Brand Awareness and Price Dispersion in Electronic Markets

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1 Assoiation for Information Systems AIS Eletroni Library (AISeL) ICIS 00 Proeedings International Conferene on Information Systems (ICIS) Deember 00 Brand Awareness and Prie Dispersion in Eletroni Markets Pei-Yu Chen University of Pennsylvania Lorin Hitt University of Pennsylvania Follow this and additional works at: Reommended Citation Chen, Pei-Yu and Hitt, Lorin, "Brand Awareness and Prie Dispersion in Eletroni Markets" (00). ICIS 00 Proeedings This material is brought to you by the International Conferene on Information Systems (ICIS) at AIS Eletroni Library (AISeL). It has been aepted for inlusion in ICIS 00 Proeedings by an authoried administrator of AIS Eletroni Library (AISeL). For more information, please ontat

2 BRAND AWARENESS AND PRICE DISPERSION IN ELECTRONIC MARKETS Pei-Yu (Sharon) Chen The Wharton Shool University of Pennsylvania Lorin M. Hitt The Wharton Shool University of Pennsylvania Abstrat Prie dispersion, the variane in prie for idential produts aross retailers, is a persistent feature of Internetbased markets, even those mediated by shopping agents (shopbots). In this paper, we propose a model for explaining this prie dispersion based on limited onsumer awareness of ompeting retailers and brand sensitivity, the willingness to pay a premium to buy from a leading retailer. We show that full awareness and the absene of brand sensitivity are neessary for markets to be harateried by Bertrand ompetition. When both of these are not simultaneously true (whih is likely for most Internet markets), a number of other priing strategies beome optimal. Branded (high awareness) retailers tend to harge higher pries on average, but in some irumstanes will randomie their pries suh that they will be lower prie than unbranded retailers on some produts or some of the time. We also show that even if an unbranded retailer an invest to improve awareness, they have weak inentives to do so as this inreases prie ompetition. These observations are onsistent with empirial researh on priing in Internet-based markets and may offer a more omplete story of Internet prie dispersion than some of the leading alternative explanations. Keywords: Eletroni markets, information eonomis. ISRL Categories: HA070, AD0 INTRODUCTION Prie dispersion, the variane in pries aross retailers and over time for idential produts, is a ommon harateristi of online markets. These prie differenes persist even though lower searh osts or inreased ompetition failitated by the Internet should redue or eliminate prie dispersion (Bailey 998a; Brynjolfsson and Smith 000a; Clemons et al. 000). While there are a variety of possible explanations for prie variation, few of these explanations would predit prie dispersion in markets heavily mediated by searh agents (or shopbots ). In these markets, onsumers presumably have very aurate information about the true distribution of pries and an easily identify the lowest prie. Nonetheless, Brynjolfsson and Smith (000b) find signifiant prie dispersion in produts searhed by shopbots. Even more strikingly, they also find that onsumers using shopbots (whom we would expet to be highly prie sensitive) are willing to pay a premium to buy from better-known retailers. While brandspeifi effets suh as overall quality, reliability, or ustomer loyalty ould explain a systemati prie premium, this is not fully onsistent with the data: the brand premium varies by produt and branded retailers sometimes harge lower pries than their less well-known ompetitors for some produts at some times. In this paper, we present a model whih links prie dispersion to differenes in brand awareness and brand sensitivity that presents one possible explanation for these observations. In our paper, we define brand awareness as: () onsumers know that the brand exists and () onsumers are atually onsidering it as one of the alternatives to buy from at some (possibly disounted) prie. If the ustomer demands a disount to purhase from a less known retailer, then in our terminology the ustomer shows brand 00 Twenty-Seond International Conferene on Information Systems 33

