Competition in the news industry: …ghting aggregators
with versions and links
Joan Calzaday and Guillem Ordóñezz
February 13, 2014
Abstract
We examine the product line of a media publisher that can release two newspapers.
The publisher competes with either a blog or with a news search engine and has to
decide on its versioning and linking strategies. The possibility that a competitor uses the
publisher’s contents to elaborate its own news items generates distinct results to those
reported in the versioning literature. We show that when the publisher competes with a
blog it is less likely to release a “…ghting newspaper” if it cannot prevent its competitor
from using its contents. When the publisher competes with a search engine, it agrees to the
links and does not release a low quality newspaper, provided that it receives a substantial
number of indirect visitors from the search engine. When this occurs, the search engine
becomes a distribution channel for the publisher and competition is weakened. Finally,
we demonstrate that when the publisher is integrated with a search engine it may link up
with other publishers to increase its audience, if their respective contents are su¢ ciently
di¤erentiated.
Keywords: Product segmentation, versioning, linking, media market, search engines,
news aggregators, Internet.
We thank Christian M. Bender, Luis Collado, Martin Peitz, Joan Santaló, Tommaso Valletti and Yaron
Yehezkel for helpful comments. We also thank participants at the 3rd Workshop on the Economics of ICTs
(Porto), EARIE (Rome), JIE (Murcia), 11th Workshop on Media Economics (Tel Aviv) and at seminars at
Paris Tech, Universitat de Barcelona, Universitat Autonoma de Barcelona and Universidad Complutense de
Madrid. We gratefully acknowledge …nantial support from the NET Institute (www.NETinst.org).
y Departament de Política Econòmica, Universitat de Barcelona. calzada@ub.edu.
z Department of Economics, University of Warwick. g.ordonez-cala…@warwick.ac.uk
1
JEL: D83, D85, L12, L22, L86, M31
1
Introduction
The newspaper industry is undergoing a major transformation.1 Internet has signi…cantly
reduced the costs of accessing information and of distributing the contents globally and this
has favored the creation of many news services that compete with online newspapers. In this
new scenario, media publishers seek out new competitive strategies and business models to
retain consumers and advertisers. This paper analyzes how the changes in the industry are
modifying publishersâeTM linking and versioning strategies.
Some of the most successful new players in the media market are news search engines and
news aggregators, which have risen to occupy the top positions in audience rankings (Nielsen
2011). Search engines, such as Google News, Bing News or Summify, provide links to the news
stories of online newspapers and display them at a single site accompanied by a title and a
brief excerpt. This represents a considerable saving to consumers in terms of time and e¤ort
as they can simultaneously check several information sources for updates.2 Search engines
use algorithms that index and group stories according to a range of criteria, including the
originality of information, their immediate interest for readers and their “contagious”capacity.
In many instances, search engines neither hang advertisements nor set user charges. Their
commercial objective is essentially to re-direct visitors to other sites on the same platform,
such as common searchers that sell advertising space or social platforms. News aggregators
di¤er slightly, inasmuch as they publish pieces of news created with information obtained
from newspapers and press agencies, and usually they do not provide links to their original
sources. For this reason, they enter into licensing agreements with information suppliers to
avoid copyright infringements. Some of the best known aggregators are Yahoo! News, Drudge
Report, and The Hu¢ ngton Post.
The emergence of search engines has generated considerable controversy in the industry
regarding their impact on competition and the future of journalism. On the one hand, search
engines give rise to a business-stealing e¤ect since they use the contents from traditional newspapers to attract visitors. Some publishers consider search engines to be free-riders reselling
1 Figures
for 2002 show that the newspaper industry represented roughly a $50 billion business and employed
around 400,000 people. However, today it is facing a severe crisis in part due to the migration of readers from
printed newspapers to online news sources (PEJ, 2011).
2 make a “transformative” use of contents and, as a consequence, do not infringe copyright law (Isbell, 2010).
1
the information they have gathered at vast expense (Frijters and Velamuri, 2010).3 On the
other hand, search engines can expand a publisher’s market share because their visitors usually
click through to the original contents of newspapers.4 Moreover, search engines increase the
number of consumers participating in the content ecosystem, as they reduce consumers’search
costs by presenting the news items of several newspapers on the same news site. This might
explain why most publishers have adopted search engines and accept their links.
Traditional publishers have adopted various strategies to defend themselves against new
competitors. Some publishers claim they still have signi…cant demand from readers that prize
high quality journalism and editorial guidance, and as a consequence have developed new
pricing schemes to increase their revenues. For example, The Times launched a pay wall in
2010 and The Wall Street Journal has recently launched “freemium”, whereby general news
remains free but premium contents and some blogs are locked behind a paywall. Similarly,
the Financial Times o¤ers subscriptions to premium and standard articles at di¤erent prices.5
Publisher have also reacted to competition by creating additional news sites that directly
compete with their own online newspapers. For example, some publishers, such as News
Corporation or the Graham Holding Company, own several radio and television stations that
o¤er news. Others have created news sites that have been speci…cally adapted to the habits
of Internet users. For example, in 2011 AOL released Editions and News Corporation released
The Daily, two news sites for iPad. The New York Times has recently launched Video, a
section of its news site that shows the news with original video programming. Finally, some
publishers have tried to increase their audiences by buying news aggregators. For example, in
2005 Gannet bought Topix.net, and in 2011 AOL bought The Hu¢ ngton Post.
This study aims to analyze the product line of a media publisher that faces competition
from a search engine. Our model should help media managers understand the implications
3 R.
is
Murdoch
theft”.
See
has
The
declared:
Guardian,
“To
aggregate
1/12/2009,
stories
“There’s
is
no
not
such
fair
use.
thing
To
as
a
be
free
impolite,
news
it
story”,
http://www.guardian.co.uk/media/2009/dec/01/rupert-murdoch-no-free-news.
4 Evidence suggests, however, that 44% of Google News! users in 2010 did not Click through to the original
articles. http://techcrunch.com/2010/01/19/outsell-google-news/.
5 Other examples include the plans of the New York Times to erect a paywall or those of News Limited to
charge for access to certain parts of the Daily Telegraph and Herald Sun. See The Conversation, 8/6/2011,
http://theconversation.edu.au/news-ltd-announces-pay-wall-plan-as-newspapers-struggle-nline-1743.
2
of their versioning and linking strategies. We show that publishers can release low quality
newspapers to …ght search engines, but that they might prefer to accommodate competitors
and accept their links if this increases the number of visitors they receive. Indeed, linking can
be a better marketing strategy than versioning because it transforms the search engines’web
sites into additional distribution channels for publishers.
Our paper contributes to the recent literature analyzing the impact of news aggregators on
the managerial strategies of publishers. Katona and Sarvary (2008) were the …rst to analyze
theoretically strategic linking between web sites in a market for advertising links. Dellarocas et
al. (2013) examine competition between news sites that generate revenue from user visits and
which compete with each other as well as with alternative media (e.g. TV, blogs, Twitter feeds)
for user attention. In their model, news sites decide how much to invest in original content
and how many links to include. The authors show that links between content providers can
increase joint pro…ts and quality. They also show that aggregators facilitate consumer access to
good content and increase the attractiveness of the content ecosystem. Moreover, aggregators
foster competition between content providers. George and Hogendorn (2012) adapt a two-sided
market model to digital media markets to examine how search technology and aggregators can
alter both market participation and the number of sites visited. They explain that both
aggregators and improved search technology tend to increase viewer multi-homing. But unlike
search engines, aggregators may not expand the market. Finally, Jeon and Nasr (2012) show
how aggregators a¤ect competition between newspapers. They …nd that the presence of a
news aggregator may lead to the specialization of newspapers when their advertising revenue
increases substantially with an increase in quality. With specialization, the aggregator increases
the average quality of newspapers, which in turn increases consumer surplus.
Our paper also contributes to the economic literature on versioning. The seminal papers
of Mussa and Rosen (1978) and Moorthy (1984) showed that the introduction of a new version
by a monopolist is pro…table when the bene…ts of expanding the market overcome the cannibalization e¤ect on the original product. Stokey (1979) and Salant (1989) later showed that
versioning is optimal when the marginal cost function of improving the quality is su¢ ciently
convex. More recently, Bhargava and Choundary (2008) have explained that versioning depends on the relation between the optimal market share of the low and high quality versions
3
when they are o¤ered alone, and Anderson and Dana (2009) have shown that versioning requires that the relative change in overall surplus associated with an improvement in product
quality is increasing in consumers’willingness to pay. Calzada and Valletti (2012) demonstrate
that the distribution of a service through di¤erent channels might arise when consumers are
allowed to buy two versions. This assumption is closely related to the case discussed here, since
the main characteristic of aggregators is to allow consumers to access the contents of several
newspapers.
Other studies have analyzed versioning in the presence of competition. Wu, Chen and
Anandalingam (2003) show that versioning can be an e¤ective instrument in the …ght against
piracy.6 Valletti and Szymanski (2006) report that pharmaceutical …rms only …nd it optimal to
release a lower quality version when they compete with a generic product. Our paper is closely
related to this study, since we analyze the versioning of a publisher that faces competition from
other web sites. A remarkable di¤erence is, however, that the contents distributed by online
newspapers can be immediately used or linked by other news sites. We show that this change
generates novel results.
Our paper extends the traditional models of Mussa and Rosen (1978) and Moorthy and
Png (1992) to examine the versioning policy of a publisher that competes with other news
sites. The publisher can o¤er two news sites of di¤erent qualities and/or editorial approaches,
as is the case of the News Corporation or The New York Times Co, which publish a large
number of online newspapers and news sites.7 As a benchmark, we …rst analyze the e¤ects
produced by a blog (or a news site) that uses the publisher’s news items to create its own
contents, but which does not link to the publisher’s newspapers. We show that a competitor
of this type reduces the publisher’s incentives to release a second news site. While in Valletti
and Szymanski (2006) the incumbent releases a “…ghting version” to defend itself against the
competitor, in our model this option is less likely because the …ghting version generates positive
spillovers that increase the quality of the blog.
