Competition for Attention in the News Media Market ∗

HENG CHEN

University of Hong Kong

WING SUEN

University of Hong Kong

October 17, 2016

Abstract. We provide an framework for analyzing the new media environ-ment, where a large number of heterogeneous firms compete by investingin the accuracy of news gathering, biased editors compete by manipulatingthe presentation of news stories, and readers allocate their attention amongmultiple outlets. New entry reduces both the accuracy of news gatheredand the clarity of news reported by incumbents, but the overall influenceof the media industry unambiguously increases. However, the number ofmedia firms that can be supported in equilibrium is bounded. Media com-petition combined with enhanced monetization of attention may explainthe proliferation of soft news.

Keywords. monopolistic competition, media bias, media quality, sender-receiver game, attention allocation

JEL Classification. D83, D84, L15, L82

∗We thank Jimmy Chan, Alessandro Lizzeri, Andrea Prat, Antonio Russo, and seminar participantsat the University of Copenhagen, Australasian Economic Theory Workshop (2016) and Media Eco-nomics Workshop (2016) for useful comments and discussions. This research project is partly fundedby the General Research Fund of the Research Grants Council of Hong Kong (Project No. 17501516).

1. Introduction

The news media industry has experienced a profound transformation. Gone are thedays when a consumer got his news from just one or two local newspapers and a fewradio and television stations. The modern news consumer faces a menu of optionsmuch richer than before: free dailies and online newspapers, news programs on cable,and an almost unlimited amount of information in the internet available at no cost.Associated with this development is the growing heterogeneity among news firms.On one side of the spectrum are the “established media” with a reputation for highquality and professional standard; on the other side are amateur “citizen journalists”who may be brilliant or simply not up to it. With such an abundant and diverse setof news outlets, how do consumers allocate their scarce resource—their attention—among these outlets? And how do firms compete for consumers’ attention in thisenvironment?

The goals of this paper are twofold. We first provide a framework to characterizethe transforming news industry, incorporating its salient new features detailed imme-diately below. We then analyze a range of classical or emerging issues in the industry,which illustrates how this framework can be applied and extended. We give particularemphasis to a set of topics related to media competition, such as its effects on mediaquality and the rise of soft news as well as the limits of competition.

Proliferation of media outlets. The lowering cost of producing and distributing news,thanks to information technologies, reduced entry barriers to the news industry andunleashed a wave of startup news firms. For example, the number of profit-oriented,independent, online news content producers has grown from roughly 20 in 1999 toalmost 300 in 2011.1 See Figure 1. These newly available information sources havegained substantial popularity. According to the Media Consumption Survey con-ducted by Pew Research Center, 26 online news sites were named by at least onepercent of the respondents in the United States as their source for accessing news in2010; but the comparable figure was only 17 sites in 2006.2 A similar pattern exists forsome traditional media, such as television.3 Given the large number of competitors,the news industry can best be described by monopolistic competition among many

1 Data are obtained from the Guide to Online News Startups of Columbia Journalism Review (http://www.cjr.org/news_startups_guide/). It keeps track of online news sites that satisfy the followingfour criteria: the outlet has to be primarily devoted to original reporting and content production; itshould have full-time employees; it is independent and not the web arm of a legacy media entity; and itattracts financial support through advertising, grants, or other revenue sources to sustain its operation.

2 We obtain data for readership of online news sources from the 2010 wave of the Biennial MediaConsumption Survey, available from the Pew Research Center website, http://www.people-press.org/files/legacy-pdf/652.pdf

3 The average number of television channels per household increased from 10 in 1985 to 130 in 2008,which is accompanied by a decline of market concentration of viewership (Webster 2014).

1

1999 2002 2005 2008 201120

60

100

140

180

220

260

300

Figure 1. Number of online news sites. Source: Compiled from the Guide to Online News Startups.

media firms, rather than by a monopoly or oligopoly model.

The new currency of business. Media firms sell content to news readers and selltheir “eyeballs” to advertisers for revenue. Such an advertising-supported free contentbusiness model is not really new; what is new is the expansion of this business modelto the whole news media industry. Even the most traditional print media industry hasbeen shaken: in the past two decades, free newspapers emerged to become “a solitarybeacon of hope” in a declining newspaper industry (Anderson 2009). This businessmodel is now so prevalent that media measurement technology has to evolve, as a re-sponse, from audience-size based measurement to attention based measurement.4 Inthe media market today, news consumers can often access their news stories at verylow or no cost.5 Given that media firms do not charge readers directly, readers’ atten-tion paid to media has become “the new currency of business,” a term coined by Dav-enport and Beck (2013). When news can be provided for free, the real constraint facingconsumers is the limited attention available for processing the information. Therefore,the primary goal of media firms is no longer to maximize readership and subscriptionrevenue, but to grab valuable attention from readers. In other words, they compete onthe intensive margin (i.e., attention) rather than on the extensive margin (i.e., size ofaudience).

Attention allocation to multiple news providers. In response to an enriched media envi-ronment, typical news consumers engage in multi-homing and spread their attention

4 Advertisers rely on media measurement to assess the advertising value of media outlets, while me-dia firms also need it to determine the market value of their products. The technology of measurementhas transformed from measuring the size of viewership (e.g., Nielson ratings) and readership (e.g., ABCaudit reports) to measuring the detailed aspects of information consumption of readers, especially theamount of attention that they pay to media outlets (Napoli 2013 and Webster 2014).

5 According to the Pew Local News Survey of 2011, 93 percent of people surveyed do not pay fornews, except for a local print newspaper. Data from this wave of survey can be downloaded fromhttp://www.pewinternet.org/2011/09/26/how-people-learn-about-their-local-community/.

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among multiple news sources to obtain information. They not only access multipletypes of media (e.g., print media, radio and television, and the internet), but also ac-cess multiple outlets within each type. The Pew Personal News Cycle Survey in 2014finds that an average American adult uses four types of media every week for gettingnews, and the Pew Online News Survey in 2010 finds that 68 percent of respondentsaccess online news from more than two websites.6 Consumers’ multi-homing deci-sions are particularly important for media competition in the era of the internet (Peitzand Reisinger 2015).

Concerns over news quality. In a market with a flood of new (and often small) mediafirms competing for attention with free content, concerns are frequently raised aboutthe quality of their news products. It seems to many that there exists a trade-off be-tween quantity and quality in the media industry: the rise of commercially run digitalmedia may threaten and deteriorate journalism standard. For example, it is arguedthat the advertising-supported business model may level the playing field betweenestablished news organizations and new entrants, which may drive out existing pro-fessionals “at a cost to quality” (Anderson 2009, p. 195). Hollifield and Becker (2009)commented that, unlike journalists and editors in established media firms, some ofthose employed in small news startups or non-institutional content providers may beless well-trained and may have fewer resources to engage in in-depth reporting oreven to check their facts.7 Concerns over news quality are thus no longer confined toslant and biases in the presentation of news, but to the scope and accuracy of newsgathering as well.

Despite these developments in the news industry, the media economics literaturehas not quite caught up. First, there is little effort taken to capture the feature of mo-nopolistic competition in media market. Much of the literature focuses on the caseswith just one or two news providers (e.g., Anderson and McLaren 2012; and Ström-berg 2004). In models with a large number of news outlets, they are typically assumedto possess identical information (e.g., Gentzkow and Shapiro 2006; and Chan and Suen2008), and the strategic interaction among media firms is often left out for tractability.8

6 Data from these two waves of survey can be found at https://www.americanpressinstitute.org/publications/reports/survey-research/download-personal-news-cycle-study/ and http://www.pewinternet.org/2010/03/15/the-economics-of-online-news/, respectively. Gentzkowand Shapiro (2011) also demonstrate that a significant share of consumers acquire news from multi-ple outlets either online or offline.

7 Keen (2007) illustrates this point with an anecdote from the aftermath of Hurricane Katrina in2005. Citizen journalists provided many inaccurate reports of the damage and photos of the devasta-tion, which facilitated the spread of rumors on inflated body counts and erroneous reports of crimesconducted. The established news media have to compete with them for people’s attention and debunkthe errors.

8 One of the exceptions is the recent work by Anderson and Peitz (2016). In that model, they charac-terize media competition as an aggregative game in which advertising messages from different mediaoutlets crowd out one another as they compete for readers’ attention. Our focus instead is on the me-

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We need a framework that explicitly characterizes how media firms strategically in-teract with many competitors producing similar but not identical news.

Second, most contributions to media economics use discrete choices models tostudy competition at the extensive margin with single-homing consumers: each con-sumer chooses to get news from only one of the news outlets, and news outlets com-pete to maximize the size of their audience. That tradition can be dated back to Steiner(1952) and is followed by many media competition models (see Prat and Strömberg2013 for a review), although Anderson et al. (2012) show that, in a context of compet-ing advertisers, the assumption about whether viewers single-home or multi-homecan lead to opposite results. With media content often available for free and attentionbeing the “new currency of business,” competition at the intensive margin has becomethe primary driver in the news industry. We need a framework to characterize the newparadigm and generate new insights about media competition for attention.

Third, the literature typically treats news consumers as Bayesian learners who pas-sively process all the available information. When the supply of news has becomeoverwhelming as is the situation today, it is natural to model how consumers selec-tively choose news providers to get news and allocate their limited attention amongthem. But an often neglected aspect is that the attention allocation decision of newsreaders in turn has implications for firms’ investment and editorial decisions. Thesedecisions are affected by each other and are determined jointly. Our approach there-fore also differs from existing works on endogenous information acquisition, wherethe information structure of the underlying signals is taken as exogenous (e.g., Hell-wig and Veldkamp 2009; Myatt and Wallace 2012; and Chen, Luo, and Pei 2015).

Finally, the media economics literature has focused almost exclusively on mediabias or news slant (e.g., Baron 2006; Chan and Suen 2008; Gentzkow and Shapiro 2006;Mullainathan and Shleifer 2005; and the survey article by Gentzkow, Shapiro, andStone 2016), but has given much less attention to the depth or accuracy of informationcollected in the news gathering stage. These two aspects of news quality are distinctbut closely related: low-cost news contents are often associated with high bias in thenews products (Hollifield and Becker 2009). In a reputation model (Gentzkow andShapiro 2006), for example, editors with more accurate information are less likely toslant the news because they are more concerned that their misrepresentation will besubsequently contradicted. Less well studied is the other side of the relationship: newsoutlets that often distort their information have less incentive to improve the accuracyof the information gathered. We develop a model to capture how the competition for

dia’s role in informing the public, and readers in our model play a more active role in allocating theirlimited attention.

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attention shapes media firms’ investment and editorial decisions.9 When attentiongrabbing is driving the news market, such a model can shed light on whether mediacompetition of this type enhances or hurts the quality of news products.

In this paper, we build a model of the news industry that incorporates the fourkey features described earlier. It has three sets of actors. Owners of news firms areprofit oriented. They invest in an infrastructure to conduct news gathering and in-vestigative research—the more they invest, the more accurate are the facts obtained.Editors (and journalists) of news firms care about informing the public, but they alsohave their own personal biases. Based on the facts obtained from news gathering, theywrite news stories that reflect a tradeoff between these two concerns. There are a largenumber of such firms in the news market, each producing a differentiated product (be-cause the facts obtained are not identical and because different editors adopt differentreporting strategies). News readers need to take an action about an uncertain stateafter consulting multiple news outlets. They decide how much attention to give toeach outlet, and their attention in turn generates revenue for the news firms. The twoaspects of news quality (accuracy of the facts and biases in reporting), readers’ atten-tion allocation, and the influence of the media on readers’ action taken are determinedjointly.

