Competition for Attention in the News Media Market

Transcription

1 Competition for Attention in the News Media Market HENG CHEN University of Hong Kong WING SUEN University of Hong Kong November 5, 2016 Abstract. We provide a framework for analyzing the new media environment, where a large number of heterogeneous firms compete by investing in the accuracy of news gathering, biased editors compete by manipulating the presentation of news stories, and readers allocate their attention among multiple outlets. New entry reduces both the accuracy of news gathered and the clarity of news reported by incumbents, but the overall influence of the media industry unambiguously increases. However, the number of media firms that can be supported in equilibrium is bounded. Media competition combined with enhanced monetization of attention may explain the proliferation of soft news. Keywords. monopolistic competition, media bias, media quality, senderreceiver game, attention allocation JEL Classification. D83, D84, L15, L82 We thank Jimmy Chan, Alessandro Lizzeri, Andrea Prat, Antonio Russo, and seminar participants at Academia Sinica, University of Copenhagen, Australasian Economic Theory Workshop (2016), and Media Economics Workshop (2016) for useful comments and discussions. This research project is partly funded by the General Research Fund of the Research Grants Council of Hong Kong (Project No ).

2 1. Introduction The news media industry has experienced a profound transformation. Gone are the days when a consumer got his news from just one or two local newspapers and a few radio and television stations. The modern news consumer faces a menu of options much 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 high quality 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 set of news outlets, how do consumers allocate their scarce resource their attention among these outlets? And how do firms compete for consumers attention in this environment? The goals of this paper are twofold. We first provide a framework to characterize the transforming news industry, incorporating its salient new features detailed immediately 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 particular emphasis to a set of topics related to media competition, such as its effects on media quality 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 and unleashed 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 to almost 300 in See Figure 1. These newly available information sources have gained substantial popularity. According to the Media Consumption Survey conducted by Pew Research Center, 26 online news sites were named by at least one percent of the respondents in the United States as their source for accessing news in 2010; but the comparable figure was only 17 sites in A similar pattern exists for some 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: // It keeps track of online news sites that satisfy the following four criteria: the outlet has to be primarily devoted to original reporting and content production; it should have full-time employees; it is independent and not the web arm of a legacy media entity; and it attracts 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 Media Consumption Survey, available from the Pew Research Center website, 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

3 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 sell their eyeballs to advertisers for revenue. Such an advertising-supported free content business model is not really new; what is new is the expansion of this business model to the whole news media industry. Even the most traditional print media industry has been shaken: in the past two decades, free newspapers emerged to become a solitary beacon of hope in a declining newspaper industry (Anderson 2009). This business model is now so prevalent that media measurement technology has to evolve, as a response, from audience-size based measurement to attention based measurement. 4 In the media market today, news consumers can often access their news stories at very low or no cost. 5 Given that media firms do not charge readers directly, readers attention paid to media has become the new currency of business, a term coined by Davenport and Beck (2013). When news can be provided for free, the real constraint facing consumers is the limited attention available for processing the information. Therefore, the primary goal of media firms is no longer to maximize readership and subscription revenue, but to grab valuable attention from readers. In other words, they compete on the intensive margin (i.e., attention) rather than on the extensive margin (i.e., size of audience). Attention allocation to multiple news providers. In response to an enriched media environment, 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 media firms also need it to determine the market value of their products. The technology of measurement has transformed from measuring the size of viewership (e.g., Nielson ratings) and readership (e.g., ABC audit reports) to measuring the detailed aspects of information consumption of readers, especially the amount 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 for news, except for a local print newspaper. Data from this wave of survey can be downloaded from 2

