Brand Awareness and Price Competition in OnlineMarkets

Michael R. BayeIndiana University

John MorganUniversity of California, Berkeley

February 2004 (Preliminary and Incomplete)

Abstract

We study a model where retailers endogenously engage in both brand ad-vertising to attract loyal customers as well as informational advertising, whichconsists of deciding whether and what price to list on a price comparison site.We derive a symmetric subgame perfect equilibrium of the model and showthat endogenous branding does not eliminate equilibrium price dispersion inonline markets, although for plausible parameter values, increased branding isassociated with lower levels of price dispersion. Price levels are also predictedto depend systematically on firms’ branding activities. These predictions areconsistent with online data from a leading price comparison site. An importantby-product of endogenizing both brand and price advertising is the asymmetricimpact of changes in advertising costs on firm profits. A reduction in the costof price advertising reduces equilibrium profits whereas a reduction in the costof brand advertising has no effect on equilibrium profits. Finally, we show thatprice dispersion persists even when the number of competing firms is arbitrarilylarge.

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1 Introduction

The persistent and substantial price dispersion observed in online markets for what

would seem to be homogeneous products has been the focus of considerable recent

empirical research.1 Brynjolfsson and Smith (2000a) argue that the observed price

dispersion is mainly due to perceived differences among retailers related to brand-

ing, awareness, and trust–factors affected to a great extent by the brand-building

activities of online retailers.2 Put differently, online retailers in these markets go to

considerable pains to induce consumers to be less price sensitive and more loyal to

their site.

Brand-building activities employed by online sellers include the prominent use

of logos, clever advertising campaigns in highly visible slots, the development of

“customized” applications on their web sites including one-click ordering and custom

recommendations for various products (in the case of Amazon), and the development

of an online “community” loyal to a particular site (as in the case of eBay).3 Indeed,

even on Internet price comparison sites, where consumers appear to be extremely

price sensitive (Ellison and Ellison estimate price elasticities of 51 for consumers on

one such site), firms choose to promote their sites by featuring their logo along with

their price listing. All of these activities are costly to firms. For example, firms listing

1See, for instance, Bailey (1998a,b); Brown and Goolsbee (2000); Brynjolfsson and Smith (2000a,b); Clemons, Hann, and Hitt (2000); Morton, Zettlemeyer, and Risso (2000); Baye, Morgan, andScholten (2001); Clay, Krishnan, and Wolff (2001); Clay and Tay (2001); Ellison and Ellison (2001);Pan, Ratchford, and Shankar (2001); Smith (2001); and Scholten and Smith (2002). See also Elberse,et al. (2003) for a survey of the relevant marketing literature.

2See also Ward and Lee (2000) and Dellarocas (2001).3Efforts to induce loyalty may also be indirect. The cost of such strategies include the implicit

costs of providing fast service or liberal returns policies in an attempt to influence reputationalratings (see Bayliss and Perloff, 2001; Resnick and Zeckhauser, 2002). It appears that these brand-building activities are somewhat successful. Brynjolfsson and Smith (2000b) report that a con-siderable fraction of consumers do not click-through to the lowest price book retailer at one pricecomparison site.

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prices at Shopper.com that attempt to create brand awareness by adding a logo pay

the price comparison site fees in addition to the usual fees firms must pay for the

privilege of listing prices at the site. Firms using other price comparison sites, such

as Nextag and Froogle, may (at a firm’s discretion) pay additional fees to influence

their position in the “list of sellers.”

Despite this, the economics literature on price competition typically treats the

fraction of consumers who view firms’ products to be perfect substitutes and the

fraction who are “loyal” to some firm as exogenous; examples include Shilony (1977),

Varian (1980), Rosenthal (1980), Narasimhan (1988), Stegeman (1991), Robert and

Stahl (1993), Dana (1994), Stahl (1994), Roy (2000), Baye and Morgan (2001), and

Janssen and Rasmusen (2002).4 One key question we address is whether endogenous

brand-building efforts on the part of firms alter conclusions about the level and dis-

persion of online prices. One can imagine that endogenizing brand-building might

matter a great deal. For instance, we show that when brand advertising by firms is

chosen endogenously, the equilibrium number of loyal customers is increasing with

the number of competing firms. If this increase ultimately led to a situation where all

consumers are loyal to some brand, then each firm would simply charge its loyal cus-

tomers the monopoly price and price dispersion would vanish in the limit. Expressed

differently, it is not at all clear that dispersed price equilibria of the sort characterized

by Varian, Narasimhan, and Baye-Morgan arise if customer loyalty is endogenously

determined by branding activities on the part of firms. This raises a number of other

questions, such as the impact of brand-building activities on the competitiveness of

online markets, and whether brand-building activities enhance the equilibrium profits

of firms pursuing such strategies.

4See also see Butters (1977); Grossman and Shapiro (1984); McAfee (1994); and Stahl (1994).

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To examine these and other questions, we offer a model that captures salient

features of online price competition. There is a fixed number of firms selling similar

products. In the first stage, firms independently choose brand advertising levels in an

attempt to influence the fraction of consumers loyal to each firm. These “branding

decisions” result in an endogenous partition of consumers into “loyals”, who are loyal

to a specific firm, and “shoppers”, who view the products to be identical. In the

second stage, firms independently make pricing decisions as well as decisions about

informational advertising. We model this as a firm’s decision to list its price only at

its own website or to pay an additional fee to list its price on a price comparison site.

As in the previous literature, the loyal consumers purchase from their preferred firm

so long as the price does not exceed their valuation of the good. Shoppers, on the

other hand, examine the list of prices at the price comparison site and purchase from

the firm charging the lowest price. If the lowest listed price exceeds the shoppers’

valuation of the product, or if no prices are listed at the price comparison site, the

shoppers visit the website of a randomly selected firm and make a purchase decision.

We analyze a symmetric subgame perfect Nash equilibrium to this game with

endogenous brand, pricing, and listing strategies. Optimal decisions by firms result

in a positive measure of loyal consumers, but in equilibrium firms’ branding efforts

stop short of converting all shoppers to loyals. As a consequence, endogenous brand-

ing does not eliminate equilibrium price dispersion in online markets, although for

plausible parameter values, increased branding is associated with lower levels of price

dispersion. Indeed, we show that price levels as well as price dispersion in online

markets are predicted to depend systematically on firms’ branding activities. We

test these predictions using online data from Shopper.com–a leading online price

comparison site for consumer electronics products–and find support for them.

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An interesting by-product of endogenizing both brand and price advertising is

the asymmetric impact of changes in advertising costs on firm profits. Specifically, a

reduction in the cost of price advertising magnifies price competition and reduces the

equilibrium profits of firms. In contrast, a reduction in the cost of brand advertising

has, at the margin, no effect on the equilibrium profits of firms.

Finally, we show that even when the number of competing firms is large (as is

arguably the case in global online markets), price dispersion persists and industry

profits remain positive. This result also obtains in the limit as the number of firms

grows arbitrarily large. This finding is in contrast to the models of Varian (1980),

Rosenthal (1980), Narasimhan (1988), which all predict that the distribution of prices

converges to a point in these settings. The findings for large online markets are also

broadly consistent with daily data we have been collecting for several years and

post weekly at our website, Nash-Equilibrium.com. Price dispersion, as measured

by the range in prices, has remained quite stable over the past three years, at 35

to 40 percent. The stability and magnitude of this dispersion is remarkable from

a theoretical perspective, since (1) the products are relatively expensive consumer

electronics products for which the average minimum price is nearly $500, (2) over the

period the Internet rapidly eliminated geographic boundaries, leading to exponential

growth in the number of consumers and businesses with direct Internet access, and

(3) according to the Census Bureau, there were nearly 10,000 consumer electronics

retail establishments in the United States who compete in the consumer electronics

market.5 Each of these 10,000 stores could,6 in principle, choose to list their prices

5This figure is based on NAICS classification code 443112, which is comprised of establishmentsknown as consumer electronics stores primarily engaged in retailing new consumer-type electronicproducts. Source: U.S. Census Bureau, 1997 Economic Census, January 5, 2001, p. 217.

6This figure probably understates the actual number of potential competitors in on-line consumerelectronic products markets, as the up-front cost to being an e-retailer is lower than being a “brickand mortar” retailer.

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on Shopper.com, yet the average product sold through Shopper.com was offered by

less than 20 firms.

The remainder of the paper is organized as follows. Section 2 presents the model.

In Section 3, we construct a symmetric subgame perfect equilibrium of the model

and provide closed form expressions for equilibrium levels of brand advertising, price

advertising, and pricing. Section 4 studies key comparative implications of the model

highlighting the effects of changes in the cost and effectiveness of brand and price

advertising on profits, loyal consumers, and price dispersion. In Section 5, we study

the limit properties of the equilibrium as the number of competing firms grows large.

Section 6 derives empirically testable implications of the model and tests these using

Shopper.com data. Finally, Section 7 concludes. The proofs of various propositions

in the text are relegated to appendices as indicated.

2 Model

Consider an online market where a continuum of consumers shop for some product

from which they all derive value, v. Consumers are interested in purchasing one unit

of the product.7 As in Narasimhan and Rosenthal, there are assumed to be two types

of consumers: Loyals visit the website of their preferred firm and purchase the product

if they obtain non-negative surplus. Shoppers costlessly visit the price comparison

site and obtain a list of the prices charged by all firms choosing to list their prices

there.8 Since shoppers view the products as perfect substitutes, they each purchase at

7It is straightforward to generalize the model to allow for downward sloping demand.8Baye and Morgan (2001) show that a monopoly “gatekeeper” that owns a price comparison

site has an incentive to set consumer subscription fees sufficiently low in an attempt to induce allconsumers utilize the site. Hence, we assume that all shoppers have access to the comparison site atno cost. This assumption is consistent with empirical evidence; virtually all price comparison sites —including Shopper.com, Nextag, Expedia, and Travelocity — permit consumers to use their services

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the lowest price available at the price comparison site — provided it does not exceed v.