We then consider the case of a publisher that competes against a search engine. We …nd
that the publisher agrees to be linked by the search engine if this generates su¢ cient indirect
6 An
early analysis of this issue can be found in Johnson and Myatt (2003).
we could consider one newspaper that commercializes high and low quality pieces of news,
7 Alternatively,
as in the freemium pricing model.
4
tra¢ c to its newspapers.8 The reason for this is that the combination of the market expansion
e¤ect and the cannibalization e¤ect is more favorable with a link than it is with a …ghting
version. The publisher can also release two versions if these are su¢ ciently complementary
and thus increase the indirect tra¢ c generated by the search engine. Finally, we show that
linking and versioning are more likely when the quality of the search engine is higher than the
stand-alone quality of the newspapers.
The last part of the paper considers the linking policy of a publisher that owns a newspaper
and a search engine. We show that the integrated publisher wants to link its competitors when
their newspapers are su¢ ciently complementary and the volume of tra¢ c generated by the
search engine is not too high. In this case, the publisher uses the link to increase the quality
of the search engine and to increase the audience of its newspaper.
The rest of the paper is structured as follows. Section 2 introduces the model. Section 3
analyzes the versioning strategy of a publisher that competes with a blog. Section 4 examines
the linking and versioning strategies of a publisher that competes with a search engine. Section
5 considers an integrated publisher that owns a newspaper and a search engine. Section 6
concludes.
2
The Model
We analyze the versioning and linking strategies of a publisher that competes with other news
sites such as blogs, search engines or news aggregators. The publisher can o¤er one or two
news sites with di¤erent editorial approaches. It always o¤ers site H of quality uH = u and
it might also release site L of a quality uL =
u; where
< 1. The quality of the sites is
exogenously determined and their content can be related. L can be a degraded version of H or
it can complement it with additional contents. For example, H can be a generalist news site
and L a site specialized in sports news or a site that contains the blogs of experts.
The competitor o¤ers site A, which essentially includes contents obtained from H and L,
or links to these services. When the publisher only releases H the quality of the competitor
8 Our
model can be related to studies in the literature that analyze the e¤ects of vertical relations on the
product line o¤ered to consumers (Mills, 1995; Villas-Boas, 1998, Yehezkel, 2008). In our case, the publisher
o¤ers its contents to the search engine in order to create an additional distribution channel.
5
is uA(H) =
u; where
<
re‡ects that A(H) neither o¤ers original contents nor follows
any speci…c editorial policy. On the other hand, when the publisher releases both H and L
, the quality of the competitor is uA(HL) = u[ + (1
s)], where s 2 (0; 1) measures the
complementarities between H and L. Notice that uA(HL) > uH when s < ( +
1)= ,
re‡ecting that consumers prefer visiting a news site that combines contents of H and L to just
visiting H.
In order to simplify the model and to make it more realistic we assume that the consumers’
search costs are so high that they only visit one site (the anchor site).9 Taking this into account,
consumers can only access the contents of the two sites when they visit the competitor. This
assumption highlights the key feature of search engines, which is to group the contents of
di¤erent newspapers on a single web site, thereby signi…cantly reducing consumer’search costs.
Consumers are characterized by the intensity of their preferences for news sites. Imagine
that they are uniformly distributed in the segment [0; 1] and de…ne as
the consumers’will-
ingness to pay for the service. Taking this into account, the consumers’net utility when they
visit site i is ui
pi , with i 2 fH; L; Ag, where pi is the price of the news sites or the perceived
costs when they visit a blog. An alternative way of interpreting our model is to imagine that
pi is the number of advertisements inserted in site i when the price of the advertisements is
exogenously set and normalized to one. In this case, the publisher would choose the number
of advertisements to maximize pro…ts, taking into account their e¤ects on consumers.
Finally, in order to focus our attention on the product line o¤ered by the publisher, we
assume that the costs associated with producing each version are sunk, and that the marginal
costs of the versions are zero. This implies that it might be expensive to generate contents for
the newspapers, but that these can be distributed at no cost via the Internet.
3
Competing with blogs: no exclusion option
This section examines the versioning policy of a publisher competing with a blog or with a
news site using third party content. Internet allows bloggers to publish opinions and pieces of
news that are largely based on information produced by traditional online newspapers. This
implies that when a publisher releases new content it feeds blogs with materials that are then
9A
similar assumption is made in Purcell et al. 2010 and Dellarocas et al. 2012.
6
used to develop their own products. In this section, we consider that the publisher cannot
prevent the blogger from using its contents and we relax this assumption in the sections that
follow when we consider competition with a search engine.
The following set of indi¤erent consumers describes the segmentation of consumers under
two possible scenarios. If the publisher only releases newspaper H the consumer indi¤erent to
visiting H and the blog A(H) is
HA
= (pH
to A(H) and not visiting any news site is
HA(H)
= pH (1
HA ).
LA
= (pL
HL
HLA(HL)
= (pH
pA )=[u(
and not visiting any news site is
pro…t is
A0
); while the consumer indi¤erent
= pA = u. In this case, the publisher’s pro…t is
On the other hand, if the publisher releases the two sites the consumer
indi¤erent to visiting H and L is
L and A(HL) is
pA )=u(1
= pH (1
A0
pL )=u(1
), the consumer indi¤erent to visiting
( + (1 s))], and the consumer indi¤erent to A(HL)
= pA =[u( + (1
HL ) + pL ( HL
LA ).
s))]. In this scenario, the publisher’s
For simplicity we restrict the analysis to
the case where uL > uA(HL) , meaning that the blog o¤ers less utility than the L because it
simply edits third party information.
The timing of the game played by the publisher and the blog is as follows: …rst, the
publisher decides how many sites it o¤ers; second, it sets the prices and releases its sites; third,
the blog creates its own contents by using the publisher’s news sites. Finally, consumers choose
a site.
The following proposition shows in which situations the publisher releases the …ghting
version L and when it only releases H and accommodates the blog. It also describes the
resulting segmentation of consumers.
Proposition 1. In the presence of a blog the optimal strategy of the publisher is:
1) When
<
, it o¤ ers H for 0
s
sb; and both H and L for sb < s
, it o¤ ers H for 0
s
s1 , and both H and L for s1 < s
always active;
2) When
is always active, except for s1 < s
1. The blog is
1. The blog
s2 .
Proof. See the Appendix.
The …rst part of the proposition shows the case where the quality of A(HL) is low in
comparison with that of L ( <
). The publisher releases L if this generates few spillovers
on A(HL) (s > sb), because L produces a market expansion e¤ect that o¤sets its cannibalization
7
on H. However, if spillovers are larger (s
sb) L generates few revenues and the publisher
prefers to accommodate A(H) than releasing L. Region C in Panel I of Figure 1 shows that for
s > sb there is a complete segmentation of consumers: high type consumers visit H, intermediate
consumers visit L, low type consumers visit A(HL), and very low type consumers do not visit
any site. Notice also that consumer access to the service is higher with versioning, since
A0
is
smaller with A(HL) than with A(H). Only when s = 1 is consumer participation the same in
both scenarios.
Figure 1: Competition with a blog (
= 0:75; u = 1; pA = 0:12). The …gure shows consumer
segmentation as a function of s. For high values of s there is complete segmentation (Regions C).
Otherwise, consumers only visit H and A(H) (Regions A) or only H and L (Region B).
The second part of the proposition considers the case where the quality of A is similar to
that of L (
< ). The results are largely the same as before, but now for intermediate
values of s (s1 < s
s2 ) the equilibrium prices do not allow A(HL) to attract any consumer
(region B in Panell II of Figure 1).
The result of this proposition can be directly related to Valletti and Szymanski’s (2006)
model, which shows that in the presence of a competitor an incumbent releases a …ghting brand
to retain part of its pro…ts. Proposition 1 reaches the same conclusion when s is close to 1,
that is, when the …ghting site generates few spillovers for the blog. However, when the new
site strengthens the blog signi…cantly, the publisher changes its versioning strategy and only
o¤ers H.
8
The next result shows that if the level of s could be decided by the publisher it would set
it as high as possible to minimize the spillover e¤ect.
Corollary 1. Suppose the publisher releases both H and L and that the cost of horizontally
di¤ erentiating them is c(s) = 1=ks. Then the publisher sets s = 1.
Proof. See the Appendix.
In order to understand this result, note that consumers can only access the contents of both
newspapers if they visit the blog. In fact, the publisher does not have any site that aggregates
its contents and, therefore, it cannot bene…t from the complementarities they generate. For
this reason, the publisher would prefer to set s = 1 to reduce the attractiveness of the blog.
For example, it could transform L in a site summarizing the information of H or reproducing
just a part of its contents.
This section has shown that when the publisher cannot prevent its contents being used by
others the release of a …ghting brand is less likely than is predicted by the versioning literature.
Despite this, in a context in which the publisher had some control over its contents it could
negotiate their use in exchange for compensation. This would allow the publisher to internalize
the complementarities of the versions.10 The next section shows that one mechanism that a
publisher can adopt to bene…t from the complementarities is to agree to be linked by a search
engine.
4
Competing with search engines: spillovers and links
Next we extend our model to examine the competition between a publisher and a search engine.
Imagine that a publisher can release one or two newspapers and that these can be linked by
a search engine. When consumers visit the search engine they read the headlines and the
excerpts of the publisher’s news items and then they click through to the original contents
with a probability , which is assumed to be the same for H and L. Hence, if
= 1 the
visitors of the search engine always click through to the links and generate indirect tra¢ c for
1 0 Some
publishers and news agencies such as Reuters, BBC News and USA Today have reached agreements
with Yahoo! News. Calzada and Ordoñez (2012) analyze the negotiation of a revenue sharing agreement between
a publisher and a news aggregator.
9
the publisher, and if
= 0 they read the headlines but never click through to any news story.
In this case, no indi¤erent tra¢ c is generated at all.
Both the publisher and the search engine must agree to the establishment of the links.
