Winners, Losers, and Facebook: The Role of Social Logins in the Online Advertising Ecosystem

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                                                                                                                   Articles in Advance, pp. 1–22                                                       ISSN 0025-1909 (print), ISSN 1526-5501 (online)

Winners, Losers, and Facebook: The Role of Social Logins in the
Online Advertising Ecosystem
Jan Krämer,a Daniel Schnurr,b Michael Wohlfartha
a Chair  of Internet and Telecommunications Business, University of Passau, 94032 Passau, Germany; b Research Group Data Policies,
University of Passau, 94032 Passau, Germany
Contact:, (JK);, (DS);, (MW)

Received: August 8, 2016                   Abstract. Social logins, such as “Log in with Facebook,” improve a website’s user experi-
Revised: July 28, 2017; November 3, 2017   ence and therefore enjoy great popularity among content providers (CPs) and users alike.
Accepted: November 10, 2017                Moreover, they also enable the social network and the CPs to share data, which individu-
Published Online in Articles in Advance:   ally improves their ability to place targeted advertising. On the basis of a game-theoretic
                                           model that offers a microfoundation for CPs’ competition for advertisements, on the one
                                           hand, and CPs’ competition for users, on the other hand, we demonstrate the strategic
Copyright: © 2018 The Author(s)            effects of social logins in the online advertising ecosystem. We fully characterize the mar-
                                           ket conditions under which social logins are offered and adopted, and when the adoption
                                           is actually profitable for the CPs. In particular, we show across several model extensions
                                           that the voluntary adoption of the social login may yield a prisoner’s dilemma outcome
                                           for the CPs.

                                           History: Accepted by Chris Forman, information systems.
                                           Open Access Statement: This work is licensed under a Creative Commons Attribution-NonCommercial-
                                             NoDerivatives 4.0 International License. You are free to download this work and share with
                                             others, but cannot change in any way or use commercially without permission, and you must
                                             attribute this work as “Management Science. Copyright © 2018 The Author(s).
                                             .1287/mnsc.2017.3012, used under a Creative Commons Attribution License: https://creative
                                           Funding: D. Schnurr acknowledges partial funding for this project from the Bavarian State Ministry of
                                             Science and the Arts in the framework of the Centre Digitisation.Bavaria.
                                           Supplemental Material: The online appendix is available at

Keywords: social login • advertising markets • targeted advertising • data sharing

1. Introduction                                                             a microfoundation and characterization on how social
Social logins (Gafni and Nissim 2014, Janrain 2014)                         logins affect CPs’ competition for users, as well as
allow users to authenticate with third-party content                        CPs’ competition in the advertising market, where bet-
providers (CPs) through their social network account.                       ter user data can be utilized to place more relevant
They have been established as one of the most popu-                         ads. Thereby, we contribute to the extant literature by
lar instruments to share user and usage data among                          explicitly considering the strategic effects of data access
otherwise unaffiliated online outlets. The most popular                     and information sharing among competitors on a CP’s
social login,1 Log in with Facebook,2 allows websites and                   ability to attract users, as well as its ability to gener-
mobile apps to access users’ public profile including                       ate advertising revenues. Moreover, we identify factors
demographic data, email address, and friends, as well                       that impact a CP’s decision to offer access to user data
as to request extended profile properties such as the                       and/or usage data. For example, we show that a higher
history of users’ likes or recorded web activities. On the                  competitive intensity between third-party CPs makes
other hand, Facebook obtains comprehensive data on                          information sharing with a social network provider
users’ activities at the third-party outlet through the                     more likely, even if this is ultimately detrimental to
programming interfaces of the login service. In fact, in                    the CPs—i.e., they may find themselves in a prisoner’s
its Platform Policy,3 Facebook states that it “can ana-                     dilemma situation. Furthermore, we identify market
lyze [a third-party’s] app, website, content, and data                      outcomes in which socially inefficient market failures
for any purpose, including commercial.”                                     occur, because the social login is not offered or adopted
   The conditions of unaffiliated CPs to share precious                     although it would increase total welfare.
user data via social logins and the resulting strategic                        Our main analysis is based on three stylized facts,
implications have thus far not been studied. In this                        which we motivate in the following. First, despite the
article, we develop a game-theoretic model that offers                      myriad of CPs that comprise the internet (including
Krämer, Schnurr, and Wohlfarth: Social Logins in the Online Advertising Ecosystem
2                                                                       Management Science, Articles in Advance, pp. 1–22, © 2018 The Author(s)

websites, mobile apps, shopping and product compar-              and Stallaert 2014). However, through the social login,
ison sites, and content and media platforms), one can            the targeting ability of the special-interest CP is also
roughly distinguish between special-interest CPs and             likely to increase, because it gains access to accurate
general-interest CPs. The special-interest CPs may be            user data from the general-interest CP. Therefore, the
thought of as specialized websites that offer a nar-             social login facilitates data sharing by which CPs can
row range of content in the same domain of interest              (individually) increase their targeting ability and thus
(e.g., on celebrities or fishing), whereas the general-          improve their competitive position in the advertising
interest CP offers a much broader range of comple-               market.
mentary content (e.g., a social networking site where               Third, social logins allow special-interest CPs to en-
users discuss celebrities and fishing). Usually, there are       hance the user experience of their site in several ways.
several special-interest CPs for each domain of inter-           For example, the social login allows the user to uti-
est and thus, special-interest CPs are in competition            lize existing login credentials, which limits password
among each other for the same subset of users (e.g.,             fatigue and lowers transaction costs of registration.
users visit either or, but            Most importantly, information sharing enables bet-
not both). By contrast, there exists only a small set            ter personalization and customization of content and
of general-interest CPs, such as Facebook, which have            better integration of the services of the special- and
been characterized as gateways to the internet (Rusli and        general-interest CP. For instance, Spotify and other
Efrati 2013, Arakali 2015), because they are used by             music streaming service providers exploit social logins
the vast majority of internet users and often serve as           to curate customized content and to allow users to
a starting point for users’ online activity. For exam-           share personal playlists and current listening activi-
ple, Facebook served 2.07 billion monthly active users           ties with their social peers. Of course, there may also
worldwide at the end of June 2017 (Facebook 2017) and            be negative effects on the users’ experience, in partic-
a 69% share of U.S. online adults in 2016 (Pew Research          ular due to concerns of privacy or a single point of
Center 2017). Thus, for the majority of our analysis, we         failure. However, the widespread popularity of social
conceive a scenario, where users single-home with a              logins indicates that most users value the benefits of
special-interest CP but split their attention (i.e., multi-      the social login more. Already in 2010, two years after
home) between the selected special-interest CP and the           the launch of Facebook’s social login, 250 million users
general-interest CP.4                                            and two million third-party websites used this fea-
   Second, although the general-interest CP is not in            ture, with an estimated growth of 10,000 sites per day
direct competition for users with the special-interest           (van Grove 2010). Currently, the installed base is esti-
CP, all CPs are in competition in the advertising mar-           mated at almost 15 million websites (SimilarTech 2017).
ket. In particular, online advertisers will choose to            According to Janrain (2014), 51% (88%) of consumers
place advertisements at a given CP based on its ability          have used (encountered) a social login at least once,
to target ad-relevant users. Targeting increases adver-          and more than half of the users (64%) “are more likely
tisers’ profits by reducing wasted impressions to users          to return to a website that remembers them without a
who are not interested in an advertiser’s product (Iyer          username and password” (p. 15). In this vein, increased
et al. 2005). Empirical studies generally support the            user engagement and interaction are often quoted as
notion that more data on users allows firms to gain              main reasons for the CPs’ decision to adopt a social
“much better information on consumers, their prefer-             login (see, e.g., Gigya 2015). In other words, the social
ences and their media habits” (Iyer et al. 2005, p. 461),        login improves the user experience derived from using
which in turn increases the effectiveness of displayed           the CP, which can give it a competitive edge in the
advertisements by means of targeting (Braun and Moe              competition for users with other special-interest CPs.
2013, Goldfarb and Tucker 2011, Urban et al. 2014)
and personalization (Ansari and Mela 2003, Bleier and            2. Related Literature
Eisenbeiss 2015, Tucker 2014).5 In particular, Goldfarb          Social logins have previously been considered in the
and Tucker (2011) find that targeted ads exhibit a               context of usability of services and user acceptance
significantly higher effectiveness than conventional             (Egelman 2013, Gafni and Nissim 2014), and from a
nontargeted ads. Moreover, in a study of advertising             technical (Ko et al. 2010, Kontaxis et al. 2012) or legal
effectiveness on Facebook, Tucker (2014) finds that per-         perspective (Van Der Sype and Seigneur 2014), but to
sonalization of ad impressions in addition to targeting          the best of our knowledge not from a strategic (i.e., eco-
further increases the likelihood that users click on dis-        nomic) perspective.
played ads. Social logins allow the general-interest CP            The technical literature views social login services
to track their users also at the special-interest CP, which      (Ko et al. 2010) in the history of (enterprise) single sign-
raises their ability for behavioral targeting—i.e., the abil-    on systems (SSOs)—i.e., systems that allow for central-
ity to select advertisements on the basis of past brows-         ized and federated identity management across remote
ing behavior and other available information (Chen               and distributed resources (Pashalidis and Mitchell
Krämer, Schnurr, and Wohlfarth: Social Logins in the Online Advertising Ecosystem
Management Science, Articles in Advance, pp. 1–22, © 2018 The Author(s)                                                            3

