Coordination Motives and Competition for Attention in Information Markets *

Transcription

1 Coordination Motives and Cometition for Attention in Information Markets * Simone Galerti and Isabel Trevino UCSD May 20, 207 Abstract We examine markets for information where consumers want to coordinate their decisions and roducers comete for consumers attention. We describe information sources in terms of their quantity, accuracy, and clarity. We find that cometition for attention leads to homogeneity of information sources, even when consumers would want to ay attention to heterogeneous sources. Clarity lays a rominent role, as it drives the comarative advantage of an information source as a coordination device for consumers. We also show that, by becoming the currency whereby consumers ay for information, attention causes information markets to work inefficiently. Keywords: information suly, coordination, ayoff interdeendence, attention, accuracy, clarity, inefficiency. JEL classification: C72, D62, D83, L0. * We thank for comments and suggestions S. Nageeb Ali, Rahul Deb, John Duffy, Joseh Engelberg, Renato Gomes, Garrett Johnson, Stehen Morris, Alessandro Pavan, Joel Sobel, Phili Strack, Xavier Vives, Rakesh Vohra, and Joel Watson. John Rehbeck rovided excellent research assistance. All remaining errors are ours. Deartment of Economics, University of California, San Diego, 9500 Gilman Dr., La Jolla, CA, addresses: sgalerti@ucsd.edu; itrevino@ucsd.edu. First draft: July 206

2 Introduction In many economic environments agents make decisions whose ayoffs deend on some unknown exogenous state of the world and on others decisions. Motivated by a desire to learn the state and to assess others beliefs in order to coordinate their actions, agents seek information by allocating attention to multile sources. Shared knowledge is imortant in a wide variety of social settings such as trading on stock markets or articiating in olitical rallies and mass media contribute to its creation see Chwe 203)). According to Shiller 205), Significant market events generally occur only if there is similar thinking among large grous of eole, and the news media are essential vehicles for the sread of ideas.. 0). This raises the question of whether and how the dual role of information sources as learning and coordination devices affects how information markets work. To answer this question, we study how suliers of information serve the demand of consumers who exerience comlementarities or substitutabilities in the use of information. Besides the aforementioned dual role of information sources, we focus on two other asects of information, which differentiate it from other commodities: Information consumes attention while being consumed and attention itself can be a source of revenues for information roviders. This leads them to comete for consumers limited attention. 2 In markets with free entry and refect cometition, we analyze how the suly of information in terms of quantity, accuracy, and clarity deends on how much its consumers care about learning the state relative to mis-)coordinating with others. We study the effects of inefficiencies in the use of information on its suly and demonstrate that, even after removing all those inefficiencies, cometitive equilibria are generically inefficient. To model information demand, we follow the leading aradigm of coordination games à la Morris and Shin 2002) and Angeletos and Pavan 2007). This framework has roven to be tractable yet flexible enough to cature many alications. To illustrate our theory, consider the following stylized scenario. Agents in a society have to take an action, like suorting a olicy for tackling some social issue. They want to suort These distinctive traits of information acquisition have been examined by rominent research, including Hellwig and Veldkam 2009), Myatt and Wallace 202), Colombo et al. 204), and Pavan 204). 2 The imortance of cometition for attention when it comes to information sources has been stressed by many scholars across discilines, including Simon 97), Benkler 2006), Lanham 2006), Sunstein 2009) Davenort and Beck 203), and Webster 204). It is also well known that advertisers are willing to ay a lot for eole s eye balls McCloskey and Klamer 995), Davenort and Beck 203), Webster 204)). 2

3 the best olicy for society, which deends on some unknown state of the world. Agents also like or dislike) conformism, namely, suorting olicies that others suort. Uncertain about which olicy is best and about others actions, each agent seeks relevant information by sending time attending to multile news sources. 3 Such agents exemlify the information consumers in our model, which are assumed to be ex-ante identical. Their anti-)conformism reference catures the consumers mis-)coordination motive and results in a desire to second-guess others beliefs ossibly to high orders in the belief hierarchy). As in Myatt and Wallace 202), information sources are characterized by their accuracy and clarity. Accuracy measures the amount of information about the state the relevant content of a news article). Clarity measures how easy it is for an agent to understand the content by aying attention to its source. The more attention she ays, the better she understands it. Higher clarity offers a higher return to attention. Imortantly, and realistically, information may be interreted differently across agents, introducing a risk of miscoordination. Contrary to the revious literature, in this aer information sources arise endogenously. Each source corresonds to a distinct rofit-maximizing sulier. We assume that attention is their only source of revenues, thereby shutting down the usual ricecometition channel. 4 We do this to better understand how cometition for attention works, which is increasingly relevant in the Internet era and seems understudied relative to rice cometition. Perfect cometition is catured by assuming free entry and nonstrategic behavior on the art of suliers. Each sulier chooses whether to roduce a iece of information with some accuracy in our illustrative story, this can be a summary reort or an in-deth analysis of the olicies that agents can suort. Given this, each sulier selects a technology to communicate its information to otential consumers, which determines the source clarity in our story, this technology can be a TV news channel or an online newsaer. For simlicity, suliers can choose between two tyes of sources, which differ either in accuracy or in clarity. 5 This allows us to uncover the differences between cometition via accuracy and via clarity and delivers useful benchmarks to understand richer cases. After suliers commit to their choices, the agents observe them, allocate their attention, udate their beliefs, and choose their actions. 3 Gentzkow 2007), Gentzkow and Shairo 20), and Webster 204) find that many eole get their news from multile outlets. 4 Setting a zero rice for accessing information may be a deliberate choice for some news outlets. Webster 204) discusses numerous examles and argues that advertising now suorts much of the world s media, both online and off. Gentzkow 2007) estimates that setting rices at zero may be otimal for online outlets in the resence of a strong demand for online advertising. 5 We also analyze the case of different accuracies and clarities, which turns out to be qualitatively similar to the case with only different clarities. 3