The publisher accepts the links if this increases its pro…ts, and the search engine links the
newspapers if this increases its audience. As before, we consider consumer’search costs to be
so high that the search engine is the only available web site for accessing the contents of the
two newspapers. Search engines aggregate and classify the contents of newspapers and reduce
consumers’search costs.
The quality of the search engine’s site depends on the contents it links. When the search
engine links H its quality is uA(H) = u
uA(HL) = u[ +
(1
and when it links both H and L its quality is
s)]. These expressions include the utility obtained by consumers when
they click through to the publisher’s original contents, which is smaller than the utility they
can obtain if they visit the news articles directly since they have already read the title and the
excerpt.11 By contrast, when the …rms do not reach an agreement the quality of A is uA = ur:
We consider that r < , implying that consumers value A less than L when the search engine
does not provide a link to the publisher.
Taking this into account, the net utility of consumers that visit the publisher is ui
with i 2 fH; Lg. The net utility of consumers that visit the search engine is u[ + (1
(pH + pL ) with A(HL), u
pH with A(H), and ur
pi ,
s)]
pA when there is no agreement
between the …rms. Notice that the search engine’s visitors only pay for the contents when they
click through to the links. This re‡ects the business model of some companies, such as Google
News!, that neither charge their consumers nor include advertisements on their sites. Their
objective is to generate a large audience for the other services they commercialize.
Finally, note that the quality of A(HL) can be higher or lower than those of H, depending
on the complementarities between H and L. To account for this situation, we …rst analyze
competition with a low quality search engine (uH > uL > uA(HL) ) and afterwards with a high
quality one (uA(HL) > uH > uL ).12
1 1 Calin
et al. (2013) study how key design parameters of news aggregators a¤ect readers propensity to visit
the content producer’s site and read the full article.
1 2 We omit the case where u
H > uA(HL) > uL for simplicity.
10
4.1
Weak complementarities
The following proposition describes the linking and versioning strategies of a publisher that
competes with a low quality search engine. When the complementarities between newspapers
are weak consumers derive greater utility by directly visiting H or L than with A(HL). Imagine, for example, that they like newspapers with an editorial policy, or that they value the
publisher’s reputation.
The timing of the game is as follows: …rst, the publisher decides how many versions to
release; second, the publisher and the search engine negotiate the establishment of links; third,
based on the outcomes of the negotiation the publisher sets the prices; and …nally, the news
sites are released and consumers make their choices.
Proposition 2. The linking and versioning strategies of a publisher that competes against
a low quality search engine ( s > = ) are:
1) If 0
1,
H and L are released, but the publisher does not accept the links. H, L and
A receive direct visitors;
2) If
1
<
2,
H is released and linked. H and A(H) receive direct visitors;
3) If
2
<
3,
H and L are released and linked. H and A(HL) receive direct visitors;
4) If
3
<
4,
H is released and linked. H and A(H) receive direct visitors;
5) If
4
<
1, H and L are released, but the search engine does not want to link them. H,
L and A receive direct visitors.
The existence and size of these intervals depend on s.
Proof. See the Appendix.
The publisher does not accept the links when it receives a small volume of tra¢ c from the
search engine (0
<
1 ).
When this happens, it releases the …ghting version L because it
does not create spillovers on A and generate revenues that compensate the reductions of direct
visitors to H (Region A in Figure 2). In this situation, there is a complete segmentation of
consumers: consumers visit H, L or A according to their preference for quality and low type
consumers do not visit any sites. As for the search engine, in this interval it would like to link
11
Figure 2: Competition with a low quality search engine (
= 0:4;
= 0:8; u = 1; r = 0:3;
pA = 0:05). For low and high values of , …rms do not reach an agreement and there is
a complete segmentation of consumers (Regions A and E). For intermediate values, there is
agreement and consumers only visit H and A(H) (Regions B and D), or H and A(HL) (Region
C).
H and L, because the gain in quality would o¤set the price increase. However, the publisher
is not interested in entering into an agreement.
When the publisher receives a larger amount of tra¢ c from the search engine it accepts
the links and uses A as its own low quality version. If
1
<
2,
the publisher releases
H and accepts the link (Region B).13 In this interval the publisher obtains more pro…ts with
the indirect tra¢ c from A(H) than by releasing a …ghting version. This implies that the link
transforms A(H) in an alternative distribution channel for the publisher when it links H. Of
course, the threshold
1
increases in pA , which means that the publisher loses interest in the
link as the search engine becomes less attractive to consumers.
If
2
3,
the publisher releases both H and L to increase the audience of the search
engine and to obtain more indirect visits. If the complementarities between H and L are not too
high, this strategy creates a moderate cannibalization on H. In this region, the segmentation
of consumers implies that high type consumers visit H and intermediate consumers visit H
and L indirectly via A(HL) (Region C). Nobody visits L at the equilibrium prices.
1 3 If
s is close to 1 the publisher always releases H and L and region B vanishes (see Panel I in Figure 2).
12
The last two parts of the proposition show that when
is high it is the search engine that is
not interested in linking up to the publisher’s contents. When
3
<
4,
the publisher only
o¤ers H because the search engine would not provide links to any of the publisher’s sites if it
releases both H and L (Region D). The reason for this is that the price of A(HL), (pH + pL )
would be too high and it would lose audience. Following the same argument, for
4
<
1
the search engine never provides links to the publisher. In this case, consumers are segmented
as in the …rst part of the proposition (Region E).
In our model the di¤erentiation between H and L plays a key role in the strategy of …rms,
but it is introduced exogenously. The following result describes how the publisher would like
to modify s when it o¤ers the two versions and these are linked.
Corollary 2. Suppose that the publisher releases H and L and that these are linked by a low
quality search engine. If the cost of horizontally di¤ erentiating the newspapers is c(s) = 1=ks,
the publisher chooses s = 1.
Proof. See the Appendix.
This result may help to explain the present con‡icts between publishers and search engines.
Publishers agree to being linked when
and s take intermediate values, but they would prefer
to reduce the attractiveness of search engines to avoid the cannibalization of A(HL) on H. In
our model, this would be possible with an increase in s.
Finally, another interesting result from the proposition is that linking a¤ects the accessibility of consumers to the service. The consumer that is indi¤erent to visiting the search engine
is
A0
= pA =ru in the absence of links and
values of
A0
= pH = u when H is linked. Therefore, for low
the increase in utility generated by the link o¤sets the corresponding price increase
and more consumers are willing to use the service, but for high values of
reversed. Figure 2 shows that when s = 3=5 the threshold
1
the situation is
takes a high value, and as a
consequence linking supposes a reduction in the accessibility of the service. This e¤ect is more
marked when the search engine links the two newspapers (Region C), because consumers click
through to both services with probability
and pay a higher price. When s = 1 there is a
small interval in which linking increases consumer participation if the search engine links H.
13
4.2
Strong complementarities
The strategy of the publisher changes signi…cantly when the utility o¤ered by A(HL) is larger
than the stand-alone utility of H, uA(HL) > uH > uL . This might occur when consumers
prefer product variety to limiting themselves to one high quality newspaper. The following
proposition analyses this situation.
Proposition 3. The linking and versioning strategies of a publisher that competes against
a high quality search engine ( s < ( +
1. If 0 <
1,
2. If
1
<
2,
3. If
2
<
1)= ) are:
H and L are released and linked. Only A(H) receives direct visitors;
H and L are released and linked. A(HL), H and L receive direct visitors;
1, H and L are released, but either the search engine (for
both …rms (for
>
3)
2
<
3)
or
are not interested in the links. H; L and A receive direct visitors.
Proof. See the Appendix.
These results show that an agreement between the publisher and the search engine is more
likely for low values of . When
agrees to be linked. As uA(HL)
is small (0
uH and
1)
the publisher releases H and L and
is small only A(HL) receives direct visitors (Region
A in Figure 3). In spite of this, the publisher obtains more pro…ts than if it was a monopolist
because all visitors consume the two newspapers. On the other hand, the audience of the
search engine is larger with the links.
When the search engine’s visitors click through more frequently to the newspapers’links
(
1
<
2)
the price of A(HL) increases and intermediate consumers prefer to visit H
or L directly. As a result, the publisher changes its pricing policy and there is a complete
segmentation of consumers: high type consumers visit A(HL), intermediate types visit H and
low types visit L (Region B). Notice that in this case L cannibalizes H in two ways: First,
some low type consumers who could visit H actually visit L. And second, some high type
consumers who could visit H now visit A(HL). Notwithstanding, as this happens for large
values of
the cannibalization of H is o¤set by the direct and indirect visits to L and by the
indirect visits to H:
14
Figure 3: Competition with a high quality search engine ( =0.4,
For low values of
=0.8, u=1, r =0.3, pA =0.05).
the publisher and the search engine reach an agreement and consumers only
visit A(HL) (Region A). For intermediate values, there is agreement and complete segmentation of
consumers (Region B). For high values, there is no agreement, but there is complete segmentation of
consumers (Region C).
Finally, for the highest values of
(
2
<
1) the …rms do not reach an agreement. The
search engine is not interested in the links because the increase in the price would o¤set the
improvement in quality. To illustrate this situation, imagine the extreme case where s = 1
and uA(HL) = uH . In this case, if consumers access H directly they pay pH and if they visit
the search engine and click through to the newspapers they pay (pH + pL ). Therefore, if
> pH =(pH + pL ) consumers are better o¤ visiting H and the search engine does not receive
visits.14
The size of the regions identi…ed in the proposition crucially depends on the values taken
by s. The more H and L are complementary (i.e., the smaller s is), the wider is the region in
which both companies cooperate (Regions A and B). In Figure 3, this corresponds to a shift
of
2
to the right. Hence, contrary to Proposition 2, spillovers make the establishment of links
more likely.
The next corollary considers the case of a publisher that o¤ers two newspapers that are
1 4 In
the proof of this proposition we also show that for high values of
being linked because A(HL) becomes very expensive and it loses audience.
15
the publisher is not interested in
linked and shows how it would like to modify their level of di¤erentiation in order to maximize
pro…ts.
