ECONOMIC RESEARCH CENTERDISCUSSION PAPER
E-Series

No.E13-6

Product differentiation and advertising in
multiple markets
byToshiki Kodera
Wenjiao Che

July 2013

ECONOMIC RESEARCH CENTERGRADUATE SCHOOL OF ECONOMICSNAGOYA UNIVERSITY

Product di¤erentiation and advertising in
multiple markets
Toshiki Kodera
Wenjiao Chey
Graduate School of Economics, Nagoya University
July 14, 2013

Abstract
A study of the Hotelling location game where media platforms compete
on two separate markets with the same content has been carried out. The…ndings show that media platforms may provide less di¤erentiated content
if non-negative price constraint binds in at least one market. Content
di¤erentiation decreases in the size of market where the constraint binds.
Keywords: Two-sided markets; Multiple markets; Product di¤erentiatione-mail: kodera@soec.nagoya-u.ac.jp
wenjiao.s.che@gmail.com; The author acknowledges the …nancial support from
China Scholarship Council.
y e-mail:1Introduction

Nowadays, many media platforms operate business simultaneously in several different markets to maximize bene…ts or to gain competitive advantage. Taking
CNN and NBC as examples, they serve their programs in the US and also operate in other countries. Besides, CNBC and Bloomberg TV provide …nance programs to both US and international audiences. They both have an Asia branch,
and Bloomberg TV Asia broadcasts its programs almost for free in China. Eachmarket is heterogeneous with respect to consumer preferences, market size andcompetitive structure; therefore, it is important to satisfy each market according to unique characteristics. However, sometimes media platforms that are
active in multiple markets are unable to tailor content (or political view in thestrict sense) to each market. So, to investigate how media platforms behave
in product positioning when operating in several heterogeneous markets is aninteresting topic, and is the purpose of this paper.
The Hotelling location game is analyzed where two media platforms compete in two separate markets, but with the same content. The platforms choose
the intensity of advertising and/or subscription fee. Our conclusions show how
product positioning is a¤ected by market size, competition intensity, and thenon-negativity constraint on prices. When there is no restriction with respect
to price, media platforms maximally di¤erentiate content. In each market ofour model competition e¤ect dominates demand e¤ect, so even if they operate
in di¤erent markets, platforms maximize di¤erentiation (just as the standard
Hotelling model) with quadratic transportation costs. However, if we restrict
price to be non-negative, the outcome changes: partial di¤erentiation may arise
if the non-negative constraint binds. Since advertising revenue is the only revenue source for the market where the constraint binds, media platforms, if competing only in this market, will choose content that o¤ers maximum advertising
revenue, but not necessarily endpoints. In contrast, competition e¤ect still
dominates in the market where the constraint unbinds, thus yielding maximaldi¤erentiation. Therefore, when the former market is su¢ ciently important inrevenue composition, the media platforms competing in multiple markets will
choose their content closer to the location to generate maximum advertising
revenues, which may lead to partial di¤erentiation.
There are several papers related to the present analysis. Gabszewicz et al.
(2001; 2002) assume that viewers are indi¤erent about the level of advertising, and show that the degree of di¤erentiation depends on unit receipt fromadvertising. When viewers dislike advertising, Gabszewicz et al. (2004) conclude that maximal di¤erentiation arises under ad-supported media (when thedisutility from advertising is linear in the advertising level). The paper by GalOr and Dukes (2003) o¤ers an explanation for minimum di¤erentiation, which
relies on the role of advertising as information about products and as a nuisance to consumers. Peitz and Valletti (2008) consider the content location andadvertising provision under pay-tv and free-to-air. Their model shares several
properties with ours. In particular, the con…guration is competitive bottlenecks
and viewers dislike ads. They show that pay-tv always maximally di¤erentiates
content whereas ad-sponsored media platforms may provide less di¤erentiatedcontent. The above papers analyze the endogenous content in a single market
within the Hotelling framework. However, none of them consider the media decisions regarding content choice when competition occurs in several heterogeneous2

markets. This is important because, with technology development and the information expansion, many media platforms compete across many markets. Ourmodel includes this impact and thereby allows us to provide an explanation to
the program diversity across markets. Of course, Loertscher and Muehlheusser(2008) also analyze a similar question. However, our models di¤er in several
aspects. First, in their model the media platforms are active in several markets
but only compete with local media in each single market with the same product, while in ours all the media platforms compete across markets. Second, ourresults depend on advertising revenues and content revenues, which are omitted
by Loertscher and Muehlheusser (2008). In addition, they show that producthomogeneity arises due to such multiple-market media, which is in contrast to
our result of content di¤erentiation.
The remainder of this paper is organized as follows: section 2 establishes thebasic model, the equilibrium is analyzed in section 3, and section 4 provides theconclusion.