2003). In essence, the studies (e.g., Kontaxis et al. 2012,               In their model, the prisoner’s dilemma occurs because
Sun and Beznosov 2012, Wang et al. 2012) suggest                          investments increase while revenues remain constant.
that social logins reduce users’ transaction costs in                     In our context, the prisoner’s dilemma occurs because
a distributed (web) context, if technical systems are                     the relative advantage of the special-interest CP offer-
designed and implemented securely and with regard                         ing (a better user experience through) the social login
to users’ privacy concerns.                                               is competed away in equilibrium, but at the same time,
   With respect to users’ motives to use the social login                 data sharing with the general-interest CP worsens its
rather than a CP’s own registration service, Kontaxis                     competitive position in the advertising market.
et al. (2012, p. 321) point to an additional “social dimen-                  Finally, our study is related to the large strand of
sion to the browsing experience” due to users’ ability                    literature on online advertising and behavioral targeting.
to share, rate, and interact with content. These features                 Above and beyond the empirical studies on target-
require the sharing of user and usage data between                        ing and ad effectiveness discussed above, we do not
the respective social network and the CP. Based on                        attempt a complete review here, and instead focus on
an exploratory survey, Gafni and Nissim (2014) iden-                      the presentation of welfare effects that were identi-
tify familiarity and convenience as factors that posi-                    fied in the extant literature. Chen and Stallaert (2014)
tively affect users’ readiness to opt for a social login                  highlight that behavioral targeting can increase social
in a world in which internet users face an increas-                       welfare, but the effect on the advertisers’ profits is
ing number of websites that require authentication.                       ambiguous as countervailing effects of competition and
In such cases, social logins avoid the need for multi-                    propensity are present. In economic theory, users bene-
ple (different) username and password combinations,                       fit from improved targeting of advertising, because the
evade repetitive registration processes, and minimize                     displayed ads are perceived as more relevant to their
the effort to update and maintain accurate information                    interest and therefore also as more informative (Anand
in the case where authentication properties change.                       and Shachar 2009, Bergemann and Bonatti 2011). How-
Relatedly, access to users’ personal data may invoke a                    ever, survey-based research has also identified poten-
range of privacy issues that have been examined by a                      tial adverse effects due to better-informed advertising
growing strand of theoretical and empirical literature                    beyond the theoretical literature (Turow et al. 2009).
(see Acquisti et al. 2016, for an extensive survey). With
regard to social logins, authors have criticized inter alia
the loss of anonymity, revelation of social information,                  3. A Model of Information Sharing in the
loss of traceability in cases of a data breach, propa-                       Online Advertising Ecosystem
gation of advertisements, and disclosure of user cre-                     3.1. Competitive Setting
dentials as potential threats to users’ privacy (Kontaxis                 We conceive an online advertising ecosystem with two
et al. 2012). However, the fact that users deliberately                   competing special-interest content providers (CP i, i 
decide to use the social login as opposed to alternative                  A, B), one general-interest content provider (CP G), and
registration options suggests that the positive effect on                 one advertiser (Z). In the context of this paper and the
users’ valuation outweighs potential privacy concerns                     preceding motivation, it will be convenient to think of
(Egelman 2013). In other words, if the social login is                    CP G as a social network provider (e.g., Facebook, Twit-
chosen over alternative registration options, data shar-                  ter, LinkedIn, or Google Plus), although the insights of
ing occurs actively and voluntarily. Such user control                    the model are of course not restricted to this scenario
has been found to be vital for successful marketing                       (see Section 7). The important aspect of the model is
campaigns in the context of social media (Fournier and                    that the special-interest CPs operate in the same domain
Avery 2011, Tucker 2014).                                                 and are thus competing directly for users, whereas the
   Social logins as data sharing mechanisms between                       general-interest CP is already used by all internet users
otherwise unaffiliated CPs can also be seen as a form                     under consideration. This captures the relevant compet-
of open access relationship (Boudreau 2010). In this                      itive dynamics of the internet, where, on the one hand,
context, the strategic impact of data sharing on the                      users split their attention between a general-interest site
competition between CPs is a priori unclear: although                     (e.g., Facebook) and a particular special-interest site,
additional data may increase the firms’ ability to price                  but, on the other hand, choose to pay attention to only
discriminate (see Fudenberg and Villas-Boas 2012) and                     one of the two comparable special-interest sites. In other
to personalize (Ansari and Mela 2003), the business                       words, whereas users multi-home between CP i and CP
stealing effect, due to the competitors’ access to the                    G, they single-home between CP A and CP B.
firm’s exclusive resources, may outweigh the benefits.                       Furthermore, we assume that all CPs offer their con-
In this spirit, Mantovani and Ruiz-Aliseda (2016) ana-                    tent free of charge to internet users and derive revenues
lyze the effects of collaboration between firms produc-                   by charging a price, p, for showing display advertise-
ing complementary products, and show that collab-                         ments on their sites. To date, this is the prevalent busi-
oration may lead to a prisoner’s dilemma outcome.                         ness model on the internet (c.f., Anderson 2012), and
Krämer, Schnurr, and Wohlfarth: Social Logins in the Online Advertising Ecosystem
4                                                                     Management Science, Articles in Advance, pp. 1–22, © 2018 The Author(s)

