, a lnear regresson was performed wth the dependent varable of the NPV Rato. Table 2 presents the results of the OLS regresson, as well as results of the same regresson wth the addton of one squared parameter to test a hypothess of a non-lnear advertsng effect, to be explaned presently. Table 2: Regresson results when the dependent varable s the NPV Rato Parameter Coeffcent Standardzed Coeffcent Standardzed coeffcent coeffcent Lnear advertsng Concave advertsng r (rato of strong tes to weak tes) d (% dsapponted adopters) p (advertsng effect) q s (strong-te word-of-mouth) q w (weak-te word-of-mouth) p squared -1, Adjusted R % 74.3% All coeffcents sgnfcant at p < From Table 2, the followng results are apparent: The effects of dssatsfacton The percentage of dssatsfed buyers (d) has the strongest effect on the NPV Rato, as measured by the standardzed coeffcent. Snce our nput was n decmals (e.g., 0.07 sets the fracton of dsapponted customers at 7%), ths result suggests that for every percentage pont of dsapponted customers, our loss due to negatve word-of-mouth ncreases by 1.82 percent. Note 22

25 that ths number represents the damage caused by negatve word-of-mouth only. If we were to calculate a repeat-purchase model n whch these customers should cease to re-purchase as well, the damage would be even greater. The strength of the weak tes Consder frst the Lnear Advertsng column n Table 2. The frst noteworthy result regards the values of the nterpersonal parameters q s and q w. Recall that the dependent varable s NPV Rato, and thus an ncrease n the dependent varable mples a weaker effect of negatve wordof-mouth. The coeffcents of both nterpersonal parameters are negatve, so the hgher the parameters, the stronger the effect of negatve word-of-mouth on profts. Ths result may be surprsng, gven the popular percepton of the generally postve role of weak tes n the spread of nformaton (Granovetter 1973; Brown and Rengen 1987). The reasonng for that can be dvded nto two categores: The frst s a mcro-explanaton that classfes weak tes as more relevant because after exhaustng ther strong-te potental, people actually share the same knowledge wth ther entre personal network. For example, Granovetter showed that weak tes have a stronger effect on job-huntng because they brng nto the consderaton set opportuntes that dd not exst n the set of a specfc network. A second explanaton s a macro-explanaton that shows that n the case of a large number of small networks, weak tes are responsble for the actvaton of nets, and they compete well even wth advertsng (Goldenberg, Lba, and Muller 2001). However, n the presence of negatve word-of-mouth, n whch both strong and weak tes dssemnate postve and negatve word-of-mouth, weak tes seem to have an especally mportant role: The standardzed regresson coeffcent of q w (weak-te strength) s about 60% hgher than the coeffcent of q s (strong-te strength). Ths dfference mples that ndeed, weak 23

26 tes should not be underestmated, but also for a reason other than the prevalng arguments n the lterature: The capacty of weak tes for decreasng the frm s profts n the presence of negatve word-of-mouth. Another way n whch the ambguous power of weak tes s manfested s found n the postve effect of the rato of strong tes to weak tes on NPV Rato. Ths would mply that f we keep the total number of tes constant, yet ncrease the number of strong tes, the destructve effects of negatve word-of-mouth somewhat dsspates. The global effect of marketng actvty Unlke nterpersonal tes, whch spread both postve and negatve nformaton, the marketng efforts of the frm (p) spread unformly postve nformaton. One may be tempted to conclude that n the presence of negatve word-of-mouth, the frm wll fnd t optmal to ncrease advertsng n order to combat and perhaps even eradcate negatve word-of-mouth. However, recall that advertsng, whle ncreasng the number of adopters, ndrectly also ncreases the number of dsapponted adopters. Ths ncrease yelds an earler start at least partally of the negatve word-of-mouth process. Thus, too much advertsng may launch a strong wave of negatve word-of-mouth that n tme can become yet stronger (due to ts logarthmc growth) than n the case of decreased advertsng efforts. In order to test ths phenomenon, we added to the regresson a squared term of advertsng (p). The results are presented n the second two columns of Table 2. As can be seen, ndeed, the coeffcents of p and p 2 have an opposte sgn, and the effect of ths non-lnear behavor s relatvely strong. Gven the fact that marketng efforts have ther own cost, ths means that there 24

27 s an optmum level beyond whch the frm s wastng ts resources: Instead of fghtng negatve word-of-mouth, advertsng drectly decreases the product s market potental. Interacton effects In order to examne possble nteracton effects among the varous parameters, we ran a regresson n whch nteracton terms were added. In ths regresson, the only two nteractons that were close to the man effects n sze were d and q s, and q w and q s. Consder frst the nteracton between d and q s that s postve (0.15, p < 0.001) and can be understood va the example of Table 3: Table 3: NPV Rato for varous levels of d (percentage of dsapponted adopters) and q s (strong-te word-of-mouth parameter) d Low d Hgh q s Low 77% 42% q s Hgh 73% 30% From Table 3, we can deduce that as the postve strong-te word-of-mouth parameter ncreases, the destructve effect of d, the percentage of dsapponted adopters, ncreases. The reason s that as q s ncreases, the dffuson of nformaton speeds up, renderng a large percentage of dsapponted consumers that s fatal to the product. The nteracton between q w and q s s more complex and can be hghlghted wth the help of the 3D plot presented n Fgure 3. 25