2

Model

There are two separated media markets k = 1; 2. These markets di¤er in size
and it is assumed that the size of market 2 is N times larger than market 1.
Consider two media platforms i = A; B that serve two types of agents: viewers
who like to watch content, and advertisers who want to inform consumers about
their products via the media. Media platforms provide the same content for bothmarkets which are in the interval [0; 1].
Viewers in each market are distributed uniformly on the interval [0; 1] with
2[0; 1] representing their preferences. When consuming content that doesk
not satisfy his or her taste, a viewer incurs a disutility that is related to thesquare of the distance of his or her chosen platform from their location on the22line, namely k ( k dA ) (or k (1 dBk ) ) with k > 0 designating thetransportation cost parameter and dA (or 1 dB ) the location of media platform
A (or B).1 Assume that the transportation cost parameter in market 1 is higher
than that in market 2, i.e., 1 > 2 , which implies that viewers consider content
more substitutable in market 2 than that in market 1.2 For example, viewers in
the US have strong persistence of political news, compared to viewers in othercountries. Viewers are assumed to dislike ads, so if content contains aki amountof advertising, the utility of type- k viewer who chooses platform A in market
k is given by
UkA = vk

akA

k( k

2

dA )

pkA ; k=1;2

where vk is the intrinsic utility in market k, which is assumed to be large enoughto ensure full market coverage.3 pkA is the subscription fee for platform A in
1 When platforms endogenously select their locations in the Hotelling model, the speci…cation of quadratic transportation costs can guarantee the existence of an equilibrium, which
may not exist with linear transportation costs. We use the speci…cation of quadratic transportation costs to simplify the analysis. Yet, this does not seem to be a very restrictive
assumption.
2 Please note that market size N has opposing e¤ects when
1 < 2 is assumed.
3 Without loss of generality, in the following we assume that v is same in both markets,
ki.e., v1 = v2 = v:

3market k and the disutility parameter for advertising. Here, 0 < < 1 isneeded to guarantee non-negative advertising levels.
Advertisers of mass 1 are characterized by parameter , which is uniformly
distributed on the interval [0; 1]. A type- advertiser can obtain pro…t fromeach viewer who sees the ads. So, advertisers will place ads on a platform withacceptable viewer size xki and advertising price rki if xki rki , thus implyingthat advertising quantity in this platform is aki = 1 rki =xki .
Media platforms have two sources of revenue: viewers and advertisers. So,
platform i’s pro…t generated in market 1 and 2 is given by:=
1i + 2i = x1i p1i + a1i r1i + N x2i p2i + a2i r2i= x1i [p1i + a1i (1 a1i )] + N x2i [p2i + a2i (1 a2i )] ; i=A;B:i

We consider a 3-stage game. Media platform A and B …rst determine theircontent locations to maximize the gross pro…ts in these two markets. Then A
and B choose a subscription fee and advertising intensity in both market 1 andmarket 2.4

3

Equilibrium

3.1

Without non-negative constraint

We …rst derive the viewer number of media platform i in market 2, which is
given as follows:x2i =1 + di2(a2i a2j ) + (p2i p2j ); i6=j, i;j=A;B:
2 2 (1 di dj )djPlatform i chooses the strategic variables a2i and p2i to maximize…rst-order conditions are as follows:@ i@x2i= N x2i +p + a2i (1@p2i@p2i 2i@ i@x2i=Np + a2i (1@a2i@a2i 2i

a2i )

a2i )

@x2i
+ (1
@a2i

(1)
i :The@x2i= 0; i=A;B
@p2i

(2)

2a2i ) x2i = 0; i=A;B:(3)

Analogous analysis can be applied to market 1. The subscription fee andadvertising level for each platform in di¤erent markets are thus given as follows:

aki =

1
2

; pki =(1didj ) (3 + di
3

dj )

k

2

1
4

; i6=j, i;j=A;B, k=1;2.

