Taxation and Privacy Protection on Internet Platforms

Transcription

1 Taation and Privacy Protection on Internet Platforms Francis Bloch Garielle Demange August 3, 016 Astract This paper studies data collection y a monopolistic internet platform We show that the optimal strategy of the platform is either to cover the market or to choose the highest data eploitation level, ecluding users with high privacy costs from the platform. We analyze the effect of different ta instruments on the level of data collection and show that user-ased taes lead to an increase in data collection and the eclusion of users. Taation with different rates according to the source of revenues, with higher ta level for revenues generated y data eploitation can reduce data collection. We also analyze the effect of opting-out options, letting users access the platform with no data collection under different financial transactions (asence of transfers, suscription fee for the opt-out option, compensation for the opt-in option). Finally, we consider the effect of competition from a platform offering access without data collection. JEL classification numers: H3, L86, L50 Keywords: options Digital services, Privacy protection, Taation, Opt-out and opt-in We are grateful to France Strategie for funding this research within the framework of a Research Project on the Evolution of the Value created y the Digital Economy and its Fiscal Consequences. We have enefited from comments and discussion with M. Bacache, P.J. Benghozi, M. Bourreau, B. Caillaud,, J. Cremer, S. Gauthier, L. Gille, J. Hamelin, L. Janin and J.M. Lozachmeur. Université Paris 1 and Paris School of Economics, Boulevard de l Hopital, Paris CEDEX 13, France. francis.loch@univ-paris1.fr. Paris School of Economics-EHESS, 48 Boulevard Jourdan, Paris, France. demange@pse.ens.fr. 1

2 1 Introduction The precipitous decline in the cost of data collection and storage linked to the development of information technologies has transformed usiness models in advertising and commerce. While records on customers and sales histories have always eisted, the digital economy now enales firms to eploit data at a much larger scale, opening up new opportunities for profit as well as new concerns aout privacy and eploitation of personal data. Large sales platforms can now use detailed records of past sales histories to target users and engage in discriminatory dynamic pricing. Other platforms, like search engines or online social networks, use data on immediate search to auction off advertising spaces to clients, or sell search histories to intermediaries who accumulate data to etter target users with ads. In fact, usiness models of all giant internet platforms rely at different degrees on the collection and eploitation of personal data. The use of personal data is clearly one of the main specificities of the digital sector in modern industrial economies. The development of ig data and its potential eploitation raises two separate questions. First, data are a valuale input for internet platforms, ut users voluntarily upload their data without any payment. One can argue that internet platforms are engaged in a arter agreement, where platforms deliver a valuale service (targeted proposals for products, targeted ads, outcomes of search, access to friends) in echange for the uploading of data. But asent any price and financial transaction, it is difficult to assess whether this arter is fair and if users receive a fair share of the surplus. The immense profits of (some not all) internet platforms suggests that it may not e the case and that platforms enefit from a free input which is not paid at its true value. Furthermore, in the asence of financial transaction, governments cannot properly ta the enefit of personal data, creating a distortion with respect to other sectors, clouding the territoriality principle for the taation of profits, and leading to etremely low levels of taation of internet platforms through a clever use of transfer prices and the asence of records of financial transaction in countries where users reside. Second, users are rightly afraid that the collection of personal data infringes on their privacy. In addition, the resale of data to unknown intermediaries through opaque arrangements results in a loss of control on the dissemination of personal data to third parties. The eploitation of data, while it provides a valuale service to users y improving targeting, also necessarily involves a cost in privacy loss. Even though the two prolems of the asence of fair payment of data and privacy loss seem unrelated at first glance, they are in fact closely connected. In this paper, we study how regulatory instruments, and in particular taation, can e used to solve oth prolems at once. We first investigate the effect of different forms of taation corporate profit taation, taation ased on users or data flows, specific ta paid y users, revenue taation ased on differentiated rates according to the origin of the platform revenues. We then study regulation which mandates platforms to offer a service without data collection (letting for eample users decide whether they want to leave cookies or not), either with no financial transaction, or with two forms of financial transaction: one where the platform collects a suscription fee from users choosing the opt-out option and one where the platform compensates users who choose the opt-in option. We construct a model where users are differentiated along their privacy cost. The collection of data enales the platform to etter target offers to users and users to products or advertisers,

