Influencer Marketing with Fake Followers

IIMB-WP N0. 580/2020

WORKING PAPER NO: 580

Abhinav Anand Assistant Professor Finance and Accounting Indian Institute of Management Bangalore Bannerghatta Road, Bangalore – 5600 76 [email protected]

Souvik Dutta Assistant Professor Social Sciences Indraprastha Institute of Information Technology Delhi - 110020 [email protected]

Prithwiraj Mukherjee Assistant Professor Marketing Indian Institute of Management Bangalore Bannerghatta Road, Bangalore – 5600 76 [email protected]

Year of Publication – January 2020

Inﬂuencer Marketing with Fake Followers

Abhinav Anand∗ Souvik Dutta† Prithwiraj Mukherjee‡

January 23, 2020

Abstract Influencer marketing is a practice where an advertiser pays a popular social media user (influencer) in exchange for brand endorsement. We develop an analytical model in a contract-theoretic setting between an advertiser and an influencer who can inflate her publicly displayed follower count by buying fake followers. There is a non-strategic third party audit which successfully detects fraud with some probability, leading to additional reputational costs for the influencer. We show that the optimal contract exhibits widespread faking which increases with the influencer’s true follower count (type). The advertiser exploits the influencer’s fraud as a screening mechanism to identify her type. The audit accuracy and penalty from being exposed do not affect optimal faking levels but the increased cost imposed by the audit to the influencer gets passed on to the advertiser in terms of higher payments. Our paper illustrates why fake followers are rife in influencer marketing, and how digital marketers can exploit this phenomenon to their advantage.

Keywords: Digital marketing, social media, inﬂuencer marketing, fake followers, optimal control, contract theory.

JEL Classiﬁcation: D82, D86, M31, M37

∗Assistant Professor of Finance, Indian Institute of Management Bangalore, abhinav.anand@iimb. ac.in †Assistant Professor of Economics, Indraprastha Institute of Information Technology Delhi, souvik@ iiitd.ac.in ‡Assistant Professor of Marketing, Indian Institute of Management Bangalore, pmukherjee@iimb. ac.in §We thank Bruno Badia, Manaswini Bhalla, Pradeep Chintagunta, Tirthatanmoy Das, Sreelata Jon- nalagedda, Manish Kacker, Ashish Kumar, Sanjog Misra and participants at the Chicago Booth-India Quantitative Marketing Conference (2018) at IIM Bangalore, and the entire review team at IJRM for their feedback and comments.

1 “At Unilever, we believe inﬂuencers are an important way to reach consumers and grow our brands. Their power comes from a deep, authentic and direct connection with people, but certain practices like buying followers can easily undermine these relation- ships.” — Keith Weed, Chief Marketing and Communications Oﬃcer, Unilever (Stewart, 2018)

1 Introduction

Advertisers often pay popular social media users known as “influencers” to endorse their products online. Many of these influencers have large numbers of self-selected followers who share their interests (travel, fashion, cooking, etc.) and look up to them for advice in these domains. According to The Economist(2016), YouTube influencers with over 7 million followers command upto $300,000 per sponsored post, while the corresponding figures for Instagram, Facebook and Twitter are $150,000, $187,500 and $60,000 respectively, allowing social media followings to be monetized lucratively. Even influencers with fewer than 250,000 followers can make hundreds of dollars per sponsored post. Figure1 shows some typical compensations for influencers on various platforms versus their follower counts. A Linqia(2018) survey across sectors including consumer packaged goods, food and beverage and retail in the US finds that 86% of marketers surveyed used some form of influencer marketing in 2017, and of them, 92% reported finding it effective. 39% of those surveyed planned to increase their influencer marketing budgets. Similar trends reported by eMarketer(2017) and IRI(2018) suggest that influencer marketing is growing. Influencer marketing has led to the emergence of shady businesses called “click farms” which offer fake followers to influencers for a price, inflate the number of “likes” on their fan pages, and post spurious comments on their posts. Influencers use these services to fraudulently command higher fees from advertisers for promotional posts. A New York Times exposé(Confessore et al., 2018) finds that several personalities including prominent social media influencers have bought fake followers from a click farm called Devumi. Sway Ops, an influencer marketing agency estimates the total magnitude of influencer fraud to be about $1 billion (Pathak, 2017). They find that in a single day, of 118,007 comments sampled on #sponsored or #ad tagged Instagram posts, less than 18% were made by genuine users. Another study by the Points North Group finds that influencers hired by Ritz-Carlton have 78% fake followers (Neff, 2018). The corresponding numbers for Procter and Gamble’s Pampers and Olay brands are 32% and 19% respectively. The quote at the beginning of this paper, by Unilever’s Chief Marketing and Communications Officer at the Cannes film festival, indicates that marketers are acutely aware of the fake

2 follower problem and seek mechanisms to deal with it.

Figure 1: Insert here

In our work, we adapt the model of fraud in Crocker and Morgan(1998) to design an optimal contract between an advertiser and an influencer. The advertiser proposes to pay the influencer in exchange for brand endorsement in order to reach her followers on a social media platform. In order to appear more popular or influential (see section 2.2 for a link between popularity and influence) and thereby command more payment, the influencer can buy fake followers. The advertiser, as a result, can only observe the publicly displayed follower count consisting of both real and fake followers. For the influencer, we assume that costs of hiring fakes and covering-up the fraud can be captured via a convex cost function which increases in the degree of misrepresentation. Further, we assume that a non-strategic third party—such as a social media audit app like IG Audit or the social media platform itself—conducts an audit and, with some probability1, successfully detects fraud by the influencer. We assume that if the influencer’s fraud is exposed in the audit, she suffers an additional detection penalty. We also assume that the audit is not commissioned by the advertiser. Optimal contract design in such a setting features an intrinsic trade-off. A contract that is sensitive to the observed number of followers ensures efficiency but generates perverse incentives for an influencer to inflate her true follower count. On the other hand, a payment scheme that is unresponsive to the observed follower count could mitigate the problem of misrepresentation but will be inefficient, as it fails to provide incentives for those with high follower counts to accept the contract. Thus the optimal contract must find a balance between these two opposing forces. We show that it is worthwhile for almost all types of influencers to buy fake followers under the optimal contract. In fact, buying fake followers is essential for the influencer to signal her true type (i.e., genuine follower count) and the advertiser exploits this to screen and ordinally rank influencers according to their type. Moreover, in equilibrium we find that the degree of fraud is independent of either the audit accuracy or penalty arising from successful detection, but the payment made out to the influencer increases. Therefore from the advertiser’s perspective, the audit and subsequent detection of fake followers leads to higher costs of influencer hiring. We note that while puzzling, such “backfiring” is observed in some manufacturer-supplier audits (Plambeck and Taylor, 2015). We draw the following important managerial implications based on the results of our