28 Fgure 3: NPV Rato for varous levels of q w (weak-te word-of-mouth parameter) and q s (strong-te word-of-mouth parameter) From the curve pattern n Fgure 3, we can deduce that ncreasng the level of weak-te word-of-mouth (q w ) decreases the NPV rato by ncreasng the power of negatve word-ofmouth. When the level of strong-te word-of-mouth s low, ths destructve effect of q w s greater (the slope of q w s more negatve for smaller q s ). The reason s that the forces of strong-te and weak-te communcatons are complementary n nature, and thus when q s s smaller, the weak-te communcaton channel becomes more domnant, causng ts destructve power, ceters parbus, to ncrease. When the level of weak-te word-of-mouth communcatons s hgh, ther ablty to spread negatve word-of-mouth s strong enough so as to cause the NPV Rato to decrease, regardless of the effect of strong-te word-of-mouth. When the weak-te effect s weaker, the NPV rato s hgher, and negatve word-of-mouth has less effect on the market. In ths stuaton, a combnaton of low weak-te word-of-mouth and low strong-te word-of-mouth creates a hgh 26

29 NPV, snce word-of-mouth s hardly dssemnated, and thus nformaton s passed manly through the postve effect of advertsng. As strong-te word-of-mouth communcatons ncrease, NPV rato decreases, as a result of the propagaton of negatve word-of-mouth (although postve word-of-mouth s also dssemnated, t has a less vsble effect, as advertsng can reach the same effects as postve word-of-mouth). At a very hgh level of strong-te word-of-mouth (and low weak-te word-of-mouth), NPV Rato ncreases agan. In ths stuaton, postve strong-te wordof-mouth starts to show ts effect on the NPV by acceleratng the dffuson process, overcomng the negatve word-of-mouth effect. 4. The underpnnngs of falures In the prevous secton, we analyzed the nfluence of negatve word-of-mouth on the adopton process and proftablty. However, negatve word-of-mouth s responsble not only for a slowdown of successful processes, but also for transformng a crtcal slowdown of processes nto falures that wll eventually be removed from the market. Thus, n ths secton we sort the effects of negatve word-of-mouth nto successes and falures. As wth success, there are varous defntons of falure, n the absence of general agreement over a sngle representatve one (Goldenberg, Lehmann, and Mazursky, 2001). Nevertheless, we adopt one commonly used measure of low sales: A product that by the end of ts dffuson process was adopted by less than 50% of the target market s defned as a falure. We also use a more strngent defnton of a falure: a product that by the end of the process was adopted by less than 16% of the market. The mechansms of advertsng (p) and weak-te word-of-mouth (q w ) are rather smlar: Both forces are responsble for actvatng nets. If p and q w are very low, nets are not actvated, and q s cannot be gnted to start workng; ergo, the entre process shuts down. However, t s 27

30 mportant to dstngush between the two forces: Whle p has purely postve nfluence, q w works n both drectons. Thus n the case of a poor product, p has an ndrect effect (ncreasng the number of dsapponted consumers), but q w drectly acts to block nets, as well as to launch and magnfy the negatve word-of-mouth process. The followng logstc regresson analyss s desgned to clarfy and quantfy these effects, as well as ther contrbuton to product falure. The same data set that was used n the prevous secton was classfed nto two sets: 1) successful process, wth sales above 50% (or 16%) by the end of the process, and 2) falures (below 50% and 16% respectvely). A bnary logstc regresson analyss was performed wth a dependent varable (1 = success, 0 = falure) and ndependent varables that nclude the same set of varables as n the prevous sectons. Table 4 presents the classfcaton results of the model wth the 50% crteron as a measure of falure. As can be seen, the logt analyss correctly classfes 95.1% of the cases. Table 4: Logt analyss classfcaton table Predcted falure Predcted success Observed falure 97.0% 3.0% Observed success 11.9% 88.1% Average correct predctons % The classfcaton table for the concave advertsng case s almost dentcal to the above table, whle that of the 16% crteron s smlar but wth a slghtly lower average correct predcton of 92.1%. Table 5 presents the coeffcents of the logt analyss. 28

31 Table 5: Logt analyss results Parameter 50% crteron 16% crteron r (rato of strong tes to weak tes) d (% of dsapponted adopters) p (advertsng effect) q s (strong-te word-of-mouth) q w (weak-te word-of-mouth) p squared All coeffcents are standardzed (Allson 1999), and are sgnfcant at p <.001. Not surprsngly, the parameter that ncreases the chances of falure most s d, the percentage of dsapponted customers. The strongest postve parameter s the advertsng coeffcent p, whch ncreases chances of success. Interestngly, strong- and weak-te word-ofmouth coeffcents affect n opposte drectons. Weak tes ncrease the chances that a product wll fal, as they are responsble for actvatng negatve nets. Strong tes, on the other hand (despte the fact that t may not be a smashng success) stll support a product s growth. Some of these dfferences are even more pronounced f we adopt the 16% fgure as a crteron of falure. Recall that wth ths new crteron, falures are real duds (84% of the market potental refuses to adopt t), so the fact that the patterns observed n the prevous regresson reman n the same sgns (except p squared, to be dscussed presently) mples that these results are stable. Consstent wth the prevous secton, t s nterestng to see whether agan, too much advertsng (whch s the most obvous acton a frm s tempted to take) can destroy growth. From Table 5 we see that there s a dfference between the success crtera. In the 50% crteron of falure, the non-lnear term has a strong effect of -0.4, mplyng that too much advertsng can push the product to hgher monetary losses and falure. In the 16% crteron, however, the nonlnear effect of advertsng s postve. The reason for ths dfference les n the unque 29