3 resulting in an increase in the enefit to users as well as the value of users to advertisers or to the firm. Initially, we suppose, following current usage in the digital industry, that platforms do not charge users for their service and that their entire revenue comes from the other side of the market (advertisers or sales of future goods). A monopolistic platform chooses (and commits to) a degree of data eploitation alancing two effects: on the one hand, an increase in data collection increases revenues y increasing the value of the user to advertisers or for targeted pricing, on the other hand, an increase in data collection may deter users with high privacy cost to access the platform. In this model, we first compute the optimal level of data eploitation chosen y the platform and the users. We show that the platform either chooses to cover the market making sure that all users access the platform, or chooses the maimal level of data eploitation, therey ecluding some users from the platform. The welfare of users is also maimized at one of three values: either at a low value, or at the level of market coverage or at the maimal degree of data eploitation. While the optimal levels of data collection from the point of view of the platform and users cannot e directly compared (they depend on the particular shape of the revenue and enefit functions), anecdotal evidence suggests that the share of revenues linked to data collection is higher than the enefits of users from etter service due to data eploitation, so that the platform s optimal level of data collection is likely to e ecessive from the point of view of users. Given that the platform chooses an ecessive degree of data eploitation, we then study how different forms of taation affect data collection. We first oserve that a ta on profits (or equivalently a ta on revenues ecause variale costs are negligile) does not affect the choice of the platform. A ta paid y the platform per user does not affect the marginal enefit of data eploitation, ut it reduces the profit made on the marginal user accessing the platform, therey reducing the cost of data collection. Hence, a ta per user (or per flow of data as users do not choose the level of data they upload), results in an increase in data eploitation. A specific ta paid y users (like a ta on internet service providers) produces amiguous effects on the degree of data eploitation, ut always increases the region where eclusion occurs. The only ta which allows to correct for ecessive data collection is a ta on revenues which treats differentially platform s revenues accruing from one-time use (like auction revenues ased on current keywords) and revenues linked to data collection (like resale of data to intermediaries). If fiscal authorities charge a higher ta level on resale of data than on auction revenues, taes deter the platform from eploiting the data, playing the classical role of a Pigovian ta correcting for eternalities. We then eplore the effect of the introduction of an option for the users to access the platform with no data collection. This allows the platform to collect access revenue from those users who choose to opt-out, segmenting the market into two groups with different revenue levels. Users will now all access the platform some with data collection and others without. We show that this changes the level of data collection chosen y the platform, resulting in a decrease in the maimal level of data eploitation for which the market is covered, ut in an increase in the region of parameters for which the platform chooses the maimal degree of data eploitation. Hence, oth from the point of view of the platform and from the point of view of users, the 3

4 introduction of an opt-out option has amiguous effects. When the access value to users is small, oth the platform and the users enefit from the introduction of the zero-option, ut when the access value to users is large, users are indifferent and the platform prefers the uniform policy. We then allow for further discrimination etween the different types of users y letting the platform use pricing instruments. We first consider the case where the platform charges a suscription fee from users selecting the opt-out option. We show that the fee will always e set at the maimal level, transferring all the surplus from users choosing the opt-out option to the platform. The platform may choose to switch its usiness model entirely, foregoing data collection completely and collecting suscription revenues. Alternatively, the platform may choose to implement market coverage or set the highest level of data collection. Because the platform collects revenues from users choosing the opt-out option, its incentive to eclude users from the opt-in option is higher, and we oserve eclusion more often than in the enchmark case. The platform always gains y proposing an opt-out option with suscription fee, and the effect on user welfare is amiguous. We also analyze the effect of competition with a platform proposing the opt-out option. If a competing platform proposes the opt-out option at no cost, the level of data eploitation under market coverage goes down and the region of parameters for which eclusion occurs increases, reflecting the competition created y the opt-out option. The platform is hurt y the presence of a competitor ut users enefit when the degree of data eploitation is initially ecessive. If the competing platform selects a suscription fee, the equilirium of the game where one platform selects the degree of data eploitation and the other platform a suscription fee results in two possile configurations: one where a single platform operates on the market, at a low level of data eploitation which guarantees market coverage and one where one platform selects the highest level of data collection and the other platform collects revenues charging the optimal suscription fee. Our analysis of the effect of taation and regulation on data collection relies on an original model, ut is related to two strands of the literature. First, it is related to the literature on the economics of media, which considers a media (television, newspaper) as a platform in a twosided market connecting readers with advertisers. (See Gasewicz, Laussel and Sonnac (001) and (004) for early contriutions to the literature and the survey y Anderson and Gaszewicz (006)). Advertisement in these models play the same role as data collection in ours. As in our model, users are assumed to suffer a linear cost from advertisements. In the initial papers in the literature, the platform only collects revenues from the advertising market. Later papers, like Peitz and Valletti (008), Choi (006), Crampes, Haritchaalet and Jullien (009)) also allow for suscription prices charged to viewers, and compare regimes of free-to-air with pay-for-view televisions. Reisinger, Ressner and Schmidtke (009) and Reisinger (01) pay close attention to competition among advertisers on different platforms. Most of the literature (with the eception of Anderson and Coate (005)) considers competition etween platforms which are horizontally differentiated. Anderson and Coate (005) analyze the ehavior of a monopolistic platform when the market is not covered. In their model, users are differentiated y their intrinsic enefit from the good and not their aversion to advertising, resulting in very different demand functions and different conclusions for eample, they find that platforms typically choose too 4