4 among multiple news sources to obtain information. They not only access multiple types of media (e.g., print media, radio and television, and the internet), but also access multiple outlets within each type. The Pew Personal News Cycle Survey in 2014 finds that an average American adult uses four types of media every week for getting news, and the Pew Online News Survey in 2010 finds that 68 percent of respondents access online news from more than two websites. 6 Consumers multi-homing decisions are particularly important for media competition in the era of the internet (Peitz and Reisinger 2015). Concerns over news quality. In a market with a flood of new (and often small) media firms competing for attention with free content, concerns are frequently raised about the quality of their news products. It seems to many that there exists a trade-off between quantity and quality in the media industry: the rise of commercially run digital media may threaten and deteriorate journalism standard. For example, it is argued that the advertising-supported business model may level the playing field between established news organizations and new entrants, which may drive out existing professionals at a cost to quality (Anderson 2009, p. 195). Hollifield and Becker (2009) commented that, unlike journalists and editors in established media firms, some of those employed in small news startups or non-institutional content providers may be less well-trained and may have fewer resources to engage in in-depth reporting or even to check their facts. 7 Concerns over news quality are thus no longer confined to slant and biases in the presentation of news, but to the scope and accuracy of news gathering as well. Despite these developments in the news industry, the media economics literature has not quite caught up. First, there is little effort taken to capture the feature of monopolistic competition in media market. Much of the literature focuses on the cases with just one or two news providers (e.g., Anderson and McLaren 2012; and Strömberg 2004). In models with a large number of news outlets, they are typically assumed to possess identical information (e.g., Gentzkow and Shapiro 2006; and Chan and Suen 2008), 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 org/publications/reports/survey-research/download-personal-news-cycle-study/ and http: // respectively. Gentzkow and Shapiro (2011) also demonstrate that a significant share of consumers acquire news from multiple outlets either online or offline. 7 Keen (2007) illustrates this point with an anecdote from the aftermath of Hurricane Katrina in Citizen journalists provided many inaccurate reports of the damage and photos of the devastation, which facilitated the spread of rumors on inflated body counts and erroneous reports of crimes conducted. The established news media have to compete with them for people s attention and debunk the errors. 8 One of the exceptions is the recent work by Anderson and Peitz (2016). In that model, they characterize media competition as an aggregative game in which advertising messages from different media outlets crowd out one another as they compete for readers attention. Our focus instead is on the me- 3

5 We need a framework that explicitly characterizes how media firms strategically interact with many competitors producing similar but not identical news. Second, most contributions to media economics use discrete choices models to study competition at the extensive margin with single-homing consumers: each consumer chooses to get news from only one of the news outlets, and news outlets compete 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 Strömberg 2013 for a review), although Anderson et al. (2012) show that, in a context of competing advertisers, the assumption about whether viewers single-home or multi-home can lead to opposite results. With media content often available for free and attention being the new currency of business, competition at the intensive margin has become the primary driver in the news industry. We need a framework to characterize the new paradigm and generate new insights about media competition for attention. Third, the literature typically treats news consumers as Bayesian learners who passively process all the available information. When the supply of news has become overwhelming as is the situation today, it is natural to model how consumers selectively choose news providers to get news and allocate their limited attention among them. But an often neglected aspect is that the attention allocation decision of news readers in turn has implications for firms investment and editorial decisions. These decisions are affected by each other and are determined jointly. Our approach therefore also differs from existing works on endogenous information acquisition, where the information structure of the underlying signals is taken as exogenous (e.g., Hellwig and Veldkamp 2009; Myatt and Wallace 2012; and Chen, Luo, and Pei 2015). Finally, the media economics literature has focused almost exclusively on media bias 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, and Stone 2016), but has given much less attention to the depth or accuracy of information collected in the news gathering stage. These two aspects of news quality are distinct but closely related: low-cost news contents are often associated with high bias in the news products (Hollifield and Becker 2009). In a reputation model (Gentzkow and Shapiro 2006), for example, editors with more accurate information are less likely to slant the news because they are more concerned that their misrepresentation will be subsequently contradicted. Less well studied is the other side of the relationship: news outlets that often distort their information have less incentive to improve the accuracy of 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 their limited attention. 4

6 attention shapes media firms investment and editorial decisions. 9 When attention grabbing is driving the news market, such a model can shed light on whether media competition 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 four key features described earlier. It has three sets of actors. Owners of news firms are profit oriented. They invest in an infrastructure to conduct news gathering and investigative 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 also have their own personal biases. Based on the facts obtained from news gathering, they write news stories that reflect a tradeoff between these two concerns. There are a large number of such firms in the news market, each producing a differentiated product (because the facts obtained are not identical and because different editors adopt different reporting strategies). News readers need to take an action about an uncertain state after consulting multiple news outlets. They decide how much attention to give to each outlet, and their attention in turn generates revenue for the news firms. The two aspects of news quality (accuracy of the facts and biases in reporting), readers attention allocation, and the influence of the media on readers action taken are determined jointly. Our model features both strategic complementarity between news readers and news firms as well as strategic substitution among firms. Strategic complementarity arises because the more attention readers give to a news outlet, the more incentive this outlet has to improve its accuracy and reduce its bias; and the higher quality are news reports, the more willingly are readers to pay attention to them. This feature of strategic complementarity is consistent with empirical evidence from online media outlets (Sun and Zhu 2013). 10 Strategic substitution among firms arises because of two key mechanisms. The first one is a free riding effect: if other news editors are providing less biased reporting to inform the public, an individual editor tends to slant his news story more to indulge in his own personal biases. The second one is attention diversion induced by readers attention allocation: an improvement in the quality of news from other outlets shifts attention away from an individual firm, which reduces the incentive for its owner to invest in news accuracy. This feature of strategic substitution is broadly consistent with evidence provided by Gentzkow (2007). In Section 3, we characterize the sender-receiver game between editors and readers, which determines 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 the first 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 the news 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 their products when attention of the readers exogenously increases. 5