1This less-than-perfect accuracy is in line with Silverman(2018) who ﬁnds that fake follower bots are increasingly hard to detect because click farms are modeling them on real user behavior

3 study. The advertiser can use the influencer’s fraud to its advantage by separating out the influencers according to their true number of followers. Another surprising implication is that compared to the no-audit case, the advertiser’s payoff is lower in the presence of an external audit. However the advertiser is willing to absorb the extra cost imposed on the influencer by the audit; and increases the payment to induce her to participate. The rest of the paper is structured as follows. Section2 provides a general overview of influencer marketing, from both practitioner and theoretical perspectives. Section3 summarizes different methodological approaches to studying various types of analogous economic fraud, with an emphasis on optimal contract theory. Section4 describes the game between the advertiser and the influencer and section5 sets up an optimal control framework to solve the problem. We offer numerical illustrations of our results in section 5.2 and, finally in section6 we discuss the managerial implications of our model and offer concluding remarks.

2 Inﬂuencer marketing: an overview

Since the practice of influencer marketing is relatively new and not very well-researched, we present a brief overview of this domain, linking it to established theories of endorsement and social influence. We divide this into three parts where we, (i) cover the general practice of influencer marketing, (ii) discuss the role of follower count in influencer marketing, and (iii) describe how it leads to the specific problem of fake followers.

2.1 Inﬂuencer marketing

Influencer marketing is a promotion method that features brand endorsement using popular social media users. This makes it a hybrid of advertising and word-of-mouth, espe- cially when commercial ties between endorsers and brands are not explicitly disclosed.2 Influencer marketing is analogous to celebrity endorsements in advertising, with source (influencer) credibility (Hovland and Weiss, 1951) and attractiveness (McGuire, 1985; McCracken, 1989) contributing to effectiveness of promotional campaigns. Just like endorsers in advertising, influencers can be domain experts (tech bloggers, cooks, etc.), celebrities (musicians, actors, etc.); or even lay endorsers (Tellis, 2003, chapter 11). A recent study of influencer campaigns (Hughes et al., 2019) finds that their effectiveness

2This has led to ethical conundrums surrounding undisclosed influencer promotions. The US Federal Trade Commission has taken cognizance of the possibility of consumers being misled by influencer marketing, and has mandated that sponsored posts must now clearly mention the relationship between the influencer and brand, usually as a hashtag such as #sponsored or #ad. Platforms like Instagram have implemented algorithms to automatically detect and tag paid influencer posts.

4 depends on the social media platform used. For example, Facebook influencer campaigns tend to be more effective when message content is more hedonic than utilitarian. Nowadays, celebrities like actor Priyanka Chopra (Tiffany and co. jewelry), racing professional Danica Patrick (Lyft ride sharing), rapper Snoop Dogg (Tanqueray gin) star in online influencer campaigns alongside expert influencers like gamer H2ODelirious (Ubisoft gaming) and fashion blogger Jaclyn Hill (Becca cosmetics), and lay influencers like blogger Kelly Lund’s pet Loki the Wolf Dog (Mercedes-Benz, Toyota automobiles). Specialist agencies like Bzzagent also enlist ordinary netizens as “micro-influencers” to promote usually inexpensive consumer brands like chocolates and yoghurt in return for free product samples (Berger and Schwartz, 2011; Berger, 2016). Figure2 provides snapshots of some famous influencer campaigns on social media.

Figure 2: Insert here

The study of influence in social networks is another well established research area relevant to influencer marketing. The effects of network structure, personality and contextual factors are extensively documented in several fields like marketing, sociology and network science. Influentials on social media are characterized by high reach and spread of mes- sages, as well as high engagement on their content, leading to social influence (Marsden and Friedkin, 1993; Kumar and Mirchandani, 2012). Aral and Walker(2012) find that men are more influential online than women, and that women influence men more than they influence other women. Kumar et al.(2013) develop an influence score for social media users using their social network data and word of mouth flow, and demonstrate its efficacy in promoting Hokey Pokey, an Indian ice cream brand. Their method of identifying influentials and incentivizing them to spread word of mouth is among the more sophisticated applications of influencer marketing. Agencies like Klout (now discontin- ued), and PeerIndex have also provided multidimensional influence metrics with mixed success. A more common practice today, as evidenced by figure1, is to identify people with large follower counts on social media, and given their personas, pay them to endorse relevant brands. In the next subsection, we outline how online follower count relates to influence.

2.2 Follower count and inﬂuence

According to the source credibility theory (Hovland and Weiss, 1951), an endorsement message is more trustworthy when it comes from a source perceived to be an “expert” in a given domain. In a qualitative study of Instagram users, Djafarova and Rushworth(2017)

5 find that non-traditional celebrities may be perceived as more credible than traditional celebrities, and have a powerful impact on consumers’ fashion choices. An experimental study by Jin and Phua(2014) finds that the perceived credibility of a Twitter user is positively related to her number of followers. Alongside source credibility is source attractiveness (familiarity, likeability and similarity) (McGuire, 1985; McCracken, 1989; Tellis, 2003). Experiments by De Veirman et al.(2017) demonstrate that Instagram influencers’ perceived likeability is positively related to their follower counts, possibly driven by perceived popularity. From a more straightforward perspective, a social media user with a larger follower count represents an advertising medium with a larger reach. While the reach of traditional media like TV, radio, hoardings and newspapers can only be approximately estimated, it is reasonable to expect a naive advertiser unaware of fake followers, to place a high amount of trust in seemingly accurate measures like follower counts, number of likes on sponsored posts, retweets and impressions offered by web analytics tools. In a large scale study of 74 million Twitter information cascades encompassing over 1.6 million Twitter users, Bakshy et al.(2011) show a positive link between follower count and online influence. Agent-based studies of targeted new product seeding like Libai et al.(2013) demonstrate that targeting hubs with high numbers of acquaintances speeds up the adoption process, while Yoganarasimhan(2012), in an empirical analysis, suggests that the popularity of a social media message over and above an individual’s immediate neighborhood is driven by her follower count. While follower count is not the only means of determining social influence (see Kan- nan and Li(2017) for a comprehensive review, or Kumar et al.(2013) for a specific application), it certainly is a popular metric used by digital marketers today to identify influentials on social networks. The above discussions shed some light on why advertisers pay more to influencers with higher follower counts, in turn generating incentives for influencers to boost their own follower counts via unethical means like buying fake followers.