Our model features both strategic complementarity between news readers andnews firms as well as strategic substitution among firms. Strategic complementar-ity arises because the more attention readers give to a news outlet, the more incentivethis outlet has to improve its accuracy and reduce its bias; and the higher quality arenews reports, the more willingly are readers to pay attention to them. This featureof strategic complementarity is consistent with empirical evidence from online mediaoutlets (Sun and Zhu 2013).10 Strategic substitution among firms arises because of twokey mechanisms. The first one is a free riding effect: if other news editors are provid-ing less biased reporting to inform the public, an individual editor tends to slant hisnews story more to indulge in his own personal biases. The second one is “attentiondiversion” induced by readers’ attention allocation: an improvement in the quality ofnews from other outlets shifts attention away from an individual firm, which reducesthe incentive for its owner to invest in news accuracy. This feature of strategic substi-tution is broadly consistent with evidence provided by Gentzkow (2007). In Section3, we characterize the sender-receiver game between editors and readers, which de-termines the news clarity and spotlights the first mechanism. In Section 4, we study

9 The existing literature typically models the media industry with a fixed-cost technology: once thefirst copy cost of producing the news stories is paid, the variable cost of providing information is zero(Veldkamp 2006). In our model, various media compete for attention by improving the quality of thenews provided, and the cost incurred is increasing in its accuracy.

10 They find that online media outlets, such as blogs, take more effort to raise the quality of theirproducts when attention of the readers exogenously increases.

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the monopolistic competition among owners who grab attention from readers, whichdetermines the news accuracy of these firms and delivers the second mechanism.

We develop a set of applications of our framework in Section 5 to illustrate how themodel can be used and extended to shed light on relevant issues in the new media en-vironment. Does increased media competition improve or reduce the quality of newsreporting and help the truth prevail? Our model predicts that stronger competitiondoes hurt the quality and influence of the incumbent firms, but the informativenessof the news industry as a whole necessarily improves upon a new entry. Section 5.1details the analysis of this issue and provides corroborating facts for our results. Wefurther show that those facts cannot be reconciled in a model with news firms com-peting for audience but not attention, therefore showcasing the necessity of modelingattention allocation.

Given that new entry is beneficial for the news consumers, is it true that the trendof escalating media competition will continue forever? And may readers eventuallybecome fully informed as the number of outlets to get news from grows indefinitely?We show in Section 5.2 that such a scenario cannot arise. The endogeneity of newsquality is the key to understanding this: those firms that fail to grab enough attentionhave to cease operation and only a finite, albeit large, number of news producers cansurvive in equilibrium.

Media competition is often blamed by media scholars for the rise of soft news anddecline of hard news, because increased market pressure causes news firms to producetoo much soft news with high audience appeal and serious hard news is crowded outas a result. In Section ??, we show how enhanced monetization of attention (a by-product of the progress made in media measurement technologies) may contribute tosuch a trend.

Other related work. Our model of attention allocation builds on Sims (2003), in whichthe assimilation of available information is plagued by receiver noise. Hellwig, Kohls,and Veldkamp (2012) review the subsequent research modeling inattention with alter-native approaches. We borrow from Myatt and Wallace (2012), who study a setting inwhich the receiver noise reduction technology is continuous, i.e., the variance in thereceiver noise decreases as readers pay more costly attention to the signal.

Our work also enriches the literature on sender-receiver games by introducing anumber of distinctive features that have not been thoroughly researched. First, muchof this literature focus on strategic information revelation with two competing senderswho intend to influence the receiver’s decision (e.g., Ambrus and Takahashi 2008;Battaglini 2002; Bhattacharya and Mukherjee 2013; Krishna and Morgan 2001; but seeGentzkow and Kamenica 2015 for a multi-sender model of persuasion). Senders are

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usually assumed to be fully informed about the true state (e.g., Ambrus and Takahashi2008; and Chan and Suen 2009). In our model, a large number of senders competewith one another to both influence readers’ actions and attract valuable attention fromreaders. Our assumption that senders acquire noisy and non-identical signals aboutthe state is both realistic and crucial for modeling media quality.11 Second, in ourmodel, both senders and receivers make decisions on information acquisition, whichturns out to be endogenously complementary. This feature is different from that inDewatripont and Tirole (2005), in which one sender and one receiver can both exerteffort to improve the amount of information understood by the receiver, but the com-plementarity in effort is exogenously assumed in the communication technology.

2. The Model

There is a continuum of ex ante homogenous readers indexed by i ∈ [0, 1], who ac-quire information from the media about an uncertain state θ and take an action qi.In the news market, there is a large but finite number of media firms indexed byj ∈ {1, . . . , J}. Each media firm j consists of two players: an owner who runs thebusiness for profit, and an editor who offers a news story about the uncertain state toinfluence readers. All players share a common normal prior about the state, namely,θ ∼ N(µ, σ2

θ ). We choose to separate the two roles within a media firm so as to cap-ture the norm of editorial independence in modern journalism, which prescribes thatowners do not get too involved in the day-to-day operation of the editorial office. Italso allows us to endogenize both accuracy (chosen by owners) and clarity (chosen byeditors)—two distinct aspects of news quality.

Each owner j decides the resources to make investigations about the state. Thisincludes decisions such as funds made available to journalists to do research, and thesize and quality of the editorial staff. Once the basic infrastructure of the news office isdetermined, the owner stays away from editorial decisions concerning the selection orpresentation of news stories. Specifically, the media firm acquires a noisy signal aboutthe true state. Let xj = θ + εj represent such a signal, where εj is normally distributedwith mean 0 and variance σ2

εj (and is independent of the state and independent acrossdifferent media firms).12 Let γj ≡ σ2

θ /(σ2θ + σ2

εj) represent the accuracy of the newsoutlet j. We assume that perfect accuracy is not feasible: γj ∈ [0, γ] for some γ < 1.The cost of investigation Cj(γj) is increasing and convex in γj. The owners choose theaccuracy of their news signals simultaneously. These decisions, once made, are knownto all readers and editors. This assumption captures the idea that the accuracy of news

11 See also Kartik, Lee, and Suen (2016) for a persuasion game model in which multiple senders havenoisy and non-identical signals.

12 It is realistic to expect that the noise term may be correlated across media firms conditional on thestate. We consider such a scenario in Section 5.4.

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outlets depends on their long term investments, which are generally well observed toplayers in the media market.13 The strategy of owners is characterized by the vectorγ = (γ1, . . . , γJ).

News outlet j receives revenue from advertisements, which is assumed for simplic-ity to be proportional to the attention received and is denoted by Sjzj, where zj is theamount of attention from readers given to that news outlet and Sj > 0 describes howattention received translates into revenue. The objective of media owner j is to choosemedia quality γj to maximize profits,

Πj = Sjzj − Cj(γj).

The editor of each news outlet j takes γ as given and writes a news story yj aboutθ to influence the readers’ actions. On the one hand, the editor prefers that the ag-gregate action taken by readers, Q =

∫ 10 qi di, is closer to the true θ. This represents

the incentive to inform the public. On the other hand, he also prefers that the mes-sage delivered from his story is not far away from his ideal position ξ j, which can beinterpreted as the established editorial stand of this news outlet or his personal viewon this issue. This represents the incentive to disseminate messages the editor prefers.Note, however, that the editor does not observe the state θ, but only a noisy signal xj,whose precision depends on the investment level chosen by the owner. He chooses yi

to maximize his payoff,

Uj = −E[(Q− θ)2 + φj(yj − ξ j)

2 | xj

], (1)

where φj is the weight assigned to the second concern. A higher φj means that theeditor cares more about his own personal views and less about the alignment betweenaggregate action and the true state. We say that editor j is more biased if φj is higher.In general, the reporting strategy is a function yj(xj) of the signal. We focus on linearequilibria in which the reporting strategy takes a linear form:

yj = αjxj + αj0. (2)

A high αj means that the story closely reflects the underlying signal obtained from thenews investigation, while a low αj represents a “cookie-cutter” style of reporting thatproduces standardized stories which fail to reflect all the nuances of the underlyingsignal. We use αj to denote the clarity of news outlet j. The strategy of news editors issummarized by the vectors α = (α1, . . . , αJ) and α0 = (α10, . . . , αJ0).

13 The assumption is made to abstract away the reputation concern, which has been thoroughly stud-ied in the media literature (e.g., Gentzkow and Shapiro 2006).

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Each news consumer chooses to acquire information from the media about θ, in-cluding which news reports they want to pay attention to and how much attentionthey pay to each report. If consumer i picks up the news report yj, he reads the newscontent with a reader noise ηji attached to the actual report. That is, he observes

yji = yj + ηji, (3)

where ηji ∼ N(0, σ2η ji) is independent of yj and independent across readers. The reader

noise is specified to capture the idea that an individual has limited capacity to processall the information contained in a story; he reads the content of a news story with ac-tual or interpretive errors. Thus the information set available to consumer i is an arrayof perceived reports,

(y1i, . . . , yJi

). Given his information set, reader i chooses action

qi to maximize −E[(qi − θ)2]. The optimal action strategy qi(y1i, . . . , yJi) is in general afunction of the J perceived news reports. In a linear equilibrium with Gaussian signals,since qi = E[θ|y1i, . . . , yJi], the action strategy is also linear:

qi = β0i +J

∑j=1

β jiyji. (4)

Because readers are ex ante identical, their strategies are the same (but their actionsmay be different since each reader perceives a different report based on the samestory). From here on, for j = 0, 1, . . . , J, we write β ji = β j for all reader i. The commonaction strategy of readers is represented by the vector β = (β0, β1, . . . , β J). We refer toβ j as the action weight of news outlet j’s report.

The variance of reader noise is not exogenous. News consumer i can read a newsstory with greater precision by paying more attention to it. Let zji represent the amountof attention devoted to news outlet j. The noise reduction technology is specified as:

σ2η ji =

χ2

zji,

where χ is a constant capturing the technological aspect of the information assimila-tion process. This noise reduction technology is commonly adopted in the attentionallocation literature; it specifies that the precision of the noise is linearly related to theattention devoted to the information source (Myatt and Wallace 2012; Mondria andQuintana-Domeque 2013).14

14 In spirit, this specification is the same as the seminal idea of rational inattention proposed by Sims(2003) that the amount of information conveyed is increased when readers devote more information-processing capacity to the underlying signal. The subtle difference is the noise reduction technology.Because entropy-based technology is neither linear nor separable, we prefer the linear technology forits tractability.

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Since yj = αjxj + αj0 and readers care about the underlying signal xj rather thanthe news story yj as such, the signal-to-noise ratio of the perceived news report isα2

j σ2θ /σ2

η ji. News stories with high clarity (i.e., high αj) have higher signal-to-noiseratios. We assume that these stories are easier to process, in the sense that the marginalcost of attention devoted to such stories is lower. In particular, we let pj = p/α2

jrepresent the marginal cost of giving attention to media outlet j.15 The net payoff toreader i is:

Vi = −E[(qi − θ)2 | y1i, . . . , yJi]−J

∑j=1

pα2

jzji.

Because readers are homogenous ex ante, they make the same information choice. Inwhat follows, we suppress the subscript i and write zj for zji unless it causes confusion.The attention allocation of readers is represented by the vector z = (z1, . . . , zJ).

3. Media Influence and Attention Allocation

3.1. Media influence

In this section, we solve the sender-receiver game, taking as given the accuracy profileγ chosen by media owners and attention allocation z chosen by readers. The solutionto this game allows us to characterize the influence of individual news outlets, as wellas to derive an aggregate variable that summarizes the influence of the media industryas a whole.

Each individual editor j chooses a story yj to maximize his payoff Uj described inequation (1), given the strategy of readers and of other editors. In a linear equilibriumwhere other editors follow the reporting strategy (2) and readers follow the identicalaction strategy (4), the aggregate action is

Q = β0 + β jyj + ∑k 6=j

βk(αkxk + αk0).

Substitute this expression into editor j’s objective function (1), the first-order conditionfor yj is

E

[β j

(β0 + β jyj + ∑

k 6=jβk(αkxk + αk0)− θ

)+ φj

(yj − ξ j

)| xj

]= 0.

For k 6= j, E[xk|xj] = E[θ|xj] = γjxj + (1− γj)µ. Therefore, the solution to the first-

15 This assumption of allowing the marginal cost to vary in clarity is not crucial for our results. InTechnical Appendix B, we explain how it improves the tractability of our analysis, and why our resultsare robust when the marginal cost does not depend on αj.

