Calzada Ordonez

Competition in the news industry: �ghting aggregators

with versions and links�

Joan Calzaday and Guillem Ordóñez,z

October 3, 2013

Abstract

We analyze the linking and versioning strategies of a media publisher when facing

competition from blogs, search engines and news aggregators. We show that when the

publisher competes against a blog it is less likely to release a ��ghting version� if this

generates signi�cant spillovers for its competitor. When the publisher competes against a

search engine, it wants to be linked when it receives enough indirect tra¢ c from it, and

in this case it uses the search engine as its own low quality version. We also demonstrate

that when the publisher is integrated with a search engine it might link other publishers

to obtain more indirect visitors if the contents are su¢ ciently di¤erentiated.

Keywords: Product segmentation, versioning, linking, media market, search engines,

news aggregators, Internet.

JEL: D83, D85, L12, L22, L86, M31

�We thank Christian M. Bender, Luis Collado, Martin Peitz, Joan Santaló and Tommaso Valletti for helpful

comments. We also thank participants at the 3rd Workshop on the Economics of ICTs (Porto), EARIE

(Rome), JIE (Murcia), and at semininars at the Universitat de Barcelona, Universitat Autonoma de Barcelona

and Universidad Complutense de Madrid. We gratefully acknowledge �nantial support from the NET Institute

(www.NETinst.org).yDepartament de Política Econòmica, Universitat de Barcelona. [email protected] of Economics, University of Warwick, g.ordonez-cala�@warwick.ac.uk

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 favoured the creation of many news services that compete with traditional newspapers.

In this new scenario, 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 the linking and versioning strategies of media publishers.

Some of the most successful new players in the media market are search engines and news

aggregators, which have risen to occupy the top positions in audience ranking (Nielsen 2011).

Search engines link the pieces of news of other on line newspapers and display them in a single

site accompanied by a title or an 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 diverse

criteria including the originality of information, their immediate interest for readers and their

�contagious� capacity. News search engines such as Google News, Bing News, and Summify

neither hang advertisements nor set user charges. Their commercial objective is essentially to

bring visitors to other Internet services on the same platform, such as common searches that

sell advertising space or social platforms.

News aggregators, by contrast, provide news articles that are created with information

obtained from newspapers and press agencies, and they do not usually include links to the

original sources. Some of the best known aggregators are Yahoo! News, Drudge Report, and

The Hu¢ ngton Post. These usually reach licensing agreements with information suppliers to

avoid copyright infringements.

The emergence of these new services has created a trade-o¤ for traditional newspapers,

who must decide between �ghting the entrants or accommodating them. On the one hand,

entrants create a business-stealing e¤ect since they use information from traditional newspapers

1Figures for 2002 show that the newspaper industry amounted to around $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 on-line news sources (PEJ, 2011).2According to this argument, U.S. legislation considers that these entrants make a �transformative� use of

contents and, as a consequence, do not infringe copyright law (Isbell, 2010).

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to create their own contents and attact visitors.3 On the other hand, they create a market

expansion e¤ect because they reduce consumer search costs by making great variety of contents

widely available from one single web site. This situation bene�ts traditional newspapers, which

receive indirect tra¢ c from the visitors of the search engines that click their links.4

The relationship between search engines and news agencies is even more complex, because

the main activity of agencies is precisely that of feeding newspapers with their content. In order

to deal with this situation, in 2004 Google News reached an agreement with the Associated

Press (AP), permitting Google to host AP contents in exchange for compensation.5 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 settled the case by signing a licensing agreement, according to which Google

was granted the right to post AFP content. In spite of this, other press associations are still

pressing public authorities to protect their content,6 and some regulators such as the Federal

Trade Commission have suggested various solutions to deal with this problem, which range

from extending copyright legislation to diverse antitrust exemptions for news organizations

(FTC, 2010).

Traditional newspapers have modi�ed their commercial strategies to defend themselves

against new competitors. Some publishers believe that they still have a signi�cant demand

from readers who prize high quality journalism, editorial guidance and the opinions of experts.

Thus, for example, The Times launched a pay wall in 2010 and The Wall Street Journal has

3Some traditional newspapers consider aggregators to be free-riders reselling the information they have

gathered at vast expense (Frijters and Velamuri, 2010). R. Murdoch has declared: �To aggregate stories is not

fair use. To be impolite, it is theft�. See The Guardian, 1/12/2009, �There�s no such thing as a free news

story�, http://www.guardian.co.uk/media/2009/dec/01/rupert-murdoch-no-free-news.4Evidence suggests that 44% of Google News! users in 2010 didn�t click through to the original articles.

http://techcrunch.com/2010/01/19/outsell-google-news/.5This agreement was broken at the end of 2009 and the search engine stopped o¤ering AP�s links. In spite of

this, in early 2010, AP reached a new agreement with Google and another with Yahoo! News. See �Associated

Press Returns to Google News�, http://mashable.com/2010/02/09/ap-google-news.6See, for instance, the lawsuit of Federazione Italiana Editori Giornali against Google in 2009; the demands

of the Federation of German Newspaper Publishers for a new copyright in 2009; the �Hamburg Declaration on

Intellectual Property Rights�, signed by the World Association of Newspapers and News Publishers in 2009; or

the case that the Newspaper Licensing Agency won in the UK High Court involving the main newspapers and

news aggregators in 2010.

2

recently launched �freemium�, by which general news remain free but premium contents and

some blogs are locked behind a pay wall. Similarly, the Financial Times o¤ers subscriptions

to premium and standard articles at di¤erent prices.7 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. Other publishers have even created their own

news aggregators with high quality contents.8

The objective of this paper is to analyze how new business models in the media market are

modifying the commercial strategy of media publishers. We present a model that examines

the linking and versioning strategies of one publisher that can compete with one blog, search

engine or news aggregator. By so doing, we identify when it wants to �ght the entrant by

releasing a low quality version and when it prefers to accept the links of the search engine. We

show that links allow the publishers to use the web sites of their competitors as an alternative

distribution channel for their contents.

Our paper contributes to the recent literature that analyzes the impact of news aggre-

gators in the managerial strategies of publishers. Katona and Sarvary (2008) were the �rst

to theoretically analyze strategic linking between web sites in a market for advertising links.

Dellarocas et al. (2010) analyze competition among news sites that generate revenue from user

visits and who 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 linking has di¤erent

implications depending on the level of di¤erentiation of the web sites. They also show that the

presence of an outside alternative may bene�t incumbent content sites, since they increase the

total tra¢ c that �ows in the content ecosystem and divert most of it to the best content sites.

George and Hogendorn (2012) adapt a two-sided market model to digital media markets to

7Other examples are the plans of the New York Times to erect a paywall or those of News Limited to

charge for access to certain parts of 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-1743.8 In 2009, Murdoch�s News Corporation launched the Project Alesia and in 2010 Gannett, the New

York Times Co. and the Washington Post Co. created Ongo. The two aggregators had to o¤er high

quality contents behind a paywall but both ceased operations short after their release. See A. LaFrance,

�Ongo, an attempt at a pan-media paywalled aggregator, is closing�; Nieman Journalism Lab, 8/5/2012,

http://www.niemanlab.org/2012/05/ongo-an-attmpt-at-a-pan-media-paywalled-aggregator-is-closing/.

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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, aggregators may not expand the

market. Jeon and Nasr (2012) show how the presence of a news aggregator a¤ects competition

among newspapers. They �nd that competition with a news aggregator can lead to the special-

ization of newspapers when their advertising revenue increases substantially with an increase

in quality. With specialization, the presence of 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 might be 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 essentially depends on the form of the cost function. In particular, versioning

is optimal when the marginal cost function of improving the quality is su¢ ciently convex.

More recently, a number of papers have sought to clarify the circumstances under which

versioning is convenient for a monopolist. Bhargava and Choundary (2008) �nd that version-

ing depends on the relation between the optimal market share of the low and high quality

versions of one product when they are o¤ered alone. Anderson and Dana (2009) show that

versioning requires that the relative change in overall surplus associated with a product qual-

ity improvement is increasing in consumers�willingness to pay. Calzada and Valletti (2012)

demonstrate that versioning might arise when consumers are allowed to buy two versions of

the same product. They examine the particular case of the movie industry and explain that

versioning is optimal when the theater and the DVD versions are not merely substitutes. In

this case, while some consumers buy both versions, others only use the theater or the DVD

version. This situation is closely related to that discussed here, since the main characteristic

of news aggregators is to allow reading 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 a very e¤ective and pro�table instrument

in the �ght against piracy.9 Valletti and Szymanski (2006) analyze parallel trade for products

9An early analysis on this issue can be found in Johson and Myatt (2003).

4

protected by intellectual property rights such as the export of pharmaceuticals. They show that

pharmaceutical �rms only �nd it optimal to release a lower quality version when they compete

with a generic product. Our paper is related to their model, since we analyze the versioning

strategy of a publisher who faces competition from other sites. A remarkable di¤erence is,

however, that the contents distributed by publishers through Internet can be immediately used

by other news sites and can be linked. We show that these situations can modify importantly

the versioning strategy of �rms.

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 commercialize two news sites of di¤erent qualities and/or di¤erent editorial

approaches, as is the case of the News Corporation or The New York Times Co.10 Taking this

into account, we �rst analyze the e¤ects of the entry of a blog (or a news site) that uses the

information released by the publisher to generate its own contents, but that doesn�t set links

to the original sources of information. 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 release a ��ghting version�to defend itself against the competitor, in our model

the �ghting version generates positive spillovers that increases the quality of the competitor.

As a result, it is more likely that the publisher accommodates the blog instead of releasing a

second version.