2.3 The fake follower problem

Influencer marketing today is plagued with a fake follower problem, possibly because endorsers are paid as per their follower count. A quick Google search for “buy instagram followers” for example yields hundreds of results, where anyone with a credit card or Paypal account can buy hundreds of thousands of fake followers instantly (see figure3). The rates for follows, retweets, likes and comments are different based on the platform in question. Paquet-Clouston et al.(2017) report that click farm clients pay an average of $49 for every 1,000 YouTube followers. The corresponding figures are $34 for Facebook,

6 $16 for Instagram and $15 for Twitter. Average prices for 1,000 likes on these platforms are $50, $20, $14 and $15 respectively.

Figure 3: Insert here

A recent audit by the Institute of Contemporary Music Performances, of the Twitter and Instagram followers of some of the most popular social media celebrities indicates significant numbers of fake followers, mostly above 40% and going up to 57% for Ellen Degeneres, a popular American entertainer (ICMP, 2019).3 Social media platforms some- times purge fake followers, though this reduces their user numbers considerably, and often causes outrage from aggrieved users as well. Of note is a recent incident where Amitabh Bachchan, a veteran Indian actor with a Twitter following of over 38 million, berated the platform publicly for reducing his follower count by purging many bot accounts following him (Mathew, 2018). Although this paper focuses exclusively on the fake follower problem in influencer marketing, the issue extends well beyond this particular domain. News reports increasingly indicate the use of fake followers and commentators to amplify certain voices and view- points for various political ends. The investigation by Confessore et al.(2018) exposes academics, consultants and actors who buy fake followers as well. Informal chats with entrepreneurs reveal the pervasive astro-turfing of new apps’ user numbers by employing click farms and thus attempting to mislead investors into overvaluing their businesses.4 A Buzzfeed investigation suggests increasing sophistication of fake follower bots. For example, shell companies that calibrate bots based on the behavioral patterns of genuine users may have siphoned off millions of dollars from advertisers (Silverman, 2018). All of these scenarios are interesting research domains in themselves, with potentially different approaches required to study them.

3 Background

We brieﬂy outline two streams of literature germane to our problem: (a) models of economic fraud and (b) applications of contract theory to marketing. Because these domains are large, we outline only a few studies in each, to motivate and contextualize

3We recognize that many click farms may make their bots follow celebrity accounts who may not have bought their services, just to mimic human behavior. In contrast, the New York Times expos´eof Devumi (Confessore et al., 2018) mentioned in section1 uncovers actual purchase of fake followers based on Devumi’s own client records 4This practice has even entered pop culture via HBO’s sitcom Silicon Valley, where the protagonists use a click farm service to fake a large user base. Following the episode, Letzter(2016) conﬁrms the prevalence of this practice among app developers to unethically boost their user numbers

7 our own work. In section 3.1 we discuss related models of economic fraud in online and oﬄine businesses, and in section 3.2, we motivate our choice of methodology of contract theory.

3.1 Economic fraud

Online businesses are prone to several kinds of marketing fraud. Advertisers paying per click frequently encounter click fraud where click farms simulate genuine clicks. Wilbur and Zhu(2009) in an important, related study investigate the problem of click fraud in search advertisement in a game theoretic setting. Their results suggest that usage of a neutral third party to audit click fraud detection can benefit the search advertising industry. Another form of online fraud consists of fake reviews, when businesses post either fake positive reviews for themselves or fake negative reviews for their competitors. Lappas et al.(2016) demonstrate how even a few fake reviews can significantly boost hotels’ visibility. Luca and Zervas(2016) find that the prevalence of suspicious restaurant reviews on Yelp has grown over time. They find that restaurants with weaker reputations tend to engage more in online review fraud when faced with increasing competition. A model of insurance and sharecropping fraud where agents involve in costly falsifi- cation is developed in a contract theoretic setting in Crocker and Morgan(1998). Their model yields results that have been extended to other fraud scenarios, like misreporting of earnings by CEOs (Crocker and Slemrod, 2007; Sun, 2014), many types of insurance fraud (Crocker and Tennyson, 2002; Dionne et al., 2009; Doherty and Smetters, 2005), and in designing optimal product return policies (Crocker and Letizia, 2014). Employee theft in retail can also be modelled analytically. Mishra and Prasad(2006) demonstrate that a complete elimination of theft may be economically infeasible and derive an optimal frequency of random inspections to minimize losses due to theft by retail employees. With this paper, we contribute to the literature on economic fraud by modeling the emerging phenomenon of fraud in influencer marketing.

3.2 Contract theory

In contract theory a principal wishes to hire an agent and designs an optimal contract which maximizes its proﬁt while respecting the agent’s participation and incentive compatibility constraints.5 Contract theoretic approaches have been used in marketing scenarios such as designing warranties and extended service contracts (Padmanabhan and Rao, 1993) and delegation of pricing decisions to salespersons (Bhardwaj, 2001; Mishra and Prasad, 2004, 2005) to name a few. Other noteworthy applications of contract the-

5See Bolton and Dewatripont(2005) for a comprehensive exposition

8 Table 1: Insert here

ory in marketing include explaining product development incentives (Simester and Zhang, 2010); and internal lobbying by salespersons for lower prices, which can elicit truthful information about market demand (Simester and Zhang, 2014). Our paper incorporates contract theory and optimal control theory in the digital marketing literature, illustrating the economics of inﬂuencer marketing fraud.

4 The model

We consider a risk-neutral advertiser who wishes to reach the followers of a risk-neutral influencer. The advertiser proposes to pay the influencer for brand endorsement via social media posts like sponsored tweets, videos or pictures. We outline the mathematical setup of the game that unfolds between the advertiser and influencer. Table1 provides a ready reckoner of terms used henceforth. The influencer privately knows her own number of genuine followers n but can inflate her public follower count by buying fake followers at a cost. The advertiser observes only the influencer’s publicly displayed follower count and not her true number of followers. However, the advertiser is aware that the true number of followers of the influencer is 6 distributed in [nL, nH ] according to the probability density function f(n). Under an optimal contract proposed by the advertiser, the equilibrium outcome is characterized by the ordered pair (v, u) where v(n) is a payment made to the influencer which depends on the latter’s follower count, and u(n) is the function used by the influencer to possibly inflate her true follower count n. The advertiser’s profit is denoted by Π(v, u) and the influencer’s payoff is denoted by Y (v, u, n). Additionally, we assume that a non-strategic third party audit is performed by the social media platform like Twitter or an independent entity similar to ICMP(2019), using a tool like IG Audit or Twitter audit. A successful detection of fraud occurs with probability γ. Upon successful detection, the influencer’s cost increases by a factor δ > 1. Higher values of δ indicate greater repuational damage or forgone monetary benefits therewith. In this paper, we assume that an influencer without any fake followers is never penalized mistakenly. While in practice we expect to observe an indirect mechanism where the advertiser’s payment to the influencer is conditioned on the displayed follower count u(n), we charac-