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order condition gives

yj =γjβ j

β2j + φj

(1−∑

k 6=jαkβk

)xj + constant. (5)

Thus, when news readers and other editors adopt linear strategies, the best-responsereporting strategy for editor j indeed takes the linear form (2), with

αj =γjβ j

β2j + φj

(1−∑

k 6=jαkβk

), (6)

and αj0 equal to the constant in equation (5). In what follows, αj0 plays no role becauseits equilibrium value is commonly known—rational readers can infer such systematicbiases in reporting and are unaffected by them. On the other hand, the slope αj iskey because it is equal to Cov[yj, xj]. A news outlet with high αj has high clarity as itsnews story yj closely tracks the underlying news signal xj (which contains informationabout the true state).

An important feature of this multi-sender game is that clarity of news reports ex-hibits strategic substitution: equation (6) shows that a higher αk (k 6= j) lowers αj. Thisfeature arises because all editors prefer that the public be informed. If other editors areproducing clearer news stories, then an individual editor can free ride on their effortsand write news stories that indulge more in his own biases instead.

Fix readers’ action strategy β, their attention allocation z, and owners’ accuracyprofile γ, equation (6) holds for every j = 1, . . . , J. The solution to this equation systemgives α = a(β; z, γ).

Lemma 1. The clarity αj = aj(β; z, γ) of news outlet j is given by:

αj =1β j

γjβ2j

(1−γj)β2j +φj

1 + ∑kγkβ2

k(1−γk)β2

k+φk

. (7)

It increases in news accuracy γj and decreases in editor bias φj. It decreases in the accuracyand increases in the bias of other news outlets.

It is worth noting that clarity αj chosen by editor j increases with accuracy γj cho-sen by owner j. When the underlying news signal xj is more informative, the trade-offbetween informing the public about the signal versus indulging in the editor’s per-sonal views tilts in favor of the former. Lemma 1 also says that αj decreases in theeditor’s bias φj, which is intuitive. Finally, because of the strategic substitution effect,

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the response with respect to other news outlets’ accuracy and bias are opposite to thatwith respect to own accuracy and bias.

Turning to readers’ action strategy, the quadratic loss function implies that qi =

E[θ|y1i, . . . , yJi]. To derive this conditional expectation, we use editors’ reporting strat-egy (2) and the communication technology (3) to write:

yji − αj0

αj= θ +

(εj +

1αj

ηji

).

Let τj represent the precision of the combined noise term above (relative to the preci-sion of the prior belief). We have

τj =1

1−γjγj

+ χ2

zjα2j σ2

θ

. (8)

Fix editors’ reporting strategy α, readers’ attention allocation z, and owners’ accu-racy profile γ, the optimal action rule β = b(α; z, γ) can be obtained from the linearBayesian updating formula.

Lemma 2. The action weight β j = bj(α; z, γ) of news outlet j’s report is given by:

β j =1αj

τj

1 + ∑k τk. (9)

It increases in the accuracy γj of news outlet j and in the attention zj given it. It decreases inthe accuracy of and the attention given to other news outlets.

Readers increase their reliance on the news report j when they pay more attentionto it and when the underlying news source is more accurate. For fixed α, editor j’sbias φj does not matter for readers’ action weight β j, because it does not directly affectthe signal-to-noise ratio of the news report. Similarly, readers decrease their relianceon report j when they pay more attention to other reports and when the other newssources are more accurate.

Given z and γ, the equilibrium (α, β) of the sender-receiver game can be obtainedby solving (7) and (9) jointly, with 2J equations and 2J unknowns. To state our formalresult, define for j = 1, . . . , J the quantity:

hj ≡ 1− χ

σθ

√φj

zjγj; (10)

12

and for any subset of media outlets G ⊆ {1, . . . , J}, let

HG ≡∑j∈G

γj1−γj

hj

1 + ∑j∈Gγj

1−γj

(11)

Proposition 1. Given attention allocation z and accuracy profile γ, there exists an equilibrium(α, β) of the sender-receiver game with a set of media outlets G ⊆ {1, . . . , J} such that: (a) ifj ∈ G, then

αj β j =γj

1− γj(hj − HG) > 0; (12)

and (b) if j /∈ G, then αj β j = 0.

In the proof of Proposition 1, we provide separate formulas for αj = aj(z, γ) andβ j = bj(z, γ). Equation (12) gives the product of the two because, with a linear actionrule and a linear reporting strategy, αj β j = Cov[Q, xj]/σ2

θ . We use αj β j to representthe influence of media outlet j: it measures how the aggregate action Q varies with theoutlet’s news sources.

The influence of news outlet j depends on the hj relative to HG. From equation (10),we see that hj increases in accuracy and attention but decreases in bias. The variableHG is the weighted average of hj, adjusted by a factor less than 1.16 The influence ofa news outlet depends on the characteristics of other news outlets only through thisaggregate variable HG. If we sum equation (12) over j, and drop the dependence on Gto avoid clutter, we can show that

H = ∑j

αj β j =Cov[Q, θ]

σ2θ

.

In other words, H is the total influence of the news industry as a whole. The higheris H, the more effective the media are in informing the public to choose an aggregateaction Q that closely tracks the true state θ. Furthermore, using Lemma 2, we have

H =∑j τj

1 + ∑j τj.

Thus, we sometimes also refer to H as total media informativeness (relative to the prior).This variable plays a key role in our model.

We call the set G in Proposition 1 the active media group because news outlets in

16 The weight on hj is γj/(1− γj) = σ2θ /σ2

εj, which reflects the precision of signal xj (relative to the

prior). The adjustment factor is ∑j σ−2εj /

(σ−2

θ + ∑j σ−2εj

), which reflects the combined precision of all

news sources as a fraction of total precision (news sources plus prior).

13

this group have positive influence. Given an equilibrium with active media group G,Proposition 1 determines a unique strategy profile (α, β) corresponding to that equi-librium.17 However, there exist multiple equilibria in this sender-receiver game, witha different active media group G in each equilibrium. Some of these equilibria involvecoordination failure: If news report j does not contain any information content, read-ers do not act on it; and if readers’ action does not rely on report j, its editor has noincentive to present any facts obtained. We can show that if there is an equilibriumwith active media group G, it remains an equilibrium if we delete an arbitrary subsetof media outlets from that group, simply because of this coordination failure.18 Ofcourse, the influence of the remaining outlets in the active media group will be differ-ent after some firms have been deleted from the group.

Lemma 3. Suppose there is an equilibrium of the sender-receiver game with active mediagroup G. For any G′ ⊂ G, there is an equilibrium with active media group G′, with HG′ <

HG.

3.2. Attention allocation

In this section, we study the attention allocation decision of readers, taking as giventhe accuracy γ chosen by owners and clarity α chosen by editors. Because qi is chosento be equal to the posterior expectation of θ, the expected value of the quadratic lossfunction (qi − θ)2 is simply the posterior variance of θ. Since the posterior precision ofθ is equal to the prior precision plus the precisions from all the signals about θ, readers’objective can be written as

V = − σ2θ

1 + ∑j τj−∑

j

pα2

jzj,

where τj is given by equation (8).

To obtain the equilibrium reporting strategy and action strategy with endogenousattention allocation, we derive the first-order conditions for zj:

τj

1 + ∑k τk

1zj−√

pχ

= 0. (13)

By Lemma 2, τj/(1 + ∑k τk) is simply the influence αjβ j of news outlet j. In other

17 If (α, β) is an equilibrium profile corresponding to G, it remains an equilibrium profile when wereplace both αj and β j by their negative values. In general, these alternative profiles are payoff equiva-lent.

18 A babbling equilibrium (one in which G is the empty set) is an extreme manifestation of this coordi-nation failure. This feature of coordination failure will be extended and generalized in the monopolisticcompetition problem. See our discussion regarding Proposition 2.

14

words, equation (13) shows that the attention given to a news outlet is proportional toits influence. To be sure, we do not ascribe a causal interpretation to this relationship,because both attention and influence are jointly determined.

Using equation (12) for αjβ j, and writing hj(zj) to emphasize the dependence of hj

on zj according to equation (10), we can express the first-order conditions (13) and theequilibrium conditions for media influence (12) solely in terms of zj in the followingkey equation:

γj(hj(zj)− HG)

1− γj

1zj

=

√p

χ. (14)

Equation (14) holds for each media outlet j that is active in equilibrium (i.e., withzj > 0 and αjβ j > 0). For any accuracy profile γ, the solution to the equation sys-tem (14) (together with equation (11) that defines HG) gives the equilibrium attentionallocation vector z. Note that the attention zj given to news outlet j depends on thecharacteristics of other outlets only through the aggregate variable HG. We can there-fore express the solution to equation (14) as zj = Dj(γj, HG(γ)).

4. Monopolistic Competition of News Firms

When the owner of a news firm tries to attract attention by investing in accuracy toraise hj, total influence HG will also rise because HG is an adjusted weighted averageof hj. However, the effect of a change in hj on HG is of order 1/|G|. When the numberof news firms in the active media group G is large, this effect is small. The proliferationof news firms in the modern news market means that a change in each individual firmonly has a tiny impact on the industry. It is therefore realistic to assume that eachmedia firm takes the overall media environment as given and ignores the impact ofits own action on the news industry as a whole. Such an assumption is commonlyadopted in monopolistic competition models of product markets, in which a producerof differentiated goods takes the aggregate price as given and chooses the price of itsown variety, while ignoring the impact of its own price on the price level. Similarly, inour model, a large number of news firms are producing differentiated products (newsstories that provide conditionally independent information about the state) and thetotal influence HG serves as an aggregate variable (akin to the aggregate price level inproduct markets) that summarizes the overall media environment.

In the following, we first characterize how total influence at the industry level andinvestment at the individual firm level affect the amount of attention that each firm re-ceives. We then establish that a monopolistic competitive equilibrium exists, in whicheach firm optimizes by taking total influence as given and the aggregation of theiroptimal choices is consistent with the conjectured aggregate.

15

b

γj(hj(zj)−HG)1−γj

1zj

Dj(γj, HG) zj

√p

χ

Figure 2. The key equation (14) either has two solutions or no solution. When there are two solutions,the demand function is defined to be the larger root.

Equation (14) can be interpreted as a reduced-form first-order condition for zj, aftertaking into account the fact that α and β are endogenously determined in the sender-receiver game. We illustrate this point with Figure 2. The left-hand-side of the equa-tion is increasing then decreasing in zj. For fixed α, we have ∂2V/∂z2

j < 0. Diminishingreturns to attention, reflected in the term 1/zj, accounts for the decreasing part of thegraph. However, readers also put more action weight β j on news outlet j as they paymore attention to it. In the sender-receiver game, a higher action weight β j induceseditor j to improve clarity αj in equilibrium. But as clarity increases, the marginal ben-efit from paying attention also increases (i.e., ∂2V/∂αj∂zj > 0). This effect is reflectedin the term hj(zj), which increases in zj, and it accounts for the increasing part of thegraph in Figure 2.

From Figure 2, it is clear that the key equation (14) either admits two solutions orno solution. When there are two solutions, we focus on the larger one because it isa locally “stable” root and gives intuitive comparative statics results. Since the left-hand-side of (14) is increasing in γj, there exists a critical γj (which depends on HG

and other parameters) such that a solution to the equation does not exist if γj is belowthis value. We therefore define the “demand function,” zj = Dj(γj, HG), to be readers’attention to news outlet j, given its accuracy γj and total media influence HG:

Dj(γj, HG) =

max{

zj :γj(hj(zj)−HG)

1−γj1zj=√

pχ

}if γj ≥ γj;

0 otherwise.

We use the term “demand function” to highlight the analogy with product markets,in which consumers’ utility maximization problem gives rise to demand for differ-ent goods as functions of all the prices. In our model, consumers’ attention allocationproblem (and the corresponding sender-receiver game) gives rise to different amounts

16

bb

γ

zjD(γ,H)

D(γ,H ′)

γ(H) γ(H ′)

Figure 3. The demand curve Dj(γj, H) is discontinuous at γj = γj(H). An increase in total media

informativeness (from H to H′) shifts down the demand curve: readers pay less attention to each newsoutlet as total media informativeness increases.

of attention to media outlets, which is used to generate revenue for the media firm.Figure 3 shows the demand functions corresponding to two different values of HG.It inherits all the intuitive comparative statics from the equilibrium of the sender-receiver game and the attention allocation decision of readers.