3 sensitivity. We examine priing in a duopoly market with a leading brand and a less well-known ompeting brand fousing on the interation of two effets: the number of onsumers who are aware of the ompeting brand and the degree of brand sensitivity (the prie premium needed to enourage a ustomer who onsiders all brands to purhase a produt from an lesser known or unbranded retailer). Our results suggest that when onsumers are indifferent to brand (ero premium) and all onsumers onsider both brands (full awareness), firms essentially engage in aggressive (Bertrand) prie ompetition. However, absent both of these effets simultaneously, a number of other priing strategies beome optimal. Branded retailers will tend to have higher pries on average, but when there are moderate levels of brand premium and limited awareness, the only prie equilibrium is in mixed strategies. In other words, branded retailers will sometimes harge lower pries than their unbranded ompetitors for some produts or at some times. In addition, we also show that ompetitive markets will be harateried by differenes in brand awareness aross firms if there is any initial asymmetry in brand awareness. Even if osts of building awareness (e.g., advertising) are symmetri, unbranded retailers have muted inentives to do so beause inreasing awareness also inreases prie ompetition eteris paribus. Our model is onsistent with a variety of empirial results on prie dispersion in Internet retailers and, as we argue in the onlusion of the paper, may provide a more reasonable explanation for the observed pattern of prie dispersion on the Internet than many of the alternative explanations suh as searh ost redutions, produt differentiation, or simple brand premia. In the eonomis literature, previous researh has linked differenes in information (informed and uninformed onsumers) to prie dispersion aross retailers and over time (Salop and Stiglit 977; Varian 980). On the other hand, Bakos (997) shows that symmetri searh osts lead to an absene of prie dispersion even in differentiated markets. The marketing literature onsiders brand identity and brand loyalty as important determinants of brand hoies, sine brand is a signal for quality or servie levels (Lal and Sarvary 999). Our analysis differs in the sense that it integrates two important aspets of onsumer searh in Internet markets: brand sensitivity due to quality unertainty and risk aversion, familiarity, or advertising, and limited awareness where not all onsumers are aware of all brands (similar to the eonomi searh ost models). In the next setion, we present the basi model of priing for two firms where awareness is onsidered fixed (that is, the unbranded retailer annot or has no inentive to invest in inreased awareness). We then extend the model to a ase where the unbranded retailer an inrease their awareness at a ertain ost. Finally, we ompare our results to observed patterns of prie dispersion on the web and disuss the relationship of our model to previous work on prie dispersion in online markets as well as the broader literature on the eonomis of prie dispersion. MODEL Introdution Consider a market where there are large numbers of heterogeneous onsumers who are onsidering a produt purhase from one of two retailers: a well-known branded retailer that all onsumers onsider, and an unbranded retailer who is known only to a fration of all onsumers. In addition, those aware of both retailers also differ on their willingness to pay a premium to use the branded retailer. 3 We assume that all retailers have the same marginal ost of the produt and that onsumers have the same Our definition of brand awareness is similar to the onept of a onsideration set. Our definition of brand sensitivity is one possible manifestation of the broader onept of brand loyalty, whih inludes both prie sensitivity effets as well as repeat purhase propensity. We do not believe the insights of the model to be unique to duopoly ompetition; however, like many other ompetitive models, extension to arbitrary number of firms vastly inreases the omplexity without muh potential gain for new insights. 3 The differene in awareness may be due to searh osts or other fators, suh as opportunity osts, risk aversion, or onsumer inertia, that tend to limit searh ombined with different abilities of retailers to reah ustomers. For example, it may be essentially free to list on an Internet shopbot, while a full advertising ampaign might be prohibitively expensive. The differenes in brand premium ould be due to a variety of fators suh as familiarity with the branded retailer, risk aversion, heterogeneous valuation of quality differenes, and swithing osts to name a few. Most of these osts result from variations in preferenes or ognitive limitations that are not likely to be altered by tehnologial progress or redutions in searh ost Twenty-Seond International Conferene on Information Systems