If no prices are listed, these shoppers visit the website of a randomly selected firm and

purchase if the price does not exceed v.9 In contrast to the models of Narasimhan and

Rosenthal, a consumer’s type is determined endogenously by brand advertising on the

part of firms, as we will describe below. In contrast to Baye and Morgan, who assume

that consumers view all firms’ products to be perfect substitutes, here we allow for

the possibility that some consumers have a preference for particular sellers. There

is considerable evidence that this is indeed the case. For instance, many consumers

prefer to purchase books from Amazon rather than Barnes and Noble.10 To capture

these effects, we normalize the measure of consumers to be unity and let βi denote

the proportion of these consumers who are loyal to firm i. Thus, the total number of

loyal consumers is B =Pn

i=1 βi. The remaining 1−B shoppers view the products as

identical.

There are N firms in this market, which produce at constant marginal cost, m.

There are three components to a firm’s strategy: Firm imust decide its price (denoted

pi), its informational advertising strategy, which is modeled as a binary decision to

spend φ > 0 to list its price at the price comparison site (or not), and its brand

advertising level, ai. Firms influence consumers’ loyalty through brand advertising.

We assume that branding leads to the acquisition of loyal customers according to the

functional form:

βi = β (ai, A−i) = δai

A−i + ai+ aiσ,

where A−i =P

j 6=i aj denotes aggregate (endogenous) branding effort by all firms

at no charge.9For simplicity, we assume that the cost of additional searches is sufficiently high to rule out the

optimality of further search.10For instance, Chevalier and Goolsbee (2002) provide evidence that the demand for books at

Barnes and Noble is about 8 times more elastic than that at Amazon.

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other than i, and where σ > 0 and δ ≥ 0 are exogenous parameters. When A−i > 0,

positive branding effort is required for firm i to enjoy any loyal consumers. Notice that

this specification captures two effects of brand advertising. When δ is small, brand

advertising by firm i mainly converts some shoppers into brand i loyal consumers.

When δ is large, firm i’s brand advertising mainly steals loyal consumers from other

firms.

Firms’ incentives to engage in branding activities depend not only on the sen-

sitivity of βi to branding efforts (that is, the magnitude of δ, σ, and the aggregate

branding efforts of rival firms), but also on brand advertising costs. Assume that the

marginal cost of a unit of brand advertising is τ > 0, so that the total cost to firm i

of utilizing ai units of brand advertising is τai.

Since the impact of branding on a firm’s stock of loyal consumers is likely to

require substantial commitment and time, we model branding and pricing decisions

as a two-stage game. In the first stage, firms simultaneously but independently choose

brand advertising levels, ai, in an attempt to create a stock of loyal consumers. In the

second stage, firms simultaneously but independently make their pricing and listing

decisions. We assume that first-stage decisions are common knowledge at the time

pricing and listing decisions are made. Finally, let αi denote the probability a firm

lists its price, and let Fi (p) denote the distribution of firm i’s listed price.

3 Equilibrium Branding, Pricing, and Listing De-

cisions

This section summarizes our main result on equilibrium branding, pricing and listing

decisions, and provides a sketch of the underlying proof (mathematical details are

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relegated to Appendix A). We also offer a few remarks regarding similarities and

differences between this equilibrium and that in other models of online price compe-

tition.

3.1 Main Result

Our main result is:

Proposition 1 Suppose τ > (v−m)σ1−δ , φ < (v−m)((1−δ)τ−(v−m)σ)

(τ−(v−m)σ) and that the strategy

space for each firm’s brand advertising is [0, a] where a = N−1N−2

³δ (N−1)(v−m)N2(τ−(v−m)σ)

´. Then

in a symmetric subgame perfect equilibrium, each firm chooses a brand advertising

level

ai = a∗ ≡ δ(N − 1) (v −m)

N2 (τ − (v −m)σ)

and obtains

βi = β∗ =δ

N

µNτ − (v −m)σ

N (τ − (v −m)σ)

¶loyal consumers. Each firm lists its price on the price comparison site with probability

αi = α∗ ≡ 1−µµ

φ

(v −m) (1−Nβ∗)

¶µN

N − 1

¶¶ 1N−1

(1)

and, conditional on listing, selects a price from the cumulative distribution function

Fi (p) = F (p) ≡ 1

α∗

⎛⎝1−Ã (v − p)β∗ + φ NN−1

(1−Nβ∗) (p−m)

! 1N−1⎞⎠ (2)

over the support [p0, v] where

p0 = m+(v −m)β∗ + φ

(N−1)N

(1− (N − 1)β∗) .

Firms that do not list a price at the price comparison site charge a price of pi = v on

their own websites. Each firm earns equilibrium profits of

Eπi = Eπ∗ = (v −m)β∗ +φ

N − 1 − τa∗. (3)

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The formal proof of this proposition is somewhat involved and is thus relegated

to Appendix A. Here, we provide a sketch of the basic arguments underlying the

analysis. We note that the parameter restrictions stated in the proposition rule out

“corner solutions” in firms’ branding and listing decisions when δ > 0.11

As usual, we solve the game backward. First, if all firms employ the same brand

advertising level in the first stage, there is a unique symmetric equilibrium in the

second stage game. In this equilibrium, each firm earns expected profits of

Eπi = β (a, (N − 1) a)× (v −m) +φ

N − 1 − τa, (4)

where a is the brand advertising level selected in the first stage.

Next, suppose that firm i chooses an ai in the first stage that differs from branding

level, a, adopted by the other N − 1 firms. Then there exists an equilibrium in

this asymmetric second-stage game in which all firms list their prices on the price

comparison site with the same frequency, but where firm i utilizes a different pricing

strategy than the other N−1 firms. In this equilibrium, firm i earns expected profits

of

Eπi = β (ai, (N − 1) a) ,× (v −m) +φ

N − 1 − τai (5)

if it chooses branding level ai in the first stage game when the other firms each utilize a

units of brand advertising. Notice that when ai = a, the expected profits in equation

(5) coincide with those in equation (4) .

Firm i’s first-stage objective is to choose a branding level that maximizes equation

(5) , given its conjecture that all other firms will choose branding level a:

maxai∈[0,a]

Eπi = β (ai, (N − 1) a)× (v −m) +φ

N − 1 − τai.

11When δ = 0, promotional advertising is zero.

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Using the definition of β (ai, A−i) and differentiating with respect to ai yields the

first-order condition:12µδ

(N − 1) a(ai + (N − 1) a)2

+ σ

¶(v −m)− τ = 0.

For this to be a symmetric equilibrium, it must be the case that ai = a. That is,

(v −m)

µ(N − 1)N2a

δ + σ

¶− τ = 0.

Since a unique value of a solves this equation, it follows that the unique symmetric

first-stage equilibrium level of brand advertising is

ai = a∗ = δ(N − 1) (v −m)

N2 (τ − (v −m)σ).

This implies that each firm enjoys

β (a∗, (N − 1) a∗) = β∗ = δNτ − (v −m)σ

N2 (τ − (v −m)σ)

loyal consumers. Notice that, while each firm creates a positive number of loyal

consumers, in equilibrium there remain (1−B∗) = (1−Nβ∗) > 0 shoppers who will

purchase from the firm charging the lowest price.

3.2 Remarks

The equilibrium identified in Proposition 1 shares features present in the models of

Varian, Rosenthal, Narasimhan, and Baye-Morgan — as well as some important dif-

ferences. Similar to all of these models, equilibrium in the present model requires any

firm listing a price on the price comparison site to use a pricing strategy that prevents

rivals from being able to systematically predict the price offered to consumers who

12It is a routine matter to show that the second-order conditions are satisfied when δ > 0.Whenδ = 0, the fact that (v −m)σ < τ means that it is a dominant strategy for firm i to choose ai = 0for all i.

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enjoy the information posted at the site (hence the distributional strategy, F ∗ (p)).

Like Baye-Morgan, our model permits firms to endogenously determine whether to

utilize the price comparison site (the other models constrain all firms to list prices

at the site with probability one, and Baye-Morgan essentially show this is not an

equilibrium if it is costly for firms to list prices at the site). As a consequence, firms

randomize the timing of price listings to preclude rivals from systematically deter-

mining the number of listings at the price comparison site (hence, the informational

advertising propensity, α∗ ∈ (0, 1)).

In further contrast to Narasimhan and Rosenthal, the present model relaxes the

assumption that firms are costlessly endowed with an exogenous number of brand-

loyal consumers. In the present model, a firm that spends nothing to promote its

“brand” or “service” in the face of positive expenditures by rivals enjoys no loyal

consumers. Unlike Varian and Baye-Morgan, the present model does not impose

the assumption that all consumers view the products sold by different firms to be

identical; indeed, in equilibrium, each firm enjoys a strictly positive number of loyal

consumers — thanks to the positive level of branding activity that arises in equilib-

rium. As we will discuss below, this implies that the price comparison site attracts

fewer consumers than in the Baye-Morgan model. Expressed differently, the branding

efforts of firms reduce the traffic enjoyed by the “information gatekeeper” operating

the price comparison site.

4 Implications for Oligopolistic Online Markets

In this section, we study the impact of endogenous branding on firms’ pricing be-

havior and e-retailer profitability in online markets. We also study how changes in

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the parameters associated with the cost of brand and price advertising as well as

effectiveness affect equilibrium outcomes. Some of the intuition provided in this sec-

tion is based on the comparative statics summarized below (Appendix B provides the

relevant mathematical details).

