An Eonomi Analysis of User-Privay Options in Ad-Supported Servies Joan Feigenbaum 1,, Mihael Mitzenmaher 2,, and Georgios Zervas 1, 1 Computer Siene Department, Yale University 2 Shool of Engineering & Applied Sienes, Harvard University Abstrat. We analyze the value to e-ommere website operators of offering privay options to users, e.g., of allowing users to opt out of ad targeting. In partiular, we assume that site operators have some ontrol over the ost that a privay option imposes on users and ask when it is to their advantage to make suh osts low. We onsider both the ase of a single site and the ase of multiple sites that ompete both for users who value privay highly and for users who value it less. One of our main results in the ase of a single site is that, under normally distributed utilities, if a privay-sensitive user is worth at least 2 1 timesasmuh to advertisers as a privay-insensitive user, the site operator should strive to make the ost of a privay option as low as possible. In the ase of multiple sites, we show how a Prisoner s-dilemma situation an arise: In the equilibrium in whih both sites are obliged to offer a privay option at minimal ost, both sites obtain lower revenue than they would if they olluded and neither offered a privay option. 1 Introdution Advertising supports ruially important online servies, most notably searh. Indeed, more than 95% of Google s total revenue derives from advertising. 1 Other advertiser-supported websites provide a growing array of useful servies, inluding news and mathmaking. Beause of its essential role in e-ommere, online advertising has been and ontinues to be the subjet of intensive study by diverse researh ommunities, inluding Eonomis and Computer Siene. In this paper, we fous on an aspet of online advertising that has reeived little attention to date: how website operators an maximize their revenue while permitting privay-sensitive users to avoid targeted ads. Targeted ads are those hosen to appeal to a ertain group of users. In ontextual targeting, ads are mathed to searh queries or other ommands issued by users; beause it does not entail the olletion and mining of any information exept that whih the user provides voluntarily and expliitly at the time Supported in part by NSF grant CNS-116875. Supported in part by NSF grants IIS-964473 and CCF-915922 and by grants from Google Researh and Yahoo Researh. Supported by a Simons Foundation Postdotoral Fellowship. 1 http://investor.google.om/finanial/tables.html P.W. Goldberg and M. Guo Eds.): WINE 212, LNCS 7695, pp. 3 43, 212. Springer-Verlag Berlin Heidelberg 212
An Eonomi Analysis of User-Privay Options in Ad-Supported Servies 31 the ad is plaed, it is not usually viewed as intrusive, and few users try to avoid it. In demographi targeting, ads are mathed to users demographi ategories suh as gender, loation, age, rae, religion, profession, or inome. Demographi targeting may involve onsiderable data olletion and analysis, and it is more ontroversial than ontextual targeting: Some users are unomfortable about being ategorized, feel more vulnerable to ads that make use of their demographi ategories, and worry that the same demographi information may be used for purposes more onsequential and nefarious than advertising; other users appreiate the fat that their membership in ertain demographi ategories, partiularly age, gender, and loation, an prevent their being shown numerous time-wasting ads that are provably irrelevant to them. In behavioral targeting, ads are mathed to individual users browsing histories. By definition, it involves the olletion and analysis of sensitive information, and many users take steps to avoid it. Unsurprisingly, targeted ads are more effetive than generi, untargeted ads, and thus they feth higher pries. Behavioral targeting, for example, has been shown to produe higher lik-through rates than no targeting; estimates of the extent of improvement in lik-through rates vary widely, however, from 2% in the work of Chen et al. [4] to a fator of six in the work of Yan et al. [13]. Conversion rate, i.e., the fration of those users who, after liking through to the advertiser s site atually buy something, is also higher for targeted ads; see Beales [2] for a disussion of the effet of behavioral targeting on onversion rates and Jansen and Solomon [9] on the effet of demographi targeting in general and gender in partiular. Although efforts to quantify the effet of ad targeting on website operators revenues are ongoing, there is redible evidene that the effet is large enough to imply that the elimination of targeted ads ould mean the end of the Web as we know it; Goldfarb