Corollary 3. Suppose that the publisher releases H and L and that these are linked by
a high quality search engine. If the cost of di¤ erentiating the newspaper is c(s) = 1=ks; the
publisher increases the level of di¤ erentiation (reduces s) if k > k .
Proof. See the Appendix.
In contrast to the previous case of a low quality search engine, the publisher now wants
to increase the complementarities of its newspapers if the cost is not too high. Indeed, high
type consumers can now buy the two services and so the consumers’total willingness to pay
increases with the level of di¤erentiation (decreases with s). In this context, the publisher does
not see the search engine as a rival, but as a distributional channel that generates more visits
and that allows it to charge higher prices.
To sum up, this section has shown that the publisher’s distribution strategies crucially
depend on the amount of indirect tra¢ c generated by the search engine and on the complementarities between its newspapers. Proposition 2 has revealed that with weak complementarities
the publisher wants to be linked if the search engine generates a substantial volume of indirect
tra¢ c. In this case, it uses the search engine as its own distribution channel and competition
is weakened. On the other hand, Proposition 3 has shown that with strong complementarities
the …rms reach an agreement if the tra¢ c redirected from the search engine to the publisher
is su¢ ciently small. Otherwise, the price of the search engine is too high and it obtains more
audience without linking.
In the last two propositions, linking appears because the search engine is the only distribution channel that allows the publisher to bene…t from the complementarities of newspapers.
We next explore if linking is also possible when the search engine belongs to a publisher that
competes with other content providers.
5
Horizontal integration and competition
In recent years, several publishers have acquired or created news aggregators in order to expand
their audiences and engage them in forums and RSS feeds. For example, in 2005 Gannet (USA
16
Today’s publisher), Knight-Rider and Tribune acquired 75% of Topix.net. Similarly, in 2011
AOL acquired The Hu¢ ngton Post, and in 2012 Gannet bought Quickish, a sports aggregator.
By making these investments traditional media groups were looking for alternative revenue
sources as well as attempting to separate their production activities from the distribution of
their contents. Other recent experiences have been less successful. For example, in 2009 News
Corporation planned to launch a news aggregator called Alesia, but the project was canceled
due to the lack of interest shown by other publishers. In 2010, Gannett, The New York Times
Company, The Washington Post Company, Reuters, Los Angeles Times and Chicago Tribune
created a news aggregator named Ongo, but this site closed two years later.15 Both Alesia and
Ongo were created from scratch with high quality news articles provided by their promoters
and they operated behind paywalls.
The integration of publishers and aggregators raises novel economic questions regarding the
impact on competition. Publishers want to integrate aggregators to obtain more indirect tra¢ c
and referrals, but they can use their position to exclude competitors or to give an advantage
to their own contents.16 To address this case, this section analyzes the marketing strategy of
an integrated publisher that manages both a high quality newspaper, H; and a search engine,
A(H). The integrated publisher competes with an independent publisher that o¤ers a low
quality newspaper, L. The utility o¤ered by each service is the same as in the previous section.
However, for simplicity we now assume that pL is set exogenously.
The integrated and the independent publishers agree to link L to A(H). When this occurs,
the complementarities between H and L determine the quality of A(HL). As in the previous
sections, if the complementarities between H and L are weak A(HL) becomes a low quality
search engine (uH > uL > uA(HL) ) and if they are strong it is transformed into a high quality
search engine (uA(HL) > uH > uL ). Note that in the former case the agreement implies that
newspaper L now has a stronger competitor "from below", whereas in the latter case newspaper
H has a competitor "from above".
1 5 One
explanation for the failure of Ongo is that their managers established a bad pricing strategy. See
http://www.niemanlab.org/2012/05/ongo-an-attempt-at-a-pan-media-paywalled-aggregator-is-closing/
1 6 De Cornière and Taylor (2013) analyze the integration of general search engines and content providers.
17
5.1
Weak complementarities
The next proposition analyzes the linking strategies of the publishers when the complementarities between H and L are weak. The timing of the game is as follows: …rst, the two publishers
negotiate the possibility of linking L; second, the integrated publisher determines pH ; and
…nally consumers decide which site to visit.
Proposition 4. The linking strategy of an integrated and an independent publisher that
o¤ er only weakly complementary contents ( s > = ) is:
1. When
= <s
sb, the integrated publisher wants to set a link L for
<
1
whereas the
independent publisher is not at all interested.
2. When sb < s
1, the integrated publisher wants to establish a link L for
the independent publisher is interested for
3
<
<
2
>
3.
Only when
>
<
2
whereas
there is a region
in which both publishers reach an agreement.
Proof. See the Appendix.
The integrated publisher wants to establish a link with L when both
and s are small.
That is, when a small percentage of A(HL)’s visitors click through to the links and the contents
of the newspapers are su¢ ciently complementary. Only in this case does the inclusion of L
expand the market share of A(HL) and increase the number of indirect visits to H. The link
of L increases the quality of A(HL) in u (1
s) and its price in pL . Hence, the integrated
publisher bene…ts from a market expansion e¤ect, which diminishes with both
and s, but it
is not a¤ected by a business stealing e¤ect. By contrast, the independent publisher is a¤ected
by the two forces. On the one hand, the link generates a market expansion e¤ect because
all the visitors of A(HL) click through to L with probability . On the other hand, A(HL)
cannibalizes L "from below" and reduces the number of direct visitors. Only when
and s are
su¢ ciently high does the …rst e¤ect o¤set the second and the publisher agrees to the link.
Figure 4 depicts the parameter regions for which the interest of the two publishers are
aligned. When s is small (s < sb) the integrated publisher wants to link L if
<
Similarly, when s is large (s > sb) the integrated publisher wants to link L only if
is su¢ ciently
1
but its
competitor is never interested because the cannibalization of A(HL) on L would be too great.
18
small ( <
When
2 ).
This is explained by the e¤ect that links have on the price of the search engine.
increases, the price of the search engine also increases. When
<
2
the publisher
compensates this with a reduction in pH , but for larger values it prefers to foreclose the rival.
By contrast, the independent publisher accepts the link for the intermediate values of , but it
becomes more and more interested as s increases. Taking this into account, only in the small
region
3
is close to
<
2
( >
do the two publishers reach an agreement. This region only exists when
).
Figure 4: Linking preferences with a low-quality search engine ( =0.4, =0.8, u=1, pA =0.05)
The proposition shows that only under very speci…c circumstances is an agreement between
the publishers possible. The reason for this is that the integrated publisher is only interested
in linking L if this produces a substantial increase in the audience of the search engine thus
compensating a lower price. But for the independent publisher the agreement is pro…table if it
produces a small expansion e¤ect in the search engine. Only in this case does it obtain indirect
visits without losing too many direct consumers.
The linking strategies described above determine the following segmentation of consumers:
Corollary 4. In the presence of an integrated and an independent publisher that o¤ er
19
weakly complementary contents ( s > = ) consumers are segmented as follows:
1. When
sb, sites H; L;and A(H) receive visits if
= <s
L are released.
2. When sb < s
1, the sites H; L;and A(H) receive visits if
links L in the interval
3
<
<
2
if
>
. If
The …rst part of the corollary shows that when
<
<
. If
only H and
<
. In this region, A(H)
only H and L are released.
the integrated publisher maintains
A(H) active because it generates indirect tra¢ c to H. As a result, high type consumers visit
H, intermediate consumers visit L; and low type consumers visit A(H). However, when
,
the integrated publisher obtains more pro…ts without releasing A(H). If it releases A(H) some
consumers will buy it at the equilibrium price and so it will lose direct visits to H. The second
part of the corollary presents the same intuition, but it shows that in the interval
3
<
<
2
in which the publishers reach an agreement the search engine links L. In this case, low quality
consumers visit A(HL).
The most striking property of the above result is that the integrated publisher might
maintain the search engine active, even without linking to other sites. The search engine plays
the same role as a …ghting version. In this case, the publisher can still set a high pH for those
consumers that visit H directly.
5.2
Strong complementarities
This section looks at the case where the publisher is integrated with a high quality search
engine. Recall that now A(HL) competes with H "from above". The timing of the model is
as before.
Proposition 5. When an integrated and an independent publisher o¤ er strongly complementary contents ( s <
+
1
) the integrated publisher always wants to be linked. The linking
strategy of the integrated publisher is:
1. When 0
s < se, it links L if 0
2. When se < s
+
1
<
1.
, it never links L.
20
Proof. See the Appendix.
The …rst part of the proposition shows that the integrated publisher only links L when
both s and
are small (Figure 5). With the link, A(HL) completely cannibalizes H (pH is
so high that nobody directly visits H) and competes with L "from above". This generates a
market expansion e¤ect of A(HL) that compensates the cannibalization e¤ect on H as long as
0<
<
1.
For
1
the publisher does not link L because the search engine would become
more expensive and it would be necessary to reduce pH substantially in order to maintain its
market share. As for the independent publisher, it always wants to be linked: although L now
competes directly with A(HL) (nobody visits H directly), its indirect visits compensate for
this e¤ect.
The second part of the proposition shows that for higher values of s (s > se) the market
expansion e¤ect of A(HL) does not compensate for the cannibalization e¤ect on H. In order
to encourage consumers to switch from L to A(HL) the integrated …rm would need to reduce
pH signi…cantly, which is never pro…table.
To sum up, the integrated publisher wants to link up with its competitor when the newspapers are su¢ ciently complementary and the link produces a signi…cant increase in the search
engine’s market share. When this happens the independent publisher always accepts being
linked up because this generates a large number of indirect visitors.
Finally, we explain how the linking decisions of …rms in‡uence consumer segmentation.
Corollary 5. In the presence of an integrated and an independent publisher o¤ ering strong
complementary contents ( s <
+
1
) consumers are segmented as follows:
1. When 0 < s < se, sites A(HL) and L receive visits if
<
1.
If
1
only H and L
are released.
2. When se < s
+
1
, sites H; L and A(H) receive visits if
and L are released.
< b1 . If
1
only H
Proof. See Proof of Proposition 5.
