Influencer Cartels*
Marit HinnosaarToomas Hinnosaar

August 19, 2024

Abstract
Social media influencers account for a growing share of marketing worldwide.
We demonstrate the existence of a novel form of market failure in this advertising market: influencer cartels, where groups of influencers collude to increase theiradvertising revenue by inflating their engagement. Our theoretical model showsthat influencer cartels can improve consumer welfare if they expand social media
engagement to the target audience, or reduce welfare if they divert engagement toless relevant audiences. We validate the model empirically using novel data on influencer cartels combined with machine learning tools, and derive policy implications
for how to maximize consumer welfare.

JEL: L82, M31, D26, L14
Keywords: influencers, marketing, collusion, Natural Language Processing, Large
Language Models, Latent Dirichlet Allocation

1

Introduction

Collusion between a group of market participants to improve their market outcomesis typically considered an anti-competitive behavior. While some forms of collusion,* We thank Daniel Ershov, John Horton, Dina Mayzlin, Matt Mitchell, Johanna Rickne, Stephen P.

Ryan, Stephan Seiler, Egor Starkov, and seminar participants at University of East Anglia, Universityof Leicester, University of Nottingham, Collegio Carlo Alberto, Mannheim Virtual IO Seminar, UK
Competition and Markets Authority, 12th Paris Conference on Digital Economics, IIOC, Munich Summer Institute, Baltic Economics Conference, Australasian Meeting of the Econometric Society, NBER
Summer Institute on IT and Digitization, Econometric Society European Meeting, EARIE, NIE Annual
Conference, 13th Workshop on the Economics of Advertising and Marketing, Bristol-Warwick Empirical
IO Workshop, Berlin IO Day, 6th Monash-Warwick-Zurich Text-as-Data Workshop, CESifo Economics
of Digitization Conference, and Text-as-Data in Economics Workshop in Liverpool for helpful comments
and suggestions. First draft: February 12, 2021.
 University of Nottingham and CEPR, marit.hinnosaar@gmail.com
University of Nottingham and CEPR, toomas@hinnosaar.net

1

such as price-fixing, are illegal in most countries, new industries provide new collusion
opportunities for which regulation is not yet well-developed. In this paper, we study one
such industry—influencer marketing. Influencer marketing combines paid endorsements
and product placements by influencers. It allows advertisers fine targeting based on
consumer interests by choosing a good product-influencer-consumer match. Influencer
marketing is a large and growing industry, with 31 billion U.S. dollars in ad spending in
2023, it is almost as large as the print newspaper advertising.1
Many non-celebrity influencers are not paid based on the success of their marketing
campaigns; instead, their compensation depends on past engagement.2 This gives incentives for fraudulent behavior—for inflating their influence. Inflating one’s influenceis a form of advertising fraud that leads to market inefficiencies by directing ads to thewrong eyeballs. An estimated 15% of influencer marketing spending was misused due
to exaggerated influence.3 To address this problem, the U.S. Federal Trade Commission
in 2023 proposed a new rule that would prohibit selling and buying false indicators ofsocial media influence, such as fake followers or views.4 In this paper, we study a wayof obtaining fake engagement that does not directly fall under the proposed rule, but
is in the same spirit. We study influencer cartels where groups of influencers collude
to increase each others’ indicators of social media influence. While there is substantial
literature in economics on fake consumer reviews (Mayzlin et al., 2014; Luca and Zervas,
2016; He et al., 2022; Glazer et al., 2021; Smirnov and Starkov, 2022) and other forms ofadvertising fraud (Zinman and Zitzewitz, 2016; Rhodes and Wilson, 2018), the economicsof this fraudulent behavior has not been studied.
We study how influencers collude to inflate engagement, and the conditions underwhich influencer cartels can be welfare-improving. Our research makes three key contributions. First, we develop a new theoretical framework for influencer cartels, a settingthat has not been studied before. Second, we use a novel dataset of influencer cartels andmachine learning tools to generate engagement quality measures from text and photos.
Third, for each type of cartel, we estimate whether it is likely to be welfare-improving or
not. We document that general interest cartels generate lower-quality engagement than
topic-specific ones, which are closer to natural engagement. This suggests that narrow,
1

Source: https://www.statista.com/outlook/amo/advertising/worldwide, accessed March 17,
2024.
2
While influencers with large followings are typically paid based on campaign success (tracked throughsales from personalized links or coupons), only 19% of firms employing influencer marketing tracked sales
as of 2020 (ANA, 2020).
3
Source: https://en.wikipedia.org/wiki/Influencer_marketing, accessed April 6, 2024.
4
Source: Federal Trade Commission, June 30, 2023, ”Federal Trade Commission Announces Proposed
Rule Banning Fake Reviews and Testimonials”, https://www.ftc.gov/news-events/news/pressreleases/2023/06/federal-trade-commission-announces-proposed-rule-banning-fakereviews-testimonials, accessed March 18, 2024.

2

topic cartels could improve welfare, while general interest cartels are detrimental to all
involved.
In an influencer cartel, a group of influencers colludes to inflate their engagement, inorder to increase the prices they can get from advertisers. Like in traditional industries,
influencer cartels involve a formal agreement to manipulate the market for members’ benefit. In traditional industries, the agreement typically involves price fixing or allocating
markets.5 Influencer cartels involve a formal agreement to inflate the engagement measures to increase their prices. Instead of smoky backroom deals, influencer cartels operate
in online chat rooms or discussion boards, where members submit links to their content
for additional engagement. In return, they must engage with other members’ content by
providing likes and comments. An algorithm enforces the cartel rules.
Our theoretical model focuses on the key market failure in this setting—the freerider problem. Engaging with other influencers’ content brings attention to someone
else’s content, creating a positive externality. Without cartels, influencers do not engage
with each others’ content enough, because they do not internalize the externality. A
cartel could lessen the free-rider problem by internalizing the externality. By joining
the cartel, influencers agree to engage more than the equilibrium engagement. They getcompensated for this additional engagement by receiving similar engagement from othercartel members. If the cartel only brings new engagement from influencers with closely
related interests, this could benefit cartel members but also consumers and advertisers.6
However, the influencer cartel can also create new distortions. The cartel may overshootand create too much low-quality engagement. The low-quality engagement may hurt all
involved parties, consumers, advertisers, and indirectly, even the influencers themselves.
The dimension that separates socially beneficial cooperation from welfare-reducing
cartels is the quality of engagement. By high quality we mean engagement coming frominfluencers with similar interests. The idea is that influencers provide value to advertisers
by promoting the product among people with similar interests, e.g., vegan burgers tovegans. If a cartel generates engagement from influencers with other interests (e.g.,meat-lovers), this hurts consumers and advertisers. Consumers are hurt because theplatform will show them irrelevant content, and advertisers are hurt because their ads
are shown to the wrong consumers. Whether or not a particular cartel is welfare-reducing
or welfare-improving is an empirical question.
In our empirical analysis, we combine data from two sources: cartel interactions from
Telegram and data from Instagram. Our cartel data allows us to directly observe cartel
activity (not predict or estimate it). We observe which Instagram posts are included in
5

Collusion in cartels doesn’t always occur via fixing prices or output (Genesove and Mullin, 2001).
Even in traditional industries, collusion can sometimes be socially desirable (Fershtman and Pakes,
2000; Deltas et al., 2012).
6

3

the cartel and which engagement originates from the cartel (via cartel rules).7 Our dataset
includes two types of cartels differentiated by cartel entry rules: three topic cartels that
only accept influencers posting on specific topics and six general cartels with unrestricted
topics.8
We use machine learning to analyze text and photos from Instagram to measure engagement (match) quality. Our goal is to compare the quality of natural engagement tothat originating from the cartel. We measure the quality by the topic match between thecartel member and the Instagram user who engages. To quantify the similarity of Instagram users, first, we use a Large Language Model (Language-agnostic BERT Sentence
Embedding) and an analogous large neural network for text and photos (Contrastive
Language Image Pre-training model) to generate numeric vectors (embeddings) from thetext and photos in Instagram posts. Then we calculate cosine similarity between theusers based on these numeric vectors. To compare the quality of natural engagement tothat originating from the cartel, we estimate a panel data fixed effects regression, where
the outcome variable is the cosine similarity of the cartel member to the users engaging with their content. To further analyze the topic match of influencers and users who
engage with their content, we use the Latent Dirichlet Allocation model to map each
Instagrammer’s content to a probability distribution over topics.
We find that engagement from general cartels is significantly lower in quality compared to natural engagement. Specifically, the quality of engagement from these cartels
is nearly as low as that from a counterfactual engagement from a random Instagramuser. In contrast, engagement from topic cartels is much closer to the quality of natural
engagement. Our back-of-the-envelope calculations show that if an advertiser pays for
cartel engagement as if it is natural engagement, they only get 3–18% of the value in thecase of general cartels and 60–85% in the case of topic cartels. Our results are robust toalternative ways to construct outcome variables and alternative samples. Our estimatesalso validate our outcome measures: advertisers are known to pay higher fees for moreengagement, and we show that users with higher similarity are more likely to engage.
This implies our similarity measures capture what advertisers value.
Our empirical and theoretical results have three policy implications. First, as generalcartels are likely to be welfare-reducing, shutting these cartels down would be socially7

The ability to directly observe cartel activity is rather unique. Most studies of cartels in traditional
industries have to rely on either historical data of known cartels from the time cartels were legal (Porter,
1983; Genesove and Mullin, 2001; Röller and Steen, 2006; Hyytinen et al., 2018, 2019) or data from thecourt cases (Igami and Sugaya, 2022), including bidding-rings in auctions (for example, Porter and Zona
(1993); Pesendorfer (2000); Asker (2010); Kawai et al. (2022)), for an overview see Marshall and Marx
(2012).
8
To make the results comparable, we only study cartels by the same cartel organizer; they all runon the same platform and have the same engagement requirements. The cartels differ only in entry
requirements: some cartels have topic restrictions, while others have minimal follower requirements.

4

beneficial. Second, regulatory rules that prohibit buying and selling fake social media
indicators should also prohibit obtaining these fake indicators via in-kind transfers, i.e.,
paying for engagement with engagement. Third, the current practice of advertisers to
reward past engagement encourages harmful collusion. A better approach would be tocompensate influencers based on the actual value they add.9 Alternatively, platforms
could improve the outcomes by reporting match-quality-weighted engagement.
The trade-offs studied in this paper arise in other settings. Academics citing otherworks create a positive externality for the cited authors. Since the citing authors do
not internalize this externality, there are not enough citations in equilibrium. Forming agroup that agrees to cite each others’ papers helps the participants of the group. Whether
this is helpful to readers depends on how closely related the group members’ topics are. If
the group members work on similar issues, agreeing to cite each others’ papers a bit moremight be helpful even for the readers. However, agreeing to cite unrelated papers does
not help readers to find relevant works. There is evidence of such agreements in academic
journals (Franck, 1999; Van Noorden, 2013; Wilhite and Fong, 2012). Due to anomalous
citation patterns, Thomson Reuters regularly excludes journals from the Impact Factor
listings.10 In contrast to journal citation cartels, where explicit agreement data is limited,the collusion and outcomes are directly observable in influencer cartels. The literature
on patents documents similar trade-offs. Lampe (2012) shows that patent applications
strategically withhold citations. To overcome the free-rider problem, firms have formed
patent pools—agreements to cross-license their patents (Lerner and Tirole, 2004; Moser,2013).
Our paper adds to the literature on social media and attention (for an overview,
see Aridor et al. (2024)). While the literature on social media has extensively studied
the consumption and production of social media content, there is less work on strategic
engagement, which is the strategic choice of which content to engage with. Our paper ismost closely related to Filippas et al. (2023), who uses Twitter data to study attention
bartering. Similarly to our paper, they model social media users’ decision to engage(in their setting, whether to follow other users). Our theoretical model of influencer
engagement and advertisement builds on classic models of product differentiation (Salop,1979) and models of attention and advertising (Anderson and Coate, 2005; Anderson andde Palma, 2012; Anderson and Peitz, 2023). Unlike all these papers, we focus on theusers’ agreement to collude when deciding whether to engage.
Our paper adds to a small but growing literature in economics on influencer marketing. The empirical literature has analyzed advertising disclosure (Ershov and Mitchell,
9

In recent years, such contracts have become more common.
Source: https://jcr.help.clarivate.com/Content/title-suppressions.htm, accessed April 6,
2024.
10

5

2023; Ershov et al., 2023), while the theoretical literature has studied the benefits ofmandatory disclosure (Pei and Mayzlin, 2022; Mitchell, 2021; Fainmesser and Galeotti,
2021), the prioritization of content (Szydlowski, 2023), and social learning with influencemotivated agents (Song, 2024). In contrast to these papers, we study collusion between
the influencers. Influencer cartels have been studied qualitatively in marketing and media
studies (O’Meara, 2019; Cotter, 2019; Miguel et al., 2022) and quantitatively in computerscience (Weerasinghe et al., 2020). None of these papers study the economics and welfare
implications of influencer cartels.
In our empirical analysis, we build on the recent literature in economics that uses
text and photos as data.11 In particular, we use Large Language Models and large neuralnetworks to generate embeddings from text and photos. Large Language Models withsocial media data have been used in economics before, for example, by Ershov et al.
(2023). We also use the Latent Dirichlet allocation model (Blei et al., 2003), which has
been recently used in economics, for example, to extract information from Federal Open
Market Committee meeting minutes (Hansen et al., 2018). We combine these tools withthe use of the cosine similarity index. This and other similarity indexes have been used
as quality measures in economics, for example, by Chen et al. (2023) and Hinnosaar et al.
(2022). While many studies have made use of text as data, using photos is still rare ineconomics (examples include Adukia et al. (2023); Ash et al. (2021); Caprini (2023)).12
As Instagram as a platform is primarily used to share photos, extracting informationfrom photos is particularly important in our setting.
The rest of the paper is organized as follows. In the next section, we provide someinstitutional details of influencer marketing and influencer cartels. Section 3 introduces
the theoretical model and discusses the welfare implications of influencer cartels. Section 4
describes the dataset used in our analysis. Section 5 presents the empirical results.
Section 6 discusses the policy implications. Section 7 concludes.