6While n is a natural number we assume for mathematical convenience that n is a non-negative real number

9 terize our solution via the corresponding direct mechanism. In other words, although the variable payment depends on the influencer’s publicly displayed, possibly inflated number of followers, i.e., v(u), the revelation principle (Myerson, 1979) guarantees that the same equilibrium outcome can be achieved under an incentive compatible direct mechanism where the influencer receives a variable payment v(n). We note that for the advertiser, the decision variable is not the underlying follower count n of the influencer but rather the display function u(n). This is because we assume that neither the advertiser nor the influencer can exercise control on the number of followers that the influencer possesses; and that the advertiser can only vary the compensation scheme v(n) in response to the display function u(n) of the influencer. In order for the equilibrium to be incentive compatible, it must be that at the optimal v∗, u∗, there is no incentive for the influencer to not act according to her own type. This happens only if:

∗ ∗ ∗ ∗ Y (v (n), u (n), n) ≥ Y (v (¯n), u (¯n), n) ∀n¯ 6= n ∈ [nL, nH ] (1)

For brevity, we denote the optimal value function Y (v∗, u∗, n) ≡ Y ∗(n) and note that since Y ∗(·) is optimal, its derivative with respect to the arguments v and u must be 0:

∗ ∗ ∂Y ∂Y = = 0 (2) ∂v v=v∗ ∂u u=u∗ Using the envelope theorem, by means of the total derivative, we establish the dependence of the optimal value function Y ∗ on the parameter n by:

dY ∗ ∂Y ∗ dv∗ ∂Y ∗ du∗ ∂Y ∗ = + + · 1 (3) dn ∂v∗ dn ∂u∗ dn ∂n This leads to the standard envelope condition:

dY ∗ ∂Y ∗ = (4) dn ∂n

Additionally, since the influencer privately knows her true number of followers, in order for her to find participation worthwhile, it must be that her realized payoff from participation is higher than the zero payoff she gets from not participating. This leads to the following participation constraint:

Y (v, u, n) ≥ 0 (5)

10 5 The optimal control problem

The advertiser wishes to maximize its expected proﬁt under the incentive compatibility and participation constraints of the inﬂuencer. Thus:

Z nH max Π(v, u)f(n)dn : (6) v,u nL dY ∂Y = (7) dn ∂n Y (v, u, n) ≥ 0 (8)

Optimization programs featuring integrals in objective functions and derivatives in the constraints can be solved by setting up an optimal control problem and ﬁnding the sta- tionary points of the associated Hamiltonian (Chiang, 1992). The expected proﬁt function (6) under the incentive compatibility constraint (7) and the participation constraint (8) can be combined into the following Hamiltonian:

H = Π(v, u)f(n) + λ(n)Yn + µY (v, u, n) (9)

In the above Hamiltonian formulation, Y (·), the inﬂuencer’s payoﬀ function is the state variable with its equation of motion represented by condition (7). The control variable is u(·); λ(n) is the co-state variable corresponding to the incentive compatibility constraint (7); and µ is the Lagrangian multiplier associated with the participation constraint (8). Proposition1 characterizes the solution of the optimal control problem further.

Proposition 1. The necessary conditions which characterize the solution of the optimal control problem are as follows:

Yu Yu f · Πu − Πv + λ · Yu,n − Yv,n = 0 (10) Yv Yv dλ Π Y λ˙ = = −f · v − λ · v,n − µ (11) dn Yv Yv

Proof. See appendixA.

5.1 The optimal contract

We now discuss the payoﬀ functions of the advertiser and the inﬂuencer in the presence of an audit.

11 5.1.1 Advertiser’s payoﬀ

The advertiser must pay the influencer v(n) for her endorsement. It makes this payment because it subjectively values the influencer’s endorsement as A(n) with A and A0 > 0. To be clear, in this context, A(n) is not a realized revenue function attributable to an influencer campaign, but rather a subjective managerial judgment by the advertiser, of the value of an influencer campaign. For example, A(n) could be based on the advertiser’s past experience, industry heuristics or managerial judgment. Furthermore, it may not even be feasible to have an exact formulation of A(n) due to possibly unreliable metrics (Lewis and Rao, 2015; Sridhar et al., 2017). The purpose of advertising (and indeed influencer marketing) often goes beyond boost- ing direct sales (usually a short-term tactical move) to more strategic long-term goals like building brand awareness, liking, and reinforcement of previous choices (Kotler and Keller, 2012, Chapter 18), or influencing various intermediate (pre-purchase) consumer mental processes (Tellis, 2003, Chapter 4). The effects of an influencer campaign on variables like brand liking, affect, recall, etc., and their subsequent quantifiable revenue effects are hard to measure. Indeed, the study of advertising effectiveness in the presence of other marketing mix variables and multiple campaigns in different media is not straightforward. On the other hand, if the exact revenue attributable to an influencer campaign were directly measurable, it would be possible for the advertiser to propose a revenue sharing contract that eliminates any incentive to buy fake followers. This is typically in short- term tactical sales promotions, where the influencer may be given her own referral code, that a consumer may enter on a shopping website while making a purchase (see figure 4).7 In such a case, the revenue attributable to the influencer can directly be measured by aggregating all purchases made through her referral code. As fake followers will not make any real purchases, the advertiser can offer the influencer a small fraction of the actually realized revenue from such sales over and above her outside option (normalized to zero in this paper), and eliminate any incentive for the influencer to spend resources buying costly fake followers.8 In fact, a quick comparison of the campaigns in figure2 with those in figure4 will confirm the prevalence of influencer campaigns with these two different objectives.

Figure 4: Insert here

We model the scenario where the inﬂuencer is paid before her endorsement and the

7Amazon has an inﬂuencer program that works on this model. See https://amzn.to/2uqRKBU 8We thank an anonymous reviewer for this observation.