Lemma 4. The demand function Dj(γj, HG) is discontinuous at γj = γj. When attentionto news outlet j is positive, it increases in the accuracy of its news sources (∂Dj/∂γj > 0);it decreases in the bias of its editor (∂Dj/∂φj < 0); it decreases in the marginal cost of at-tention (∂Dj/∂p < 0); and it decreases when total influence of the media industry is higher(∂Dj/∂HG < 0).

The key result is that attention to news outlet j falls when the total influence HG ofthe news industry is higher. It emerges for two reasons. First is attention diversion:a more informative news industry means that news outlet j faces competition frombetter substitutes when readers allocate their attention. Second is free riding: a moreinformative news industry creates more incentive for editor j to rely on other editors’reports to inform the public, which causes him to write stories with lower clarity thatattracts less attention. In this model, the strategic substitutability among media firms isendogenous, and this result is broadly consistent with empirical findings about mediasubstitutability.19

In this model, firms that intend to grab more attention and reap more advertisingrevenues achieve this by offering higher-quality content, because ∂Dj/∂γj > 0. This

19 For example, Gentzkow (2007) finds that online and print versions of news sources are significantsubstitutes instead of complements, once consumer heterogeneity is properly controlled for. Wallsten(2015) also finds that increased attention spent on internet, such as obtaining news, is associated withless attention to television.

17

result is consistent with observations on the news industry (Peitz and Reisinger 2015,p. 449). Lemma 4 also states that the demand function is discontinuous, which followsfrom the fact that the left-hand-side of equation (14) is hump-shaped. This property isimportant for determining the number of news outlets that can be active in the newsmarket. We will elaborate on this point in Section 5.2.

Given the properties of the demand function Dj(γj, HG), the equilibrium levels ofinvestment in this market are defined as follows.

Definition 1. A monopolistic competitive equilibrium is described by an active media groupG ⊆ {1, . . . , J} and a profile {γ∗, H∗G} such that:

1. (a) For each j ∈ G, γ∗j = gj(H∗G) > 0, where

gj(H) = arg maxγj

SjDj(γj, H)− Cj(γj);

and (b) for each j /∈ G, γ∗j = 0.

2. Given the accuracy profile {gj(H∗G)}j∈G, there exists an equilibrium in the sender-receiver game with endogenous attention allocation in which the active media group is Gand total influence of the media is H∗G, i.e., H∗G = κG(H∗G), where

κG(H) =∑j∈G

gj(H)

1−gj(H)

(1− χ

σθ

√φj

Dj(gj(H),H)gj(H)

)1 + ∑j∈G

gj(H)

1−gj(H)

.

Given an equilibrium profile {γ∗, H∗G}, the corresponding equilibrium attentionallocation is z∗j = Dj(γ

∗j , H∗G) for j ∈ G. Equilibrium clarity and action weight for an

active news outlet j are, respectively, α∗j = aj(z∗, γ∗) and β∗j = bj(z∗, γ∗) (specified inthe proof of Proposition 1). If j /∈ G, then z∗j = α∗j = β∗j = 0.

To study the existence and the properties of equilibrium, we first provide a resultfor the optimal investment function gj(H) and for the aggregator function κG(H).

Lemma 5. For each media firm j, there exists pj such that, when the marginal cost of attentionp is lower than pj, optimal investment in accuracy gj(H) decreases in H, p, and φj. Further,if p ≤ min{pj : j ∈ G}, then the aggregator function κG(H) decreases in H, p, and φj.

Lemma 4 already establishes that ∂Dj/∂H < 0. To show that optimal investmentdecreases in H, we need to establish that H lowers the marginal benefit from invest-ment, i.e., ∂2Dj/∂H∂γj < 0. Lemma 5 shows that this is indeed true when the marginalcost of attention is sufficiently low. Furthermore, an increase in H also lowers the

18

H

κ

κG′b

κGb

κG′′b

HGH∗GH∗

G′

45o

Figure 4. The function κG(H) is well-defined on the interval [0, HG], and is downward sloping whenthe marginal cost of attention is low. The fixed point of κG(·) is an equilibrium. There is also anequilibrium with active media group G′ for any G′ ⊂ G, but there may not be an equilibrium withactive media group G′′ if G′′ ⊃ G.

aggregated total influence κG(H)—both through a direct channel where lower accu-racy, gj(H), reduces influence, and through an indirect channel where lower attention,Dj(gj(H), H), reduces influence.

In Figure 4, we show the aggregated total influence function for three differentactive media groups, G′′ ⊃ G ⊃ G′. The function κG(·) is downward sloping, as statedin Lemma 5, and is undefined beyond some HG < 1. When H > HG, some firm j ∈ Gfaces a demand function Dj(γj, H) = 0 for any γj. This firm has no incentive to investin γj and will never be active when total influence is equal to H. To ensure that κG(·)is continuous on [0, HG], we also require that the cost functions of the active firms aresufficiently convex (specifically, C′′j (γj)/C′j(γj) ≥ d(γj) for some function d(·) and forall j ∈ G), so that the owners’ profit maximization problems are quasi-concave.

Proposition 2. Fix any set of media firms G ⊆ {1, . . . , J}, and assume that the cost functionsof the active firms are sufficiently convex. There exists pG such that for any p ≤ pG, thereis a monopolistic competitive equilibrium in which the active media group is G and the corre-sponding profile {γ∗, H∗G} is uniquely determined. Further, for any G′ ⊂ G, an equilibriumwith active media group G′ also exists, with H∗G′ < H∗G.

The two fixed points in Figure 4 indicate two equilibria, one associated with activemedia group G and one with G′ ⊂ G. Equilibrium exists for the smaller group G′,because news consumers can simply ignore news firms in the set G \ G′, and becausethose firms also quit producing news when they receive no attention at all. It is thesame manifestation of the coordination failure in the sender-receiver game of Section3. Observe that the equilibrium with the larger active media group is more informative(H∗G′ > H∗G).

Also observe that there may not exist an equilibrium with a very large active media

19

group (say, G′′ ⊃ G). When a large number of firms are making positive investmentsin accuracy, news readers can only give a little attention and assign a small actionweight to each news outlet. But this tilts editors’ trade-off against informing the publictoward indulging in their biases. Lower clarity causes readers to pay even less atten-tion to news outlets, which in turn have less incentive to invest. The firms’ accuracyand consumers’ attention choices reinforce each other, which produce a downwardspiral. Therefore, in equilibrium, such a large active media group G′′ cannot be sup-ported with all firms making positive investment. When the cost of attention p is low,however, such problem is less likely to occur. Indeed, when the cost of attention issufficiently low, there is an equilibrium in which all J firms are active.

When there are multiple equilibria with different sets of active media firms, oneequilibrium active media group may neither be a subset nor a superset of anotherequilibrium active media group. We can, however, rank different equilibria in termsof the equilibrium aggregate informativeness H∗. In the following, we will often focuson the most informative equilibrium for analysis. If firms are homogenous, the mostinformative equilibrium is the one that features the highest number of active firms.

5. Applications and Extensions

In this section, we use our model to deal with various aspects of media competitionin the new media environment. We show that new entry does hurt the quality and in-fluence of incumbent firms, but at the industry level the increased quantity of news issufficient to compensate for the reduced quality. Without the explicit model developedin this paper, it is no obvious how the quality-quantity tradeoff resulting from new en-try will necessarily produce a more informative media. Further we show that thereexists an endogenous limit to media competition: the proliferation of media outletscannot continue indefinitely because very small media outlets will face a downwardspiral of reduced attention allocation and reduced quality investment. In Section 5.3,we extend the model to include hard news and soft news. We illustrate that increasedcompetition and enhanced monetization of attention may contribute to the displace-ment of hard news by soft news. In the remainder of this section, we deal with relatedissues such as correlation in news sources and the effects of editors’ bias.

5.1. New entry and media competition

We begin with the question: Is increased competition (specifically, a larger numberof media firms) beneficial to news consumers? The answer to this question is byno means settled in the theoretical literature. Gentzkow and Shapiro (2006) creditscompetition for strengthening the incentive of building reputation. The availabilityof truthful feedback on a news outlet’s report increases in the number of competing

20

firms that offer their independent reports, and they show that competition is alwaysbeneficial by disciplining bias effectively. In Mullainathan and Shleifer (2005), con-sumers prefer hearing news from sources that are likely to confirm their priors even atthe expense of news accuracy. Stronger competition may exacerbate bias because con-sumers can self-segregate even more. In essence, these two papers (and much of thesender-receiver game literature) focus on how multiple senders distort informationwhen they face competition.

However, a more common concern among media practitioners often centers aroundhow competition affects the incentive for firms to invest in news production. Com-mentators typically worry that there exists a vicious cycle of intense media competi-tion: new entrants would compress the demand and therefore the production budgetfor each news producer, “which compromises the quality . . . , further reducing the au-dience and alienates the advertisers” (Keen 2007, p. 33). Becker et al. (2009, p. 376) alsowrote, “As competition among news providers becomes extreme, the organization’sfinancial commitment to quality news is expected to decline, as will the market per-formance of the organization. The quality and diversity of news content should fall,as will journalists’ wages, the size and quality of the editorial staff, and the numbersof bureaus and subscriptions to wire services and other external sources of content.”

Our framework integrates both a strategic model of information distortion and anindustrial organization model with investment in news accuracy, so that it can addressthe effects of increased competition on both news slant and news production, whichare the key issues in the two strands of literature described above. It can also addresshow news slant and news production affect each other. In the following, we start withsome stylized facts regarding to the consequences of competition in the current newsenvironment and then demonstrate how they can be reconciled in this framework.

The rise of news outlets in the digital sector has left many existing and establishedorganizations struggling, which is probably one of the most striking phenomenon inthe recent development of the news market. For example, the newspaper industry inthe United States lost 70 percent advertising revenues since 2000 (Chandra and Kaiser2015). Due to the financial strains that beset news organizations, the total number ofreporters, editors and other journalists has gone down from a peak of 56,400 in 2000to 32,900 in 2014, a decline of more than 40 percent.20 The new entrants also hada hard time attracting resources for their operation, and some media commentators(e.g., Grubisich 2005; and Carpenter 2008) have expressed strong reservations aboutthe financial viability of these operations as well as their commitment to news qualityand journalism standards.

20 Data obtained from the American Society of News Editors, Newsroom Employment Census 2015(http://asne.org/content.asp?pl=121&sl=415&contentid=415).

21

b

b

b

bb b b

bb b

b

b

bb

bbb b b b b

b

bb b

55

45

35

25

15

51985 1990 1995 2000 2005 2010

%

Get facts straightAdmitting mistakes

(a) Accuracy

bbb

b

b

b

b

bb

bb

bb b

b

bb

b b b

b

b

bb b

%

80

70

60

50

40

301985 1990 1995 2000 2005 2010

Tend to favor one sidePolitically biased

(b) Bias

Figure 5. The fraction of respondents who believe that news organizations are providing accurate newsreports in general steadily declines and the fraction who believe news are likely to be biased increases.Source: Media Consumption Survey, 2013.

Such a sharp decrease in input to news production contributed to two generaltrends in the public’s perception about the quality of individual news outlets: a steadydecline in news accuracy and a gradual increase in bias. In the annual Media Con-sumption Survey conducted by Pew Research Center, respondents are asked whetherthey believe that the news organizations “get the facts straight” and are “willing toadmit their mistakes.” There is a clear trend that the fraction of respondents who offera positive answer has been dwindling in the last three decades; see Figure 5(a). In1985, 55 percent of the respondents claimed that news organizations have their factsstraight, but in 2013 only 26 percent believed so. Similar questions regarding other di-mensions of news accuracy have also been asked, for example, “Do you think that theirstories and reports are often inaccurate?” and “Would you say news organizations arehighly professional?” The trend of decreasing accuracy is consistently confirmed bythe responses to these related questions.21

The same survey reveals that the public’s perception of bias in news stories issteadily increasing as well. The survey asks, for example, “In presenting the newsdealing with political and social issues, do you think that news organizations tendto favor one side?” and “Would you say news organizations are politically biasedin their reporting?” The fraction of respondents who agree with these statements in-creased from 53 percent and 45 percent in 1985 to 76 percent and 58 percent in 2013,respectively. See Figure 5(b).

