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Link to Success: How Blogs Build an Audience by Promoting Rivals
November 2006
Dina Mayzlin
dina.mayzlin@yale.edu
203-436-4262 Fax: 203-432-3003
Hema Yoganarasimhan hema.yoganarasimhan@yale.edu
Yale School of Management1 135 Prospect Street P.O. Box 208200 New Haven, CT 06520-8200
1 Dina Mayzlin is an Assistant Professor of Marketing at the Yale School of Management. Hema Yoganarasimhan is a PhD student at the marketing department of the Yale School of Management. We would like to thank David Godes, Birger Wernerfelt, Jose Silva, Jiwoong Shin, K. Sudhir, and Sachin Sancheti for comments that have improved the paper. We would also like to thank participants at the Yale SOM PhD seminar, Marketing Science Conference 2006, SICS 2006 conference, and the SOM Wednesday lunch seminar for helpful comments. Both authors contributed equally and their names are listed in alphabetical order.
Link to Success: How Blogs Build an Audience by Promoting Rivals
Abstract
According to a recent survey by Pew Internet Project, 12 million US adults keep web logs (or blogs), websites that provide commentary on various topics. In addition, 57 million adults read blogs. However, it is not obvious how readers find blogs that provide useful information given 1) the multitude of blogs, 2) the heterogeneity in their quality, and 3) the lack of brand equity in this context. The main research question of this paper is to explain the popularity of blogs given these obstacles.
We suggest that linking is the reason behind the success of blogs. We explain why an author chooses to link to another blog, despite the fact that this may result in losing a reader to that blog. In our model blogs differ along two dimensions: the ability to produce useful information and the ability to link to other blogs with useful information. Thus, by linking a blog demonstrates its ability to link to informative blogs in future periods. The downside of a link is that it demonstrates that a competing blog is able to produce information. In equilibrium, links enable a system of mutual monitoring: blogs that more reliably produce information are more likely to have more incoming links and hence receive more visitors.
Keywords: networks and marketing, competitive strategy, game theory, media, e-commerce.
1. Introduction According to Lenhart et al (2006), 12 million US adults keep web logs (or “blogs”), websites that provide commentary on topics ranging from product recommendations to current events. In addition, 57 million adults read blogs. At least some of the reading takes place at work: 35 million workers on average spend about 3.5 hours of the work week reading or posting comments in blogs.2 Firms are also paying attention to this phenomenon. For example, during this year’s Fashion Week in NYC, 40 fashion bloggers were given coveted access to designer runway shows. This was due to the popularity that these sites enjoy: PerezHilton.com (a celebrity gossip site) is viewed 40 million times per month compared to the established Style.com’s 87 million monthly views.3 Bloggers’ popularity has also been noticed by the political establishment: the June 2006 political bloggers’ convention (called YearlyKos after a popular liberal blog) drew Democratic party luminaries such as General Wesley Clark, Howard Dean, as well as other 2008 Presidential hopefuls4.
To consumers, the rise of blogs means an increase in availability of information on a variety of topics. For example, on May 11, 2006, a visitor to the blog daddytypes.com (“the weblog for new dads”)5 could find several new posts. For instance,
1) there was a picture featuring an “unidentified Red Sox fan” pushing a baby in a Gecko stroller, and 2) there was a post announcing a two-day sale at Netto Collection, an upscale kid furniture store in New York City. The Netto post credited (and linked to) another blog, daddydrama.com (“a blog that’s all about the baby (well, hip dads and chic moms too)!”), with the original post on the sale.
2 Johnson, (October 24, 2005), “What Blogs Cost American Business,” Advertising Age.
3 Dodes, (Sept 12, 2006), “Bloggers Get Under the Tent,” Wall Street Journal.
4 Nagourney, (June 10, 2006), “Gathering Highlights Power of Blogs,” New York Times.
5 The NYTimes featured the author of daddytypes, Greg Allen, in an article that described him as a filmmaker and a writer. (“Changin’ in the Boys’ Room,” Newman, Feb 5, 2006).
In fact, while daddyypes posted the information on May 11 (the first day of the sale), daddydrama had the information posted on May 9.
The example above illustrates several interesting aspects of blogs. The first is that a blog can provide useful information that may not be available in the mainstream media, (e.g., the Netto Collection announcement). However, since blogs do not have the brand equity of a mainstream publication and given the large number of blogs and the uncertainty regarding their quality, it is not obvious how readers are able to find blogs that provide useful information. From the consumer’s perspective, telling apart the useful from the useless is important since blogs are often outlets for the author as opposed to a useful tool for the reader: 52% of bloggers state “to express yourself creatively” as a major reason for blogging (Lenhart et. al. (2006)). The main research question of this paper is to explain the blogs’ success, despite the obstacles discussed above.