4 Our first main result characterizes how the cometitive equilibrium suly of information deends on the value that agents assign to coordinating with others relative to resonding to the state. A key roerty of the demand for information, shown by Myatt and Wallace 202) and Pavan 204), is that stronger coordination motives induce the agents to shift attention from oaque low-clarity) to clear high-clarity) sources for fixed accuracies. To see why, recall that if all agents ay more attention to one source, they better understand its content, which therefore becomes more ublic among them. Publicity hels coordination. Since clearer sources are easier to understand, they enjoy a comarative advantage as coordination devices, which secures more attention as the coordination motive strengthens. We find that this mechanism is magnified by the endogeneity of suly. surrisingly, only one tye of information sources is rovided in equilibrium. Perhas This is caused by the cometition for attention, not by the agents demand for only one tye of sources. 6 When sources differ only in accuracy, the one with lowest cost er unit of accuracy dominates the market. As more suliers enter the market, they drive down how much attention each receives er unit of accuracy. Therefore, only the most efficient suliers survive cometition. By contrast, when sources differ only in clarity, which tye wins the cometition deends on the agents coordination motive. The low-clarity tye wins when that motive is below a certain threshold; otherwise, the high-clarity tye wins. 7 This is because the cometition for attention renders only one of the two tyes rofitable. For instance, in a strongly anti-conformist society where agents dislike coordination low-clarity sources are rewarded with higher attention. This draws more suliers to choose low clarity, who in turn steal attention from high-clarity suliers, thereby drying u their rofits. This imlies, among other things, that cometition for attention need not romote the information sources which offer a high return to attention. In fact, an increase in clarity may damage high-clarity sources: Being too clear can decrease the attention revenues and oen the door for low-clarity sources to win the market. This may go against a common view that more clarity is always better in the attention economy, as suggested by Davenort and Beck 203). A general message of our analysis is to draw a distinction between having many information sources and many tyes of sources, with cometition for attention ushing towards homogeneity of tyes. This echoes Webster s 204) observation that the digital 6 Consistent with this result, Boczkowski 200) argues that the rise of homogenization in the news has led to a state of affairs that neither journalists nor consumers like but feel owerless to alter.. 6) 7 Chwe 203) observes that communication aimed at creating common knowledge and facilitate coordination often uses simle and reetitive language so as to ensure that the message gets through. 4

5 media marketlace is less diverse than its sheer numerical abundance might suggest. 6) and increasing the cometition doesn t do much to imrove the diversity of news roducts.. 58) Our second contribution is to investigate the efficiency of information markets. By assuming erfect cometition, we can focus on inefficiencies caused by the very nature of information as the traded good. Inefficiencies may arise for other usual reasons, like market ower, but we intentionally rule them out. From Angeletos and Pavan 2007) and Pavan 204), we know that ayoff interdeendencies between information consumers can cause inefficiencies in the acquisition and use of information. We exlain how this distorts the suliers incentive to rovide information and ultimately the equilibrium. For instance, a difference between the consumers rivate coordination motive and its socially otimal level can affect not only the quantity of sulied information, but also its tye. If we remove all inefficiencies in the use and acquisition of information erhas adoting the olicies suggested by Angeletos and Pavan 2009)), would the resulting cometitive equilibrium be efficient? The answer is no, generically. This is in contrast with the first welfare theorem for markets with standard goods. This result suggests that information markets are different and exhibit a novel source of inefficiency: The fact that attention acts as the currency whereby consumers ay for information. The allocation of attention deends on its cost for the consumers. Thus, it does not adjust as flexibly as does the standard rice mechanism in order to make both sides of the market correctly internalize the costs and benefits of roducing information. The aer also shows that the efficient information suly can involve multile tyes of sources, in shar contrast to the laissez-faire outcome. These findings may have significant imlications for all those real-world settings where we obtain news for free in exchange for our attention. This seaks to Webster s 204) oint that, there is a broad consensus that the way eole allocate their attention will go a long way toward determining digital media s social imact. In short, a second central message of our analysis is that the revenue channel rovided by attention causes information markets to work inefficiently. 2 Related Literature A rich literature studies information in strategic environments with coordination motives. Morris and Shin 2002) highlight the role of information as a coordination device in a beauty-contest model with rivate and ublic information. They show that increasing 5