(4)
Sum up the pro…ts generated in market 1 and 2, and the equilibrium pro…tis given by:i =1( 1 + N 2 ) (di182

dj + 3) (1didj ) :

4 The results will not change if media platforms make decisions in market 1 and 2 simultaneously.

4By di¤erentiating the pro…t function, we can show that media platforms
locate at the endpoints, i.e., d1 = d2 = 0.5
In our model, since market 1 and 2 are independent and almost homogeneous,
except for market size and the degree of substitution, we focus on market k
2
to interpret the equilibrium prices and location. The term (1)=4 in thesubscription fee pki in (4) denotes the advertising revenue per viewer. The
price expression in (4) implies that all the per viewer advertising revenues are
passed onto viewers by a form of lower price, namely advertising revenues do
not a¤ect the pro…ts of platforms.6 In our model, there is no competition forviewers and advertisers across these two markets, so, together with the result of"pro…t neutrality", we can regard each market as a standard Hotelling model.
Two counteracting forces a¤ect the location in each market: the increase of
captive consumers (i.e., the demand e¤ect) and the intense price competition(i.e., the competition e¤ect) when platforms move closer to each other. With
quadratic transportation costs the latter e¤ect always dominates, thus maximum
di¤erentiation arises in our model.

3.2

With non-negative constraint

The above analysis allows for negative prices, but in some cases platforms do not
subsidize viewers. This may be due to huge transaction costs, technical reason
or platforms’ unwillingness to do so. Thus from now on we consider the casein which platforms only charge zero price when non-negative constraint binds.
Since 1 > 2 , there are two cases: one that only the constraint in market 2binds and the other where the constraint binds in both markets. In this paper,
we mainly consider the …rst case.7 To consider the case where the subscription
fee in market 2 is negative, suppose that is su¢ ciently small given platform
locations, i.e., 2 < 1 4 (1 di dj ) (3 + di dj ) 2 =3: In this case, the …rstorder condition to determine the advertising intensity for platform i in market
2 changes as follows:@ i= N a2i (1
@a2i

a2i )

@x2i
+ (1
@a2i

2a2i ) x2i = 0; i=A;B:

For symmetric locations, the equilibrium advertising level in market 2 is givenbysa2 = a2i =

1
+
2

2 (1

2d)

(2d

2

1)

2
1
2
2 + 4:

This symmetric equilibrium advertising level corresponds to the uniform distribution case of Peitz and Valletti (2008). It can be shown that when viewers do
not mind much being exposed to advertising, the advertising level a2 decreases
with the disutility parameter for advertising . For the …rst market, the …rstorder conditions are still analogous to expressions (2) and (3), so given locationsof platforms we can obtain the same results as those in section 3.1.
5 In our model, the …rst-order condition at stage 1 is similar to that in the standard Hotellingmodel.
6 According to Peitz and Valletti (2008), this phenomenon is called "pro…t neutrality". It issurely an artifact of the model setup that media platforms choose the intensity of advertising,and this setting simpli…es the analysis without loss of generality.
7 It can be derived that platforms may locate partially on the line when the non-negative
constraint binds in both markets.

5We now consider the stage where platforms choose the content. If the …rstorder condition at stage 1 holds, we have the following equation:@ i= [p1i + a1i (1@dia1i )]+N a2i (1

a2i )

@x1i
@x1i @a1j@x1i @p1j++@di@a1j @di@p1j @di@x2i@x2i @a2j
+
= 0:
@di
@a2j @di

For symmetric equilibrium, the above equation can be expressed as(1 + 4d)
61+ N a2 (1

a2 )

1
+
2 2 (1@a2j2d) 2 @didi =dj =d

= 0:

(5)

By analyzing the relationship between market size N and the content di¤erentiation, we have the following proposition.
Proposition 1 When non-negative price constraint binds in market 2, for small, the symmetric equilibrium content di¤ erentiation decreases in N , and for suf…ciently small N maximal di¤ erentiation arises.
Proof is available in the appendices.
When the non-negative constraint on prices binds in market 2, advertising revenue becomes the only revenue source. So, if platforms compete onlyin this market, then the location is chosen at the point where the advertising
revenue is maximized. In market 2, there are two e¤ects for location decision:
demand e¤ect and competition e¤ect of advertising level, whose relative magnitude is ambiguous.8 As for market 1, the non-negative constraint does notbind. Thus, the analysis in the last section can be applied here: competitione¤ect dominates demand e¤ect, thus the principle of maximum di¤erentiationarises. When competing in multiple markets with the same content, media
platforms trade-o¤ revenues generated from these two markets: the e¤ects inmarket 1 make maximum di¤erentiation desirable while the advertising revenues
in market 2 may induce incentives to increase content duplication. When market 2’s size is relatively large, advertising revenue becomes more important. So
media platforms choose content which is much closer to the advertising-revenuemaximizing point. When market 2’s size N is su¢ ciently large, media platforms
decrease the di¤erentiation between contents: the larger N , the closer the location to the case where media platforms operate only in market 2. In contrast,
when market 2’s size is not so large, the revenues from market 1 are relatively
important than those from market 2, namely platforms maximally di¤erentiate
the content when N is small. Figure 1 displays the relationship between the
program content d and market 2’s size N for 1 = 1, = 0:2 and 2 = 0:2.
The horizontal dashed line corresponds to the case where ad-supported media
competes only in market 2, while the solid curve represents the case where platforms operate in two markets. Figure 1 shows that d is increasing in N and forsmall N , d = 0.
Di¤erentiating d with respect to , 1 and 2 yields the following comparativestatic results on the equilibrium content:
8 According to Peitz and Valletti (2008), when advertising is not so much of a nuisance(i.e., is small), platforms provide less di¤erentiated content if competing only in market 2.