2

Influencer Marketing and Influencer Cartels

In influencer marketing, firms pay influencers for product placement and product endorsement. Compared to TV or newspaper advertising, influencer marketing allows finetargeting, generating a great product and influencer match, and hence, a great productand consumer match. Influencer marketing is a large industry: in 2023, influencer marketing ad spending was about $31 billion, which is close to the ad spending for print
11

For recent surveys of the uses of text as data in economics, see Gentzkow et al. (2019); Ash and
Hansen (2023).
12
One exception is the use of satellite images mostly in development economics, and typically, tomeasure electricity use, air pollution, land use, or natural resources (Donaldson and Storeygard, 2016).

6

newspaper ads. Instagram is one of the leading platforms for influencer marketing. It is aplatform where users share photos and videos, engage with other users’ content by liking
and commenting on their posts, and follow other users to see more of their content.
Many influencers are not compensated based on the actual success of their current
marketing campaigns but rather on past engagement, such as comments and likes fromprevious posts. This payment model encourages fraudulent behavior, including inflating
one’s influence. An estimated 15% of influencer marketing spending is misused due
to exaggerated influence.13 While influencers with large followings are typically paid
based on campaign success (tracked through sales from personalized links or coupons),
only 19% of firms employing influencer marketing tracked sales as of 2020 (ANA, 2020).
Instead, most smaller influencers receive payment before a campaign begins based on
their historical influence metrics. Originally, Instagram influencers were compensatedbased on follower count, which led to the acquisition of fake followers. The industry
responded by starting to detect fake followers and measure genuine engagement throughlikes and comments. There are alternative ways of generating fake engagement. Somefake engagement is generated by automatic bots, which are relatively easy to detect. In
this paper, we study a more challenging type of fraud: Instagram cartels, where realhumans create real engagement that mimics natural interactions, making it difficult todistinguish from genuine engagement.
Instagram influencer cartels. In Instagram influencer cartels, influencers collude
to inflate each other’s engagement in order to increase the prices they can get fromadvertisers. As the cartels’ activity of artificially increasing engagement is fraudulent,
the groups are secret. Instagram considers these groups to be violating Instagram’s
policies.14
How do the influencer cartels operate? They operate on other online platforms, either
in a chat room or a discussion board (typically on Telegram or Reddit).15 In the chatroom, members of the cartels submit links to their Instagram content for which theywould like to receive additional engagement. In order to receive that engagement, they
themselves must engage with a fixed set of links submitted by other users. Specifically,
before submitting a link themselves, they must like and write meaningful comments toprevious N posts from other members. The rules of the cartel are enforced automatically13

Source: https://en.wikipedia.org/wiki/Influencer_marketing, accessed August 19, 2024.
Source: Devin Coldewey, Apr 29, 2020, “Instagram ‘pods’ game the algorithm by coordinating likes
and comments on millions of posts”, TechCrunch. https://techcrunch.com/2020/04/29/instagram-pods-game14

the-algorithm-by-coordinating-likes-and-comments-on-millions-of-posts/.
15

For more details, see a computer science overview of Instagram cartels operating on Telegram(Weerasinghe et al., 2020) or for example: Apr 9, 2019 “Instagram Pods: What Joining One Could Do For
Your Brand”, Influencer Marketing Hub. https://influencermarketinghub.com/instagram-pods/.

7

by an algorithm.
The cartel increases engagement via both direct effect and indirect effects. The direct
effect is the cartel members engaging with each other’s posts. This additional engagement generates two types of indirect effects. First, the Instagram algorithm gives higher
exposure to posts with higher engagement, leading to even more engagement. Second,an influencer engaging with another user’s post increases the likelihood of it being shown
to its followers. This happens as the Instagram algorithm is more likely to show posts
that the user’s social network has engaged with, that is, posts that the users who theuser follows have commented on or liked.16
The cartels in our sample operate in Telegram chatrooms and advertise themselves asa way to ”attract lucrative brand partnerships” (see screenshots in Online Appendix A1).
The cartels in our sample have the requirement that before submitting a post, the member must like and write comments to the last five posts submitted by other members.
The process ensures that each post receives five likes and comments when submitted.
Figures A1.3 and A1.4 in Online Appendix show an example of a post submitted to thecartel receiving the required comments. The rules are enforced by an algorithm that
deletes submissions by users who don’t follow the rules. The cartels in our sample haveentry requirements: either thresholds for the minimum number of followers (ranging from
1,000 to 100,000 followers) or restrictions on the topics of the posts.
A natural question is how widespread influencer cartels are. This question is difficult
to answer conclusively, as the goal of influencers joining the cartel is to receive engagementthat is indistinguishable from natural engagement. The answer to the question also
depends on the interpretation. Many social media users have helped their friends andfamily to boost their social media profiles with comments and likes. Such engagement
has similar characteristics to cartel engagement.
Formal influencer cartels have caught the interests of influencer marketing practioners,
academic researchers, media, and Instagram itself. The influencer cartels are commonly
called “influencer pods”, “engagement pods”, or “Instagram pods”. Influencer market
practitioners have debated the pros and cons of joining these groups.17 Influencer cartels have been studied by academic researchers in media studies (O’Meara, 2019; Cotter,2019), marketing (Miguel et al., 2022), and computer science (Weerasinghe et al., 2020).
In 2018, after inquiry by journalists, Instagram closed down influencer cartels with hundreds of thousands of members.18
16

Figure A1.5 in Appendix A1 shows a screenshot of an Instagram post that was suggested to the user
because the user’s friend has liked it.
17
Source: https://influencermarketinghub.com/glossary/instagram-pod/, accessed August 19,
2024.
18
Source:https://www.buzzfeednews.com/article/alexkantrowitz/facebook-removes-teninstagram-algorithm-gaming-groups-with, accessed August 19, 2024.

8

3

Theoretical Model

To build intuition, we present the theoretical results in three steps. We start with a basicmodel of influencer engagement without collusion and the advertising market. We then
add collusion and, finally, the advertising market. Our focus is solely on engagement
between influencers, we abstract away from all other aspects of influencer marketing,including content creation. All proofs are in appendix A2.

3.1

Basic Model

We assume that there is an infinite sequence of players (influencers), indexed by t ∈{−∞, . . . , −1, 0, 1, . . . , ∞}. Player t is characterized by two-dimensional type (αt , Rt ).19
The first parameter αt captures the topic, which we model as Salop (1979) circle, it
is an angle from 0◦ to 360◦ on the circle. The second parameter is the player’s reachRt ≥ 1, which measures how many people the player’s content regularly reaches (numberof followers and typical search traffic). The distribution of topics is assumed to be uniform
and reach has a power law distribution with mean 2. That is, the probability density
function is f (Rt ) = 2Rt−3 .20 Both parameters are independent draws from corresponding
distributions.
In this analysis, we focus on engagement. Player t has a piece of content and chooses
between two actions at ∈ {0, 1}: to engage with the previous player’s content at = 1
or not to engage at = 0. This can be thought of as a wall of content and the choice iswhether to like and comment the previous post or not. We normalize all payoffs without
engagement to zero.
Player t’s choice to engage creates a social benefit and a social cost. We think of
the benefit as providing information and entertainment to the audience and the costas attention by the audience. The cost and benefit are both proportional to reach Rt ,which measures the size of the audience. Both are also function of the topic differenceof the influencer and the content she is engaging with. If the topics are similar, then thebenefit is high and cost is low. If the topics are different, then the cost is high and thebenefit is low.21 We model the cost and benefit separately, because we need to model the19

Our treatment of player types is inspired by conventional wisdom in influencer marketing practice(Burns, 2020), which emphasizes the importance of “three R’s”: (1) Relevance: how relevant is thecontent to the audience, (2) Reach: the number of people the content could potentially reach, and (3)Resonance: how engaged is the audience. We model the first one as αt and combine the latter two into
Rt , which we call reach for brevity.
20
The uniform assumption for the topic is the standard in literature since Salop (1979). Power law
distribution is a natural assumption for reach as it is the prevalent distribution for the number of readers,followers, comments (Gabaix, 2016). The mean 2 assumption is for tractability.
21
We do not explicitly model the mechanisms that generate these costs and benefits. For example,
Figure A1.5 in Appendix A1 shows that Instagram suggests posts to users based on their friends’ likes.

9externality.22
Specifically, we assume that the social benefit is Rt cos(∆t ), where ∆t = |αt − αt−1 |is the difference between players’ t and t − 1 topics.23 If ∆t is close to 0◦ (so thatcos(∆t ) = 1), the players’ content is on similar topics, whereas if the difference is close
to 90◦ their content is unrelated (cos(∆t ) = 0), and if it is close to 180◦ the content is
contradictory (e.g. political content, then we can have cos(∆t ) = −1).24 The engagement
generates also a social cost Rt C(∆t ), where C(∆) = sin(∆) for all ∆ ≤ 90◦ and 1
otherwise.25 Formally, the social welfare generated by action at by player t with reach Rt
and topic difference ∆t with the previous player t − 1, is
Wt (at ) = at Rt cos(∆t ) −at Rt C(∆t ) .
| {z }| {z }
Benefit(1)

Cost

The costs and benefits of engagement are divided asymmetrically between players. We
assume that players capture a constant fraction β of social costs and benefits. As factor
β multiplies all payoffs related to engagement, without loss in generality we normalize β
to one. If a player engages with previous content, then only she pays the cost, but thebenefits are divided between the creator of the content and the one who engages. Theseassumptions capture the long-term relationships with the audience. If the influencer
engages with content that her audience is not interested in, she incurs the full cost of
misdirected attention. It captures the idea that her followers will pay less attention to
her future content, they may even stop following her. On the other hand, the influencer
who engages gets only a fixed fraction γ < 1 of the benefit, the remaining 1 − γ goesto the content creator. Thus, engagement creates a positive externality to the content
creator.
Therefore, liking a post (1) increases the likelihood that followers are shown the same post, and (2) if
the followers don’t appreciate the post (for example, from the opposite political party), there is a chancethey can stop following the influencer.
22
Our modeling assumptions regarding the costs and benefits of attention are similar to models of
attention and advertising (Anderson and Coate, 2005; Anderson and de Palma, 2012; Anderson andPeitz, 2023), who also model the cost of attention as a difference between consumers preferences and thecontent they consume. This literature does not differentiate the costs and benefits as they don’t consider
the externality that is our main focus.
23
Distance |αt − αt−1 | ∈ [0◦ , 180◦ ] denotes the shortest angle difference on a circle. Formally, |αt −αt−1 | = min {abs(αt − αt−1 ), 360◦ − abs(αt − αt−1 )}, where abs(x) is the absolute value.
24
The modeling choice of using cos(·) and sin(·) instead of more general functions is motivated partiallyby tractability and partially by the empirical analysis, where it is standard to use cosine similarity as ameasure of similarity. The functional form assumptions are not crucial for our results.
25
The assumption that the cost function is 1 beyond the 90◦ threshold simply accounts for the factthat sin(∆) function would be decreasing. Any weakly increasing function in this region would give
similar results.

10

In summary, the payoff of player t depends only on actions at and at+1 as follows:ut (at , at+1 ) = at γRt cos(∆t ) −at Rt C(∆t ) +at+1 (1 − γ)Rt+1 cos(∆t+1 ) .
{z}| {z }|{z}|
Internalized benefit

Cost

(2)

Externality

We assume that players’ actions are not observable to the following players.26 We also
assume that player t observes the topic αt−1 of preceding player t − 1, but does not know
the follower’s type. We consider Bayes-Nash equilibria, where players choose optimal
action at , observing their own and previous player’s type, and taking an expectation overthe follower’s type.
The free-riding problem. The positive externality of engagement creates a free-riding
problem and therefore in equilibrium, there is less engagement than socially optimal.
Specifically, in equilibrium player engages only with players whose topic is sufficiently
similar (∆t is small enough). We can therefore say that only high quality engagement(in terms of match value) occurs in equilibrium. On the other hand, when taking into
account the positive externality, it would be socially optimal to also engage with players whose topic is less similar. We can therefore say that in equilibrium there is too
little engagement and even somewhat lower-quality engagement is socially optimal. The
following proposition formalizes this intuition.
Proposition 1. There is more engagement in social optimum than in non-cooperativeequilibrium, but the additional engagement is of lower quality. In particular,
1. in non-cooperative equilibrium, at = 1∆t ≤tan−1 (γ) ,2. in social optimum, at = 1∆t ≤45◦ .
The comparison between socially optimal and equilibrium engagement shows that
there is room for improvement from cooperation. If players could commit to engage
somewhat more and get more engagement in return, they would be happy to do so.

3.2

Influencer Cartels

Our model of influencer cartels is simple, as the rules in those cartels are enforced by analgorithm. Therefore, we do not need to model the incentives of the cartel members tofollow the rules as tacit collusion or repeated game. Instead, we model a cartel as an entry
game, where they choose whether to enter a given cartel agreement. After learning theirown types (αt , Rt ), but before learning other players’ types, players simultaneously choose
26This assumption eliminates equilibria, where players engage conditional on past engagement.