and Tuker [6], for example, studied the effet of EU privay regulation on ad revenue and onluded that, all else equal, advertisers would have to spend approximately $14.8B more annually to ahieve the same effetiveness under a strit privay regime i.e., one that is less friendly to targeted ads) and that the dependene on targeted ads is highest among general-audiene websites, suh as those that provide news or weather. Beause targeted ads are lurative for website operators, users are being observed, ategorized, and traked ever more preisely. Understandably, some users fear loss of privay, and various tools offered by website operators e.g., opt-outs and other ustomizable privay settings) and by third parties e.g., anonymizing browser plug-ins suh as Torbutton 2 ) that promise online-privay protetion are proliferating. These tools allow users to avoid targeted ads, but of ourse people who use them an still be shown generi, untargeted ads. Although many suh tools are available without harge, they an impose non-monetary osts on users, e.g., time and effort spent figuring out the often obsure privay options presented by a UI, time and effort spent on installation of new software suh as a privayenhaning browser plug-in, and redued ease of use, speed, and/or quality of servie. To a onsiderable extent, these osts an be ontrolled by website operators. 2 See https://www.torprojet.org/torbutton/.
32 J. Feigenbaum, M. Mitzenmaher, and G. Zervas We ask when it is to website operators advantage to make the ost of suh privay options low. Our major ontributions inlude: Eonomi models in whih to address the problem, both for the ase of a single site and for that of multiple sites that ompete both for users who value privay very highly and for users who value it less. A omplete analysis of the ase of a single site with homogeneous users and normally distributed utilities. In this setting, if a privay-sensitive user is worth at least 2 1 times as muh to advertisers as a privay-insensitive user, the site operator should strive to make the ost of a privay option as low as possible. A omplete analysis of the ase of two sites with user demand funtions that denote their privay preferenes. In this setting, we show how a Prisoner s- Dilemma situation an arise: In the equilibrium in whih both sites are obliged to offer a privay option at minimal ost, both sites obtain lower revenue than they would if they olluded and neither offered a privay option. 2 Related Work To the best of our knowledge, we are the first to study the question of when it is to the advantage of website operators to minimize the ost of providing users with privay options. However, several related aspets of web users ability to ontrol their personal information have been studied. Riederer et al. [1] propose a market for personal information based on the notion of transational privay. Users deide what information about themselves should be for sale, and aggregators buy aess to users information and use it to deide what ads to serve to eah user. The information market that onnets users and aggregators, handles payments, and protets privay ahieves truthfulness and effiieny using an unlimited-supply aution. Carrasal et al. [3] use experiene sampling to study the monetary value that users plae on differene types of personal information. They find, for example, that users plae a signifiantly higher value on information about their offline behavior than they do on information about their browsing behavior. Among ategories of online information, they value finanial and soial-network information more highly than searh and shopping information. Iyer, Soberman, and Villas-Boas [8] onsider advertising strategies in segmented markets, where ompeting firms an target ads to different segments. They find that firms an inrease profits by targeting more ads at onsumers who have a strong preferene for their produt than at omparison shoppers who might be attrated to the ompetition. Interestingly, targeted advertising produes higher profits regardless of whether the firms an prie disriminate. Moreover, the ability to target advertising an be more valuable to firms in a ompetitive environment than the ability to prie disriminate. Telang, Rajan, and Mukhopadhyay [12] address the question of why multiple providers of free, online searh servies an oexist for a long time. In standard