12 revenue attributable to her services is not directly measurable with a referral code. This is the norm for celebrity influencer deals. Furthermore, there are platforms like Shoutcart, Influenster and Webfluential, that allow advertisers to enlist the services of thousands of freelance influencers signed up with them, with payments usually based on follower counts. Payments are always collected from advertisers by these platforms before the campaign. Some platforms may hold part of the money in escrow till the campaign is completed. Nonetheless the influencer is paid based on their follower count and not on attributable revenue. The advertiser’s payoff function Π(v, u) is the difference between A(n) and v(n):

Π(v, u) = A(n) − v(n) (12)

We note that A(n) is exogenous to v and u, thus converting the maximization problem to cost minimization for the advertiser:

Z nH Π∗ = max Π(v, u)f(n)dn {v,u} nL Z nH = max (A(n) − v(n)) · f(n)dn {v,u} nL Z nH Z nH = A(n) · f(n)dn + max (−v(n))f(n)dn (13) {v,u} nL nL

We leave the discussion of appropriate formulations of A(n) for section 6.3. However, we note that for the advertiser to find it worthwhile to propose a contract for hiring an influencer, A(n) must be sufficiently high.

5.1.2 Inﬂuencer’s payoﬀ

For the influencer, payoff is gained due to the payment v(n) from the advertiser but there is a cost of inflating follower count. This cost function includes the costs of hiring fake followers, as well as that of covering up the fraud, which rises as the extent of faking u(n) − n rises. We assume that c ≥ 0; c(0) = 0; c0(0) = 0 and c00 > 0. This captures the notion that costs are at least zero, no faking entails no cost and the costs of faking rise progressively higher as the extent of fraud increases. In other words, our assumption of the cost function being increasing and convex captures the hiring and cover up expenditures incurred by the influencer.9

9It is important to note that an influencer cannot just get away by buying fake followers. To pull off the fraud convincingly, she must also pay for more engagement such as fake replies, fake comments and fake likes on her social media posts. Unlike the purchase of fake followers which may be a one-time expense, buying fake online engagement from click farms is a recurrent expense, and thus our assumption of a convex cost function is justifiable, as it incorporates not just buying fakes, but also sustaining the deception.

13 Under an audit, the influencer’s fraud is exposed with probability γ. Upon successful detection of fraud, the influencer’s cost increases to δ · c(u(n) − n) where δ > 1. Thus the influencer’s payoff is given by:

Y (v, u, n) = (1 − γ) · (v(n) − c(u(n) − n)) + γ · (v(n) − δc(u(n) − n)) = v(n) − (1 − γ + γδ) · c(u(n) − n) (14)

This leads us to proposition2, which characterizes the optimal contract:

Proposition 2. The optimal contract is characterized by the following conditions:

c0(u − n) F (n) = (15) c00(u − n) f(n)

u(nL) = nL and u(n) > n ∀n ∈ (nL, nH ] (16) Z n v(n) = (1 − γ + γδ) · c(u − n) + c0(u(t) − t)dt (17) nL

Proof. See appendixB.

Thus, we see that except for the influencer at the lowest end of the [nL, nH ] interval, i.e. with n = nL followers, all other types resort to buying fake followers. The advertiser is aware of such faking, but must tolerate it because such a behavior guarantees efficiency, helping the advertiser ordinally rank, and thus distinguish high type influencers from lower types. Indeed, in the absence of such faking, influencers cannot signal their true type credibly. A payment mechanism which enforces no faking is not incentive compatible and leaves the advertiser with no way to distinguish high type from low type influencers. Further it is clear from equation (17) that the optimal payment is increasing in γ as well as δ. This implies that as the detection technology improves and as the penalty from detection increases, the increased costs to the influencer are passed to the advertiser in the form of increased payments. However the advertiser is willing to bear the drop in payoff because it helps it sort the influencer based on her genuine follower count.

Implementability and suﬃciency

Implementability requires that:

∂ Y du u · > 0 (18) ∂n Yv dn

14 The first term is the Spence-Mirrlees single-crossing condition. Since Yu,n = (1 − γ + 00 00 γδ)c (·) and Yv = 1, the first term reduces to c (u − n) · (1 − γ + γδ) > 0. This implies that u0 > 0 is necessary for implementability. For a quadratic cost function of buying fake d 0 followers, this is satisfied if dn F (n)/f(n) > 0. u > 0 implies that displayed follower count increases with the true number of followers of the influencer.

For suﬃciency, it is enough that Yn > 0 which in turn guarantees that the participation constraint binds only at n = nL leading to Y (nL) = 0; and Y (n) > 0 ∀n > nL. This is ensured if c0 > 0.

5.2 Illustration: quadratic costs of faking

From the conditions imposed on the inﬂuencer’s cost function: c(0) = 0, c0(0) = 0, c00(·) > 0, the only admissible quadratic function is of the form:

2 c(u − n) = c2 · (u − n) , c2 > 0 (19)

From proposition2, equation (15) yields:

F (n) F (n) u∗(n) = n + ⇒ u∗(n) − n = (20) f(n) f(n)

5.2.1 Uniform distribution

For a uniformly distributed n ∼ U[nL, nH ]

∗ u (n) = 2n − nL (21)

Using equation (17), the variable payment is:

∗ 2 v (n) = 2c2(n − nL) (1 − γ + γδ) (22)

Thus the optimal display function is aﬃne and increases with n; and the variable payment assumes a quadratic functional form. The level of faking u(n) − n increases with the number of true followers as: ∗ u (n) − n = n − nL (23)

If the mean of the uniform distribution increases (nH increases) there is no change in the number of fake followers hired by the inﬂuencer. This special feature disappears once we consider other distributions.

Figure 5: Insert here

15 5.2.2 Exponential distribution

It is reasonable to expect that an experienced advertiser assumes diﬀerent functional forms of the density f based on the the platform’s degree distribution and managerial intuition. Here we illustrate what happens to the level of faking when the advertiser

assumes that true followers are spread as a truncated exponential between [nL, nH ] = [100, 200000]. We vary the mean follower count by considering truncated exponentials with mean parameters as 50000, 60000, 70000 and 80000 respectively. We compute faking levels from the ratio of their distribution and density functions as in equation (15).

Figure 6: Insert here

5.2.3 Normal distribution

We illustrate what happens to the level of faking when the advertiser assumes that true followers are spread as a truncated normal between [nL, nH ] = [100, 200000]. We vary the mean follower count by considering truncated normal with mean parameters as 50000, 60000, 70000 and 80000 respectively and assume that the standard deviations for each equal 50000 to preserve comparability.

Figure 7: Insert here

With both exponential and normal distributions, we observe that for any given mean, there is convexity in the faking levels—i.e., those with more followers fake at a higher rate than those with fewer followers. Faking levels from low-mean distributions dominate those from high-mean distributions.

6 Discussion

Given the analytical results in the previous section, we highlight some important obser- vations.