11whether to join the cartel. A player who does not join the cartel gets outside option,
which we normalize to 0. Players who join, form a subsequence (. . . , s−1 , s0 , s1 , s2 , . . . ),where st is the t’th member of the cartel.
We model cartel as a simple agreement defined by a single parameter Λ. The cartel
member st must engage with the content of previous member st−1 whenever their topic
difference is less or equal than Λ, that is ∆st = |αst − αst−1 | ≤ Λ. The topic-difference
parameter Λ is a convenient way to model how topic specific is the cartel. In a cartel thatis not topic-specific, the parameter Λ = 180◦ , while in a narrowly topic specific cartel the
topic difference is small.
The payoff from joining the cartel are the similar to the payoff without cartels, but instead of choice whether to engage, now the engagement is defined by the cartel agreement.
When deciding whether to join the cartel, players take an expectation over other cartel
members’ types. A player with type (αst , Rst ), who joins the cartel, gets the expected
payoff:ucartel (Rst ) = E 1∆st ≤Λ (γRst cos(∆st ) − Rst C(∆st ))hi+ E 1∆st+1 ≤Λ (1 − γ)Rst+1 cos(∆st+1 ) ,(3)

where ∆st and ∆st+1 are the topic differences with previous and next member of thecartel respectively, and the expectations over ∆st , ∆st+1 , and Rst+1 are taken over the
distribution of cartel members.
Equilibria. We focus on symmetric equilibria, where players join the cartel independently of topic αt . Therefore, the distributions of ∆st and ∆st+1 are still uniform. Let us
first focus on the case where Λ ≤ 90◦ , so that the cost function C(∆st ) = sin(∆st ). Thenthe cartel benefit from equation (3) is
carteluZ Λ[γ cos(∆st ) − sin(∆st )] d∆tZ Λ+ (1 − γ)ERst+1 2cos(∆st+1 )d∆st+10
4λ(λ − γ) 1 − γ
ERst+1 − Rst ,=λ2 + 1λ−γ(Rst ) = Rst 2

0

(4)


where we simplified the expressions by using a monotonic transformation λ = tan Λ2 .27
Using this expression, we can study the entry to the cartel and formalize it withproposition 2 below. There are three cases depending on the engagement requirement
27

Note that 1+cos(Λ)
sin(Λ) = tanΛ2= λ and sin(Λ) = sin(2 tan−1 (λ)) = λ22λ
+1 .

12

Λ. If the engagement requirement is low, then all players join the cartel. It is easy to
see this when Λ ≤ tan−1 (γ) as then the direct benefits exceed the costs. But even if theengagement requirement is slightly larger, benefits the player expects from the cartel arelarger than the costs of fulfilling the engagement requirement. If engagement requirement
is moderate, only players with smaller reach join the cartel. This is because the benefitof the engagement from the cartel depends on the average reach of a cartel member,
ERst+1 , but the cost depends on the player’s own reach Rst . Hence, the first players tostay out of the cartel are with the highest reach. Therefore the equilibrium is describedby a threshold R, so that only players with reach Rst ≤ R join the cartel. Finally, if theengagement requirement is Λ = 90◦ , nobody joins the cartel. Furthermore, if Λ > 90◦ ,then equation (4) is an upper bound for the cartel payoff, and it is strictly negative, soin this case also nobody joins the cartel.
Proposition 2. Depending on cartel agreement, we can have three possible types of equilibria in the entry game to the cartel:
1. If λ ≤ γ, all players join the cartel.
join the cartel.
2. If γ < λ < 1, all players with Rt ≤ R = 2−γ−λλ−γ
3. If λ ≥ 1, nobody joins the cartel.
Welfare. The proposition implies that only cartels with engagement requirement lessthan 90◦ are sustainable. Within this range, all cartels are welfare-improving. In appendix A3, we derive welfare-maximizing cartels and show that the engagement requirement is always weakly less than 45◦ . In other words, based on this model of influencer
cartels, we would only expect to see cartels with some restrictions on topics.28

3.3

Advertising Market

We model the advertising market as a competitive market, where a continuum of advertisers each has an ideal target topic α. The target topic captures the audience theadvertiser tries to reach rather than the characteristics of the product. For example, anadvertiser of vegan burgers instead of choosing vegan food, could choose animal rights
or diabetes as the target topic. Each influencer t is matched with an advertiser with thesame target topic α = αt .
We study how the existence and type of cartel affects the price that advertisers pay
to influencers. The key aspect of the analysis is that the advertiser cannot observe the28

In appendix A3 we also show that having a minimal reach requirement could be beneficial for the
cartel. This can explain why some cartels have a minimum reach requirement in practice.

13

quality of engagement and hence the price that the advertiser offers reflects the expected
quality of such engagement instead of its true value. In other words, the advertiser pays
for the quantity of engagement.29
The realized value of engagement from the follower t + 1 to the advertiser is
at+1 (1 − γ)Rt+1 × cos(∆t+1 ) ×|{z}| {z }

quantity of engagement

match quality

v
|{z}

,

(5)

marginal value

where v is the value of a marginal unit of engagement. This expression captures the ideathat advertisers can measure the quantity of engagement quite accurately (number ofviews, clicks, likes, comments), but it is much harder to determine whether the engagement comes from the target audience. The product of the last two terms, cos(∆t+1 )v, isthe unit value of engagement to the advertiser and its expectation determines the priceof engagement.30
As we assume that the advertising market is competitive, the price of engagement isequal to the expected unit value of engagement to the advertiser,
pengagement = E [cos(∆t+1 )] v,(6)

where the expectation is taken over the distribution of the influencers who engage, conditional on their equilibrium behavior.31
Benchmark: only natural engagement. Before studying the impact of cartels, let
us consider the case when all engagement comes from natural equilibrium behavior, as
discussed in section 3.1. Adding the advertising value to the influencer’s payoff function,
we getnaturaluad,(7)t (at , at+1 ) = ut (at , at+1 ) + at+1 (1 − γ)Rt+1 p
where ut (at , at+1 ) is the payoff defined by (2) and price of engagement is the price of
natural engagement pnatural = vE[cos(∆st+1 )|Natural].
Notice that the new term at+1 (1 − γ)Rt+1 pnatural is independent of player t’s action at ,therefore equilibrium behavior is unchanged. By proposition 1, player t engages if and29
As discussed in the introduction, it is a common practice in influencer marketing not to measureengagement quality. As of 2020, only 19% of firms employing influencer marketing tracked sales (ANA,2020). As we show in an earlier working paper version, if advertisers can measure the quality of advertising, the distortion caused by the advertising market would be much less severe.
30
A good way to think of this assumption is that if the engagement occurs, then (1 − γ)Rt+1 more
people see the advertisement by influencer t, and each of them will buy the product with probabilitycos(∆t+1 ). This is analogous to the way the attention literature models the benefits of advertising(Anderson and Coate, 2005).
31
Our results remain unchanged if players are able to capture a constant fraction of the value theadvertiser gets from the engagement, for example via Nash bargaining.

14

only if ∆t ≤ tan−1 (γ). Hence, the price of natural engagement is
pnatural = vE cos(∆st+1 ) ∆st+1 ≤ tan−1 (γ) = v

γp∈ (0.9v, v).
tan (γ) γ 2 + 1−1(8)Cartels with advertising market. We assume that the advertiser is unable to distinguish cartel engagement from natural engagement. In particular, we assume that withprobability 1 − ε, the engagement is natural, i.e., comes from equilibrium behavior discussed above, and with the remaining probability ε ∈ (0, 1) the engagement comes froma cartel. The price of engagement is therefore
pengagement = (1 − ε)pnatural + εpcartel ,(9)where pnatural is the price of natural engagement from (8) and pcartel = vE[cos(∆st+1 )|Cartel]is the price of engagement coming from cartels.32
To determine the equilibrium price of engagement, we need to study how the advertising market affects the engagement within a cartel. The payoff function of a player
joining the cartel with the added value from advertising ishiucartel+ad (Rst ) = ucartel (Rst ) + E 1∆st+1 ≤Λ (1 − γ)Rst+1 pengagement= ucartel (Rst ) +Λ(1 − γ)E[Rst+1 |Cartel]pengagement ,
180◦

(10)

where ucartel (Rst ) is defined by (3) and E[Rst+1 |Cartel] is the expected reach of a cartel
member.
For clarity, let us focus on the case when the advertising market incentives are large,i.e., the marginal value of engagement, v is large enough. Then also pengagement is large,
because by (8) and (9), pengagement ≥ (1 − ε)0.9v. For any fixed reach Rst , the first term
ucartel (Rst ) in equation (10) is bounded, so with sufficiently large pengagement , the second
part of the expression dominates. This means that for any Λ > 0 there is v > 0, such thatthe payoff from joining the cartel is positive for players with reach below some threshold
R > 1. This implies the following result.
Proposition 3. With advertising market, for all Λ > 0 and any R > 1, there exists
v > 0, such that all players with Rt ≤ R join the cartel.
32

Let us emphasize that equation (9) holds under the assumption that the advertiser only observes theengagement quantity (i.e., whether engagement occurred or not) but not the engagement quality (i.e.,
whether it came from someone with similar interest or not). This assumption is motivated by the realityof influencer marketing, where most advertisers do not track engagement quality. If the advertiser could
track the engagement quality, the engagement price would reflect the actual topic match, and thus, thedistortion would be considerably smaller.

15

We can conclude that if the incentives from the advertising market are large, thena cartel with Λ = 180◦ is sustainable. In fact, it is even in some sense desirable forcartel members, as joining such a cartel brings more engagement than a cartel that limits
engagement to a narrower topic. Thus, we would expect to see such general cartels inpractice. Indeed, most of the cartels in our sample are non-specific cartels that require
engagement regardless of the topic and do not put any restrictions on the topics of theposts.
Welfare impact of general cartels. Such general cartels reduce the welfare of consumers and influencers outside cartels, and can also be undesirable for the advertisers
and some influencers within the cartel. In particular, as the following corollary 1 states,
they unambiguously reduce the welfare of consumers and influencers outside the cartel.33
Such cartels provide no social value in expectation, but create substantial cost due to theattention cost for the audience. They always hurt influencers who do not belong to thecartel, because these influencers get a lower price of engagement from their advertisers.
The effect on other parties is subtler. The advertising market is competitive, so that
their expected value is always zero. General cartels drive down the price of engagement,so that the advertisers who happen to be matched with an influencer involved in natural engagement, actually benefit from the cartel by paying a lower price, whereas theadvertisers who are matched with cartel members, pay for worthless engagement. The
expectation over the two possibilities is zero, just the outcomes are more uncertain, andthe uncertainty itself could be undesirable for advertisers.
Finally, let’s consider the members of the cartel. They receive a positive expected
benefit from belonging to the cartel; otherwise, they would not have joined. However,when the share of engagement coming from cartels becomes large enough (with ε > 1/2),
even members of general cartels would prefer that these cartels would have a stricter
engagement requirement Λ < 180◦ . This is because the reduction in the quantity ofengagement is offset by the increase in the price.
Corollary 1. With sufficiently large v, general cartels with Λ = 180◦ are sustainable.
1. General cartels strictly reduce consumer welfare.
2. General cartels strictly reduce the welfare of influencers outside the cartel.
3. General cartels create uncertainty for the advertisers.
33
Without advertising, all sustainable cartels have Λ < 90◦ and are welfare-improving, with zerowelfare effect at the limit Λ = 90◦ . The advertising market improves welfare for any given Λ but also
makes welfare-reducing cartels sustainable. The threshold where welfare is zero is strictly between 90◦
and 180◦ .

16

4. If ε > 1/2, then all members of general cartels would prefer that these cartels would
have slightly lower Λ.

4Data and Measures of Engagement Quality

4.1

Data Sources

We combine data from two sources: first, the detailed cartel communications from Telegram, and second, Instagram posts and engagement data. A detailed description of ourdata collection is in Online Appendix A4.
Telegram cartel history. From Telegram, we collected the communication history ofnine cartels: six general interest cartels and three topic-specific cartels: fitness & health,fashion & beauty, travel & food. This history provided us with three relevant pieces of
information for each submission: the Telegram username, Instagram post shortcode, andthe time of submission. According to the rules of these cartels, a user must commenton and like the five posts preceding their own submission before submitting a post to
the cartel for engagement. This rule allows us to clearly identify which cartel members
were bound to engage with which Instagram posts. In other words, we directly observe,
instead of having to infer, which posts are included in the cartel. Similarly, we observe,
instead of having to infer, which engagement originates from the cartel according to thecartel rules. The Telegram cartels include 220,893 unique Instagram posts that we wereable to map to 21,068 Instagram users.
Instagram data. Our goal is to compare natural engagement to that acquired via cartels. In engagement, we focus on comments instead of likes or views because information
on who views the post is not available, and data on who likes the post is more difficult
to collect than comments. We already know which cartel members have to comment according to the cartel rules. For comparison, we needed to collect information on natural
engagement.
We define natural engagement as comments from users who don’t belong to any of
the cartels in our data. To obtain information on natural engagement, we focus on eachcartel member’s first post in any of the nine cartels. For each cartel member’s first postin cartels, we collected information on who commented on the post. Then, we used arandom number generator and picked a random non-cartel user who had commented on
the post. The randomly chosen commenting Instagram users who don’t belong to any of
our cartels form our control group. Since these are from the earliest post in the cartel,they are less likely to be indirectly affected by the cartel activity.
17

We collected the text of all public Instagram posts and a photo for cartel members andfor the randomly picked non-cartel users.34 We were unable to collect the content if theinitial post had been deleted or made private. We were also unable to collect informationon the non-cartel commenters if the initial post had no non-cartel commenters, or if
the commenting user’s account was private. We also didn’t collect information on noncartel commenting users if they had less than ten Instagram posts. Additionally, we
excluded about 5% of the non-cartel commenting users who had associated posts withcartel members.35

4.2

Measuring Engagement Quality

Our goal is to compare engagement that originates from cartels to that of natural engagement. As demonstrated above, the relevant quality measure in this context is thesimilarity between the interests of the post author and the commenting user. In our analysis, we therefore consider engagement to be of high quality if it comes from Instagramusers whose own Instagram content has similar topics. Therefore, we measure the similarity of the posts of commenting users to those of the post author. To analyze similarity,
we use text and/or photos in Instagram posts and three alternative methods.
4.2.1

Text Embeddings and Cosine Similarity of Users

First, we use a large language model named Language-agnostic BERT Sentence Embedding (LaBSE) to construct embeddings of text in Instagram posts (Feng et al., 2022).
An embedding represents text as a numerical vector in a multidimensional vector space.
The vector representation of text is useful, allowing quantitative similarity comparisonof texts via cosine similarity. Cosine similarity is a standard measure of text similarity.
This measure is defined as the cosine of the angle between two vectors, providing a similarity score between -1 and 1, where close to 1 means that the texts (vectors) are highly
similar. LaBSE builds upon one of the first large language models, Bidirectional Encoder
Representations from Transformers (BERT), which was developed by Google researchers(Devlin et al., 2019). While BERT was originally implemented for the English language,
LaBSE extends it to more than 100 languages. The multilingual effectiveness is necessary
for us because our sample is multilingual. The LaBSE model transforms each post into
34

In our main analysis, we do not use the text of comments. In the Online Appendix (Table A5.1), welook at whether the comment is substantial and relevant to the post. We find that cartel comments are
longer and more related to the post, while non-cartel comments are more likely to include only emoticons.
This is to be expected, as the cartel rules require writing substantial comments, while non-cartel users
do not have such restrictions.
35
The association can happen as Instagram allows posts to be associated with multiple users (this isdifferent from tagging a user), or it can happen when the user changes usernames.