6 the accuracy of ublic information can decrease welfare, as agents who strongly value coordination may underweight their rivate information when choosing actions. For more general coordination games, Angeletos and Pavan 2007) characterize the use and social value of information as a function of the agents coordination motive. In these aers the agents do not choose which information to acquire; they automatically absorb every signal that reaches them. Subsequent research has endogenized information acquisition. Hellwig and Veldkam 2009) show that information acquisition inherits the strategic motives from the coordination game and that strategic comlementarities can give rise to multile equilibria. Colombo et al. 204) characterize how ayoff interdeendences affect the efficiency in the acquisition and use of information, and study the social value of ublic information when agents can also access costly rivate information. Myatt and Wallace 202) examine information acquisition when its sources differ in accuracy and clarity as in the resent aer) and attention is a continuous decision, which can remove the multilicity of equilibria found by Hellwig and Veldkam 2009) at least for convex attention costs). Using the same information structure, Pavan 204) examines the equilibrium and efficient allocation of attention, when layers may also exhibit bounded recall. All these aers assume exogenous and heterogeneous information sources. The resent aer calls this heterogeneity assumtion into question by finding that cometition for attention ushes towards an homogeneous information suly. The literature has shown that the decentralized demand of information need not serve the social interest; this aer shows that its suly need not either. Few aers endogenize information sources in coordination games. Dewan and Myatt 2008) examine how olitical leaders may adjust, at no cost, the clarity of their seeches to gain influence and guide activists who care about arty cohesion. Dewan and Myatt 202) allow benevolent arty leaders to also control the length of their seeches. In these aers, the accuracy and quantity of information sources remain exogenously given. Cornand and Heinemann 2008) show that in beauty-contest games increasing the accuracy of ublic information always imroves welfare, as long as one can restrict who can access it. Myatt and Wallace 204) study the central banks roblem of designing information so as to stabilize outut, exectations, and volatility. Chahrour 204) shows that a lanner may otimally withhold information if there is a risk that agents ay attention to different information sources. None of these aers analyze cometitive information markets and their efficiency. A broad literature has investigated news markets focussing on the henomenon of 6

7 media bias and its olitical-economy consequences. 8 Media bias, which refers to deliberate and systematic distortions of reorted information, is orthogonal and comlementary to the focus of the resent study. The idea of cometition for attention and the distinction between accuracy and clarity are mostly absent from that literature, which asks whether cometition broadly defined romotes media indeendence, timeliness, and unbiasedness. 3 A Model of Information Markets We first resent the demand side of the information market, which follows the broadly used setu of Myatt and Wallace 202) and Pavan 204). We then add the novel art: the suly side. The model is intentionally simle and abstracts from institutional details in order to retain tractability. Following the story sketched in the introduction, agents in a society have to choose an action, which can be broadly interreted as a stance about some olicy with uncertain consequences, a forecast of some unknown event, adoting a new technology with risky returns, or merely which toic to bring u in conversation. The agents want to do the right thing, but are also subject to anti-)conformist eer ressures a desire to not) follow oular trends or grou norms. They may also want to coordinate with others because of network or scale externalities. For instance, consider the case of adoting a new technology like electric cars, which require a dense network of charging stations. Before acting, the agents acquire information by sending time attending to news sources, who comete for their attention to maximize rofits. 3. Demand of Information Consumers, Information Sources, and Attention. Society is oulated by a unit mass of ex-ante identical agents the information consumers indexed by n and distributed uniformly on 0,. 9 Their ayoff deends on an unknown state of the world θ. The agents share a common rior: θ N0, σθ 2 ). Let the rior s recision be σ 2 θ. Intuitively, a higher means that the agents initially know more about θ. To learn more, they have access to multile news sources. The information contained in source m is given by y m = θ + z m, where z m N0, σ 2 z m ) 8 See Gentzkow and Shairo 2008) and Prat and Stromberg 203) for literature reviews. 9 Section 7 discusses the ossibility of heterogeneous agents. 7

8 and z m is distributed indeendently of θ and z m for every m m. Note that, even though z m and z m are indeendent, y m and y m are correlated. Myatt and Wallace 202) called z m the sender noise, which reflects the accuracy of source m. Accuracy is measured by a m σ 2 z m, so that increasing a m shrinks the variance of the sender noise. Accuracy can also be interreted as the amount of content about the state: When a m is low, y m is mostly driven by the noise z m and hence has relatively little content; when a m is high, y m is mostly driven by θ and hence has relatively more content. To understand the content of source m, agent n has to ay attention to it. Attention is reresented by e n m 0. We find it helful to think of e n m as the time agent n sends attending to source m. Intuitively, aying more attention raises the chances of correctly understanding a source s content. Formally, for each source m, agent n rivately observes the signal s n m = y m + x n m, where x n m N0, σ 2 x n m ) and x n m is distributed indeendently of θ, all y m, and all x n m for m m and n n. Myatt and Wallace 202) called x n m the receiver noise. It reflects the imerfect communication between source m and agent n, whose outcome deends jointly on how clearly it conveys information and how attentively she listens to it. Following Myatt and Wallace 202), to cature this comlementarity let c m measure the clarity of source m and let σx 2 n c2 m me n m. 0 Increasing c m raises the return of attending to source m in terms of imroving the understanding of its content that is, shrinking σx 2 ). In this sense, we n m can readily interret e n m = 0 as the decision to ignore source m the resulting s n m is just noise and hence fully uninformative). Actions and Payoffs. Each agent s von-neumann-morgenstern utility function is uk n, K, σ, θ) Ce n ), where k n R is agent n s action, K 0 kn dn is the average action in the oulation, σ 2 0 kn K 2 dn is the disersion of the individual actions around their average, and e n is the vector of n s attention allocations e n m. The function C denotes the attention cost. For tractability Ce n ) = τ m en m, where τ > 0 can be interreted as the oortunity cost of the time sent acquiring information. This rominent case, analyzed also by Myatt and Wallace 202) and Pavan 204), involves the substantive assumtion that 0 This way of modeling communication is reminiscent of Dewatriont and Tirole 2005), if we reinterret c 2 m as the sender s effort and e m as the receiver s effort in their model with moral hazard in teams. We square c m in the definition of σx 2 only to simlify some of the exressions below. n m An alternative interretation is that each agent has a finite budget of time T > 0 which she can allocate to attending to information sources and τ is the Lagrange multilier for this constraint. Of course, in this case τ would be endogenous, but this would not change the thrust of the aer. 8