The corollary describes how
(probability that consumers click through to the links) and s
(complementarity of the sites) determine the versioning strategy of publishers. The …rst result
21
Figure 5: Linking preferences with a high-quality search engine ( =0.4, =0.8, u=1, pA =0.05).
shows that when 0 < s < sb and
<
1
the integrated publisher maintains A(HL) active. As
a consequence, high type consumers visit A(HL) and low type consumers visit L: However,
when
1
the price of A(HL), (pH + pL ), becomes too high and the publisher prefers to
remove it. As a result, only H and L are active and the publisher can set a high pH . The
second part of the corollary shows that for s > sb the integrated publisher does not link L. For
< b1 it maintains A(H) active to attract indirect visitors to H, while if
A(H) and sets a higher pH .
6
b1 it eliminates
Conclusions
In recent years, blogs, search engines, and news aggregators have come to occupy the top positions in audience rankings of news sites. While traditional publishers accuse these entrants of
“stealing’their contents and revenues, they argue that they “expand the market“ by improving
accessibility to newspapers and their contents. This claim might be justi…ed given that aggregators reduce consumers’search costs by o¤ering links to many news sites and/or by editing
the contents originated by others. In this paper we have examined the product line response
22
of publishers to this type of competition.
Our …rst contribution has been to show that when a publisher cannot prevent its contents
from being used, versioning is less likely than what we are led to believe in the literature.
The reason for this is that a …ghting version is not very e¤ective in increasing revenues if it
improves the quality of the competitor. We then analyzed the linking and versioning strategies
of a publisher in competition with a search engine. We have shown that the publisher accepts
the link when the search engine is able to exploit the complementarity of the publisher’s
newspapers and when it generates substantial indirect tra¢ c to the publisher. When this
occurs, the search engine becomes an additional distribution channel for the publisher and
competition is moderated. Finally, we have shown that when the publisher is integrated with
a search engine it can link up with the newspapers of its competitors in order to increase its
audience.
To the best of our knowledge, these results represent a novel …nding in the literature on
versioning, which hitherto has not considered the role of links in moderating competition.
Dellarocas et al. (2013) have shown that content aggregators make it easier for consumers
to access good contents and that they increase competition between content sites. In our
model, the main property of the search engines is that they allow publishers to internalize the
complementarities of their newspapers, thus increasing the total tra¢ c in the content ecosystem
and avoiding the release of …ghting versions. Special attention should be paid to the e¤ects of
these strategies on the quality and a¤ordability of contents.
Our study has revealed that the disputes between publishers and search engines are highly
dependent on the volume of tra¢ c that publishers receive from search engines and on the
complementarities between aggregated newspapers. As such a relevant empirical question is
whether traditional publishers obtain su¢ cient tra¢ c from search engines, and whether search
engines maximize their audience with their linking policies. Recent papers by Chiou and
Tucker (2010) and Athey and Mobius (2012) present evidence that Google News generates signi…cant indirect tra¢ c to traditional online newspapers, but it is still unclear which publishers
bene…t most from search engines and how they should adjust their marketing strategies to
accommodate them.17
1 7 Chiou
and Tucker (2013) investigate the e¤ects of the breakdown of the agreement between Google News
and AP in 2009, and show that the event coincided with a decline in the demand for content from AP sources.
23
Our analysis can be extended in several directions in order to understand recent developments in the media market. It would be interesting, for example, to study if publishers accept
links to certain speci…c news items in order to attract visitors and to promote premium contents
(freemium model).18 Our model could also be extended to examine the role of news agencies
in the new media market. As the recent con‡icts between Google News and several press associations illustrate, news agencies provide fundamental information to traditional newspapers.
Thus, thus, as well as seeing news aggregators as clients they might also perceive them to be
major competitors.19
7
Appendix
Proof of Proposition 1. When the publisher only o¤ers H the indi¤erent types are
(pH
pA )=(1
)u and
A0
= pA = u. The …rm sets pH to maximize
HA(H)
HA
= pH (1
=
HA )
and as a result the price and the pro…ts are:
pH =
pA + u (1
2
)
With this price, it is veri…ed that
;
HA(H)
HA
=
1
2
=
u(1
)
4
pA
u(1
)
1
+
>
pA
pA
(2 +
4
u (1
A0
=
pA
u
)
):
(1)
as long as pA <
u(1
2
)
.
To ensure the participation of the blog we consider that this condition is always satis…ed.
Imagine now that the publisher releases H and L. In this case, the indi¤erent types are
HL
(1
= (pH
pL )=u(1
);
LA
= (pL
pA )= [u(
s))]. The …rm sets pH and pL to maximize
( +
HLA(HL)
(1
s))] ; and
= pH (1
A0
= pA =[u( +
HL ) + pL ( HL
LA ).
Athey and Mobius (2012) analyze the e¤ect of introducing a “local news” feature in the French version of
Google News in 2009, whereby users were able to see news from local outlets on the web site.
1 8 Rutt (2012) considers how aggregators a¤ect the pricing decisions of …rms and the quality of their contents.
He assumes that …rms randomize between providing the article for free and charging a price, and shows that
this behavior creates a mixture of advertiser and subscription business models.
1 9 In 2004 Google News reached an agreement with the Associated Press (AP), whereby Google was permitted
to host AP contents in exchange for compensation. This agreement was broken in 2009 and Google stopped
o¤ering AP’s links. But in 2010, AP reached a new agreement with Google and Yahoo! News. Similarly, in
2005 Agence France Press (AFP) …led a lawsuit against Google News for removal of copyright management
information and “hot news” misappropriation. After two years of litigation, AFP and Google News signed a
licensing agreement.
24
Solving the publisher’s problem we obtain:
pH
=
HLA(HL)
=
1
[pA + u( s
2
u
[ s
+1
4
+1
]+
)]; pL =
pA
pA
[2 +
4
u( s
1
[pA + u( s
2
To ensure the participation of the blog we need that s > s2 =
If this is satis…ed, then
HL
=
1
2
>
LA
=
1
2
pA
( s
)u
1
)
]:
(2)
( +2 )u pA
>
)];
A0
=
p
p2A 6 pA u+
2 u
pA
u( + (1 s)) :
pH (1
HL )
LA
+ pL (
=
A0
HL
=
L0 .
L0 ).
pH
=
HLA(HL)
=
Moreover, it establishes pH to maximize
.
On the
other hand, when s 6 s2 this ranking is not preserved and the publisher sets pL =
to ensure that
2 u2
pA
+ (1 s)
=
HLA(HL)
The prices and the associated pro…t are:
1
2 pA
[(1
)u +
]; pL =
2
+ (1 s)
[( + (1 s))u 2pA ]2
u
:
4
4u( + (1 s))2
In this case, the indi¤erent types are:
HL
=
1
2
>
L0
=
pA
+ (1
s)
;
(3)
pA
( + (1 s))u .
Next, we analyze the publisher’s optimal versioning policy. First, notice that for s > s2 it
is satis…ed that
p2A + (1
sb=
HLA(HL)
>
HA(H)
)( + )u2 +
r
2
for s > sb, where
p4A + 2 (1
2
2
(1
) p2A u2 ( +
2) + (
2
) (
2
1) u4
:
) u2
(4)
Therefore, the publisher releases H and L for sb < s
segmentation emerges when sb > s2 , which occurs when
satis…es sb = s2 (the expression for
1 and only H for s
<
; where
sb. This
is the value that
is long and we don’t report it for simplicity). For
we obtain that sb < s2 . When this happens, for s2
s
>
1 the publisher releases H and L and
the blog is active. For s < s2 , if the publisher o¤ers the two versions the relevant prices and
pro…ts are those in (3). In this case, we obtain that HLA(HL) > HA(H) for s > s1 , where
p
2(
2
1)p2A (p2A 2 (
1) pA u + (
1) u2 ) + ( ( + )p2A 2(1
) pA u (
s1 =
2 [2 (
1) pA u p2A + (
)(
1)u2 ]
(5)
Hence, for s1 < s < s2 the publisher o¤ers the two versions and the blog is not active. And
for s < s1 it releases H and the blog is active.Q.E.D.
25
)(1
)( + )u2
:
Proof of Corollary 1. Consider the pro…t function of the publisher in (2) when it releases
the two versions and the cost of di¤erentiation is c(s) = 1=ks: For s > s1 the three news sites
have positive market share and the pro…t of the publisher is:
The FOC of
u
[ s
4
HLA(HL)
=
HLA(HL)
with respect to s is
@
+1
HLA(HL)
@s
]+
u
1
= 2+
ks
4
"
pA
pA
[2 +
4
u( s
1
This expression can only be negative if p2A > ( u
In spite of this, notice that s1 >
Finally, for s
u +pA
u
)
p2A
2
( u
su)
#
1
;
ks
]
(6)
:
2
su) , which happens for s 2
for pA > 0. Therefore,
@
HLA(HL)
@s
u
pA
u
;u
> 0.
s1 the prices and the pro…ts are those in (3). Taking this into account, the
FOC of the pro…t with respect to s is:
@
HLA(HL)
@s
=
2
1
ks2
[2pA u( (1 s) + )]pA
u( (1 s) + )3
A su¢ cient condition for this to be positive is u [ (1
for pA <
u (1
)
(2
) ,
s) + ] > 2pA . This is always satis…ed
which has been previously assumed.Q.E.D.
Proof of Proposition 2. Imagine that the publisher releases both H and L and that these
are not linked. In this case, the consumer indi¤erent to H and L is
the indi¤erent to L and A is
visiting any site is
HLA
= pH (1
A0
HL )
LA
= (pH
pA )=u(
HL
= (pH
pL )=u(1
),
r); and the indi¤erent to A and not
= pA =ur. Taking this into account, the …rm sets pH and pL to maximize
+ pL (
pH
=
HLA
=
HL
LA ),
which yields the following prices and pro…ts:
1
1
[pA + u(1 r)] ; pL = [pA + u(
2
2
1
p2A
u
2pA + u(1 r) +
< :
4
u(
r)
4
Moreover, the audience for the search engine is AHLA =
LA
r)] ;
A0
=
1
2
(7)
pA (2
r)
2(
r)ur .