consequently, this is the dominant modeling assump-            Figure 1. Competitive Setting of the Model
tion in the related literature (see, e.g., Kourandi et al.                                                                      Advertiser Z
2015, Athey et al. 2018).6 To fix ideas, we assume
that CPs offer advertisement space based on pricing
per impression (CPM model). Although, of course,                              Competition for                 Competition for
there exist also other means to sell advertisement                            advertisements                  advertisements
space, in particular based on pricing per click (CPC                          A            G                  B            G
                                                                                    Ad                              Ad
model) or per transaction on the advertiser’s site (CPA
model), CPM is still widely adopted by large CPs (e.g.,
                                                                  CP G
Facebook, Google AdSense), and consequently, this is
the standard assumption used in the context of dis-
play advertisement markets (see, e.g., Anderson and
De Palma 2013, Johnson 2013).7 In particular, CPM                                               Competition
pricing implies that the advertisers’ performance met-                                           for users

ric is based on view-throughs (i.e., the long-term effect
                                                                                    CP A                          CP B
on users’ purchase decision; Bleier and Eisenbeiss
2015), as opposed to click-throughs (i.e., the immedi-         Notes. Each user chooses exactly one of the two special-interest CPs
ate engagement with the advertisement). Next to the            A and B (single-homing) and splits attention between the chosen
potential brand-building effects (Yoo 2009) and long-          special-interest CP and the general-interest CP G (multi-homing).
                                                               All CPs are ad-financed and receive advertisement revenues accord-
term impact on users’ decision (Manchanda et al. 2006,
                                                               ing to their relative ability to reach ad-relevant users. Because of
Lewis and Reiley 2014), which are usually neglected by         users single-homing special-interest CPs, the total advertising mar-
click- or action-based measures, the academic literature       ket splits into two submarkets, and in each submarket, one special-
has identified moral hazard as a potential impediment          interest CP and the general-interest CP compete for display adver-
                                                               tisements from advertiser Z.
to the adoption of pricing models associated with pure
click-through measures (Asdemir et al. 2012) or action-
                                                               although the general-interest CP is not in direct compe-
based measures (Hu et al. 2016). View-throughs (which
                                                               tition for users with any of the special-interest CPs, it is
include click-throughs) are therefore commonly con-
                                                               still in competition with them for users’ attention to ad
sidered as the relevant performance measure in display
                                                               impressions over time. This basic competitive set-up of
advertising markets (Hamman and Plomion 2013) and
                                                               the model is summarized in Figure 1.
especially by advertisers in social networks. Accord-
ing to market research (Ross 2015), more than 60% of           3.2. Details of the Model
total advertising budget spent at Facebook is allocated        We now provide a more detailed description of the in-
via optimized CPM (oCPM), a metric where advertisers           gredients of the model, the strategic variables of each
are billed on the basis of impressions, while Facebook         of the entities involved, and their possible actions.
optimizes bidding for the effective cost per impression
                                                               Internet Users. There is a unit mass of heterogeneous
according to advertisers’ preferred mix of user inter-
                                                               internet users that have a natural preference for one
action (actions, reach, clicks, or social impressions).8
                                                               of the two special-interest CPs. Users’ preference for
With close to 24% of total revenues in 2014 (eMarketer
                                                               CPs is denoted by x and assumed to be uniformly
2015) and a third of total display impressions to U.S.         distributed between zero and one (Hotelling 1929).
internet users in 2011 (comScore 2011), Facebook has           The two special-interest CPs are horizontally differen-
become the clear market leader in display advertising,         tiated and located at either end of the users’ preference
and its share is estimated to grow further over the com-       spectrum—i.e., CP A at x  0 and CP B at x  1. Thus,
ing years (Marshall 2015).                                     a type x consumer derives utility of UA (x)  u A − τx
   To focus on the competition between CPs, we assume          or UB (x)  u B − τ(1 − x), when consuming the content
that there is a single advertiser, Z, that wishes to buy       of CP A or CP B, respectively. Thereby, u i (i  A, B)
advertisement space for a special-interest ad (in the          denotes the utility that is derived from the viewing
same domain as the special-interest CPs) at any one of         experience and usability of the site (e.g., the quality
the CPs. As will be described in detail later, CPs differ      of the content or the hassle of the login procedure),
in their targeting ability, and because of competition         and τ is the degree of competition between the two
and split attention between CPs, each CP reaches a dif-        special-interest CPs. When τ is large, the users’ innate
ferent subset of the users at any given point in time.         preference for the CPs becomes more important, such
Depending on a CP’s ad price relative to how many              that competition on the basis of u i becomes weaker.
view-throughs can be achieved at this CP, the adver-           A user will visit only the special-interest CP that gives
tiser will choose at which subset of the CPs to advertise      her the highest utility. We denote this user demand for
to maximize its profit. Thus, it is important to see that,     CP i by Di . Furthermore, we assume that u i is large
Krämer, Schnurr, and Wohlfarth: Social Logins in the Online Advertising Ecosystem
Management Science, Articles in Advance, pp. 1–22, © 2018 The Author(s)                                                                              5