However, despite the substantial decline in quality of individual news outlets over

21 For example, in 1985 only 34 percent of respondents claimed that news organizations often provideinaccurate stories, but 67 percent did so in 2013 (Pew Research Center Media Consumption Survey, “ThePeople and the Press,” 2013).

22

time, Americans are spending more time on news (Kohut et al. 2010). The 2010 waveof Pew Media Consumption Survey shows that, for an average American, the totaltime of getting news in a given day has risen from 57 minutes in 2000 to roughly67 minutes in 2006, and to 70 minutes in 2010. That upward trend is largely drivenby news consumption online, which offsets the mild decline in time spent with newsoffline. This measure does not take into account time spent getting news on cell phonesor other digital devices; otherwise the increase may be even sharper. As a result oflonger time with news, Americans are better informed. The 2014 wave of Pew Mediasurvey reveals that 62 percent of respondents claim that they are better informed aboutlocal news compared with five years ago, 75 percent claim so about national news and74 percent about international news.22

It seems to be interesting that Americans on average spend more time on newsand become better informed, while they believe that the quality of news has fallen.Increased competition may not necessarily lead to either of these changes. In productmarkets, the relationship between competition and product quality is theoretically am-biguous (Schmalensee 1979 and Spence 1975).23 Moreover, the proliferation of newsoutlets by itself need not cause news consumers to spend more time on them. Never-theless, the model of competition for attention can reconcile both trends we describe.

Proposition 3. Compare the most informative equilibrium with no entry to that when a newfirm e is introduced. In the latter equilibrium: (a) total media influence H∗ is higher; (b) totalattention spent on news, z∗e + ∑j z∗j , is higher; and (c) when p < pj, incumbent firm j thatremains active invests less in accuracy γ∗j , produces news reports with lower clarity α∗j , andreceives less attention z∗j and action weight β∗j from readers.

Assume for simplicity that all J firms are active in equilibrium with no entry (Propo-sition 3 does not rely on this assumption), and the equilibrium total influence is H∗.Upon new entry, as long as the new firm is active in equilibrium, we have κe(H∗) >

κ(H∗) = H∗, where κe(·) and κ(·) are the aggregator functions with and without entry,respectively. It follows that the fixed point of κe(·) is higher than H∗. In this model,total attention paid to news media is proportional to total influence H∗. Therefore,when there is new entry into the industry, news consumers also pay more attention toall the news media combined. This result is consistent with the observed trend thatAmericans are spending more time on news.

In Lemma 5, we have already shown that, if the marginal cost of attention is low22 Data from this survey can be downloaded from http://www.pewinternet.org/files/2014/12/

SurveyQuestions_InformedWeb_01.pdf.23 The news media is a platform industry, selling news readers’ attention to advertisers. A recent

study of another platform industry—supermarkets—finds that more intense competition raises thequality of supermarket service; in particular, it reduces the probability of product stockouts (Matsa2010).

23

enough, a higher total informativeness H∗ in the media industry discourages invest-ment in news accuracy—thanks to the direct effect of a diversion of readers’ attentionto other news media, and to the indirect strategic effect due to more severe free-ridingamong news editors. The decrease in γ∗j in our model corresponds to a reduction in theprecision of the facts obtained in the news gathering process. Our model prediction isconsistent with the trend shown in Figure 5(a).

Our model exhibits a strategic complementarity between two aspects of news qual-ity: accuracy and clarity. The returns from writing a news story that closely reflectsthe facts gathered is lower when the facts are a less precise signal about the true state.When editors reduce the clarity of their stories, it will attract less attention from read-ers, which in turn motivate owners of news firms to invest less in accuracy. Thus,when there is new entry, α∗j decreases together with γ∗j in our model. A fall in α∗j canbe interpreted as a greater perceived “bias” of the news outlet. Recall that editor j’s re-porting strategy is yj = αjxj + αj0. A lower αj means that the constant term αj0 (whichis affected by the editor preferred message ξ j) accounts for a relatively larger sharein the report, while the facts xj get a smaller share. Moreover, for the same amountof attention paid to the news outlet, the noise contained in its news report is largerwhen αj falls. This interpretation of news “bias” is broadly consistent with that inMullainathan and Shleifer (2005).24 Thus the fall in α∗j is broadly consistent with therising perception about media bias shown in Figure 5(b).

Because the quality (i.e., α∗j and γ∗j ) of existing firms falls when new firms enter, theproliferation of media outlet induces a trade-off between quantity and quality at theindividual firm level. Nevertheless, our model shows that the terms of this trade-offare unambiguous: overall media informativeness H∗ necessarily increases. In otherwords, a more competitive media industry also produces a more informed citizenry.We stress that this conclusion follows from a setup in which readers endogenouslyallocate their attention to multiple news firms, and is not obtainable if we do not studythe attention allocation problem. To expound this point further, we outline below acomparable case in which firms compete at the extensive margin.

Consider a discrete choice model in which reader i has a fixed amount of atten-tion (normalized to 1) and chooses to consume news from only one media outlet. Thevalue from choosing news outlet j is vij = vj + ωij, where vj = −σ2

θ /(1 + τj)− p/α2j ,

and ωij is an idiosyncratic preference for news outlet j that follows the extreme valuedistribution. The total amount of attention (from all citizens) given to news outlet j isevj / ∑k evk . We can show that the marginal benefit from investing in news accuracy in

24 Mullainathan and Shleifer (2005) define media bias as the expected difference between news readby readers and data obtained by media. In our model, because αj = Cov[yj, xj], such a difference riseswhen the clarity is lower.

24

this logit demand model decreases when there are more firms in the industry. Thus,each news outlet becomes less informative. Because each reader only gets news fromone firm, each reader’s action will deviate further from the state. As a result, Cov[Q, θ]

also falls. This result is opposite to that of our model, in which H∗ = Cov[Q, θ] riseswhen there is new entry into the industry. In other words, media competition im-proves the aggregate informativeness of the industry only when firms compete at theintensive margin (i.e., competing for attention); and news consumers as a whole maybe worse off when firms compete only at the extensive margin (i.e., competing foraudience).

5.2. Information overflow

In this section, we deal with a relative new issue in the current media market: when thenumber of media outlets is skyrocketing, how do consumers cope with the abundanceof information and are they becoming better informed?

There are two common conjectures regarding the proliferation of largely free infor-mation. First, it seems plausible that news consumers would get better and better in-formed as the number of media firms continues to grow. For example, Chan and Suen(2008) show that, in a Hotelling model in which media outlets compete for audiencesize, the proliferation of news firms as entry cost shrinks to zero produces the full-information outcome (see also Chan and Stone 2013). Gentzkow and Shapiro (2006)show that biased reporting by a news outlet can be completely eliminated when a suf-ficiently large number of other news outlets are competing against it. Second, somecommentators argue that the flourishing new media cause concerns of “informationoverload,” i.e., massive amounts of information may distract readers and hinder theirdecision-making, as well as “information pollution,” i.e., useful information is buriedin the wealth of information that may not be entirely accurate (see Lincoln 2011 for asurvey).

However, our model with endogenous news quality and competition for attentionpredicts otherwise: both the informativeness of the news industry and the number ofactive firms would eventually reach a limit, despite the seemingly unbounded avail-ability of news sources.

Two factors are at play in our model that limit the benefit from having new en-try into the media industry. The first is the cost of attention. The marginal benefitfrom having more information falls as news readers become better informed, whilethe marginal cost of attention does not. In the limit, even if the number of news out-lets goes to infinity so that perfect information is feasible, readers rationally choose toremain partially uninformed (by paying very little attention to each news outlet). Thesecond factor is novel in our model. We show that even if the number of news out-

25

lets goes to infinity, only a finite number of them can be active, simply because newsquality is endogenous in our model.

To illustrate these two factors, assume for simplicity that media firms are identicalwith fixed accuracy γ. We first consider the effect of costly attention and shut downthe mechanism of endogenous quality (in this particular case, the free riding incentiveof the editors). To do so, we fix α exogenously at α. Let the number of media firms beJ, then the optimal attention given to each news outlet is:

z =

χ√

pγ

1−γ

1−√

pχ

α2σ2θ

1+J γ1−γ

if α2 >√

pχ/σ2θ ;

0 otherwise.

When α2 exceeds√

pχ/σ2θ , we have z > 0 regardless of J. That is, readers spread

their attention evenly among different news outlets. As the number of firms increases,the attention z given to each news outlet falls and the total informativeness, H =

1/(1 + Jτ), increases. But the total informativeness of the media industry approachesa limit:

H ≡ limJ→∞

11 + Jτ

= 1−√

pχ

α2σ2θ

.

The higher is the marginal cost of attention p, the lower is this limit informativeness,which reflects the rational decision of news readers to remain partially uninformedwhen attention is costly.

Next, we allow for the effect of the endogenous determination of clarity. In thiscase, the equilibrium value of α is determined by, among other things, editors’ bias φ.To maintain comparability with the model of exogenous clarity in the previous case,we choose the parameter φ so that the equilibrium value of α is equal to α.

Proposition 4. In any equilibrium in which clarity of the active firms is equal to α, equilibriumtotal influence satisfies

H∗G ≤ 1− 32

√pχ

α2σ2θ

,

regardless of the total number of news firms J in the industry.

Even when the number of news firms goes to infinity, the total informativeness ofthe media is bounded away from H. This result arises because the free rider problem inthe model with endogenous clarity imposes a constraint on the number of active mediafirms in the industry. Figure 6 illustrates. When there are more active media outlets,holding attention to each firm constant, the influence of each firm will fall. This followsfrom equation (12), in which an increase in HG (induced by a larger number of active

26

αβ

z2 z1 z

αβ(z;n3)

αβ(z;n2)

αβ(z;n1)z(αβ)

b

b

Figure 6. The solid curves illustrate that media influence increases in attention received, see equation(12). The dashed line illustrates that attention to each medium is propositional to its influence, seeequation (13). When the number of firms increases from n1 to n2, the equilibrium amount of attentiondrops from z1 to z2. In this case, n2 is the largest number of media that can be attended and z2 is thesmallest possible amount of attention paid to each medium. Any equilibrium with even larger numberof active firms (e.g., n3) cannot be sustained.

firms) causes αβ to fall. But attention z is proportional to influence in equilibrium. So zalso falls in response, which triggers a multiplier effect. This is shown in the decreasefrom z1 to z2 in Figure 6 as the number of active firms increases from n1 to n2. If thenumber of firms further increases to n3, the free rider problem among editors becomeso severe that it cannot sustain an equilibrium with all n3 firms being active.

Proposition 5. For any given φ and γ, there exists an upper bound n(φ, γ) such that inany equilibrium with active media group G, the number of active firms in G is lower than n,regardless of the total number of firms J in the industry. Furthermore, n decreases in φ andincreases in γ.

It follows from Proposition 5 that, when the total number of firms J is large enough,readers’ attention allocation is asymmetric: they pay attention to at most n mediaoutlets and ignore the rest. Since the number of active firms remain finite, the attentionthat each active media outlet receives remains bounded away from zero even when Jgoes to infinity (it cannot fall below z2 in Figure 6).

Proposition 5 offers a prediction for the future of the media industry: the seeminglyever-increasing trend in the number of news outlets, documented in Section 1 and par-ticularly illustrated in Figure 1, will eventually cease and news consumers will neverchoose to be fully informed either. The complementarity of information acquisitionbetween news consumers and new firms that we analyze above implies one crucialdifference between the equilibrium of the news market in this model and that of theproduct markets. That is, the “zero-profit condition” does not necessarily apply. Evenif there is no entry barrier to the news industry, new firms may not be able to enter the

27

market when all the existing firms earn positive profits.

Further, our analysis reveals that models with exogenous and endogenous infor-mation quality can deliver qualitatively different predictions about the news market.Our results that attention allocation is asymmetric even among symmetric media, andthat there exist a maximum for the number of media firms that can receive attentionand a minimum for the amount of attention that has to be paid to each active firm,are driven by the endogenous choice of editorial strategy. They are different from thepredictions of models with exogenous clarity, where readers diversify their attentionto all existing firms, with each firm getting an amount of attention that approacheszero.