We propose that linking may help solve the consumers’ search problem. From the blogger’s perspective, a one-way link to a potential rival seems to be a risky strategy since a reader may defect to the linked blog. Moreover, recommending a rival is not confined to this space. For example, Amazon features links to other book sellers who often have a new version of the book at a discounted price. While Amazon takes a commission from sales generated through a link, it is nonetheless interesting that it chooses to facilitate a relationship between its customer and another bookstore. Another recent example involves the decision by the
WashingtonPost.com (among others) to feature links to related articles and blog posts in other publications next to the Post’s article.6
The common thread between blogs as well as Amazon and WashingtonPost is that they all offer information to their customers. We focus on a particular aspect of information: the ability to deliver timely news. The news may relate to current events, but may also deal with new gadgets, the coolest cars at an auto show, a listing of family events in Boston, etc. To capture the heterogeneity between blog types, we allow the bloggers to differ along two dimensions: 1) the ability to post news-breaking content, and 2) the ability to find news in other blogs. That is, the downside of a link to daddydrama’s announcement of the sale is that it demonstrates that daddydrama is likely to generate useful information. The upside is that it allows Greg Allen of Daddytypes to signal that he is able to direct readers to information posted on other blogs. Similarly, we suggest that one reason behind Amazon’s decision to connect consumers to other booksellers allows it to be viewed as a “destination” site. Hence, the consumer will go to Amazon next time because she will be able to find a book either on Amazon or on another site through Amazon. This incentive is echoed in the words of a publishing executive of the Oklahoman on the decision to include links on its site, “This lets us be a search engine. We look at it like we just hired 30,000 journalists, because now we can give you our story and what the rest of the world is saying about it.”
Note that as a by-product of these incentives, there emerges a self-sustaining system of quality monitoring between different blogs. Monitoring may be especially important in light
6 “Newspapers to Use Links to Rivals on Web Sites,” Tedeschi, NYTimes E-Commerce Report, July 31, 2006.
of the incentives that companies have to influence bloggers, as exemplified7 by recent WalMart’s PR campaign to have bloggers post pro-company comments. That is, by linking to a blog with information, a consumer is able to find information by following links and a blogger who is more likely to produce information has a higher readership. This effect is further accentuated by search engines that commonly give higher placement to sites with more incoming links.8
The rest of the paper is organized as follows: in Section 2, we discuss previous literature. In Section 3, we present the model. We examine how the incentive to link depends on whether a blog was able to generate original content. We also examine the conditions under which linking is an equilibrium. In Section 4, we show that the blog’s incentives and visitor’s interests may be misaligned in that the blog prefers to slow down the visitor learning about a rival’s ability. In Section 5, we conclude and discuss future work.
2. Previous Work There are several streams of literature (in marketing, computer science and economics) that relate to the problem studied here. First, we turn to literature that deals with the role of hyperlinks in the Internet. This has been studied in computer science since Kleinberg’s 1999 paper. Kleinberg proposed that hyperlinks have valuable information because they reflect the subjective judgment of the author who made them. Kleinberg assumes that the world is divided into hubs and authorities. Authorities are authoritative homepages on a subject, while hubs are pages that link to authorities. Brin and Page (1998) eliminated the hubs-andauthorities structure and introduced PageRank – an algorithm which computes the page rank
7 Barbaro, (March 7, 2006), “Wal-Mart Enlists Bloggers in P.R. Campaign,” New York Times.
8 In fact, there has been a debate in the computer science literature whether Google accentuates the bias towards popular sites or allows small sites access: does Google create a Googlearchy or Googleocracy? See, for example, Hindman et al (2004) and Fortunato et al (2006).
of a webpage for a given query. This forms the basic framework behind Google and assumes that there is “wisdom of crowds” (Surowiecki (2004)) behind the link structure.
While the computer science literature has assumed that there is valuable information in links, it takes the structure of the network as given. In contrast, a seminal paper by Bala and Goyal (2000) studies network formation as an equilibrium of a non-cooperative game. Since then, there have been a number of papers that study network formation, including issues such as stability and efficiency, learning, and coalitions. See Demange and Wooders (2005) for an excellent collection of essays on group formation in economics. While the literature in this area has been extensive, to our knowledge no one has studied the issue of a third party (the reader in our case) that makes inferences based on the observed pattern of links.
Katona and Sarvary (2006) bridge the gap between the economics and computer science literature on network formation by suggesting that links are formed strategically on the Internet. In particular, they propose a market for advertising, where a site may sell advertising space on its site or buy an incoming link from another site. There are some similarities between this paper and the current work in that Katona et. al. also find that a site with better content will have more incoming links. However, the two papers differ in the mechanisms governing this basic result. While Katona et. al. focus on an explicit pricing scheme (which is surely the case for the commercial web) behind the exchange of links, we focus on the inference made by a consumer following the observation of a link.
Two papers that directly study the referral process are Garicano and Santos (2004) and Chen et al (2002). Garicano et. al. show that in a situation where one expert diagnoses a problem
and decides to either address or refer it to another expert, different revenue-sharing schemes have different implications on an efficient allocation of clients. While we also look at referrals, we look at a very different setting where an explicit payment structure between sites is not possible. Chen et. al. consider infomediaries: Internet services that direct visitors to the retailers that are members of their network. The authors find that these services will lead to lower online prices. Again, while these authors examine a related problem, their paper deals with an explicit contractual arrangement between the infomediary and its clients. In addition, no inference is drawn by the consumer on the infomediary ability to link to others.
The final relevant stream of literature deals with mutual monitoring in teams. For example, Bowles and Gintis (1998) model mutual monitoring in teams. Varian (1990) models how incentives can be designed so that agents would monitor each other. Studies of Grameen Bank in Bangladesh (Islam et. al (1993)) have shown that social norms are monitors for not defaulting on group loans. Knez and Simester (2001) empirically show that monitoring that occurs in small teams can prevent free-riding that can happen in team-level incentives. Past research has primarily dealt with explicit incentive structures that enforce mutual monitoring by agents. We study a context where the monitoring occurs not due to an optimal group incentive structure but due to an individual’s desire to “impress” the visitor.