enough, such that the market is fully covered—i.e., at                    not relevant for the economic effects that arise in any
any time DA + DB  1.                                                     given special-interest advertising market.
   Next to one of the special-interest CPs, users also                       CP G may choose to offer CP i a social login. If CP i
visit the general-interest CP. To model how users split                   chooses to adopt the social login service on its site,
attention between those two CPs, we assume that there                     the two CPs implicitly agree to cooperate by means of
are two time periods, indexed by t  1, 2. In each time                   sharing data about their users. Formally, this has two
period, a user visits the special-interest CP with prob-                  implications: First, we assume that CP i’s utility, u i ,
ability δ and the general-interest CP with probability                    increases by θ ≥ 0, because of a better user experience
1 − δ. We will thus refer to δ and 1 − δ as the screen                    at CP i, as motivated above. Consequently,
attention probability of CP i and CP G, respectively.                            (
Consequently, in each time period t, a special-interest                              u ib ,      if CP i does not adopt the social login,
CP i expects to be viewed by a total of Di, t  Di δ users,                          u ib + θ,   if CP i adopts the social login.
whereas the general-interest CP G expects a total of
DG, t  (DA + DB ) (1 − δ)  1 − δ viewers per time period.                  Thereby, we adopt the convention to denote the base-
                                                                          line value—i.e., a situation without the social login—
Content Providers. All content providers j  A, B, G                      with superscript b. For now, we will assume that CPs
receive revenues from selling advertisement space to                      are symmetric—i.e., u Ab  u Bb  u b .10 Second, because of
the advertiser. Each CP demands a total price for dis-                    information sharing about the user, the targeting rates
playing the ads of Z on its site in both time periods.                    of CP G and CP i are increased by a factor of φ G ≥ 1
We normalize the costs of providing content of each                       and φ i ≥ 1, respectively. Consequently,
CP to zero and assume that ads can be displayed at
zero marginal costs. Moreover, for reasons that will                             
                                                                                  α bj ,
                                                                                     for the mass of users, Di , of CP i that does
become clear later, after users have chosen a particu-                           
                                                                                    not use the social login,
lar special-interest CP, each CP i is only in competition                 αj 
                                                                                       j · α j , 1}, for the mass of users, Di , of
                                                                                min{φ
with CP G for views.9 Thus, prices will depend on the
                                                                                    CP i that uses the social login.
market share—i.e., the submass of users, Di —of the
CP i that is considered. Therefore, we must differen-                     Advertiser. The advertiser wants to place an informa-
tiate between CP i’s price, denoted by p i , and CP G’s                   tive ad that is targeted at a specific audience. The goal
price for the submarket Di , denoted by p G(i) .                          of the advertiser is to generate attention for its prod-
   Since we do not consider costs, the profit of CP i is                  uct or service, which, for example, can be a visit to its
Πi  p i , whereas the profit of CP G is ΠG  iA, B p G(i) .             online or offline store sometime after the ad has been
While a CP seeks to maximize its profit from advertis-                    viewed. Thus, the effectiveness of an ad is measured
ing, p j will depend on CPs’ ability to reach ad-relevant                 with respect to the rate of effective view-throughs.
users, which is influenced by two factors: (i) the num-                   In particular, we assume that the value of the first ad
ber of a CP’s viewers in time period t, which again                       impression that is displayed to a user belonging to the
depends on competition and screen attention, and                          target audience is v  1. Because the ad is assumed to
(ii) its ad targeting rate α j ≤ 1. A CP’s targeting rate                 be informative, all subsequent ad impressions on the
denotes which fraction of viewers that actually see the                   same user are wasted and thus do not create additional
ad belong to the advertiser’s target group—i.e., how                      value for the advertiser (for a similar assumption, see,
well a CP can transform views into relevant advertising                   e.g., Ambrus et al. 2016).11 The objective of the adver-
impressions (view-throughs).                                              tiser is to select the subset of CPs at which to advertise
   In this context, we emphasize that our model is set                    to maximize its profit
up to analyze the economic effects that arise in compe-                                                              X
                                                                          ΠZ  ΓA (n A − p A ) + ΓB (n B − p B ) +            ΓG(i) (n G(i) − p G(i) ),
tition for the advertising budget of a particular adver-                                                             iA, B
tiser targeting a specific special-interest group. Thus,
we restrict attention only to that subset of the online                   where Γi (ΓG(i) ) is an indicator function, returning one if
advertisement ecosystem that is relevant for this adver-                  an ad is placed for the mass of Di users at CP i (CP G),
tiser, comprised of special-interest websites (targeted                   and zero otherwise. Moreover, n i (n G(i) ) denotes the
at roughly the same audience as the advertiser) and                       expected number of ad-relevant viewers from the total
general-interest websites. Evidently, the special-interest                mass of users Di at CP i (CP G) that see the ad for
CPs are considered by a much smaller number of adver-                     the first time, and thus have a value of v  1 for the
tisers (which we approximate by a single advertiser                       advertiser. In the following, we refer to n simply as
here) than the general-interest CP, who will display a                    view-throughs.
larger variety of ads. The revenue streams that may arise                 Structure and Timing. We consider the following four-
for the general-interest CP from these other advertis-                    stage game:
ers are not explicitly modeled (see, instead, Athey and                      Stage 1. General-interest CP G decides whether to
Gans 2010, Chen and Stallaert 2014), because they are                     offer a social login to both special-interest CPs.
Krämer, Schnurr, and Wohlfarth: Social Logins in the Online Advertising Ecosystem
6                                                                                          Management Science, Articles in Advance, pp. 1–22, © 2018 The Author(s)

  Stage 2. Special-interest CPs i (i  A, B) simultane-                          any of the two CPs are relevant for the advertiser—i.e.,
ously but independently decide whether to adopt the                              Di − n i, 1 − n G(i), 1 . In period two, the mass of users Di
social login and users decide which CP to use.12                                 again redistributes its attention randomly between CP i
  Stage 3. All CPs simultaneously set advertisement                              and CP G according to δ—i.e., users that have been
prices p j .                                                                     targeted at CP i may now visit CP G, and vice versa.
  Stage 4. The advertiser decides at which CPs to                                Thus, CP i and CP G expect to generate n i, 2  α i δ(Di −
advertise.                                                                       n i, 1 − n G(i), 1 ) and n G(i), 2  α G(i) (1 − δ)(Di − n i, 1 − n G(i), 1 )
                                                                                 new view-throughs in the second period, respectively.
                                                                                 In summary, this yields a total number of expected
4. Competitive Effects of the Social Login                                       view-throughs by CP j of13
   and Market Outcomes
We continue by solving for the subgame-perfect equi-                                  n i  α i δDi + α i δ(Di − α i δDi − α G(i) (Di − δDi )) ,                  (1)
librium through backward induction.                                                           |{z}           |                          {z               }
                                                                                             period t1                             period t2
Stage 4: Advertiser’s Decision. To decide at which                                            X
CPs to advertise, Z calculates the expected view-                                   nG                α G(i) (Di − δDi )
                                                                                              iA, B   |      {z           }
throughs per CP, n j . Recall that CP A and CP B do not                                                    period t1
compete in the advertising market. In the following, it
therefore suffices to consider the advertising competi-                                       + α G(i) (1 − δ)(Di − α i δDi − α G(i) (Di − δDi )) .               (2)
                                                                                                |                               {z                       }
tion between CP i and CP G in a given submarket Di .                                                                          period t2
In the first period every ad impression is, by definition,
new to a visitor, so that CP i expects view-throughs of                             Figure 2 provides an example of a special-interest
n i, 1  α i δDi . In reverse, the remaining Di − δDi users                      advertising submarket that we consider and illus-
visit CP G in the first period, and thus CP G expects                            trates how different targeting rates translate into view-
n G(i), 1  α G(i) (Di − δDi ) view-throughs in the first period                 throughs. In the example, there is a total of six relevant
from the mass of users that multi-home between CP i                              users, which in expectation split attention between the
and CP G. Recall that CP G’s targeting rate can differ                           special-interest CP and the general-interest CP evenly
between different masses of users, Di , depending on                             (δ  1/2) in both time periods t  1, 2. We assume that the
whether or not CP i has adopted the social login. We                             special-interest CP can target its users perfectly (α i  1),
denote this by α G(i) . In the second period, only those                         so that it is able to achieve expected view-throughs
users that have not seen the ad in the first period at                           of n i, 1  3 in the first period by simply displaying the