An Eonomi Analysis of User-Privay Options in Ad-Supported Servies 33 models of vertial or quality) differentiation, a lower-quality produt or servie must sell for a lower prie than its higher-quality ompetitor if it is to remain in the marketplae; if the pries are equal, all onsumers hoose the higher-quality alternative. Similarly, in standard models of horizontal or taste) differentiation, sustained differentiation among produts or servies ours when users inur high transportation osts. Yet, neither prie nor transportation ost is a strategi variable in online searh. Telang, Rajan, and Mukhopadhyay point out that, although the quality of one searh servie may learly be higher than that of its ompetitors on average, the quality of results of apartiularsearhbyapartiular user is highly variable and inherently stohasti. Thus, there is a nontrivial probability that a user will be dissatisfied with the results of a partiular searh and wish to searh again for the same information, using a different searh servie. It is preisely the zero-prie, zero-transportation-ost nature of the user s task that may ause him to use more than one searh servie in a single session. In the aggregate, this feature reates residual demand for lower-quality searh servies, allowing them to oexist with their higher-quality ompetitor. Aquisti and Varian [1] onsider the onditions under whih a merhant should prie-disriminate based on onsumers past purhases. They find that it may be profitable to do so when anonymizing tehnologies are too ostly for onsumers to use. Conitzer et al. [5] study a similar setting, where the merhant has ontrol over the anonymity option. They find that onsumers will hose anonymity when it is ostless, a behavior whih also maximizes the merhant s profit. Similar to our results, they demonstrate at Prisoner s Dilemma: the onsumers ould have obtained higher welfare by jointly deiding to dislose their identities. Consequently, ostly anonymity ould be benefiial to all parties. 3 Single-Provider Case We begin by presenting a general model of an ad-supported servie with a single provider. Let n be the size of the market for this servie i.e., thenumberof users), v be the revenue extrated by the servie provider for eah user that allows targeted ads referred to below as a targeted user ), and γv, with<γ 1, the revenue extrated for eah user that avoids targeted ads referred to below as a private user ). The total revenue extrated by the provider is given by: r = nvs + γp), 1) where s is the fration of the market that onsists of targeted users, and p is the fration that onsists of private users. In this setting, we model the users by way of their utilities. For a speifi user, the random variables U S and U P denote the utilities that the provider derives from the targeted and private servies, respetively. We disount the utility by a ost, whih an be thought of as fixed ost that the user pays to set up the privay option. In our model, we assume is under the ontrol of the servie provider; hene, the provider will hoose the ost of the privay option
34 J. Feigenbaum, M. Mitzenmaher, and G. Zervas to optimize revenue. 3 We assume, but one ould expand our analyses to inlude settings in whih the provider pays users to use its servie and thereby indues a negative ost. LetU =U S,U P ) be the orresponding joint distribution. Let fx, y) =Pr[U S = x, U P = y] be the joint density, and similarly let F x, y) =Pr[U S x, U P y] be the joint distribution funtion. Ausermay: 1. use the targeted option and derive utility U S ; 2. use the privay option and derive utility U P ; 3. abstain from using the servie for a utility of. Users hoose among the above options to maximize their utility. Their hoies determine the values of s and p. From the standpoint of the provider, finding the revenue-maximizing ost involves omputing trade-offs between s and p. Wehave: s =Pr[U P U S <,U S ] = p =Pr[U P U S, U P ] = +y +y fx, y)dxdy, 2) fx, y)dxdy + fx, y)dxdy. 3) We emphasize that, in this model, s + p may be less than 1, beause users with negative utility from both targeted and privay options will not use the servie at all. 3.1 Normally Distributed User Utilities We now explore this model by onsidering the ase of normally distributed user utilities. Assume that U =U S,U P ) follows a standard bivariate normal distribution with mean vetor zero and ovariane matrix Σ = {{1, ρ}, {ρ, 1}}; here, ρ is the orrelation oeffiient between U S,andU P.Useφ 2 to denote U s density and Φ 2 to denote its distribution funtion. The marginal distributions U S and U P are standard normal with mean, variane 1, [ density funtion ] φx) = 1 2π exp x 2 /2), and distribution funtion Φx) = 1 2 1+erfx/ 2). We first onsider the ase in whih ρ =. 3 One ould imagine more elaborate models, where the ost was governed by a distribution, and the provider ould, for example, ontrol the mean of the distribution; for simpliity, we fous on the onstant-ost model in this first paper.