3. Model 3.1 Set-Up We have a finite-period game with an infinite number of risk-neutral consumers (we refer to a consumer as R, reader) and an infinite number9 of blogs. We assume that bloggers obtain
9 This is a technical assumption that simplifies the model. Qualitatively, the results are not changed as long as we assume that there is a finite but very large number of blogs. The model does not at all depend on the assumption that the number of consumers is infinite.
utility from the size of the readership. This is either due to commercial or social reasons. That is, a blogger with a bigger audience will make more revenue if she chooses to place ads on her site through a service such as Google’s Ad Sense. However, perhaps an even bigger motivating force in this context is the social utility that a blogger derives from having a bigger audience. According to Lenhart (2006), 61% of bloggers listed the desire to “motivate others to action” as a reason for blogging, and 51% listed the desire to “influence the way others think” as a reason.
We model bloggers as producers of information and visitors as consumers of information. Bloggers are differentiated along two dimensions: i) The ability to break the news on its site (for example, finding out the short-list of nominations to the Supreme Court or finding which store will have a swimwear sale); and ii) The ability to find other blogs that contain news and hence the ability to link to news-breaking blogs. These abilities are assumed to be independent. We can explain the differences in abilities due to differences in costs: while some bloggers have lower costs of obtaining valuable information, others have low search costs when it comes to searching for information in other blogs. For example, while it may be less costly for Daddytypes to obtain the scoop on the latest in baby gear since he lives in Manhattan where there is a high demand for upscale baby products, another blogger may spend a large amount of time surfing others’ blogs and thus have consistently good links. Note that, as we argued above, bloggers face the same non-trivial search problem as the consumers. Moreover, the fact that bloggers are active readers of other blogs is very realistic: 90% of bloggers read blogs as opposed to 39% of all Internet users according to Lenhart (2006).
Hence, a blog can be either a High (H) type (probability v of acquiring information) or Low
(L) type (probability w < a0 =".v" 0 ="dp" t =" 1" t =" 2" href="http://www.thesmokinggun.com/jamesfrey/0104061jamesfrey1.html">http://www.thesmokinggun.com/jamesfrey/0104061jamesfrey1.html 13 For example, one irate blogger complained that he had been plagiarized, “I recently lost out on a boatload of potential new readers because a blogger plagiarized my work verbatim. A high-traffic blogger (Michelle Malkin) then unwittingly linked to the plagiarist's blog instead of mine, and I missed out on all the traffic that came before I found the mistake and asked Michelle to fix the link.” http://davidm.blogspot.com/2004/10/serial-plagiarism-exposed.html
sensitive to the timing of the reader’s entrance: the results would not change even if the consumer visits the blogs after information is released since a blogger is constrained not to plagiarize others’ content.
A consumer who has not yet seen the news derives a utility u – c if she sees a link to a news-breaking blog (let’s call it blog B). Note that we assume that the value of information declines with time. We alternatively refer to c as the travel cost that must be paid to travel to blog B. For example, if the information is the name of the store that is having a sale, there is urgency in finding out the information since the store may sell out of the consumer’s sizes. A consumer who has already seen the news derives no extra utility from the link to blog B.
After seeing a link to blog B, the consumer updates upwards her belief on B’s ability to break the news. At the same time, depending on the presence of a link and on the equilibrium of the game, the consumer may update her belief on A’s ability to find the news. This is the key tension in the model: by linking blogger A makes itself look good, but at the same time he also makes blogger B, a potential competitor in the next period, look good as well.
In order to simplify the analysis, we assume that the consumer does not update her prior on B’s ability to find news in other blogs. This is either due to the fact that the consumer simply does not observe B’s links (the information from B may be consumed through A’s post) or it may be due to the fact that by the time the consumer visits blog B and observes its links, the news has become stale and the links have no signaling value. The results of our analysis are qualitatively the same if we assume that the consumer is able to resolve her uncertainty about B’s ability to find the news but the analysis is much more cumbersome.
We also assume that the consumer does not learn about the abilities of any other blog during this time period. Again, this can be either due to constraints on the reader’s time or simply because information quickly becomes stale in this environment.
At the beginning of the second period (stage 4), the consumer decides which blog she should visit next. If blog A had linked to blog B, she chooses between A and B. If on the other hand, blog A had not linked to another blog, the reader must choose between A and a random blog (let’s call it blog C). When making this choice, the consumer also experiences a reader-blog-specific random shock to her utility from that blog. For example, one may “crave” the ironic tone of Daddytypes one day or a more factual style of another blogger.
At stage 5, a piece of information is released to some blogs, and blogs who obtain this information go on to post it. If a news item is posted, the reader derives a utility u from the item. At stage 6, blogs will link to news-breaking blogs if they find a blog that contains the news. In the absence of strategic considerations (which is the case at the last round of the game), we assume that all blogs link if they find news. If a reader is exposed to the item for the first time, she experiences a utility u – c from the news item. The game ends after this.