9 the cost deends on the total attention aid to information sources, but not on how it is divided between them. The idea is that, in terms of oortunity cost, sending time on one source is the same as sending time on another; the return to attention may be different, but this is catured by clarity. Linearity of C is mostly a technical simlification to obtain closed-form exressions of the attention allocations, which enable a cleaner analysis of the interaction between demand and suly. 2 As is standard in the literature, 3 we assume that i) u is a second-order olynomial, ii) σ 2 has only a non-strategic externality effect, so that in terms of artial derivatives u kσ = u Kσ = u θσ = 0 and u σ k, K, 0, θ) = 0 for all k, K, θ), iii) u kk < 0, iv) α = u kk /u kk <, and v) u kθ 0. By i), the agents best resonses are linear functions, delivering tractability. By ii), u is additively searable in σ 2 ; let the coefficient on σ 2 be u σσ /2. By iv), the best-resonse functions have sloe smaller than, which delivers uniqueness of equilibrium actions and hence facilitates the analysis of the market as a whole. 4 Part v) rules out uninteresting cases where the agents do not care about resonding to θ. These assumtions allow for rich ayoff externalities. A simle examle of the function u is the quadratic loss function γ)k θ) 2 γk K) 2 for γ 0, ), which is often used in beauty-contest games à la Morris and Shin 2002). Timing. After learning the accuracy and clarity of all news sources, first the agents simultaneously choose their attention allocations; then, they rivately observe their signals and udate beliefs; finally, they simultaneously choose actions, and ayoffs are realized. Consistent with the literature, we consider Perfect Bayesian equilibria of this game among the information consumers, called consumer equilibria for short. 3.2 Suly of Information We aim to cature two fundamental asects of information suly: News sources comete with each other, and attracting attention is a key art of this cometition. To do this in the simlest and starkest way, we assume that each sulier cares directly about how 2 Linearity and more generally convexity) of C rules out cost functions based on entroy, used in the rational-inattention literature Sims 2003), Sims et al. 200)). As exlained in Myatt and Wallace 202), convexity of C ensures that the agents behavior is described by a unique equilibrium, a very useful roerty to study information suly. We leave the analysis with rational-inattention costs for future research. 3 See Angeletos and Pavan 2007), Myatt and Wallace 202), Bergemann and Morris 203), Colombo et al. 204), Pavan 204), and Vives 206), among others. 4 See Angeletos and Pavan 2007) for a detailed exlanation of this uniqueness roerty. 9

10 much attention its source attracts and cannot charge a rice for accessing it. 5 While rice cometition has been extensively studied in economics, cometition for attention not so much. Yet, in the Internet era, many outlets suly news for free and rely on grabbing attention to make money. One interretation is that revenues come from selling eye balls to advertisers. 6 Production. Each sulier m can roduce one unit of the good information, which takes the form of a signal with accuracy a m > 0 and clarity c m > 0. It can also choose to rovide no information equivalently, a signal with a m = c m = 0), which we interret as leaving the market. In order to understand the role of accuracy and clarity in the cleanest way, we assume that each sulier can choose between two tyes of signals, indexed by i {h, l} for high and low, which can differ in terms of accuracy, clarity, or both. We find it helful to associate accuracy with a reorting style of the news source for examle, summary vs. in-deth reorts) and clarity with a communication technology for examle, TV news vs. online newsaers). 7 Finally, let d i > 0 be the cost of roducing a signal of tye i. That is, suliers incur a fixed cost of creating a iece of news, but a zero marginal cost of communicating it a tyical cost structure for information goods in the digital age Hamilton 2004)). Note that suliers have no information about θ when they choose whether to rovide information and of which tye. Profits. Sulier m s rofit from roducing a signal of tye i is ˆ 0 e n mdn d i. Suliers have no reference over which agents ay attention to which source and how they use information. One interretation here is that suliers sell ad imressions not to be confused with s n m) to advertisers. As a first aroximation, revenues are assumed to be roortional to the amount of attention received. Intuitively, the more time agents send 5 More generally, suliers may also comete in rices. This can introduce a trade-off between rice and attention revenues see, for examle, Crames et al. 2009)) and lead to multilicity of equilibria as in Hellwig and Veldkam 2009), due to the discreteness of the cost of acquiring an information source given by its rice. We leave the study of this otentially interesting issues for future research. 6 These are key asects of the attention economy as argued by Davenort and Beck 203) and Webster 204). 7 We are agnostic on whether TV channels or newsaers have higher clarity. This ultimately seems an emirical question, whose answer may also deend on the tye of news considered for examle, financial or business news vs. general-interest news). Broadcast media have a multisensorial aroach that enables otential higher-imact reorting than rint media, but the static nature of rint media allows for indefinite exosure, as oosed to the fleeting nature of broadcast media, whose content is lost as soon as it is delivered. Webster 204) argues that the technology used to deliver media is a key dimension of audience-making strategies. The imortance of technologies in news rovision is also raised by Prat and Stromberg 203). 0