The second part of the paper analyzes the case when the publisher competes against a

search engine. The search engine bene�ts from the news sites of the publisher when it links

them. We show that the publisher accepts the links of the search engine when it receives

su¢ cient indirect tra¢ c from it. The reason is that the link can generate more revenues than

a low quality version. In fact, for the publisher the link plays a similar role than a low quality

version. When the indirect tra¢ c generated by the link is even higher the publisher accepts

the links but releases a second version in order to expand the audience of the search engine.

Although the new version cannivalizes its high quality news site it generates enough indirect

tra¢ c to compensate this e¤ect. As in Calzada and Valletti (2012), the publisher releases two

versions because some consumers buy both of them. Finally, we examine the case where the

10Alternatively, we could think in one newspaper that commercializes high and low quality pieces of news

that cover the same event, as in the freemium pricing model.

5

quality of the search engine can be higher than the quality of the news sites o¤ered by the

publisher, and we show that in this case linking and versioning are more likely.

The last part of the paper considers an integrated publisher that owns a newspaper and a

search engine. We explain that the publisher can be interested in linking its competitors when

their news sites are su¢ ciently complementary and the indirect tra¢ c generated by the search

engine is not too high. We also show that the publisher can maintain the search engine active

but without links to its competitors because it constitutes a pro�table distribution channel.

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 high and a low quality

search engine. Section 5 considers an integrated publisher that owns a news site and a search

engine. Section 6 concludes.

2 The Model

We analyze the versioning and linking strategies of a publisher that can have di¤erent competi-

tors such as a blog, a search engine or a news aggregator. The publisher can o¤er one or two on

line newspapers with di¤erent editorial approaches. It always o¤ers the news site H of quality

uH = u and it might also release the site L of a quality uL = �u; where � < 1. The quality

of each site is exogenously determined and their content can be related. For example, L may

be a degraded version of site H and consumers might not obtain any additional utility from

it after having visited H. Alternatively, H and L can be complementary sites. For example,

H can be a site with general information and L a site specialized in sports or a site with the

blogs of experts.

The competitor o¤ers the news site A, which can include contents obtained from H and

L, or links to these products. When the publisher only releases H the quality of A is uA = �u;

where � < � re�ects that A doesn�t o¤er original contents and doesn�t follow any editorial

policy. On the other hand, when the publisher releases H and L , the quality of A is uA =

u[�+�(1�s)], where s 2 (0; 1)measures the positive spillovers that the release of L generates on

the consumers that are already consuming H. Notice that uA > uH when s < (� + �� 1)=�.

This occurs when consumers prefer contrasting the information of several news sites than

6

visiting just one newspaper with a particular editorial policy.

In order to simplify the model and to make it more realistic we assume that the consumers�

searching costs are so high that they can only visit one site (the anchor site). In spite of this,

when consumers visit a search engine or a news aggregator they can click through to the

original contents of all newspapers (see Purcell et al. 2010 and Dellarocas et al. 2012). This

assumption highlights the key feature of search engines and news aggregators, which is to

group the contents of di¤erent newspapers on a single web site, thereby signi�cantly reducing

consumer�s search costs.

Consumers are characterized by the intensity of their preferences for news sites. Imag-

ine that they are uniformly distributed in the segment [0; 1] and de�ne as � the consumers�

willingness to pay. Taking this into account, the consumers�net utility when they visit the

publisher�s version i is �ui�pi, with i 2 fH;L;Ag, where pi is the price of the news sites or the

consumers�costs when they visit the entrant. An alternative way of interpreting our model is

to imagine that pi is the number of advertisements inserted on the news site i when the price

of the advertisements is exogenously set and normalized to one. Under this interpretation the

publisher would choose the number of advertisements that maximizes its pro�ts, taking into

account that advertisements reduce the utility of consumers.

Finally, in order to focus our attention on the �rm�s linking and versioning strategy, we

assume that the costs associated with producing each version are sunk, and that the marginal

costs of the versions are zero. This assumption means that it could be expensive to generate

contents for the newspapers, but that they can be distributed at no cost through the Internet.

3 Competing with blogs: no exclusion option

This section examines the commercial policy of a publisher competing with a blog, or 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 on line newspapers. As a result,

when a publisher releases new contents it feeds these sites with materials that improve their

quality. In this section, we assume that the publisher is not able to prevent the use of its

contents by others, as it happens with bloggers.

The following set of indi¤erent consumers describes the segmentation of consumers under

7

two possible scenarios. If the publisher only releases newspaper H the consumer indi¤erent

to visiting the newspaper and the blog is �HA = (pH � pA)=u(1 � �); while the consumer

indi¤erent to visiting the blog and not visiting any news site is �A0 = pA=�u. In this case, the

publisher�s pro�t is �HA(H) = pH(1 � �HA). On the other hand, if the publisher releases H

and L the consumer indi¤erent to visiting H and L is �HL = (pH�pL)=u(1��), the consumer

indi¤erent to visiting L and A is �LA = (pL � pA)=[u(� � (� + �(1 � s))], and the consumer

indi¤erent to visiting A and not visiting any news site is �A0 = pA=[u(� + �(1 � s))]. In this

case, the publisher�s pro�t is �HLA(HL) = pH(1� �HL) + pL(�HL � �LA). In this section, we

assume for simplicity that uL > uA, which means that the quality of the blog can never be

larger than the quality of L.

The timing of the game played by the publisher and the blog is as follows: �rst, the

publisher decides how many versions it o¤ers; second, it sets the prices and releases its news

sites; third, the blog creates its own contents using the information generated by the publisher.

Finally, consumers choose their preferred news site.

The following proposition shows when the publisher only releases H and accommodates

the blog, and when it releases a �ghting version. It also describes the resulting segmentation

of the consumers.

Proposition 1. In the presence of a blog the publisher reacts as follows:

1) If � < �1 its optimal versioning strategy is:

� When 0 � s � bs, the �rm only o¤ers H, and the blog is active;

� When bs < s � 1, the �rm supplies H and L, and the blog is active;

2) If � � �1 its optimal versioning strategy is:

� When 0 � s � s2, the �rm only supplies H, and the blog is active;

� When s2 < s � s1, the �rm supplies H and L; but the blog is not active;

� When s1 < s � 1; the �rm supplies H and L, and the blog is active;

Proof. See the Appendix.

8

The �rst part of this proposition presents the strategy of the publisher when the quality

of A is low in comparison with that of L (� < �1). In this case, the �rm releases L when the

spillovers generated on A are small (s > bs), because the market expansion e¤ect obtained withL o¤sets the cannibalization e¤ect of L on H (Figure 1). However, when spillovers are large

(s � bs) the release of L generate little revenues and the publisher accommodates A instead ofreleasing L. Also notice that for s > bs there is a complete segmentation of consumers: thosewith a high type visit H, those with an intermediate type visit L; those with a low type visit

A; and those with an even lower type don�t visit any news sites at all (region C in the two

panels of Figure 1).

Figure 1: Competition with a blog (� = 0:45 in Panel I and � = 0:5 in Panel II; � = 0:75; u = 1;

pA = 0:12). The �gure shows the consumers�segmentation as a function of s. In Panell II, for s < s2

the publisher only o¤ers H : low type consumers don�t visit any site, intermediate consumers visit A,

and high type consumers visit H . For s > s2 the publisher o¤ers L and H . If s2 < s � s1, pL is

low and the blog is not active; if s1 < s � 1, pL is higher and some consumers visit A.

The second part of the proposition considers the case where A and L have similar qualities

(�1 � � < �). The intuition of the result is the same than before, but now when s takes an

intermediate value (s2 < s � s1) the publisher sets a low pL and A fails to attract consumers

(region B Panell II in Figure 1).

This proposition can be directly related to the model of Valletti and Szymanski (2006) who

show that under the presence of a competitor an incumbent will release a �ghting brand to

9

retain part of its pro�ts. Proposition 1 reaches the same conclusion when s is close to 1, that

is, when the blog gains few spillovers from the �ghting newspaper. However, when the new

site strengthens signi�cantly the blog, the publisher only o¤ers H.

The model reveals that the publisher�s versioning strategy depends on the externalities

generated by L. The next result shows that when the publisher releases L it would prefer to

o¤er a close substitute to H in order to minimize the spillover e¤ect.

Corollary 1. Suppose the publisher�s cost of horizontally di¤erentiate L from H is c(s) =

1=ks. Then when it releases L it prefers the lowest possible level of di¤erentiation, s = 1.


The key element to understand this result is that consumers can only access the information

o¤ered in both H and L when they visit the blog. In fact, the publisher doesn�t has any site

that aggregates the contents of the versions and for this reason it can not bene�t of their

complementarity. For this reason, it if was able to determine the quality of L it will just create

a degraded version of H (i.e. s ! 1). For example, L could summarize the main information

in H or could reproduce part of the contents. The reduction of s reduces the utility of A and

allows the publisher to increase its prices. In spite of this, some switch from A to L.

The main result of this section has been to show that when publishers can�t avoid its con-

tents being used by others versioning is less likely than what was previously considered in the

literature. The reason is that a �ghting versions improves the quality of the blog. In spite

of this, if the publisher was able to control the use of its contents it could also accomodate

the entrant in exchange of an appropiate compensation. This is the case of several publishers

and news agencies such as Reuters, BBC News, or USA Today which have reached an agree-

ment with Yahoo! News. In this case, the negotiation gives the publishers the possibility of

internalizing the complementarity generated by their versions.11 The next section examines

an alternative mechanism that allows the publisher to bene�t of the complementarity between

the versions, which is the establishment of links in the aggregators�web sites.

11Calzada and Ordoñez (2012) analyze the negotiation of a revenue sharing agreement between a publisher

and a news aggregator.