An Eonomi Analysis of User-Privay Options in Ad-Supported Servies 35 Fig. 1. Optimal privay-option setup ost and value for various γ and n = 1, v =1 γ).2.4.6.8 1. 1 2 3 4 5 μ μ S = μ, μ P = μ S =, μ P =μ μ S = μ, μ P =μ Fig. 2. The value of γ) where the privay option takes on zero ost for three settings: U P s mean fixed at, U S s mean fixed at, and U P and U S have the same mean 3.2 Unorrelated User Utilities, ρ =. The fration of targeted users is s =Pr[U P U S <,U S ] 4) = +y Similarly, the fration of private users is φx)φy)dxdy. 5) p =Pr[U P U S, U P ] 6) = +y φx)φy)dxdy + φx)φy)dxdy, 7) where erfx) = 1 erfx). Observe that s is monotonially inreasing in, while p is monotonially dereasing in. The rate of hange of the fration of targeted users as a funtion of is: s = φy)φ + y) dy 8) = e y2 2 2π e 1 2 +y)2 2π dy 9) e 1 2 +y)2 y2 2 = 2π = e 2 4 erf ) 2 4 π dy 1), 11)
36 J. Feigenbaum, M. Mitzenmaher, and G. Zervas whih is easily seen to be dereasing in. Using similar alulations, we an ompute the rate of hange of the fration of private users with respet to : p = e 2 2 = φ)φy) dy + φy)φ + y) dy 12) e 2 4 erf ) ) 2 + 2 4 π, 13) whih is similarly inreasing in. The provider is indifferent with respet to revenue earned between the two types of users when: s p = γ. 14) Denote by γ) the value of for whih equality holds. Substituting and solving for γ), we obtain: 2 γ) =1 2e 2 4 erf ). 15) 2 +2 We ontinue by proving an auxiliary lemma. Lemma 1. γ) in dereasing in. Proof. Consider the derivative e 2 4 erf ) 2 = 1 2 e 2 ) 4 erf 1. 16) 2 π We show that it is negative for all >; this suffies to prove the lemma. Note the following equivalenes. 1 2 e 2 ) 4 erf 1 < 17) 2 π e 2 4 ) erf < 2 18) 2 π e 2 2 4 e t2 dt < 2 19) π π /2 e 2 4 /2 e t2 dt < 1. 2) We prove the last line above, using the following bound of [11] a tighter version of Komatsu s inequality [7]): e x2 e t2 dt < 2/ 3x + ) x 2 +4. 21) At x = /2, we obtain e 2 4 x /2 e t2 dt < 2/ 3/2+ ) 2 /4+4, 22)
An Eonomi Analysis of User-Privay Options in Ad-Supported Servies 37 whih yields e 2 4 /2 e t2 dt < 2/ 3/2+ ) 2 /4+4 < 1, 23) proving the lemma. We have that γ) = 2 1. Furthermore, beause γ) is dereasing in, for any γ γ), it follows that the provider s best strategy is =,i.e., offeringa free privay option. Using the above, we are now ready to state the main theorem of this setion. Theorem 1. If U follows a standard bivariate normal distribution with orrelation ρ =, then the provider will offer a free privay option whenever γ 2 1. Remark 1. The speifi value 2 1 arises from our assumption that U P and U S were distributed aording to a standard normal distribution of mean. Similar results for other means and varianes an be alulated in a similar fashion. Figure 2 demonstrates three variations: where the mean of U P is fixed at but the mean of U S varies; where the mean of U S is fixed at but the mean of U P varies; and where the means vary but are equal. All varianes remain 1.) For example, where U S and U P have equal means, we see that γ) onverges to 1 very quikly, as offering privay annibalizes more lurative targeted users more readily than it garners new private users. 3.3 Correlated Utilities, ρ. Assume that U =U S,U P ) follows a standard bivariate normal distribution with orrelation ρ. Useφ 2 to denote its density funtion. We derive an indifferene ondition similar to the one in Equation 14: γ φ 2, y) dy + ) φ 2 + y, y) dy = φ 2 + y, y) dy. 24) Substituting for the density funtion of the standard bivariate normal and integrating, we obtain an expression for γ in terms of and ρ: ) 2 1 2ρ) 2 2ρe 4ρ 1) erf ρ 2 2ρ 2 γ = ) +1 erf As before, setting =yields γ) = 2 ρ+1 1. 25) 1 1+ 2 2ρ. 26)