The assumption that linking will take place in the last round of the game is important in that the early learning is motivated by a desire on the part of the visitor to learn the blogger’s type which is reflective of the blogger’s actions in the future. For example, if we assume that no linking takes place in the last period, the early signal about the ability to link would have no value to the visitor. On the other hand, we could specify a model such that the bloggers would have a constant incentive to link. For example, consider an overlapping generations
model where a blog would have to demonstrate its abilities to new entrants to the blogosphere every period. However, this would introduce asymmetric uncertainty in that the bloggers would eventually learn about their own abilities. Thus, the assumption on terminal period play is a simplification in that it allows us to solve a less complicated model. However, the model could be generalized in a way that may be more realistic in that the real world does not end (we hope).
3.2 Perfect Bayesian Nash Equilibrium Note that given the symmetry assumed in the model, all blogs and all readers face the same problem in the beginning of the game. This allows us to focus on the decision faced by a random reader and a random blog. We can then generalize the findings to all other blogs and readers. We look for a Perfect Bayesian Nash Equilibrium with respect to the linking behavior of a blogger in the beginning of the game (stage 3). At this time, the blogger has either broken the news or has failed to do so and has also either found the news in another blog or has failed to do so. By definition, if a blog does not find the news, he is not able to link (see Table 2). Because of this, from now on we concentrate on the scenario where the blog is able to find the news in another blog. In this case, there are 4 possible equilibria: a blog must decide to either link or not to link based on whether he was able to break the news on his own blog. We will refer to the first equilibrium as (Link, Link) where the first cell refers to the action when the blog has broken the news and the second one refers to the action when the blog did not break the news. Since a blog is only able to link if he finds information in another blog, linking is a potential signal of ability to search.
Table 2 – Possible Equilibria
1 2 3 4
Found news in another blog Broke the news Did not break the news Link Link Link Don’t Link Don’t Link Link Don’t Link Don’t Link
Did not find news in another blog Broke the news Did not break the news Don’t Link Don’t Link Don’t Link Don’t Link Don’t Link Don’t Link Don’t Link Don’t Link
Each equilibrium generates a different set of posterior beliefs by the consumer. For example, compare the difference in inference generated by no link in the (Link, Link) versus the (Don’t Link, Don’t Link) equilibria. In the first equilibrium, the lack of a link is seen as a negative signal on the blog’s ability to find the news since in equilibrium the blogs that find the news post the link. On the other hand, in the (Don’t Link, Don’t Link) equilibrium blogs choose not to link even when they find the news. Hence, the reader does not view an absence of a link as a negative signal.
In addition, as is the case for the majority of signaling models, some actions are not in equilibrium, and hence we have to specify off-equilibrium beliefs. Specifically, if linking is observed but is not played in equilibrium, Bayes’ Rule does not apply. (Note that an absence of a link can always be attributed to the fact that the blogger did not find the news and thus is never seen as an out-of-equilibrium action). We assume that a reader updates upwards her beliefs on the blogger’s ability to find information when she observes a link, even if linking is not in equilibrium. Note that this is a reasonable belief, given the structure of the model. That is, a link implies that the blogger found information in other blogs, which makes it
more likely that he is the H-type on that dimension. The fact that the blogger plays an outof-equilibrium strategy should not interfere with that inference.
The posterior beliefs are summarized in Table 3 (as stated previously, aA refers to the probability that A will break the news next period, and ßA refers to the probability that A will find a link to another blog next period). As noted earlier, if blog A contains no link to
blog B, the consumer does not learn about the abilities of blog B and next period will choose between A and a random blog C.
Table 3 – Posteriors
Cases aA ßA aB ßB A breaks the news A links to B Prior A breaks the news No link if (L,L) or (L,DL) Prior otherwise --A fails to break the news A links to B Prior A fails to break the news No Link if (L,L) or (DL,L) Prior otherwise --
As can be seen in Table 3, the potential benefit of linking to another blog is that it credibly signals to the reader that the blogger can find news in other blogs. The potential cost is that the link is a recommendation that a rival is a news-breaking blog. Below we analyze when the potential benefit outweighs the costs. That is, when would we expect each equilibrium to hold? How is linking affected by the state of information: does a blogger who already obtained a news-breaking story have a higher or a lower incentive to link to another blog?
We start solving for the equilibrium by analyzing the reader’s problem when she chooses a blog to visit at t = 4. The perceived utility from a blog i at t = 4 is a function of whether the blog will either post a news-breaking item or will link to a news-breaking blog:
EUi =au + (1 -a )ß (u - c) +e = V +e (1)
i ii iii
where ai and ßi are the updated probabilities that the blog will either break the news or find the news respectively. Vi is the deterministic part of the expected utility. We assume that e is distributed with cumulative distribution function F.