10

4 Competing with search engines: spillovers and links

Next we extend our model to examine the versioning strategy of a publisher that competes

against a search engine. Imagine that the publisher can release one or two newspapers and

that the search engine can link them in its web site. The visitors of the search engine read the

headlines of the news articles (or excerpts of them) and click through to them with a probability

�, which we assume to be the same for H and L. For example, � = 1 means that the visitors

of the search engine always click the links and generate indirect tra¢ c for the publisher, and

� = 0 means that they read the headlines but never click through to any news articles.

Both the publisher and the search engine must agree in the establishment of the links. The

publisher will accept the links to its newspaper if this increases its pro�ts; and the search engine

links the newspapers if this increases its audience. We consider that consumers�searching costs

are so high that the search engine is the only available mechanism for accessing the contents of

two newspapers. In fact, the main feature of search engines is that they aggregate and classify

the contents of several newspapers and reduce consumers�searching cost.

The quality of the search engine�s site, which we call A, depends on the links that it

contains. When it reaches an agreement with the publisher its quality is uA = u� if the publisher

releases H and uA = u[� + � (1� s)] if the publisher releases both H and L. Contrary, when

there is no agreement its quality is uA = ur; with r < �. This implies that consumers value A

less than L when the search engine doesn�t link the publisher.

Taking this into account, the net utility of consumers that directly visit H is �u� pH and

that of those who directly visit L is ��u� pL. The net utility of consumers that visit A when

this links H and L is �u[�+� (1� s)]� �(pH +pL), when it links H is �u�� pH , and when it

doesn�t link any newspaper is �ur� pA. Notice that the search engine consumers only pay for

the contents when they click through to the links. This re�ects the present situation of some

search engines like Google News!, which neither charge any price to consumers nor include

advertisements in their sites.

When the search engine linksH and L it has a quality that can be higher or lower than those

of H, depending on the complementarity between H and L. To account for this possibility,

we �rst analyze the case of a low quality search engine (uH > uL > uA) and afterwards we

11

examine the case of a high quality one (uA > uH > uL).12

The following proposition describes the linking and versioning strategies of a publisher that

compete with a low quality search engine. This is the case where users derive greater utility

from directly accessing one news site than from visiting one search engine that links several

news sites (e.g. they like the editorial policy of the newspapers and value their 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 about setting links on the publisher�s

sites, and taking into account the results of the negotiation the publisher set the prices; and

third, the news sites are released and consumers choose their preferred service.

Proposition 2. The linking and versioning strategies of a publisher and a low quality

search engine ( s > �=�) are:

1) If 0 � � � �1 the publisher releases H and L, but it doesn�t accept the links. H, L and A

receive direct visitors;

2) If �1 < � � �2 the publisher releases H and both �rms agree on linking it. H and A receive

direct visitors;

3) If �2 < � � �3 the publisher releases H and L and both �rms agree on linking them. Only

H and A receive direct visitors;

4) If �3 < � � �4 the publisher releases H and both �rms agree on linking it. H and A receive

direct visitors;

5) If �4 < � � 1 the publisher releases H and L, but the search engine is not interested in

linking them. H, L and A receive direct visitors;

The existence and size of these intervals depend on s.


The �rst part of the proposition shows that the publisher doesn�t accept to be linked when

it receives a small amount of tra¢ c from the search engine (0 � � < �1). In spite of this, the

publisher releases the �ghting version L because it doesn�t create spillovers on A (region A in

the two Panels of Figure 2). As a consequence, there is a complete market segmentation of

12We omit the case where uH > uA > uL for simplicity.

12

Figure 2: Competition with a search engine (� = 0:4; � = 0:8; u = 1; r = 0:3; pA = 0:05).The

�gures show the consumers�segmentation as a function of �. Each panel considers a di¤erent

level of spillovers and is divided in regions according to the parts of Proposition 2. In region

A the publisher doesn�t want to be linked. In region B the publisher is linked and releases H.

In regions C the publisher is linked and releases H and L: In region D the publisher is linked

and releases H. Finally, in region E the search engine doesn�t want to link the publisher.

consumers: lowest-type consumers do not visit any site and the rest of consumers visit H, L

or A according to their preference for quality. It is interesting to mention that �1 is increasing

in pA, which means that when the search engine becomes more unattractive to consumers the

publisher is less interested in reaching an agreement with it. Regarding the search engine, in

this interval it wants to link the H and L. Indeed, although this implies an increase in its price

�(pH + pL) the increase in quality would compensate this situation and it will attract more

visitors.

The second and third parts of the proposition show that when the publisher receives a

larger amount of tra¢ c from the search engine it accepts to be linked and uses A as its own

low quality version. If �1 < � � �2, the publisher only releases H. If it also releases L this

would generate positive spillovers on A that would reduce its pro�ts. Particularly, when � and s

are small the market expansion e¤ect generated by L does not compensate the cannibalization

e¤ect on H.13 Note that in this interval the link of H transforms A in the low quality version

13 If s is close to 1 the publisher always releases L and region B vanishes (see Panel I in Figure 2).

13

of the publisher. Thus, the publisher prefers to accept the link and to use A as an alternative

distribution channel for H than to release L.

If �2 � � � �3, the publisher releases L. Like in the previous case, it transforms the search

engine in its low quality version. Speci�cally, it segments the market in such a way that high

type consumers visit H and a group of intermediate consumers visit H and L indirectly via

the search engine (see region C). In fact, the publisher releases L to increase the audience of

A and to obtain indirect visits from both versions. If the level of complementarity between H

and L is not too high, this strategy does not create a large cannibalization e¤ect on H.

The last two parts of the proposition show that the search engine doesn�t want to link

the publisher�s newspapers when � is high. When �3 < � � �4, the publisher only releases H

because if it releases H and L the search engine would not link any site. The reason is that

the price of the seach engine, �(pH + pL) would be very high (see region D).

Finally, when � is su¢ ciently large (�4 < � � 1) the search engine never links the publisher.

The links would increase importantly its price and reduce its audience. In this case, consumers

are segmented as in the �rst part of the proposition (see region E).

In our model the complementarity between H and L plays a key role in the strategy of

the �rms, but it is introduced exogenously. The following result considers how the publisher

would set s once 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¤erentiate L from H is c(s) = 1=ks,

then the publisher will choose the lowest possible level of product di¤erentiation, s = 1.


Therefore, even when the publisher accommodates the search engine and releases the two

newspapers it prefers to increase s in order to reduce spillovers as much as possible.

The strategy of the publisher changes signi�cantly when the quality of the search engine

is larger than the quality of H and L consumed separately, uA > uH > uL. This situation

re�ects the case where consumers prefer product variety to limiting themselves to one high

quality newspaper. The following proposition describes the commercial strategy of �rms in

this situation.

14

Proposition 3. The linking and versioning strategy when the publisher competes against

a high quality search engine ( s < (�+ � � 1)=�) is:

1. If 0 < � � �1, the publisher releases H and L and accepts the links. Only A receives

direct visits;

2. If �1 < � � �2, the publisher releases H and L and accepts the links. A, H and L receive

direct visits;

3. If �2 < � � 1, the publiser releases H and L, but either the search engine (for �2 < � �

�3) or both �rms (for �3 < �) are not interested in the links.


The �rst part of the proposition focuses on the case in which � is small (0 � � � �1). In

such a situation, the publisher releases H and L and allows the links of the search engine. As �

is small and uA � uH only A receives direct visitors. In spite of this, the publisher maximizes

pro�ts with this segmentation of the market because it can set high prices for the two services.

Indeed, it obtains more pro�ts that if it was a monopolist. Hence, the presence of one search

engine that aggregates contents makes both �rms better o¤ because consumers indirectly visit

both H and L.

The second part of the proposition shows that when the users of the search engine make

more visits to the newspapers (�1 � � < �2) prices become too high for some consumers to

visit the two versions. As a result, there is a complete segmentation of the market: high type

consumers visit A, intermediate types visit H, low types visit L, and very low types don�t visit

any site. Notice that in this scenario, version L cannibalizes H in two ways. First, some low

type consumers who could consume H actually visit L. And second, some high type consumers

who could visit H now visit A. In spite of this, as � is high the cannibalization over H is o¤set

by the direct and indirect visits to L and the indirect visits to H:

The last part of the proposition presents the case for the highest values of � (�2 < � � 1).

In this case, both �rms lose incentives to reach an agreement. When � > �2 the high price

of A will o¤set the increase in the quality of A generated with the links. As a result, the

search engine prefers not to link the publisher. To illustrate this situation, imagine that s = 1

15

Figure 3: Consumers�segmentation when the publisher competes with a high quality search engine

(�=0.4, �=0.8, u=1, r=0.2, pA=0.05). Each panel considers a di¤erent level of spillovers s and is

divided in regions according to Proposition 3. In region A the publisher releases two versions that are

linked, but only the seach engine is active. In region B the publisher releases two versions that are

linked, and all products are active. In region C the publisher releases two versions that are not linked

and the three sites are active.

and uA = uH . In this case, if consumers access H directly they pay pH , but if they use the

search engine and click through to the two newspapers they pay �(pH + pL). Therefore, if

� > pH=(pH + pL) consumers are better o¤ buying only H and the search engine does not

receive visits. Similarly, for � > �3 (�3 > �2 is not shown in Figure 2) the publisher doesn�t

accept to be linked and releases a �ghting version. This is because it faces a trade o¤ when

setting the prices. If they are too high, A becomes very expensive and loses audience, so H

and L receive less indirect visitors. And if they are too low A totally cannibalizes H and L.

Finally, notice that the size of the regions identi�ed in the proposition crucially depends

on the values taken by s. When s increases the region in which both companies are willing to

cooperate increases. In Figure 3 this corresponds to the areas A and B. Thus, spillovers make

more likely the establishment of links.