Notice that the publisher always releases L since in this case it doesn’t create spillovers
26
+pA
u
.
on A.20 On the other hand, with these prices we obtain
=
A0
pA
ur
ur(
2
as long as pA < pA =
r)
r ,
HL
=
1
2
>
=
LA
which we assume for simplicity.
h
pA
2u(
r)
1
2
i
>
Imagine next that the publisher only releases H and that this is linked. In this case, the
consumer indi¤erent to H and A(H) is
and not visiting any site is
maximize
A0
= pH (1
HA(H)
= pH (1
HA
)=u(1
= pH =u . Taking this into account, the publisher sets pH to
HA )
+ pH (
A0 )
HA
and obtains:
4(
u(1
2
Moreover, the search engine’s audience is AHA(H) =
HA
pH =
satis…ed that
HA
=
2(
(1
2
u(1
2
2(
)
+
), and the indi¤erent to A(H)
2)
)
;
+ 2)
>
=
A0
HA
(1
2
2(
)
+
=
2)
if
)
:
+ 2)
A0
=
(8)
2(
2
+
2)
and it is
< .
When the publisher o¤ers both H and L and these are linked the consumer indi¤erent to
H and L is
)
= (pH
HL
pH )=u( s
LA )
HL
pH
=
pL
=
), the indi¤erent to L and A(HL) is
LA
), and the indi¤erent to A(HL) and not visiting any site is
pL )=u[ + (1
pL (
pL )=u(1
s)]. The publisher sets pH and pL to maximize
+ (pH + pL ) (
[ (1
)(2
[ (
)
A0 ).
LA
1+ )+ (
2[4
2
( 2
2[4
(1
2
= (pH +
= pH (1
1 + 2 ) + (1 2
2 )s + 2 (
(1 s + (3 + 4(s 1)))]
2
HL
A0
HL )
+
The solution of its problem yields:
s) + s(1
With these prices we observe that
HLA(HL)
= (pL (1
>
1 + s)2 ]u
s)) + ( (1 +
2s)
(1
(1 s + (3 + 4(s 1)))]
LA
;
s))]u
if > b = [ + (1 s)]=(1+ ), and
LA
: (9)
>
A0
< b. This implies that the publisher can’t get a positive market share for the two news
if
sites. As an alternative, for
HL
=
LA
=
HLA ;
< b the publisher can set pL =
where now
HLA
HLA
A0 ).
pH
=
HLA(HL)
=
2 0 When
HLA(HL)
= pH (1
to guarantee that
HLA )
+ (pH +
The price and the associated pro…ts are:
2[ (1
) + 4(
1)
4[ (1
) + 4(
1)
[
+ +
[
2
+ +
2
+ (1
(1 2
+ (1
(1 2
s)][
)(1
s)][
)(1
1+
s 2
1+
s 2
+ (1
s)]2 u
(2
2s)) + 2 ( + s
+ (1
s)]2 u
(2
2s)) + 2 ( + s
the publisher only releases H and there are not links the results are pH =
[pA +(1 r)u]2
:
4u(1 r)
s)
s)
is the consumer indi¤erent to H and A(HL). Taking
this into account, the publisher sets pH to maximize
pL ) (
pH (
(1
)
1+ + (1
It can be veri…ed that
HLA
>
HA for
pA > 0:
27
pA +(1 r)u
2
and
HA
=
;
1)(1
s + (4s
3))]
1)(1
s + (4s
(10):
3))]
The audience for the search engine is AHLA =
HLA
=
A0
=
2[ (1
) + 4(
1)
2[ (1
) + 4(
1)
It can be checked that now
the publisher sets pL =
pH (
+
HLA
A0 ,
where:
(2
1)( + (1 s))(
1 + + (1
s))
2
2
+ + (1 2 )(1 s 2 (2
2s)) + ( + s
(1
+ ( + s 1))(1 2 + (2s 1))
+ 2 + (1 2 )(1 s 2 (2
2s)) + 2 ( + s
HLA
>
A0
+ (1+ s))
( +s 1)
< b. On the other hand, for b <
for
to guarantee that
HLA
=
A0
=
HLA0 ,
1)(1
s + (4s
3))]
1)(1
s + (4s
3))]
<
where
is the consumer indi¤erent to H and not visiting any site. In this situation, L and
HLA0
A(HL) are released, but nobody visits them. As a result, the publisher maximizes
HLA0 )
by setting pH =
u( +
( +s 1))
. Notice that if s
(1
pH (1
u( +
8
is not relevant. Finally, for
>
( +s 1))
4
and obtains
HLA0
= 1=2 and
b, so the strategy described for
) then
H0(LA)
=
H0(LA)
=
h
2 b;
nobody wants to visit A. Hence, the publisher releases H;
sets pH = u=2 and obtains the monopoly pro…t
H
= u=4.
Taking into account the previous results, next we examine the linking and versioning policy
of the …rms. Consider …rst the case where the publisher releases H and L and compare its
h
pro…ts with and without links. For 0; b , we …nd b1 such that HLA > HLA(HL) for <
b1 and
HLA
HLA(HL)
Analogously, in the region
HLA
>
HLA(HL)
for b2
b2 =
for b1
h
2 b;
< b. The value of b1 is not shown for simplicity.
there is b2 that satis…es
HLA(HL)
< .21 The expression for b2 is:
(
2
2pA + 4pA (
r)( + (1
r)u + (1 +
s))u2
2r)(
r)u2
HLA
if
b2 and
.
Now compare these results with those that will obtain the publisher if it o¤ers H and this
h
is linked. First, observe that in the interval 2 0; b1 there is 1 such that HLA > HA(H)
for
1
<
1
and
p
(
=
HA(H)
HLA
otherwise. The expression for
1) [p2A + 2pA (
r)u + (1
[p2A + 2pA (
Next, it is veri…ed that in the interval
1
is:
r)(
r)u2 ][p2A + 2pA (
r)u r(
r)u + (1 r)(
r)u2 ]
h
2 b1 ; b there exists 2 satisfying
r)u2 ]
HA(H)
;
>
for < 2 and HLA(HL)
< b. Also note that in the interval
HA(H) for 2
h
2 b; b2 there is a threshold b3 that satis…es H0(LA) > HA(H) for < b3 . The expressions
HLA(HL)
for
2
and b3 are not shown for simplicity. Furthermore, it is con…rmed that
2 1 Recall
that for
1
< b1 <
b if two versions are released and linked pH is high and nobody visits A.
28
2
as
;
:
(1 + )] =(1 + ).22 Similarly, one can show that
h
Finally, for values 2 b2 ;
we …nd that HA(H) > HLA .
long as s < sb with sb = [ +
).23
if s > (1
2
< b < b3
Now consider the linking strategy of the search engine, which maximizes its audience. Let
3
and
be the values of
4
that satisfy AHLA(HL) = AHLA and AHA(H) = AHLA ; respectively.
The expression for 3 is long and we don’t present it for simplicity.24 The expression for 4 is:
8
9
<
=
(4 pA + ur(1 2 )) r(2 pA ur(1 2 ))
q
2
:
[2 pA (2
r) + ur(1 2 )(
r)] + 4 pA (2
r) [r(pA ru) + (ru 2pA )] ;
4 =
4 pA 2rpA 2 ru + 2r2 u
One can show that
3
4
if r is su¢ ciently small. We use this restriction in order to reduce
the number of possible cases and to focus on the interesting situations. Taking this into account,
when
2 [0;
3)
it holds that AHLA < M infAHLA(HL) ; AHA(H) g so the search engine accepts
to link the publisher’s newspapers regardless of the number of versions released. If
then AHA(H) > AHLA
2 [ 3;
4)
AHLA(HL) , implying that the search engine accepts to link H but not
both H and L. Finally, for
2 [ 4 ; 1] it is satis…ed that AHLA
M axfAHLA(HL) ; AHA(H) g;
so it doesn’t link any newspaper of the publisher because this increases too much its price and
reduces the audience.
Last, we contrast the strategies of the two …rms to derive the market outcome established
in the proposition. Note that for
<
engine in any situation, whereas for
1
the publisher does not want to be linked by the search
>
4
it is the search engine that does not want to link
any newspaper. In such cases the publisher releases both H and L; and H, L, and A receive
direct visits (Panel II in Figure 2). However, recall that when s
the relevant threshold is b1 . In this case, for
(Panel I in Figure 2).
For
that
1
2 [ 1;
<
2 2 When
b
2
<
regions
<
3
s = sb then
1 ; 1 ) and
2 3 When s = (1
2[
4)
2[
2;
25
4:
for
= b1 =
2)
) then
b) and
2
1
and when
< b1 the publisher doesn’t accepts the links
the …rms reach an agreement. In this case when s < s < sb it is veri…ed
1
2 [b1 ;
sb then
2.
2 [ 1;
2)
the publisher releases H; for
For s > sb it holds that
1
> b1 and
2
2 [ 2;
3)
it releases H
< b1 . This implies that the regions
vanish and the relevant threshold is then b1 .
b b
) it holds that 2 > b and b3 < b. This implies that the
2 = = 3 . For s < (1
2 [b; b3 ) vanish.
h
b. If AHLA(HL) > A
only exists in the interval 0; b as AHLA(HL) = 0 when
HLA for
h
the whole interval 2 0; b then b applies instead of 3 .
2 5 For s = s then
2 = 3 = 4 and the intervals [ 2 ; 3 ) and [ 3 ; 4 ) shrink. The value s is small and we
2 4 Note
that
3
29
and L (only H and A(HL) are active); and for 2 [ 3 ; 4 ) it releases H. Finally, for s > sb the
h
relevant threshold is b1 . For 2 b1 ; 3 the publisher releases H and L (only H and A(HL)
are active), and for
2 [ 3;
4)
it releases H. Q.E.D.