11 attending a news source, the more adds it can show them, and the more imressions it can charge to advertisers. 8 Perfect Cometition. There is an arbitrarily large number of otential suliers. To cature erfect cometition in the usual way, we assume free entry and exit. 9 When making its decisions, each sulier takes the number of existing suliers as given and anticiates the agents behavior as described by the consumer equilibrium. Suliers roduce a tye-i signal if this yields ositive rofits, and leave the market when rofits are negative. We will use this zero-rofit condition for each tye to solve the model. Let the number of active suliers of tye i be q i for i {h, l}. We say that q = q h, q ) l is a cometitive equilibrium if, given q, no active sulier wants to leave the market and no new sulier wants to enter for either tye of signals. Abusing notation, we also use q i to denote the set of active suliers of tye i. 4 Attention Allocation: A Review We start by reviewing the key asects of the consumer equilibria for the rest of the analysis. The full descrition, based on Pavan 204), is deferred to Aendix B. Given q = q h, q l ), a consumer equilibrium consists, for each n, of an attention allocation e n = e n m) m q h q l and a strategy kn s n ; e n ) maing attention and signals s n = s n m) m q h q l into actions. As is standard in the literature, we focus on the unique equilibrium where e n and k n ; ) are the same for all agents symmetry) and k n s; e) is linear in s. We therefore dro the suerscrit n from now on. Note that symmetry does not mean that all agents behave identically, as each observes different signal realizations and may choose different actions. Our goal is to show how the dual role of information sources as learning and coordination devices shaes the suly of information. This obviously hinges on the consumers coordination motive. As Angeletos and Pavan 2007) show, this motive is measured by α = u kk u kk, because in every equilibrium each agent s otimal action must satisfy ks; e) = E α)κ + αk s, e, 8 Webster 204), Ch. 4, describes measures that media use to assess their audience which are consistent with this aroximation. Davenort and Beck 203) describe the stickiness of online news outlets namely, their ability to grab and kee attention as the time sent on a site and the number of visits and viewed ages er erson. 9 Free entry seems a reasonable assumtion in the news market. Webster 204) argues that erhas the most astonishing thing about digital media is their numerical abundance.

12 where κθ) κ 0 + κ θ is the unique equilibrium strategy under comlete information, with κ 0 u k0,0,0,0) u kk +u kk and κ u kθ u kk +u kk. The exlicit exression of k ; ) is rovided in Aendix B. Thus, α measures the imortance of coordination relative to resonding to the state. Our analysis will consist of comaring the information suly across markets that exhibit different values of α. Consider now the agents attention allocation. Of course, they ay no attention to suliers of tye i if q i = 0. Thus, suose that q h > 0 and q l > 0. As Aendix B shows, the agents ay the same amount of attention to each source of tye i {h, l}, denoted by e i. Also, they attend to some source rovided that the marginal attention cost or rior s recision is sufficiently small. To avoid uninteresting cases, we assume this roerty for the rest of the analysis. Let c i be the clarity of each source m of tye i {h, l}. Assumtion Non-trivial demand). τ < κ α)c i u kk 2 for i {h, l}. One useful interretation of Assumtion is that ex ante the agents know sufficiently little about θ so that it is always worth aying some attention to the available sources indeendently of their tye. The next result describes the agents attention allocation as a function of q. 20 Without loss of generality, assume that c h c l. For every α <, define κ q h α)c l u kk c h if c h > c l 2τ a α) = h c h c l ). + if c h = c l Lemma Attention Functions). Suose q satisfies q h > 0 and q l > 0. Then, a l u κ e l +a q) = h q h +a l q l )c l kk ah q h ) if q h < q h α) 2τ α)c l α c l c h, 0 if q h q h α) a h u κ +a h q h +a l q l )c h kk + al q l ) if q h < q h α) 2τ α)c h α c l c h e h q) =. a h u κ +a h q h )c h kk if q h q h α) 2τ α)c h As exected, the attention for each source decreases in the quantity of cometitors of the same tye as well as of the other tye when q h < q h α)) Its roof aears in Aendix A together with all the others. 2 While for e l this is immediate, for e h one can show that eh q) < 0 if q h < q h α). q l It also decreases in the 2

13 rior s recision: If the agents already know a lot about θ high ), they have a weaker incentive to acquire information. The effect of clarity is ambiguous, as noted by Myatt and Wallace 202): A clearer source offers a higher return to attention, which can raise e i, but consumes less attention to convey the same content, which can lower e i. 22 The coordination motive α has two effects on attention. The first, catured by α, is negative. As the agents care more about coordination, their otimal action deends more on their rior and less on their signals, since the rior catures knowledge that they all share. This reduces the value of acquiring information in the first lace. Therefore, suliers comete not only with each other to attract the agents attention, but also with the rior. The second effect of increasing α exists only if c h > c l. It is negative for lowclarity sources and ositive for high-clarity ones, which reflects the latter s comarative dis-)advantage as mis-)coordination devices. 23 As the agents ay more attention to a source, they interret its content more similarly. As a result, the content becomes more ublic among them, enhancing coordination. Clearer sources offer a higher return to attention and so attract more attention when α is larger. That oaque sources have an advantage when the agents instead want to mis-coordinate may be counterintuitive, but it has a simle logic. Roughly seaking, each agent now wants to resond in oosite directions to shared information suggesting that the state is high and everybody else s action is high. As a result, such information has little value. It is, however, less likely to arise from oaque and hence more rivate sources, which are then more desirable for the agents. Finally, for every degree of coordination, high-clarity suliers can crowd out the agents attention so that nobody attends to low-clarity suliers but not vice versa). Note that q h α) is indeendent of q l and decreases in α. This is because a larger α increases the value the agents assign to higher clarity and hence their willingness to attend to high-clarity suliers, which can now more easily exhaust their attention. Of course, if q h exceeds q h α), no tye-l sulier wants to enter the market. To determine whether tye-h suliers dominate the market, we turn to equilibrium analysis. 22 The roerty that agents ay attention to all sources of either tye is clearly driven by their symmetry in the model. Although this is in art at odds with reality, there exists evidence of significant overla in audiences across news sources Gentzkow and Shairo 20), Webster 204)). 23 That clear sources are better coordination devices seems to be a general roerty that holds beyond the Gaussian framework considered here see Chwe 203)). 3