7 the monopolistic competition among owners who grab attention from readers, which determines 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 the model can be used and extended to shed light on relevant issues in the new media environment. Does increased media competition improve or reduce the quality of news reporting and help the truth prevail? Our model predicts that stronger competition does hurt the quality and influence of the incumbent firms, but the informativeness of the news industry as a whole necessarily improves upon a new entry. Section 5.1 details the analysis of this issue and provides corroborating facts for our results. We further show that those facts cannot be reconciled in a model with news firms competing for audience but not attention, therefore showcasing the necessity of modeling attention allocation. Given that new entry is beneficial for the news consumers, is it true that the trend of escalating media competition will continue forever? And may readers eventually become 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 news quality is the key to understanding this: those firms that fail to grab enough attention have to cease operation and only a finite, albeit large, number of news producers can survive in equilibrium. Media competition is often blamed by media scholars for the rise of soft news and decline of hard news, because increased market pressure causes news firms to produce too much soft news with high audience appeal and serious hard news is crowded out as a result. In Section 5.3, we show how enhanced monetization of attention (a byproduct of the progress made in media measurement technologies) may contribute to such a trend. Other related work. Our model of attention allocation builds on Sims (2003), in which the assimilation of available information is plagued by receiver noise. Hellwig, Kohls, and Veldkamp (2012) review the subsequent research modeling inattention with alternative approaches. We borrow from Myatt and Wallace (2012), who study a setting in which the receiver noise reduction technology is continuous, i.e., the variance in the receiver noise decreases as readers pay more costly attention to the signal. Our work also enriches the literature on sender-receiver games by introducing a number of distinctive features that have not been thoroughly researched. First, much of this literature focus on strategic information revelation with two competing senders who intend to influence the receiver s decision (e.g., Ambrus and Takahashi 2008; Battaglini 2002; Bhattacharya and Mukherjee 2013; Krishna and Morgan 2001; but see Gentzkow and Kamenica 2015 for a multi-sender model of persuasion). Senders are 6

8 usually assumed to be fully informed about the true state (e.g., Ambrus and Takahashi 2008; and Chan and Suen 2009). In our model, a large number of senders compete with one another to both influence readers actions and attract valuable attention from readers. Our assumption that senders acquire noisy and non-identical signals about the state is both realistic and crucial for modeling media quality. 11 Second, in our model, both senders and receivers make decisions on information acquisition, which turns out to be endogenously complementary. This feature is different from that in Dewatripont and Tirole (2005), in which one sender and one receiver can both exert effort to improve the amount of information understood by the receiver, but the complementarity 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 acquire information from the media about an uncertain state θ and take an action q i. In the news market, there is a large but finite number of media firms indexed by j {1,..., J}. Each media firm j consists of two players: an owner who runs the business for profit, and an editor who offers a news story about the uncertain state to influence readers. All players share a common normal prior about the state, namely, θ N(µ, σθ 2 ). We choose to separate the two roles within a media firm so as to capture the norm of editorial independence in modern journalism, which prescribes that owners do not get too involved in the day-to-day operation of the editorial office. It also allows us to endogenize both accuracy (chosen by owners) and clarity (chosen by editors) two distinct aspects of news quality. Each owner j decides the resources to make investigations about the state. This includes decisions such as funds made available to journalists to do research, and the size and quality of the editorial staff. Once the basic infrastructure of the news office is determined, the owner stays away from editorial decisions concerning the selection or presentation of news stories. Specifically, the media firm acquires a noisy signal about the true state. Let x j = θ + ɛ j represent such a signal, where ɛ j is normally distributed with mean 0 and variance σɛj 2 (and is independent of the state and independent across different media firms). 12 Let γ j σθ 2/(σ2 θ + σ2 ɛj ) represent the accuracy of the news outlet j. We assume that perfect accuracy is not feasible: γ j [0, γ] for some γ < 1. The cost of investigation C j (γ j ) is increasing and convex in γ j. The owners choose the accuracy of their news signals simultaneously. These decisions, once made, are known to 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 have noisy and non-identical signals. 12 It is realistic to expect that the noise term may be correlated across media firms conditional on the state. We consider such a scenario in Section