Figure 2. Illustration of View-Throughs per CP

                                                         t=1         General (G)                    t=2           General (G)
                                 General (G)
                                                                    1        2                                            6                      E(nG(i)) = 4/3
      Ad                         Special (i)
                                                                             3                                   4
                                    Ad                              E(nG(i), 1) = 1                              E(nG(i), 2) = 1/3
                                                                        Special (i)                                  Special (i)
                                   Special                                                                                                       E(ni) = 4
                                                                    4        5         6                         3        1         5

                                                                        E(ni, 1) = 3                                 E(ni, 2) = 1

                                                         Relevant users that have                       Set of users that see
              Irrelevant users      Relevant users
                                                         seen the ad in t – 1                           the ad in period t

Notes. In total there are six ad relevant users in the example that split attention evenly between the CPs. The considered CPs have different
targeting rates (α G(i)  1/3, α i  1) in the special-interest advertising submarket Di . The advertiser Z buys three impressions per period from
each CP.
Krämer, Schnurr, and Wohlfarth: Social Logins in the Online Advertising Ecosystem
Management Science, Articles in Advance, pp. 1–22, © 2018 The Author(s)                                                                            7

ad to all its special-interest users. On the contrary, the                the competition for selection by advertiser Z. The best
general-interest CP faces a larger, more heterogeneous                    response function of a CP is then given by choosing
user base (including irrelevant users as denoted by                       the maximum price that ensures that the advertiser
Figure 2), but can possibly also display ads from var-                    still decides to display advertising at that CP. In other
ious other advertisers, which are interested in differ-                   words, a CP sets its own price such that the advertiser is
ent special-interest groups. In particular, the general-                  indifferent between displaying ads at both CPs and dis-
interest outlet cannot simply display a particular ad                     playing ads exclusively at the competitor. This yields
to all users, because, in contrast to the special-interest                Condition (3) for the special-interest CP and Condi-
CP, it is also interested in serving other advertisers                    tion (4) for the general-interest CP.
(see the demand-side efficiency effect mentioned by Athey
and Gans 2010). Although we do not model this inter-                                             ∗
                                                                                      n G(i) − p G(i) + n i − p i∗  n G(i)
                                                                                                                       e        ∗
                                                                                                                            − p G(i) ,            (3)
action with other advertisers explicitly, we can nev-
                                                                                      n G(i) −     ∗
                                                                                                 p G(i)   + ni −   p i∗      n ie   −   p i∗ .   (4)
ertheless capture this effect by assuming a lower tar-
geting rate of the general-interest CP in the example
                                                                          As shown in Online Appendix A.1, solving this set of
(α G(i)  1/3), which then translates into lower expected
                                                                          conditions yields a unique advertising pricing equi-
view-throughs of n G(i), 1  1. In the second period, rele-
                                                                          librium. Because CPs do not incur any costs, each
vant users again decide which CP to visit according to
                                                                          special-interest CP i obtains profit Π∗i  p i∗ , while the
probability δ. Hence, the same expected share of rel-
                                                                          general-interest CP obtains profit Π∗G  p G(A) ∗
                                                                                                                              + p G(B)
evant users at CP i and CP G has already seen the ad
                                                                          equilibrium (see Online Appendix A.2). Note that it is
in the previous period. Thus, the general-interest CP is
able to achieve expected view-throughs of n G(i), 2  1/3 in              easy to verify that in equilibrium indeed neither CP
the second period, whereas the special-interest CP can                    has a unilateral incentive to deviate from its price. On
capture the view-throughs of the one remaining user at                    the one hand, a unilateral price increase by any CP
its outlet that has not seen the ad before—i.e., n i, 2  1.              would yield a lower (zero) profit for that CP, because
   It is important to see that n j does not only depend                   the advertiser would then prefer to show advertising
on CP j’s own targeting rate, α j , but, in t  2, also on                exclusively at the competing CP. On the other hand, a
the other CP’s targeting rate. This is the basis for com-                 price decrease would also yield a lower profit, because
petition between the CPs in the advertising market.                       it would not affect the advertiser’s allocation decision
Intuitively, the two time periods are the most parsimo-                   and the CP would simply make less revenue.
nious way to model the inherent competition between                          See that equilibrium prices p ∗j (and thus CPs’ equilib-
targeting an ad-relevant user now (t  1) at CP j, or                     rium profit) behave intuitively with respect to changes
in the future (t  2) at some other CP. With regard                       in the targeting rate. For example, in line with Athey
to the mass of users Di , the advertiser faces the deci-                  and Gans (2010), a higher targeting rate, which in turn
sion to display advertising either exclusively at CP i or                 yields more view-throughs, allows CPs to demand a
CP G, or at both outlets at the same time. Obviously, the                 higher equilibrium price p ∗j and thus yields a higher
latter option maximizes view-throughs n  n G(i) + n i .                  profit (i.e., ∂π ∗j /∂α j > 0). Moreover, because of the com-
However, the advertiser maximizes profit Γi (n i − p i ) +                petition between CPs in the advertising market, an
ΓG(i) (n G(i) − p G(i) ) and may decide to switch exclusively             increase in the rival CP’s targeting ability reduces the
to a CP if it can gain a higher net benefit through a                     equilibrium profit (i.e., ∂π ∗i /∂α G(i) < 0 and ∂πG(i)
                                                                                                                                    /∂α i
lower price p for the view-throughs. For example, the                     < 0, respectively).
advertiser will decide to reach the mass of Di users                         Note that we assume that the CPs set the same,
exclusively through CP i if n ie − p i > n G(i) − p G(i) + n i            static price in both time periods. This is necessary
− p i . Thereby, n ie , which denotes the total view-                     so that (intertemporal) competition between CPs in
throughs at i when CP i is the advertiser’s exclusive                     the advertising market can unfold. If instead we as-
outlet, is larger than CP i’s total view-throughs when                    sume that CPs can choose different prices in each
CP i is not exclusive. This is because CP i can gener-                    period, then this competition will break down, and
ate more view-throughs in the second period, because                      each CP would set its monopoly price p j, t  n j, t (see
the same ad has not been displayed to users at CP G                       Online Appendix A.6). Consequently, the static pricing
already in the first period. The advertiser’s decision                    scheme that we assume here confers the pricing power
where to advertise will thus depend on view-throughs,                     on the advertiser and therefore constitutes a lower
as identified above, and CPs’ prices, which are deter-                    bound on advertising prices. By contrast, a dynamic
mined next.                                                               pricing scheme would confer the pricing power on the
Stage 3: CPs’ Ad Pricing. A CP j chooses its adver-                       CPs, as if advertisers were in perfect competition, and
tising price p j by taking into account its competitors’                  therefore it would constitute an upper bound on adver-
prices and the ensuing allocation decision by the adver-                  tising prices. Nevertheless, under dynamic pricing the
tiser. Thus, CPs’ pricing decision is constrained by                      comparative statics of equilibrium prices and profits
Krämer, Schnurr, and Wohlfarth: Social Logins in the Online Advertising Ecosystem
8                                                                                                               Management Science, Articles in Advance, pp. 1–22, © 2018 The Author(s)