6.1 The extent of fraud

In the illustrative example in section 5.2.1 with quadratic costs and a uniform distribution, the optimal display function for the inﬂuencer is u(n) = 2n − nL which leads to

an interesting observation. Consider the inﬂuencer of the highest type n = nH . This

inﬂuencer has the maximum follower count nH but will display the following:

16 u(nH ) = 2nH − nL = nH + (nH − nL) > nH (24)

In other words, the number of followers displayed exceeds the upper limit nH of the distribution’s support. Clearly the advertiser who knows that the true number of followers cannot be more than nH will not believe this overstated follower count and will conclude correctly that the influencer is faking. In particular, all influencer-types with n > (nL + 10 nH )/2 display a follower count strictly higher than nH . The reason why the advertiser allows such obvious faking is related to the efficiency of the optimal contract because it allows the advertiser to ordinally rank, and thereby distinguish between privately informed influencers of different types (i.e., true follower count n). In the absence of fraud, an influencer cannot signal her true type credibly. Since for a given displayed follower count, the costs of faking are different for different types, the advertiser can harness this variation to screen an influencer with high underlying true follower count from one with lower true following.

6.2 The eﬀect of audit

In our setup, there is a non-strategic third party audit which exposes the influencer’s fake followers with probability γ. For the influencer, this implies an escalation in total cost since detection of fake followers could result in reputational damage, monetary loss due to suspension from the platform, etc. Hence compared to the no-audit case, the influencer’s cost increases from c(u − n) to δc(u − n). The parameters γ ∈ (0, 1) and δ > 1 are assumed to be exogenous and completely characterize the audit. Note that in our model, the advertiser does not commission the audit. The optimal display function u∗(n), is determined by equation (15) in proposition2 and shows no dependence on the audit parameters γ, δ. The equation also indicates that the optimal faking level depends only on c0 and c00—i.e., only on how fast the cost rises from hiring fake followers and covering-up the subsequent fraud. Consequently, compared to no-audit, there is no change in the optimal display function u∗ of the influencer. On the other hand, the additional cost of being exposed in an audit leads to a drop in the expected payoff of the influencer. To induce her to participate, the advertiser bears this additional cost itself and incentivizes the influencer with higher payments. Increasing γ, and/or δ increases the payment that the advertiser must offer but does not cause any change in the level of fraud. Thus an improvement in auditing technology is worse for the advertiser since it needs to earmark increased payments to the influencer,

10While this observation may seem puzzling, we note that such results have also been noted in Maggi and Rodriguez-Clare(1995) and Crocker and Morgan(1998) where a sharecropper agent under-reports her yield to an egregiously low level to avoid sharing it with a principal who is aware of this scenario

17 which in turn leads to lower payoffs. From this perspective auditing “backfires” for the advertiser. This seems puzzling but we note that similar results have been observed in other scenarios as well. For example, Plambeck and Taylor(2015) demonstrate backfiring conditions for brands who audit suppliers, leading to greater effort by the latter to evade detection by hiding information.

6.3 Characteristics of A(n)

An implicit assumption in our model (indeed, in any general contract-theoretic model) is that the participation constraint of the advertiser is satisfied. If this were not so, it would not be worthwhile for the advertiser to draw up a contract in the first place. In order for the (implicit) participation contraint of the advertiser to be satisfied, its payoff at the optimal payment schedule must be positive. This condition imposes constraints on the class of admissible functions. In particular, at the optimal v∗, u∗:

Π(v∗, u∗) = A(n) − v∗(n) > 0

Hence while A(n) is ﬁxed and exogenous, it must belong to a certain class of functions with growth rate at least as high as that of the payment function. Further, we note that as δ > 1, there is a natural upper limit beyond which the advertiser’s (implicit) participation constraint is violated. While the optimal payment v∗(n) increases with δ and thereby ensures that the inﬂuencer always participates, for δ high enough, the advertiser may drop out owing to A(n) < v∗(n). Hence the following inequality naturally holds:11

! 1 A(n) 1 < δ ≤ − (1 − γ) γ c(u(n) − n) + R n c0(u(t) − t)dt nL

6.4 Managerial implications

At first glance, widespread faking in equilibrium may seem detrimental to the advertiser. However, our optimal contract helps the advertiser turn it into an advantage for itself by separating out the influencers according to their true number of followers. Intuition may suggest that audits and subsequent reputational costs to the influencer from detection of her fraud may deter her from buying fake followers. However, our results show otherwise. Thus, it is not beneficial for the advertiser to encourage third- party audits or indulge in public exposure of fraudulent influencers. In fact, in the absence of any control over audits, the advertiser should be willing to absorb the extra

11We thank an anonymous reviewer for this observation.

18 cost imposed on the inﬂuencer by the audit; and increase the payment to induce her to participate.

6.5 Concluding remarks

We develop an analytical model in a contract-theoretic setting between an advertiser and an influencer who can inflate her follower count by buying fake followers. There is a non-strategic third party audit which successfully detects fraud with probability γ, leading to additional reputational costs for the influencer. Under such conditions, the optimal contract allows faking by the influencer which is exploited by the advertiser as a screening mechanism to distinguish high influencer types from low influencer types. The audit characteristics have no effect on the optimal level of faking. However the higher costs thereof to the influencer are passed on to the advertiser in the form of increased payments. An interesting extension of our model is when fake followers could actually attract more genuine followers, making the type itself endogenous. While such an approach is interesting, it can be done justice to only in a dynamic setting which is beyond the scope of our study. Given the prevalence of click farms and fake followers in influencer marketing today, our model illustrates the economics of this practice. We offer insights into understanding why fake followers are rampant in influencer marketing and how advertisers can use this phenomenon to their advantage.

Appendices

A Proof of Proposition 1

The ﬁrst order Pontryagin conditions are:

1. Optimality condition:

dH max H ∀n ∈ [nL, nH ] ≡ = 0 u du

2. Equation of motion for state:

dY ∂ = H = Y dn ∂λ n

19 3. Equation of motion for costate:

dλ ∂ = − H dn ∂Y

4. Transversality condition for state:

λ(nL) = 0

A.1 Optimality condition

Since the control function is u(·) the derivative of H with respect to u(·) must be 0, yielding:

dΠ dY dY · f + λ · n + µ · = 0 (25) du du du

We also note that:

dΠ ∂v = Π + Π (26) du v ∂u u dY ∂Y ∂v ∂Y n = n · + n · 1 (27) du ∂v ∂u ∂u dY ∂Y ∂v ∂Y = · + · 1 (28) du ∂v ∂u ∂u

Reinserting the above in (25):