Variable δ σ τ N φ v mEπi + 0 0 − + + −a∗ + + − − 0 + −β∗ + + − − 0 + −B∗ + + − + 0 + −p∗0 + + − ? + + ?α∗ − − + ? − ? ?

4.1 Firm Profits

One of the implications of endogenous branding in oligopolistic online markets is

that equilibrium brand advertising expenditures by firms result a fraction B∗ > 0 of

consumers who directly visit the websites of individual firms rather than utilizing the

gatekeeper’s site. In Baye-Morgan, the gatekeeper enjoys traffic from all consumers

(due to its incentive to set consumer subscription fees low). By allowing firms to

choose branding levels, we see that firms have an incentive to create loyal consumers,

which reduces traffic at the gatekeeper’s site to (1−B∗).

Do firms benefit, in equilibrium, from the costly branding activities that ultimately

redirect B∗ consumers to their own websites? Or do firms’ incentives to promote their

brands or services stem from an “oligopolistic lock-in” (see Tauber, 1970), such that

the overall profits of firms are lower than would arise if the firms could credibly commit

to spend nothing on branding? Notice that the equilibrium profits of a representative

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firm may be written as

Eπ∗ = {(v −m)β∗ − τa∗}+ φ

N − 1 .

The term in brackets simplifies to (v −m) δN2 ,which yields

Eπ∗ =δ

N2(v −m) +

φ

N − 1 . (6)

In contrast, when firms are unable to engage in brand-building activity, equilibrium

profits are:13

Eπ∗∗ =δ

N(v −m) +

φ

N − 1 .

Thus,

Proposition 2 In equilibrium, the ability to create brand-loyal consumers (at positive

cost) decreases each firm’s expected profits by

δ

N2(v −m) (N − 1) ≥ 0

compared to the case where firms cannot create loyal consumers.

When δ > 0, the expression in Proposition 2 holds with a strict inequality. That is,

firm profitability is strictly lower owing to the option to differentiate their offerings

from rivals. Interestingly, the profitability of the industry is independent of the

marginal benefit of brand expansion (σ) .Thus, even if the main effect of branding

is to “grow” the number of loyal customers rather than stealing existing loyals from

13To see this, note that when µ = 1− δ in the Baye-Morgan model, each firm’s expected profitsare φ/ (N − 1) + 1−µ

N (v −m); see Baye-Morgan, Proposition 3.

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other firms, it is still the case that adding the option of engaging in brand advertising

leaves firms individually and collectively worse off. The profits foregone due to this

oligopolistic lock-in are greater in high-margin (v −m) markets, and lower in markets

with many firms.

The next proposition summarizes the effects of changes in the parameters of the

model on profits in the symmetric equilibrium we constructed in Proposition 1.

Proposition 3 The equilibrium profits of firms are:

1. increasing in the cost of informational advertising (φ) , but independent of the

cost of brand advertising (τ) ;

2. increasing in the effectiveness of brand stealing (δ) , but independent of the ef-

fectiveness of brand expansion (σ) ;

3. decreasing in the number of competitors (N) .

As in Baye-Morgan, each firm’s expected profits are increasing in φ. Notice, how-

ever, that equilibrium e-retailer profits are independent of the marginal cost of brand

advertising, τ . At first this result might seem surprising, since an increase τ reduces

each firm’s equilibrium number of loyal consumers. However, even though a firm’s

profits are increasing in its number of loyal consumers, competition to create such

consumers entails a long-term commitment of resources. At the time of pricing deci-

sions, however, these expenditures represent sunk costs. The price competition that

ensues in the online marketplace thus makes a firm’s expected profits invariant to

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the cost of brand advertising. In contrast, note that expected profits are increasing

in firms’ costs of listing prices on the gatekeeper’s comparison site (φ). These costs

drive a wedge between the expected profits earned from listing prices in the online

market and those from not listing at the gatekeepers site. Higher listing fees reduce

firms’ equilibrium propensities to advertise (α∗), which lessens price competition and

results in higher equilibrium profits.

It is clear from equation (6) that profits are increasing in δ. Roughly, this means

that firms earn higher equilibrium profits in markets where there are greater incentives

to engage in brand advertising to steal consumers from other firms. In contrast,

equilibrium profits are independent of σ. Finally, expected profits are decreasing in

the number of potential competitors, N .

4.2 Firm Advertising

The model also sheds light on interrelations between two different types of advertising

strategies. As would be expected, firms’ demands for brand and price advertising (a∗

and α∗, respectively) are decreasing functions of their respective prices (τ and φ,

respectively). The demand for brand advertising is an increasing function of both

the direct (σ) and brand-stealing (δ) parameters. The model predicts that efforts

to create loyal consumers are more prevalent in markets where it is relatively easy

(markets with higher δ or σ) or where it is less costly (markets with lower τ) to

engage in branding. As a consequence, both the individual and aggregate number of

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loyal consumers (β∗ and B∗, respectively) will be larger in markets where it is easier

or less costly to induce consumers to become loyal to a given firm.

Brand advertising is a substitute for informational advertising; increases in the

unit cost of brand advertising (τ) induce firms to increase their propensities to run

price advertisements (α∗). The intuition is as follows: higher brand advertising costs

result in less brand-building and hence fewer loyal consumers. This reduces the

profits firms earn through traffic at their own websites, and therefore induces them

to list more frequently at the gatekeeper’s site. The converse is not true, however;

an increase in the cost of listing prices at the gatekeeper’s site has no effect on firms’

demand for branding efforts: ∂a∗/∂φ = 0. The asymmetric cross price effects stem

from the asymmetric manner in which τ and φ are paid. Listing fees (φ) are paid

only when a firm lists prices at the gatekeeper’s site, while brand advertising costs

(τ) are incurred regardless.

We summarize the effects of changes in the parameters of the model on brand and

price advertising in the symmetric equilibrium we constructed in Proposition 1:

Proposition 4 Brand advertising is:

1. decreasing in the marginal cost of brand advertising (τ) , but independent of the

cost of informational advertising (φ) ; and

2. increasing in its effectiveness (δ, σ) .

Informational advertising is:

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1. decreasing in the cost of listing a price on the comparison site (φ) and increasing

in the cost of brand advertising (τ) ; and

2. decreasing in the effectiveness of brand advertising (δ, σ) .

As a consequence of the invariance of equilibrium brand advertising levels to the

fees the gatekeeper charges for listings at its site, the equilibrium number of shoppers

(1−B∗) as well as each firm’s number of loyal customers (β∗) are unaffected by fees

charged by the gatekeeper.

Remark 1 The gatekeeper setting fees at a price comparison site can do nothing

through its fee structure to keep firms from diverting traffic from its price comparison

site to individual firm websites.

It would seem that this would require an additional tool on the part of the gate-

keeper, such as its own branding efforts aimed at creating loyalty to the price compar-

ison site. This is only suggestive, however, and formal analysis is beyond the scope

of the present paper.

4.3 Price Dispersion

We close this section with a look at how endogenous branding efforts by firms influ-

ences the levels of price dispersion observed in online markets. Proposition 1 implies

a nondegenerate distribution of prices, as firms stop short of converting all consumers

into loyals. One of the more widely used measures of dispersion for online markets is

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the range,14 which may be written (using Proposition 1) as

R∗ = v − p0

=(v −m) (1− β∗N)− φ

(N−1)N

(1− (N − 1)β∗)

This permits us to establish the following relationship between the costs of brand and

price advertising and levels of price dispersion observed in online markets.

Proposition 5 Equilibrium price dispersion, measured by the range, is greater in

online markets where:

1. it is less costly to list prices at the gatekeeper’s site (φ is lower);

2. it is more costly to create loyal customers (τ is higher), or alternatively, it is

more difficult to create loyal consumers (δ and/or σ are lower).

The first part of this proposition follows from the fact that, other things equal,

a reduction in φ increases the profitability of listing prices at the gatekeeper’s site

but results in no change in the total number of loyal consumers. Since in equilibrium

firms must be indifferent between listing prices and not, firms compete away these

potential profits by pricing more aggressively at the gatekeeper’s site. This reduces

the lower bound of the distribution of prices, and the result is a wider range in prices

listed on the Internet.

The second part of this proposition stems from the impact of reduced branding

incentives on the total number of loyal consumers in the online marketplace. Increases14This is the principle measure used in Brynjolfsson and Smith (2000a, b).

19

in τ (or decreases in δ and/or σ) induce each firm to spend less on branding. In

equilibrium, this reduces the total number of loyal consumers in the market, thereby

heightening competition for the resulting larger number of shoppers. This heightened

competition results in a reduction of the support of the distribution of prices listed

at the gatekeeper’s site, thereby increasing range of observed prices.

The intuition underlying the second part of the proposition — that the range in

prices is decreasing in the aggregate number of loyal consumers — gives rise to a curious

possibility. Recall that each firm’s level of branding (and hence its number of loyal

consumers) declines as the number of potential firms increases. Nonetheless, the total

number of loyal consumers, B∗ is increasing in N. This means that if an increase in

the number of firms ultimately leads to a market in which B∗ = 1, then there would

be no shoppers and all firms would maximize profits by charging v at their individual

websites. Expressed differently, it is not clear whether a nondegenerate distribution

of prices will prevail in “large” online markets.

This is the opposite of the usual conclusion drawn about the relationship between

price dispersion and the competitiveness of markets. Whereas it is usual to associ-

ated more price dispersion with less competitive markets, in our model there is no

systematic relationship. When fees at the gatekeeper’s site are lower there is more

price dispersion and lower industry profits. The same pattern holds for changes in

the effectiveness of brand stealing. The less effective is brand stealing, the greater the

dispersion, but the lower are industry profits. In contrast, when the costs of brand

20

advertising are higher, price dispersion is greater but industry profits are unaffected.