9 outlets depends on their long term investments, which are generally well observed to players in the media market. 13 The strategy of owners is characterized by the vector γ = (γ 1,..., γ J ). News outlet j receives revenue from advertisements, which is assumed for simplicity to be proportional to the attention received and is denoted by S j z j, where z j is the amount of attention from readers given to that news outlet and S j > 0 describes how attention received translates into revenue. The objective of media owner j is to choose media quality γ j to maximize profits, Π j = S j z j C j (γ j ). The editor of each news outlet j takes γ as given and writes a news story y j about θ to influence the readers actions. On the one hand, the editor prefers that the aggregate action taken by readers, Q = 1 0 q i di, is closer to the true θ. This represents the incentive to inform the public. On the other hand, he also prefers that the message delivered from his story is not far away from his ideal position ξ j, which can be interpreted as the established editorial stand of this news outlet or his personal view on 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 x j, whose precision depends on the investment level chosen by the owner. He chooses y i to maximize his payoff, ] U j = E [(Q θ) 2 + φ j (y j ξ j ) 2 x j, (1) where φ j is the weight assigned to the second concern. A higher φ j means that the editor cares more about his own personal views and less about the alignment between aggregate action and the true state. We say that editor j is more biased if φ j is higher. In general, the reporting strategy is a function y j (x j ) of the signal. We focus on linear equilibria in which the reporting strategy takes a linear form: y j = α j x j + α j0. (2) A high α j means that the story closely reflects the underlying signal obtained from the news investigation, while a low α j represents a cookie-cutter style of reporting that produces standardized stories which fail to reflect all the nuances of the underlying signal. We use α j to denote the clarity of news outlet j. The strategy of news editors is summarized by the vectors α = (α 1,..., α J ) and α 0 = (α 10,..., α J0 ). 13 The assumption is made to abstract away the reputation concern, which has been thoroughly studied in the media literature (e.g., Gentzkow and Shapiro 2006). 8

10 Each news consumer chooses to acquire information from the media about θ, including which news reports they want to pay attention to and how much attention they pay to each report. If consumer i picks up the news report y j, he reads the news content with a reader noise η ji attached to the actual report. That is, he observes ŷ ji = y j + η ji, (3) where η ji N(0, σ 2 ηji ) is independent of y j and independent across readers. The reader noise is specified to capture the idea that an individual has limited capacity to process all the information contained in a story; he reads the content of a news story with actual or interpretive errors. Thus the information set available to consumer i is an array of perceived reports, ( ŷ 1i,..., ŷ Ji ). Given his information set, reader i chooses action q i to maximize E[(q i θ) 2 ]. The optimal action strategy q i (ŷ 1i,..., ŷ Ji ) is in general a function of the J perceived news reports. In a linear equilibrium with Gaussian signals, since q i = E[θ ŷ 1i,..., ŷ Ji ], the action strategy is also linear: q i = β 0i + J β ji ŷ ji. (4) j=1 Because readers are ex ante identical, their strategies are the same (but their actions may be different since each reader perceives a different report based on the same story). From here on, for j = 0, 1,..., J, we write β ji = β j for all reader i. The common action strategy of readers is represented by the vector β = (β 0, β 1,..., β J ). We refer to β 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 news story with greater precision by paying more attention to it. Let z ji represent the amount of attention devoted to news outlet j. The noise reduction technology is specified as: σ 2 ηji = χ2 z ji, where χ is a constant capturing the technological aspect of the information assimilation process. This noise reduction technology is commonly adopted in the attention allocation literature; it specifies that the precision of the noise is linearly related to the attention devoted to the information source (Myatt and Wallace 2012; Mondria and Quintana-Domeque 2013) 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 informationprocessing 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 for its tractability. 9