5 little advertising whereas we oserve that the level of data collected y the platform is likely to e ecessive. Another difference stems from the shape of the utility that users otain from ads. All models, with the eception of Crampes, Haritchaalet and Jullien (009) assume that users suffer a linearly increasing utility loss for ads, whereas we assume that, in addition to a linearly decreasing loss, they otain a concave utility gain due to improved service. (Crampes, Haritchaalet and Jullien (009) allow users to have a positive value for low levels of ads, which is similar ut not equivalent to our assumption.) The main difference etween our analysis and the literature on media as two-sided platforms stems from the questions raised. The literature on media focuses on program differentiation and competition, while we are mostly interested in regulatory régimes and taation to improve privacy protection. In that sense, our paper is more closely connected to recent work on ad-avoidance (Anderson and Gans (011), Tag (009) and Johnson (013)), ut differences in the models preclude a direct comparison etween our results and theirs. Second, our paper is more distantly related to the literature on taation on two-sided markets (see Kind et al. (008), (010a), (010), Kind et al. (013) and Kotsogiannis and Serfes (010)), ut again the focus of the analyses are different, as we focus on the effect of taes on privacy protection rather than revenues and distortion. Finally, we note that our paper is closely related to the two contriutions y Crémer (015) and Bourreau, Caillaud and De Nijs (015) as all three papers consider the effect of specific taation on the ehavior of internet platforms, even though the three papers rely on different models of internet platforms and focus on different choice variales. The rest of the paper is organized as follows. We introduce our model in the net Section. Section 3 is devoted to the aseline model of a uniform data collection policy. Section 4 analyzes the effect of different ta instruments. Section 5 considers the introduction of a free option to access the platform with no data collection. Section 6 studies the inary model with financial transfers (either the platform paying users for data collection or users playing the platform for option zero). Section 7 allows for competition from a platform with no data collection. Section 8 concludes. All proofs not given in the tets are collected in Section 9. The Model.1 Platform and users We consider an internet platform which provides services to users. The platform collects revenues either directly (as in the case of e-commerce) or from third parties like advertisers in the case of search engines or digital social networks. The platform also collects data from users, recording their history of activity on the platform. We distinguish etween two sources of revenues: some of the revenues like sales revenues from e-commerce or instantaneous search-ase advertising revenues are collected immediately, whether the platform records data on the customer or not. Other revenues, like the sale of personal data to aggregators or the epected revenue from future targeted advertising, only accrue if personal data are collected and stored. We suppose that the platform commits to the degree of eploitation of personal data, denoted [0, 1]. The degree can e interpreted along different dimensions. It can represent the duration of time during which personal histories are stored y the platform, the fraction of personal data which are sold 5

6 y the platform to third parties or kept for direct eploitation, or any specified limitation on the use of personal data. We denote y v 0 the fied value generated y a user independently of data collection and y v() the value generated y data eploitation, where v( ) is supposed to e increasing and concave. The total value of a user to the platform is V () = v 0 + v(). Users get a enefit from using the platform, which is also decomposed into a fied component, u 0 and a component which depends on the collection of data. Data collection allows the platform to etter match the user with products and hence results in an improvement in the service. We let u() denote the enefit from the improvement in match quality, so that the enefit of a user can e written as U() = u 0 + u(), where u( ) is increasing and concave. In addition, we suppose that users are aware that they may e harmed y the collection of storage and personal data, and suffer a privacy cost which is proportional to the degree of data eploitation. We suppose that users are heterogeneous in their sensitivity to privacy loss, and let θ denote the characteristic of the user with privacy cost θ. We normalize the payoff of a user who does not access the platform to zero. We let F ( ) denote the distriution of privacy costs in the population of users. Given, the marginal user accessing the platform, T () is given y the solution to the equation: or u 0 + u() T () = 0, T () = u 0 + u(). and, assuming that the marginal cost of providing digital services is negligile, the profit of the platform is given y Π() = [v 0 + v()]f ( u 0 + u() ). (1) The total surplus of users accessing the platform with data collection is given y W () = T () 0 [u 0 + u() θ]df θ () Our model can e compared to models of interaction on media markets when users are averse to advertisement. In these models, is interpreted as the level of advertising, v() the revenues from advertising and θ the cost of ads to users. Models of advertising in media markets typically assume that v 0 = 0 (the media does not make any direct revenue from users) and that u() = 0 6

7 (users have no positive value for advertising). 1 A more important difference stems from the dimension of heterogeneity of users. We assume that users have the same value for the service ut different privacy costs, whereas models of media markets suppose that users have the same cost of advertising ut differ in their value of the service or in their ideal point in models of horizontal differentiation across media. This difference etween our model and other models of media with advertising avoidance results in non-trivial consequences. When users differ in their value for the service or ideal points, demand is linearly decreasing in ; when users differ in their advertising or privacy cost, demand is no longer linear and in fact includes a part u 0 which is decreasing and conve in. This simple oservation will lead to a major difference in the characterization of optimal levels of data eploitation.. Regulatory instruments The ojective of the paper is to assess how different regulatory instruments affect the level of data collection chosen y the platform and the welfare of users. We distinguish etween ta instruments and regulations imposing opt-out options. We investigate the incidence of four different ta instruments: A ta τ levied on the revenue of the platform A ta t P levied on the platform per user A differentiated revenues ta system, with two different ta rates τ 1 and τ applied to the revenues v 0 and v() A ta t U levied on each user for accessing the platform. As an alternative regulation, we consider a policy mandating that the platform offer a inary choice to the user with an opt-out option letting users access without data collection. We look at two possiilities The opt-out option is offered at no charge The platform charges a suscription price f for the opt-out option The platform charges a suscription price f for the opt-out option and pays users p for the opt-in option The platform faces competition from an other platform offering the opt-out option 1 One eception is Haritchaalet et al. (009) who allow users to have a positive value for low levels of advertising as we do. 7