The same pattern holds for reductions in the effectiveness of brand expansion. In

short, without knowing the variable primarily responsible for changing the levels of

dispersion, one cannot draw definitive conclusions about industry profitability from

dispersion alone.

Finally, note that the distribution of prices remains non-degenerate even in the

special case where firms cannot profitably create brand loyal consumers. To see this,

suppose δ = 0. Optimal firm behavior then implies a∗ = 0 (since τ > (v −m)σ by

assumption). This in turn implies β∗ = B∗ = 0, so all consumers in the market

are shoppers. Despite this, Proposition 1 still implies that the distribution of online

prices remains dispersed.

5 Implications for "Large" Online Markets

To examine whether the distribution of online prices converges to a point when the

number of firms is large, we examine the properties of the model as N → ∞. Note

that the number of potential competitors, N , generally exceeds the actual number of

firms listing prices at any instant in time. In particular, given that each firm lists a

price with probability α∗, the actual number of listings is a binomial random variable

with mean,

n = Nα∗ < N.

21

It is easy to verify that

limN→∞

β∗ = limN→∞

Eπ∗ = 0.

This implies that, in markets where N is large, each firm enjoys a negligible number

of loyal consumers and essentially earns zero economic profits. Thus, the environment

we study in this section shares two features with perfectly competitive markets: (1)

each firm is small relative to the total market, and (2) firms earn zero equilibrium

profits.

As we will see, however, even though firms are atomistic and earn zero economic

profits in the limit, the resulting equilibrium does not entail marginal cost pricing.

In fact, prices remain dispersed and exceed marginal cost with probability one, even

as the number of competitors becomes arbitrarily large. The reason stems from the

fact that even though each firm is attracting fewer and fewer loyal customers, in

the aggregate the fraction of loyal customers converges to a positive amount (when

δ > 0).This is given by

BL = limN→∞

B∗

=δτ

τ − (v −m)σ.

Before we formalize these arguments, it is useful to determine the aggregate levels

of brand and price advertising that arise in the limit. Aggregate brand advertising is

AL = limN→∞

Na∗

= δ(v −m)

τ − (v −m)σ.

22

Note that the aggregate demand for brand advertising is downward sloping and in-

creasing in δ and σ.

The expected number of price listings at the gatekeeper’s site is, in the limit,

nL = limN→∞

n

= ln

µ(v −m) ((1− δ) τ − (v −m)σ)

φ (τ − (v −m)σ)

¶.

Thus the expected number of listed prices at any instant in time is positive and finite

since φ < (v−m)((1−δ)τ−(v−m)σ)(τ−(v−m)σ) <∞.

Taking into account that α∗ and B∗ depend on N , we take limits to obtain

FL (p) = limN→∞

F ∗ (p)

=ln³

φ(τ−(v−m)σ)(p−m)((1−δ)τ−(v−m)σ)

´ln³

φ(τ−(v−m)σ)(v−m)((1−δ)τ−(v−m)σ)

´ .To see that this is a well-defined distribution function, notice that FL is a non-negative

fraction, since

ln

µφ (τ − (v −m)σ)

(p−m) ((1− δ) τ − (v −m) σ)

¶< ln

µφ (τ − (v −m)σ)

(v −m) ((1− δ) τ − (v −m)σ)

¶.

Second, FL is strictly increasing in p over its support. To see this, notice that

dFL (p)

dp= − 1

(p−m) ln³

φ(τ−(v−m)σ)(v−m)((1−δ)τ−(v−m)σ)

´ > 0,

where the inequality follows from the fact that φ(τ−(v−m)σ)(v−m)((1−δ)τ−(v−m)σ) < 1.

It is a simple matter to verify that the lower support of the limit distribution is:

pL0 = m+φ (τ − (v −m)σ)

(1− δ) τ − (v −m)σ,

23

and that

pL0 = m+φ (τ − (v −m)σ)

(1− δ) τ − (v −m)σ

< m× (1− δ) τ − (v −m)σ

(1− δ) τ − (v −m)σ+

(v−m)((1−δ)τ−(v−m)σ)(τ−(v−m)σ) (τ − (v −m)σ)

((1− δ) τ − (v −m)σ)

=v ((1− δ) τ − (v −m) σ)

(1− δ) τ − (v −m)σ

= v,

where the inequality follows from the fact that φ < (v−m)((1−δ)τ−(v−m)σ)(τ−(v−m)σ) .

To summarize:

Proposition 6 In online markets where an arbitrarily large number of firms endoge-

nously choose their brand and price advertising intensities:

1. The average number of prices listed at the gatekeeper’s site is

nL = ln

µ(v −m) ((1− δ) τ − (v −m)σ)

φ (τ − (v −m)σ)

¶.

2. The aggregate demand for brand advertising is

AL = δ(v −m)

τ − (v −m)σ.

3. The total number of loyal consumers is

BL =δτ

τ − (v −m) σ.

4. Prices listed at the gatekeeper’s site are dispersed according to the distribution

FL (p) =ln³

φ(τ−(v−m)σ)(p−m)((1−δ)τ−(v−m)σ)

´ln³

φ(τ−(v−m)σ)(v−m)((1−δ)τ−(v−m)σ)

´24

on£pL0 , v

¤, where

pL0 = m+φ (τ − (v −m)σ)

(1− δ) τ − (v −m)σ.

It follows immediately that–even in online markets where the number of firms is

arbitrarily large–price dispersion will remain significant.

The range in prices

RL = v − pL0

will remain sizeable. Moreover, as in the oligopoly case, price dispersion will be higher

in markets where it is more difficult or more costly to create loyal consumers, and

lower at gatekeeper’s sites that charge higher listing fees. Also, note that even when

δ = 0 (so that all consumers are shoppers), price dispersion remains; the range of the

limit distribution when δ = 0 is simply

RL = v −m− φ,

which is non-degenerate.

6 Empirical Analysis

Many of the primitives of our model are difficult to observe in field data. In this

section, we derive comparative static implications of our model that are readily tested

with field data and then analyze online pricing in light of these predictions using a

dataset consisting of price quotes for the top 100 consumer electronics products listed

25

at the popular Internet price comparison site Shopper.com for the period 21 August

2000 until 22 March 2001.

6.1 Testable Predictions of the Theory

Obviously, advertised prices are readily observable in our dataset. Thus, we focus

on implications on the distribution of advertised prices of changes in the intensity of

branding activity (denoted by a in our model) by firms. Specifically, we repeatedly

rely on Proposition 7 below, which shows that one can rank advertised price distrib-

utions by first-order stochastic dominance as brand advertising changes, to derive a

set of testable hypotheses.

Proposition 7 All else equal, in markets where the intensity of brand advertising

is higher, the distribution of prices listed on the price comparison site first-order

stochastically dominates those where intensity of advertising is lower.

The proof of Proposition 7 is contained in the Appendix.

We first examine the average advertised price. As a consequence of Proposition 7

we immediately obtain Corollary 1.

Corollary 1 All else equal, in markets where brand advertising is higher, average

listed prices are also higher.

In our model, “shoppers” buy from the firm offering the lowest listed price. Thus,

there is an important welfare effect associated with changes in this price statistic.

26

Since the distribution of the lowest advertised price when n firms list prices is Fn, it

then follows as a consequence of Proposition 7 that:

Corollary 2 All else equal, in markets where brand advertising is higher, the average

minimum listed price is also higher.

Price Dispersion In the preceding sections, we derived comparative static im-

plications related to the range in prices, which we defined as the difference between

the upper and lower supports of the equilibrium price distribution. Since we cannot

directly observe these in the data, a more empirically useful definition is the sam-

ple range, which we define as the difference between the highest and lowest prices

listed on the comparison site. Thus, the key comparison is in the change between

the average maximum and minimum listed prices. Proposition 7 also implies that

the average maximum listed price increases, so, as a consequence, the sample range,

could, in principle, either increase or decrease depending on the magnitude of these

changes. Indeed, as we show below, there is no monotonic relationship between brand

advertising intensity and changes in the sample range; however, for reasonable para-

meter values, we would expect the sample range to be decreasing in brand advertising

intensity.

Specifically, we performed the following calibration. We set consumers’ maximal

winglessness to pay, v, equal to the average maximum price observed in the data,

which is $549.20. We set the number of potential firms, N, at 68, which is the

largest number of firms listing prices for any product in our dataset. To illustrate

27

the particular relationship between the range and the intensity of advertising, we set

the number of firm’s listing prices at 28, which is the average in our sample. We set

the listing fee for posting a price on the comparison site at φ = $3.33, which is the

average cost per day of listing a price at Shopper.com during the period of our study.

To calibrate the marginal cost figure is more involved. We assumed a 38.5% gross

margin on the average transaction price, which is based on the US Census Bureau’s

estimate of the average margin for Electronic Shopping and Mail Order Retailers

(NAICS 4541).15 To obtain the average transaction price, we supposed that 13%

of customers bought items at the average minimum price–that is were shoppers in

our terminology–while the reminder bought items at the average price–that is were

loyal customers. The 13% figure is based on estimates by Brynjolfsson, Montgomery,

and Smith [2003] for the percentage of Internet users using price comparison sites

over the 2000-2002 period. This completely calibrates the model.

The parameter of interest is the change in the intensity of advertising by firms

or, equivalently, the change in the fraction of the population consisting of “loyal”

customers. In Figure 1, we display the change in the average price, the average

minimum and maximum prices, and the range in prices. As the figure shows, for

low numbers of loyal customers, the range in prices is modestly increasing. As the

fraction of loyal customers becomes sufficiently large, the range decreases sharply.

The calibrated values for average price and so on in our dataset lie in the region

15 Table 6: Estimated Gross Margin as Percent of Sales by Kind of Business, US Census Bureau,

Revised June 1, 2001.