11 Since y j = α j x j + α j0 and readers care about the underlying signal x j rather than the news story y j as such, the signal-to-noise ratio of the perceived news report is α 2 j σ2 θ /σ2 ηji. News stories with high clarity (i.e., high α j) have higher signal-to-noise ratios. We assume that these stories are easier to process, in the sense that the marginal cost of attention devoted to such stories is lower. In particular, we let p j = p/α 2 j represent the marginal cost of giving attention to media outlet j. 15 The net payoff to reader i is: V i = E[(q i θ) 2 ŷ 1i,..., ŷ Ji ] J j=1 p z ji. Because readers are homogenous ex ante, they make the same information choice. In what follows, we suppress the subscript i and write z j for z ji unless it causes confusion. The attention allocation of readers is represented by the vector z = (z 1,..., z J ). 3. Media Influence and Attention Allocation 3.1. Media influence In this section, we solve the sender-receiver game, taking as given the accuracy profile γ chosen by media owners and attention allocation z chosen by readers. The solution to this game allows us to characterize the influence of individual news outlets, as well as to derive an aggregate variable that summarizes the influence of the media industry as a whole. Each individual editor j chooses a story y j to maximize his payoff U j described in equation (1), given the strategy of readers and of other editors. In a linear equilibrium where other editors follow the reporting strategy (2) and readers follow the identical action strategy (4), the aggregate action is α 2 j Q = β 0 + β j y j + β k (α k x k + α k0 ). k =j Substitute this expression into editor j s objective function (1), the first-order condition for y j is E [β j ( ) ] ( ) β 0 + β j y j + β k (α k x k + α k0 ) θ + φ j yj ξ j xj = 0. k =j For k = j, E[x k x j ] = E[θ x j ] = γ j x j + (1 γ j )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. In Technical Appendix B, we explain how it improves the tractability of our analysis, and why our results are robust when the marginal cost does not depend on α j. 10

12 order condition gives y j = γ jβ j β 2 j + φ j ( ) 1 α k β k x j + constant. (5) k =j Thus, when news readers and other editors adopt linear strategies, the best-response reporting strategy for editor j indeed takes the linear form (2), with α j = γ jβ j β 2 j + φ j ( ) 1 α k β k, (6) k =j and α j0 equal to the constant in equation (5). In what follows, α j0 plays no role because its equilibrium value is commonly known rational readers can infer such systematic biases in reporting and are unaffected by them. On the other hand, the slope α j is key because it is equal to Cov[y j, x j ]. A news outlet with high α j has high clarity as its news story y j closely tracks the underlying news signal x j (which contains information about the true state). An important feature of this multi-sender game is that clarity of news reports exhibits strategic substitution: equation (6) shows that a higher α k (k = j) lowers α j. This feature arises because all editors prefer that the public be informed. If other editors are producing clearer news stories, then an individual editor can free ride on their efforts and write news stories that indulge more in his own biases instead. Fix readers action strategy β, their attention allocation z, and owners accuracy profile γ, equation (6) holds for every j = 1,..., J. The solution to this equation system gives α = a(β; z, γ). Lemma 1. The clarity α j = a j (β; z, γ) of news outlet j is given by: α j = 1 β j γ j β 2 j (1 γ j )β 2 j +φ j 1 + k γ k β 2 k (1 γ k )β 2 k +φ k. (7) It increases in news accuracy γ j and decreases in editor bias φ j. It decreases in the accuracy and increases in the bias of other news outlets. It is worth noting that clarity α j chosen by editor j increases with accuracy γ j chosen by owner j. When the underlying news signal x j is more informative, the trade-off between informing the public about the signal versus indulging in the editor s personal views tilts in favor of the former. Lemma 1 also says that α j decreases in the editor s bias φ j, which is intuitive. Finally, because of the strategic substitution effect, 11