Table 1. Normal Form Game Representing Special-Interest                                                  the login unilaterally, then φ i is always large enough
CPs’ Social Login Adoption Decision                                                                      so that the CP would also adopt the social login jointly.
                                                                                                         Because of the symmetry of special-interest CPs, it fol-
                                                                      CP B
                                                                                                         lows immediately that each CP has a dominant strategy
                                         Social login (l)                           No login (b)         to adopt the social login for φ i ≥ Φa and to not adopt
                                                                                                         the login for φ i < Φa , such that in equilibrium either
 Social login (l)                            (ΠAl, l , ΠBl, l )                     (ΠAl, b , ΠBb, l )   both or none of the special-interest CPs adopt the login.
 No login (b)                                (ΠAb, l , ΠBl, b )                     (ΠAb, b , ΠBb, b )   We therefore denote Φa in Equation (5) as the adoption
                                                                                                         threshold of the social login.
                                                                                                            Notice that, in any case, CPs’ adoption decision coin-
with respect to targeting rates, identified in the pre-                                                  cides, such that neither eventually gains a competitive
vious paragraph, remain intact. In consequence, the                                                      advantage in the user market—i.e., Di  1/2. Therefore,
market outcomes derived under static pricing do not                                                      even though it is each special-interest CP’s dominant
change qualitatively in a setting with dynamic pricing.                                                  strategy to adopt the social login if φ i ≥ Φa , each

Stage 2: Special-Interest CPs’ Social Login Adoption.                                                    may indeed receive a lower profit than if both CPs
Provided the social login is offered by CP G, each                                                       would not have adopted the login. In other words,
CP i decides independently whether to adopt the social                                                   special-interest CPs may find themselves in a prisoner’s
login. Thereby, each CP i considers, given the adop-                                                     dilemma situation, where none can commit not to
tion decision of the rival special-interest CP, how the                                                  adopt the login to improve its user experience by θ and
adoption of the social login would affect its adver-                                                     gain a competitive advantage in the user market, but as
tising profit Π∗i (i) through an increase in targeting                                                   each CP adopts the login, this competitive advantage
rates α j , affecting its competitive position in the adver-                                             vanishes. In reverse, adoption of the social login may
tising market, and (ii) through an increase in the user                                                  intensify competition in the advertising market with
experience by θ, affecting its market share Di and con-                                                  CP G, because CP G’s targeting rate may improve rel-
sequently its competitive position in the user market.                                                   atively more because of the information shared via the
In summary, four different adoption scenarios can be                                                     social login than CP i’s own targeting rate. The pris-
distinguished, which are highlighted in the normal                                                       oner’s dilemma situation arises if the social login is
form game depicted by Table 1. The corresponding                                                         adopted and Πil, l − Πb,
                                                                                                                                      < 0, which is satisfied if
profits are derived in Online Appendix A.3.
   In the following, it is shown that if special-interest                                                   0                  1
                                                                                                         Φa ≤ φ i < Φap :          · (α Gb (δ −1)φ G +1)− (φ G α Gb (δ −1))2
CPs are symmetric, either both or none adopt the social                                                                       δα bi
login. Thereby, CP i considers the net effect of the social                                                                   +2(δ −1)α Gb (φ G − δα bi )+(δα bi −1)2
login on its anticipated profit, given its rival’s decision.                                                                                                                       (7)
CP i adopts the social login, given that its rival does
not adopt it, iff Πl,i b − Πb,
                                 ≥ 0, which is satisfied if its                                          We therefore denote Φap as the adoption profitability
increase in targeting rate is above the critical thresh-                                                 threshold at which special-interest CPs are actually bet-
old Φa :                                                                                                 ter off by (jointly) adopting the social login. It can be
         0                 1                                                                             shown that Φap > Φa for θ > 0, such that the prisoner’s
φ i ≥ Φa :                       · (α Gb (δ − 1)(τ + θ)φ G + τ + θ)                                     dilemma outcome always exists when θ > 0 and the
              δ   α bi    (τ + θ)
                                                                                                         social login is offered.
                          ((φ G α Gb (δ − 1))2 + 2α Gb (δ − 1) · (φ G − δα bi )
                                                                                                         Stage 1: General-Interest CP’s Social Login Offer. An-
              + (δα bi − 1)2 )τ + θ(τ + θ)(1 + φ G α Gb (δ − 1))2
                                1/2                                                                    ticipating special-interest CPs’ adoption decision and
              · (τ + θ)                  .                                                       (5)     ensuing effects on advertising prices, CP G decides
                                                                                                         whether or not to offer the social login. To this end,
On the other hand, CP i adopts the social login, given                                                   CP G weighs the positive effect on its own targeting
that its rival also adopts it, iff Πl,i l − Πb,
                                                  ≥ 0, which is                                          ability against the negative effect of CP i’s improved
satisfied if                                                                                             targeting ability, both of which will affect competition
        00     1                                                                                         in the advertising market. In general, CP G is willing to
φ i ≥ Φa :          · (α Gb (δ −1)τφ G + τ)− τ(φ G α Gb (δ −1))2
                                                                                                         offer the social login iff ΠGl, l − ΠGb, b ≥ 0, anticipating that
              δα i τ
                                                                                                         symmetric special-interest CPs always coincide in their
              +2(δ −1)· α Gb (τφ G − δ(τ − θ)α bi )+(δ + α bi )2                                         adoption decision (see Online Appendix A.4 for a full
              ·(τ − θ)−2δ(τ − θ)α bi + τ τ                                      .                (6)     characterization of CP G’s profits). This is satisfied if
                  0           00
Formally, Φa > Φa and therefore, if φ i is large enough                                                                     α Gb (φ 2G − 1)(δ − 1) + 2(δα Gb + φ G − 1)
                                                                                                            φ i ≤ Φo :                                                       .    (8)
so that a special-interest CP finds it attractive to adopt                                                                                     2δφ G α bi
Krämer, Schnurr, and Wohlfarth: Social Logins in the Online Advertising Ecosystem
Management Science, Articles in Advance, pp. 1–22, © 2018 The Author(s)                                                                          9