18a vector of length 768. It does so using a large neural network with approximately 470
million parameters. This enables the model to capture a large range of semantic featuresin multiple languages.
To create the input for the embedding, we restrict the sample in the following way.
First, we restrict the sample to users who have at least ten posts. In the main analysis,
we focus on 100 posts per user closest in the symmetric time window to the first post
for the cartel member and to the post they commented on for the non-cartel users.
Results are qualitatively similar when using a random sample or all posts from 2017 to2020 (presented in Online Appendix A5). In our main analysis, we create an embeddingof each post using hashtags in the post. We focus on hashtags because they typicallyinformatively capture the essence of Instagram posts. Online Appendix A5 presents
results where the embeddings are created using the whole text of the posts.
To create the input for the embedding, we pre-process the text: (i) transform to lower
case; (ii) replace all characters that are not letters, numbers, underscores, or hashtags
with a space (these are the only characters allowed in Instagram hashtags); (iii) add aspace before each hashtag; (iv) keep only words that start with a hashtag; (v) keep only
the first 30 hashtags in each post because Instagram allows only up to 30 hashtags perpost; (vi) drop all hashtags that have only a single character because these tend to be
uninformative; (vii) drop all hashtags that don’t include any letters because these tend
to be uninformative. Before creating embeddings, we replace the hashtag and underscore
symbols with a space.
Using the embeddings we calculate the cosine similarity of users. To do that, first, wecreate an embedding for each Instagram post separately. After obtaining embeddings ofeach separate post, we generate a single measure for each user by taking the average of thepost embeddings for each user. Online Appendix A5 presents results where instead of post
embeddings, we first combine all user’s posts for each month, and obtain one embedding
per user and month pair, and then take the average over the months for each user. Using
the average embeddings, we calculate the cosine similarity of user pairs. How do weinterpret the cosine similarity of average embeddings of users? Since cosine similarity is alinear transformation, the cosine similarity of average embeddings is essentially equivalent
to calculating cosine similarity separately of all the posts of the two users and then taking
the average of the cosine similarities of all these post pairs.
4.2.2

Photo and Text Embeddings and Cosine Similarity of Posts

We also construct embeddings of photos and text. As the above LaBSE model can encode only text, we have to use a different model for processing photos alongside text. We
use the Contrastive Language Image Pre-training (CLIP) model, developed by OpenAI
19

(Radford et al., 2021). CLIP maps the contents of photos and text into a shared embedding space. Because CLIP generates embeddings for photos and text that are directlycomparable, it allows us to calculate similarity by combining both forms of information.
The CLIP model transforms the text and photos into a vector of length 512. It does sousing a neural network with approximately 86 million parameters. The advantage of the
CLIP model is that it allows combining photos and text. On the other hand, the LaBSE
model more precisely captures text.
We use a photo and the text from a single Instagram post for each user. For cartel
members, we use the first post each cartel member posted to the cartels. For non-cartel
members, we select their closest post within a symmetric time window to the cartel
member’s post they commented on. To create the text input for the CLIP embedding,we first pre-process the text keeping the entire text, not just the hashtags: (i) transform it
to lower case; (ii) replace question marks, exclamation marks, and new line breaks with afull stop; (iii) replace all characters that are not letters, numbers, full stops, underscores,
hashtags, at symbols, or apostrophes with a space; (iv) drop separate groups of charactersthat don’t include any letters or numbers; (v) add a space before each hashtag; (vi) discard
posts that are shorter than three characters. Since the CLIP model has a binding limitof 77 for the number of tokens (text units such as words or subwords), we have to split
the text. Specifically, we split the text into sentences. In a small share of cases where
the sentence is longer than 77 tokens, we further split it at the 77-token mark. Then, we
generate the embedding for each sentence and take the average over all sentences in that
post. We also generate an embedding for each photo. Then we take the average of text
and photo embeddings of each post. Finally, using the average embeddings, we calculate
the cosine similarity for each author and commenter pair.
4.2.3

Determining Users’ Topics Using Latent Dirichlet Allocation

The models that generate embeddings allow us to measure similarity, but they are somewhat black boxes. To shed some light on the comparison of users’ topics, we use a Latent
Dirichlet Allocation (LDA) model. The LDA algorithm estimates a probability distribution of topics for each user based on the words used in their posts, and a probability
distribution over the words for each topic.
We train the LDA model using hashtags from the same sample of posts with the sametext pre-processing as in the LaBSE model used above. To improve learning from theunderlying content, we reduce the set of hashtags using standard thresholds following
a common approach in text analysis. Specifically, we exclude hashtags that fewer than
50 users use or more than 33% of the sample uses. This reduces the number of unique
hashtags from about 1.5 million to 19,032, giving us a typical medium-sized dictionary
20

suitable for LDA models. To improve the model’s performance and avoid giving moreweight to users with longer content, we homogenize the length of content over the users.
To do that, for each user, we cap the length of content at 1000 hashtags, which is about
the 75th percentile and slightly less than three times the median length. Finally, we
exclude users with less than 15 unique hashtags because there is not enough information
to learn their topics. This reduces the number of users by 17 percent. We fix the numberof topics to six based on interpretability and the coherence score (Figure A5.1). We
assign each topic a label based on the most representative hashtags in each topic, thatis, the hashtags with the highest probability (Table A5.2). The labels are fitness, beauty,
fashion, food, entrepreneur, and travel.

4.3

SampleOur analysis is within subject. That is, for the same author, we compare his similarity tocartel commenters versus his similarity to non-cartel commenters. For this comparison,
we need to be able to evaluate both similarities for each author. As described above, forsome authors we were not able to collect information on their non-cartel commenters.
Furthermore, not all users had enough posts with text to calculate the outcome measures(the embeddings, cosine similarity, LDA topics). The main sample includes only theauthors for whom: (A) we were able to find commenters both from cartels and not fromcartels; and (B) we had sufficient data to calculate the similarity measures for both typesof commenters. Table A5.3 in the Online Appendix describes how each restriction reduces
the sample and Online Appendix A4 provides further details.
The main regression analysis focuses on 8507 cartel members as authors of content.
For those authors, we were able to calculate both the LaBSE and CLIP embeddings, aswell as the same embeddings for at least one cartel and non-cartel commenter. The topic
analysis focuses on an analogous sample of 6654 authors with LDA topic measures forboth cartel and non-cartel commenters.36 The authors excluded from the main samples
due to data limitations are similar to included authors in terms of their LDA topics(Figures A5.2 and A5.3), but, as expected, have fewer posts and use fewer words per post
(Table A5.4).
Summary statistics of the main sample are presented in the Online Appendix. Table A5.5 compares members of general cartels to members of topic cartels, and table A5.6
compares cartel members to users not in the cartel. The distribution of topics in the cartels is as expected (Figure 1). In the fashion & beauty cartel, authors are posting more
about fashion and beauty; in the fitness & health cartel, about fitness; in the travel &36

The sample is smaller because the LDA topic estimation has stricter data requirements as it uses
only hashtags that are sufficiently common in the sample.

21

.6
.4

Topic share

.2
0

0

.2

Topic share.4.6

food cartel, about travel and food. In the general cartels, the topic distribution is rather
uniform, with slightly more concentration on the topics of fashion and travel.

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Figure 1: Authors’ LDA topic distributions
Notes: The bars correspond to the average topic shares across authors and capped spikes describe the
95% confidence intervals.

5

Empirical Results

5.1

Empirical Strategy

Our empirical question is whether engagement from cartels is of lower quality comparedto natural engagement. To answer the question, we estimate a panel data fixed effects
regression where the outcome variable is the cosine similarity of an author and theircommenter. An observation is an author and their commenter pair. For each author,
we focus on the first post in the cartel. Thus, we have only one post for each author.
However, we have three types of commenters for each post. Type one are the cartel

22

members that were required to comment according to the cartel rules.37 Furthermore,here we separate general and topic cartel commenters. Type two is what we call natural
engagement: this is the non-cartel user that actually commented on the post. This gives
us the first benchmark and allows us to measure whether cartel commenters are worse
than natural engagement. That is, whether cartel commenters have lower similarity (toauthors) than non-cartel commenters. Type three are what we call the counterfactual
random users: these are randomly chosen non-cartel users who didn’t comment on thepost. This third group gives us another benchmark. It allows us to measure whether
cartel commenters are better than random users. That is, whether cartel commenters
have higher similarity (to authors) than random users. Our sample is a balanced panel,in a sense that we have all three types of commenters for each author: one non-cartel
commenter, five random users, and on average four cartel commenters.
For the first post in cartels of author i, the similarity to their commenter j is:
Similarityij = βGen GeneralCartelCommenterj + βT op T opicCartelCommenterj+βRan RandomU serj + InstagramAuthorF Ei + εij ,(11)where Similarityij refers to the cosine similarity between author i and commenter j;
GeneralCartelCommenterj is an indicator for a general cartel member j who is required
to comment; T opicCartelCommenterj is an indicator for a topic cartel member j who
is required to comment; RandomU serj is an indicator for a random Instagram user notin the cartel who didn’t actually comment. InstagramAuthorF Ei is the fixed effect foreach author. Since we only have one post per author, this is equivalent to the post fixed
effect. The base category is natural engagement, that is, a commenter who is not in thecartel.
In the main analysis, we use two alternative similarity measures as outcome variables:
first, cosine similarity of users calculated using the text embeddings from the LaBSE
model, and second, cosine similarity of the corresponding users’ posts calculated using
the photo and text embeddings from the CLIP model.38 We look at three mutually
exclusive samples, each defined by the type of cartel in which the author’s first cartel
post is included. The first sample consists of authors whose first post is only in generalcartels; the second consists of those whose first post is only in topic cartels; and third,
includes those whose first post is in both general and topic cartels.39
37
In the main analysis, we focus on cartel members required to comment instead of those actuallycommenting. We do this because we don’t observe all comments. The robustness analysis shows thatthe results are similar when looking at who actually commented (Online Appendix A5).
38
The details of the outcome variables are described in Section 4.2.
39
With some abuse of terminology, we say that a post is only in general (or topic) cartel even if it wasposted in both but we have information on the commenters from only one of these. This affects only a23

Density

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To preview our main results, let us first look at the raw distributions of outcome
variables. Figure 2 presents the density of both outcome variables separately for generaland topic cartels. It shows that non-cartel commenters have the highest similarity withthe author, and random users have the lowest. Commenters from general cartels havealmost as low similarity as the random users (Figures 2a and 2c). In contrast, commentersfrom topic cartels have relatively higher similarity (Figures 2b and 2d).

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1.2

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.4

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Similarity of posts, photo+text embeddings1

Non-cartel commenters
Topic cartel commenters
Random users(c) General cartels, posts’ similarity(d) Topic cartels, posts’ similarity

Figure 2: Probability density of authors’ similarity to commenters and random users
Notes: The figures present kernel density estimates using the Epanechnikov kernel function of authors’cosine similarity to non-cartel commenters (grey line with solid circle markers), to random users (reddotted line), to general cartel commenters (blue dashed line on Figures 2a and 2c), and to topic cartel
commenters (green dashed and dotted line on Figures 2b and 2d). The cosine similarity is calculated
either: as the similarity of users using the text embeddings from the LaBSE model (Figures 2a and 2b) or
the similarity of posts using the photo and text embeddings from the CLIP model (Figures 2c and 2d).

small number of posts.