The next corollary shows how the publisher would like to modify the complementarity level

between H and L once these have been released and linked.

16

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 L from H is c(s) = 1=ks the publisher

will increase the complementarity of the versions as long as k > k�.


While in the case of a low quality search engine the publisher prefers the higher possible level

of sustitutability between the versions, in this case it prefers to increase the complementarity

of the versions to be able to increase the prices. This result reveals that the publisher does

not see the search enigne as a rival, but as an opportunity to receive a higher number of

visitors. Consumers now can visit the two versions and their total willingness to pay for the

two products decreases with s.

To sum up, in this section we have shown that the distribution strategies of the publisher

and the search engine crucially depend on the amount of indirect tra¢ c that can generate the

search engine and on the complementarity of the contents. Proposition 2 shows that when

uA < uL; the publisher wants to reach an agreement with the search engine if this generates

su¢ cient tra¢ c for its sites. In this case, the publisher uses the search engine as its low quality

version. Furthermore, the publisher can release a second site to strengthen the quality of the

search engine.

Proposition 3 examines the case where spillovers are larger and uA > uH . In this situation,

if the search engine redirects a large number of consumers to the publisher the �rms don�t

want to reach an agreement. Indeed, the search engine loses audience and the publisher has to

set low prices. However, if smaller volumes of tra¢ c are redirected to the publisher both �rms

are interested in reaching an agreement. The results of the two propositions are in line with

Calzada and Valletti (2012), who show that a monopolist might release two versions when a

part of the consumers can buy both of them. Interestingly, in our model it is precisely the

search engine that permits this possibility.

5 Vertical integration and linking strategy

In the last years, several news publishers have acquired or created news aggregators with the

aim to grow and engage their audiences through forums and RSS feeds. For example, in

17

2005 Gannet (the USA Today�s publisher), Knight-Rider and Tribune acquired the 75% of

Topix.net, in 2011 AOL acquired The Hu¢ ngton Post, and in 2012 Gannet bought Quickish,

a sports aggregator. With these investments traditional media groups look for alternative

revenue sources and separate their activities of production and distribution of contents. Other

recent experiences have been less successful. For example, in 2009 News Corporation planned

to launch the news aggregator Alesia, but the project was canceled due to the trouble of

�nding other publishers interested. In 2010, several leader publishers in the US market such

as Gannett, The New York Times Company, The Washington Post Company, Reuters, Los

Angeles Times or Chicago Tribune created a news aggregator named Ongo, but this site closed

two years later.14 One distinctive feature of Alesia and Ongo is that they were created from

scratch with high quality pieces of news of their promoters and behind a pay ball. In the

acquisitions of The Hu¢ ngton Post and Topix, by contrast, the publishers were interested in

buying an alternative and successful distribution channel for their contents.

The vertical integration between publishers and aggregators rises novel economic questions

regarding its e¤ects in the linking strategies of �rms and in competition. Publishers want to

integrate aggregators to obtain indirect tra¢ c and referrals, but they can use their position to

eliminate the links of their competitors or to give an advantage to their own contents.

To address this case, we next analyze the linking and versioning strategy of a vertically

integrated publisher that commercializes both a high quality newspaper H and an aggregator

A.15 The publisher competes with an independent publisher that o¤ers a low-quality newspaper

L. For simplicity, we assume that the price of the independent publisher, pL, is set exogenously.

The integrated and the independent publisher can agree to link L. When this happens,

the level of complementarity between H and L determines the quality of A. When H and

L are close substitutes A becomes a low quality search engine and when their contents are

more complementary A is transformed in a high quality aggregator. Notice that the quality of

the aggregator in�uences the strategies of the �rms. Indeed, in the �rst case we obtain that

uH > uL > uA which means that the independent publisher has a stronger competitor "from

14One of the explanations of the failure of Ongo is that the managers established a bad pricing strategy. See

http://www.niemanlab.org/2012/05/ongo-an-attempt-at-a-pan-media-paywalled-aggregator-is-closing/15De Cornière and Taylor (2013) analyze the e¤ects of the integration between search engines and publishers

of contents in the internet search engine markets.

18

below", and in the later case the link implies that uA > uH > uL which means that H has a

competitor "from above".

The next proposition analyzes the linking strategies of the publishers when the contents

are close substitutes. The timing of the game is as follows: �rst, the two publishers negotiate

about setting a link to L; once they have taken a decision the integrated publisher sets pH ;

and �nally consumers decide which news site to visit.

Proposition 4. The linking strategy of an integrated and an independent publisher that

commercializes close substitute contents ( s > �=�) is:

1. When �=� < s � bs, the integrated publisher wants to link L when � < �1 whereas the

independent publisher is never interested.

2. When bs < s � 1, the integrated publisher wants to link L when � < �2 whereas the

independent publisher wants when � > �3. Only when � > �� there is a small region

�3 < � < �2 in which the two publishers reach an agreement.Proof. See Proof in the

Appendix.

The proposition shows that the integrated publisher is interested in linking L when � and

s are su¢ ciently small; when a small percentage of A�s visitors click the link and the two

newspapers are su¢ ciently complementary. Only in this case the link expands the market

share of A and increases the indirect visits to H. When the publisher links L the quality

of A increases in u�(1 � s) and its price in �pL. Therefore, the market expansion e¤ect on

A depends on the relation between � and s. In the case of the independent publisher, the

pro�tability of the link depends on two opposite e¤ects. On the one hand, the link generates a

market expansion e¤ect because all the visitors of A click through to L with probability �. On

the other hand, it creates a cannibalization e¤ect, because A competes with L from below and

it reduces part of its direct. visitors. Only when � and s are su¢ ciently high the �rst e¤ect

compensates the second and the publisher accepts the link

The �rst part of the proposition shows that when s is small (s < bs) the integrated publisherwants to link L if � < �1 but its competitor is not interested because the cannibalization over L

is too important (Figure 4). The second part shows that when s is large (s > bs) the integrated19

publisher wants to link L when � is small (� < �2) and that it becomes less and less interested

as s increases. Indeed, for larger values of � and s the �rm has to reduce signi�cantly pH in

order to generate a market expansion e¤ect. On the other hand, the independent publisher

wants to be linked when � is su¢ ciently large and becomes more and more interested in the

agreement as s increases. Taking this into account, only in the small region �3 � � < �2 the

two publishers agree on linking L, but this region only exists when � is close to �.

Figure 4: Linking strategy of the integrated and the independent publishers (�=0.4, �=0.8,

u=1, pA=0.05)

The linking strategies of the �rms described above determine the segmentation of con-

sumers, which is characterized below.

Corollary 4. In the presence of an integrated and an independent publisher that commer-

cialize close substitutes contents ( s > �=�) consumers are segmented as follows:

1. When �=� < s � bs and � < �� the news sites H;L;and A receive direct visits and A

links H. For � � �� A is not active.

2. When bs < s � 1 and � < �� the news sites H;L;and A receive direct visits and A links20

H, except when � > ��, in which case it links both H and L in the interval �3 < � < �2:

For � � �� A is not active.

Proof. See Proof of Proposition 4 in the Appendix.

The �rst part of the corollary shows that for � < �� the integrated publisher maintains

A active as a low quality version because this generates indirect visitors. But for � � �� the

price of A, �pH ; is too high and it would receive few visitors. For this reason, the publisher

eliminates it and sets a higher pH . The second part of the corollary presents the same results,

but as we have seen before in Proposition 4 in the interval �3 < � < �2 the �rms reach an

agreement and the search engine links both H and L.

The main insight of these results is that an integrated publisher might maintain active its

low quality search engine, even when it doesn�t link other sites. The search engine is used like a

�ghting version, although in this case the publisher can only use pH to implement its strategy.

Next we examine the strategies of the �rms in the case of a high quality search engine.

Recall that in this case the linking decisions of the �rms can change importantly since the link

implies that A competes with H "from above". The timing of the model is as before.

Proposition 5. The linking strategy of an integrated and an independent publisher that

o¤er complementary contents ( s < �+��1� ) is:

1. When 0 � s < es, the integrated publisher wants to link L when 0 � � < �1, whereas theindependent publisher always wants to be linked.

2. When es < s � �+��1� , the integrated publisher is never interested in linking L, whereas

the independent publisher always wants to be linked.


As in Proposition 4 these results show that the integrated publisher only links L when both

s and � are small. When this occurs, it creates a high quality news aggregator that completely

cannibalizes H (pH is so high that nobody directly visits H) and that directly competes with

L. The market expansion e¤ect of A compensates the cannivalization e¤ect on H as long as

� < �1. For larger values of � the publisher doesn�t link L because the search engine would

21

become more expensive and it would need to reduce pH signi�cantly in order to maintain its

market share. On the other hand, contrary to what happens in Proposition 4, the independent

publisher always want to be linked: although A directly competes with L from above, it obtains

many indirect consumers that compensate this e¤ect.

The second part of the proposition shows that for higher values of s the market expansion

e¤ect generated when A links L does not compensate the cannibalization e¤ect on H. Again, in

order to incentive consumers to switch from L to A the �rm would need to reduce signi�cantly

pH , which is not pro�table.

The proposition shows that the integrated publisher only wants to link its competitor when

s is small and it obtains a signi�cant increase in the market share of A. And when this happens

the independent publisher can accept to be linked because this expands its market share with

indirect visitors.

Figure 5: Linking strategy of the integrated and the independent publishers (�=0.4, �=0.8,

u=1, pA=0.05).

Finally, we examine how the linking decisions of �rms in�uence consumers�segmentation.