Prob(A will be chosen over blog j) = Pr(ej-eA
V(d, u) -V(u,n) > V(d,d) - V(n,n) (7) That is, when A breaks the news, the difference between A (with a link to B) and B is greater than the difference between A (without a link) and a random blog C. The same holds when A is not able to break the news. Note that while we solve blogger A’s problems, here all bloggers are a priori identical and face the same problem. 2) In (L, DL), the blogger chooses to link only if he had broken the news:
V(u,u) -V(u,n) > V(u,d) - V(n,n) (6) V(d,u) -V(u,n) = V(d,n) - V(n,n) (8)
3) In (DL, L), the blogger chooses to link only if he had not broken the news: V(u,u) -V(u,n) = V(u, n) - V(n,n) (9) V(d,u) -V(u,n) > V(d,d) - V(n,n) (7)
4) In (DL, DL), the blogger never chooses to link:
V(u,u) -V(u,n) = V(u,n) - V(n,n) (9)
V(d,u) - V(u,n) = V(d,n) - V(n,n) (8) The expressions above can be also re-written in terms of the marginal benefit (increase in
own utility) and marginal cost (increase in rival’s utility) from linking. For example, (6) can be re-written as [V(u,u) - V(u,d)] -[V(u,n) - V(n,n)] > 0 , where [V(u,u) -V(u,d)] is the marginal benefit and [V(u,n) -V(n,n)] is the marginal cost of linking, while the difference between the two can be interpreted as the incentive to link.
Note that holding beliefs constant, a blogger has less incentive to link when he has broken the news. This is due to the fact that the marginal benefit from being perceived as more likely to be H-type on finding the news is lower since he is now perceived as being more likely to be H-type on breaking the news. This is of course due to the assumption that the information that can be found on the two blogs is substitutable. However, an added difficulty comes from the change in beliefs across the two states of information. For example, under the (L,DL) equilibrium, the reader’s inference following no link is more punishing if the blog had broken the news: the blog would have a bigger incentive to link if he had broken the news. Hence, these two forces may go in opposite directions. In fact, the different beliefs across different equilibria account for the fact that a priori we would expect there to be multiple equilibria in at least some regions.
Next, we describe the equilibria that exist in the different regions of the parameter space. In the Appendix we show the existence of all the sub-regions under certain parameters.
Proposition 1
The regions below (each with a different set of equilibria) partition the space. Region I: (6) holds, (8) does not hold, (9) holds: (DL, L) & (L,L) exist. Region II: (9) does not hold: (L,L). Region III: (6) does not hold, (8) holds, (7) holds: (DL,DL) & (DL, L). Region IV: (7) does not hold: (DL,DL). Region V: (6) does not hold, (8) does not hold: (DL,L). Region VI: (6) holds, (8) holds: all four equilibria exist.
As we can see, (L,DL), the equilibrium in which the blogger only chooses to link if he had broken the news, only occurs in region VI. Since this equilibrium is the only one which defies the intuition that the incentive to link is greatest if the blog had not broken the news, it is comforting to see that this equilibrium is relatively rare and is never unique. On the other hand, all other equilibria may be unique in certain regions.
Next we investigate when we expect to observe linking to occur. We illustrate the relative placement of the 6 regions above in the (v - w) - (p - q) space (see Figure 2). That is, we fix w and q, and vary v and p. By varying these two parameters we vary the informativeness of the signal associated with either breaking the news or with finding information in other blogs, which in turn changes the incentive to link as well as the resulting equilibrium. For example, if v and w are very close to each other, there is little difference between types on the ability to break the news. Hence, a link to another blog would not greatly move the prior on the other blog’s ability to break the news (marginal cost of linking is minimal). On the other hand, if p >> q , linking would greatly improve the prior on own ability to search for
news (marginal benefit of linking is high). The boundaries of the regions are defined by the isocurves derived from (6) – (9). That is, we define 6= as the equality where V(u, u) -V(u, n) = V(u,d) - V(n, n) (marginal benefit = marginal cost) and so on.
Proposition 2 summarizes facts about the relative placement of regions that we would expect to see across all values of w, q, u and c.
Figure 2: Equilibria
( .=d= 0.5, q = 0.2, w = 0.1, u = 10 , c = 1)
Proposition 2
6= and 9= are increasing in v; 8= and 7= are either increasing in v or are increasing and then , 9= 7=
decreasing in v. For all, 0 =q < p =" 1" 0 =" w" v =" 1" 6="," 8="," 7=";" 6="," 8=" and" 9="."> 0 .
UU0 U0 00
2) (DL, DL) is unique in the non-empty southeast region, described by: (1-a )(ß -ß )(u - c) - (a -a )[(1-ß )u +ß c] = 0 .
DUD U0 00
3) (DL, L) and (L,DL) exist between the two regions above.
As we can see, there always exists a region where (L,L) is unique: i.e. where blogs always prefer to link. The condition on this region states that if the blog prefers to link even if he broke the news and if the belief is not punishing following no-link, only (L,L) can exist. As we can see from Proposition 2 and from Figure 3, this occurs when p is high relative to v. That is, the signal on own ability to search is relatively more informative than the signal on rival’s ability to break the news: marginal benefit is higher than marginal cost. We can also see that (DL, DL) is unique in the region where v is high relative to p (here the blogger prefers not to link even if he did not break the news and if the belief is punishing following no-link). On the other hand, both (DL, L) and (L, DL) exist on the “margin” – v and p are relatively similar. That is, the cost and the benefit are relatively close to each other so that the differences in incentives depending on whether the blog broke the news and the differences in beliefs depending on whether a link is expected affects the desire to link.