∂v ∂v ∂v f · Π · + Π + λ · Y · + Y + µ · Y · + Y = 0 (29) v ∂u u v,n ∂u u,n v ∂u u

dY ∂Y Additionally, at the optimal, since dn = ∂n

∂Y dv ∂Y du · + · = 0 (30) ∂v dn ∂u dn

leading to: ∂v Y = − u (31) ∂u Yv We now express the optimality condition for the optimal control problem as:

Yu Yu f · Πu − Πv + λ · Yu,n − Yv,n = 0 (32) Yv Yv

20 A.2 Equation of motion for costate dλ ∂ = − H (33) dn ∂Y Consider the right hand side:

∂ ∂ ∂v ∂ ∂u H = H · + H · ∂Y ∂v ∂Y ∂u ∂Y

From the optimal condition the last term is 0. Thus

∂ ∂ ∂v H = H (34) ∂Y ∂v ∂Y ∂H 12 Expanding ∂v and substituting it back in the equation of motion for costate, we get:

dλ Π Y λ˙ = = −f · v − λ · v,n − µ (35) dn Yv Yv

B Proof of Proposition 2

We note that the participation constraint is slack (Y > 0) and hence the corresponding Lagrange multiplier µ = 0. Using this in equation (11), we obtain:

dλ = f(n) (36) dn

which along with the transversality condition λ(nL) = 0 yields:

λ(n) = F (n)

where F (n) = R n f(t)dt. Using this value of the costate variable λ in equation (10) we nL obtain,

c0(u − n) F (n) = (37) c00(u − n) f(n)

0 0 At the realization n = nL, since F (nL) = 0, it must be that c (u(nL) − nL) = 0 = c (0),

which immediately implies that u(nL) = nL. Additionally for any n 6= nL, since the right hand side is positive, it implies that c0(u(n) − n) > c0(0) which yields:

u(n) > n ∀n ∈ (nL, nH ] and u(nL) = nL (38)

Finally, noting that

12 ∂Y Assuming ∂v 6= 0.

21 Z Y Z n dY Z n ∂Y dY = dn = dn 0 nL dn nL ∂n

Z n Y = (1 − γ + γδ) · c0(u(t) − t)dt (39) nL Z n v(n) = c(u(n) − n) + c0(u(t) − t)dt (1 − γ + γδ) (40) nL

22 References

Aral, S. and D. Walker (2012). Identifying inﬂuential and susceptible members of social networks. Science 337 (6092), 337–341.

Bakshy, E., J. M. Hofman, W. A. Mason, and D. J. Watts (2011). Everyone’s an inﬂu- encer: quantifying inﬂuence on Twitter. In Proceedings of the fourth ACM international conference on Web search and data mining, pp. 65–74. ACM.

Berger, J. (2016). Contagious: Why things catch on. Simon and Schuster.

Berger, J. and E. M. Schwartz (2011). What drives immediate and ongoing word of mouth? Journal of Marketing Research 48 (5), 869–880.

Bhardwaj, P. (2001). Delegating pricing decisions. Marketing Science 20 (2), 143–169.

Bolton, P. and M. Dewatripont (2005). Contract theory. MIT press.

Chiang, A. C. (1992). Elements of dynamic optimization. McGraw-Hill.

Confessore, N., G. Dance, R. Harris, and M. Hansen (2018). The Follower Factory. New York Times.

Crocker, K. J. and P. Letizia (2014). Optimal policies for recovering the value of consumer returns. Production and Operations Management 23 (10), 1667–1680.

Crocker, K. J. and J. Morgan (1998). Is honesty the best policy? Curtailing insurance fraud through optimal incentive contracts. Journal of Political Economy 106 (2), 355– 375.

Crocker, K. J. and J. Slemrod (2007). The economics of earnings manipulation and managerial compensation. RAND Journal of Economics 38 (3), 698–713.

Crocker, K. J. and S. Tennyson (2002). Insurance fraud and optimal claims settlement strategies. Journal of Law and Economics 45 (2), 469–507.

De Veirman, M., V. Cauberghe, and L. Hudders (2017). Marketing through Instagram in- ﬂuencers: the impact of number of followers and product divergence on brand attitude. International Journal of Advertising 36 (5), 798–828.

Dionne, G., F. Giuliano, and P. Picard (2009). Optimal auditing with scoring: Theory and application to insurance fraud. Management Science 55 (1), 58–70.

23 Djafarova, E. and C. Rushworth (2017). Exploring the credibility of online celebrities’ In- stagram proﬁles in inﬂuencing the purchase decisions of young female users. Computers in Human Behavior 68, 1–7.

Doherty, N. and K. Smetters (2005). Moral hazard in reinsurance markets. Journal of Risk and Insurance 72 (3), 375–391. eMarketer (2017). Attitudes Toward Inﬂuencer Marketing Among US Agency and Brand Marketers, Nov 2017 (% of respondents). Technical report.

Hovland, C. I. and W. Weiss (1951). The inﬂuence of source credibility on communication eﬀectiveness. Public Opinion Quarterly 15 (4), 635–650.

Hughes, C., V. Swaminathan, and G. Brooks (2019). Driving brand engagement through online social inﬂuencers: An empirical investigation of sponsored blogging campaigns. Journal of Marketing 83 (5), 73–96.

ICMP (2019). Who has the most fake followers?

IRI (2018). BzzAgent and IRI Find Everyday Inﬂuencer Marketing Programs Drive the Highest Return on Ad Spend. Technical report.

Jin, S.-A. A. and J. Phua (2014). Following celebrities’ tweets about brands: The impact of twitter-based electronic word-of-mouth on consumers’ source credibility per- ception, buying intention, and social identiﬁcation with celebrities. Journal of Adver- tising 43 (2), 181–195.

Kannan, P. K. and H. A. Li (2017). Digital marketing: A framework, review and research agenda. International Journal of Research in Marketing 34 (1), 22–45.

Kotler, P. and K. Keller (2012). Marketing management 15th edition pearson education ltd.

Kumar, V., V. Bhaskaran, R. Mirchandani, and M. Shah (2013). Practice prize win- ner—creating a measurable social media marketing strategy: increasing the value and ROI of intangibles and tangibles for hokey pokey. Marketing Science 32 (2), 194–212.

Kumar, V. and R. Mirchandani (2012). Increasing the ROI of social media marketing. MIT Sloan Management Review 54 (1), 55.

Lappas, T., G. Sabnis, and G. Valkanas (2016). The impact of fake reviews on online visibility: A vulnerability assessment of the hotel industry. Information Systems Re- search 27 (4), 940–961.