5.3. Hard news, soft news, and monetization of attention

Another salient trend in the news industry is that soft news has taken up an increas-ingly larger share in news coverage. While hard news largely consists of “public af-fairs, government action, or international relations stories” (Hamilton 2004, p. 165),soft news is “typically more sensational, more personality-centered, less time-bound,more practical, and more incident-based than other news” (Patterson 2000, p. 4). Theproliferation of soft news has been remarkable over the last few decades. Besidesvarious qualitative studies, Patterson (2000) quantified the trend by showing that theproportion of news stories without a public policy component has risen from 35 per-cent since 1980 to reach roughly 50 percent in 2000, and that such a trend exists forall types of media.25 In this section, we analyze the rise of soft news and demonstratehow our framework can help rationalize it.

Many media scholars and practitioners blame intensified media competition forthis phenomenon. The development of media technology had made possible the ex-pansion of cable, the emergence of satellite television and the proliferation of internet,which reduced the cost for new entry and therefore created a highly competitive me-dia environment (Patterson 2000; Baum and Kernell 1999). In response to the ferociouscompetition, media firms begin to produce materials with high audience appeal (i.e.,soft news) so as to grab the audience who do not care about news otherwise (Baum2000; Zaller 1999).

As a complement to the existing hypothesis, we propose another plausible expla-nation, motivated by the following two observations. First, it is less costly to improvethe quality of soft news than that of hard news (Baum 2000), possibly because raisingthe quality of serious news stories requires thorough investigative efforts. Second, the

25 Patterson (2000) also illustrates the same trend with several other measurements of softness of newsstories, including the proportion of stories containing “sensationalism in news stories” or featuring“crime and disaster as a subject of news stories.”

28

media measurement technology has developed over the last few decades, to the pointwhere the attention paid to the media products can be measured so accurately thatthe attention received by media firms can be monetized and transformed into adver-tisement revenues much more easily than before (Napoli 2013). We argue that thesetwo features combined may give rise to an asymmetric response of investment in softand hard news, which leads to the disproportional expansion of soft news in newscoverage.

To illustrate this idea, we study a variant of our benchmark model. There exist twosectors in the news industry, one with J firms covering hard news and the other withJs firms specializing in soft news. Hard and soft news cover independent issues. Forexample, hard news covers politics and the economy, while soft news targets human-interest stories.26 Readers take two separate actions to maximize their utilities. Specif-ically, the utility function for reader i is:

Vi = −(1− λs)E[(qi − θ)2 | y1i, . . . , yJi]− λsE[(qsi − θs)2 | ys

1i, . . . , ysJsi],

where θs is the uncertain state in the soft news sector, qs is the action taken accordingly,ys

ji is the information collected from soft news producer j by reader i and λs capturesthe weight attached to the soft news by readers.

We further assume that the number of media firms is fixed in both hard and softnews sectors so as to shut down the effect of media competition, and that the amountof attention available to readers to allocate across media is also fixed so as to focus onthe attention allocation channel. That is,

J

∑j=1

zji +Js

∑j=1

zsji = Zi,

where zji and zsji are the attention paid to each hard and soft news firm, and Zi is the

total amount of attention available to reader i.

To capture the supply-side characteristics of the news production, we assume thatthe marginal costs of both hard and soft news are increasing in news accuracy, but themarginal cost of accuracy for hard news rises more steeply than that for soft news.

Assume that the commercial value of each unit of attention received by firm j (i.e.,Sj) is the same for all firms producing hard news or soft news and is denoted by S.Enhanced monetization of attention is captured by an increase in the value of S.

26 It may be more reasonable to assume that the two sectors are not completely unrelated. For exam-ple, Baum and Jamison (2006) show that people may watch talk shows to get political news. However,the substitutability between hard and soft news only amplifies the effect of the mechanism proposedhere.

29

Soft News

Hard News

S

γ∗j

(a) Accuracy of Hard and Soft News

S

Equilibrium

Share

(b) Share of Attention Paid to Soft News

Figure 7. In this figure, we assume that firms are homogenous within each sector and heterogeneousacross sector. When the commercial value of each unit of attention increases, the equilibrium accuracyrises faster in the soft news sector, which receives a larger share of attention from readers.

First, when S becomes larger, it shifts up the marginal benefit for both hard andsoft news so that firms have greater incentive to invest in news quality in both sectors.However, the news accuracy of soft news increases faster, given its marginal cost ofinvestment is less responsive to increased accuracy. See the panel (a) of Figure 7 for anillustration. Second, holding constant the attention allocated to each media firm, theaggregate influence rises in both sectors because all the firms provide news of higherquality. But the influence of the soft news increases faster, since its quality rises faster.Third, since the share of the attention allocated to each news firm is increasing in itsinfluence relative to the aggregate influence, the share of attention to soft news rises.In other words, given that the total amount of attention is fixed, the share of attentionpaid to soft news rises, which crowds out the attention paid to hard news. Panel (b) ofFigure 7 illustrates.

In this exercise, we hold constant the number of firms and rule out the effects ofnew entry. If we also allow for an increase in the number of firms, which capturesthe more intense competition experienced in the industry, two mechanisms will beat work. On the one hand, these two mechanisms have the opposite implicationsfor the media quality—stronger competition reduces the quality of individual mediafirms, while enhanced monetization raises it. On the other hand, they both imply thatthe share of attention received by soft news rises. When competition intensifies, thedemand curves for both soft and hard news shift down, which results in lower in-vestment in both sectors. But the reduction in soft news is smaller, since its marginalcost is less responsive. This asymmetric response of investment in news quality raisesthe share of attention received by soft news. In sum, our model produces a pattern

30

which is largely in line with the phenomenon of proliferating soft news in the last fewdecades: as media competition intensifies and monetization of attention becomes eas-ier, media firms favor the production of soft news, which in turn receive an increasingshare of readers’ attention, and the coverage of hard news declines as a result.

5.4. Correlated information production

In our benchmark model, we assume the facts obtained by media firms are condition-ally independent. However, journalists from competing news outlets may share com-mon news sources—they may interview similar sets of witnesses or consult overlap-ping groups of experts. Thus, the news gathering process is likely to produce sourcematerials that are correlated across media firms even conditional on the true state.Sender-receiver games where multiple senders have conditionally correlated signalsare typically not easy to solve. But thanks to the linear structure of the model, we canuse the model to examine how correlation in news production may affect the deci-sions of media owners, editors and readers, as well as the total influence of the newsindustry.

Assume that the news source for firm j is a signal xj = θ + εj + ζ j, where εj ∼N(0, σ2

εj) is independent across firms as before. The noise ζ j ∼ N(0, σ2ζ ), however, is

correlated across firms. Specifically, let Cov[ζ j, ζk] = ρσ2ζ , where ρ ∈ [0, 1] indicates the

degree of correlation. Define γj ≡ σ2θ /(σ2

θ + σ2εj + σ2

ζ ) as the accuracy of xj. We assumethat the owner of firm j’s investment only affects σ2

εj, so that the accuracy of anotherfirm is not affected by firm j’s decision.

When editor j writes his story based on xj, he has to anticipate what stories othereditors are writing. In our correlated signals model,

E[yk|xj] = Rγjxj + (1− Rγj)µ,

where R = 1 + ρσ2ζ /σ2

θ . When the degree of correlation is high (i.e., when R is large),editor j expects other editors to write stories that are similar to his own news source xj.His incentive to write a story that closely reflects xj to inform the public is diminished,because he can expect other editors to do the job. More specifically, given (γ, z, β) andgiven other editors’ reporting strategy α−j, we can obtain the best response reportingstrategy of editor j:

αj =β jγj

β2j + φj

(1− R ∑

k 6=jβkαk

).

This equation reduces to (6) in the benchmark case when R = 1. Observe that the clar-ity chosen by editor j is decreasing in R, that is, the free-riding problem is exacerbatedby a higher correlation in information production.

31

Furthermore, when the news stories are conditionally correlated, these stories be-come jointly less informative about the state. Not only is the posterior variance of thereaders larger, the marginal benefit from paying attention to reduce this variance isalso lower. In particular, the first-order conditions of their attention allocation prob-lem are:

τj

1 + ∑k τk

1Rzk−√

pχ

= 0.

whereτj =

11−γjRγj

+ χ2

Rzjα2j σ2

θ

− R−1R

.

These conditions reduce to (13) when R = 1. A higher value of R tends to lowerreaders’ attention and the action weights they put on the news stories. Since αj and β j

are complementary in the sender-receiver game, this has the effect of further loweringthe clarity chosen by editors.

Finally, total influence of the media also declines when the correlation is higher.There are two direct effects of raising correlation: statistically, more correlated signalsare less informative and less influential; and lower clarity of news reports, causedby the free-riding incentives, also dampens their impact on actions. Further, readersrespond endogenously by reducing their information acquisition, which also pushesdown the marginal revenue for firm owners, undermining their incentive to invest.These mechanisms combined contribute to the following result.

Proposition 6. Suppose all firms are identical (i.e., φj, Sj, and Cj(·) do not vary with j). In asymmetric equilibrium, a higher correlation in news production reduces the total informative-ness of the media industry. The influence of and the attention given to each media firm alsofalls.

This result rationalizes why the production of original content and independentjournalistic investigation are encouraged in the news market and why they are bene-ficial for news consumers.

While the result that correlated signals may reduce the overall informativeness ofthe media may seem intuitive, such a feature is not particularly prominent in existingmodels of media economics or sender-receiver games. Economic models of the mediaindustry often emphasize the “cross-checking” effect: a strategic sender is less likelyto hide or distort his facts if he thinks the receiver can get similar facts from othersources (Gentzkow and Shapiro 2006). In such models, the cross-checking effect tendsto be stronger when signals are more correlated.27 In fact, when signals are perfectly

27 In a different context, Chan, Li, and Suen (2007) and Damiano, Li, and Suen (2008) show thatschools (or credit-rating agencies) are less likely to distort their grades (or credit ratings) when theirprivate information are more correlated.

32

correlated, multiple-sender models can often support perfect information revelation(Krishna and Morgan 2001). Instead, our approach brings the free riding problemin multiple-sender games into sharper focus and we show how this effect may helpexplain why independent news sources are valuable.

5.5. Editors’ biases

We turn next to another frequently discussed issue in media economics: How do edi-torial preferences affect the performance of the media industry?

In the following, we assume that the marginal cost of attention p is sufficiently lowso that, in the most informative equilibrium, all firms are active. Moreover, p is low sothe condition stated in Lemma 5 holds for all firms.

Proposition 7. If editor j becomes more biased (i.e., φj increases), then (a) total media infor-mativeness H∗ falls; (b) the influence of firm j, the clarity of its news reports, and the attentionit receives decrease; and (c) other firms in the active media group will invest more in accuracy,present clearer reports, and receive more attention and a greater action weight.

A more biased editor tends to write news stories yj that do not closely track theunderlying news sources xj. This reduces the marginal benefit from investing in pre-cision of the news source (i.e., ∂2Dj/∂φj∂γj < 0). The aggregator function κ(·) shiftsdown, because of both the direct effect of a higher φj and the indirect effect due to alower gj and Dj. Therefore, the fixed point of κ(·) decreases. By the endogenous sub-stitution effects we describe earlier, an industry with a lower total influence H∗ causesα∗k , β∗k , γ∗k and z∗k to increase for any other active news outlet k. The media firm j losesinfluence and therefore attention to its competitors.28

In our model, a more biased editor is one who puts more weight φj on conformingto his preferred position relative to informing the public. The direction of the editor’sbias (i.e., the exact location of his ideal position ξ j) does not matter. The value of ξ j

only affects the constant αj0 in editor j’s reporting strategy. But since readers know hisreporting strategy in equilibrium and they make Bayesian inferences, αj0 has no effecton their actions. An ideologically diverse media in this model does not help increasethe informativeness of the news media.