24

5.2

Quality of Engagement Measured by Cosine Similarity

We find that in general cartels (columns 1 and 4 in Table 1), authors’ similarity to cartel
commenters is significantly lower than their similarity to non-cartel commenters, whoform the base category. Furthermore, similarity to general cartel members is almost as
low as to random users. In contrast, in topic cartels (columns 2 and 5), authors’ similarity
to cartel commenters is only slightly lower than to non-cartel commenters. Similar results
hold for posts which are in both general and topic cartels (columns 3 and 6).
Table 1: Panel data fixed effects estimates of authors’ similarity to cartel commentersand random users versus non-cartel commenters
(1)

(2)
(3)
(4)
(5)
(6)
Dependent variable: Cosine similarity
Posts in general or topic cartels
GeneralTopic
BothGeneralTopic
Both
Similarity of users
Similarity of posts
Text embeddings
Photo+text embeddings
General cartel commenter-0.058***(0.003)Topic cartel commenter
Random user
Wald test, βGen = βT op , p-value
Base (non-cartel) mean
Author fixed effects
Authors
Observations-0.071***(0.003)-0.023***(0.003)-0.076***(0.003)

0.574
Yes
4756
44900

0.585
Yes
3263
30569

-0.060***(0.008)-0.009(0.008)-0.062***(0.008)
0.000
0.577
Yes
488
6665

-0.033***(0.001)-0.040***(0.001)-0.016***(0.001)-0.040***(0.001)

0.657
Yes
4756
44900

0.657
Yes
3263
30569

-0.034***(0.003)-0.012***(0.003)-0.037***(0.003)
0.000
0.659
Yes
488
6665

Notes: Each column presents estimates from a separate panel data fixed effects regression. Unit ofobservation is an author and another user pair. Outcome variable is the cosine similarity of the author
to his commenter or to a random user. In columns 1-3, the cosine similarity of users is calculated using
the text embeddings from the LaBSE model; in columns 4-6, the cosine similarity of the corresponding
users’ posts is calculated using the photo and text embeddings from the CLIP model. Each regression
includes author fixed effects (equivalent to the post fixed effects because only one post per author). In
all the regressions, the base category is the author’s similarity to a non-cartel commenter; and Base(non-cartel) mean presents their average cosine similarity. General cartel commenter is an indicatorvariable whether the commenter to whom the author’s cosine similarity is calculated, is in the generalcartel, and Topic cartel commenter whether he is in the topic cartel. Random user indicates that theauthor’s similarity is calculated to a random non-cartel user who didn’t comment. The sample consistsof authors whose first cartel post is either: only in general cartels (columns 1 and 4); only in topic cartels(columns 2 and 5; or in both general and topic cartels (columns 3 and 6). Standard errors in parenthesis
are clustered at the author level.

Both Figure 2 and Table 1 also validate our outcome measures. Although we do not
observe advertising fees for engagement originating from cartels, advertisers are known
to pay higher fees for more engagement when they do not directly track sales. The
results show that users with higher similarity measures are more likely to engage withthe content (non-cartel commenters versus random users). Therefore, according to our25measures, users with higher similarity provide greater value for advertisers.
The regression results are robust to alternative ways to construct outcome variables
and alternative samples. The Online Appendix (Tables A5.7 to A5.9) presents results
where first, outcome variables in columns 1–3 are constructed based on (A) random
sample of posts; (B) all posts in 2017–2020; (C) the whole text instead of hashtags;
second, outcome variables in columns 4–6 are constructed based on (A) only the photos,(B) only the text. It also presents the results where the sample includes only the cartel
commenters for whom we observe that they actually commented (Table A5.10). In allthese specifications, the estimates remain similar to the main results. When looking at
each of the topic cartels separately, we find that cartel commenters from the fitness &health cartel are the most similar to natural engagement (Table A5.11).
To interpret these estimates, we can do back-of-the-envelope calculations based on ourtheoretical model. According to our theoretical model, the value of engagement to theadvertiser is proportional to the content author’s cosine similarity with the commenter.
Our empirical estimates suggest that general cartels reduce cosine similarity measuresby 5–10%, and topic cartels reduce them by 2–4%. However, these numbers are hardto interpret directly. In our sample, a completely random pair of users has a cosine
similarity of 0.57–0.66, while in the theoretical model, the expected similarity of a random
user is zero. One could argue that as advertisers use influencer marketing for targeted
advertising, they would gain negligible value from a purely random match. To accountfor this, we normalize cosine similarity by the random match similarity. Using thiscomparison, engagement from general cartels is 82–97% worse than natural engagement(relative to purely random matching), whereas engagement from topic cartels is 15–40%
worse. In other words, these back-of-the-envelope calculations suggest that an advertiser
paying for engagement from general cartels, expecting it to be like natural engagement,
only gets 3–18% of the value (essentially paying for almost nothing). In contrast, if theengagement comes from a topic cartel, the advertiser overpays but still gets 60–85% of
the value.

5.3

Quality of Engagement Measured by LDA Topic Match

To further study the quality of engagement, we compare the LDA topic distributionsof cartel versus non-cartel commenters, separately for general and topic cartels. To dothat, first, for each author, we define their main topic as the topic with the largest
LDA probability. Then, for each group of authors who share the same main topic, we
compare the same topic share of the post’s cartel versus non-cartel commenters. Figure 3aillustrates that the topic match from general cartels is worse than natural (non-cartel),separately for each topic. For the authors posting in general cartels, their non-cartel
26

0

.2

.4

Topic share.6commenters post on this topic about 42% of the time according to the LDA probability.
In contrast, their cartel commenters post on the main topic of the author only 22% of thetime. This comparison is different for topic cartels. Figure 3b focuses on the topics mostprevalent in each of the topic cartels and the authors whose main topic it is. It showsthat the topic match from topic cartels isn’t worse than natural (non-cartel).

ss
ne
Fit

ty
au
Be

ion

Fo

sh
Fa

od

r
eu

n
pre
tre

av
Tr

el

En

Non-cartel commenters
General cartel commenters

0.2

Topic share.4.6(a) General cartel versus non-cartel commenters

FashionFitness

TravelNon-cartel commenters
Topic cartel commenters(b) Topic cartel versus non-cartel commenters

Figure 3: LDA topic shares of commenters from cartels versus non-cartels (natural)
Notes: The bars correspond to the average topic shares across commenters and capped spikes describe
the 95% confidence intervals. The grey bars capture the non-cartel commenters and blue bars thecartel commenters. The sample is restricted to general cartel commenters on Figure 3a and topic cartel
commenters on Figure 3. Each set of bars use a sample of commenters that is further restricted by themain topic of the author of the post they comment on, where the main topic is defined as the topic withthe highest LDA probability. For example, on Figure 3a, for the first grey and blue bar, the sample isrestricted to commenters on the posts in general cartels of the authors whose main topic is fitness.

27

6

Policy Implications

Our empirical and theoretical results suggest three main policy implications. Our theoretical results show that cartels that require engagement with only closely related influencers
improve welfare, whereas cartels that require engagement regardless of the topic match
are welfare-reducing. Our empirical results show that general cartels generate low-quality
engagement. This engagement is about as bad as counterfactual engagement, where comments would come from random Instagram users. On the other hand, the topic cartels
generate engagement, which quality is closer to natural engagement. Our results indicatethat regulators should prioritize addressing general cartels, which our findings identify ascertainly harmful. Our theoretical analysis suggests that engagement should come frominfluencers who are closely aligned in their topics, implying that narrowly focused cartels
could potentially improve welfare. Practically, this means that cartels concentrating on
specific topics can potentially be beneficial, such as the “fitness and health” cartel in our
setting.
Second, our analysis points out that prohibiting obtaining fake social media indicators
via monetary transfers is not enough. The regulation that prohibits buying and selling
fake social media indicators, such as the U.S. Federal Trade Commission’s proposed newrule, should also prohibit obtaining these fake indicators via in-kind transfers.
The third implication of our theory is that monetary incentives based on the quantityof engagement amplify the creation of distorted engagement. According to our results,
this scenario is the only situation where cartel members may prefer to participate in general cartels, which require engagements without regard to topics. The logic is straightforward: if the market provides strong rewards for the volume of engagement, it is best
to join cartels that provide the largest engagement quantity, even though this may besocially detrimental. It is still common in the industry to base the payments on pastengagement quantity. Our results suggest that this practice should be discontinued. Instead, it should be feasible in most cases to adopt an alternative compensation schemethat combines lump-sum payments with performance-based payments, such as bonuses
for added sales. Furthermore, advertisers or platforms could use our methodology toassess the quality of engagement matches. For instance, rather than compensating basedon the sheer number of comments, they could adjust payments according to the quality ofthe topic match. Implementing these changes would significantly diminish the incentive
to produce fake engagement.
One more natural conclusion that does not directly follow from our analysis but isnevertheless worth mentioning is that engagement via cartels is easier to sustain if theengagement is public. The cartels we study can immediately punish deviators because

28their required actions (likes and comments) are publicly verifiable. In other platforms(such as YouTube and recently also X), likes are not public, which means that inducing
cartel likes on these platforms requires more complex and harder-to-implement cartel
rules. However, comments are public on all major platforms, so some cartel agreements
would always be possible.

7

Discussion

Collusion can take many forms, especially in new and evolving industries. In this paper,
we have documented and studied influencer cartels, a form of collusion in the rapidly
growing influencer marketing industry, which has stayed under regulators’ radar. Our
empirical results indicate that engagement from general cartels is significantly lower inquality compared to natural engagement, while engagement from topic cartels is closer
to natural engagement. Our theoretical model sheds light on the trade-offs involved
and explores the associated welfare implications. The key distortion is the free-rider
problem, which cartels could help mitigate through enforced commitment. However,cartels also introduce new distortions, such as over-engagement and the exclusion of highreach influencers. These issues become particularly severe when the advertising market
heavily rewards the quantity of engagement, encouraging the creation of fake engagement.
Our theoretical model assumed that cartel members are exogenously heterogeneous in
two ways: topic and reach. The differences in reach could reflect differences in influencers’
abilities to provide value to their audience. As our analysis does not focus on reach, we
took a reduced-form approach and did not study its microfoundations. The analysis inappendix A3 shows that, in addition to topic mismatch, cartels also distort the reachof commenters—high-reach cartel members are less interested in joining a cartel. This
explains why cartel organizers set a minimal reach requirement. Future research studying
more explicit vertical differentiation would help to shed more light on these issues.
While our focus in this paper is to study specifically the distortions that influencer
cartels create, the market structure and available data are rich enough to study otherrelated questions. Future research could analyze whether joining a cartel really brings thedesired growth in real followers and better advertising deals. While the cartel organizers
claim this is the case, the causal impact is difficult to measure because members might
often join a cartel at the same time they do many other activities to induce growth.
Weerasinghe et al. (2020) provide some correlational evidence that joining a cartel coincides with increased natural engagement and reach. A nice feature of our dataset is thatit gives us a natural experiment: when a cartel member submits a post to the cartel for
additional engagement, the kind of engagement they get in return is random regarding29

match quality and reach. This randomness can be used to identify a causal impact.
Other potential extensions require additional data collection. To compare general andtopic cartels that are similar in other dimensions, we focused only on Instagram influencer
cartels that were organized by the same cartel organizer, have similar engagement rules,
and are all relatively large. Future research could study heterogeneity in other dimensions:platforms, engagement requirements, and cartel sizes.

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Contents of Online Appendix
A1 Screenshots of Wolf Global Instagram Engagement Pods . . . . . . . . . . . . A2
A2 Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A6
A3 Additional Theoretical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . A10
A4 Data Collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A15
A5 Additional Empirical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . A19

List of Online Appendix Tables
A5.1 How substantial and relevant are cartel versus non-cartel comments . . . .
A5.2 Most representative hashtags for each LDA topic . . . . . . . . . . . . . . .
A5.3 Sample construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A5.4 Summary statistics of authors in cartel included/excluded from the sample
A5.5 Summary statistics of authors in different types of cartel . . . . . . . . . .
A5.6 Summary statistics of users in cartels versus not in cartels . . . . . . . . .
A5.7 Alternative outcome variables: random posts; all posts in 2017–2020 . . . .
A5.8 Alternative outcome variable: whole text instead of hashtags . . . . . . . .
A5.9 Alternative outcome variables: photo embeddings, text embeddings . . . .
A5.10 Alternative sample: commenters who actually commented . . . . . . . . .
A5.11 Heterogeneity by topic cartel . . . . . . . . . . . . . . . . . . . . . . . . . .

A19
A19
A20
A20
A20
A21
A21
A22
A23
A24
A25

List of Online Appendix Figures
A1.1
A1.2
A1.3
A1.4
A1.5
A2.1
A3.1
A5.1
A5.2
A5.3

Main page of https://www.wolfglobal.org/ . . . . . . . . . . . . . . . .
Description of how influencers can amplify their earnings . . . . . . . . . .
Wolf Onyx Comments on Telegram app mapped to Instagram users . . . .
Instagram comments coming from Wolf Onyx Comments . . . . . . . . . .
Suggested Instagram post and a user who liked it . . . . . . . . . . . . . .
Benefits and costs of an engagement . . . . . . . . . . . . . . . . . . . . . .
Welfare as a function of engagement requirement . . . . . . . . . . . . . .
LDA model coherence scores by the number of topics . . . . . . . . . . . .
Authors’ topics: regression sample versus excluded . . . . . . . . . . . . . .
Authors’ topics: LDA sample versus excluded . . . . . . . . . . . . . . . .

A1

A2
A3
A4
A4
A5
A6
A11
A26
A27
A28

A1

Online Appendix: Screenshots of Wolf Global Instagram Engagement Pods(a) Main page(b) How it works?

Figure A1.1: Main page of https://www.wolfglobal.org/
Notes: Screenshots of https://www.wolfglobal.org/, taken on March 4, 2024.

A2

Figure A1.2: Description of how influencers can amplify their earnings
Notes: Screenshot of https://www.wolfglobal.org/, taken on March 4, 2024.

A3

Figure A1.3: Wolf Onyx Comments on Telegram app mapped to Instagram users
Notes: Screenshot of Telegram Wolf Onyx Comments, taken on March 4, 2024.

Figure A1.4: Instagram comments coming from Wolf Onyx Comments
Notes: Screenshot of Instagram, taken on March 4, 2024. To preserve anonymity, the Instagram accountnames are blurred and the photo is replaced with a analogous photo generated by AI image generator.

A4

Figure A1.5: Suggested Instagram post and a user who liked it
Notes: Screenshot of Instagram, taken on May 9, 2024. To preserve anonymity, the Instagram accountnames are blurred and the photo is replaced with a analogous photo generated by AI image generator.
Upper red oval shows that the post was suggested to the viewer (who was not follower for this Instagram
account) and lower red oval shows a specific user that the viewer does follow liked the post, indicatingthat one reason the post was suggested to the viewer was because of this engagement.