8 3 The enchmark model In the enchmark model, there is no pulic intervention and the platform freely chooses the degree of data eploitation. For tractaility, we suppose that oth the platform s value v() and the user s enefit u() are iso-elastic in and that the distriution of privacy costs is uniform on [0, 1]: Assumption 1 Suppose that v() = β and u() = a α with a, > 0 and α, β [0, 1]. In addition, let the distriution F (θ) e uniform over [0, 1]. Under Assumption 1, we compute the maimal level of data collection for which all users access the platform the coverage level as a function of the enefit of the platform u 0 and the parameters a, α. The coverage level ξ(u 0 ) is the solution to the equation: u 0 + a α = 0. (3) If u 0 + a > 1, all users access the platform even at the maimal degree of data eploitation = 1. We focus attention on situations where the enefit of the platform to users is lower, so that the coverage level ξ is an interior value in [0, 1]. The following Lemma computes the effect of changes in the parameters on the coverage level ξ: Lemma 1 The coverage level ξ(u 0 ) is increasing in u 0 and a and decreasing in α. Finally, notice that ξ(1) = 1 and ξ(1 a) = a 1 1 α. 3.1 Platform profit To compute the optimal level of data collection of the platform, we write down the platform s profit as Π() = v 0 + v() if ξ(u 0 ), = [v 0 + v()]t () if ξ(u 0 ). When the level of data eploitation is elow the coverage level, all users access the platform and the profit is increasing in. When the level of data eploitation is aove the coverage level, the profit is no longer increasing in everywhere. Instead, we compute the derivative of the profit for ξ(u 0 ) and derive the elasticity of profit with respect to data eploitation: Π Π = v () v 0 + v() + T () T () = β v 0 β α u 0 a α

9 The elasticity of profit with respect to data eploitation is thus the sum of two conve functions of. Figure 1 illustrates the shape of the profit of the platform as a function of. Because of the fied terms u 0 and v 0, the elasticity of profit is strictly increasing in. The profit of the platform is thus maimized at one of the two etreme values ξ(u 0 ) or 1. There are two possile régimes depending on the values of the parameters: a régime of uniform coverage where the platform chooses = ξ(u 0 ) and serves all users and a régime of eclusion where the platform selects = 1 and serves users with a privacy cost smaller than u 0 + a. We summarize this finding in the net Proposition. < Insert Figure 1> Proposition 1 The platform optimally chooses a degree of data eploitation {ξ(u 0 ), 1}. It chooses ξ(u 0 ) if and only if v 0 ν(u 0 ) u 0+a ξ(u 0 ) β 1 u 0 a. Proposition 1 estalishes the eistence of a threshold ν(u 0 ) such that the platform chooses uniform coverage the market when the fraction v 0 is larger than ν(u 0 ) and eclusion otherwise. This result is easily understood. The fraction v 0 measures the relative importance of the value due to one-time access v 0 over the value due to data eploitation v(). When the value due to access is large relative to the value due to data eploitation, the platform has an incentive to serve all users and hence will choose low enough so that it covers the market. If the value of data eploitation is large relative to the value of access, the opposing intuition holds and the platform optimally chooses to restrict access and set a high degree of data eploitation. The net Lemma provides comparative statics results on the effect of changes in the parameters on the threshold ν(u 0 ). Lemma The threshold ν(u 0 ) is increasing in α and β and decreasing in u 0. By Proposition 1, the platform is more likely to choose uniform coverage when ν(u 0 ) is small. Lemma thus shows that the platform chooses optimal coverage for low values of α and β (when values and enefits are not too concave) and for high values of u 0 (when the enefit of users for access is high). 3. User welfare We net turn to the characterization of the degree of data eploitation which maimizes the welfare of users, W. Under Assumption 1, we compute the sum of welfare of users as or W () = T () 0 [u 0 + u() θ]dθ W () = u 0 + u() if ξ(u 0) = [u 0 + u()] u 0 + u() [u 0 + u() ] = 1 [u 0 + u()] if ξ(u 0 ). 9

10 When the level of data eploitation is elow the coverage level, all users access the platform, and welfare is strictly concave in. The maimum is attained at = (aα) 1 1 α, whenever ξ(u 0 ) or at ξ(u 0 ). When the level of data eploitation is aove the coverage level, the epression for welfare captures the fact that some users are ecluded from the platform < Insert Figure> Proposition The welfare maimizing level of data collection is either or 1. The welfare maimizing level is if α 1 or if α 1 and u 0 is large enough. Proposition details the configurations of parameters for which welfare is maimized at the low value of data collection or the highest level 1. While the conditions are comple, they reflect the following intuitions. When the enefit function is concave enough (α < 1), user welfare is maimized at the lowest value of data collection,, which maimizes the welfare of the average user. When, on the other hand, the enefit function is not too concave (high values of α > 1) and the access enefit u 0 is small enough. welfare is maimized with the maimal level of data collection generating eclusion. Propositions 1 and show that the optimal level of data collections of the platform and of users may differ and cannot e ranked uniformly for all parameters. The platform is more likely to choose eclusion when the access revenue is small and the revenue function not too concave; similarly, users are more likely to prefer eclusion when the access enefit is small and the enefit function is not too concave. The comparison etween the optimal choice of the platform and of users thus depends on a comparison etween the parameters u 0 and v 0 and α and β. Based on simple anecdotal evidence, we argue that users enefit more from access and the platform cares more aout data collection, so that α < β, and if α > 1/, u 0 is likely to e large. We thus epect the optimal level of data collection of the platform to eceed the welfare maimizing level of data collection of users. 4 Taation In this Section, we analyze the effect of the imposition of a ta on the optimal data eploitation strategy of the platform. The imposition of different taes can e interpreted as changes in the parameters of the model. A ta τ on the revenues only scales down the profit and has no effect on the strategy of the platform. A ta per user paid y the platform reduces the access revenue from v 0 to v 0 τ P. A differentiated revenues ta reduces the access revenue from v 0 to v 0 τ 1 and the revenues generated from data collection from v() to v()(1 τ ). A ta per user paid y users reduces the access enefit from u 0 to u 0 τ U. The effect of taes on the optimal choice of the platform can thus e computed y using the comparative statics results of the previous Section. They are summarized in the following Proposition. Proposition 3 The imposition of a ta has the following effects on the degree of data eploitation y the platform: An ad valorem ta τ on the profits or revenues of the platform has no effect on the degree of data eploitation 10