4 reservation prie for the produt, whih is greater than marginal ost. 4 One ould onsider this setup to be similar to online book retailing in some sense: all ustomers know about Amaon.om, but only the fration of ustomers that use shopbots are likely to know about ABooks.om. Moreover, even when ABooks is heaper, not all onsumers will buy from them. It is important to note that there are a variety of reasons that both brand premia and limited awareness ould persist even if searh osts were to beome negligible or even ero. 5 Notation We designate the branded retailer as Retailer and the unbranded retailer as Retailer. Retailers fae a ommon marginal ost of per unit and onsumers have a ommon reservation prie of r per unit, and we assume that onsumers purhase at most one unit of the good. Retailer is known to all ustomers, while Retailer is onsidered only by " perent of ustomers (thus, -" only onsider Retailer ). We assume that the degree of prie sensitivity (brand premium) of ustomers is given by a uniform distribution for those ustomers aware of both retailers with lower support 0 and upper support. That is, Retailer ould obtain all of the ustomers that onsider both retailers if it underuts the prie of Retailer by, and proportionally less as the disount dereases (Figures and ). With this setup, we an ompute the quantities sold (q, q ) and profits (p, p ), given pries (p, p ) and exogenous parameters (",, r and ):, if p p p p q + ( ) if p p p + if p p + p if p p p + p π ( + ) ( p ) if p p p + ( ) ( p ) if p p +, if p p p p q if p p p 0, if p p ( p ) if p p p p π ( p ) if p p p 0, if p p 4 Fixed reservation prie is a ommon assumption, but not essential to our results. Variations in reservation prie ould be subsumed in the brand premium in our model setup; this is a mathematial observation rather than a deeper statement of the eonomis of this problem. 5 Even if searh osts drop to ero, onsumers an still inur osts for evaluating alternatives, enouraging limited searh. Also, as noted by Varian and Shapiro (999), swithing osts, loyalty, or simple ustomer inertia may deter onsumers from onsidering alternative retailers. 00 Twenty-Seond International Conferene on Information Systems 35

5 q q - p p + r p p - p r p Figure. Demand Curve for Retailer for a Given p Figure. Demand Curve for Retailer for a Given p Analysis Our analysis will proeed by deriving the priing strategies that represent equilibrium behavior by the two retailers given various values for the exogenous parameters: reservation prie (r), fration of informed onsumers ("), marginal ost (), and distribution parameter of brand premium (). We begin by omputing the region in whih priing is harateried by a pure strategy equilibrium that is, the region in whih firms offer fixed pries aross produts and over time. 9 Proposition : (a) When and ( ) 3 there is an unique non-ooperative Nash Equilibrium (NE) in 3 4 r * * 3 whih ( p, p) = ( +, + ). (b) When and there is an unique NE in whih r * * + r ( p, p) = ( r, ). () When and, the unique NE is. (d) When 3 r * * ( p, p) = ( r, r ) and, the unique NE is. 3 + r ( p * * r, p) = ( r, ) Proof: See Appendix. The various regions in whih pure strategy equilibria exist are depited in Figure 3. When there are a relatively small proportion of informed ustomers (" ~ 0) the priing strategy depends on the strength of brand preferenes. When brand preferenes are weak (lower left orner of Figure 3), firms essentially divide up the market. The branded retailer harges reservation prie, and the unbranded retailer harges reservation prie less brand premium and serves all ustomers that know they exist. As the brand premium beomes larger, this transitions into a monopoly-like priing region (upper left in Figure 3): the branded firm ontinues to harge the onsumers reservation prie, but the unbranded firm now pries based on the tradeoff between higher pries for non-brand loyal ustomers and stealing share from the branded retailer. When onsumers have high awareness of both brands (upper right), firms ompete by dividing up the market in proportion to the brand premium. In all of these ases, the branded retailer harges a lower prie and ompetition intensifies between the retailers as the " moves away from the origin in Figure 3. Note, however, that there is a large area in the enter of the graph for whih no pure strategy equilibrium exists. We now turn our attention to harateriing this region. For the region without a pure Nash Equilibrium in this model, there exists at least one mixed strategy equilibrium (Dasgupta and Maskin 986). In the priing games we onsider, this strategy appears as pries flutuate aross time or over different produts aording to a probability distribution. This tehnique has been used in both eonomi and marketing literature to apture either onsumers or firms ations in a strategi interation (Raju et al. 990; Varian 980). A neessary and suffiient ondition for the mixed strategy profile to be a Nash equilibrium is that eah player, given the distribution of strategies played by his opponents, is indifferent among strategies played with positive probability. That is, all strategies yield the same expeted profits Twenty-Seond International Conferene on Information Systems