Consequently, Φo is denoted as the offer threshold at                                To provide more insights under which conditions
which the general-interest CP offers the social login to                          the social login is offered, adopted, and profitable to
both special-interest CPs.                                                        the special-interest CPs, respectively, we investigate
                                                                                  how the critical thresholds Φa , Φap , and Φo change
Market Outcomes and Comparative Statics. Based on
                                                                                  ceteris paribus in response to a change in one of the
the previous analysis and the therein derived thresh-
                                                                                  model’s parameters. While the details of the compara-
olds, we are now able to fully characterize the possi-
                                                                                  tive statics are relegated to Online Appendix A.5, the
ble market outcomes that may arise. As special-interest
                                                                                  main insights from this analysis are summarized as
CPs are symmetric, it will generally suffice to consider
any submarket Di to discuss the possible market out-
                                                                                     First, parameters τ and θ, which both relate exclu-
comes. Thereby, it is possible to delineate the differ-
                                                                                  sively to the horizontal competition for users between
ent market outcomes in terms of CP i’s and CP G’s
                                                                                  special-interest CPs, only have an impact on the adop-
increase in targeting rate φ j due to the social login.                                                    0                         0
                                                                                  tion threshold Φa . This is because Φa is derived
In particular, the market outcomes are determined by
                           0                                                      under the condition that exactly one special-interest
the adoption threshold (Φa ), the adoption profitability
                                                                                  CP adopts the social login. In this case, τ and θ deter-
threshold (Φ ), and the offer threshold (Φo ). In total,
                                                                                  mine the competitive advantage (in terms of market
there are six possible market outcomes, which are illus-
                                                                                  share increase) of the special-interest CP that adopts
trated in Figure 3. In particular, see that there exists
                                     0                                            the social login exclusively. However, we have shown
an intermediate range Φo ≥ φ i ≥ Φa , where the social
                                                                                  that, in equilibrium, special-interest CPs will indeed
login is offered and adopted (market outcome I and II),
                                                                                  always act symmetrically—that is, either both or none
whereas in all other regions, the social login would
                                                                                  adopt the social login, and thus neither special-interest
not be offered (market outcomes III and V), would not
                                                                                  CP can gain a competitive advantage over the other
be adopted (market outcome IV), or both (market out-
                                                                                  (both have the same market share). Therefore, the
come VI). Moreover, note that the prisoner’s dilemma
occurs in market outcome II leaving special-interest                              offer and adoption profitability thresholds Φo and Φap ,
CPs worse off with the social login, whereas in mar-                              which have both been derived under the condition that
ket outcome I, the social login improves the profit of                            special-interest CPs act symmetrically, are not affected
all CPs.                                                                          by changes in τ and θ. In reverse, this means that
                                                                                  parameters α bi , α Gb , and δ, which relate to the vertical
                                                                                  competition in the advertising market, and not exclu-
Figure 3. Illustration of Possible Market Outcomes                                sively to the horizontal competition between special-
                                                                                  interest CPs, have an effect on all three thresholds.
                       Φo: Offer threshold                                        In particular, they have qualitatively the same effect on
      2.0                                                                                       0
                       Φa : Adoption threshold                                    Φap and Φa .
                       Φap: Adoption profitability                                   Second, the offer threshold Φo increases, thus mak-
                            threshold                         III         VI
      1.8                                                                         ing it more likely that the general-interest CP offers
                                                                                  a social login if, everything else equal, (i) the special-
                                                                                  interest CP’s baseline targeting rate, α bi , decreases
                                                                                  (∂Φo/∂α bi < 0), (ii) the general-interest CP’s baseline tar-
                                                                                  geting rate, α Gb , decreases (∂Φo/∂αGb < 0), (iii) the special-
                                                                                  interest CP’s screen attention probability, δ, decreases
                                 I                      II          IV            (∂Φo/∂δ < 0), and (iv) the general-interest CP’s improve-
                                                                                  ment in targeting rate, φ G , increases (∂Φo/∂φG > 0).
                                                                                     Third, the adoption threshold Φa decreases, thus
                                                                                  making it more likely that the special-interest CPs adopt
                                                                                  a social login if, everything else equal, (i) the special-
                                                                                  interest CP’s baseline targeting rate, α bi , decreases
      1.0                                                                             0
            1.0      1.2          1.4             1.6        1.8         2.0      (∂Φa /∂α bi > 0), (ii) the general-interest CP’s baseline tar-
                                             G                                   geting rate, α Gb , decreases (∂Φa /∂αGb > 0), (iii) the special-
                                                                                  interest CP’s screen attention probability, δ, increases
Notes. The social login is offered in outcomes I, II, and IV, and not                 0

offered otherwise. It is adopted in outcomes I and II, and not adopted            (∂Φa /∂δ < 0), (iv) the general-interest CP’s improvement
in outcome IV. In outcome I special-interest CPs are better off and in            in targeting rate, φ G , decreases (∂Φa /∂φG > 0), (v) the
outcome II they are worse off by adopting the social login. The figure            special-interest CPs’ utility increase due to the social
is derived for α bi  0.5, α Gb  0.5, τ  0.5, θ  0.1, and δ  0.5. Numerical                               0
                                                                                  login, θ, increases (∂Φa /∂θ < 0), and (vi) competition for
values are chosen such that all six market regions exist. For other
values, some regions may not exist, but otherwise, the properties of              users between special-interest CPs increases (i.e., when
the regions remain qualitatively the same.                                        τ decreases (∂Φa /∂τ > 0)).
Krämer, Schnurr, and Wohlfarth: Social Logins in the Online Advertising Ecosystem
10                                                                           Management Science, Articles in Advance, pp. 1–22, © 2018 The Author(s)