22

Corollary 5. In the presence of an integrated and an independent publisher that commer-

cialize complementary contents ( s < �+��1� ) consumers are segmented as follows:

1. When 0 < s < es and � < �1 news sites A and L receive direct visits and A links H and

L. For � � �1 H and L receive direct visits and A is not active.

2. When es < s � �+��1� and � < b�1 the news sites H, L and A receive direct visits and A

only links H: For � � b�1 H and L receive direct visits and A is not active.

Proof. See Proof of Proposition 5.

The corollary shows how � (indirect visitors to H) and s (complementarity of the sites)

determine the versioning strategy of the publishers. The �rst part shows that when 0 < s < bsand � < �1 the integrated publisher maintains A active. As a consequence, high type consumers

visit A (which links H and L ) and low type consumers visit L: However, when � � �1 the

publisher eliminates A because it has a high price �(pH + pL) and receives few visitors. Hence,

only H and L are active and pH is higher. The second part of the corollary shows that for

s > bs the integrated publisher doesn�t link L, although for � < b�1 it maintains A active becauseit attract low type consumers that can click through to H. Finally, when � � b�1 the publishereliminates A and increases pH :

6 Conclusions

In recent years, blogs, search engines, and news aggregators have reached the top positions

in audience ranking of news sites. While traditional publishers accuse these news sites of

�stealing� their contents and revenues, entrants argue that they are in fact �expanding the

market�by improving accessibility to newspapers and their contents. The reason for this is

that they reduce consumer search costs by o¤ering links to many news sites and/or by editing

the contents originated by other �rms. In this paper we have examined the product line

response of publishers to this type of entrants.

Our �rst contribution has been to show that when publishers can�t avoid its contents being

used by others versioning is less likely than what was previously considered in the literature.

The reason is that �ghting versions improve the quality of competitors. We have also ana-

23

lyzed the linking and versioning strategies of a publisher in competition with a search engine.

We have demonstrated that the publisher can accept to be linked when it receives su¢ cient

tra¢ c from the search engine. When this occurs, the search engine becomes an additional

distribution channel of the publisher that helps to weaken the e¤ects of competition. In the

case of an integrated publisher, the search engine can set links to its competitor to bene�t of

the complementarity of the contents and increase its audience. To the best of our knowledge,

this results represents a novel �nding in the literature on versioning, which hitherto has not

considered the possibility of links substituting �ghting versions.

All in all, our results show that the disputes between publishers and search engines are

essentially dependent on the amount of tra¢ c that search engines send to the news sites and

on the complementarity of the aggregated contents. It is therefore an empirical question to

examine whether publishers obtain su¢ cient tra¢ c from search engines to justify their links,

and whether search engines maximize their audience with their linking policies. The recent

papers of Chiou and Tucker (2010) and Athey and Mobius (2012) show evidence that Google

News generate signi�cant indirect tra¢ c, but it is still unclear which publishers are bene�ting

of search engines and how they adjust their marketing strategies to accomodate them.16

Our analysis can be extended in several directions in order to understand recent develop-

ments in the media market. Here, we have focused on the optimal versioning strategy of a

publisher that can create news sites of di¤erent qualities; however, it would be interesting to

study how publishers accept the links to some pieces of news to attract visitors to their web

sites and to promote their premium contents (freemium model).17 On the other hand, our

model could be extended to examine the role of news agencies in the media market. As the

recent con�icts between Google News and some press associations illustrates, news agencies

provide fundamental information to traditional newspapers and they are very concerned about

their use by news aggregators.

16Chiou and Tucker (2010) investigate the e¤ects of the breakdown of the agreement between Google News

and AP in 2009, and show that the event was correlated with a decline in the demand for content from AP

sources. 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.17Rutt (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.

24

7 Appendix

Proof of Proposition 1. When the publisher only o¤ers H the indi¤erent types are �HA =

(pH � pA)=(1� �)u and �A0 = pA=�u. The �rm sets pH to maximize �HA(H) = pH(1� �HA)

and as a result the price and the pro�ts are:

pH =pA + u (1� �)

2; (1)

�HA(H) =u(1� �)

4+pA4(2 +

pAu (1� �) ): (2)

With this price, it is veri�ed that �HA = 12

�1� pA

u(1��)

�> �A0 =

pA�u 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 = (pH � pL)=u(1 � �); �LA = (pL � pA)= [u(�� (� + � (1� s))] ; and �A0 = pA=[u(� +

� (1� s))]. The �rm sets pH and pL to maximize �HLA(HL) = pH(1� �HL) + pL(�HL � �LA).

Solving the �rm�s problem we obtain:

pH =1

2[pA + u(�s� � + 1� �)]; pL =

1

2[pA + u(�s� �)]; (3)

�HLA(HL) =u

4[�s� � + 1� �] + pA

4[2 +

pAu(�s� �) ]; (4)

To ensure the participation of the blog now we need that s > s1 =(�+2�)u�pA�

pp2A�6�pAu+�2u2

2�u .

If this is satis�ed, we obtain that �HL = 12 > �LA =

12

�1� pA

(�s��)u

�> �A0 =

pAu(�+�(1�s)) : On

the other hand, when s 6 s1 the ranking is not preserved and the publisher sets pL = �pA�+�(1�s)

to ensure that �LA = �A0 = �L0. Taking this into account, it sets pH to maximize �HLA(HL) =

pH(1� �HL) + pL(�HL � �L0). The prices and the associated pro�t are:

pH =1

2[(1� �)u+ 2�pA

� + �(1� s) ]; pL =�pA

� + � (1� s) ; (5)

�HLA(HL) =u

4� �[(� + �(1� s))u� 2pA]

2

4u(� + �(1� s))2 : (6)

Moreover, the indi¤erent types are: �HL = 12 > �L0 =

pA(�+�(1�s))u .

Next, we analyze the publisher�s optimal versioning policy. Note that for s > s1 it is

satis�ed that �HLA(HL) > �HA(H) for s > bs, where

25

bs = �p2A + �(1� �)(�+ �)u2 +r�2�p4A + 2 (1� �) p2Au2(�+ � � 2) + (�� )

2(� � 1)2 u4

�2�2 (1� �)u2 :

(7)

Therefore, the publisher releases H and L for bs < s � 1 and only H for s � bs. Notice thatthis segmentation only emerges when bs > s1, which occurs when � < �1; where �1 is the valuethat satis�es bs = s1 (the expression for �1 is long and we don�t report it for simplicity). For� > �1; then bs < s1 and the publisher o¤ers H and L for s1 � s � 1 and the blog is always

active.

Consider now the case for s < s1. If the �rm o¤ers the two versions the relevant prices and

pro�t functions are those in (5) and (6), respectively. In this case, we obtain that �HLA(HL) >

�HA(H) for s > s2, where

s2=2p�2(� � 1)p2A (p2A � 2 (� � 1) pAu+ (� � 1)�u2) + �(�(�+ �)p2A � 2(1� �)�pAu� (�� )(1� �)(�+ �)u2

�2[2 (� � 1) pAu� p2A + (�� ) (� � 1)u2]:

(8)

Hence, for s2 < s < s1 the publisher o¤ers the two versions and the blog is not active. And

for s < s2 it only releases H and the blog is active.Q.E.D.

Proof of Corollary 1. Consider the pro�t function of the publisher in (4) 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 publisher�s pro�t is:

�HLA(HL) =u

4[�s� � + 1� �] + pA

4[2 +

pAu(�s� �) ]�

1

ks; (9)

The FOC of �HLA(HL) with respect to s is

@�HLA(HL)

@s=

1

ks2+u�

4

"1� p2A

(�u� �su)2

#:

This expression can only be negative if p2A > (�u� �su)2, which happens for s 2

�u��pAu� ; u�+pAu�

�.

In spite of this, notice that s1 >u�+pAu� for pA > 0. Therefore, it must be that

@�HLA(HL)

@s > 0.

Finally, for s � s1 the publisher sets the prices in (5) and the pro�ts are those in (6).

Taking this into account, the FOC of the pro�t with respect to s is:

@�HLA(HL)

@s=

1

ks2� �

2[2pA � u(�(1� s) + �)]pAu(�(1� s) + �)3

26

A su¢ cient condition for this to be positive is u [�(1� s) + �] > 2pA. This is always satis�ed

for pA <u�(1��)(2��) , 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 by the search engine. In this case, the consumer indi¤erent to H and L is

�HL = (pH�pL)=u(1��), the consumer indi¤erent to L and A is �LA = (pH�pA)=u(��r); and

the consumer indi¤erent between visiting A and not visiting any site is �A0 = pA=ur. Taking

this into account, the �rm sets pH and pL to maximize �HLA = pH (1� �HL)+pL (�HL � �LA),

which yields the following prices and pro�ts:

pH =1

2[pA + u(1� r)] ; pL =

1

2[pA + u(�� r)] ; (10)

�HLA =1

4

�2pA + u(1� r) +

p2Au(�� r)

�<u

4:

Moreover, the audience for the search engine is AHLA = �LA � �A0 = 12 �

pA(2��r)2(��r)ur .

Notice that the publisher always releases L since in this case it doesn�t create spillovers on

A.18 On the other hand, with the above prices we obtain �HL = 12 > �LA =

h12 �

pA2u(��r)

i>

�A0 =pAur as long as pA < pA =

ur(��r)2��r , which we assume for simplicity.

Imagine next that the publisher only releases H and that this is linked by the search

engine. In this case, the consumer indi¤erent to H and A is �HA = pH(1 � �)=u(1 � �), and

the indi¤erent to A and not visiting any site is �HA = �pH=u�. Taking this into account, the

publisher sets pH to maximize �HA(H) = pH (1� �HA) + pH� (�HA � �A0). As a result, the

price and the pro�ts are:

pH =�u(1� �)

2(� � 2�� + �2); �HA =

�u(1� �)4(� � 2�� + �2)

: (11)

Moreover, the search engine�s audience is AHA(H) = �HA � �A0 = ��2(��2��+�2) and it is

satis�ed that �HA =�(1��)

2(��2��+�2) > �A0 =�(1��)

2(��2��+�2) if � < �.