24 Letzter, R. (2016). Yes, the click farms on HBO’s ’Silicon Valley’ are a real thing and they aren’t going away.

Lewis, R. A. and J. M. Rao (2015). The unfavorable economics of measuring the returns to advertising. Quarterly Journal of Economics 130 (4), 1941–1973.

Libai, B., E. Muller, and R. Peres (2013). Decomposing the Value of Word-of-Mouth Seed- ing Programs: Acceleration Versus Expansion. Journal of Marketing Research 50 (2), 161–176.

Linqia (2018). The state of inﬂuencer marketing. Technical report, Linqia.

Luca, M. and G. Zervas (2016). Fake it till you make it: Reputation, competition, and Yelp review fraud. Management Science 62 (12), 3412–3427.

Maggi, G. and A. Rodriguez-Clare (1995). Costly distortion of information in agency problems. RAND Journal of Economics, 675–689.

Marsden, P. V. and N. E. Friedkin (1993). Network studies of social inﬂuence. Sociological Methods & Research 22 (1), 127–151.

Mathew, S. (2018). Oh my! Amitabh Bachchan is so touchy about his Twitter followers. The Quint.

McCracken, G. (1989). Who is the celebrity endorser? Cultural foundations of the endorsement process. Journal of Consumer Research 16 (3), 310–321.

McGuire, W. J. (1985). Attitudes and attitude change. The handbook of social psychology, 233–346.

Mishra, B. K. and A. Prasad (2004). Centralized pricing versus delegating pricing to the salesforce under information asymmetry. Marketing Science 23 (1), 21–27.

Mishra, B. K. and A. Prasad (2005). Delegating pricing decisions in competitive markets with symmetric and asymmetric information. Marketing Science 24 (3), 490–497.

Mishra, B. K. and A. Prasad (2006). Minimizing retail shrinkage due to employee theft. International Journal of Retail & Distribution Management 34 (11), 817–832.

Myerson, R. B. (1979). Incentive compatibility and the bargaining problem. Economet- rica 47, 61–73.

Neff, J. (2018). Study of influencer spenders finds big names, lots of fake followers. AdAge India.

25 Padmanabhan, V. and R. C. Rao (1993). Warranty policy and extended service contracts: Theory and an application to automobiles. Marketing Science 12 (3), 230–247.

Paquet-Clouston, M., O. Bilodeau, and D. D´ecary-H´etu(2017). Can We Trust Social Media Data?: Social Network Manipulation by an IoT Botnet. In Proceedings of the 8th International Conference on Social Media & Society, #SMSociety17, New York, NY, USA, pp. 15:1–15:9. ACM.

Pathak, S. (2017). Cheatsheet: What you need to know about inﬂuencer fraud. Digiday.

Plambeck, E. L. and T. A. Taylor (2015). Supplier evasion of a buyer’s audit: Implica- tions for motivating supplier social and environmental responsibility. Manufacturing & Service Operations Management 18 (2), 184–197.

Silverman, C. (2018). Apps Installed On Millions Of Android Phones Tracked User Behavior To Execute A Multimillion-Dollar Ad Fraud Scheme. BuzzFeed.

Simester, D. and J. Zhang (2010). Why are bad products so hard to kill? Management Science 56 (7), 1161–1179.

Simester, D. and J. Zhang (2014). Why do salespeople spend so much time lobbying for low prices? Marketing Science 33 (6), 796–808.

Sridhar, S., P. A. Naik, and A. Kelkar (2017). Metrics unreliability and marketing over- spending. International Journal of Research in Marketing 34 (4), 761–779.

Stewart, R. (2018). Unilever’s Keith Weed calls for ’urgent action’ to tackle inﬂuencer fraud. The Drum.

Sun, B. (2014, April). Executive compensation and earnings management under moral hazard. Journal of Economic Dynamics and Control 41, 276–290.

Tellis, G. J. (2003). Eﬀective advertising: Understanding when, how, and why advertising works. Sage.

The Economist (2016). Celebrities’ endorsement earnings on social media - Daily chart.

Wilbur, K. C. and Y. Zhu (2009). Click fraud. Marketing Science 28 (2), 293–308.

Yoganarasimhan, H. (2012, March). Impact of social network structure on content prop- agation: A study using YouTube data. Quantitative Marketing and Economics 10 (1), 111–150.

26 Term Description n True follower count of the influencer (influencer type) f(n),F (n) Probability density and cumulative distribution function of n [nL, nH ] Support of the probability density function f A(n) Advertiser’s subjective valuation of an influencer with n true followers u(n) Influencer’s displayed number of followers (true + fake) v(n) Payment to the influencer c(u(n) − n) Cost of displaying u(n) followers when true followers are n Π(v, u) Advertiser’s payoff Y (v, u, n) Influencer’s payoff H Hamiltonian λ(n) Co-state variable µ Lagrange multiplier γ Probability of successful detection of the influencer’s fake followers δ Penalty factor imposed due to successful detection of fake followers

Table 1: Summary of notation used in our model 300

200 Platform Facebook Instagram and Snapchat Twitter YouTube

100 Payment (in thousands of USD) Payment

>7m

1m−3m 3m−5m 500k−1m 100k−500k Follower count

Figure 1: Typical compensation schemes for influencers versus follower counts on various platforms. Adapted from The Economist (2016) Figure 2: Some prominent influencer campaigns on social media. Clockwise from top left: Priyanka Chopra for Tiffany and co. jewelry (Instagram), H2ODelirious for Ubisoft gaming (YouTube) and Snoop Dogg for Tanqueray gin (Instagram) Figure 3: Snapshots from some websites selling fake followers for different social media platforms Figure 4: Examples of influencer campaigns with a referral codes to track sales 200000

150000

100000

Fake Follower Count u(n)−n Follower Fake 50000

0 50000 100000 150000 200000 Follower Count n

F (n) Figure 5: Faking levels u(n) − n = f(n) for the uniform distribution in [nL, nH ] with nL = 100 and nH = 200000 1500

1000

Mean of exponential 50000 60000 70000 80000

500 Fake follower count, u(n)−n follower Fake

0 50000 100000 150000 200000 True follower count, n

F (n) Figure 6: Faking levels u(n) − n = f(n) for truncated exponential distributions. The truncation points are at nL = 100 and nH = 200000. Means reported in the legend are for untruncated distributions 1500

1000

Mean of normal 50000 60000 70000 80000

500 Fake follower count, u(n)−n follower Fake

0 50000 100000 150000 200000 True follower count, n

F (n) Figure 7: Faking levels u(n)−n = f(n) for truncated normal distributions. The truncation points are at nL = 100 and nH = 200000 and the standard deviation is 50000. Means reported in the legend are for untruncated distributions