14 5 Equilibrium Information Suly We first derive the zero-rofit conditions that characterize cometitive equilibria, given the attention functions obtained before. We find it helful to view these functions as an analog of demand functions in standard markets. We use those conditions to analyze the equilibrium suly of information. Recall that suliers can choose between two tyes of signals, which can differ in clarity, accuracy, or both. We cover these three cases searately so as to better demonstrate the differences between cometition via accuracy and via clarity. 5. Zero-rofit Conditions Consider the suliers entry and exit decision. Given that q h and q l suliers are already in the market, a new sulier enters and roduces a signal of tye i if and only if e i q i +, q i ) d i. ) Since all suliers of each tye are identical, if ) holds for the last entrant, it also holds for all tye-i suliers already in the market. In other words, ) imlies that q i + )e i q i +, q i ) q i + )d i. Conversely, if this condition holds and only q i suliers of tye i are already in the market, an additional tye-i sulier wants to enter. Letting E i q) = q i e i q) be the total attention for tye-i suliers, we get the following observation. Lemma 2. q h, q l ) is a cometitive equilibrium if and only if, for all i {h, l}, E i q i, q i ) q i d i and E i q i +, q i ) < q i + )d i. These conditions characterize all equilibria if any exists), but are inconvenient to use due to the discreteness of q h and q l. This is analogous to the issue that arises in textbook analysis of long-run cometitive equilibria when rofits jum from being strictly ositive to being strictly negative if one more firm enters the market. This issue is tyically removed by assuming that each firm is small so that equilibria can be characterized by a zero-rofit condition. A similar aroach can be adoted here by letting q h and q l be non-negative real numbers. Given this, cometitive equilibria are now characterized by E i q i, q i ) = q i d i, i {h, l}, 2) 4

15 and q i > q i E i q i, q i ) < q i d i, i {h, l}. 3) To exlain these conditions, Figure reresents the total roduction cost q i d i and the attention function E i q i, q i ) when ositive), which is strictly increasing and concave in q i. The quantity q i = 0 always satisfies 2), but can be art of an equilibrium only if, given q i, no tye-i sulier can rofitably enter the market. In Figure, this holds for d i, but not for ˆd i. In this case, condition 3) rules out q i = 0 and q i as an equilibrium. q i d i q i ˆdi E i q i, q i ) 0 q i Figure : Attention-revenue and roduction-cost curves The interretation of continuous quantities is that each sulier is small relative to the whole market, which is consistent with the idea of erfectly cometitive environments. In this model, however, letting the number of information sources become arbitrarily large involves some intricacies: Since each rovides an indeendent signal about the state, they could eventually allow the agents to fully learn it. We avoid this uzzle and maintain the sirit of the model by aroriately rescaling the accuracies a h and a l as we let the number of sources grow. We resent the details in Aendix C. 5.2 Cometition via Clarity Consider the case where suliers can use clarity as a lever to attract attention, but they all roduce the same content c h > c l and a h = a l = a). For examle, this content may be the narration of some event whose accuracy a stands for the currently available facts, and each sulier can communicate this either via a TV news channel or an online newsaer. Arguably, the same content cannot be conveyed in the same way using videos and sounds and using ictures and written words, and the attention required to rocess it might differ between media For a similar oint, see Dewan and Myatt 2008) and Webster 204). 5

16 It is useful to add two simle assumtions. First, higher clarity costs more: d h > d l. Second, the demand for information is sufficiently strong that, if only one tye of signals were feasible either h or l), there would be a ositive suly of information. Let ˆq i be the largest solution to E i q i, 0) = q i d i. Assumtion 2 Strong demand). ˆq i d i c i κ u kk 2τ α)c i a i > 0 for i {h, l}. Note that this assumtion is satisfied if is sufficiently small, which can be interreted as situations where ex ante the agents know little about the state. Desite Assumtion 2, generically in equilibrium only one tye of suliers is active. To state this, define ˆα = a c h d h c l d l c ). l c h Proosition. There exists a cometitive equilibrium q. If α ˆα, the equilibrium is unique and satisfies ˆq h, 0) if α > ˆα q =. 0, ˆq l ) if α < ˆα If α = ˆα, there is a continuum of equilibria which satisfy q l 0, ˆq l and q h = dl c l d h c h ˆq l q l. To see the intuition, think of d i a/c i as the cost er unit of content of sulying information of tye i, taking into account its return to attention for consumers. Similarly, think of ei q) as the er-unit revenue the rice ) earned from a tye-i source. When a/c i both tyes attract ositive attention, one can easily see that e h q) a/c h Using the definition of ˆα, we have that α c l c h el q) a/c l = α ) dh a/c h c l c h ). 4) dl a/c l if and only if α ˆα. 5) That is, α > ˆα res. α < ˆα) imlies that high-clarity sources are more res. less) rofitable than low-clarity ones. This also imlies that when one tye yields zero rofits, the other must yield strictly negative rofits and so no sulier wants to choose it. Note that this result follows from roerties of the attention functions that are derived not assumed) from more rimitive roerties of how agents use information in a variety of social contexts. Although based on Section 4 one should exect that high α s favor clear suliers and low α s favor oaque suliers, it is erhas surrising that, generically, only one tye is 6