When the publisher o¤ers both H and L and these are linked the consumer indi¤erent to H

and L is �HL = (pH�pL)=u(1��), the indi¤erent to L and A is �LA = (pL(1��)��pH)=u(�s�18When the publisher only releases H and there are not links the results are pH =

pA+(1�r)u2

and �HA =

[pA+(1�r)u]24u(1�r) : It can be veri�ed that �HLA > �HAfor pA > 0:

27

�), and the indi¤erent to A and not visiting any site is �A0 = �(pH + pL)=u[�+�(1� s)]. The

publisher sets pH and pL to maximize �HLA(HL) = pH (1� �HL) + pL (�HL � �LA) + (pH +

pL)� (�LA � �A0). The solution of its problem is:

pH =[�(1� �)(2� � 1 + �) + �(� � 1 + 2�) + �(1� 2� � 2�)s+ �2(� � 1 + s)2]u

2[4�� 2 � �(1� s+ �(3� + 4(s� 1)))];(12)

pL =[�(� � �)� �2(�2 � �(1� s) + s(1� s)) + �(�(1 + � � 2s)� �(1� � � s))]u

2[4�� 2 � �(1� s+ �(3� + 4(s� 1)))]:

With these prices we observe that �HL > �LA if � > b� = [� + �(1 � s)]=(1 + �), and

�LA > �A0 if � < b�. This implies that the publisher can�t get a positive market share forthe two news sites. As an alternative, for � < b� the publisher can set pL = pH(��(1��)��s)

��1+�+�(1��s)

to guarantee that �HL = �LA = �HLA; where now �HLA is the consumer indi¤erent between

visiting H and visiting A when this links H and L. Taking this into account, the �rm sets

pH to maximize �HLA(HL) = pH (1� �HLA) + �(pH + pL) (�HLA � �A0). The price and the

associated pro�ts are:

pH =[� + �(1� s)][� � 1 + � + �(1� � � s)]2u

2[�(1� �) + 4(� � 1)�� + �2 + �(1� 2�)(1� s� 2�(2� � � 2s)) + �2(� + s� 1)(1� s+ �(4s� 3))];(13)

�HLA(HL) =[� + �(1� s)][� � 1 + � + �(1� � � s)]2u

4[�(1� �) + 4(� � 1)�� + �2 + �(1� 2�)(1� s� 2�(2� � � 2s)) + �2(� + s� 1)(1� s+ �(4s� 3))]:

The audience for the search engine is AHLA = �HLA � �A0, where:

�HLA =(2� � 1)(� + �(1� s))(� � 1 + � + �(1� � � s))

2[�(1� �) + 4(� � 1)�� + �2 + �(1� 2�)(1� s� 2�(2� � � 2s)) + �2(� + s� 1)(1� s+ �(4s� 3))];

�A0 =�(1� � � � + �(� + s� 1))(1� 2� + �(2s� 1))

2[�(1� �) + 4(� � 1)�� + �2 + �(1� 2�)(1� s� 2�(2� � � 2s)) + �2(� + s� 1)(1� s+ �(4s� 3))]:

It can be checked that now �HLA > �A0 for � < b�. On the other hand, for b� < � < �

the publisher sets pL =pH(��+�(1+��s))�+��(�+s�1) to guarantee that �HLA = �A0 = �HLA0, where

�HLA0 is the consumer indi¤erent between H and not visiting any site when the publisher

also releases L at pL and the price of A is �(pH + pL). As a result, the publisher maximizes

�H0(LA) = pH (1� �HLA0) by setting pH = u(�+��(�+s�1))4� and obtains �HLA0 = 1=2 and

�H0(LA) =u(�+��(�+s�1))

8� . Notice that if s � (1 � �) then � � b�, so the strategy describedfor � 2

hb�; �� is not relevant. Finally, for � > � nobody wants to visit A. Hence, the publisherreleases H; sets pH = u=2 and obtains the monopoly pro�t �H = u=4.

28

Taking into account the previous results, next we examine the linking and versioning policy

of the �rms. Consider �rst the publisher when it releases H and L and compare its pro�ts

with and without links. For �h0;b��, we �nd b�1 such that �HLA > �HLA(HL) for � < b�1 and

�HLA � �HLA(HL) for b�1 � � < b�. The value of b�1 is not shown for simplicity. Analogously,in the region � 2

hb�; �� there is b�2 that satis�es �HLA(HL) � �HLA if � � b�2 and �HLA >�HLA(HL) for b�2 � � < �.19 The expression for b�2 is:

b�2 = (�� r)(� + �(1� s))u22p2A + 4pA(�� r)u+ (1 + �� 2r)(�� r)u2

.

Now compare these results with those that will obtain the publisher if it o¤ers H and this

is linked. First, observe that in the interval � 2h0;b�1� there is �1 such that �HLA > �HA(H)

for � < �1 and �HA(H) � �HLA for � � �1. The value for �1 is:

�1 = � �p(� � 1)�[p2A + 2pA(�� r)u+ (1� r)(�� r)u2][p2A + 2pA(�� r)u� r(�� r)u2]

[p2A + 2pA(�� r)u+ (1� r)(�� r)u2];

Next, it is veri�ed that in the interval � 2hb�1;b�� there exists �2 satisfying �HA(H) >

�HLA(HL) for � < �2 and �HLA(HL) � �HA(H) for �2 � � < b�. Also note that in the interval� 2

hb�;b�2� there is a threshold b�3 that satis�es �H0(LA) > �HA(H) for � < b�3. The expressionsfor �2 and b�3 are not shown for simplicity. Furthermore, it is con�rmed that �1 < b�1 < �2 aslong as s < bs with bs = [�+ � � �(1 + �)] =(1 + �).20 Similarly, one can show that �2 < b� < b�3if s > (1� �).21 Finally, for values � 2

hb�2; �� we �nd that �HA(H) > �HLA.Now consider the linking strategy of the search engine, which maximizes its audience. Let

�3 and �4 be the value of � that satisfy AHLA(HL) = AHLA and AHA(H) = AHLA; respectively.

The expression for �3 is long and we don�t present it22 , and the expression for �4 is:

�4 =

8<: �(4�pA + ur(1� 2�))� r(2�pA � ur(1� 2�))

�q[2�pA(2�� r) + ur(1� 2�)(�� r)]2 + 4�pA(2�� r) [r(pA � ru) + �(ru� 2pA)]

9=;4�pA � 2rpA � 2�ru+ 2r2u

19Recall that for � � b� if two versions are released and linked pH is high and nobody visits A.20When s = bs then �1 = b�1 = �2. For s > bs it holds that �1 > b�1 and �2 < b�1. This implies that the regions

� 2 [�1;b�1) and � 2 [b�1; �2) vanish and the relevant threshold is b�1.21When s = (1� �) then �2 = b� = b�3. For s < (1� �) it holds that �2 > b� and b�3 < b�. This implies that the

regions � 2 [�2;b�) and � 2 [b�;b�3) vanish.22Note that �3 only exists in the interval

h0;b�� as AHLA(HL) = 0 when � � b�. If AHLA(HL) > AHLA for

the whole interval � 2h0;b�� then b� applies instead of �3.

29

One can show that �3 � �4 if r � r. 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 < MinfAHLA(HL); AHA(H)g so the search engine accepts to link

the publisher�s newspapers regardless of the number of versions that are released. If � 2 [�3; �4)

then AHA(H) > AHLA � AHLA, 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 �MaxfAHLA(HL); AHA(H)g so

it never links the publisher�s newspapers 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 � < �1 the publisher does not want to be linked by the search

engine in any situation, whereas for � > �4 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. However, recall that when s � bs then �2 < �1 and the relevant threshold is b�1. In thiscase, for � < b�1 the publisher doesn�t accepts the links (Panel I in Figure 2).

Consider now the interval � 2 [�1; �4) in which the �rms can reach an agreement. In this

case when s� < s < bs it is veri�ed that �1 < �2 < �3 < �4.23 Hence, when � 2 [�1; �2) the

publisher only releases H, when � 2 [�2; �3) it releases H and L (only H and A(HL) are active)

and when � 2 [�3; �4) it only releases H. Finally, for s > bs the relevant threshold is b�1. In thiscase when � 2

hb�1; �3� the publisher releases H and L (only H and A(HL) are active), and

when � 2 [�3; �4) the publisher only 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 � < b� the �rm sets the price

in (13) and obtains the corresponding pro�ts �HLA(HL). Recall that for � < b� only H and

A(HL) are active. Moreover, for � > b� the search engine doesn�t link the newspapers becauseonly H is active at the equilibrium price. Next, notice that @�HLA(HL)=@s � 0 for � � b�,implying that for � < b� the �rm sets s = 1. Finally, notice that this result is veri�ed for any

di¤erentiation cost c(s) = �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 pro�ts �HLA are those in (10).

23For s� = s then �2 = �3 = �4 and the intervals [�2; �3) and [�3; �4) shrink.

30

On the other hand, if only H is released and it is linked then pH and �HA(H) are those in

(11).

Consider next that the publisher releases H and L and that the �rms reach an agreement.