6 given the behavior of the other retailer. Moreover, firms will never play a dominated strategy in a mixed-strategy equilibrium (Mas-Colell et al. 995). By eliminating priing strategies that are stritly dominated, we get: Proposition : The set of non-dominated strategies for firm is given by for firm is given by p = [ p, r ]. p = [ p, r] and the set of non-dominated strategies Proof: See Appendix r * * + r ( p, p ) = ( r, ) ( p, p ) * * = (, rr ) ( p, p ) * * = ( +, + ) 3 3 No NE Figure 3. Possible Equilibria for Different Parameter Values Within this set of feasible, non-dominated strategies, we an use the tehnique of Moulin (98) and Raju et al. (990) to onstrut a mixed-strategy equilibrium of this game, harateried by two (umulative) distribution funtions ( F( p), F( p) ). These distribution funtions yield the probability that the firm will hoose a prie at or below this value. Beause we know from Proposition that no pure strategy equilibrium exists in this region of the parameter spae, Proposition 3 guarantees that the optimal priing strategies will inlude firms randomly varying their pries in equilibrium. Proposition 3: ( F( p), F( p) ) onstitutes a mixed strategy equilibrium for this game: F () r = p + p p ( p ) ( F( p + )) + ( p ) f( p) dp = ( p ) p [ p, r ] p F( p) = 0 F ( r ) = p + p = ( r )( ) p [ p, r] F( p ) = 0 p ( p )( ) F( p ) ( p )[ f( p) dp ( p )( F( p)) p Proof: The distribution funtions ( F( p), F( p) ) were onstruted following the neessary and suffiient onditions of a mixed strategy equilibrium given by Mas-Colell et al. (995). Q.E.D. 00 Twenty-Seond International Conferene on Information Systems 37

7 Given that we have a general, but omplex, harateriation of priing behavior in this region, it is useful to examine the behavior of these priing strategies under different onditions. One interesting ase is when there is no brand premium (that is = 0): ustomers may or may not be well informed about the existene of Retailer, but are unwilling to pay just for brand. The priing strategy in this ase is given by Proposition 4: Proposition 4: when =0, there exists an unique mixed strategy equilibrium whih onstitutes: F( p) = ( f( p) = ( )) if p = r ( r )( ) F( p) = if p [( r )( ) +, r) ( p ) F( p) = 0 if p [0,( r )( ) + ) F( p) = ( f( p) = 0) if p = r ( r )( ) F( p) = if p [( r )( ) +, r) ( p ) F( p) = 0 if p [0,( r )( ) + ) Proof: Follows diretly by setting = 0 in the result from Proposition 3. Q.E.D. Figure 4 shows the equilibrium distributions for both retailers under some parameter settings based on Proposition 4. Proposition 4 shows that when brand premia do not exist, Retailer will plae more weight on high pries in their randomiation strategy when fewer ustomers know about the existene of Retailer. That is, ompetition is determined by onsumer awareness. If this randomiation is interpreted as priing strategy over time, this result would predit that when not all ustomers use shopbots (or other tehnologies for identifying little-known retailers), pries will vary aross Internet retailers even though shopbots exist and even if there is no brand premium. However, the branded retailer will have higher pries on average, even though onsumers are brand indifferent (beyond awareness). 6 In Figures 5 and 6, we show the behavior of the average prie premium and prie dispersion (measured as the variane in differene in pries harged by the two retailers) respetively when F (p ) F (p ) - Figure 4. Equilibrium Distributions (Mixed Strategy Equilibrium) for the Case Where = 0, " = 0.5, r =, and = 0 6 This is true beause the prie distribution for Retailer stohastially dominates the distribution for Retailer for all parameter values where these distributions are non-degenerate Twenty-Seond International Conferene on Information Systems