11 A ta paid y the platform per user τ P results in an increase in the degree of data eploitation In a differentiated revenues ta system, a ta τ 1 on the access revenues results in an increase in the degree of data eploitation, whereas a ta τ on the revenues generated y data eploitation results in a decrease in the degree of data eploitation A ta paid y users for accessing the platform τ U has amiguous effects on the degree of data collection ut increases the proaility that eclusion occurs. Proposition 3 shows that most taes are likely to induce the platform to increase its degree of data eploitation. The only eception is a differentiated ta on revenues, which targets profits due to the use of personal data and, as any Pigovian ta, leads to a reduction in data eploitation. With the eception of the ta on users which generates amiguous results, all other ta effects are roust and hold for general enefit and payoff functions. Clearly, a uniform ta on profits, or revenues are marginal cost are negligile, is neutral, and does not affect the platform s choice of data eploitation. A ta per user paid y the platform has no effect on the marginal enefit of data eploitation on the users accessing the platform, ut it lowers the loss of not serving the marginal user who chooses not to access on the platform. Hence a ta per user results in a higher degree of data eploitation. Similarly, a ta τ 1 on the access revenue of users leaves the marginal enefit of data eploitation unchanged ut reduces the loss of not serving the marginal user. A ta targeted at the revenues linked to data eploitation necessarily leads to a reduction in the ratio V () V () while leaving the effect on demand unchanged. It thus reduces the platform s incentive to collect and eploit data and results in a lower optimal value of data eploitation. The imposition of a ta per user τ P may induce another negative effect when users are differentiated along an additional dimension: a value η [0, η] parametrizing the revenue of the user to the platform (measured for eample in frequency of access or demographic characteristics). If the legal system allows the platform to discriminate among users, it will optimally choose to eclude users with low value, namely those users for whom η i V () τ P Any user with low value who accesses the platform will thus switch from a positive enefit U() θ() to a enefit of 0: eclusion following the imposition of a ta per user will further reduce the welfare of users. 5 Binary policy with no payment In this section, we suppose that the platform is mandated to propose an opt-out policy, where users are guaranteed that data will not e collected ut suffer from the resulting loss in service quality. For eample, users may refuse to e geo-localized or refuse to let cookies monitor their activity, ut will in consequence otain a lower quality of service on the platform. Users now freely choose etween two options: one with no data collection and one with a single positive 11

12 level of data collection. As each user prefers the free service with no data collection to the outside option (u 0 > 0) all users access the platform. We eamine the optimal level of data collection with an opt-out option, compare the profit of the platform and the welfare of users with and without the opt-out option. A θ-user chooses the positive level of data collection instead of the opt-out option if and only if u() + u 0 θ u(0), or θ < u(). With the opt-out option, the coverage level is the solution to a α = 0, or ξ(0) = a 1 1 α, the coverage level defined in the enchmark model when u0 = 0. The profit of the platform is Π() = v 0 + v() if ξ(0), Π() = v 0 + v() u() if ξ(0). Notice that the platform now collects the access revenue v 0 on all users, and that the demand for data collection is independent of the access enefit u 0. Inspection of the profit shows that Π() is increasing in for ξ(0) and either increasing or decreasing in for ξ(0) depending on whether α + β eceeds 1 or not. Hence we characterize the profit-maimizing degree of data collection as follows. Proposition 4 With a inary policy without payment, the platform optimally chooses a degree of data eploitation {ξ(0), 1}. It chooses ξ(0) if and only if α + β 1. Proposition 4 shows that, as in the enchmark case, the platform either chooses to cover the market or sets the highest possile degree of data eploitation. It covers the market when the revenue and enefit functions are highly concave, α + β 1. It chooses the maimal degree of data eploitation whenever the revenue and enefit functions are less concave. The comparison etween the level of data collection of the platform with and without the opt-out option produces amiguous results. On the one hand the coverage level ξ(0) is always lower than the coverage level in the enchmark case, ξ(u 0 ). The eistence of the opt-out option forces the platform to reduce. On the other hand, the region of parameters for which the platform chooses eclusion may increase. The platform now collects the access revenue v 0 on all users and does not have an incentive to lower to attract users when the access revenue is high as in the enchmark case. This effect may lead the platform to choose eclusion at the highest degree of data eploitation when the opt-out option is present, whereas it chooses to cover the market in the enchmark case. We net compare the profit of the platform in the enchmark case and with the opt-out option. For reasons of tractaility and technical implementaility, we do not consider more comple policies where the platform discriminates among users y proposing several positive degrees of data collection. 1