One of the key implications of a linking equilibrium (that is, either (L,L), (DL,L) or (L,DL)) is that it enforces an internal quality monitoring system. Since the H-type on news-breaking ability blogs are more likely to generate a news-breaking story, they are also more likely to have incoming links. To illustrate, consider two blogs, C and D where C breaks the news with probability v and D breaks the news with probability w. The probability of obtaining an incoming link depends on the ability to produce information, as well as on other factors such as which equilibrium is being played, whether other blogs were able to break the news,
etc. All of these factors, with the exception of the probability of breaking the news, remain constant across the two blogs. The difference in the two blogs obtaining an incoming link is proportional to the difference in breaking the news. Thus, our model provides a micro-foundation for why incoming links may serve as a measure of quality. Figure 3 presents a snapshot of the blogosphere capturing this phenomenon.
From a consumer’s perspective linking increases the attractiveness of the blogosphere since links enable readers to locate information. From a blogger’s perspective outgoing links enable them to signal their ability to locate information. Hence, the desire to signal generates an incentive for blogs to engage in mutual monitoring to promote the better blogs. The quality monitoring system generated in this model is not the result of altruism; rather it is a by-product of the selfish behavior of blogs.
Figure 3 Snapshot of Blogosphere
Blogs with information;
Blogs without information; Arrows – Links.
3.3 Comparative Statics Next we examine how the incentive to link within an equilibrium changes with the level of heterogeneity across types and with changes in the delay cost c. It is important to investigate the effect of the former on the incentive to link since we motivated heterogeneity as a major
obstacle to finding information in blogs, and this allows us to examine whether the incentive to link coincides with the severity of the problem (when heterogeneity is greatest). Moreover, as with other Internet institutions, we may expect there to be a consolidation in the blogosphere, which may in turn lead to a decrease in blog heterogeneity. Changing the latter (c) allows us to compare the incentive to link online and offline.
Increasing the heterogeneity between types echoes the analysis we performed for Proposition 2. However, while before we looked at the changes in incentives to link across equilibria, here we look at the change within in equilibrium. In addition, here we perform a slightly different exercise. Before we changed v (p): the probability that the high type breaks the news (finds breaking news in other blogs). This changes the prior probability that a blog breaks the news and changes the posterior probability that a blog breaks the news following either a positive signal or a negative signal. Here we spread the posterior probabilities but keep the prior fixed, which allows us to concentrate purely on the change in learning associated with the signal. That is, we compare the incentive to link under (p,q) and
(p'=p +.,q'= q -.) where . is a small change; and under
(v, w) and (v'= v +., w'= w -. ). Finally, we examine how the incentive to link changes with c. The findings are summarized below:
Proposition 3
1. The incentive to link is higher under (p',q') than under (p,q) . 2. If the blog had broken the news, the incentive to link is lower under (v', w') than under (v, w) . 3. If the blog had not broken the news, • If either (L,L) or (DL,L) is being played, the incentive to link under a(1-ß )u +ß c0 00
(v', w') is lower iff < t="4," the ="Sjexp(V" s =" ln(exp(V"> (a -a )[(1-ß )u +ß c] (6)
UUD U0 00
(1-a)(ß -ß )(u - c) > (a -a )[(1-ß )u +ß c] (7)
DUD U0 00
2) (L, DL): (1-a)(ß -ß )(u - c) > (a -a )[(1-ß )u +ß c] (6)
UUD U0 00
(1-a)(ß -ß )(u - c) = (a -a )[(1-ß )u +ß c] (8)
DU0 U0 00
3) (DL, L): (1-a)(ß -ß )(u - c) = (a -a )[(1-ß )u +ß c] (9)
UU0 U0 00
(1-a)(ß -ß )(u - c) > (a -a )[(1-ß )u +ß c] (7)
DUD U0 00
4) (DL, DL): (1-aU )(ßU -ß0 )(u - c) = (aU -a0 )[(1-ß0 )u +ß0c] (9)
(1-aD )(ßU -ß0 )(u - c) = (aU -a0 )[(1-ß0 )u +ß0c] (8)
.v2 + (1-.)w 2 .v(1- v) + (1-.)w(1- w)
a0 =.v + (1-.)w , aU =aD = ,
.v + (1-.)w .(1- v) + (1-.)(1- w) dp2 + (1-d)q2 dp(1- p) + (1-d)q(1- q)
ß0 =dp + (1-d)q , ßU = ,ßD = .
dp + (1-d)q dp(1- p) + (1-d)q(1- q)
Here aU >a >aD and ß >ß >ß . Since there are 4 different constraints categorizing
0 U0D
the equilibria above, there theoretically could be up to 16 different regions. However, the constraints are not independent. We can show that (6) holds .. (7) holds, (6) does not hold .. (9) holds, (8) holds .. (9) holds, (8) does not hold .. (7) holds. Below we provide a partition of the space and describe which equilibria hold in each region:
a) Suppose (6) holds and (8) does not hold. (8) does not hold .. (DL, DL) and (L, DL) can be ruled out. (6) holds .. (7) holds. Thus, if, in addition, (9) holds .. (L,L) and (DL,L) exist. If, however, (9) does not hold .. only (L,L) exist. b) Suppose (6) does not hold and (8) holds. (6) does not hold .. (L,L) and (L,DL) can be ruled out. (6) does not hold .. (9) holds. Thus, if (7) holds .. (DL, DL) and (DL,L) exist. If (7) does not hold .. only (DL,DL) exists. c) Suppose that (6) holds and (8) holds. (6) holds .. (7) holds. (8) holds .. (9) holds. Here all four equilibria hold. d) Suppose that (6) does not hold and (8) does not hold. (6) does not hold rules out (L,L) and (L, DL). (8) does not hold .. (DL,DL) is ruled out. (6) does not hold .. (9) holds. (8) does not hold .. (7) holds. Thus, only (DL,L) exists.