6

d
0.5

0.3

0.1

5

10

15

20

Figure 1: The Relationship Between d and N

25

N

Corollary 1 If market 2’s size N is su¢ ciently large (i.e., partial di¤ erentiation arises when platforms compete in multiple markets), the equilibrium content
d increases with 2 but decreases with and 1 .
As the nuisance cost parameter increases, platforms di¤erentiate more.
This is due to high value of that makes viewers become more sensitive to advertising. In market 2, platforms, by di¤erentiating content, obtain some degreeof market power over their viewers. This allows them to place ads without losing viewers. In market 1, the parameter does not have impact on the location
choice. Thus, with the same argument as above, platforms, when competingin those two markets, di¤erentiate more as increases. We can make a similar
analysis for 2 . But platforms’incentive to di¤erentiate content decreases as 2
increases. The fact that viewers regard content as hardly substitutable (large2 ) makes platforms’market power over viewers increase. Equilibrium content
d and 1 also have a negative relationship: as 1 gets smaller, the competitionin market 1 becomes more intense, which makes the pro…t generated from thismarket shrink relative to that from market 2. Thus platforms have incentives
to move away from the endpoints, which can be explained by the same reason
previously mentioned.

4

Conclusion

In this paper we investigate a Hotelling model where media platforms compete
in two heterogeneous markets. Our …ndings are closely related to the nonnegative constraint imposed on the per-viewer price: it shows that if there is norestriction on price, media platforms maximally di¤erentiate their content; bycontrast, less di¤erentiated content may be provided if non-negative constraint
binds.
7

We have speci…ed a relatively simple model where there is no competition
for viewers and advertisers across media markets. Our model can …t some phenomena. However, in some cases there still exists competition for viewers, advertisers, or both. So, relaxing this assumption might yield interesting insights,
which should be undertaken in future research.

Appendix
Proof of Proposition 1.
In equation (5), the e¤ect of a change in content of platform i on advertisingintensity of platform j in market 2 can be expressed as
h 2
i
2
2a
(1
a
)
(2
d)
a
(1
a
)
+
2
(1
d)
(1
2d)
2
2
2
2
2
@a2j
2
< 0:
d =d =d =2@di i j
4
2
2
2
2 (1
a
)
+
2
a
a
(1
a
)
+
2
(1
2d)
4
2
2
2
2
2
2
2

2

We focus on the second term of (5) to consider location choice in market 2.
The second term of (5) is similar to equation (12) in Peitz and Valletti (2008),
therefore it is easy to show that platformsqnever duplicate content for > 0 andpdi¤erentiate content maximally if > 2 2 1 + 2 =a2 (1 a2 ) in market 2.
For lower values of , a platform has an incentive to partially di¤erentiate fromthe other platform in market 2. If we consider the case which is small andplatforms compete in both market 1 and 2, the content choice at the …rst stage
depends on the relative size of these two markets, i.e., N . If N is close to in…nite,a platform chooses its content paying attention to market 2 only, whose analysis
is similar to Peitz and Valletti (2008). At N ! 0, the LHS of (5) is negative,
namely@ i(1 + 4d) 1lim< 0;
di =dj =d =N !0 @di6
so maximal di¤erentiation arises.
Next, when N has intermediate values, we consider the e¤ect of a larger
market size on content di¤erentiation. We de…ne '(d; N ) as the equation (5)divided by N :'(d; N )(1 + 4d)
6N

1+ a2 (11+
2 2 (1

a2 )

2d)

@a2j
2 @di

di =dj =d= 0:

Using the implicit function theorem,dd=dN@'(d; N )=@N=@'(d; N )=@d

(1 + 4d) 1> 0:@'(d; N )=@d6N 2

The term @'(d; N )=@d consists of the second-order condition in stage ofddcontent choice, which is negative. Therefore, dN> 0, namely, content di¤erentiation is decreasing in N in the symmetric sub-game perfect equilibrium

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