As a result, uA > uH because uA = u[� + �(1 � s)] and s < (� + � � 1)=�. In this case, the

indiferent consumers are �AH = [�(pH+pL)�pH ]=u[�+�(1�s)�1], �HL = (pH�pL)=u(1��),

and �L0 = pL=u�. The �rm sets the prices pH and pL to maximize �A(HL)HL = �(pH +

pL) (1� �AH) + pH (�AH � �HL) + pL (�HL � �L0). Taking this into account, the prices and

the associated pro�ts are:

pH =�[� � 1 + �(� + � � s� �(� + s� 1))]u2[� + �(� � 2) + �(1 + �(3� � 2)� s)] ; pL =

��[2� � 1� � + �(1 + � � 2s)]u2[� + �(� � 2) + �(1 + �(3� � 2)� s)]

(14)

�A(HL)HL =�2[� � 1 + �(3� � 1� s� �(3s� 2))]u4[� + �(� � 2) + �(1 + �(3� � 2)� s)] : (15)

With these prices, the audience for the search engine is AA(HL)HL = 1� �AH . Moreover,

it is guaranteed that �AH > �HL > �L0 as long as � > �1, where �1 = [� +�(1� s)]=(1 +�):24

�AH =�[� � 1 + �(3� � 1)]

2[� + �(� � 2) + �(1 + �(3� � 2)� s)] ;

�HL =�[� � 1 + �(2� � s)]

2[� + �(� � 2) + �(1 + �(3� � 2)� s)] ; (16)

�L0 =�[2� � 1� � + �(1 + � � 2s)]

2[� + �(� � 2) + �(1 + �(3� � 2)� s)] :

Imagine �rst that � > �1. Then there is a value �3 for which �A(HL)HL = �HLA. Then,

for s < (� + � � 1)=� it holds that �A(HL)HL � Max��HA(H); �HLA

when � 2 [�1; �3) and

�HLA �Max��HA(H); �A(HL)HL

for � 2 [�3; 1].25

Consider next that � � �1. In this case, with the prices in (14) it is satis�ed that �AH � �L0,

which implies that only A has direct visits. Taking this into account, the consumer indiferent

between A and not visiting any news site is �A0 =�(pH+pL)

u(�+�(1�s)) . In order to ensure that

�A0 = �L0 the publisher sets pL = pH��+�(1�s��) . Taking this into account, it sets pH to

24The expression for �1 is the same than in the proof of Proposition 2. Indeed, this is the value of � for which

the three indiferent types are the same, which has to be the same � in the two propositions.25Recall from the prof of Proposition 2 that for � � �1 it is satis�ed that �HLA � �HA(H) and �1 � �3 holds

if r < r, which is assumed.

31

maximize �A(HL) = �pH (1� �A0) + �pL (1� �A0). This yields:

pH =� + �(1� s� �)u

2�; pL =

�u

2; (17)

�A(HL) =[� + �(1� s)]u

4>u

4: (18)

Note that �A(HL) >u4 > �HLA. Furthremore, in the interval � 2 [0; �1) it is satis�ed that

�A(HL) �Max��HA(H); �HLA

for the relevant values of s.

Consider now the linking strategy of the search engine. It can be checked that for � 2 [0; �1)

it holds AHLA � Min�AHA(H); AA(HL)

so the search engine wishes to link the publisher�s

content independently of the number of versions released. Furthermore, when � 2 [�1; �3)

it holds that AA(HL) > AHLA � AHA(H) and when � 2 [�1; �2) that AA(HL)HL � AHLA >

AH(A)H , where �2 is the value that satis�es AA(HL)HL = AHLA and �1 � �2.26 Hence, when � 2

[�1; �2) the search engine only links the content maker when this releases the two versions. Last,

it can be shown that in the interval � 2 [�2; 1] we obtain AHLA � MaxfAHA(H); AA(HL)HLg,

which implies that the search engine doesn�t link the publisher.

Finally, we compare the linking strategies of the two �rms. Taking into account that

�2 < �3 the publisher releases both H and L and these are linked when � 2 [0; �2). On the

other hand, the two versions are releases but are not linked for � 2 [�2; 1].Q.E.D.

Proof of Corollary 3. The proof of Proposition 3 has shown that in the interval �1 �

� < �2 the publisher releases the two versions and that these are linked by the search engine.

Taking into account the pro�ts in (14) and the costs c(s) = 1ks the FOC of the pro�t with

respect to s is:

@��A(HL)HL � 1

ks

�@s

=1

ks2� ��2[� + �(3� � 1)� 1]2u4[� � �(2� �) + �(1� �(2� 3�)� s)]2 .

De�ne s� as the value of s that satis�es @��A(HL)HL � 1

ks

�=@s = 0. The expression for

s� is not shown for simplicity but it can be shown that @��A(HL)HL � 1

ks

�=@s > 0 for s < s�

and that s� is a decreasing function of k. Taking this into account, we can de�ne k such that

if k < k then s� > (�+��1)� and k > k such that s� < �+��(1+�)

� , where:27

k =4� [1 + � (� + �(3� � 2)� 2)]2

(�+ � � 1)2 �2 [� + �(3� � 1)� 1]2 u; k =

4�

[�+ � � (1 + �)�]2 u;

26When pA ! 0 then AHLA ! AA(HL) = 1=2 and as a consequence �2 ! �1. Graphically, this implies that

in Figure 3 region B vanishes.27Note that s < �+��(1+�)

�is equivalent to � < �1. Hence, it de�nes the domain of our analysis.

32

Suppose now that � < �1 and therefore s 2h0; �+��(1+�)�

�. In this case the publisher

sets the prices in (17) and obtains the pro�ts in (18). Taking this into account and the cost

function, we �nd that the FOC of the pro�t with respecto to s is:

@��A(HL) � 1

ks

�@s

=1

ks2� �u4

It is easy to see that, @��A(HL) � 1

ks

�=@s < 0 when s > s�� = 2p

�pkpu. Moreover, as s��

is decreasing in k we can �nd a value k�� such that when k < k�� 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

can show that k�� = k.Q.E.D.

Proof of Proposition 4.

Consider �rst the case where the integrated publisher doesn�t link L. The consumer in-

di¤erent to H and L is �HL = (pH � pL) =u (1� �), the consumer indi¤erent to L and A

is �LA = (pL � �pH) =u (�� ), and the consumer indi¤erent to A and not visiting any site

is �A0 = �pH=�u. Taking this into account, the integrated publisher sets pH to maximize

�1HLA(H) = pH(1� �HL) + �pH(�LA � �A0). On the other hand, the pro�t of the independent

publisher is �2HLA(H) = pL(�HL � �LA). Solving the �rm�s problem we get:

pH =��pL � u�2 � �(u+ pL) + � [u(1 + �) + pL(1� �)]

�2��(� + �2)� �2 � �2�2

� ; (19)

�1HLA(H) =� [(�� + � � ��) pL + (1� �)(�� )u]2

4(1� �)(�� )�(�� )� + (1� �)��2

�u; (20)

�2HLA(H) = pL

8<:�2(1� �)�(�� )� + (1� �)(� � �(2� �))�2 � (�� )�(2� �� )

pL

�(1� �)(�� )�(� � �(1� �)� �)u

9=;2(1� �)(�� )

�(�� )� + (1� �)��2

�u

:(21)

With this price it holds that:

�HL =1

u(1� �)

��pL (�� + � � ��) + (1� �)(�� )�u

2(1� �)��2 + 2�(�� )� pL

��LA =

1

u(�� )

�pL �

�� [pL (�� + � � ��) + (1� �)(�� )u]2(1� �)��2 + 2�(�� )

��A0 =

�pL (�(1� �)� �) + (1� �)(�� )�u2�(�� )� + (1� �)��2

�u

.

33

In order to ensure the participation of the independent publisher we assume pL <(1��)(�s��)u2��(2�s)�� .

28

Note that the above prices are valid as long as �HL > �LA > �A0. However, for � � b�1 we �ndthat �A0 � �LA, where

b�1 = �2 (pL + u(1 + �))� u�3 � ��(u+ pL)�r�(�� )

h�(�� ) (pL + u(1� �))2 � 8(1� �)�p2L

i2(1� �)�pL

:

(22)

Therefore, when � � b�1 A doesn�t receive visits and the relevant indi¤erent consumers are�HL = (pH � pL) =u (1� �) and �L0 = pL=u�. In this case, the pro�ts are �1HL = pH(1��HL)

and �2HL = pL(�HL � �L0). Solving for pH yields:

pH =u(1� �) + pL

2; (23)

�1HL =[u(1� �) + pL]2

4(1� �)u ; �2HL =pL2

�1� (2� �)pL

(1� �)�u

�: (24)

With this price it is satis�ed that �HL = 12

�1� pL

u(1��)

�> �L0 =

pL�u . Notice, however,

that �1HL > �1HLA(H) for � � �

�, where

�� =2(�� )�pL(pL + u� �u)

(�2 � �)p2L + 2(1� �)�(�� )pLu(�� 1)2�(�� )u2< b�1.

Therefore, the integrated publisher o¤ers A for � < �� and it eliminates it otherwise.

Consider now the case where the aggregator links L. The quality ofA is uA = u [� + �(1� s)]

and the indi¤erent types are �HL = (pH � pL)=u (1� �), �LA = [pL � � (pH + pL)] =u (�s� �)

and �A0 = � (pH + pL) =u [� + �(1� s)]. The integrated publisher sets pH to maximize �1HLA(HL) =

pH(1 � �HL) + �pH(�LA � �A0) and the pro�t of the independent publisher is �2HLA(HL) =

pL(�HL � �LA) + �pL(�LA � �A0). Solving the problem yields:

pH =pL��(� � �) + �2(�2 � �(1� s) + s(1� s))� �(�(1 + � � 2s) + �(� + s� 1))

�+ �2

�2� ;(25)

�1HLA(HL) =

�pL��(� � �) + �2(�2 � �(1� s) + s(1� s))� �(�(1 + � � 2s) + �(� + s� 1))

�+ �

�24��

:(26)

where � =��(2�s+ �2 � �)� �2 � �2(�2 � (1� s)s)

�and � = (�� 1) (�s� �) (�+ � � �s)u.