13 Proposition 5 The profit of the platform is higher in the enchmark case than under the inary policy without payment whenever α + β < 1. If α + β 1, there eists a threshold ũ 0 (0, 1 a) of the access enefit such that the profit of the platform is higher in the enchmark case than in the inary policy without payment if and only if u 0 > ũ 0. Proposition 5 shows that the only situation where the platform willingly proposes a inary policy without payment is when the access enefit of the users is low and the revenue and profit functions are not very concave. In all other circumstances, the platform is hurt y the introduction of the opt-out policy. The intuition underlying Proposition 5 is easy to grasp. When α + β < 1, the platform covers the market at level ξ(0) < ξ(u 0 ). Given that, when the market is covered, profit is increasing in, this policy is always dominated y a coverage policy at ξ(u 0 ) which can e chosen y the platform in the enchmark case. When α + β 1, the argument is ased on the oservation that the profit of the platform in the inary policy is independent of u 0. Instead, in the enchmark case, the profit of the platform is strictly increasing in u 0, as an increase in u 0 uniformly increases demand to the platform. At u 0 = 0, the choice etween coverage and eclusion is identical under the uniform and inary policies (oth choose to eclude when α + β 1), and the profit of the platform is strictly higher under the inary policy as it collects access revenue v 0 on all users. On the other hand at u 0 = 1 a, the profit of the platform is higher under the uniform policy, as it attracts all users y setting the maimal level of data collection. Hence there eists a threshold ũ o (0, 1 a) under which profit is higher under the inary policy and over which profit is higher in the enchmark case. We now ask whether users enefit from the switch from a uniform to a inary policy. The answer to this question is not easy. On the one hand, if the uniform policy involves eclusion, ecluded users enefit from the introduction of the opt-out option. On the other hand, the introduction of the opt-out option may lead to a deviation of the level of data collection away from the optimum, hurting users who access the platform. The following Proposition details situations under which the uniform and inary options are preferred y users. Proposition 6 If α+β 1, user welfare is larger under the inary policy than in the enchmark case if and only if (i) the platform chooses market coverage under the uniform policy and < ξ(u 0 ) or (ii) the platform chooses eclusion under the uniform policy and (u 0+a) < u 0 + a 1 α 1. If α + β 1, user welfare is larger under the inary policy than in the enchmark case if and only if (i) the platform chooses market coverage under the uniform policy and a > aξ(u 0) α ξ(u 0) or (ii) the platform chooses eclusion under the uniform policy Proposition 6 characterizes situations under which users favor the introduction of the optout option. When oth policies result in market coverage, users prefer the inary policy which results in lower levels of data collection if and only if the welfare maimizing level of data collection is < ξ(u 0 ). When oth policies result in eclusion, users prefer the inary policy which provides access to ecluded users the access enefit u 0. When the two policies result in different levels of market coverage, the comparison is unclear and depends on the values of the parameters. 13

14 6 Binary policy with payments 6.1 Suscription fee for the opt-out option We analyze in this Susection the situation where the platform charges a suscription fee f for the opt-out option. The policy is thus characterized y two variales: the degree of data eploitation and the suscription fee f. Charging a suscription fee results in two positive effects for the platform: it provides an additional source of revenue and makes the opt-out option less attractive, increasing the user s incentive to choose the option with data collection. Notice that the platform can also choose to concentrate on the suscription fee, y committing not to eploit any data. We denote this option y. Given the policy (, f) a θ-user chooses the positive level of data collection rather than the opt-out option if u() + u 0 θ ma(u 0 f, 0). It is never optimal for the platform to charge a suscription price f larger than u 0. 3 Thus we assume f u 0. Hence a θ-user picks the opt-out option if and only if θ u()+f. The suscription price f formally plays a similar role than the access enefit u 0 in the enchmark case. The coverage level is thus ξ(f) and the profit of the platform is equal to Π(, f) = v 0 + v() if 0 < < ξ(f), Π(, f) = [v() f]( u() + f ) + v 0 + f if > ξ(f) When the option is chosen, the platform collects f + v 0 from each user. 4 charges the maimal fee: f = u 0 and otains a profit The platform Π(, u 0 ) = u 0 + v 0. This profit associated to policy (, f) is smaller than the profit achieved at if v() < u 0, which necessarily happens if < u 0. In that case, the platform has an incentive to focus on the suscription fee and forego any revenue due to data eploitation. Otherwise, as in the enchmark case, the platform chooses a positive level of data eploitation which is either equal to the coverage level or to the maimal level. Proposition 7 Under a inary policy where the platform charges for the opting-out option, the platform always chooses the maimal fee f = u 0. If < u 0, the platform commits not to collect data: the optimal policy is and the revenues are generated y the suscription fee collected on all users. If > u 0, the platform collects data and optimally chooses {ξ(u 0 ), 1}. It chooses the lower level ξ(u 0 ) when ν(u 0 ) + u For f > u 0, agents who do not choose do not access the platform at all. By charging the price f = u 0 ɛ for a positive and small ɛ, the platform could generate a positive profit equal to u 0 + v 0 ɛ on each of these users. 4 The policy (, f) is not equivalent to ( = 0, f): = 0 allows the user to access the service without a fee charge. This eplains why the profit Π(0, f) differs from Π(, f). 14