There is some evidence that demand-driven factors are more important in explain-ing news slant than supply-driven factors (Gentzkow and Shapiro 2010). Althoughwe adopt the interpretation that the second part of the editor’s payoff, −φj(yj − ξ j)

2,reflects his “taste” or ideological preference, we may alternatively interpret it as re-flecting the desire to conform to readers’ priors. In this alternative interpretation, ξ j

28 Even though more biased editors hurt the firms’ profits, owners may still hire them because ofcompensating wage differentials, as in Baron (2006).

33

would represent the editor’s belief about his readers’ preferred position, and φj wouldrepresent his desire to write stories that confirm readers’ prior beliefs. Our results donot depend on which interpretation is being adopted.

6. Conclusion

Probably, in the internet era, few industries have been transformed and restructuredby new entrants more profoundly than the news industry. New media such as TheHuffington Post and Politico, have achieved record-breaking growth in readership, read-ers’ attention as well as revenue in the last few years. On the one hand, they grabbedthe market shares of the existing mainstream news media and leave them strugglingfor survival; on the other hand, they expand the base of news readers and offer freshperspectives to news consumers so that people are spending more time on news thanever before. In this paper, we propose a framework to analyze such a new mediaenvironment and study various issues related to media competition.

We deliberately abstract away from some important issues in media economics,such as market segmentation, heterogeneous readers with biased beliefs, and the in-teractions between media and politics. Our paper, however, lays the groundwork forinvestigating them in the changing landscape of media competition. For example,when readers hold biased beliefs and seek confirmation from media, the presentationof news stories is not just a matter of clarity (as in our benchmark model), and it maybe slanted to cater to different audiences. This issue and many others can be studiedin extended versions of our framework.

Our work also makes theoretical contributions to the literature of endogenous in-formation acquisition and sender-receiver games. We extend the former by allowingboth accuracy and clarity of underlying signals to be chosen in response to informa-tion acquisition of readers. We enrich the latter by developing a workable approach tocharacterize sender-receiver games in which a large number of heterogeneous senderswho possess non-identical private information attempt to influence the same set ofdecision makers. This model can be useful in other information markets that featuremonopolistic competition.

34

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Appendix

Proof of Lemma 1. For j = 1, . . . , J, define tj ≡ γjβ2j /(β2

j + φj). Multiply equation (6)by β j and subtract tjαjβ j from both sides of the equation to get

(1− tj)αjβ j = tj(1−∑k

αkβk).

Divide both sides by 1− tj and sum over all j, we obtain:

∑k

αkβk =∑k tk/(1− tk)

1 + ∑k tk/(1− tk).

Thus,

αjβ j =tj/(1− tj)

1 + ∑k tk/(1− tk),

which is equivalent to equation (7). The comparative statics results are obtained bytaking derivatives of (7) with respect to the relevant variables.

Proof of Lemma 2. By the Gaussian updating formula, the posterior expectation of θ

isE[θ|y1i, . . . , yJi] =

11 + ∑k τk

µ + ∑j

τj

1 + ∑k τk

yji − αj0

αj.

Comparing coefficients with the linear action strategy qi = β0 + ∑j β jyji gives theformula (9) for β j. The comparative statics results are obtained by taking derivativesof (9) with respect to the relevant variables.

Proof of Proposition 1. For any j, the equilibrium values of αj and β j must satisfyequations (7) and (9). Comparing these two equations gives

τj =γjβ

2j

(1− γj)β2j + φj

=tj

1− tj,

where we adopt the definition tj ≡ γjβ2j /(β2

j + φj). Use (8) for the relative precisionτj, this equation reduces to:

σ2θ zj

χ2 α2j =

γjtj

γj − tj.

Multiply both sides by β2j and use equation (7), we obtain:

σ2θ zj

χ2

(tj/(1− tj)

1 + ∑k tk/(1− tk)

)2

= β2j

γjtj

γj − tj=

φjγjt2j

(γj − tj)2 ,

39

where the second equality follows because the definition of tj implies β2j = φjtj/(γj −

tj). Define

H ≡ ∑k tk/(1− tk)

1 + ∑k tk/(1− tk).

Then the earlier equation reduces to

t2j

(1− tj)2 (1− H)2 =χ2

σ2θ

φj

γjzj

γ2j t2

j

(γj − tj)2 = (1− hj)2

γ2j t2

j

(γj − tj)2 ,

where the second equality is implied by the definition of hj in equation (10). Obviously,tj = 0 is a solution to the above equation, which would entail αj = β j = 0. Sinceγj < 1, the equation admits a non-zero solution if and only if hj > H. For a non-trivialequilibrium, suppose there is a non-empty subset G of media outlets such that tj > 0if j ∈ G and tj = 0 otherwise. The non-zero solution to the equation is:

tj =γj(hj − H

)(1− H)− γj

(1− hj

) .

Use such value of tj for j ∈ G and use tj = 0 for j /∈ G to substitute into the definitionof H, we can solve for H to obtain H = HG, as is given by equation (11).

For j ∈ G, we can recover the equilibrium value of β j from the non-zero solution tj

using the definition of tj. This yields:

β2j =

(hj − H)φj

(1− γj)(1− hj).

Substitute this value of β j into equation (7) to get:

α2j =

γ2j (hj − H)(1− hj)

(1− γj)φj.

Multiplying these two equations gives equation (12).

Proof of Lemma 3. From equation (11), we can write

HG =1 + ∑j∈G′

γj1−γj

1 + ∑j∈Gγj

1−γj

HG′ +∑j∈G\G′

γj1−γj

hj

1 + ∑j∈Gγj

1−γj

.

40

Therefore,

HG − HG′ =∑j∈G\G′

γj1−γj

(hj − HG′)

1 + ∑j∈Gγj

1−γj

>∑j∈G\G′

γj1−γj

(HG − HG′)

1 + ∑j∈Gγj

1−γj

,

where the inequality follows because hj > HG for all j ∈ G. If HG − HG′ is non-positive, the above inequality is a contradiction. Thus, we must have HG′ < HG.

Proof of Lemma 4. We rewrite the key equation (14) using the definition of hj fromequation (10):

γ2j

φj(1− γj)

(hj − HG

) (1− hj

)2=

√pχ

σ2θ

.

The left-hand-side of this equation attains a maximum at hj = (1+ 2HG)/3. We defineγj to be the value of γj for which equation (14) holds at such hj, i.e.,

427

γ2j

φj(1− γj)(1− HG)

3 =

√pχ

σ2θ

.

Therefore, at γj = γj, D(·, HG) jumps up from 0 to z∗ > 0, where z∗ satisfies hj(z∗) =(1 + 2HG)/3.

When a solution to the key equation (14) exists, the left-hand-side is locally de-creasing in zj at the larger root. Because the left-hand-side increases in γj, decreases inφj, and decreases in HG, the comparative statics results follow from the implicit func-tion theorem. Similarly, because the right-hand-side of equation (14) increases in p, wehave ∂Dj/∂p < 0 at the larger root.

Proof of Lemma 5. Claim 1 in Technical Appendix A establishes that ∂2Dj/∂H∂γj < 0when p is sufficiently small. Therefore the function Πj = SjDj(γj, H)− Cj(γj) is sub-modular in γj and H. This immediately implies that gj(H) decreases in H. Similarly,∂2Dj/∂p∂γj < 0 and ∂2Dj/∂φj∂γj < 0 when p is sufficiently small, which imply thatgj(H) decreases in p and φj.

From equations (11) and (10), we see that HG increases in γj and zj. The aggregatorfunction κG(H) is simply HG evaluated at γj = gj(H) and zj = Dj(gj(H), H). Sincegj(H) decreases in H and Dj(gj(H), H) decreases in H when p satisfies the conditionstated in the lemma, we have κG(H) decreases in H. Similar reasoning shows thatκG(H) decreases in p and φj.

Proof of Proposition 2. Suppose there are n firms in the set G. Define H ∈ (0, 1) such

41

thatn

γ

1− γ(1− H)− H = 0.

Provided that κG(H) is well-defined, we have

κG(H)− H <n γ

1−γ

1 + n γ1−γ

− H = 0.

The first inequality follows because γj ≤ γ and hj < 1; and the second equality followsfrom the definition of H. Let

Π∗j (H, p) = maxγj∈[0,γ]

SjDj(γj, H; p)− Cj(γj),

where we include the dependence on p explicitly into the demand function Dj(·).Then κG(H) is well-defined if and only if Π∗i (H, p) > 0 for all j ∈ G. Since Π∗j (H, p)is continuous and weakly decreases in p, it goes to infinity as p goes to 0, and is equalto 0 when p is sufficiently high. Therefore, there is a pj such that Π∗j (H, p) > 0 forp < pj. Let pG = min{ pj : j ∈ G}. Then, for any p < pG, κG(H) is well-defined withκG(H) < H.

Next, because Dj(γj, H; p) is decreasing in H by Lemma 4, Π∗j (H, p) > 0 impliesΠ∗j (0, p) > 0. Thus, for p < pG, κG(0) is well-defined, and it satisfies κG(0) > 0.

Finally, when ∂Πj/∂γj = 0, we have

∂2Πj

∂γ2j

= Sj∂Dj

∂γj

∂2Dj/∂γ2j

∂Dj/∂γj− C′j(γj)

C′′j (γj)

C′j(γj)

≤ Sj∂Dj

∂γj

(d(γj)−

C′′j (γj)

C′j(γj)

)< 0,

where the first inequality follows from Claim 2 in the Technical Appendix, and thesecond inequality follows because Cj(·) is sufficiently convex. This establishes thatΠj(γj, H) is quasi-concave in γj. Since Πj(γj, H) is also continuous in H, its maximizergj(H) is continuous on [0, H]. Thus, κG(H) is also continuous on [0, H]. It follows thata fixed point exists such that κG(H∗G) = H∗G. Furthermore, if we let pG = min{ pG, pj :j ∈ G}, then for any p < pG, Lemma 5 implies that κG(H) is decreasing in H. Thevalue of the fixed point H∗G is uniquely determined.

For any H, if κG(H) is well-defined, then κG′(H) is well-defined. Moreover, byLemma 3, we have H∗G = κG(H∗G) > κG′(H∗G). Because κG′(0) > 0, there exists H∗G′ <H∗G such that κG′(H∗G′) = H∗G′ .

42

Proof of Proposition 3. Take any equilibrium with no entry and suppose the activemedia group in that equilibrium is G. After firm e enters, G is still an equilibrium(firm e is simply inactive in this equilibrium). But when there is an equilibrium withactive media group G ∪ {e}, Proposition 2 says that H∗G∪{e} > H∗G. Therefore, totalinfluence in the most informative equilibrium must be higher.

Recall that equation (13) implies that, in equilibrium, the attention z∗j given to eachoutlet is proportional to its influence α∗j β∗j . Aggregating this equation over all firmsin the active media group shows that total attention is proportional to total influence.Thus, a higher H∗ means that total attention, i.e., z∗e + ∑j z∗j , is also higher.

For the incumbent firms, γ∗j = gj(H∗). Since gj(·) is decreasing, γ∗j falls. The atten-tion given to firm j is z∗j = Dj(γ

∗j , H∗), where Dj(·) is increasing in the first argument

and decreasing in the second. Thus, z∗j falls.

From the proof of Proposition 1, equilibrium clarity is given by

α2j =

γ2j (hj − H)(1− hj)

(1− γj)φj.

Furthermore, we can rewrite the key equation (14) using the definition of hj to get

γ2j

φj(1− γj)

(hj − H

) (1− hj

)2=

√pχ

σ2θ

.

Combining these two equations, we obtain:

α2j =

11− hj

√pχ

σ2θ

.

We have shown that both z∗j and γ∗j fall in equilibrium, which implies that the equilib-rium value of hj decreases. Therefore, equilibrium α∗j also decreases.

Finally, we can write the key equation (14) as:

hj − H1− γj

=

√p

χ

zj

γj.

New entry lowers h∗j and γ∗j and raises H∗, so the right-hand-side of the above equa-tion decreases. This implies that z∗j /γ∗j decreases. From the proof of Proposition 1,equilibrium action weight is given by

β2j =

(hj − H)φj

(1− γj)(1− hj)=

√p

χ

zj

γj

φj

1− hj,

43

where the second inequality follows from the key equation (14). Since both z∗j /γ∗j andh∗j fall in equilibrium, β∗j also falls.