17 active in equilibrium. This is a consequence of the cometition for attention, not the lack of demand for one tye of sources. Excet for large α s, one tye of suliers dominates the market not because the agents do not want to attend to the other at all, but because cometition renders this tye unrofitable. Indeed, the zero-rofit quantity ˆq h satisfies ˆq h < q h α) if and only if α < α a c h d h c ), l c h where α > ˆα. Thus, if for instance α < ˆα and q l = ˆq l, high-clarity suliers do receive some attention after entering the market, but the comarative advantage of low-clarity suliers as mis-coordination devices renders entry unrofitable. Another interesting roerty is that low-clarity sources can win the cometition for attention. This may seem counterintuitive, as such sources offer a low return to attention and they can never entirely steal attention from high-clarity ones. But the deendence of the result on the coordination motive being sufficiently weak hels exlain the uzzle and demonstrates the imortance of recognizing the role of information sources as coordination devices to understand their suly. To see the intuition, suose the agents actions are strong strategic substitutes so that α < ˆα. We then know that the agents favor low-clarity sources, as they better hel them choose actions far from the oulation average. With endogenous sources cometing for attention, this redilection for low clarity deresses the rofitability of high-clarity sources, which can entirely dry u their market share. The threshold ˆα itself has some noteworthy roerties. It is indeendent of the agents ayoff function u which determines κ and u kk ), rior recision, and attention cost τ. These asects affect how much time the agents are willing to ut overall into acquiring information, but not how they divide it between sources. Accordingly, the sulied quantity ˆq i is decreasing in higher rior knowledge weakens the incentive to acquire information), in κ a smaller κ weakens the agents desire to resond to θ and hence to acquire information), and in τ. 25 The threshold ˆα deends only on asects of the suly side of information, as summarized in the next result. Proosition 2. ˆα decreases in the accuracy of information, a, and the cost of low-clarity sources, d l, while it increases in the cost of high-clarity sources, d h. Holding ch c l fixed, ˆα 25 We conjecture that the equilibrium characterization in Proosition and 3 below) remains qualitatively unchanged if the attention cost function is Ce) = C i e i), where the function C satisfies C 0) > 0 and C > 0. Indeed, in this case the key equations 3) and 4) in the roof would still not have a solution with e h > 0 and e l > 0, generically. 7

18 increases both in c l and in c h. Finally, there exists λ > such that, given c l, increasing c h raises ˆα if and only if c h > λc l ; given c h, increasing c l always raises ˆα. Intuitively, a higher common accuracy lowers ˆα because the richer content takes more time to be understood and hence is more rone to being interreted differently, causing mis-coordination. This effect is mitigated by higher clarity, so consumers assign a remium to it at even lower α s. The threshold ˆα also falls when clarity worsens for tye l or for both tyes roortionately, because this boosts the net comarative advantage of high-clarity sources see 4) and 5)). These sources, however, may not benefit from an increase in their clarity: Being very clear i.e., c h > λc l ) can decrease the attention revenues and thus has to be offset by a stronger coordination motive for them to cover the roduction costs. 5.3 Cometition via Accuracy We now analyze the case where suliers use accuracy as a lever to comete for attention, but they all communicate via the same technology a h > a l and c h = c l = c). As an illustrative examle, consider a stylized scenario where there are only online newsaers and each can choose between running a summary reort a l ) or an in-deth analysis a h ) of some event or toic of ublic interest. Note that, in this case, neither low- nor high-accuracy suliers can crowd out attention: For all q h > 0 and q l > 0, e i a i ukk q) = κ + a h q h + a l q l > 0 for i {h, l}, 6) )c 2τ α)c where the inequality follows from Assumtion. This already suggests that cometition via accuracy is qualitatively different from cometition via clarity. We assume that higher accuracy costs more d h > d l ) and that the demand for information is sufficiently strong. Let q i be the largest solution to E i q i, 0) = q i d i. Assumtion 3 Strong demand ). q i u κ d i c kk > 0 for i {h, l}. 2τ α)c a i This assumtion can again be interreted as caturing situations where ex ante the agents know little about the state. Desite this assumtion, the equilibrium suly of information is again dominated by one tye of sources, generically. 8