   We can therefore characterize the market condi-                    thus only the general-interest CP will be able to in-
tions under which a social login would be offered and                 crease its targeting rate through information sharing
adopted as follows:                                                   via the social login—i.e., φ G > φ i ≡ 1. In this case, the
Proposition 1 (Offer and Adoption of the Social Login).               special-interest CP cannot gain a competitive advan-
(a) The social login is only offered and adopted (market out-         tage in the advertising market from adopting the social
comes I and II) if the resulting improvement in the special-          login. Therefore, it will base its adoption decision
interest CP’s targeting rate is intermediate, i.e., Φo ≥ φ i          solely on the expected impact of the social login on the
      0          0
≥ Φa , with Φa and Φo given by Equations (5) and (8),                 competition for users, provided θ > 0. From Figure 3 it
respectively.                                                         is evident that at φ i  1 only two market outcomes are
   (b) Everything else equal, an increase in any one of the           feasible. The general-interest CP will always offer the
CP’s baseline targeting rates, α bi or α Gb , makes it less likely    social login and either both special-interest CPs adopt
that the social login is adopted, and that it is offered. More-       it and are worse off (outcome II if φ G is low), or they do
over, (i) an increase in the screen attention probability of          not adopt it (outcome IV if φ G is high). Consequently,
the special-interest CP, δ, (ii) an increase in improvement           if CPs adopt the social login, they are always in a pris-
of the targeting rate of the special-interest CP, φ i , or (iii) a    oner’s dilemma.
decrease in the improvement of the targeting rate of the                 Second, consider the polar case where the social
general-interest CP, φ G , respectively, make it more likely that     login does not offer any improvement in user expe-
the social login is adopted, but less likely that it is offered.      rience—i.e., θ  0. In this case the special-interest CPs
                                                                      will base their decision whether or not to adopt the
  Moreover, with the help of comparative statics, we
                                                                      social login solely on the effect in the advertising mar-
can derive two more important insights with respect to                                           0
                                                                      ket. This means that Φa and Φap coincide in this (and
the profitability of the social login for special-interest
                                                                      only in this) case, because special-interest CPs adopt
CPs. First, adoption of the social login is less likely
                                                                      the social login if and only if it is eventually profitable
to be profitable for special-interest CPs if α bi is high,
                                                                      for them. Thus, market outcomes II and III do not exist
because an increase in α bi diminishes market region I
                                                                      and the prisoner’s dilemma situation never arises here.
because of the fact that ∂Φo/∂α bi < 0 and ∂Φap/∂α bi > 0. Sec-
ond, an increase in the competition for users between
special-interest CPs (either through a decrease in τ                  5. Model Extensions
or an increase in θ) makes the occurrence of a pris-                  In the following, we explore several extensions of the
oner’s dilemma outcome more likely, because market                    base model, which will show that our main insights
region II is increased because of the fact that ∂Φa /∂θ < 0           from Propositions 1 and 2 are robust, and which offer
and ∂Φa /∂τ > 0, but ∂Φap/∂θ  ∂Φap/∂τ  0.                           more nuanced insights. The extensions considered in
  We can therefore characterize the market conditions                 Sections 5.1 to 5.3 alter the competitive market struc-
for which the adoption of the social login is profitable              ture and are summarized by Figure 4. In addition, in
for special-interest CPs as follows:                                  Section 5.4 we endogenize φ j by allowing the CPs to
Proposition 2 (Profitability of the Social Login for Special-         invest in the improvement of their targeting ability that
Interest CPs). (a) Adoption of the social login may yield             results from the social login.
a prisoner’s dilemma for special-interest CPs (market out-
                                                                      5.1. Asymmetric Special-Interest CPs
come II), i.e., after the voluntary adoption of the social login,
                                                                      First, we extend our analysis to the case where special-
special-interest CPs may be worse off than if they had not
                                                           0          interest CPs are asymmetric with respect to the util-
adopted the social login. This occurs for Φap > φ i ≥ Φa , with
   0                                                                  ity that they offer to users—i.e., CPs differ vertically
Φa and Φap given by Equations (5) and (7), respectively.
                                                                      in quality. For example, the website of an established
   (b) Everything else equal, adoption of the social login is
                                                                      media organization may differ significantly in size and
less likely to be profitable for a special-interest CP (market
                                                                      thus in the amount of content that they can offer to
region I) when its baseline targeting rate, α bi , increases.
   (c) The prisoner’s dilemma (market outcome II) becomes             users, relative to, e.g., other news blogs. Without loss
more likely when either the CPs’ improvement of user expe-            of generality, we assume that users derive a higher
rience due to the social login, θ, increases, or when the             baseline utility when consuming content of CP A—i.e.,
competition for users between special-interest CPs increases          u Ab  u Bb + ν with ν > 0. Market outcomes are derived as
(τ decreases).                                                        described in Section 3.2, but market shares (see panel 2
                                                                      in Figure 4) and thus profits of CP A and CP B as
Illustrative Market Scenarios. To conclude our main                   well as their relative benefit from the social login now
analysis, we highlight two specific market scenarios                  differ. Consequently, the adoption thresholds of CP A
that are illustrative as they represent extrema of the                and CP B generally differ and are therefore denoted by
feasible spectrum of possibilities.                                   ΦAa and ΦBa , respectively (see Online Appendix B.1 for
   First, consider the case where the special-interest                the derivation of these thresholds). In fact, CP B, as the
CPs have already attained a high targeting rate and                   lower-quality firm, has a greater incentive to adopt the
Krämer, Schnurr, and Wohlfarth: Social Logins in the Online Advertising Ecosystem
Management Science, Articles in Advance, pp. 1–22, © 2018 The Author(s)                                                                                           11

Figure 4. Comparison of Market Structures Considered in the Various Model Extensions
                                             (1) Section 4: Base model                      Z              (2) Section 5.1: Asymmetric special-interest CPs       Z

                                    A   Ad    G                        B    Ad       G                          A   Ad    G                      B    Ad   G

    CP G                                                                                         CP G

                             CP A              Competition for users                 CP B               CP A             Competition for users           CP B

                               (3) Section 5.2: Competing general-interest CPs              Z            (4) Section 5.3: Users multi-home special-interest CPs   Z

    CP F
                                    A   Ad    F                    B       Ad    F
     Competition for users

                                                                                                                              A   Ad    B

                                                                                                 CP G
                                    A   Ad    G                    B       Ad    G

    CP G

                             CP A              Competition for users                 CP B               CP A                                             CP B

social login because it benefits relatively more from                                           is reduced relative to the baseline where both would
the increase in consumer valuation θ than its higher-                                           not adopt the social login.
                                     0    0        00     00
quality rival CP A. Formally, ΦAa > ΦBa and ΦAa > ΦBa                                              More specifically, we can investigate how the degree
for any ν > 0, given θ > 0. In contrast, the profitability                                      of asymmetry affects the CPs’ social login adoption
threshold Φap is identical for both CPs, irrespective of ν,                                     decisions, everything else being equal. An increase in
and also the same as in the base model, and thus given                                          asymmetry, ν, makes it less likely for CP A to adopt
                                                                                                                      0                00
by Equation (7). Similarly, CP G’s rationale to offer the                                       the social login (∂ΦAa /∂ν > 0 and ∂ΦAa /∂ν > 0), and makes it
social login is unaffected by the asymmetry of special-                                         more likely for CP B to adopt the social login (∂ΦBa /∂ν < 0
interest CPs and thus Φo is given by Equation (8). For a                                        and ∂ΦBa /∂ν < 0). The effects of the remaining exogenous
complete analysis, see Online Appendix B.2.                                                     parameters are in line with the effects observed in the
   With asymmetric special-interest CPs, the market                                             base model (see Online Appendix B.3). The insights
outcomes identified in Propositions 1 and 2 continue                                            from this extension are summarized as follows.
to hold. In particular, the area of market outcome I                                            Proposition 3. When special-interest CPs differ in quality,
wherein all CPs are better off is identical. However,                                           the social login may be adopted by one of the two special-
under asymmetry also two additional market out-                                                 interest CPs exclusively. In these cases, the social login is
comes may arise (see market outcomes VII and VIII                                               adopted by the lower quality CP, and never adopted exclu-
in panel 2 of Figure 5). When CP A’s quality advan-                                             sively by the higher quality CP. Otherwise, Propositions 1
tage is large enough relative to the additional quality                                         and 2 continue to hold.
gain that is possible through adopting the social login
(i.e., when ν > 21 θ), CP A will not adopt the social login                                     5.2. Competition Between General-Interest CPs
if CP B adopts it (market outcome VII). Formally, for                                           Although the social login offered by Facebook is clearly
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ν > 12 θ: ΦAa > ΦBa and Φai > Φai for each CP i. In these                                       the most widespread single sign-on solution among
cases CP B’s profit is increased whereas CP A’s profit                                          users and content providers, there exist alternative
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