8 we normalie marginal ost to ero and reservation prie to. 7 Although mean pries harged by the two retailers are stritly dereasing in awareness ("), the differene in mean pries is maximied when " is lose to the middle (the maximum is approximately " =.57). The variane in pries is inreasing in awareness up to a point where awareness is large (approximately " =.83) and then falls dramatially as pries are driven to marginal ost. Note that these utoff levels are exat but we present them as approximations due to their omplex mathematial form. Prie Premium degree of prie dispersion prie premium alpha variane of pries alpha r is normalied to and is normalied to 0 Figure 5. Prie Premium Charged by the Branded Retailer ( = 0) r is normalied to and is normalied to 0 Figure 6. Degree of Prie Dispersion ( = 0) Another interesting result is to derive the onditions under whih Bertrand (pure prie) ompetition would arise in this market. Using our previous results, it is easy to show that the absene of brand premium ( = 0) and full onsumer awareness of ompeting retailers onsumers (" = ) is neessary for the existene of pure prie ompetition. Stated another way, as long as not all onsumers utilie shopbots (or other tehnologies where onsumers an searh all retailers), we would expet firms to earn positive eonomi profits. 8 Proposition 5: When = 0 and " =, both firms harging marginal ost is the unique pure Nash Equilibrium. Proof: Follows diretly from setting " = in Proposition 4. Q.E.D. Finally, we an summarie the key points of all of these propositions regarding the existene of prie dispersion in Internetmediated markets. Theorem : Prie dispersion exists in a market with well-known brands and less-known brands as long as the following two onditions do not hold at the same time: (a) = 0 and (b) " =. Prie dispersion is a result of either a persistent prie premium for well-known brands or firms randomiing their pries. Proof: This is a diret result of Proposition and Proposition 3. Q.E.D. 7 Note that the values of r and only sale up or down the urve but do not hange the shape of the urve. 8 The fat that most Internet retailers are not profitable is not neessarily inonsistent with this result. This result states that they earn a prie above marginal ost. It does not neessarily say anything about whether this margin is suffiient to all average osts and thus reates overall profitability. 00 Twenty-Seond International Conferene on Information Systems 39

9 Overall, we have shown that in markets where not all onsumers are aware of the existene of all firms or where ustomers are brand sensitive, prie dispersion will be a natural feature of the market. Branded firms will, on average, harge higher pries, either persistently or as a result of the randomiation, and they may not always be the highest ost retailer. A key assumption of this analysis is that the hoie of awareness level is fixed. There was no ation that an unbranded firm ould take to inrease their awareness level. However, given that branded retailers earn higher profits than unbranded retailers, it raises the question as to why unbranded retailers, in a market with few entry barriers and available advertising (at a ost), do not invest to build their awareness. Interestingly, we show in the next setion that even if firms an invest in advertising or otherwise build awareness on the same terms, they will tend not to do so. Thus, markets that begin with this differene in awareness tend to show a form of first mover advantage without firm learning or ost advantages, two typial explanations of first mover advantage. Model Extension: Awareness as a Choie Consider the same model as in the previous setion. Instead of " being a fixed, exogenous variable, we allow Retailer (the unbranded retailer) to make an investment in awareness to hange the level of ". Let the ost of awareness be designated by C( ) = a. The marginal ost of a unit of awareness is a", whih is learly inreasing in ". We use the parameter a to vary this ost for omputing omparative statis. The onvexity of this funtion suggests that small improvements in awareness are relatively inexpensive, but the ost of large improvements in awareness grows rapidly. Using the same notation as before, the quantities and profits are given by: 9, if p p q, if p > p p, if p p π ( ) ( p ), if p > p, if p > p q 0, if p p ( p ) C( ), if p > p π 0, if p p Unlike the previous analysis, where there was a substantial region of the parameter spae where firms hose fixed pries (pure strategy equilibria), no suh equilibria exist in this game. This is formalied below: Proposition 6: There exists no non-ooperative pure Nash Equilibrium in this game. Proof: See Appendix. In addition, when a is suffiiently low, there is no equilibrium where firms set pries simultaneously or when the branded firm ats as a prie leader and the unbranded firm follows. In other words, when investing in awareness is an option, branded firms will behave as prie followers rather than preemptively hanging prie strategy beause any attempt at setting a new prie will enourage other firms to underut on prie and alter awareness. Thus, it is in the interest of both firms to allow the unbranded firm to set pries first. Speifially: 9 We have assumed ero degree of brand sensitivity here Twenty-Seond International Conferene on Information Systems