13 the response with respect to other news outlets accuracy and bias are opposite to that with respect to own accuracy and bias. Turning to readers action strategy, the quadratic loss function implies that q i = E[θ ŷ 1i,..., ŷ Ji ]. To derive this conditional expectation, we use editors reporting strategy (2) and the communication technology (3) to write: ) ŷ ji α j0 = θ + (ɛ α j + 1αj η ji. j Let τ j represent the precision of the combined noise term above (relative to the precision of the prior belief). We have τ j = 1 1 γ j γ j + χ2 z j α 2 j σ2 θ. (8) Fix editors reporting strategy α, readers attention allocation z, and owners accuracy profile γ, the optimal action rule β = b(α; z, γ) can be obtained from the linear Bayesian updating formula. Lemma 2. The action weight β j = b j (α; z, γ) of news outlet j s report is given by: β j = 1 α j τ j 1 + k τ k. (9) It increases in the accuracy γ j of news outlet j and in the attention z j given it. It decreases in the accuracy of and the attention given to other news outlets. Readers increase their reliance on the news report j when they pay more attention to it and when the underlying news source is more accurate. For fixed α, editor j s bias φ j does not matter for readers action weight β j, because it does not directly affect the signal-to-noise ratio of the news report. Similarly, readers decrease their reliance on report j when they pay more attention to other reports and when the other news sources are more accurate. Given z and γ, the equilibrium (ˆα, ˆβ) of the sender-receiver game can be obtained by solving (7) and (9) jointly, with 2J equations and 2J unknowns. To state our formal result, define for j = 1,..., J the quantity: h j 1 χ σ θ φj z j γ j ; (10) 12

14 and for any subset of media outlets G {1,..., J}, let H G j G γ j 1 γ j h j 1 + j G γ j 1 γ j (11) Proposition 1. Given attention allocation z and accuracy profile γ, there exists an equilibrium (ˆα, ˆβ) of the sender-receiver game with a set of media outlets G {1,..., J} such that: (a) if j G, then and (b) if j / G, then ˆα j ˆβ j = 0. ˆα j ˆβ j = γ j 1 γ j (h j H G ) > 0; (12) In the proof of Proposition 1, we provide separate formulas for ˆα j = â j (z, γ) and ˆβ j = ˆb j (z, γ). Equation (12) gives the product of the two because, with a linear action rule and a linear reporting strategy, ˆα j ˆβ j = Cov[Q, x j ]/σ 2 θ. We use ˆα j ˆβ j to represent the influence of media outlet j: it measures how the aggregate action Q varies with the outlet s news sources. The influence of news outlet j depends on the h j relative to H G. From equation (10), we see that h j increases in accuracy and attention but decreases in bias. The variable H G is the weighted average of h j, adjusted by a factor less than The influence of a news outlet depends on the characteristics of other news outlets only through this aggregate variable H G. If we sum equation (12) over j, and drop the dependence on G to avoid clutter, we can show that H = j ˆα j ˆβ j = Cov[Q, θ] σθ 2. In other words, H is the total influence of the news industry as a whole. The higher is H, the more effective the media are in informing the public to choose an aggregate action Q that closely tracks the true state θ. Furthermore, using Lemma 2, we have H = j τ j 1 + j τ j. 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 h j is γ j /(1 γ j ) = σθ 2/σ2 ɛj, which reflects the precision of signal x j (relative to the ( ) prior). The adjustment factor is j σ 2 ɛj / σ 2 θ + j σ 2 ɛj, which reflects the combined precision of all news sources as a fraction of total precision (news sources plus prior). 13

15 this group have positive influence. Given an equilibrium with active media group G, Proposition 1 determines a unique strategy profile (ˆα, ˆβ) corresponding to that equilibrium. 17 However, there exist multiple equilibria in this sender-receiver game, with a different active media group G in each equilibrium. Some of these equilibria involve coordination failure: If news report j does not contain any information content, readers do not act on it; and if readers action does not rely on report j, its editor has no incentive to present any facts obtained. We can show that if there is an equilibrium with active media group G, it remains an equilibrium if we delete an arbitrary subset of media outlets from that group, simply because of this coordination failure. 18 Of course, the influence of the remaining outlets in the active media group will be different after some firms have been deleted from the group. Lemma 3. Suppose there is an equilibrium of the sender-receiver game with active media group G. For any G G, there is an equilibrium with active media group G, with H G < H G Attention allocation In this section, we study the attention allocation decision of readers, taking as given the accuracy γ chosen by owners and clarity α chosen by editors. Because q i is chosen to be equal to the posterior expectation of θ, the expected value of the quadratic loss function (q i θ) 2 is simply the posterior variance of θ. Since the posterior precision of θ is equal to the prior precision plus the precisions from all the signals about θ, readers objective can be written as V = where τ j is given by equation (8). σ2 θ 1 + j τ j j p z j, To obtain the equilibrium reporting strategy and action strategy with endogenous attention allocation, we derive the first-order conditions for z j : τ j 1 p 1 + k τ k z j χ α 2 j = 0. (13) By Lemma 2, τ j /(1 + k τ k ) is simply the influence α j β j of news outlet j. In other 17 If (ˆα, ˆβ) is an equilibrium profile corresponding to G, it remains an equilibrium profile when we replace both ˆα j and ˆβ j by their negative values. In general, these alternative profiles are payoff equivalent. 18 A babbling equilibrium (one in which G is the empty set) is an extreme manifestation of this coordination failure. This feature of coordination failure will be extended and generalized in the monopolistic competition problem. See our discussion regarding Proposition 2. 14