28This is a general condition. When s = 1 it simpli�es to pL <(1��)(��)u

2�� .

34

We don�t show �2HLA(HL) for simplicity. The price in (25) implies that:

�HL =pL��(� + �) + �2(3�2 � �(1� s)� s(1� s)) + �(� � �(3� + s)� �(� + 2s� 1))

�+ �

2(1� �)u� ;

�LA =

pL

8<: ��(1 + s� �)�2 + �(4s+ �(3 + � � 6s)� 2)

��

��(2� 3�) + �2

��2

�3�(1� s)s+ �2(1 + s)� �3 � 2(1� s)

�9=;+ �

2(�s� �)u� ;

�A0 =�pL

��(� � 3�) + �(�(1 + � � s)� �(3 + � � 6s))� �2(� + �2 � �s� 3(1� s)s)

�+ �

2 [�(1� s) + �]u� :

The relation �HL > �LA > �A0 is satis�ed for � < b�2 (we don�t show b�2 because it is along expression). When � � b�2 it holds that �LA � �A0 so nobody visits A. In this case, theindependent publisher sets the price in (23) and obtains the pro�ts in (24).

Next, we examine the linking strategy of both publishers taking into account the pro�t

functions de�ned above. In the case of the integrated publisher, notice that in the interval

� 2 [0; ��) it is veri�ed that �1HLA(HL) > �1HLA(H). On the other hand, we de�ne as �1 the value

of � for which �1HLA(HL) = �1HL. As a result, for � 2 [0; �1) we obtain that �1HLA(HL) > �1HL

and for � 2 [�1; 1) that �1HL � �1HLA(HL). Finally, notice that �1 is a decreasing function in

s and that �� = �1 for s = bs. Hence, for s 2 (0; bs] the integrated publisher wants to link L if� 2 [0; �1) and only o¤ers H if � 2 [�1; 1).

On the other hand, in order to analyze the region s 2 [bs; 1) we de�ne as �2 the value of �for which �1HLA(HL) = �

1HLA(H). Therefore, for � < �2 we obtain that �

1HLA(HL) > �

1HLA(H)

and for � 2 [�2; 1) that �1HLA(H) � �1HLA(HL). Also notice that �2 = �� = �1 for s = bs and�2 = 0 for s = 1. Taking this into account, in the region s 2 [bs; 1) the integrated publisherwants to link L if � 2 [0; �2), maintains A 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 �3 the values of � for

which �2HLA(H) = �2HLA(HL). In the space f�; sg this de�nes a set of parameter combinations

for which �2HLA(HL) � �2HLA(H). In the rest of cases the publisher don�t accept to be linked.

Finally, we identify in which situations the two publishers will reach an agreement over

L. When � > �� it can be shown that �2 intersects �3 twice in the f�; sg space: call these

roots (e�1; s1) and (e�2; s2), where s1 < s2. In particular, when s > s1 and s < s2 it is satis�edthat �2 > �3 and therefore the two �rms agree on setting the link to L. For s1 � s � s2 the

35

agreement is not pro�table for one of the publishers. Q.E.D.

Proof of Proposition 5. The results for the case in which the integrated publisher

doesn�t link L are shown in the proof of Proposition 4. Consider now the case where A links

L and s < �+��1� . In this case it is satis�ed that uA > uH > uL and the relevant indi¤erent

consumers are: �AH = [� (pH + pL)� pH ] =u [� + �(1� s)� 1], �HL = (pH � pL) =u (1� �),

and �L0 = pL=�u. According to this, the integrated publisher sets pH to maximize �1A(HL)HL =

�pH(1� �AH) + pH(�AH � �HL). The resulting price and pro�ts are:

pH =pL [� + �(1� �) + �(1� �(1� �)� s)� 1]� (1� �) � [1� � � �(1� s)]u

2�� 2(1� �)� + (1� �)�2 � �s

� ;(27)

�1A(HL)HL =[pL [� + �(1� �) + �(1� �(1� �)� s)� 1]� (1� �) � [1� � � �(1� s)]u]2

4(1� �) [1� � � �(1� s)] [� � (1� �)(2� �)� + �s]u :(28)

The pro�ts of the independent publisher �2A(HL)HL are not shown for simplicity. The price

in (27) leads to the following expressions for the indi¤erent consumers:

�AH =

8<: pL [1 + �(3� � �(2� �))� � � 2� � �(1� s� �(2 + (2� �)� � 3s))]

�(1� �)(1� �)�(� + �(1� s)� 1)u

9=;2 [1� � � �(1� s)] [�s+ (1� �)(1� �)� � �]u ; (29)

�HL =pL�5� � 3�2 � 1� � + �(1 + �(3� � 5) + s)

�+ (1� �)�(� + �(1� s)� 1)u

2(1� �) [� � (1� �)(2� �)� � �s]u ;

�L0 =pL�u:

With the above prices, it can be shown that �AH < �HL when s < s1, implying that any

consumer visits H directly. The value s1 that satis�es that �AH = �HL is:

s1 =

8<: [�+ 2� � 1� 2(1� �)� + 3(1� �)�2]pL

�(1� �)q(1� �)2(1� �)2�2u2 � 2(1� �)(1� �)�[1 + �(5� � 4)]upL + [1� �(8� �(18� �(16� 9�)))] p2L

9=;2�[pL � (1� �)�u]

Notice that for s < s1 the relevant indi¤erent consumers are �AL = [� (pH + pL)� pL] =u (� � �s)

and �L0 = pL=�u. As a result, the publisher sets pH to maximize �1A(HL)L = �pH(1 � �AL),

which leads to the following results:

36

pH =pL(1� �) + (� � �s)u

2�; (30)

�1A(HL)L =[pL(1� �) + (� � �s)u]2

4(� � �s)u ; (31)

�2A(HL)L =pL

h�(1 + �)(� � �s)u� pL

�2� + �

�(1� �)2 � 2s

��i2�(� � �s)u :

With this price we also observe that �AL = 12

h1� (1��)p

L

(��s)u

i> �L0 =

pL

�u .

Suppose now that s < s1. Then, it can be shown that �1A(HL)L > �1HLA(H) for � <b�1,

where b�1 is de�ned as in (22). On the other hand, �1A(HL)L � �1HL for � � �1, where�1 = 1 +

(1� �)pL(� � �s)�p(1� �)p2L(1� �+ pL)2(� � �s)(1� �)p2L

> b�1:Taking this into account, if s < s1 the aggregator is never active if � > �1 and it wants to

link L if � < �1: In the later case, high type consumers visit A and intermediate consumers L.

Next, de�ne as s2 the value of s for which indi¤erent consumers in (??) satisfy �AH = �L0.

s2 =

�2� � (�+ � � 1)�� 4� + (3 + �)�� + (2� �� 2)�2

�pL � (1� �)(�+ � � 1)��u

� [(2� �)pL � (1� �)��u]

Notice that s1 intersects s2 once at the f�; sg space: call this root (e�; es): For (e�; es) it isveri�ed that �AH = �HL = �L0. Moreover, for s > es and s < s2 we �nd that �HL < �L0 andfor s < es and s < s1 that �AH < �HL.

For s < s2 L does not receive direct visits and the relevant indi¤erent consumers are

�AH = [� (pH + pL)� pH ] =u (� + �(1� s)� 1) and �H0 = pH=u. Thus, the publisher sets pH

to maximize �1A(HL)H = �pH(1� �AH) + �pH(�AH � �H0), which yields:

pH =�[(� � 1)pL � (� + �(1� s)� 1)u]

2[�s� (�+ � + (� � 2)�)] ; (32)

�1A(HL)H =�2[(� � 1)pL � (� + �(1� s)� 1)u]2

4(� + �(1� s)� 1)[�+ � + (� � 2)� � �s] ; (33)

�2A(HL)H = �pL[1��[pL(2� � 1 + (� � 2)� + 2�(1� s)) + (� � 1)(� + �(1� s)� 1)u]

2(� + �(1� s)� 1)[�+ � + (� � 2)� � �s] ]:(34)

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 (29) satisfy �AH = 1.

s3 =1

4u�2

8<: � [2(�+ 2� � 1)u� pL(3� � 1)� (1� �)(3� �)�u]

�q�2�((3� � 1)2p2L + 2(1� �)(1� �)(2� �(3 + �))pLu+ (1� �)2(2� 3� + �

2)2u2�9=;

37

This implies that for s > s3 A is never active and consumers only visit H or L:

Taking this into account we now determine the linking strategy of the publishers. For s < esand s > s1 and for s > es and s2 < s < s3 all A, H and L are active when A links L, and

the price and pro�ts are those in (27) and (28) (see Figure 5). In this region, it is satis�ed

that �1HLA(H) > �1A(HL)HL for � <b�1 and �1HL > �1A(HL)HL for � � b�1.29 Therefore, the

integrated publisher does not want to link its competitor. For s > es and s < s2 only A and Hreceive direct visits when A links L, and the price and pro�ts are those in (32) and (33). In

this interval, it can be found that �1A(HL)H < �1HLA(H) for � <b�1 and that �1HL > �1A(HL)H

for � > b�1:30 As before, the integrated publisher does not want to link L. Finally, for s > esand s � s3 no consumer visits A. As a consequence, the optimal price and pro�ts are those in

(19) and (20) if � < b�1, or the ones in (23) and (24) otherwise.Consider now the linking strategy of the independent publisher. For s � s1 it holds that

�2A(H)L > �2HLA(H) when � <b�1 if pL > 0 and �2A(H)L > �2HL for � � b�1 if pL > 0. These

results imply that both publishers agree to set a link on L for � < �1. When s > s1 the

integrated publisher is not interested on linking L. Q.E.D.

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