A5

A2

Online Appendix: Proofs

A2.1

Proof of Proposition 1

Proof In equilibrium, player t chooses at = 1 if and only if the benefits outweigh thecosts, γRt cos(∆t ) ≥ Rt C(∆t ). As costs are always non-positive, it requires that ∆t ≤ 90◦
and thus γ cos(∆t ) ≥ sin(∆t ), which is equivalent to ∆t ≤ tan−1 (γ).
On the other hand, engagement is socially optimal whenever total benefits outweighthe costs, γRt cos(∆t ) + (1 − γ)Rt cos(∆t ) ≥ C(∆t ) or equivalently ∆t ≤ tan−1 (1) = 45◦ .
As γ < 1, there exist socially optimal engagements that don’t occur in equilibrium.
Finally, any engagement that is socially optimal, but not individually optimal, hasstrictly lower quality than compared to those that are individually optimal. That is, forany ∆t ≤ tan−1 (γ), we have cos(∆t ) ≥ cos(∆′t ) for any ∆′t ∈ (tan−1 (γ), 45◦ ].
The proof can be summarized by the following figure A2.1.

Rt

Cost

∆t
ExternalityBenefit

Figure A2.1: Benefits and costs of an engagement
Notes: The angle in blue depicts a particular example where the direct benefit is lower than the cost,
and therefore, it is not optimal for the player. It would be optimal if the topics were more similar sothat the angle would be within the red region. On the other hand, this engagement is socially optimal
because the social benefit is greater than the cost.

A2.2

Proof of Proposition 2

Proof Consider first the case when λ < γ. Then equation (4) is a product of two strictly
negative values and therefore strictly positive, so that all players join the cartel. If λ = γ,then the expression simplifies to 4γ(1−γ)
ERst+1 > 0.
γ 2 +1
Next, suppose that γ < λ < 1. Then ucartel (Rst ) is a strictly decreasing function of
Rst , so the equilibrium must be characterized by a (possibly infinite) threshold R, so that
players join the cartel if and only if Rst ≤ R, which happens with probability 1 − 12 .
R

A6

Therefore, the expected reach of the following cartel member is E[Rst+1 |Rst+1 ≤ R] =2
−1 . This allows us to determine the marginal player’s reach R as
1+Ru

cartel4λ(λ − γ)(R) =λ2 + 1

1−γ
2−R
λ − γ 1 + R−1= 0 ⇐⇒ R =

2−γ−λ
.
λ−γ

Finally, suppose that λ = 1, so that Λ = 90◦ . Then equation (4) simplifies to 2(1 −γ) ERst+1 − Rst , which is positive only if the player’s own reach Rst is smaller than the
average reach. This means that only players with the lowest reach Rst = 1 would be
willing to join, but we assume that the probability of such an event is zero.
To conclude the proof, observe that if λ > 1 (that is Λ > 90◦ ), then the expressionin equation (4) is strictly negative. Also, remember that equation (4) was computedwith cost equal to sin(∆st ). However, if ∆st > 90◦ the cost is C(∆st ) = 1 > sin(∆st ).
Therefore, the cartel payoff is strictly lower than the expression in equation (4). Thisimplies that the cartel payoff would always be strictly negative, and nobody would join
the cartel.

A2.3

Proof of Proposition 3

Proof Fix Λ > 0 and R > 1. The first term ucartel (R) in (10) is strictly negative butbounded for a player with reach R. Therefore, there exists value v > 0 such that thesecond term in (10) dominates it and the cartel payoff ucartel+ad (R) for player with reach
R. As ucartel (Rst ) is decreasing in Rst , we must have that ucartel+ad (Rst ) > 0 for all
Rst ≤ R.

A2.4

Proof of Corollary 1

Proof We prove each part separately:
1. The realized welfare generated by engagement was defined by (1). When taking the expectation over this expression over ∆st+1 that is distributed uniformly
in [0◦ , 180◦ ], the benefit term becomes zero, whereas the expected cost is strictly
positive, therefore such engagement is always reducing consumer welfare.
Even when replacing general cartels with cartels that have lower Λ, this change
would clearly be welfare-improving for consumers.
2. With general cartels, the price of engagement is equal to pengagement = (1 − ε)pnatural .
Without the cartels, the price of engagement would be pnatural > pengagement , while
all other parts of the payoff would remain the same.

A7

Again, just reducing the engagement requirement Λ would increase the price ofengagement, therefore increasing the welfare of influencers that do not belong tocartels.
3. The cartels cannot affect advertisers’ profits as they are equal to zero due to theassumption that the market is perfectly competitive. Cartels drive down the priceof engagement so that advertisers who happen to be matched with an influencer
who does not belong to a cartel get a positive expected profit, as they pay less than
the true value of engagement in expectation. However, advertisers who are matchedwith general cartel members pay for worthless engagement. The expectation over
the two possibilities is zero; the outcomes are just more uncertain.
As in earlier cases, replacing Λ = 180◦ with a slightly lower value lowers thisuncertainty.
4. Consider a general cartel with an engagement requirement equal to 180◦ and suppose v is large enough so that the cartel has members. It is straightforward tocheck that there exists a marginal type whose reach is R, whose payoff of joining
the cartel is zero.
Consider a cartel with Λ that is marginally smaller than 180◦ . We claim that if
ε > 1/2, then the payoff of R is strictly larger with Λ than with the general cartel.
To see this, observe that under such a scenario, the expected reach of the follower,
E[Rst+1 |Cartel], is strictly increased. This is because the former marginal player R
now gets a strictly positive value, and the payoff function is decreasing in reach, so
the new marginal player has higher reach.
Now, the payoff of R from joining the cartel, ucartel+ad (R), as defined by equation (10), has two elements. It is easy to see that ucartel (R) is strictly increased.
Moreover, the payoff from advertising isΛ(1 − γ)E[Rst+1 |Cartel]pengagement ,
180◦

(12)

where the term (1 − γ)E[Rst+1 |Cartel] is again increased by the same argument.
Λengagement
What remains to show is that the remaining term 180
is increased. By◦pequation (9),Λ engagementsin(Λeq )Λsin(Λ)(1 − ε)
p
=v
+ε
180◦
180◦
Λeq
Λ

A8

Λ
engagement
where Λeq = tan−1 (γ).40 If we differentiate 180
with respect to Λ, we get
◦p





sin(Λeq )Λcos(Λ)sin(Λ)1sin(Λ)(1 − ε)
+v
ε
−ε
.
v
+ε
180◦
Λeq
Λ
180◦
Λ
Λ2
To analyze a marginal decrease of Λ from 180◦ , we can take Λ = 180◦ and get
v
180◦




(1 − ε) sin(Λeq )
−ε .
Λeq

This expression is negative if and only ifε>γ1sin(Λeq )
p
=
.
<
eq
eq
Λ + sin(Λ )2γ + tan−1 (γ) γ 2 + 1

Therefore, indeed, if ε > 1/2, the payoff of R is strictly higher under Λ than under180◦ .
Finally, note that the same argument applies for any member with Rst ≤ R. Thisis because ucartel (Rst ) is decreasing in Λ near 180◦ for the same reason as above,and the second term, i.e., the payoff from the advertising market is independent of
Rst and therefore decreasing as well.

40

Note that
pcartel = vE[cos(∆st+1 )|∆st+1 ≤ Λ] = v2

Z Λcos(∆st+1 )0A9d∆st+1sin(Λ)
=v
.
2Λ
Λ

A3

Online Appendix: Additional Theoretical Results

A3.1

Welfare from Cartels

Using the equilibrium description from proposition 2, we can now study the welfare
implications of the cartel. As with individual payoffs, we normalize social welfare without
any engagements to zero. Then the social welfare generated by the cartel, which wedenote again by W , is proportional to the average payoff of all players in the model.41
It is useful to compute also another measure V cartel , which denotes the average payoffof cartel members. Both measures depend on the engagement requirement Λ, and it isconvenient to express these in terms of the transformed version λ = tan Λ2 . Formally,
V cartel (λ) = ERst ucartel (Rst )|ucartel (Rst ) ≥ 0 ,
W (λ) = ERst max 0, ucartel (Rst ) = P r(ucartel (Rst ) ≥ 0)V cartel (λ).

(13)
(14)

Using proposition 2, we can directly compute the welfare. We postpone the explicit
calculations to the end of the subsection and use figure A3.1 to discuss the results.
Suppose that all players would belong to the cartel. Then, the welfare would initially
increase with the engagement requirement λ, as the social benefits exceed the social cost.
√
The social welfare reaches the peak at the first-best level λf b = 2 − 1 (corresponding
to Λ = 45◦ ) and then starts to decline, going back to zero at λ = 1 (corresponding toΛ = 90◦ ). At this level, the average social cost is exactly equal to the average social
benefit, so the welfare generated by engagement would be zero. The hypothetical welfare
from a cartel that everyone joins it is an upper bound for welfare generated by the cartel
and it is depicted by the dashed gray line on the figure. When λ ≤ γ, the cartel achieves
this upper bound, but if the engagement requirement is larger, some players choose notto join the cartel, and therefore the welfare is lower than the upper bound.
There are three qualitatively different possibilities for the free-riding parameter γ.
First, at a high level, for example, γ = 12 (the green line with circle markers), the cartel
can achieve the first-best outcomes by requiring first-best engagement λf b . Naturally,
above this level, welfare starts to decrease as costs exceed the benefits. At λ = γ there isa kink due to a second distortion—above this engagement requirement, players with thehighest reach choose not to participate. At a moderate level, for example, γ = 38 (the redline with square markers), the first-best outcome is not achievable by the cartel because
at λf b , players with the highest reach would not participate in the cartel. The welfaremaximizing engagement is λ = γ = 38 , the highest engagement where all players join the41

Remember that the players extract constant fraction (β, normalized to 1) of social welfare as theirown payoffs.

A10

W

=1/2
=3/8
=1/10

1

0 λeq1
10

1
10

eq
λeq
3 λ1
8

2

3 fb
8λ

1
2

1 λ

Figure A3.1: Welfare as a function of engagement requirement
Notes: λf b denotes the first-best engagement requirement, and λeq
γ the equilibrium engagement threshold.
Corresponding dashed lines indicate mean payoffs for cartel members (V cartel ).
1(the blue line with cross markers),
cartel. Finally, at a low level, for example, γ = 10
the optimal cartel is such that not all players join the cartel. It balances the trade-off
between requiring more engagement and excluding fewer high-reach players. Figure A3.1
also shows the mean payoffs to cartel members, V cartel , which coincides with W whenλ ≤ γ as all players join the cartel, but is strictly higher when λ is higher, as it does notaccount for the fact that the cartel only includes a fraction of influencers.
These results are formally characterized by the following corollary, where γ inc is defined as
!
q
√
11
1
3
inc
−2 − p(15)γ =√ + 64 + 9 67 ≈ 0.3444.
33
64 + 9 67

Corollary 2. Depending on γ, we have one of three cases:
1. If γ ≥ λf b , then first-best outcomes are achieved by a cartel with λ = λf b . BothV cartel (λ) and W (λ) are strictly increasing in λ for λ < λf b and strictly decreasingfor λ > λf b .
2. If γ inc ≥ γ < λf b , then first-best outcomes are not achievable by a cartel and thewelfare maximizing engagement is λ = γ, the highest λ where all players join thecartel. Again, both V cartel (λ) and W (λ) are strictly increasing in λ for λ < γ andstrictly decreasing for λ > γ.
3. If γ < γ inc , then the first-best outcomes are not achievable by a cartel. Welfaremaximizing λ∗ ∈ (γ inc , 1) involves some players staying out of the cartel.
A11

Proof By proposition 2, when λ ≤ γ, all players join the cartel and therefore ERst =ERst+1 = 2, so that
W (λ) = V cartel (λ) =8λ(1 − λ)4λ(1 − λ)E[R] =.
2λ +1
λ2 + 1(16)

This expression is strictly increasing for λ ∈ [0, λf b ) and strictly decreasing for λ ∈ (λf b , 1].
When γ < λ < 1, some players with highest reach choose not to join the cartel. By
proposition 2, then the expected reach of a cartel member is E[Rst |Rst ≤ R] = 2 −1 =
1+R

2−γ−λ
. Therefore, the expressions become1−γ

V cartel (λ) =4λ(1 − λ) 2 − γ − λ,λ2 + 11−γ

W (λ) = P r(Rst ≤ R)V cartel (λ) =(17)
16λ(1 − λ)2.
(λ2 + 1)(2 − γ − λ)(18)

The derivative of W (λ) is
W ′ (λ) =16(1 − λ) (γλ3 + γλ2 + 3γλ − γ − 6λ + 2)
(λ2 + 1)2 (2 − γ − λ)2 .

For brevity, let us denote
w(λ) = γλ3 + γλ2 + 3γλ − γ − 6λ + 2.
Then sgn W ′ (λ) = sgn w(λ). The function w(λ) is a continuous, w(0) = 2 − γ < 0 andw(1) = −4(1 − γ) < 0, so w(λ) has a root in (0, 1). Let us denote it by λ∗ . Moreover,as w(λ) is a polynomial, with leading coefficient γ > 0, w(λ) > 0 for sufficiently large λand w(λ) < 0 for sufficiently small λ < 0. Therefore it must have one root in (1, ∞) and
one root in (−∞, 0). As it is a third-order polynomial, it has at most three roots. We
have therefore determined that λ∗ is its only root in (0, 1).
These arguments establish that W ′ (λ∗ ) = 0, W ′ (λ) > 0 for all λ < λ∗ , and W ′ (λ) < 0
for all λ > λ∗ . Therefore W (λ) is maximized at λ∗ . If we set γ = λ, we get a polynomial
w(λ) = λ4 + λ3 + 3λ2 − 7λ + 2. In this case, we can directly check the roots and see thatit again has a unique root in (0, 1), which is γ inc defined by equation (15).
The
combination of these observations proves all claims for V cartel (λ).
The proof for V cartel (λ) is analogous, with the exception that its derivative with respectto λ has a slightly higher root λ∗∗ > λ∗ . Notice that if we set γ = λ to this expression,
we get the same polynomial as before, and its root is again γ inc . This is not surprisingbecause at the limit λ = γ = γ inc all players participate in the cartel, and therefore

A12V cartel (λ) coincides with W (λ).