10 ( 5 )( r ) Proposition 7: When 0 a, there is an equilibrium in whih firm moves first: * r * ar+ r * ( r ) = and p = with π = ; ( a+ r ) ( a+ r ) 4( a+ r ) * * ( a+ r )( r ) p = r and π = ( a+ r ) Proof: See Appendix. Of ourse, when the ost of awareness is suffiiently large, this issue is no longer a onern: the unbranded firm will simply realie that there are not suffiient profits to be made by hanging awareness level (under the optimal priing strategy) and thus the general struture of the solutions desribed in the previous setion will hold. Another interesting feature of Proposition 7 is that even if awareness is free, it is not optimal for the unbranded retailer to be reognied by the entire market (that is, irrespetive of a, "* is never ). This may seem ounterintuitive at first, but is easily rationalied by noting that awareness is somewhat analogous to produt differentiation. Sine the branded retailer is loated at one extreme in awareness spae, ompetition is softened when the entrant loates further away in this spae, taking a smaller share of the market and induing less aggressive prie responses from the branded retailer. This strategy maximies profits for both the branded and unbranded retailers (although the branded retailer would, of ourse, prefer no ompetition at all). Thus, by being an early mover and ahieving high awareness, firms an lok in a profit advantage: they will be the most profitable firm in the industry (in prie-ost margin terms) as long as there is any profit to be made in the industry at all. This also is onsistent with the observation that most Internet markets are harateried by a few (or even a single) dominant firm in terms of onsumer awareness, with large numbers of other firms restriting their promotional ativities to nihe markets or low ost hannels like shopping agents. DISCUSSION AND CONCLUSIONS Our theoretial analysis has shown that prie dispersion is a general phenomenon in the market where retailers have different levels of onsumer awareness. As long as priing is above marginal ost, well-known brands will harge higher pries on average than lesser-known brands. Under some onditions (espeially brand loyalty that is not too high ), firms will tend to randomie prie. These observations are onsistent with previous researh that showed that brand premia exist even for shopbots users, but that branded retailers are not always the highest prie. Our results suggest that these phenomena will exist as long as some onsumers are brand loyal (unlikely to hange) and not all onsumers are fully aware of all available retailers and pries (also unlikely to hange). This will also hold as long as any one of these onditions is still present. In the absene of awareness differenes and brand loyalty, the inevitable outome is Bertrand ompetition, as predited by some observers of online markets. Our assertion of limited onsumer awareness and brand loyalty is onsistent with observed behavior of Internet shoppers. For instane, in July, 000, using data from Media Metrix, we found that only 36 ustomers out of 3,77 traked who visited a book seller used a shopbot for books. 0 In this same sample, 80% of the ustomers who visited an online book retailer visited only one retailer in that ategory. This highlights the relevane of limited awareness and brand loyalty. These theoretial results also suggest why it may not be in the retailers interest for the limited awareness situation to hange substantially: expansion of awareness of unbranded retailers brings inreased prie ompetition, whih may lead to dereased profits for all partiipants. Our results are onsistent with (and may address unanswered questions from) previous work on prie dispersion. The brand premia for well-known retailers at shopbots found by Brynjolfsson and Smith (000b) are onsistent with our results. It is also onsistent with previous work that shows branded retailers are not always highest ost, although they are less likely to be the lowest ost (Bailey 998b; Brynjolfsson and Smith 000a). Our results on mixed strategy equilibrium in priing suggest that this 0 The list of shopbots we onsidered were: dealtime.om(evenbetter.om); priesan.om, bsilly.om, searhbook.net, addall.om, bestbookbuys.om, bigsoop.om, mysimon.om, searhvalue.om, ompare.om, webmarket.om, shopping.altavista.om, shopping.yahoo.om, and valuefind.om. 00 Twenty-Seond International Conferene on Information Systems 4