15 Proposition 7 shows that the optimal policy is to focus on the suscription fee and serve all users when the value of data is low relative to the access enefit, < u 0. In that case, the maimal revenue that the platform can otain from data collection is v() < u 0 = f and the platform has no incentive to collect and eploit data. If instead, the value of data is high relative to access enefit, > u 0, the platform optimally proposes an option with positive data collection. The maimal level = 1 can only improve the profit over the option ecause it leads to the etraction of value (rather than u 0 ) from users who choose to provide data. We then show, as in the enchmark case, that the profit reaches a maimum either at the coverage level ξ(u 0 ) or at the maimal level 1, and characterize the condition under which profit is reached as a function of the threshold ν(u 0 ) defined in the enchmark case. We now compare the optimal policy with the uniform optimal policy descried in Proposition 1. In contrast to the uniform policy, the optimal choice does not depend on the access revenue v 0 ecause this revenue is collected from each user independently of the data collection policy. Furthermore, the maimal degree of eploitation is chosen more often than under the uniform policy. Covering the market with the inary policy is only profitale if ν(u 0 ) < u 0 whereas market coverage is the optimal policy in the enchmark case when ν(u 0 ) < v 0. Hence there is an interval of threshold values [ u 0, v 0 ] for which the platform chooses eclusion under the inary policy and market coverage under the uniform policy. This can e eplained intuitively as follows. Under market coverage, the platform does not collect any fee, and the revenues are the same under the two policies. Under eclusion at = 1, the users who choose the costly option at f = u 0 are eactly those who do not access the platform under the uniform policy. As the platform collects revenues from the users opting out, it receives a higher profit under the inary policy with payment than under the uniform policy. This argument also shows that the profit of the platform is always higher under the inary policy than in the enchmark case. User welfare is lower under the inary policy when the platform commits not to collect data, as all users receive a zero utility. When > u 0, users welfare is identical under the two policies when they result in the same market coverage. If ν(u 0 ) < u 0, all users access the platform at the level of data collection ξ(u 0) for oth policies. When ν(u 0 ) > v 0, under oth policies eclusion occurs at the maimal level of data collection, and users who do not access the platform under the uniform policy or select the opt-out option under the inary policy receive a zero utility. When u 0 < ν(u 0 ) < v 0, the comparison etween user welfare under the two policies depends on the parameters. User welfare is higher under the inary policy if and only if ξ(u 0 ) < (u 0 + a), a condition which, as we saw in the proof of Proposition, is satisfied whenever α > 1 and ξ(u 0) <. 6. Suscription price for the opt-out option and payment for data collection In this Susection, we suppose that the platform can not only charge a fee for the opt-out option ut also pay users for their data. 5 The platform thus chooses three instruments: the degree of data eploitation, the fee f paid y users for the opt-out option and the price p paid to 5 We assume that the price paid to users is always positive. We do not consider the case where the platform asks for a suscription fee oth from users choosing the opt-out option and users choosing to opt in. 15

16 users who choose the opt-in option. As in the previous susection, we can focus attention on suscription fees f u 0 and assume that all users access the platform. As in the previous Susection, the platform can choose to commit not to collect data ( ) and charge the suscription fee u 0 from all users, resulting in the profit Π( ) = u 0 + v 0. As in the previous Susection, this policy is optimal if and only if u 0. We now consider the case > u 0. A θ-user chooses the positive level of data collection rather than f the opt-out option if and only if u() + u 0 θ + p u 0 f. Hence a θ-user picks the opt-out option if and only if θ u()+f+p. The coverage level is equal to ξ(f + p) and the situation is similar to the enchmark case when u 0 is replaced y p + f. Oserve that the suscription fee and the data price have the same impact on the user s choice etween the opt-out and opt-in options. The profit of the platform is Π(, f, p) = v() p + v 0 + f if ξ(f + p), Π(, f, p) = (v() p f)( u() + p + f ) + v 0 + f if ξ(f + p). Notice that in order to induce users to choose the opt-in option, the platform can either use the data price or the suscription fee. The fee results in additional revenues whereas the price results in additional costs. Hence, the platform always has an incentive to increase the suscription fee f rather than the price p. And a positive price only emerges when the platform cannot raise the suscription fee anymore, i.e. when the suscription fee is equal to u 0. In order to analyze situations where the platform chooses a positive price for the data, we may thus restrict attention to the situation where f = u 0. In addition, we oserve that it cannot e optimal for the platform to choose a degree of data eploitation < ξ(p + u 0 ) so that we must have ξ(p + u 0 ). For any fied, we now derive the optimal price data price p chosen y the platform, y computing the derivative of profit with respect to p: Π p = v() u() (p + u 0) if > ξ(u 0 + p) At = ξ(u 0 + p) the profit has a kink with a right derivative equal to 1. The optimal price satisfies p = 0 if v() u() u 0 0 p = u() u 0 if 0 < u() u 0 p = v() u() u 0 if 0 < v() u() v() u() u 0 u 0 u() u 0 The condition v() u() u() is equivalent to where is the unique positive 16