A3.2

Entry Requirements to the Cartel

Our model can also shed some light on the reasons why influencer cartels in practice often
impose entry requirements. A typical requirement is to have at least some minimum
number of followers, ranging from 1,000 to 100,000 in our sample.
We saw that the cost of joining the cartel depends on the player’s own reach, while
the benefit depends on the average reach of a cartel member. By imposing a minimum
entry requirement for reach, the cartel can increase the average reach, making the cartel
more appealing to players with higher reach. The combination of these two effects raises
the average reach and benefits all members. Therefore, we would expect the entry requirement to raise the average benefits for the cartel member, V cartel (λ). On the other
hand, excluding players with low reach means that fewer players are eligible to join thecartel, which may reduce the social welfare, W (λ). The following proposition confirms
this intuition.
Proposition 4. Suppose that in addition to engagement requirement Λ > 0, the cartel
imposes an entry requirement R > 1, so that only players with Rt ≥ R are eligible tojoin.
The mean payoff of a cartel member, V cartel (λ), is proportional to R and themean payoff of a player, W (λ), is proportional to R−1 .
The cartel may, therefore, choose to restrict the eligibility as such a restriction would
raise the cartel member’s welfare. On the other hand, the cartel organizer must be waryof the downside—eligibility restriction reduces the number of cartel members, and thiseffect is large enough to reduce the overall welfare. If there is a single cartel, it depends
on the cartel organizer’s objective whether the restriction is beneficial. However, it iseasy to imagine an extension where multiple cartels can be arranged: some that focus
on smaller players who will then engage more actively and others that limit access tolarge players and require less engagement. As we see in the data, this is what happens
in practice.
Proof If λ ≤ γ, then by the same arguments as above, all eligible players join the cartel,and therefore the expected reach of cartel members is E(Rst |Rst ≥ R) = 2R. The mean
payoff for cartel members is
V cartel (λ) =8λ(1 − λ)R.
λ2 + 1This is the same expression as above, in equation (16), but multiplied with R. The
difference is that now players with Rt < R cannot join. Their probability that player is
A13eligible is P r(Rt ≥ R) = R−2 . Therefore the, social welfare is
W (λ) =

8λ(1 − λ) −1R .
λ2 + 1

Again, the same expression as equation (16), but now multiplied with R−1 .
Suppose now that γ < λ < 1. By the same arguments as before, only players with areach below marginal value R will join the cartel. Therefore, the average reach of a cartel
member is nowRR

E Rst | R ≤ Rst ≤ R =R

dRst
Rst 2Rs−3
t

RR

2Rs−3
dRst
t
R

2

=
R

−1

+R

−1 .

Using this value, we can now compute the marginal type using ucartel (R) = 0 and get R =2−γ−λR. Therefore, the expected reach of a cartel member is in equilibrium E(Rst |R ≤λ−γ
R. Inserting this into the expected payoff expression gives the expected
Rst ≤ R) = 2−γ−λ1−γpayoff for a cartel member,
V cartel (λ) =4δλ(1 − λ) 2 − γ − λR.
λ2 + 11−γ

Again, this expression is identical to the unconditional payoff expression, just scaled with
R. Finally, the probability that a player is eligible and chooses to join the cartel is
P r(R ≤ Rst ≤ R) = R−2 − R−2=4(1 − γ)(1 − λ) −2R .
(2 − γ − λ)2Therefore the, social welfare is
W (λ) =16δλ(1 − λ)2R−1 .
(λ2 + 1)(2 − γ − λ)In each case, our findings are the same. Increasing R increases the mean cartel member’s payoff, V cartel (λ) from the cartel linearly. However, it reduces cartel membership
quadratically and, therefore, reduces the overall average payoff W (λ) linearly.

A14

A4

Online Appendix: Data Collection

A4.1

Telegram Cartel History

We collected Telegram cartel interaction history for 9 cartels: 6 general cartels (1K, 5K,
10K, 30K, 50K, 100K) and 3 topic cartels (fashion & beauty, health & fitness, travel &food). The 9 cartels were formed the earliest in August 2017 (10K and 50K) and thelatest in February 2018 (5K). We downloaded the data in June 2020. In June 2020 all
cartels had new posts.
The Telegram cartel interaction history consists of three pieces of information: Telegram username, Instagram post shortcode, and time. The interaction history tells us
which Telegram user, added when, and which Instagram post to the cartel. According to
the cartel rules, this information allows to determine which cartel member has to comment and like which post. This is because one has to comment and like five posts byother users directly preceding one’s own.

A4.2

Mapping Telegram Posts to Instagram Users

The Telegram cartels included 220,893 unique Instagram posts that we were able to map
to 21,068 Instagram users. Specifically, the Telegram cartels included 316,462 unique
Instagram posts altogether. Some posts are posted multiple times and/or multiple cartels, the 316,462 unique Instagram posts were posted in total 527,498 times. The cartel
interaction files don’t include the Instagram username of the author of the Instagram
post. We mapped the Instagram posts included in cartels to Instagram users using thefollowing interactive procedure. For the first Instagram post in the cartel of each Telegram user, we searched for the post on Instagram to learn the Instagram username of thepost’s author. Then we obtained from CrowdTangle the full list of all the Instagram postsof that Instagram username and matched those to the posts in the cartel. We checked
the remaining unmatched posts in the cartel one by one until we either found a matchfor it on Instagram or determined that the post had been deleted on Instagram or madeprivate. In this way, we were able to determine the Instagram usernames of 70% of theposts in the cartels, altogether 21,068 Instagram usernames.
Of the 21,068 Instagram users, 22% of users had posted in both topic and generalcartels. Altogether, 11,158 users had posted in topic cartels and 14,566 users in general.
This includes 4,656 users who had posted in both. Hence, the total number of users
equals 11,158 + 14,566 - 4,656 = 21,068.
From CrowdTangle, for all the 21,068 Instagram users, we obtained the history of
all their Instagram posts. This data included the time of the post, and the text of the

A15

post including the hashtags. The data was downloaded from August 19 to September 16,
2021.

A4.3

Instagram Comments

For each Instagram user, for their first post in cartels (no matter which cartel), wecollected information on who commented on the post. Our goal was to learn who engaged
with the post and compare natural (non-cartel) engagement to that obtained via cartels.
Therefore, we did not focus on the comment but instead only on the username that posted
the comment. We restricted attention to the commenters on the post itself, and excluded
commenters who commented on a comment.
We focused on each user’s first post in cartels to minimize the possibility that involvement in cartels had affected engagement. However, when the first post did not haveenough information for the analysis, that is, when for the first post none of the cartel
members who were required to comment existed anymore, then we focused on the second (if the second post existed) and so on. We did not require that the cartel members
actually commented, only that the users still existed. For 18 users no post existed thatsatisfied the requirement reducing the sample to 21,050 users. Among the remaining
21,050 users, for 99.8% (20,999), it was of their actual first posts. To simplify the exposition, in going forward, we call all the first posts satisfying the requirement, simply the
first posts.
We used Apify to collect the comments. It allows access to the comments that areavailable without logging in to Instagram and provides only up to 50 comments for eachpost. The data included the username of the commenter and the text of the comment.
While we don’t use the text of the comment in our main analysis, we do analyze it inAppendix A5. The comments were downloaded in January 2024.
We were able to collect comments only for 16,630 posts, which is 79.0% of the 21,050
first posts. We could not collect comments for all the first posts, because these posts
either did not have any comments but mostly because we attempted to collect thesecomments more than two years after collecting posts itself, and in two years these users
or their posts were either deleted or made private. Of the posts for which we were able
to collect comments, some had no non-cartel comments, leaving us with 16,386 posts.
Hence, we were able to find non-cartel comments for 77.8% of the total 21,050 first posts.
For both topic and general cartels the percentage of first posts for which we got non-cartel
comments was similar, 78%.

A16

A4.4

Random Non-Cartel Commenter on Each Cartel Member’s First Cartel Post

For each cartel member’s first post in cartels, we used a random number generator andpicked a random non-cartel user who had commented on the post. We picked these random non-cartel users for 16,386 posts. Some of the randomly picked non-cartel commenting users were the same across posts. Hence, we were left with 14,490 unique non-cartel
commenting users.
For these 14,490 non-cartel users, we collected their information about their numberof public posts. We collected this information using Apify in January 2024. Of theseusers, 24 didn’t exist anymore. So that we were left with 14,466 non-cartel users. Of
those, 3,049 (21.0%) had no public posts. We had to exclude those user because they
had no information we could analyze. So that we were left with 11,417 public non-cartel
users. We further limited the sample to non-cartel users who had at least 10 public posts
and this restriction reduced the sample to 10,394 non-cartel users.
For these random non-cartel users, we obtained the history of all their Instagram posts
from CrowdTangle. We did this to calculate authors’ similarity to the non-cartel users
who commented on the post. For these non-cartel users, the data was downloaded from
CrowdTangle in January 2024. We were able to get the history only for 10,280 non-cartel
users (99%). For the remaining 114 usernames either they had changed the username,made the account private or deleted it. Furthermore, we learned that 551 (5%) of the
10,280 non-cartel users were associated with cartel members as they had posted at least
one post associated with a cartel member. The association can happen as Instagram
allows posts to be associated with multiple users (this is different from tagging a user)or it can happen when users change usernames. We excluded those 551 non-cartel users
from our sample, while keeping the corresponding cartel members. That reduced thesample of non-cartel users to 9,729. These 9,729 non-cartel users mapped to 10,683 firstposts because, as said above, some of these non-cartel users were commenting on multiple
posts.

A4.5

Photos from First Posts

We collected a photo from a single Instagram post for each user. For cartel members, we
use the first post each cartel member posted to the cartels. For non-cartel members, weselect their closest post within a symmetric time window to the cartel member’s post theycommented on. The photos were downloaded in February and March in 2024. We wereable to get the photos for only 16,693 (79%) cartel members and 9,269 (95%) non-cartel
users. The reason why we did not get photos for 21% of the cartel members is the sameA17

as for the comments, that in the two years the posts were either deleted or made private.
Similarly, due the delay, we did not get photos for 5% of the non-cartel users.
In the end, we were left with 5244 authors whose first post was in general cartels and3751 authors whose first post was in topic cartels. Therefore, the percentage reduction
due to data limitations was similar for general cartels and topic cartels. Thus we haveno reason to expect that the data collection affected different cartel types differently.

A18

A5

Online Appendix: Additional Empirical Results

Table A5.1: How substantial and relevant are cartel versus non-cartel comments
(1)

(2)

(3)

(4)
(5)
(6)
(7)
(8)
(9)
Posts in general or topic cartels
General Topic
Both General Topic
Both General Topic
Both
Comment has text
Log. comment length
Photo-comment similarity
General cartel comment 0.104***
0.101*** 0.369***
0.386*** 0.005***
0.004**(0.005)(0.016) (0.020)(0.060) (0.001)(0.002)
Topic cartel comment
0.119*** 0.113***0.464*** 0.524***0.008*** 0.008***(0.006) (0.016)(0.023) (0.059)(0.001) (0.002)
Base (non-cartel) mean 0.873
0.868
0.863
2.693
2.719
2.662
0.221
0.220
0.219
Author fixed effects
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Authors
4432
3399
380
4432
3399
380
4398
3369
376
Observations
14922
11862
2328
14922
11862
2328
14045
11210
2218
Notes: Each column presents estimates from a separate panel data fixed effects regression. Unit ofobservation is an author and commenter pair. Outcome variable in columns 1–3 is an indicator whether
the comment includes any text; in columns 4–6, the logarithm of the comment length measured incharacters; in columns 7–9, the cosine similarity between the photo (in the author’s first post in cartels)
and the text of the comment, and it is calculated using embeddings from the CLIP model. Each regression
includes author fixed effects (equivalent to the post fixed effects because only one post per author). In
all the regressions, the base category is the non-cartel comment; and Base (non-cartel) mean presents
the average value of the outcome variable for the base category. General cartel comment is an indicatorvariable for the comment from the general cartel, and Topic cartel comment whether it is from the topic
cartel. The sample consists of authors whose first cartel post is either: only in general cartels (columns
1, 4, and 7); only in topic cartels (columns 2, 5, and 8); or in both general and topic cartels (columns 3,
6, and 9). Standard errors in parenthesis are clustered at the author level.