28

where the range is strongly decreasing in the intensity of firm advertising. Thus, we

offer the following “remark”:

Remark 2 All else equal, in Shopper.com markets where brand advertising intensity

is higher, price dispersion (measured by the range in prices) is lower.

In the next subsection, we describe in more detail the data used to test the im-

plications derived above.

6.2 Data

In order to test the empirical implications of the model, we assembled a dataset for 96

best-selling products sold at Shopper.com during the period from 21 August 2000 to

22 March 2001. During this period, Shopper.com was the top price comparison site

for consumer electronics products (including specific brands of printers, PDAs, digital

cameras, software, and the like). A consumer wishing to purchase a specific product

(identified by a unique part number) may query the site to obtain a page view that

includes a list of sellers along with their advertised price. “Shoppers” can easily sort

prices from lowest to highest and, with a few mouse clicks, order the product from

the firm offering the lowest price. “Loyals,” on the other hand, can easily sort sellers

alphabetically or scan the page for their preferred firm’s logo and click through to

purchase the item from that firm.

We used a program written in PERL to download all the information returned

in a page view for each of the products each day, which amounted to almost 300,000

29

observations over the period. While we have been tracking daily online prices and

advertising for the top 1000 products from the late 1990s to the present (2004),

several factors led us to focus on the time period and products in the present study.

During these seven months (214 days), there is considerable cross-sectional and time

series variation in the brand advertising intensities of firms. Since then, both the

online strategies of firms and the structure of the Shopper.com site have evolved

in ways that makes it more difficult to study the impact of branding on levels of

price dispersion. Today there is less cross-sectional variation in branding (many more

firms promote their logos at Shopper.com), and product searches at Shopper.com

now return mixtures of new and refurbished products. This makes it difficult to

determine whether any observed increases in price dispersion stem from increased

product heterogeneity (comparing new versus used product prices) or increased brand

advertising by firms. In contrast, during the seven months in the present study,

Shopper.com treated new and refurbished versions of otherwise identical products as

different products. In fact, all but one of the 96 products in our sample are new

products (see Appendix A for a complete description of the products).

During the period of our study, firms upload their prices into Shopper.com’s data-

base, which then fetches the uploaded data specified times twice each day. Thus,

daily pricing decisions reflect simultaneous moves. Moreover, there is a minimum

twelve hour lag for any firm to “answer” a pricing move by its rival owing to the

upload/refresh cycle. To advertise its price, a merchant was required to pay a fixed

30

fee of $1,000 to set up an account at Shopper.com, plus an additional fee on the

order of 50 cents each time a consumer “clicked through” from the Shopper.com site

to the firm’s own website. This fee structure provides merchants incentives to post

accurate prices; a firm advertising a bogus price in an attempt to lure customers to

its own website would generate many qualified leads (costing at least 50 cents each),

but would likely alienate potential customers. We confirmed this via an audit; more

than 96 percent of advertised prices were accurate within $1.

Table 1 provides basic summary statistics for these data. On average, 28.18 firms

listed prices for each product. While the average price of a product was $455.99, there

is considerable variation in the prices different firms charge for a given produced. The

average lowest price is $386.95, while the average highest price charged is $549.20.

The average level of price dispersion is substantial, with an average range of $162.25.

As shown in Figure 2, the range is fairly stable and quite sizeable during the period

of our study.

In the predictions developed above, both price levels and price dispersion are pre-

dicted to vary systematically with the level of branding activity undertaken by firms.

While we cannot directly observe the magnitude of expenditures firms undertake on

brand advertising over the period of our sample, we do observe whether a firm uti-

lized one form of brand advertising–the posting of a logo.16 One might expect that

16Since the majority of the firms in our sample are not publically traded, expenditures on brandadvertising are not readily available. Even they were, disentangling “brand” advertising from otherforms of advertising expenditure would prove a formidable task since most forms of firm advertisingare a combination of both branding and informational advertising.

31

this form of brand advertising is correlated with the overall level of brand advertising

undertaken by the firm. As shown in Table 1, on average, only 8.05 percent of the

firms advertising a price for a given product engaged in branding activity of this sort.

In the next section, we attempt to isolate the effects of temporal and cross-

sectional differences in levels of brand advertising on price levels and price dispersion.

As a proxy for difference in brand advertising, we use the fraction of listing firms

choosing a logo for a given product-date. Indeed, this proxy is broadly consistent

with the conventional view of branding activity by firms, which emphasizes the use of

logos and other symbols by firms in an attempt to product differentiate. For instance,

Keller (2002, p. 152) notes: “A brand is a name, term, sign, symbol, or combination

of them that is designed to identify the goods or services of one seller or group of

sellers and to differentiate them from those of competitors.”

6.3 Results

In Tables 2-4 we report regression results that summarize the estimated impact of

branding on, respectively, average prices, average minimum prices, and the range in

prices. All specifications also include product fixed effects to control for differences in

the levels of prices across different products, and a variety of other controls to account

for the impact of market structure, product life cycles, and other factors. Model 1

represents a baseline regression in which the dependent variable associated with prod-

uct j at time t is regressed on branding activity, the number of firms listing prices on

32

that date, and product fixed effects. Models 2 through 6 add controls for nonlinear

branding effects, nonlinear number of firm effects, product popularity,17 date fixed

effects, and potential endogeneity of the number of firms, respectively. Product pop-

ularity fixed effects are based on Shopper.com’s Product Rank (which ranges from 1

to 100 for the products in our sample). These rankings are based on clickthroughs,

and thus these fixed effects control for the possibility that product popularity also

influences the dependent variable. Date fixed effects consist of dummies for each date

in our sample and help to control for time varying demand and product life-cycle

effects. Model 6 is a crude attempt to deal with the potential endogeneity in the

number of firms listing prices by using product popularity as an instrument for the

number of firms posting prices for a given product-date.

Table 2 summarizes results for the average price regressions. In all cases, the

results indicate that, at the 1 percent significance level, average prices positively

covary with branding intensity; thus, the results are robust to a variety of controls

and specifications. These results indicate that average price increases by between

$12.61 (Model 1) and $14.65 (Model 6) with a one percent increase in branding (at

the product level). More importantly, these results are consistent with the Corollary

1. Finally, we also find that average price falls with an increase in the number of firms

listing prices on the site, as one might expect from standard models of oligopolistic

competition.

17The popularity fixed effects are based on Shopper.com’s Product Rank (which ranges from 1to 100 for the products in our sample). These rankings are based on clickthroughs, and thus thesefixed effects control for the possiblity that product popularity also influences average prices.

33

Table 3 summarizes results for the minimum price regressions. As with average

prices, minimum prices positively covary with branding intensity and are significant

at the one percent level. As in Table 3, the results are qualitatively similar across

a variety of controls and specifications. These results indicate that minimum price

increases by between $25.95 (Model 1) and $30.08 (Model 5) with a one percent

increase in branding. These results are consistent with the Corollary 2.

While Tables 2 and 3 focus on changes in price levels with changes in branding,

table 4 examines how price dispersion changes with branding. In this table the

dependent variable is the sample range. In all cases, the results indicate that, at

the 1 percent significance level, price dispersion negatively covaries with branding

intensity. Again, the relationship is robust to a variety of controls and specifications.

These results indicate that price range decreases by between $22.29 (Model 1) and

$36.43 (Model 5) with a one percent increase in branding (at the product level). These

findings are consistent with the calibration of the theoretical model as summarized

in Remark 2.

7 Conclusions

We have shown that firms have individual incentives to use branding strategies to

divert some (but not all) consumers directly to their own websites even though doing

so does not increase firms’ equilibrium profits. Branding activities are also harmful

to information gatekeepers running price comparison sites, in that they are deprived

34

of traffic from consumers who would otherwise visit. Moreover, there is nothing

the gatekeeper can do to stop the exodus of traffic by lowering the fees they charge

firms. Even so, the resulting equilibrium in online product markets exhibits price

dispersion, and the levels of price dispersion are related to the costs and benefits

of brand advertising. This price dispersion persists as the number of firms becomes

arbitrarily large, as well as when branding opportunities do not justify the costs and

all consumers are shoppers seeking to purchase at the best price. Our theoretical

and empirical results suggest that, while increased branding activity results in higher

average prices, the levels of price dispersion observed in online markets are likely to

remain substantial.

35

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40

A Proof of Proposition 1

We establish the existence of a symmetric equilibrium of the form specified in Propo-

sition 1. In what follows, it is useful to let Li ∈ {0, 1} denote firm i’s listing decision,

where Li = 0 represents a decision not to list the price and Li = 1 indicates that the

firm has opted to pay φ to list its price.

A.1 Second Stage Game

In the second stage, the fraction of loyal customers attached to each firm is already

determined. Suppose that in the first stage, firms 2 throughN chose branding level a∗

identified in Proposition 1 and that firm 1 chose branding level a1 ∈ [0, a] . This means

that the fraction of loyal customers for firms 2 though N is β2 = β3 = ... = βN = β

and that β1 is arbitrary. Notice that this nests the symmetric case while allowing for

a unilateral deviation. We construct an equilibrium under these conditions.

Suppose that there exists an equilibrium where all firms are stochastically active

(αi ∈ (0, 1)) and where all firms earn equilibrium profits by listing their price and

pricing at v.Then,

Lemma 1 In any equilibrium where firms are all active with positive probability and

where they earn equilibrium profits by listing and pricing at v, then αi = α = 1 −³³φ

(v−m)(1−B)

´ ¡N

N−1¢´ 1

N−1.

Proof. Since a firm stochastically enters, it must earn equal profits from pricing

41

at v and entering and from pricing at v and staying out. That is,

Eπi (Li = 0) =

Ãβi +

Yj 6=i(1− αj)

1

N(1−B)

!(v −m)

=

Ãβi +

Yj 6=i(1− αj) (1−B)

!(v −m)− φ

= Eπi (Li = 1, v) .