16 words, equation (13) shows that the attention given to a news outlet is proportional to its 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 α j β j, and writing h j (z j ) to emphasize the dependence of h j on z j according to equation (10), we can express the first-order conditions (13) and the equilibrium conditions for media influence (12) solely in terms of z j in the following key equation: γ j (h j (z j ) H G ) 1 γ j 1 z j = p χ. (14) Equation (14) holds for each media outlet j that is active in equilibrium (i.e., with z j > 0 and α j β j > 0). For any accuracy profile γ, the solution to the equation system (14) (together with equation (11) that defines H G ) gives the equilibrium attention allocation vector z. Note that the attention z j given to news outlet j depends on the characteristics of other outlets only through the aggregate variable H G. We can therefore express the solution to equation (14) as z j = D j (γ j, H G (γ)). 4. Monopolistic Competition of News Firms When the owner of a news firm tries to attract attention by investing in accuracy to raise h j, total influence H G will also rise because H G is an adjusted weighted average of h j. However, the effect of a change in h j on H G is of order 1/ G. When the number of news firms in the active media group G is large, this effect is small. The proliferation of news firms in the modern news market means that a change in each individual firm only has a tiny impact on the industry. It is therefore realistic to assume that each media firm takes the overall media environment as given and ignores the impact of its own action on the news industry as a whole. Such an assumption is commonly adopted in monopolistic competition models of product markets, in which a producer of differentiated goods takes the aggregate price as given and chooses the price of its own variety, while ignoring the impact of its own price on the price level. Similarly, in our model, a large number of news firms are producing differentiated products (news stories that provide conditionally independent information about the state) and the total influence H G serves as an aggregate variable (akin to the aggregate price level in product markets) that summarizes the overall media environment. In the following, we first characterize how total influence at the industry level and investment at the individual firm level affect the amount of attention that each firm receives. We then establish that a monopolistic competitive equilibrium exists, in which each firm optimizes by taking total influence as given and the aggregation of their optimal choices is consistent with the conjectured aggregate. 15

17 p χ γ j (h j (z j ) H G ) 1 γ j 1 z j D j (γ j, H G ) z j 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 z j, after taking into account the fact that α and β are endogenously determined in the senderreceiver game. We illustrate this point with Figure 2. The left-hand-side of the equation is increasing then decreasing in z j. For fixed α, we have 2 V/ z 2 j < 0. Diminishing returns to attention, reflected in the term 1/z j, accounts for the decreasing part of the graph. However, readers also put more action weight β j on news outlet j as they pay more attention to it. In the sender-receiver game, a higher action weight β j induces editor j to improve clarity α j in equilibrium. But as clarity increases, the marginal benefit from paying attention also increases (i.e., 2 V/ α j z j > 0). This effect is reflected in the term h j (z j ), which increases in z j, and it accounts for the increasing part of the graph in Figure 2. From Figure 2, it is clear that the key equation (14) either admits two solutions or no solution. When there are two solutions, we focus on the larger one because it is a locally stable root and gives intuitive comparative statics results. Since the lefthand-side of (14) is increasing in γ j, there exists a critical γ j (which depends on H G and other parameters) such that a solution to the equation does not exist if γ j is below this value. We therefore define the demand function, z j = D j (γ j, H G ), to be readers attention to news outlet j, given its accuracy γ j and total media influence H G : { max z j : γ } j(h j (z j ) H G ) 1 p 1 γ D j (γ j, H G ) = j zj = χ if γ j γ j ; 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 different goods as functions of all the prices. In our model, consumers attention allocation problem (and the corresponding sender-receiver game) gives rise to different amounts 16