Proof of Corollary 2. Suppose that the publisher o¤ers H and L and accepts the links
of the search engine. From Proposition 2 we know that when
(10) and obtains the corresponding pro…ts
are active. Moreover, for
HLA(HL) .
< b the …rm sets the price in
< b only H and A(HL)
Recall that for
> b the search engine doesn’t link the newspapers because only H
is active at the equilibrium price. Next, notice that @
HLA(HL) =@s
0 for
…rm would set s = 1. This result is veri…ed for any di¤erentiation cost c(s) =
b, implying the
1=ks. Q.E.D.
Proof of Proposition 3. When the publisher and the search engine don’t reach an
agreement, the publisher releases H and L and its prices and
HLA
are those in (7). On the
other hand, if only H is released and it is linked then pH and
HA(H)
are those in (8).
Consider next that the publisher releases H and L and that it releases an agreement with
the search engines. As a result, uA(HL) > uH because uA(HL) = u[ + (1
1)= . In this case, the indi¤erent consumers are
HL
= (pH
maximize
pH =
pL )=u(1
A(HL)HL
), and
L0
= (pH + pL ) (1
AH
s)] and s < ( +
= [ (pH +pL ) pH ]=u[ + (1 s) 1],
= pL =u . The publisher sets the prices pH and pL to
AH ) + pH
(
AH
HL ) + pL
[
1+ ( +
s
( + s 1))]u
[2
; pL =
2[ + (
2) + (1 + (3
2) s)]
2[ + (
(
HL
L0 ).
This yields:
1
+ (1 +
2) + (1 + (3
2s)]u
2) s)]
(11)
2
A(HL)HL
=
[
1 + (3
1 s
(3s 2))]u
:
4[ + (
2) + (1 + (3
2) s)]
With these prices, the audience for the search engine is AA(HL)HL = 1
don’t comment this case for simplicity.
30
(12)
AH .
Moreover,
it is guaranteed that
AH
=
HL
=
L0
=
>
1.
>
L0
HA(H) ;
1.
>
1,
where
1 + (3
1)]
2) + (1 + (3
[
1 + (2
s)]
2[ + (
2) + (1 + (3
[2
1
+ (1 +
2[ + (
2) + (1 + (3
1
Then there is a value
M ax
A(HL)HL
for
3
2)
s)]=(1 + ):26
= [ + (1
[
A(HL)HL
Consider next that
as long as
2[ + (
1)= it holds that
M ax
HLA
HL
AH
Imagine …rst that
for s < ( +
>
s)]
;
;
2) s)]
2s)]
:
2) s)]
for which
HA(H) ;
(13)
=
A(HL)HL
HLA
when
HLA .
2 [ 1;
Then,
3)
and
2 [ 3 ; 1].27
In this case, with the prices in (11) it is satis…ed that
L0 ,
AH
which implies that only A has direct visits. Taking this into account, the consumer indi¤erent
between A and not visiting any site is
the publisher sets pL =
pH (1
A0 )
+ pL (1
Note that
M ax
A0 ).
+ (1
pH =
A(HL)
pH
+ (1 s
).
s
u
4
>
HA(H) ;
>
=
(pH +pL )
u( + (1 s)) .
In order to ensure that
Taking this into account, it sets pH to maximize
)u
;
HLA .
HLA
pL =
u
;
2
A(HL)
[ + (1
4
=
Furthermore, in the interval
and
1
2 [ 1;
28
2.
2)
A(HL)
=
s)]u
>
u
:
4
(14)
2 [0;
1)
it is veri…ed that
2 [0;
1)
it holds AHLA
so the search engine wishes to link the publisher’s newspapers inde-
pendently of the versions released. For
and for
L0
for the relevant values of s.
Consider now the linking strategy of the search engine. For
M in AHA(H) ; AA(HL)
=
A0
This yields:
2
A(HL)
A0
that AA(HL)HL
Hence, when
2 [ 1;
3)
we …nd that AA(HL) > AHLA
AHLA > AH(A)H , where
2 [ 1;
2)
2
AHA(H)
satis…es AA(HL)HL = AHLA
the search engine only links the content maker
if this releases two versions. Last, it can be shown that for
2 [ 2 ; 1] we obtain AHLA
M axfAHA(H) ; AA(HL)HL g, implying that the search engine doesn’t want to link the publisher.
Finally, taking into account the strategy of the two …rms we obtain that the publisher
always releases the two newspapers, provided that
2 6 The
expression for
1
2
<
3
and that these are linked for
is the same than in the proof of Proposition 2. Indeed, in the two propositions the
three indiferent types are the same for the same value of .
2 7 Recall from the prof of Proposition 2 that for
1 it is satis…ed that
if r < r, which is assumed.
2 8 When p ! 0 then A
A
HLA ! AA(HL) = 1=2 and as a consequence
in Figure 3 region B vanishes.
31
2
HLA
!
1.
HA(H)
and
1
3
holds
Graphically, this implies that
2 [0;
2 ).
Q.E.D.
Proof of Corollary 3. When
<
1
the publisher releases the two versions and
2
that these are linked. Taking into account the pro…ts in (11) and the costs c(s) =
1
ks
the FOC
of the pro…t with respect to s is:
@
1
ks
A(HL)HL
=
@s
2
1
ks2
[ + (3
(2
) + (1
4[
De…ne s as the value of s that satis…es @
1
ks
A(HL)HL
is not presented for simplicity but it can be shown that @
1) 1]2 u
(2 3 )
s)]2
.
=@s = 0. The expression for s
A(HL)HL
1
ks
=@s > 0 for s < s
and that s is a decreasing function of k. Taking this into account, we de…ne k such that if
k < k then s >
k=
( +
1)
4 [1 + ( + (3
2 2
( +
1)
Suppose now that
+
and k > k such that s <
<
1
, where:29
2
2)
[ + (3
(1+ )
2)]
2
1)
1] u
h
and therefore s 2 0;
;
k=
+
4
[ +
(1+ )
2
(1 + ) ] u
;
. In this case, the publisher’s
prices and pro…ts are those in (14). Taking this into account, the FOC of the pro…t with
respect to s is:
@
1
ks
A(HL)
=
@s
It is easy to see that, @
A(HL)
1
ks
is decreasing in k we can …nd a value k
1
ks2
u
4
=@s < 0 when s > s
=
such that when k < k
2
p p p .
k u
Moreover, as s
then s
>
+
(1+ )
so
the publisher always wants a high degree of di¤erentiation. Oppositely, when k ! 1 then
s
! 0 and the publisher always wants the versions to be perfect substitutes. Finally, one
= k.Q.E.D.
can show that k
Proof of Proposition 4. Consider …rst the case where the integrated publisher doesn’t
link L. The consumer indi¤erent to H and L is
to L and A(H) is
any site is
maximize
is
2
HLA(H)
2 9 Note
A0
LA
pH ) =u (
= (pH
pL ) =u (1
), the indi¤erent
), and the indi¤erent to A and not visiting
= pH = u. Taking this into account, the integrated publisher sets pH to
1
HLA(H)
= pL (
that s <
= (pL
HL
+
= pH (1
HL
HL ) +
LA ).
(1+ )
pH (
A0 ).
LA
The pro…t of the independent publisher
Solving the problem of the integrated publisher we get:
is equivalent to
<
1.
Hence, it de…nes the domain of our analysis.
32
pH
=
1
HLA(H)
=
2
HLA(H)
pL
2
u
(u + pL ) +
2
[(
4(1
8
<
= pL
+
2
( +
[u(1 + ) + pL (1
2
)
)(
) pL + (1
)(
) (
) + (1
)
2(1
) (
) + (1
:
2(1
;
2
)u]
;
2
u
)(
(1
)]
2 2
(15)
(2
)(
))
) (
)(
2
(
(1
) (
)
) + (1
9
) pL =
;
) (2
)u
)
2
u
:
With the above is price it holds that:
HL
=
LA
=
A0
=
1
pL (
u(1
+
2(1
[pL (
)
1
u(
pL
)
pL ( (1
2 (
)
) + (1
)(
)
+2 (
)
+
) + (1
2(1
) 2+2 (
)(
) u
.
2
)
u
) u
pL ;
2
) + (1
) + (1
)(
)
)u]
;
(1
2
In order to ensure the participation of the independent publisher we assume pL <
Note that the above prices are valid as long as
that
LA ,
A0
2
b1 =
(pL + u(1 + ))
u
3
r
(u + pL )
>
LA
(
2(1
A0 .
b1 we …nd
However, for
)
h
(
2
) (pL + u(1
))
8(1
) pL
(16)
HL
HL )
= (pH
and
pH =
b1 A(H) doesn’t receive visits and the relevant indi¤erent consumers
2
HL
pL ) =u (1
= pL (
u(1
HL
) + pL
2
) and
L0 ).
L0
2
;
1
HL
1
HL
>
1
HLA(H)
=
3 0 This
(
for
2
1
HL
= pL =u . In this case, the pro…ts are
=
[u(1
) + pL ]
;
4(1
)u
HL
=
1
2
1
2
HL
=
pL
u(1
)
pL
2
>
(2
(1
1
L0
=
)pL
) u
pL
u.
2(
+ 2(1
) pL (pL + u
) (
)pL u(
is a general condition. When s = 1 it simpli…es to pL <
33
u)
1)2 (
(1
)(
2
)u2
)u
.
:
(17)
Notice, however,
, where
)p2L
= pH (1
Solving for pH yields:
With this price it is satis…ed that
that
>
where
Therefore, when
are
HL
)( s
)u 30
.
(2 s)
< b1 .
) p2L
i
:
Therefore, the integrated publisher o¤ers A(H) for
<
and it eliminates it otherwise.