It is equivalent to write

Eπi (Li = 1, v)− Eπi (Li = 0)

=Yj 6=i(1− αj) (1−B) (v −m)

µN − 1N

¶− φ

= 0.

Hence, for all i Yj 6=i(1− αj) =

φ

(v −m) (1−B)

N

N − 1 ,

and since the right-hand side is independent of i and j, it then follows that

Yj 6=i(1− αj) = (1− α)N−1 =

φ

(v −m) (1−B)

N

N − 1

or

1− α =

µµφ

(v −m) (1−B)

¶µN

N − 1

¶¶ 1N−1

. (7)

QED

Notice that when B = Nβ¡a∗, a∗−i

¢, the above expression for α corresponds ex-

actly to equation (1) in Proposition 1.

The following equality is used repeatedly in the remainder of the analysis. For

future reference, we will refer to it as Fact 1.

42

Fact 1:

(1− α)N−1 =1−BN(v −m) (1− α)N−1 + φ

(1−B) (v −m)

To see that the fact is true, notice that, from (7) ,we can rewrite

φ = (1− α)N−1 (v −m) (1−B)

µN − 1N

¶.

Hence, we have

(1− α)N−1 =

µ1

N+

N − 1N

¶(1− α)N−1 ,

and the result is obvious.

Next, we derive price distributions for each of the firms in an equilibrium satisfying

Lemma 1. Let F denote the distribution of prices chosen by firms 2 through N for

prices in the support of firm 1. Let F denote the distribution of prices chosen by firms

2 through N outside this support. Let F1 denote the distribution of prices chosen by

firm 1.

A.1.1 Derivation of F

Firms 2 through N choose prices such that firm 1 is indifferent between listing any

price in its support and not listing its price (and choosing p = v). That is, for all

prices in the support of 1’s price distribution,µβ1 +

1−B

N(1− α)N−1

¶(v −m) =

³β1 + (1−B) (1− αF (p))N−1

´(p−m)− φ.

Solving for 1− αF (p) yields

1− αF (p) =

Ãβ1 (v − p) + 1−B

N(1− α)N−1 (v −m) + φ

(1−B) (p−m)

! 1N−1

. (8)

43

Notice that for the case where, for all i, βi = β¡a∗, a∗−i

¢, this expression is identical

to that in Proposition 1.

Next, we verify that this is a well-defined cdf.

Claim 1. F (·) is strictly increasing in p.

Proof. To see this, notice that

∂ (1− αF )

∂p= − 1

N − 1 (1− αF )2−Nµ

β1 (v −m)

(1−B) (p−m)2

¶< 0.

QED.

Claim 2. F (v) = 1

Proof. At p = 1,we have

1− αF (v) =

Ã1−BN(1− α)N−1 (v −m) + φ

(1−B) (v −m)

! 1N−1

.

Now use fact 1 to simplify the right hand side of this expression to

1− αF (v) = 1− α,

and the claim is proven. QED

To find the lower support of F, we need that 1 − αF (p0) = 1. Solving for p0 in

equation (8) yields

p0 =

½1

1−B + β1(β1v + (1−B)m)

¾+

1

1−B + β1

µ1−B

N(1− α)N−1 (v −m) + φ

¶.

Notice that p0 > m since the term in brackets is a convex combination of m and v

and the other term is positive.

44

Claim 3. p0 is increasing in β1.

To see this, differentiate p0 with respect to β1 to obtain

∂p0∂β1

=1

(1−B + β1)2

µ(v −m) (1−B)− 1−B

N(1− α)N−1 (v −m)− φ

¶=

(v −m) (1−B)

(1−B + β1)2

µ1− 1

N(1− α)N−1 − N − 1

N(1− α)N−1

¶=

(v −m) (1−B)

(1−B + β1)2

³1− (1− α)N−1

´> 0

where the second equality follows from substituting for φ in terms of 1− α and the

inequality follows from the fact that α < 1.

To summarize, we have shown that F is a well-defined, atomless cdf with support

[p0, v] .

A.1.2 Derivation of F

For prices outside the support of 1’s distribution of prices, firms 2 through N choose

prices to keep any of them firm indifferent between listing any price outside 1’s support

and not listing a price (and choosing p = v). That is, for all prices outside the support

of 1’s price distribution, indifference requires:

µβ +

1−B

N(1− α)N−1

¶(v −m) =

³β + (1−B)

¡1− αF (p)

¢N−2´(p−m)− φ.

Solving for 1− αF (p) yields

1− αF (p) =

Ãβ (v − p) + 1−B

N(1− α)N−1 (v −m) + φ

(1−B) (p−m)

! 1N−2

. (9)

45

Next, we verify that this is a well-defined cdf.

Claim 4. F (·) is strictly increasing in p.

To see this, notice that

∂¡1− αF

¢∂p

= − 1

N − 1¡1− αF

¢2−N µ β (v −m)

(1−B) (p−m)2

¶< 0

QED.

Claim 5. The upper support of F , p1 < v.

Proof. Suppose to the contrary that F (v) ≤ 1. This implies

1− α ≤ 1− αF (v) . (10)

Using fact 1, we may rewrite equation (9) as

1− αF (v) ≤ (1− α)N−1N−2 .

Finally, since α ∈ (0, 1) , we know that

(1− α)N−1N−2 < 1− α. (11)

Equations (10) and (11) are mutually contradictory. This proves the claim. QED.

To find the lower support of F , we need that 1 − αF (p0) = 1. Solving for p0 in

equation (9) yields

p0 =

½1

1−B + β(βv + (1−B)m)

¾+

1

1−B + β

µ1−B

N(1− α)N−1 (v −m) + φ

¶.

Notice that p0 > m since the term in brackets is a convex combination of m and v

and the other term is positive.

46

Together, this establishes that F is a well-defined, atomless cdf with support

[p0, p1] where v > p1 > p0 > m.

A.1.3 Derivation of F1

For prices in the intersection of the support of the distribution of firms 2 through N

and firm 1, firms 2 through N must be indifferent between listing a price in this set

and not listing a price (and choosing p = v).

µβ +

1−B

N(1− α)N−1

¶(v −m) =

³β + (1−B) (1− αF )N−2 (1− αF1)

´(p−m)−φ.

Solving for 1− αF1 yields

1− αF1 (p) =1

(1− αF (p))N−2

Ãβ (v − p) + 1−B

N(1− α)N−1 (v −m) + φ

(1−B) (p−m)

!. (12)

It will sometimes be more convenient to write this expression as

1− αF1 (p) =

µ1− αF (p)

1− αF (p)

¶N−2

. (13)

Before proceeding, the following lemma proves useful:

Lemma 2 Suppose that a ∈ [0, a] where a =N−1N−2a

∗ and that firms 2 through N choose

branding levels a∗ identified in Proposition 1, for all a1,

β1β≤ N − 1

N − 2 . (14)

Proof. Since β1 is increasing in a1. It is sufficient to check that equation (14) hold

for a1 close to a.

47

Suppose that a1 = a and firms i = 2, 3, ..., N choose ai = a∗ then

(N − 1)β − (N − 2)β1

=(N − 1) a∗

a+ (N − 1) a∗ δ + (N − 2)σa∗ − (N − 2) a

a+ (N − 1) a∗ δ + (N − 1)σa

=

µδ

a+ (N − 1) a∗ + σ

¶((N − 1) a∗ − (N − 2) a)

= 0

where the last equality follows from the fact that a=N−1N−2a

∗. Since ((N − 1) a∗ − (N − 2) a)

is decreasing in a, it then follows that for all a < a, (N − 1)β − (N − 2)β1 > 0 or,

equivalently, that β1β< N−1

N−2 . QED.

We are now in a position to show that F1 is a well-defined cdf.

Claim 6. F1 (·) is strictly increasing in p.

Proof.

∂ (1− αF1)

∂p=

N − 2(1− αF (p))2

µ1− αF

1− αF

¶N−2µ−α∂F

∂p(1− αF ) + α

∂F

∂p1− αF

¶.

We require that for all p, ∂(1−αF1)∂p

< 0.

Notice that the sign of this expression is negative if and only if

−α∂F∂p(1− αF ) + α

∂F

∂p

¡1− αF

¢< 0

or equivalently

α∂F∂p

1− αF>

α∂F∂p

1− αF.

We show that this inequality holds.

48

First, we substitute for ∂F∂pand ∂F

∂p, we obtain

∆ =α∂F

∂p

1− αF−

α∂F∂p

1− αF

=

µ(v −m)

(1−B) (p−m)2

¶Ãβ

(N − 2)¡1− αF

¢N−2 − β1

(N − 1) (1− αF )N−1

!

=

³(v−m)

(1−B)(p−m)2

´¡1− αF

¢N−2(1− αF )N−1

Ãβ (1− αF )N−1

N − 2 −β1¡1− αF

¢N−2N − 1

!.

Now substitute for (1− αF )N−1 and¡1− αF

¢N−2and factor the denominator to

obtain

∆ = Z

µµβ

N − 2 −β1

N − 1

¶µ1−B

N(1− α)N−1 (v −m) + φ

¶+ (v − p)

ββ1(N − 2) (N − 1)

¶where Z =

(v−m)(1−B)2(p−m)3

(1−αF)N−2

(1−αF )N−1> 0.

Notice that when v = p, ∆ reduces to

Z

µµβ

N − 2 −β1

N − 1

¶µ1−B

N(1− α)N−1 (v −m) + φ

¶¶≥ 0

since β1β≤ N−1

N−2 . Notice that ifβ1β= N−1

N−2 , then ∆ = 0 when v = p but is strictly

positive for all p < z.Hence, the claim is proven. QED

Claim 7. F1 (v) = 1

Proof. To see this, use fact 1 and Claim 2 in equation (12) to obtain

1− αF1 (v) =(1− α)N−1

(1− α)N−2

= 1− α.