18 z j D(γ, H) D(γ, H ) γ(h) γ(h ) γ Figure 3. The demand curve D j (γ j, H) is discontinuous at γ j = γ j (H). An increase in total media informativeness (from H to H ) shifts down the demand curve: readers pay less attention to each news outlet 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 H G. It inherits all the intuitive comparative statics from the equilibrium of the senderreceiver game and the attention allocation decision of readers. Lemma 4. The demand function D j (γ j, H G ) is discontinuous at γ j = γ j. When attention to news outlet j is positive, it increases in the accuracy of its news sources ( D j / γ j > 0); it decreases in the bias of its editor ( D j / φ j < 0); it decreases in the marginal cost of attention ( D j / p < 0); and it decreases when total influence of the media industry is higher ( D j / H G < 0). The key result is that attention to news outlet j falls when the total influence H G of the 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 from better substitutes when readers allocate their attention. Second is free riding: a more informative 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 that attracts less attention. In this model, the strategic substitutability among media firms is endogenous, and this result is broadly consistent with empirical findings about media substitutability. 19 In this model, firms that intend to grab more attention and reap more advertising revenues achieve this by offering higher-quality content, because D j / γ j > 0. This 19 For example, Gentzkow (2007) finds that online and print versions of news sources are significant substitutes 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 with less attention to television. 17

19 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 follows from the fact that the left-hand-side of equation (14) is hump-shaped. This property is important for determining the number of news outlets that can be active in the news market. We will elaborate on this point in Section 5.2. Given the properties of the demand function D j (γ j, H G ), the equilibrium levels of investment in this market are defined as follows. Definition 1. A monopolistic competitive equilibrium is described by an active media group G {1,..., J} and a profile {γ, HG } such that: 1. (a) For each j G, γ j = g j (HG ) > 0, where and (b) for each j / G, γ j = 0. g j (H) = arg max γ j S j D j (γ j, H) C j (γ j ); 2. Given the accuracy profile {g j (H G )} j G, there exists an equilibrium in the senderreceiver game with endogenous attention allocation in which the active media group is G and total influence of the media is HG, i.e., H G = κ G(HG ), where κ G (H) = j G g j (H) (1 χσθ 1 g j (H) 1 + j G g j (H) 1 g j (H) φ j D j (g j (H),H)g j (H) ). Given an equilibrium profile {γ, HG }, the corresponding equilibrium attention allocation is z j = D j (γ j, H G ) for j G. Equilibrium clarity and action weight for an active news outlet j are, respectively, α j = â j (z, γ ) and β j = ˆb j (z, γ ) (specified in the 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 result for the optimal investment function g j (H) and for the aggregator function κ G (H). Lemma 5. For each media firm j, there exists p j such that, when the marginal cost of attention p is lower than p j, optimal investment in accuracy g j (H) decreases in H, p, and φ j. Further, if p min{p j : j G}, then the aggregator function κ G (H) decreases in H, p, and φ j. Lemma 4 already establishes that D j / H < 0. To show that optimal investment decreases in H, we need to establish that H lowers the marginal benefit from investment, i.e., 2 D j / H γ j < 0. Lemma 5 shows that this is indeed true when the marginal cost of attention is sufficiently low. Furthermore, an increase in H also lowers the 18

20 κ κ G 45 o κ G κ G H G H G H G H Figure 4. The function κ G (H) is well-defined on the interval [0, H G ], and is downward sloping when the marginal cost of attention is low. The fixed point of κ G ( ) is an equilibrium. There is also an equilibrium with active media group G for any G G, but there may not be an equilibrium with active media group G if G G. aggregated total influence κ G (H) both through a direct channel where lower accuracy, g j (H), reduces influence, and through an indirect channel where lower attention, D j (g j (H), H), reduces influence. In Figure 4, we show the aggregated total influence function for three different active media groups, G G G. The function κ G ( ) is downward sloping, as stated in Lemma 5, and is undefined beyond some H G < 1. When H > H G, some firm j G faces a demand function D j (γ j, H) = 0 for any γ j. This firm has no incentive to invest in γ j and will never be active when total influence is equal to H. To ensure that κ G ( ) is continuous on [0, H G ], we also require that the cost functions of the active firms are sufficiently convex (specifically, C j (γ j)/c j (γ j) d(γ j ) for some function d( ) and for all 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 functions of the active firms are sufficiently convex. There exists p G such that for any p p G, there is a monopolistic competitive equilibrium in which the active media group is G and the corresponding profile {γ, H G } is uniquely determined. Further, for any G G, an equilibrium with active media group G also exists, with H G < H G. The two fixed points in Figure 4 indicate two equilibria, one associated with active media 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 because those firms also quit producing news when they receive no attention at all. It is the same manifestation of the coordination failure in the sender-receiver game of Section 3. 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