17 value that satisfies v( ) + u( ) = 0. 6 To summarize, if v() u() u 0 0 the price is null, and if v() u() u 0 0 the price is given y p = u() u 0 if v() u() p = u 0 if For, the price is chosen to cover the market and the profit is given y v() + u() + u 0 + v 0. The platform optimally selects the level of data eploitation that maimizes v() + u() over [ξ(0), ], assuming ξ(0) <. 7 In that case, offering a positive data price allows the platform to increase the degree of data eploitation at which the market is covered. Notice that, since v() is the value of data to the platform and u() the enefit of a user with maimal privacy cost, the degree of data eploitation maimizes the sum of the surplus of the platform and of the user with highest privacy cost. For >, the optimal price leads to eclusion. As in the enchmark case, the elasticity of profit is increasing in so that the platform optimally chooses the highest degree of data eploitation. We summarize our findings in the following Proposition. Proposition 8 Let u 0. The platform always chooses the maimal fee f = u 0. If v() u() < u 0 for any, the platform never chooses to pay for data, and the choice is descried in proposition 7. If v() u() u 0, the platform 1. either chooses to cover the market, with a level of data eploitation is ξ(u 0 ) or if ξ(u 0 ) < <. In the first case, the price is null, in the second case, it is positive given y u( ) u 0 ;. or to eclude and pick = 1. The price is null if a < u 0, or positive given y p = a otherwise. u 0 Proposition 8 shows that two situations can happen when the platform chooses to pay users for their data. In the first case, when is chosen, the platform covers the market and uses the payment to increase the degree of data eploitation. In the second case, the platform selects eclusion at the highest degree of data eploitation and uses payment to increase the numer of users choosing the opt-in option. The platform s choice etween the two strategies depends on the parameters in a comple way. The platform s degree of data eploitation can e higher or lower than the optimal degree when the platform does not pay users fro the data. We illustrate the optimal choice of the platform in the simple case where u 0 = 0. In that case, with no payment for data, y Proposition 4, the optimal degree of data eploitation is ξ(0) = a 1 1 α if α + β 1 and 1 if α + β 1. Note that that is the unique solution to the equation a α = β = and the unique solution to the equation αa α 1 + β β 1 = 1. 6 The eistence of a unique value satisfying this condition follows from the fact that the condition is equivalent to v()+u() and that v()+u() is decreasing, larger than for = 0 and smaller than for = Notice that does not depend on u 0. 7 Again, notice that does not depend on u 0. 17

18 Assume first that ξ(0) (a 1 β 1 α ) or < ξ(0) (a + β 1) or < 1. Then the optimal policy if the market is covered is to choose ξ(0) with a price equal to zero. If eclusion is chosen, the price is 0 if < a and equal to a if > a. We oserve that if α + β < 1, the platform may switch from market coverage in the régime without payment to eclusion in the régime with payment with a positive price for the data. 8 Net consider the case where ξ(0) < <. In that case, positive prices may emerge oth when the market is covered and under eclusion. We simplify the analysis y assuming α = β. We then have = ( a+ ) α and = (α(a + )) 1 α and ξ(0) < if a < α(a + ), < if α < 1. The optimal policy when the market is covered is to choose with a profit equal to (a + ) α = (1/α 1) (up to v 0 ). The optimal policy when the market is not covered is to choose = 1, offering the positive price ( a)/ with a profit equal to ( a+ ) (up to v 0 ). Thus, the optimal policy is to cover the market if (1/α 1) ( a+ ). When α = 1/, = ( a+ ) and the two profit epressions are equal. This profit is otained either y covering market with and a price equal to u( ) = ( a+ a )( ), or y proposing = 1 with the larger price ( a ). As (1/α 1) decreases with α we conclude that the eclusion régime is chosen for α < 1/, as in the case without payment for the data. 7 Competition with a platform without data collection In this Section, we analyze the effect of competition from another platform offering access without data collection. 9 Competition etween advertising-ased and fee-ased platforms has een analyzed in the economics of media (see Choi (006), Peitz and Valletti (008), Crampes, Haritchaalet and Jullien (009)). In the contet of our model, this competition can easily e analyzed, oth when the competing platform only collects access revenues v 0 and when can it charge a suscription fee f. 7.1 Competition with a platform without suscription fee If the platform faces competition from another platform which does not charge a suscription fee, a θ-user accesses the platform if and only if u 0 + u() θ u 0. Hence the coverage level is the same as when the platform proposes the opt-out option for free and given y ξ(0) = a 1 1 α ξ. As in the enchmark case, we oserve that Π() is either maimized at ξ(0) or at 1 and otain the following characterization: 8 For eample if a 1 β 1 α, this switch may happen if a 1 β 1 α > a, a condition which requires β > α and > a. 9 A recent eample of of a platform proposing access without advertising nor data collection is the digital social network Ello which was launched in March 014 and claims aove a million users. 18