Below we summarize the regions as well as provide a numerical example to show that the regions are not empty: (Assume that u=10, d=0.5, .=0.5 for the numerical examples) Region I: (6) holds, (8) does not hold, (9) holds: (DL, L) & (L,L) exist. Example: c=0, v=0.8, w=0.2, p=0.8, q=0.2. Region II:(6) holds, (8) does not hold, (9) does not hold: (L,L). Also note that (9) does not hold .. (6) holds and (8) does not hold, so it is sufficient to describe the region by stating that (9) does not hold. E.g.: c=0, v=0.3, w=0.2, p=0.8, q=0.2. Region III: (6) does not hold, (8) holds, (7) holds: (DL,DL) & (DL, L). E.g.: c=5, v=0.95, w=0.2, p=0.95, q=0.2. Region IV: (6) does not hold, (8) holds, (7) does not hold: (DL,DL). Note that (7) does not hold .. (6) does not hold and (8) holds, so it is sufficient to describe the region by stating that (7) does not hold. E.g.: c=6, v=0.95, w=0.2, p=0.95, q=0.2.
Region V: (6) does not hold, (8) does not hold: (DL,L). E.g.: c=2, v=0.95, w=0.2, p=0.95, q=0.2 Region VI: (6) holds, (8) holds: all four equilibria exist. E.g.: c=5, v=0.5, w=0.3, p=0.3, q=0.2.
Proposition 2
6=, 9=, 8= and 7= are the iso-curves of the inequalities (6) – (9) in the v -p plane. That is, if f = (1-a )(ß -ß )(u - c) - (a -a )[(1-ß )u +ß c]
6 UUD U0 00
f = (1-a )(ß -ß )(u - c) - (a -a )[(1-ß )u +ß c]
7 DUD U0 00
f = (1-a )(ß -ß )(u - c) - (a -a )[(1-ß )u +ß c]
8 DU0 U0 00
f = (1-a )(ß -ß )(u - c) - (a -a )[(1-ß )u +ß c]
9 UU0 U0 00
6= is defined as f6 = 0 ; 7= is defined as f7 = 0, and so on. The derivatives of the iso-curve are obtained using the implicit function theorem and are:
dv dp 6 = - dp df dv df 6 6 = (dp )d(c))(u(1 (u[u dv d c))(u( U DU U 0 U DU + a- ßß-- a - ß+ a-- ßß dp d c))(u dv )d(c)] 0 0 0U ß-- a - aa- dv dp 7 = - - dp df dv df 7 7 = (dp )d(c))(u(1 (u[u dv d c))(u( U DU D 0 D DU + a- ßß-- a - ß+ a-- ßß dp d c))(u dv )d(c)] 0 0 0U ß-- a - aa- dv dp 8 = - - dp df dv df 8 8 = (dp )d(c))(u(1 (u[u dv d c))(u( U 0U D 0 D 0U + a- ßß-- a - ß+ a-- ßß dp d c))(u dv )d(c)] 0 0 0U ß-- a - aa-
df da d(a -a )
9 UU0
(ß -ß )(u - c) + [u -ß (u - c)]
U0 0
dp
dvdv dv
=-- =
9 df9 d(ßU -ß0) dß0
dv
(1-a )(u - c) + (a -a )(u - c)
U U0
dpdp dp
where all the following terms are positive:
da.[.(v - w)2 + (2v - w)w] d(a -a ) .(1-.)(v - w)[.(v - w) + 2w]
U U0
= 2 > 0 , = 2 > 0
dv [.v + (1-.)w] dv[.v + (1-.)w] d(ßU -ß0) d(1-d)(p - q)[d(p - q) + 2q]
=> 0
dp [dp + (1-d)q]2 dß d(ß -ß ) d(1-d)(p - q)[2(1- q)q +d(p - q)(1- 2q)]
0 UD
=d> 0 , = 22 > 0
dp dp[dp + (1-d)q] [d(1- p) + (1-d)(1- q)] daD .{1+.v2 - (1-.)w 2 - 2v[1- (1-.)w]}
The only possible negative term is, = 2 .
dv [.(1- v) + (1-.)(1- w)] da D
is negative when the numerator is negative. Solving for the roots of the numerator,
dv
1- w +.w - 1-.- 2w + 2.w + w2 -.w2
v1 =.
1 - w +.w + 1-.- 2w + 2.w + w2 -.w2
v =
2 .
The first root is always positive and lies between 0 and 1. The second root is also always
da D
positive but lies above 1, and hence is excluded from the analysis. Hence, is positive
dv
for v
, the numerator could become negative. So,
and
are
dv
dv
dv7 dv8
always increasing for small values of v (till v1 ) and may decrease after that.