Consider now the case where the aggregator links L. The quality of A(HL) is uA =
u [ + (1
and
= (pH + pL ) =u [ + (1
A0
pH (1
pL (
s)] and the indi¤erent types are
HL )
+ pH (
LA )
HL
pH
=
1
HLA(HL)
=
where
=
+ pL (
pL
=
pL
( + )+
pL
LA
=
A0
=
2
2
HLA(HL)
8
<
:
pL
The relation
2
2
(
(1
2
(
s) + s(1
(1
2
)
2
2
(3
)
2
2
2
2
(
(1
(1
s)
expression). When
( (1 +
s))
4
s)s) and
1
HLA(HL)
2
HLA(HL)
2s) + ( + s
( (1 +
=(
s(1 s)) + (
2(1
)u
+ (4s + (3 +
3 (1
s)s +
3 ) + ( (1 +
>
s))
2
s) + s(1
2
6s)
LA
>
A0
s)
=
1)) +
)( +
(3 + s)
3
2(1
(3 +
6s))
2 [ (1 s) + ] u
LA
(2
( + 2s
s) u.
3 )+
A0
2
2
;
s)
2
( +
s
1)) +
9
=
)u
is satis…ed for
b2 it holds that
3(1
;
s)s) +
< b2 (we don’t show b2 because it is a long
so nobody visits A(HL). In this case, the
Next, we examine the linking strategy of the publishers. In the case of the integrated
publisher, notice that in the interval
2 [0;
1)
we obtain that
notice that
1
1
2 [0;
) it is veri…ed that
the value of
1
HLA(HL)
>
1
HL
2 [0;
1)
=
1
HLA(H)
Therefore, for
1
HLA(HL) .
<
2
we obtain that
Also notice that
2
=
1
2
=
1
1
HL .
1
HLA(H) .
As a result, for
1
HLA(HL) .
Also,
2 [ 1 ; 1).
>
for which
1
HLA(H)
for s = sb and
2
and for
1
HLA(HL)
=
2 [ 2 ; 1) that
= 0 for s = 1. Taking
this into account, in the region s 2 [b
s; 1) the integrated publisher wants to link L if
34
On
for s = sb. Hence, for s 2 (0; sb] the
the value of
1
HLA(HL)
>
1
HL
and only o¤ers H if
In order to analyze the region s 2 [b
s; 1) de…ne as
1
HLA(H) .
=
2 [ 1 ; 1) that
is a decreasing function in s and that
integrated publisher wants to link L if
1
HLA(HL)
for which
and for
1
HLA(HL)
;
+
price and the pro…ts of the independent publisher are those in (17).
the other hand, we de…ne as
=
1)) +
2s) + ( + s
1) ( s
2)
(1 + s)
2( s
HL
(pH + pL )] =u ( s
for simplicity. The price in (??) implies that:
(1 + s
(
= [pL
Solving the problem yields:
2
)+
(2 s +
LA
and the pro…t of the independent publisher is
)+
(
),
s)]. The integrated publisher sets pH to maximize
A0 ).
LA
(
pL
We don’t show
HL
A0 )
LA
= (pH pL )=u (1
HL
2 [0;
2 ),
:
2
;
2
(18):
)
maintains A(H) without linking L if
2 [ 2;
], and only o¤ers H if
2 [ ; 1).
To examine the preferences of the independent publisher we de…ne as
2
HLA(H)
which
=
2
HLA(HL) .
2
HLA(HL)
for which
3
the values of
for
In the space f ; sg this de…nes a set of parameter combinations
2
HLA(H)
(Figure 4). In the rest of cases the publisher doesn’t accept
to be linked.
Finally, we identify the situations in which the two publishers reach an agreement over L.
It can be shown that for
>
2
intersects
twice in the f ; sg space: call these roots
3
(e1 ; s1 ) and (e2 ; s2 ), where s1 < s2 . In particular, when s > s1 and s < s2 it is satis…ed
that
>
2
3
and therefore the two …rms agree on setting the link to L. For s1
s
s2 the
agreement is not pro…table for one of the publishers. Q.E.D.
Proof of Proposition 5. Results for the case in which A doesn’t link L are shown in the
proof of Proposition 4. When A(H) links L and s <
uL and the relevant indi¤erent consumers are:
HL
= (pH
pL ) =u (1
sets pH to maximize
), and
1
A(HL)HL
L0
AH
+
1
it is satis…ed that uA(HL) > uH >
= [ (pH + pL )
pH ] =u [ + (1
s)
1],
= pL = u. According to this, the integrated publisher
= pH (1
AH )
+ pH (
HL ).
AH
The resulting price and
pro…ts are:
pH
=
1
A(HL)HL
=
pL [ + (1
) + (1
2
(1
2(1
)
[pL [ + (1
) + (1
4(1
) [1
(1
)
(1
The pro…ts of the independent publisher
s) 1]
) + (1
s)
s)] [
2
A(HL)HL
(1
) 2
) [1
s
(1
1] (1
) [1
(1
(1
)(2
) + s] u
s)] u
;
2
s)] u]
(19):
are not shown for simplicity. The price
in (??) leads to the following expressions for the indi¤erent consumers:
AH
=
HL
=
L0
=
8
< pL [1 + (3
:
(2
))
(1
2 [1
pL 5
3
2
1
)(1
(1
2
(1
) ( + (1
s)] [ s + (1
s
(2 + (2
s)
)(1
+ (1 + (3
5) + s) + (1
2(1
)[
(1
)(2
)
)
1)u
)
]u
) ( + (1
s] u
9
3s))] =
;
s)
;
1)u
;(20)
pL
:
u
It can be shown that
AH
<
HL
when s < s1 , implying that any consumer visits H
35
directly. The value s1 for which AH = HL is:
8
<
[ +2
q
: (1
) (1
)2 (1
)2 2 u2 2(1
s1 =
1
2(1
)(1
) [1 + (5
2 [pL
When s < s1 the relevant indi¤erent consumers are
and
L0
pH
pL (1
=
pL
2
A(HL)L
=
h
)+(
2
s)u
(1 + )(
s)u
With this price we observe that
for s < s1 it can be shown that
On the other hand,
1
=1+
1
A(HL)L
(1
AL
1
A(HL)L
1
HL
)pL (
>
1
HLA(H)
for
1,
Taking this into account, if s < s1 and
for
where
p
(1
(1
s)
)pL
s)u
>
1
(18
=
2s
pL
u.
(16
s)
and gets:
2
s)u]
s)u
i
;
+ pL )2 (
(21)
:
On the other hand,
s)
A(H) is never active. If
> b1 :
1;
high type
consumers visit A(HL) and intermediate consumers L. In this case, the integrated publisher
wants to link L since
1
A(HL)L
>
1
HLA(H) :
Next, de…ne as s2 the value of s for which the indi¤erent consumers in (20) satisfy
AH
=
L0 .
2
s2 =
( +
1)
4 + (3 + )
[(2
2
+ (2
)pL (1
)
)
2
pL
(1
)( +
1)
u
u]
Notice that s1 intersects s2 once at the f ; sg space: call this root (e; se)(Figure 5). For
(e; se) it is veri…ed that
HL
<
L0
AH
=
HL
=
L0 .
and for s < se and s < s1 that
AH
Moreover, for s > se and s < s2 we …nd that
<
HL .
For s < s2 L does not receive direct visits and the relevant indi¤erent consumers are
AH
= [ (pH + pL )
to maximize
pH
=
2
A(HL)H
=
1
A(HL)H
pH ] =u ( + (1
= pH (1
AH )
s)
1) and
+ pH (
AH
H0
= pH =u. Thus, the publisher sets pH
H0 ),
which yields:
2
[(
1)pL ( + (1 s) 1)u]2
1)pL ( + (1 s) 1)u]
1
;
=
;
A(HL)H
2[ s ( + + (
2) )]
4( + (1 s) 1)[ + + (
2)
s]
[pL (2
1+(
2) + 2 (1 s)) + (
1)( + (1 s) 1)u]
pL [1
]:
(22)
2( + (1 s) 1)[ + + (
2)
s]
[(
36
9
=
9 )))] p2L ;
< b1 , where b1 is de…ned as in (16).
)p2L (1
)p2L
>
2
)
L0
AL )
)+(
4(
i
(8
pL ] =u (
= pH (1
(1
s)u
(1
(
= [ (pH + pL )
[pL (1
=
pL 2 +
2 (
h
= 21 1
4)]upL + [1
) u]
1
A(HL)L
1
A(HL)L
;
(1
AL
= pL = u. As a result, the publisher maximizes
) 2 ]pL
) + 3(1
With this price we obtain that
AH
>
H0
if pL is su¢ ciently high.
Finally, let s3 be the value of s for which the indi¤erent consumers in (20) satisfy AH = 1.
8
9
=
[2( + 2
1)u pL (3
1) (1
)(3
) u]
1 <
q
s3 =
4u 2 :
2 ((3
1)2 p2L + 2(1
)(1
)(2
(3 + ))pL u + (1
)2 (2 3 + 2 )2 u2 ;
This implies that for s > s3 A(H) is never active and consumers only visit H or L:
Taking these results into account we can now determine the linking strategy of the publishers. For s < se; we have seen that the integrated publisher wants to link L for
<
1 and
doesn’t want otherwise. For s > se and s2 < s < s3 the services A(HL), H and L would be
active if A(H) links L and the price and pro…ts are those in (19) (see Figure 5). In spite of
1
HLA(H)
this, as
1
A(HL)HL
>
for
< b1 and
1
HL
1
A(HL)HL
>
b1 31 the integrated
for
publisher doesn’t want link L. For s > se and s < s2 only A and H would receive direct visits if
A(H) links L, and the price and pro…ts are those in (22). But against, as
< b1 and
for
s > se and s
1
HL
>
1
A(HL)H
for
1
A(HL)H
> b1 the integrated publisher doesn’t link L. Finally, for
< b1 , or the ones in (17) otherwise.
Consider now the linking strategy of the independent publisher. For s
for s
>
2
HLA(H)
s1 and
1
HLA(H)
s3 no consumer visits A(H). As a consequence, the optimal price and pro…ts
are those in (15) if
2
A(H)L
<
when
< b1 if pL > 0 and
2
A(H)L
>
2
HL
for
s1 it holds that
b1 if pL > 0. Therefore,
< b1 the publishers agree to link L. Otherwise the integrated publisher is not
interested. Q.E.D.
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