QED.

We leave aside the issue of the lower support of F1 until the next subsection.

49

A.1.4 Equilibrium Pricing

First, it’s obvious that F1 and F defined above both have atomless upper supports

at v. The conditions required to apply lemma 1 are satisfied.

For prices that are in the intersection of the supports of all sellers, it is clear

that each seller is indifferent over all such prices. Pricing above the upper support

v, which is the same for all sellers, is clearly not a profitable strategy. Therefore, we

only need to examine the possibility of non-intersecting supports at the bottom of

the distribution.

Define the lower support of seller i to be pi0. Since sellers 2, 3, ..., N are following

identical strategies, let p0 = pi0 for i > 1.

There are three cases to consider:

1. p10 = p0.

In this case, there are no non-intersections of the support. Clearly, a seller pricing

at p0 captures all the shoppers consumers with probability 1. Lowering his price is

therefore not a profitable deviation. Thus, we have shown that for the case where

βi = βj for all i 6= j, the strategies given in Proposition 1 for the second stage game

constitute an equilibrium.

2. p10 < p0.

In this case, the F1defined above does not comprise an equilibrium, as seller 1 can

profitably deviate by reallocating below p0 to p0 However, the resulting distribution,

50

F ∗1 , satisfying

F ∗1 (p) =

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

0 if p < p0

F1 (p0) if p = p0

F1 (p) if v ≥ p > p0

1 if p > v

is part of a Nash equilibrium (Note that even though seller 1 has a mass point at p0,

none of the other sellers distributions contain mass points and thus the probability

of a tie at that price is zero).

3. p10 > p0.

In this case, we only need to check that the distribution of prices for sellers j > 1,

conditional on listing at the gatekeeper’s site, is a legitimate distribution. Recall that

this distribution, which we’ll call F ∗ (p) satisfies

F ∗ (p) =

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

0 if p < p0

F (p) if p0 ≤ p < p10

F (p) if v ≥ p ≥ p10

1 if p > v

.

For this to be a well-defined cdf, we need that

1− αF¡p10¢= 1− αF

¡p10¢.

51

But since at p = p10, F1 (p10) = 0, it follows that

1− αF1¡p10¢

=

µ1− αF (p10)

1− αF (p10)

¶n−2

= 1,

which immediately implies that 1− αF (p10) = 1− αF (p10) .

Thus, we have shown that, conditional on all firms choosing identical branding

levels in the first stage, the pricing strategies listed in Proposition 1 comprise an

equilibrium to the continuation game. Further, we have identified the profitability of

off-equilibrium nodes for the second stage game when one seller deviates. Thus, we

are in a position to analyze the first-stage game.

A.2 First Stage Game

Fix the branding strategies of all firms j 6= i to be aj = a∗. Then from the com-

putations for the second stage game, we know that firm i’s expected profits when it

chooses branding level ai are:

Eπi =

µδ

aiai + (N − 1) a∗

+ aiσ

¶(v −m) +

φ

N − 1 − τai.

Differentiating this expression with respect to a1 and setting this equal to zero, we

obtain the necessary condition for i to maximize its profits:

∂Eπi∂ai

= (v −m)

µ(N − 1) a∗

(ai + (N − 1) a∗)2δ + σ

¶− τ

= 0.

52

Notice that the second order-order conditions also hold, so a solution to this equation

is both necessary and sufficient to constitute a maximum.

In a symmetric equilibrium, it must be that ai = a∗ is a solution to

(v −m)

µ(N − 1) a∗

(ai + (N − 1) a∗)2δ + σ

¶− τ = 0.

That is, a∗must solve:

(v −m)

µ(N − 1)N2a∗

δ + σ

¶− τ = 0

Therefore,

a∗ = δ(N − 1) (v −m)

N2 (τ − (v −m) σ),

which agrees with the expression in Proposition 1.

Thus, we have found a symmetric subgame perfect equilibrium.

Substituting a∗into the β function yields:

β∗ =

µδa∗

A∗+ a∗σ

¶= δ

Nτ − (v −m)σ

N2 (τ − (v −m)σ).

Finally, substituting β∗, a∗ into the expected profits yields the profit expression shown

in Proposition 1.

This completes the proof of Proposition 1.

53

B Comparative Statics Properties of Proposition

1

B.1 Oligopoly Case

This section verifies the comparative statics provided in Table 1 for the case where

N <∞.

Expected Profits (Eπ∗):

Recall

Eπ∗ = (v −m)β∗ +φ

N − 1 − τa∗

= (v −m)δ

N2+

φ

N − 1 .

Hence, it is immediate that ∂Eπ∗/∂δ > 0; ∂Eπ∗/∂σ = ∂Eπ∗/∂τ = 0; ∂Eπ∗/∂N <

0; ∂Eπ∗/∂φ > 0; ∂Eπ∗/∂v > 0; and ∂Eπ∗/∂m < 0.

Branding (a∗):

Recall

a∗ = δ(N − 1) (v −m)

N2 (τ − (v −m) σ).

Hence, it is immediate that ∂a∗/∂δ > 0; ∂a∗/∂σ > 0; ∂a∗/∂τ < 0; ∂a∗/∂φ = 0;

∂a∗/∂v > 0; and ∂a∗/∂m < 0. The final comparative static follows from the fact that

∂a∗

∂N= − (v −m) δ

N − 2N3 (τ − (v −m)σ)

≤ 0.

54

Beta (β∗):

Recall

β∗ =δ

N

µNτ − (v −m)σ

N (τ − (v −m)σ)

¶> 0.

Hence, it is immediate that ∂β∗/∂δ > 0 and ∂Eβ∗/∂φ = 0. The other comparative

statics are:

∂β∗

dσ= δ (v −m) τ

N − 1N2 (τ − (v −m)σ)2

> 0;

dβ∗

dτ= −δσ (v −m) (N − 1)

N2 (τ − (v −m)σ)2< 0;

dβ∗

dN= −δ Nτ − 2 (v −m)σ

N3 (τ − σ (v +m))< 0;

and

dβ∗

d (v −m)= δστ

N − 1N2 ((v −m)σ − τ)2

> 0.

Aggregate loyals (B∗):

Recall

B∗ = Nβ∗.

Hence, all comparative statics (save ∂B∗/∂N) follow directly from those for β∗.

Note that

dB∗

dN= δ (v −m)

σ

N2 (τ − (v −m)σ)> 0.

Lower Support (p0):

Recall that

p0 = m+(v −m)β∗ + φ

(N−1)N

(1− (N − 1)β∗) .

55

Notice that p0 is increasing in β∗. It follows (using the comparative statics for β∗)

that ∂p0/∂δ > 0; ∂p0/∂σ > 0; ∂p0/∂τ < 0; ∂p0/∂φ > 0; and ∂p0/∂v > 0.

Alpha (α∗):

Recall

α∗ ≡ 1−µµ

φ

(v −m) (1−B∗)

¶µN

N − 1

¶¶ 1N−1

Notice that α∗ is decreasing in B∗. It follows (using the comparative statics for

B∗) that ∂α∗/∂δ < 0; ∂α∗/∂σ < 0; ∂α∗/∂τ > 0; and ∂α∗/∂φ < 0.

B.2 Properties as N →∞

This section verifies the comparative statics provided in Table 1 also hold for the case

where N →∞.Note that comparative statics for Eπ, a∗, and β∗ are not relevant, as

individual firms are atomistic in the limit.

Aggregate loyals (B∗):

Recall

BL = limN→∞

Nβ∗

= δτ

τ − (v −m)σ> 0

It is immediate that ∂BL/∂δ > 0; ∂BL/∂σ > 0; ∂BL/∂φ = 0; ∂BL/∂v > 0; and

∂BL/∂m < 0.

Furthermore,

dBL

dτ= −δσ v −m

(τ − (v −m)σ)2< 0

56

Lower Support (pL0 ):

Note that

pL0 =

µm+

φ (τ − (v −m) σ)

(1− δ) τ − (v −m)σ

¶=

µm+

φ

(1−BL)

¶,

and notice that pL0 is increasing in BL. It follows (using the comparative statics for

BL) that ∂pL0 /∂δ > 0; ∂pL0 /∂σ > 0; ∂pL0 /∂τ < 0; ∂pL0 /∂φ > 0; and ∂pL0 /∂v > 0.

Range (RL):

Recall

RL = v − pL0 .

It follows (using the comparative statics for pL0 ) that ∂RL/∂δ < 0; ∂RL/∂σ < 0;

∂RL/∂τ > 0; and ∂RL/∂φ < 0.

B.3 Proof of Proposition 7

To establish this result, it helps to rewrite the equilibrium distribution of advertised

prices as:

F =1

α

³1− (ρ)

1N−1´

where ρ =µ(v−p)β+φ N

N−1(1−Nβ)(p−m)

¶.

Next, we note the following “facts” about various partial derivatives of interest:

1.

57

dα

dβ= − N

(N − 1) (1−Nβ)(1− α) < 0

2.

dp0dβ

=v −m+ φN

(−1 +Nβ − β)2> 0

3.

dρ

dβ=

(v − p) (N − 1) + φN2

(N − 1) (1−Nβ)2 (p−m)> 0

4.

∂ρ

∂p=−β (v −m) (N − 1)− φN

(N − 1) (1−Nβ) (−p+m)2< 0

5.

∂2ρ

∂β∂p=− (v −m) (N − 1)− φN2

(N − 1) (1−Nβ)2 (p−m)2< 0

Finally, it is useful to note that p = v, F = 1 hence

1− (ρ (v))1

N−1 = α

ρ (v) = (1− α)N−1

Further

dρ

dβ|p=v =

φN2

(N − 1) (1−Nβ)2 (v −m)

=N

(1−Nβ)

φ

(v −m) (1−Nβ)

N

N − 1

=N

1−Nβ(1− α)N−1

We are now in a position to prove Proposition 7.