Table A5.2: Most representative hashtags for each LDA topic
Topic number
Topic 1

Topic label
Fitness

Topic 2

BeautyTopic 3

FashionTopic 4

Food

Topic 5

Entrepreneur

Topic 6

TravelMost representative hashtags#fitness #gym #workout #motivation #fitnessmotivation #fitfam #fit
#bodybuilding #health #training#art #music #makeup #artist #photography #beauty #makeupartist#design #mua #yoga#fashion #ootd #instagood #style #photooftheday #fashionblogger#picoftheday #beautiful #photography #beauty#foodie #foodporn #food #instafood #liketkit #foodphotography#foodstagram #foodblogger #yummy #delicious#motivation #entrepreneur #success #business #inspiration #luxury#quotes #motivationalquotes #mindset #entrepreneurship#travel #travelgram #travelphotography #wanderlust #travelblogger#nature #photography #instatravel #photooftheday #beautifuldestinations

A19

Table A5.3: Sample construction
Number of authors
Panel A: Number of authors in the regression sample
Total number of authors in the cartel
21068.. with cartel commenters21050.. and with non-cartel commenters10683.. and author has embeddings
10171.. and cartel commenter has embeddings
10022.. and non-cartel commenter has embeddings
8507
Panel B: Number of authors in the LDA sample
Total number of authors in the cartel
21068.. with cartel commenters21050.. and with non-cartel commenters10683.. and author has LDA
8936.. and cartel commenter has LDA
8835.. and non-cartel commenter has LDA
6654

Table A5.4: Summary statistics of authors in cartel included/excluded from the sample(1)(2)
Authors included vs excluded from the sample
Excluded
Included
Regression sample
Number of posts
Number of words per post
Average number of hashtags per post
Observations

583.0
47.0
13.2
12561

735.7
54.9
14.4
8507
LDA sample

Number of posts
Number of words per post
Average number of hashtags per post
Observations

615.0
46.8
12.5
14414

709.0
57.6
16.3
6654

Notes: According to the t-test, all differences between columns 1 and 2 are statistically significant at 1
percent level.

Table A5.5: Summary statistics of authors in different types of cartel
(1)
(2)
(3)
Authors in cartels
General Topic Both
Number of posts
Number of posts in cartel
Number of words per post
Average number of hashtags per post
Observations

860.8
13.3
51.4
14.0
4756

570.1
10.0
59.3
15.0
3263

624.3
12.7
58.9
14.4
488

Notes: The table includes authors in the main regression sample. According to the t-test, all differences
between columns 1 and 2 are statistically significant at 1 percent level.

A20

Table A5.6: Summary statistics of users in cartels versus not in cartels(1)
User not in cartel(2)
User in cartel

769.1
48.9
13.7
7847

730.9
53.8
14.4
12088

Number of posts
Number of words per post
Average number of hashtags per post
Observations

Notes: The table includes users (authors and commenters) in the main regression sample. According to
the t-test, all differences are statistically significant at 5 percent level.

Table A5.7: Alternative outcome variables: random posts; all posts in 2017–2020
(1)
(2)
(3)
(4)
(5)
(6)
Dependent variable: Cosine similarity from text embeddings
Posts in general or topic cartels
GeneralTopic
BothGeneralTopic
Both
Random 100 posts
All posts 2017-2020
General cartel commenter-0.044***(0.002)

Topic cartel commenter
Random user
Wald test, βGen = βT op , p-value
Base (non-cartel) mean
Author fixed effects
Authors
Observations-0.073***(0.002)-0.012***(0.003)-0.075***(0.003)

0.626
Yes
4749
44752

0.630
Yes
3261
30459

-0.044***(0.007)0.006(0.007)-0.062***(0.007)
0.000
0.623
Yes
487
6630

-0.028***(0.002)-0.066***(0.002)-0.000(0.003)-0.068***(0.003)

0.651
Yes
4750
43650

0.656
Yes
3261
29745

-0.038***(0.007)0.010(0.007)-0.062***(0.007)
0.000
0.647
Yes
488
6546

Notes: Each column presents estimates from a separate panel data fixed effects regression. Unit ofobservation is an author and another user pair. Outcome variable is the cosine similarity of the author
to his commenter or to a random user. In columns 1–3, the outcome variable is calculated based on thehashtags in user’s 100 randomly chosen posts; in columns 4–6, it is calculated based on hashtags in all
posts in 2017–2020 (for further details see Section 4.2.1). Each regression includes author fixed effects(equivalent to the post fixed effects because only one post per author). In all the regressions, the basecategory is the author’s similarity to a non-cartel commenter; and Base (non-cartel) mean presents theiraverage cosine similarity. General cartel commenter is an indicator variable whether the commenter towhom the author’s cosine similarity is calculated, is in the general cartel, and Topic cartel commenter
whether he is in the topic cartel. Random user indicates that the author’s similarity is calculated to arandom non-cartel user who didn’t comment. Standard errors in parenthesis are clustered at the author
level.

A21

Table A5.8: Alternative outcome variable: whole text instead of hashtags
(1)
(2)
(3)
Dependent variable: Cosine similarity from text embeddings of full text
Posts in general or topic cartels
GeneralTopic
BothGeneral cartel commenter-0.043***-0.042***(0.002)(0.006)
Topic cartel commenter-0.014***-0.003(0.003)(0.006)
Random user
-0.073***-0.079***-0.063***(0.002)(0.003)(0.006)
Wald test, βGen = βT op , p-value
0.000
Base (non-cartel) mean
0.659
0.665
0.662
Author fixed effects
Yes
Yes
Yes
Authors
4756
3263
488
Observations
44900
30569
6665
Notes: Each column presents estimates from a separate panel data fixed effects regression. Unit ofobservation is an author and another user pair. Outcome variable is the cosine similarity of the author
to his commenter or to a random user. It is calculated using the whole text instead of only hashtags (forfurther details see Section 4.2.1). Each regression includes author fixed effects (equivalent to the post
fixed effects because only one post per author). In all the regressions, the base category is the author’s
similarity to a non-cartel commenter; and Base (non-cartel) mean presents their average cosine similarity.
General cartel commenter is an indicator variable whether the commenter to whom the author’s cosine
similarity is calculated, is in the general cartel, and Topic cartel commenter whether he is in the topic
cartel. Random user indicates that the author’s similarity is calculated to a random non-cartel user who
didn’t comment. Standard errors in parenthesis are clustered at the author level.

A22

Table A5.9: Alternative outcome variables: photo embeddings, text embeddings
(1)

(2)
(3)
(4)
(5)
(6)
Dependent variable: Cosine similarity of posts
Posts in general or topic cartels
GeneralTopic
BothGeneralTopic
BothPhotos embeddings
Text embeddings
General cartel commenter-0.033***(0.002)

Topic cartel commenter
Random user
Wald test, βGen = βT op , p-value
Base (non-cartel) mean
Author fixed effects
Authors
Observations-0.051***(0.002)-0.008***(0.002)-0.053***(0.002)

0.487
Yes
4756
44900

0.493
Yes
3263
30569

-0.037***(0.005)-0.004(0.005)-0.044***(0.005)
0.000
0.491
Yes
488
6665

-0.019***(0.001)-0.016***(0.001)-0.009***(0.002)-0.018***(0.002)

0.777
Yes
4756
44900

0.780
Yes
3263
30569

-0.021***(0.004)-0.008**(0.004)-0.022***(0.004)
0.000
0.784
Yes
488
6665

Notes: Each column presents estimates from a separate panel data fixed effects regression. Unit ofobservation is an author and another user pair. Outcome variable is the cosine similarity of the author
to his commenter or to a random user. It is calculated using embeddings from the CLIP model of either
only photos (columns 1–3), or only text (columns 4–6). Each regression includes author fixed effects(equivalent to the post fixed effects because only one post per author). In all the regressions, the basecategory is the author’s similarity to a non-cartel commenter; and Base (non-cartel) mean presents theiraverage cosine similarity. General cartel commenter is an indicator variable whether the commenter towhom the author’s cosine similarity is calculated, is in the general cartel, and Topic cartel commenter
whether he is in the topic cartel. Random user indicates that the author’s similarity is calculated to arandom non-cartel user who didn’t comment. Standard errors in parenthesis are clustered at the author
level.

A23

Table A5.10: Alternative sample: commenters who actually commented
(1)

(2)
(3)
(4)
(5)
(6)
Dependent variable: Cosine similarity
Posts in general or topic cartels
GeneralTopic
BothGeneralTopic
Both
Similarity of users
Similarity of posts
Text embeddings
Photo+text embeddings
General cartel commenter-0.055***(0.003)Topic cartel commenter
Random user
Wald test, βGen = βT op , p-value
Base (non-cartel) mean
Author fixed effects
Authors
Observations-0.067***(0.003)-0.020***(0.004)-0.074***(0.003)

0.566
Yes
3361
27379

0.581
Yes
2635
21797

-0.062***(0.011)
0.005(0.011)-0.056***(0.010)
0.000
0.573
Yes
281
2961

-0.033***(0.002)-0.037***(0.001)-0.014***(0.002)-0.040***(0.002)

0.652
Yes
3361
27379

0.655
Yes
2635
21797

-0.032***(0.005)-0.011**(0.005)-0.035***(0.004)
0.000
0.656
Yes
281
2961

Notes: The table presents estimates from the same regressions as in Table 1 except the sample includes
only these cartel commenters who actually commented. Each column presents estimates from a separate
panel data fixed effects regression. Unit of observation is an author and another user pair. Outcome
variable is the cosine similarity of the author to his commenter or to a random user. Each regression
includes author fixed effects (equivalent to the post fixed effects because only one post per author). In
all the regressions, the base category is the author’s similarity to a non-cartel commenter; and Base(non-cartel) mean presents their average cosine similarity. General cartel commenter is an indicatorvariable whether the commenter to whom the author’s cosine similarity is calculated, is in the generalcartel, and Topic cartel commenter whether he is in the topic cartel. Random user indicates that theauthor’s similarity is calculated to a random non-cartel user who didn’t comment. Standard errors inparenthesis are clustered at the author level.

A24

Table A5.11: Heterogeneity by topic cartel
Posts in topic cartels, by the topic
FashionFitness
TravelFashionFitness
Travel& beauty & health& food& beauty & health& foodSimilarity of users
Similarity of posts
Text embeddings
Text+photo embeddings
Topic cartel commenter
Random user
Base (non-cartel) mean
Author fixed effects
Authors
Observations-0.014**(0.007)-0.059***(0.006)
0.572
Yes
728
6386

0.005
(0.008)-0.081***(0.008)
0.569
Yes
573
4953

-0.033***(0.004)-0.081***(0.004)
0.596
Yes
1881
18184

-0.011***(0.003)-0.038***(0.003)
0.662
Yes
728
6386

-0.006(0.004)-0.050***(0.004)
0.666
Yes
573
4953

-0.018***(0.002)-0.038***(0.002)
0.652
Yes
1881
18184

Notes: The table presents estimates from the same regressions as in Table 1 except the sample is asubset of the sample in columns 2 and 5 of Table 1. Specifically, the sample consists of authors whose
first cartel post is either: only in Fashion and beauty cartel (columns 1 and 4), only in Fitness and healthcartel (columns 2 and 5), or only in Travel and food cartel (columns 3 and 6). Note that those authors
whose post is in multiple cartels are excluded. Each column presents estimates from a separate panel
data fixed effects regression. Unit of observation is an author and another user pair. Outcome variable
is the cosine similarity of the author to his commenter or to a random user. In columns 1–3, the cosine
similarity of users is calculated using the text embeddings from the LaBSE model; in columns 4–6, thecosine similarity of the corresponding users’ posts is calculated using the photo and text embeddings
from the CLIP model. Each regression includes author fixed effects (equivalent to the post fixed effects
because only one post per author). In all the regressions, the base category is the author’s similarity
to a non-cartel commenter; and Base (non-cartel) mean presents their average cosine similarity. Topic
cartel commenter is an indicator variable whether the commenter to whom the author’s cosine similarity
is calculated, is in the topic cartel. Random user indicates that the author’s similarity is calculated to arandom non-cartel user who didn’t comment. Standard errors in parenthesis are clustered at the author
level.

A25

.2
Coherence score
.05
.1
.15
0

2

5

8

11
14
Number of topics

17

20

Figure A5.1: LDA model coherence scores by the number of topics
Notes: The figure presents the Normalized Pointwise Mutual Information (NPMI) coherence score (yaxes) for each LDA model, comparing models with the number of topics (x-axes) ranging from two totwenty. The score is calculated for the top ten words in each topic with a window size of five words.

A26

.6
0

.2

.4

Average topic share

.6
.2

.4

Average topic share

0

ss
ne
Fit

ty
au
Be

ion
sh
Fa

r
eu
ren

od

Fo

p
tre
En

Excluded

el

ss
ne
Fit

av
Tr

ty
au
Be

Sample

sh
Fa

ion

od

Fo

Excluded

r
eu

el

av
Tr

Sample.2.4

Average topic share

0

0

.2

.4

Average topic share.6(b) Fashion & beauty cartel.6(a) General cartels

ren

p
tre
En

ss
ne
Fit

ty
au
Be

ion
sh
Fa

Excluded

r
eu
ren

od

Fo

p
tre
En

el

ss
ne
Fit

av
Tr

Sample

ty
au
Be

sh
Fa

ion

Excluded(c) Fitness & health cartel

od

Fo

ren

p
tre
En

r
eu

el

av
Tr

Sample(d) Travel & food cartel

Figure A5.2: Authors’ topics: regression sample versus excluded
Notes: Average LDA topic distribution of the authors in the regression sample versus excluded cartel
members.

A27

.6
0

.2

.4

Average topic share

.6
.2

.4

Average topic share

0

ss
ne
Fit

ty
au
Be

ion
sh
Fa

r
eu
ren

od

Fo

p
tre
En

Excluded

el

ss
ne
Fit

av
Tr

ty
au
Be

Sample

sh
Fa

ion

od

Fo

Excluded

r
eu

el

av
Tr

Sample.2.4

Average topic share

0

0

.2

.4

Average topic share.6(b) Fashion & beauty cartel.6(a) General cartels

ren

p
tre
En

ss
ne
Fit

ty
au
Be

ion
sh
Fa

Excluded

r
eu
ren

od

Fo

p
tre
En

el

ss
ne
Fit

av
Tr

Sample

ty
au
Be

sh
Fa

ion

od

Fo

Excluded(c) Fitness & health cartel

ren

p
tre
En

r
eu

el

av
Tr

Sample(d) Travel & food cartel

Figure A5.3: Authors’ topics: LDA sample versus excluded
Notes: Average LDA topic distribution of the authors in the LDA sample versus excluded cartel members.

A28