38 J. Feigenbaum, M. Mitzenmaher, and G. Zervas We observe that, as the orrelation oeffiient inreases reps., dereases) the value of γ beyond whih it makes sense to offer a privay option at no ost also inreases reps., dereases). That is, greater orrelation means one requires higher revenue from private users in order to offer privay at no ost; in partiular, when U P = U S, Equation 26 reasonably requires that γ) = 1. We an now state a generalized version Theorem 1, taking into aount orrelated user utilities. Theorem 2. If U follows a standard bivariate normal distribution with orrelation ρ, then the provider will offer a free privay option whenever γ 1 1+ 2 2ρ. 4 A Two-Player Game We provide a general model of the two-player version of the game. We then explore the model by delving into a onrete example. Throughout this setion, we use the terms player and provider interhangeably. As in the singleprovider ase, a targeted user is one who does not use the privay option, and a private user is one who does. The game proeeds in two periods t =1, 2. To begin, at t = 1, we have two providers S i,fori =1, 2, that offer ompeting, advertising-supported, nonprivate servies. We let S denote a user s outside option, whih in this ase is to use neither servie. Denote the fration of users who hoose S i at time t by s it.wehave 2 i= s i1 =1. At t = 2, simultaneously, both providers an introdue private variants, i.e., ones in whih users avoid targeted ads; we denote these by P i. The providers an determine an assoiated ost that ontrols the utility of the private variants, with the goal of tuning the market share for eah servie they provide. We denote these osts by i. The fration of users that hoose P i at time t is given by p it.we have 2 i= s i2 + 2 j=1 p j2 = 1. The fration of users left using the non-private options or neither option) at t =2isgivenby: s i2 = s i1 1 F i 1, 2 )) for i =, 1, 2. That is, F i 1, 2 ) is the fration of users who were using S i or were not using either servie but are now using one of the private variants. The users s i1 s i2 swithing to a private variant are distributed among the two providers as follows: p i2 = H i 1, 2 ) 2 s j1 s j2 )fori =1, 2. j= Here, H i 1, 2 ) is a funtion determining the split, among the ompeting privateservie providers, of users swithing to a private variant; note H 1 1, 2 )=1 H 2 1, 2 ). Also, reall that p i1 =. Let v i be the value that provider i derives from the standard servie. Let γ i v i be the value it derives from the private servie, where γ i, 1]. Let r i denote the revenue funtion of provider i at the seond stage of the game. We have:
An Eonomi Analysis of User-Privay Options in Ad-Supported Servies 39 r i = v i s i2 + v i γ i p i2 = v i s i1 1 F i 1, 2 )) + v i γ i H i 1, 2 ) = v i s i1 1 F i 1, 2 )) + v i γ i H i 1, 2 ) = v i s i1 1 F i 1, 2 )) + γ i H i 1, 2 ) 2 s j1 s j2 ) j= 2 s j1 s j1 1 F j 1, 2 ))) j= 2 s j1 F j 1, 2 ) j= 27) for i =1, 2. In equilibrium, neither provider an inrease its revenue by unilaterally deviating. The first-order onditions FOC) are given by r i i =,fori =1, 2. 28) Let {ĉ 1, ĉ 2 } be a solution to this system of equations. Then, the seond-order onditions SOC) are given by: 2 r i 2 ĉ 1, ĉ 2 ) <, for i =1, 2. 29) i Our questions revolve around the equilibrium of this game. 4.1 A Prisoners Dilemma The framework desribed above was designed to be very general; however, this makes it somewhat diffiult to get a handle on the nature of the game. We onsider a worked example in order to gain more insight. For simpliity, we will assume F i = F for i =, 1, 2. There are ertain natural properties that we want for the funtion F : F should be dereasing in the osts i,andf should go to as both i go to infinity. We simplify things further by assuming that, if either ost i goes to, all users will prefer the zero-ost privay option, and thus F will go to 1. This may not be the ase in all settings, but it is a reasonable and instrutive plae to start. A relatively straightforward funtion with these properties is if 1 = 2 =, F 1, 2 )= 1 if 1 =,or 2 =, 3) exp 12 otherwise. 1+ 2 )
4 J. Feigenbaum, M. Mitzenmaher, and G. Zervas We define H i so that the fration that goes to P i is proportional to its ost. if 1 =, 1 H 1 1, 2 )= 2 if 1 = 2 =, 31) otherwise. 2 1+ 2 We define H 2 similarly. Also, for notational simpliity let s i1 = s i. Under these assumptions, the payoff funtion for player 1 is: ) r 1 = v 1 e 1 2 1 + 2 2 γ 1 1 + 2 ) s 1 ) / 1 + 2 )+s 1, 32) and similarly, for player 2. Note that the payoffs are ontinuous. Furthermore, under the assumption that F i = F, the first and seond derivatives of the revenue funtion assume the following forms: and r i i = v i 2 r i 2 i s i1 F i + γ i H i i F 1, 2 )+γ i H i 1, 2 ) F i = v i s i1 2 F 2 i + γ i 2 H i i F i + 2 H i 2 i F + 2 F 2 i ), 33) )) H. 34) 4.2 Computation of Equilibria We now assume that γ i >, i.e., that both players an derive some revenue from private users. Theorem 3. The game has two possible equilibria: 1. at { 1 =, 2 =}, withr i = v i γ i /2, 2. at { 1 =, 2 = }, ifs i >γ i,withr i = s i v i. Remark 2. Theorem 3 demonstrates how the Prisoners Dilemma arises naturally in this two-player game. For example, if s i = 3 4 γ i for i =1, 2, then, when neither provider offers a privay option, their revenue is 3 4 γ iv i. However, this is not an equilibrium point; at equilibrium, both players offer zero-ost privay options, and their revenue is redued to 1 2 γ iv i. Proof. The proof proeeds in a sequene of lemmas. We begin by onsidering ases in whih one player offers a free privay option, while the other harges a possibly infinite) ost. Lemma 2. The game does not admit solutions of the form { i =, i > }. Proof. Beause the game is symmetri, it suffies to onsider the ase in whih 1 =, and 2 =, forsomeonstant >. From Equations 3 and 31, we have F,)=1,H 1,) = 1, and H 2,) =. From Equation 27, the revenue for player 1 is r 1 = v 1 γ 1, and for player 2 it is r 2 =. Suppose player 2 unilaterally deviates by playing 2 =. In this ase, H 2, ) = 1/2, and r 2 = v 2 γ 2 /2. Therefore, beause γ 2 >, 1 =, 2 =, does not onstitute an equilibrium.