19 Proosition 3. There exists a cometitive equilibrium q. If dh a h unique and satisfies If dh a h q h, 0) if dh a q = h 0, q l ) if dh a h < dl a l > dl a l. dl a l, the equilibrium is = dl a l, there is a continuum of equilibria which satisfy q l 0, q l and q h = al a h q l q l. d To gain intuition, think of i as the er-unit cost of roducing information of tye i a i /c and ei q) as the er-unit revenue again, the rice ) earned from sulying it. Because a i /c both tyes have the same clarity, they earn the same rice: e h q) a h /c = el q) a l /c = ukk κ + a h q h + a l q l 2τ. α)c Moreover, this rice falls as more suliers enter. Free entry then imlies that only the suliers with the cheaest roduction can rofitably survive in the market. A few remarks are in order. The result is again driven by the cometition for attention. By 6), the agents would always ay attention to both tyes, and one can find examles of q h > 0 and q l > 0 such that both tyes would make ositive rofits. Yet, such situations cannot survive the cometition for attention. Another interesting asect is that the equilibrium tye of suliers does not deend on the agents coordination motive: α only affects negatively the sulied quantity of information q i ) due to the aforementioned cometition with the agents rior. This is in stark contrast with the case of cometition via clarity. The effects of τ,, and κ on q i follow the same logic as for ˆq i. Finally, clarity has a non-monotonic effect on q i : q i c = ukk 2 κ d i c 2 + > 0 if and only if c < 2τ α)c 8τ. α) κ u kk This reflects the non-monotonic effect of clarity on attention exlained after Lemma : Excessive clarity can deress the attention revenues, thereby reducing market entry. 5.4 Cometition via Accuracy and Clarity The case where the tyes of sources differ in both accuracy and clarity turns out to be qualitatively similar to the case where they differ only in clarity. Clarity remains the driver of the cometitive outcome. For this reason, we only exlain the differences from the revious analysis at an intuitive level. The formal stes are shown in the roof of Proosition. We have two ossibilities to consider, deending on whether the choice 9

20 between tyes involves a trade-off between accuracy and clarity. These ossibilities relax the indeendence between accuracy and clarity that was imlicit in the revious sections. High-accuracy-low-clarity vs. low-accuracy-high-clarity. In this case, the feasible tyes are described by a h, c l ) and a l, c h ), where a h > a l and c h > c l. Without risk of confusion, we label the first hl and the second lh. As an intuitive interretation, suose that each news source is conveying information on the desirability of some ublic olicy. One otion is to ublish a short article stating that the olicy is desirable in simle words which are easily understandable for everybody tye lh). Another otion is to ublish an in-deth reort exlaining the olicy effects and all arguments in favor or against it, which may involve data, grahs, technical jargon, and subtle logics and hence are more likely to be interreted in different ways by the agents tye hl). These tyes may corresond to the distinction in the news industry between soft and hard news. To exlain the outcomes of cometition, we need the following notation: ˆα = c h d a lh cl d l a hl c ) and α = al l c h c h d lh c ) <. l c h h Note that ˆα can exceed, in contrast to ˆα < α < in Section 5.2. This haens if the high-accuracy-low-clarity sources cost significantly more: d hl > ch c l a h a l d lh. If ˆα < α, the characterization of cometitive equilibria is as in Proosition, excet that ˆα relaces ˆα. If instead α < < ˆα, for every α < there exists a unique equilibrium where lowaccuracy-high-clarity suliers dominate the market. Intuitively, when d hl > ch c l a h a l d lh, a tye-hl source costs simly too much relative to the little attention it attracts because the agents have to rocess more content that is also more difficult to understand. Abstracting from details, this model suggests that a transition from hard news tye hl) to soft news tye lh) may be driven not by an increase in the scarcity of consumers attention its cost τ does not affect ˆα but by an increase in social conformism or technological changes in news roduction. High-accuracy-high-clarity vs. low-accuracy-low-clarity. In this case, the feasible tye are described by a l, c l ) and a h, c h ), where again a h > a l and c h > c l. A reasonable assumtion here is that d hh > d ll. For illustration, consider a stylized situation where news roviders can hire two tyes of journalists. Tye hh is an exert, hard-working, ercetive journalist with excellent writing skills, who can roduce accurate as well as clear articles; tye ll is a novice, lazy, dull journalist with oor writing skills, who cannot achieve the same accuracy and clarity of tye hh. 20

21 Turning to equilibrium analysis, we now need the following notation: ˆα = c h d a hh cl d h a ll c ) and α = ah l c h c h d hh c ) l c h l Again, it is ossible that ˆα > > α. This haens if and only if accuracy differs a significantly between tyes: h > ch d hh. If ˆα < α, the characterization of cometitive a l c l d ll equilibria is again as in Proosition, excet that ˆα relaces ˆα. Note that in this case, when α < ˆα, in equilibrium suliers rovide the unambiguously dominated tye of sources, which is worse in terms of both accuracy and clarity; and this occurs, even though the agents would be willing to ay some attention to the better sources hh. If instead α < < ˆα, we again have a unique equilibrium for every α < where tye-hh suliers dominate the market. Intuitively, when ah > ch d hh, a tye-ll source can simly a l c l d ll attract too little attention to be rofitable, due to its extremely low accuracy. <. 6 Inefficiencies in Information Markets What inefficiencies can arise in information markets? Some inefficiencies can arise from familiar causes, such as monoolistic ower or adverse selection. We rule these out by considering cometitive settings, so as to focus on inefficiencies that are secific to information markets. From Angeletos and Pavan 2007) and Pavan 204), we know that ayoff interdeendencies between agents distort their use and acquisition of information. We first investigate how these distortions affect the suly of information. We then demonstrate a general inefficiency of cometitive equilibria, caused by the fact that information suliers rely on attention to make money. For the sake of brevity, we will focus on the more interesting case of cometition via clarity and only discuss cometition via accuracy for the generic cases with a unique equilibrium). 6. Inefficient Use of Information and Suly of Information We can identify the inefficiencies in the demand of information by studying the attention allocation and use of information that would maximize the agents ex-ante utility for any given set of information sources. Based on Angeletos and Pavan 2007), this efficiency criterion takes as a constraint that information is disersed in the economy and cannot be transferred between agents. 26 The agents failure to internalize interdeendencies among their ayoffs leads to three kinds of inefficiencies Pavan 204)): 26 Angeletos and Pavan 2009) investigate olicies that can achieve efficiency in the use of information. 2