Relative Positions of the Iso-curves
We can show that the left-hand-sides of 6=, 7=, 8=, and 9= are increasing in p. Thus, if f (p, v) > g(p, v) Æ g(p, v) =0 lies above f (p, v) =0 in the v -p plane ( f (p, v) =g(p', v) = 0 where p'> p ). We can also show that the LHS of 6= is always greater than the LHS of 9= .. 9= lies above 6=. Similarly, LHS of 6= < 7="," 6=" lies" 7="." 7=" "> 8= .. 8= always lies above 7=. In summary, 1) (L, L) exists above 6= and (DL, L) exists between 9= and 7=. Since, 9= lies above 6=, both
(DL, L) and (L, L) exist between 9= and 6=, whereas (L, L) uniquely exists above 9=. Since 9= goes through the origin (v = w, p = q) and has a positive slope, the region where (L,L) is unique is non-empty.
2) (DL, DL) exists below 8= and (DL, L) exists between 9= and 7=. Since 7= lies below 8=, both (DL, L) and (L, L) exist between 8= and 7=, whereas (DL, DL) uniquely exists below 7=. Since goes through the origin (v = w, p = q) and has a positive slope for small v, the region where (DL,DL) is unique is non-empty.
3) (DL, L) exists between unique regions of (L, L) and (DL, DL), i.e. in between 9= and 7=.
Proposition 3
22 22
v + w (v +.) + (w -.)
a =a '= 0.5v + 0.5w , a= , a '=
00 UU
v + wv + w v(1- v) + w(1- w) (v +.)(1- v -.) + (w -.)(1- w +.)
aD = , aD'=
2 - (v + w) 2 - (v + w)
22 22
p + q (p +.) + (q -.)
ß0 =ß0'= 0.5p + 0.5q , ßU = ,ßU'=
p + qp + q p(1- p) + q(1- q) (p +.)(1- p -.) + (q -.)(1- q +.)
ß= ,ß '=
D2 - (p + q)D 2 - (p + q) - 2.(v - w) - 2.22.(v - w) + 2.2
Also, aD'-aD =< au =""> 0 ,
2 - (v + w) v + w 4.(p - q) + 4.2
(ß '-ß ') - (ß -ß ) => 0
UD UD
[2 - (p + q)][p + q] The incentive to link are defined by a subset of f6 , f7 , f8 , and f9 , depending on which equilibrium is under consideration.
We can show that the incentive to link is always higher under (p',q') than under (p,q) : 4e(p - q) + 4e2
f6 (p', q') - f6 (p, q) = [(ßU'-ßD') - (ßU -ßD )](1 -aU )(u - c) = (1 -aU )(u - c) > 0
[2 - (p + q)][p + q]
4.(p - q) + 4.2
f7 (p', q') - f 7 (p, q) = [(ßU'-ßD') - (ßU -ßD )](1 -aD )(u - c) = (1 -aD )(u - c) > 0
[2 - (p + q)][p + q]
2.(p - q) + 2.2
f8 (p', q') - f8 (p, q) = [(ßU'-ß0') - (ßU -ß0 )](1 -aU )(u - c) = (1 -aD )(u - c) > 0
p + q 2.(p - q) + 2.2
f9 (p', q') - f9 (p, q) = [(ßU'-ß0') - (ßU -ß0 )](1 -aU )(u - c) = (1 -aU )(u - c) > 0
p + q To compare the incentive to link under (v',w') and under (v,w) f (v',w') - f (v, w) = (a -a ')[(ß -ß )(u - c) + (1 -ß )u +ß c] =
6 6 UUUD 00
- 2.(v - w) - 2.2
= [(ßU -ßD )(u - c) + (1 -ß0 )u +ß0c] < 2 =" (ßU" 2 =" {a" 000 =" exp(ß" a =".v" a=" B"> 0
0U 0
.v + (1-.)w .aU vw(v - w) .a0
and
v - w
.. = 2 .. =
(.v + (1-.)w) vw
F'(.) = B(v - w) exp(ß0 (u - c)){exp(aUB) - exp(a0B)}(.v + (1 -.)w)2
vw vw
Let . * be s.t. = 1. We can see that for .<. * , > 1
(. *v + (1-.*)w)2 (.v + (1-.)w)2 .a
.a vw .a
U0 U0
) and for .=. * , = 1 ( .. =.a ).
..
( ..> .. (.v + (1-.)w)2
41
Due to this and to the fact that exp(aaUB) > exp(a0B) , for all .<. * , F'(.) > 0 . Since F'(.= 1) <>. * , F'(.) = 0 only once. Suppose that .* <.1 <. 2 and vw F'(. ) = F'(. ) = 0 . That is, exp(a (. )B) = exp(a (. )B)} and 12 U101 (.1v + (1 -.1)w)2 vw exp(a (. )B) 2 = exp(a (. )B)}. Taking the ratio of these two U2 02 (. 2v + (1 -.2 )w) expressions yields: (.1v + (1 -.1)w)2 exp((a (. ) -a (. ))B) 2 = exp((a (. ) -a (. ))B)} . Since .1 <.2 , U2U1 0201 (.2v + (1 -.2 )w) (.1v + (1-.1)w)2 2 <>a0(.2) -a0(.1) . However, this is a
(.2v + (1-.2 )w)
contradiction since in this domain .aU .. =.a0 . Hence, F'(.) > 0 for .ˆ <.
.. (where .* <.ˆ < 1 ) and F'(.) = 0 for .ˆ =. : F is strictly increasing and then strictly decreasing in . . b) This part is shown in the text before Proposition 4 in the text.