An Eonomi Analysis of User-Privay Options in Ad-Supported Servies 41 Next, we onsider settings in whih both players offer the privay option for a finite, non-zero ost. Lemma 3. The game does not admit solutions of the form { i >, i > }. Proof. We onsider andidate equilibria suggested by solutions to the FOC: F 1, 2 ) 2 v 1 2 1 + 2 ) s 1 2 ) ) 2 + 2 + 1 γ1 / 1 + 2 ) 3 = 35) F 1, 2 ) 1 v 2 1 1 + 2 ) s 2 2 ) ) 1 + 1 + 2 γ2 / 1 + 2 ) 3 =. 36) First, note that, beause osts are finite, F 1, 2 ) >. Therefore, the FOC an be simplified to the following equivalent onditions: 2 1 + 2 ) s 1 2 2 + ) 2 + 1 γ1 =, 37) 1 1 + 2 ) s 2 2 1 + ) 1 + 2 γ2 =. 38) Solving the first equation above for 1 and substituting into the seond one, we obtain the following solution: { 1 = γ 2 K, 2 = γ } 1 K, 39) s 2 γ 2 s 1 γ 1 where K = γ 1s 2 + γ 2 s 1 2γ 1 γ 2. 4) γ 1 s 2 + γ 2 s 1 γ 1 γ 2 Next, we need to hek the SOC for this solution. A long sequene of alulations yields: 2 r 1 2 1 2 r 2 2 2 1, 2 )= γ4 1v 1 e 1, 2 )= γ4 2 v 2e γ 1 γ 2 γ 1 s 2 +γ 2 s 1 γ 1) s 1 γ 1 )s 2 γ 2 ) 4 γ 1 s 2 + γ 2 s 1 γ 1 γ 2 ) γ 1 s 2 + γ 2 s 1 2γ 1 γ 2 ) 5 <, γ 1 γ 2 γ 1 s 2 +γ 2 s 1 γ 1) s 2 γ 2 )s 1 γ 1 ) 4 γ 1 s 2 + γ 2 s 1 γ 1 γ 2 ) γ 1 s 2 + γ 2 s 1 2γ 1 γ 2 ) 5 <, whih an be further simplified to the equivalent onditions s 1 γ 1 ) γ 1s 2 + γ 2 s 1 γ 1 γ 2 = s 1 γ 1 <, γ 1 s 2 + γ 2 s 1 2γ 1 γ 2 K 41) s 2 γ 2 ) γ 1s 2 + γ 2 s 1 γ 1 γ 2 = s 2 γ 2 <. γ 1 s 2 + γ 2 s 1 2γ 1 γ 2 K 42) Notie that s 1 γ 1 )/K has the same sign as 1 in Equation 39. Similarly, s 2 γ 2 )/K has the same sign as 2. Beause osts are non-negative, the seondorder onditions are not met; this solution minimizes rather than maximizes the revenue of the players and is therefore not an equilibrium point. Next, we onsider the ase in whih both players offer free privay options. Lemma 4. Both players offering free privay options i.e., 1 = 2 =)onstitutes an equilibrium of the game.
42 J. Feigenbaum, M. Mitzenmaher, and G. Zervas Proof. In this ase, users swith en masse to the private servies and are distributed equally between the two providers. The revenue for player i is v i γ i /2. Furthermore, if a player unilaterally deviates and swithes to a non-zero ost for privay, his revenue instantly ollapses to zero. Therefore, 1 = 2 =onstitutes an equilibrium to the game. Finally, we onsider the ase in whih neither player offers a privay option. Lemma 5. Neither player s offering a privay option i.e., 1 = 2 = ) onstitutes an equilibrium of the game if s i <γ i,fori = {1, 2}. Proof. Suppose that neither player offers a privay option; so r i = v i s i.now, onsider the ase in whih player 1 wishes to deviate unilaterally. The ase for player 2 an be argued identially.) First, note that lim 2 F 1, 2 ) = exp 1 ), and lim 2 H 1 1, 2 ) = 1. Therefore, if player 2 doesn t offer a privay option, i.e., 2 =, player 1 deviates and plays 1 ; his new revenue will be r 1 = s 1 v 1 1 exp 1 )) + v 1 γ 1 exp 1 )=s 1 v 1 + v 1 exp 1 )γ 1 s 1 ). 43) If γ 1 <s 1, then player 1 annot improve his position; therefore, not offering a privay option onstitutes an equilibrium. If γ 1 >s 1, player 1 an inrease his revenue by dereasing his ost; therefore, not offering a privay option is not an equilibrium. If γ 1 = s 1, player 1 annot stritly improve his revenue by deviating, and we have a weak equilibrium.) This onludes the proof of Theorem 3. This example demonstrates what we see as the potentially natural outomes of this two-player dynami that would extend to three or more players as well. It is possible that no servie provider is inentivized to offer a privay option in this game. In suh a setting, one might expet a new entrant to enter the game and disrupt the status quo by offering a suitable privay option, potentially foring