58

Proof. Since β is decreasing in τ , it is sufficient to show that F is decreasing in β.

Since p0 is increasing in β, we need only show that, for all p ∈ [p0, v] , ∂F (p)∂β

< 0.

Differentiating F with respect to β yields

∂F

∂β=

d

dβ

µ1

α

³1− ρ

1N−1

´¶= − 1

α2

³1− ρ

1N−1

´ ∂α

∂β− 1

α

1

N − 1ρ1

N−1−1dρ

dβ

<

µ− 1α2

³1− ρ

1N−1

´ ∂α

∂β

¶|p=v −

µ1

α

1

N − 1ρ1

N−1−1dρ

dβ

¶|p=v

=1

α2(1− (1− α))

N

(N − 1) (1−Nβ)(1− α)− 1

α

1

N − 1 (1− α)2−NN

1−Nβ(1− α)N−1

=1

α

N

(N − 1) (1−Nβ)(1− α)− 1

α

1

N − 1N

1−Nβ(1− α)

= 0

where the inequality follows from the facts derived above.

59

Appendix B: List of Products1 ADOBE ACROBAT 4.0 49 Linksys EtherFast 4-port Cable/DSL Router2 ADOBE PHOTOSHOP V5.5 50 19IN/18.0V 26MM 1600X1200 85HZ SYNCMASTER 950P TCO99 MPRII PNP3 AMD K6 2 - 500 MHz 51 3dfx Voodoo 3 30004 AMD K7 - 700 MHz 52 64MB 8X64 SDRAM PC133 8NS5 AMD K7 - 750 MHz 53 72Pin Simm NonParity Edo 64MB6 AMD K7 - 800 MHz 54 NORTON ANTIVIRUS 2000 V6.0 RETAIL BOX WIN95/98/NT SINGLE 1DOC7 AMD K7 - 850 MHz 55 NORTON ANTIVIRUS V5.0 WIN 95/98/NT SINGLE 1-DOC8 BE6-II 56 NORTON CLEANSWEEP 2000 V4.7 WIN95/98/NT SINGLE 1-DOC9 COMPAQ PRESARIO 7360 REFURBISHED BY COMPAQ 57 NetGear RT311 DSL & Cable Modem Router

10 Canon PowerShot S10 58 Nikon Coolpix 80011 Canon PowerShot S100 59 Nikon Coolpix 95012 Canon PowerShot S20 60 Nikon Coolpix 99013 Compaq CPWAP500 (Pentium II 450 MHz) 61 Office 2000 - Professional Edition14 Compaq Presario 1200-XL118 62 Olympus C-2020 Zoom15 Compaq Presario 5868 63 Olympus C-3000 Zoom16 Compaq Presario 7940 64 Olympus C-3030 Zoom17 Compaq iPaq H3650 Pocket PC 65 Olympus D-460 Zoom18 Creative Labs 3D Blaster Annihilator 66 PAINT SHOP PRO V6.0 CD W9X/NT19 Creative Labs 3D Blaster Annihilator Pro 67 PC100 Sdram NonEcc 64MB 8x6420 Creative Labs Desktop Theater 5.1 DTT2500 Digital 68 PENTIUM III P3 733MHZ 256KB L2 133MHZ SLOT1 COPPERMINE .18MU21 Creative Labs Nomad 64 MP3 Player 69 POWERSHOT PRO70 DIGITAL CAMERA CCD SENSOR W/CONTINUOUS ZOOM CPBL22 Creative Labs Nomad II 70 Palm III23 Creative Labs PC DVD-RAM (SCSI) 71 Palm IIIc24 Creative Labs Sound Blaster Live Platinum 72 Palm IIIe25 Creative Labs Sound Blaster Live Value 73 Palm IIIe Special Edition26 Creative Labs Sound Blaster PCI128 sound card 74 Palm IIIx27 DESKPRO EN P3-450 9.1GB 64MB 75 Palm IIIxe28 Dell Inspiron 7500 (Pentium III 600MHz 96MB RAM 6GB HD) 76 Palm M10029 ELSA Gladiac GeForce2 GTS 77 Palm V30 EPHOTO CL50 COL DIGTLCAM DIGITAL CAMERA 78 Palm VII31 Epson Stylus Photo 1270 79 Palm Vx32 Epson Stylus Photo 870 80 Panasonic KXL-RW10A33 EpsonStylus Color 740 81 Pentium III - 600 MHz34 Fuji FinePix 4700 Zoom 82 Pentium III - 700 MHz35 HP CD-Writer Plus 8200i (24X/4X/4X Internal) 83 Pentium III - 800 MHz36 HP CD-Writer Plus 9100i (32X/8X/4X) 84 Plextor PlexWriter 32X/8X/4X CD-RW drive37 HP Kayak XA 85 Plextor Plexwriter 12X/10X/32X CD-RW38 HP LaserJet 1100xi 86 SATELLITE 2210XCDS CEL-500 6GB 64MB 13 DSCAN 24X V90 WIN 9839 HP ScanJet 6300Cxi 87 Sony Cyber Shot DSC-S7040 Handspring Visor 88 Sony MVC-FD91 Digital Mavica41 Handspring Visor Deluxe 89 Sony MVC-FD95 Digital Mavica42 IBM ThinkPad 240 90 Sony VAIO PCG-F420 (128MB RAM 12.0GB HD)43 IBM Thinkpad T20 91 Toshiba Satelite 2180CDT (AMD K6-2 475 MHz 4.3GB HD)44 INTELLIMOUSE EXPLORER CD W9X PS2/USB 92 ViewSonic PF79045 INTELLIMOUSE INTELLIEYE SOLID STATE PS2/USB - NO MOVIN 93 WINDOWS 2000 PROFESSIONAL W2K46 Iomega 250MB USB ZIP Drive 94 WINDOWS 98 SECOND EDITION47 Kodak DC280 Zoom 95 Western Digital Caviar 20.5GB EIDE48 Kodak DC290 Zoom 96 emachines eOne 433

Figure 1: Calibrated Means

$50

$100

$150

$200

$250

$300

$350

$400

$450

$500

$550

$600

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Fraction of Loyal Customers

Range Average Price Minimum Price Maximum Price

Figure 2: Price Range over Time

Ave

rage

Pric

e R

ange

(in

Dol

lars

)

Collection Date21aug2000 22mar2001

0

50

100

150

200

250

Number of Products 96Number of Dates 214Number of Prices 291,365

Price Mean Std. Dev MedianAverage Price $455.99 $496.22 $321.92Lowest Price $386.95 $414.20 $279.95Highest Price $549.20 $584.47 $399.99

Advertising Levels Mean Std. Dev MedianNumber of Advertised Prices 28.18 17.66 29.00Promotion Intensity 8.05% 6.67% 7.89%

Price Dispersion Mean Std. Dev MedianPrice Range $162.25 $227.98 $100.01

Table 1: Data Summary

Total Observations

Product Summary Statistics

1 2 3 4 5 6Branding 126.11 127.65 21.15 131.25 127.52 146.47

(4.87)** (4.92)** -0.67 (5.24)** (3.77)** (5.79)**Branding^2 332.43

(2.16)*# of Firms -0.59 -1.18 -0.94 -0.24 -1.17 -2.42

(8.05)** (4.74)** (3.98)** -1.19 (6.46)** (6.52)**# of Firms^2 0.01 0.01 0.00 0.01

(3.02)** (2.37)* -0.57 (3.39)**

Product Fixed Effects Y Y Y Y Y YRank Fixed Effects Y YDate Fixed Effects YInstrumental Variables Y

Observations 10013 10013 10013 10013 10013 10013R-squared 0.99 0.99 0.99 0.99 0.99 0.99Robust t statistics in parentheses* significant at 5%; ** significant at 1%

Table 2: Average Price Regressions

Model

1 2 3 4 5 6Branding 259.48 261.84 24.67 268.85 300.77 283.59

(5.22)** (5.25)** -0.43 (5.49)** (4.69)** (5.86)**Branding^2 740.28

(2.52)*# of Firms -1.05 -1.95 -1.41 -1.13 -2.28 -3.22

(10.64)** (5.83)** (4.75)** (3.32)** (7.46)** (7.61)**# of Firms^2 0.02 0.01 0.01 0.02

(3.42)** (2.40)* -1.41 (4.63)**

Product Fixed Effects Y Y Y Y Y YRank Fixed Effects Y YDate Fixed Effects YInstrumental Variables Y

Observations 10013 10013 10013 10013 10013 10013R-squared 0.98 0.98 0.98 0.98 0.99 0.98Robust t statistics in parentheses* significant at 5%; ** significant at 1%

Table 3: Minimum Price Regressions

Model

1 2 3 4 5 6Branding -222.89 -227.48 64.12 -226.19 -364.27 -237.49

(4.91)** (5.02)** -1.09 (5.04)** (6.87)** (5.31)**Branding^2 -910.19

(3.37)**# of Firms 2.64 4.41 3.74 4.10 1.91 3.95

(22.63)** (11.43)** (10.18)** (9.37)** (4.98)** (8.75)**# of Firms^2 -0.03 -0.02 -0.03 0.00

(5.17)** (4.14)** (4.35)** -0.62

Product Fixed Effects Y Y Y Y Y YRank Fixed Effects Y YDate Fixed Effects YInstrumental Variables Y

Observations 10013 10013 10013 10013 10013 10013R-squared 0.89 0.89 0.89 0.89 0.9 0.89Robust t statistics in parentheses* significant at 5%; ** significant at 1%

Table 4: Range Regressions

Model