Proof of Proposition 4. From the proof of Proposition 1, the equilibrium value of α

for an active firm must satisfy:

α2 =γ2(h− HG)(1− h)

(1− γ)φ.

The key equation (14) also requires:

γ2

φ(1− γ)(h− HG)(1− h)2 =

√pχ

σ2θ

.

These two equations imply that

1− h =

√pχ

α2σ2θ

.

Recall that the left-hand-side of the key equation above is increasing then decreasingin h, and that the equilibrium h is the larger root to the key equation. Therefore, in anyequilibrium,

h ≥ arg maxh

(h− HG)(1− h)2 =1 + 2HG

3.

If equilibrium clarity is α and equilibrium total influence is H∗G, we must have

1− 1 + 2H∗G3

≥√

pχ

α2σ2θ

,

which establishes the upper bound stated in the proposition.

Proof of Proposition 5. Let n be the number of firms in an active media group G.From the definition of HG, we have

h− HG =h

1 + n γ1−γ

.

Substitute this into the key equation to obtain:

γ2

φ(1− γ)

h(1− h)2

1 + n γ1−γ

=

√pχ

σ2θ

.

The maximum value of h(1− h)2 is 4/27. So an upper bound on the number of active

44

firms that can be supported in any equilibrium is the largest integer n such that

427

γ2

φ(1− γ)

11 + n γ

1−γ

≥√

pχ

σ2θ

.

It is obvious that such n increases in γ and decreases in φ.

Proof of Proposition 7. For any active media group G, suppose φ′j > φj for some j ∈G. Then κG(H) decreases for every H because (i) it is directly decreasing in φj, holdinggj and Dj constant; (ii) gj(H; φ′j) < gj(H; φj) and κG(H) is increasing in gj; and (iii)Dj(gj(H; φ′j), H; φ′j) < Dj(gj(H; φj), H; φj) and κG(H) is increasing in Dj. Thus, thefixed point H∗G decreases.

When H∗G decreases, for all k 6= j, α∗k , β∗k , γ∗k , and z∗k all increase; the proof is thesame as that for Proposition 3.

Since α∗j β∗j = H∗G −∑k 6=j α∗k β∗k , the equilibrium influence of news outlet j decreases,which means that z∗j also decreases. Moreover, h∗j must fall. Suppose this is not true,i.e., h∗j weakly increases. Then the key equation (14) would imply that γ∗j weakly de-

creases. But then h∗j = 1− (χ/σθ)√

φj/(z∗j γ∗j ) must strictly decrease, a contradiction.

In the proof of Proposition 3, we show that in equilibrium, α2j =√

pχ/(σ2θ (1− hj)).

Since h∗j decreases, α∗j falls.

Proof of Proposition 6. Following the proof of Lemma 1, we can use the best-responseof αj against α−j to solve for the fixed point α:

αj =1

Rβ j

tj/(1− tj)

1 + ∑k tk/(1− tk),

where tj ≡ Rγjβ2j /(β2

j + φj). Moreover, readers assign action weights using Bayes’rule:

β j =1

Rαj

τj

1 + ∑k τk.

We can solve for tj using similar steps as described in the proof of Proposition 1 toobtain:

tj =

(1− 1−hj

1−RH

)Rγj

1− 1−hj1−RH Rγj

,

where

H ≡ 1R

∑jRγj

1−Rγjhj

1 + ∑jRγj

1−Rγj

.

45

The influence of media outlet j is:

αjβ j =γj

1− Rγj

(hj − RH

).

Readers allocate attention by maximizing

V = −σ2θ

(1− 1

R∑j τj

1 + ∑j τj

)−∑

j

pα2

jzj.

Combining the first-order conditions with Bayes’ rule and the formula for influenceαjβ j, we derive the counterpart to the key equation (14) in the benchmark model:

γj(hj − RH)

1− Rγj

1zj

=

√p

χ.

Define Dj(γj, H) as the larger solution to zj in this key equation (and let Dj(γj, H) = 0if it has no solution). The derivative of the left-hand-side of the above with respect toR has the same sign as γjhj − H. In a symmetric equilibrium,

γh− H =−(J − 1)γh

1 + J Rγ1−Rγ

< 0,

(where we have dropped the subscript for media firms). Moreover, the derivative ofthe left-hand-side of the key equation with respect to zj is negative at the larger root.It following from the implicit function theorem that ∂Dj/∂R < 0.

Claim 3 in the Technical Appendix A shows that, if the marginal cost of attentionis low enough, then ∂2Dj/∂R∂γj < 0. This in turn implies that gj(H) decreases in R.

In a symmetric equilibrium, let

κ(H) =1R

J Rg(H)1−Rg(H)

(1− χ

σθ

√φ

D(g(H),H)g(H)

)1 + J Rg(H)

1−Rg(H)

.

One can verify that

∂κ

∂R= −(J − 1)J

g(H)1−Rg(H)

1 + J Rg(H)1−Rg(H)

2(1−− χ

σθ

√φ

D(g(H), H)g(H)

)< 0.

46

Furthermore, we have ∂κ/∂g > 0 and ∂κ/∂D > 0. Therefore,

dκ

dR=

∂κ

∂R+

∂κ

∂g∂g∂R

+∂κ

∂D

(∂D∂g

∂g∂R

+∂D∂R

)< 0.

We conclude that the fixed point of κ(·) falls when R increases. Since H∗ = Jα∗β∗,the influence of each firm also falls. Since attention is proportional to influence inequilibrium, attention to each firm z∗ falls.

47

Technical Appendix(Not intended for publication)

A. Claims

Claim 1. There exists pj such that if p ≤ pj, then ∂Dj/∂γj decreases in p, φj and H.

Proof. Implicit differentiation of the key equation (14) shows that

f 2z DγH = ( fzzDH + fzH) fγ −

[fγz (− fH) + fz fγH

]= γ

34

2z(−1) (1− H)

m[(

12 − 1

1−γ

)m + 1

1−γ

]3m− 2

+1z

γ (1− H)

[5− γ

4(1− γ)m− 1

1− γ

],

where we let m ≡ (1− h)/(1− H). Further manipulation shows that DγH has thesame sign as: (

91−γ

)m2 −

(14−γ1−γ

)m + 4

1−γ

6m− 4.

The above expression is negative for any γj when m is equal to 0. By continuity, it isnegative for any γj when m is small. Observe that the key equation (14) can also bewritten as:

γ2j

φj(1− γj)(1− HG)

3 (1−m)m2 =

√pχ

σ2θ

.

The smaller solution in m (which corresponds to the larger root in zj), is decreasing inp, and goes to 0 as p goes to 0. Thus, for p sufficiently small, m is small, which impliesthat ∂2Dj/∂H∂γj < 0.

Similarly, ∂2Dj/∂p∂γj has the same sign as:

−3(γj + 1

)m2 +

(γj + 10

)m− 4;

and ∂2Dj/∂φj∂γj has the same sign as:

−3(γj + 1)m2 + 4(γj + 1)m− 2γj.

When p is small, m is small, and both of the above expressions are negative.

Claim 2. For any j and any H, there exists d(γ) such that

∂2Dj(γ, H)/∂γ2j

∂Dj(γ, H)/∂γj≤ d(γ) < ∞.

48

Proof. Let

f (z, γ) ≡ γ(h(z)− H)− z(1− γ)

√p

χ.

The demand function is given by the larger root in z to the equation f (z, γ) = 0.Implicit differentiation gives:

fzDγ + fγ = 0,

fzzD2γ + 2 fzγDγ + fzDγγ + fγγ = 0,

where we write Dγ and Dγγ for the first and second derivatives of Dj with respect toγj. Thus,

Dγγ

Dγ=

fzz fγ

f 2z− 2 fzγ

fz+

fγγ

fγ.

Let m ≡ (1− h)/(1− H). The restriction that the demand function is the largerroot to f (z, γ) = 0 is equivalent to h ≥ (1 + 2H)/3 (see the proof of Lemma 4), whichis equivalent to requiring m ≤ 2/3. Writing the derivatives of f in terms of m, weobtain:

Dγγ

Dγ=

(−3γ4z2 m(1− H)

) ((12 m + 1

1−γ (1−m))(1− H)

)(−γ2z (2− 3m)(1− H)

)2

−2(

1z

(14 m + γ

1−γ (1−m))(1− H)

)−γ2z (2− 3m)(1− H)

+1

4γ m(1− H)(12 m + 1

1−γ (1−m))(1− H)

=

−3γ m

(12 m + 1

1−γ (1−m))

(2− 3m)2 +

4γ

(14 m + γ

1−γ (1−m))

2− 3m+

14γ m

12 m + 1

1−γ (1−m)

<(8− 15m)

(12 m + 1

1−γ (1−m))

γ(2− 3m)2 +1

4γ m12 m + 1

1−γ (1−m).

Both the first term and the second term in the final expression are bounded above form ∈ [0, 2/3]. So if we let

d(γ) = maxm∈[0,2/3]

−3γ m

(12 m + 1

1−γ (1−m))

(2− 3m)2 +

4γ

(14 m + γ

1−γ (1−m))

2− 3m+

14γ m

12 m + 1

1−γ (1−m),

then the claim is established

49

Claim 3. In the model with correlated information production, if the price of attentionis sufficiently low, then ∂Dj/∂γj decreases in R.

Proof. From the proof of Proposition 6, equilibrium attention Dj(·) is the solution in zj

to the following key equation:

γj(hj(zj)− RH)

1− Rγj

1zj

=

√p

χ.

Implicit differentiation of this equation shows that ∂2Dj/∂R∂γj has the same sign as:[−5

4(1− hj) + (hj − RH)12(1− hj)− (hj − RH)

+γj(hj − RH)

H − γjhj

] [12+

hj − RH(1− Rγj)(1− hj)

]+

34

.

When p is small enough, hj goes to 1. The first bracketed term goes to −1 + 1/(J − 1),which is negative. The second bracketed term approaches +∞. Therefore, ∂2Dj/∂R∂γj

is negative.

B. Discussion on marginal cost of attention

In the benchmark model, we assume that the marginal cost of giving attention tomedia outlet j consists of two components: p, the opportunity cost of paying attentionto media; and 1/α2

j , obscurity or the difficulties to process news stories from mediaoutlet j. In the main text, we claim that allowing the marginal cost to vary in clarity αj

only simplifies our analysis and does not affect our results qualitatively. We elaboratethis point in this section.

Consider an alternative model with constant marginal cost, p. In this case, the char-acterization of the sender-receiver game is not affected and Proposition 1 holds. Butin this specification, the first order condition for the consumer’s attention allocationbecomes:

τj

1 + ∑k τk= zj

√p

χαj.

Combining the equation above with equation (12), we derive the counterpart of thekey equation (14):

γj(hj(zj)− HG)

1− γj= zj

√p

χαj.

Similar to the benchmark case, the larger solution to this equation implicitly deter-mines the demand function of attention for media outlet j. The left-hand-side is themedia outlet j’s influence which is a function of zj. That is exactly the same as thebenchmark case. The right-hand-side gives how attention to media outlet j is relatedto its influence. The proof of Proposition 1 shows that αj increases in zj. Therefore,

50

αβ

z∗ z

αβ(z)

z(αβ)b

(a) Marginal cost of attention, p/α2j

b

αβ

z∗ z

z(αβ)αβ(z)

(b) Marginal cost of attention, p

Figure 8. The specifications of marginal cost of attention. When the marginal cost varies in clarity,attention given to media outlet j is in proposition to its influence, illustrated by the red dashed line inFigure 8(a). When the marginal cost is constant, attention increases in the influence of media outlet j,illustrated by the red dashed line in Figure 8(b). Both cases lead to similar qualitative results.

attention given to media outlet j increases in its influence. The difference from thebenchmark case is that the relation is not linear anymore. We illustrate such a differ-ence in Figure 8. The two cases are rather similar qualitatively. But it is more intuitiveand technically convenient to allow the marginal cost of attention to vary in clarityand to work with the linear case.

51