11 is indeed an outome of a well defined eonomi game, albeit one that abstrats some details away from the market. Finally, while the result that branded firms may prefer to be prie followers seems fairly abstrat, it is indeed onsistent with an unusual finding in Kauffman and Wood (000, Table 3). They found that branded retailers tend to be followers to their ompetitors prie hanges while many smaller retailers did not tend to respond to prie hanges at branded retailers (although they did not test the exat predition of our model, that branded retailers might be prie followers to unbranded retailers, but it is onsistent with the same argument). It is also onsistent with the finding that not all Internet retailers are investing in awareness; some simply prefer to utilie shopbots and other low ost hannels for reahing onsumers. Our theory may also be more theoretially plausible than other possible explanations of prie dispersion, espeially given known empirial results. For instane, the presene or absene of searh osts are neither neessary nor suffiient for the existene of equilibrium prie dispersion (see Bakos 997). Similarly, prie dispersion is not a feature of models of horiontal differentiation (produts of equality that appeal to different onsumer tastes). Prie dispersion is a natural onsequene of vertial (quality) differentiation, but in ommodity markets suh as book retailing, any differentiation has to be in harateristis of the retailer, not in harateristis of the good. As a result, this is equivalent to a brand premium. In our model (and arguments from previous work), this ould reate systemati prie premia for some retailers, but does not explain why these retailers might randomie around this value. Previous authors have also proposed the notion of variation in swithing osts as a ontributor of prie variation. Again, this explains stati differenes in priing, but does not explain the variane within a partiular retailer. While these do not exhaust all possible explanations, it does suggest that the relative explanatory power of our model (at least in terms of mathing existing empirial results) is substantial. An extension of our model is to onsider a multi-firm setting, inluding both stati oligopoly and sequential entry situations, and study the effets of the number of firms on ompetition and priing behaviors. In addition, it would be useful to provide diret empirial tests of our results, better distinguishing between our preditions and their alternatives. Referenes Bakos, Y. Reduing Buyer Searh Costs: Impliations for Eletroni Marketplaes, Management Siene (43:), Deember 997. Bailey, J. P. Eletroni Commere: Pries and Consumer Issues for Three Produts: Books, Compat Diss, and Software, Organiation for Eonomi Co-Operation and Development, OCDE/GD(98) 4, 998a. Bailey, J. P. Intermediation and Eletroni Markets: Aggregation and Priing in Internet Commere, Unpublished Ph.D. Dissertation, Tehnology, Management and Poliy, Massahusetts Institute of Tehnology, Cambridge, MA, 998b. Bailey, J. P., Brynjolsson, E., and Smith, M. In Searh of Frition-Free Markets : An Exploratory Analysis of Pries for Books, CDs and Software Sold on the Internet, Working Paper, Sloan Shool of Management, Massahusetts Institute of Tehnology, 998. Brynjolsson, E., and Smith, M. Fritionless Commere? A Comparison of Internet and Conventional Retailers, Management Siene, 000a. Brynjolsson, E., and Smith, M. The Great Equalier? Consumer Choie Behavior at Internet Shopbots, Working Paper, Sloan Shool of Management, Massahusetts Institute of Tehnology, 000b. Clemons, E. K., Hann, I-H., and Hitt, L. M. T he Nature of Competition in Eletroni Markets: An Empirial Investigation of On-Line Travel Agent Offerings, Working Paper, The Wharton Shool, University of Pennsylvania, 00. Dasgupta, P., and Maskin, E. The Existene of Equilibrium in Disontinuous Eonomi Games, I and II, Review of Eonomi Studies (53), 986, pp.-4. Kauffman, R. J., and Wood, C. A. Follow the Leader? Strategi Priing in E-Commere, Proeedings of the Twenty-First International Conferene on Information Systems, W. J. Orlikowski, S. Ang, P. Weill, H. C. Krmar, and J. I. DeGross (eds.), Brisbane, Australia, 000. Lal, R., and Sarvary, M. When and How Is the Internet Likely to Derease Prie Competition?, Marketing Siene (8:4), 999. Mas-Colell, A., Whinston, M. D., and Green, J. R. Miroeonomi Theory, Oxford University Press, New York, 995. Moulin, H. Game Theory for the Soial Sienes, New York University Press, New York, 98. Raju, J., Srinivasan, V., and Lal, R. The Effets of Brand Loyalty on Competitive Prie Promotional Strategies, Management Siene (36), 990, pp Salop, S., and Stiglit, J. Bargains and Ripoffs: A Model of Monopolistially Competitive Prie Dispersion, Review of Eonomi Studies, Twenty-Seond International Conferene on Information Systems