other providers to do so as well. It is also possible that all ompetitors are inlined to offer a privay option. In our example, this led to all users opting to offer privay, but we ould have utilized arguably more realisti funtions F to aount for the fat that some users might find more value in not offering privay or might find the ost of doing so non-trivial regardless of the efforts they exert to drive the ost down. Under suh settings, we would expet other equilibria to arise; in our example, there were other points at whih the first-order onditions but not the seond-order onditions were met, but, more generally for other funtional relationships), we ould have other equilibria. 5 Conlusion The results of Setions 3 and 4 suggest that website operators ould have their ake and eat it, too. By arefully ontrolling the ost to users of opting out of
An Eonomi Analysis of User-Privay Options in Ad-Supported Servies 43 targeted ads, they ould maximize their revenue and respet their users privay onerns. Putting this approah into pratie would require surmounting at least two major obstales. First, a servie provider would need a good estimate of the parameter γ, i.e., the fration of the revenue derived from a targeted user that an be derived from a private user. The value of γ is losely related to the extent to whih likthrough and onversion rates are improved by various forms of ad targeting, whih in turn is still the subjet of intensive, ongoing researh. Seond, the servie provider would need to translate the abstrat ost i of our eonomi analysis into a onrete privay-enforement tool that an be installed and used at a ost of i. It may suffie to be able to hoose between two tehnologial options, one of whih is learly more ostly to users than the other, but even this would be nontrivial given the state of the art of privay enforement. Referenes 1. Aquisti, A., Varian, H.: Conditioning pries on purhase history. Marketing Siene 243), 367 381 25) 2. Beales, H.: The value of behavioral targeting, http://www.networkadvertising.org/pdfs/beales_nai_study.pdf 3. Carrasal, J.P., Riederer, C., Erramilli, V., Cherubini, M., de Oliveira, R.: Your browsing behavior for a big ma: Eonomis of personal information online, http://arxiv.org/abs/1112.698 4. Chen, Y., Pavlov, D., Canny, J.F.: Large-sale behavioral targeting. In: Proeedings of the 15th ACM SIGKDD International Conferene on Knowledge Disovery and Data Mining KDD 29), pp. 29 218 29) 5. Conitzer, V., Taylor, C., Wagman, L.: Hide and seek: Costly onsumer privay in a market with repeat purhases. Marketing Siene 312), 277 292 212) 6. Goldfarb, A., Tuker, C.E.: Online advertising, behavioral targeting, and privay. Communiations of the ACM 545), 25 27 211) 7. Ito, K., MKean, H.: Diffusion proesses and their sample paths. Springer, Heidelberg 1965) 8. Iyer, G., Soberman, D., Villas-Boas, M.: The targeting of advertising. Marketing Siene 243), 461 476 25) 9. Jansen, B.J., Solomon, L.: Gender demographi targeting in sponsored searh. In: Proeedings of the 28th ACM International Conferene on Human Fators in Computing Systems CHI 21), pp. 831 84 21) 1. Riederer, C., Erramilli, V., Chaintreau, A., Krishnamurthy, B., Rodriguez, P.: For sale: Your data, by: You. In: Proeedings of the 1th ACM Workshop on Hot Topis in Networks, HotNets-X 211) 11. Ruskai, M.B., Werner, E.: A pair of optimal inequalities related to the error funtion, http://arxiv.org/abs/math/971127 12. Telang, R., Rahan, U., Mukhopadhyay, T.: The market struture for internet searh engines. Journal of MIS 212), 137 16 24) 13. Yan, J., Liu, N., Wang, G., Zhang, W., Jiang, Y., Chen, Z.: How muh an behavioral targeting help online advertising? In: Proeedings of the 18th International World Wide Web Conferene WWW 29), pp. 261 27 29)