12 Smith, M. D., Bailey, J., and Brynjolfsson, E. Understanding Digital Markets: Review and Assessment, in Understanding the Digital Eonomy, E. Brynjolfsson and B. Kahin (eds.), MIT Press. Cambridge MA, 999. Varian, H. R. Model of Sales, The Amerian Eonomi Review (70:4), September 980, pp Varian, H., and Shapiro, C. Information Rules, Harvard Business Shool Press, Cambridge, MA, 999. Proof of proposition : Appendix Retailer, in searhing for its best response to any prie hoie by Retailer, an restrit itself to pries in the interval [p -, p ]. Any prie p > p yields the same profits as setting p = p (namely, ero), and any prie p < p - yields lower profits than setting p = p -. Thus, Retailer best response to p solves p p s. tp p p max ( p ) p The neessary and suffiient (Kuhn-Tuker) first order ondition for this problem is: 0 if p = p ( + p p ) = 0 if p p p 0 if p = p Solving this, retailer s best response funtion is: if p + p p( p) if p + p if p + Retailer an always get at least a profit of (-")(r-) by setting prie equal to r. The profit maximiing prie for a solution s.t. p [ p, p + ] solves: p + p + p st.. p p p + max ( ) ( ) p By solving the first order onditions, we get: p + if p + + p p( p) + if + p + p if p + 00 Twenty-Seond International Conferene on Information Systems 43

13 * * when, ( p, p) = ( +, + ) and * * 4 ( π, π) = (, ) ( ) ( )( r ) 9 r 4 For this solution to be a NE,. 3 + r 3 r Q.E.D. Proof of Proposition : The proof follows diretly from two Lemmas proven below. Lemma : p =r dominates p p r ( )( ), where p = max{ +,( ) r+ }. Proof: Retailer is assured of at least (-") of the market at p = r with profit (-")(r-). So even if retailer gets the full market at a prie p < ( ) r+, its profit will be less than setting the prie at r. pl + p( pl) Assume pl is suh that ( + ) ( p( pl ) ) = ( )( r ), where the left hand side is an inreasing funtion of p r ( )( ) r ( )( ) l, we get p and, that is, l = + p( p l ) = + + r ( )( ) is the prie on Retailer best response funtion that makes retailer indifferent from harging a prie of r, and Retailer will never hoose a prie smaller than that, as its profit is less than harging a prie of r. Q.E.D. Lemma : p = p dominates p < p r ( )( ), where p = max{ +,( ) r+ } and p = r dominates p ( r, r]. Proof: Given that p p, Retailer is assured of at least " of the market at p = p. Its profits are less when p < p as it does not inrease any demand while at the same time it redues the profit margin. The best response funtion of Retailer implies p = r dominates p ( r, r]. Q.E.D Twenty-Seond International Conferene on Information Systems

14 Proof of Proposition 6: Retailer best response solves: max ( p ) a st.. p < p p, or by expressing " as a funtion of p, ( p ) ( p) =, we solve the following funtion: a ( p ) 4a max.. p s t p < p Solving first order onditions gives us retailer s best response funtions: p ε if p > p( p) if p Retailer s best response funtion: ar + ( r ) r if p a+ r p( p) ar + ( r ) p if p > a+ r p p (p ) r p (p ) ar + ( r ) a + r r p Given these best response funtions, there an exist any NE, as shown in the graph, these two best response funtions do not ross anywhere. Q.E.D. 00 Twenty-Seond International Conferene on Information Systems 45

15 Proof of Proposition 7: Case : When Retailer moves first: Knowing that retailer will respond to its prie in the following way: r if p ( r )( ) + p( p) p if p > ( r )( ) + The highest prie Retailer an set while earn positive profits is ( r )( ) +. Plugging this into Retailer profit funtion: we get: ( r )( ) a * = arg max ( r )( ) a * r = ( a+ r ) * * * * * ( a+ r )( r ) p = r, q =, π = ( ) ( r ) = ( a+ r ) p = ( ) r+, q =, * * * * * * * * * ( r ) π = ( ) ( r ) ( ) = 4( a+ r ) Case : When Retailer moves first: Knowing that Retailer will respond to its prie in the following way, p ε if p > p( p) if p Retailer will hoose:. Retailer will then hoose an " to maximie its profit given Retailer s response: and thus we get: p p = arg max ( p )( ) a * p * * * a a p = a + ; p = a + ε ; = ; π = and π = 4 ( r ) a ( 5 )( r ) Given these, Retailer prefers moving first as long as: 0 a, and Retailer prefers 4( a+ r ) 4 ( a+ r )( r ) a Retailer moving first as long as: 0 a ( r ). But sine a an be greater than (r-), it is ( a+ r ) always in Retailer s interest to let Retailer move first. Colletively, we get an equilibrium in whih Retailer moves first ( 5 )( r ) when 0 a. Q.E.D Twenty-Seond International Conferene on Information Systems