ISSN (Print) 0473-453X

Discussion Paper No. 1108

ISSN (Online) 2435-0982

DATA-DRIVEN MERGERSANDPERSONALIZATION

Zhijun Chen
Chongwoo Choe
Jiajia Cong
Noriaki Matsushima

November 2020

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

Data-Driven Mergers and Personalization∗
Zhijun Chen†, Chongwoo Choe‡, Jiajia Cong§, and Noriaki Matsushima¶
November 4, 2020

First draft. Comments welcome.

Abstract
Recent years have seen growing cases of data-driven tech mergers such as Google/Fitbit, inwhich a dominant digital platform acquires a relatively small firm possessing a large volume
of consumer data. The digital platform can consolidate the consumer data with its existingdata set from other services and use it for personalization in related markets. We developa theoretical model to examine the impact of such mergers across the two markets that are
related through a consumption synergy. The merger links the markets for data collection
and data application, through which the digital platform can leverage its market powerand hurt competitors in both markets. Personalization can lead to exploitation of someconsumers in the market for data application. But insofar as competitors remain active, themerger increases total consumer surplus in both markets by intensifying competition. Whenthe consumption synergy is large enough, the merger can result in monopolization of bothmarkets, leading to further consumer harm when stand-alone competitors exit in the longrun. Thus there is a trade-oﬀ where potential dynamic costs can outweigh static benefits.
We also discuss policy implications by considering various merger remedies.
Key words: big data, personalization, tech mergers
JEL Classification: D43, L13, L41, K21∗
We are grateful to Arthur Campbell, Greg Crawford, Jacques Crémer, Doh-Shin Jeon, Bruno Jullien, Paul
Heidhues, Vai-Lam Mui, Patrick Rey, Greg Taylor, Tommaso Valletti, Chengsi Wang, and Xiaojian Zhao formany helpful comments. We also thank the audience at Economics of Platforms Seminar (TSE Digital Center),Monash IO seminar, and Toulouse digital seminar. We gratefully acknowledge the financial support from the Japan
Society for the Promotion of Science (JSPS), KAKENHI Grant Numbers JP15H05728, JP17H00984, JP18H00847,
JP18K01593, JP19H01483, and JP20H05631, Osaka University for its International Joint Research Promotion
Program, and the program of the Joint Usage/Research Center for “Behavioral Economics” at ISER, Osaka
University. The usual disclaimer applies.
†‡§¶

The corresponding author. Department of Economics, Monash University (chenzj1219@gmail.com).
Centre for Global Business and Department of Economics, Monash University (chongwoo.choe@monash.edu).
Department of Industrial Economics, School of Management, Fudan University (jiajiacong@gmail.com).
Institute of Social and Economic Research, Osaka University (nmatsush@iser.osaka-u.ac.jp).

1

Introduction

Remarkable advances in digital computing technologies, underpinned by information and communication technologies, are making fundamental changes to virtually every part of the modern
world. At the heart of the digital revolution is the vast amount of granular data – big data
– that has become the ‘new oil’ for the functioning of many industries.1 Consumer data analyzed by powerful machine-learning tools can allow firms to improve the quality of products
they oﬀer, utilize more target-oriented business models, and exploit new business opportunities.
Due to strong network eﬀects and data-powered economies of scale and scope that are mostprominent in the digital economy, data can also contribute to market tipping and entry barriers
through a positive feedback loop: firms with larger data sets can oﬀer better-targeted products thanks to data-enabled learning, thereby attracting more customers, which leads to moredata, hence creating a self-reinforcing loop. Given the increasing availability of granular data
due to the advances in information and communication technologies, and the improvements inmachine-learning algorithms, the importance of data can only increase.
The most important source of data for many firms is the interaction with existing and potential customers, which produces various user-generated content and data, or machine-generated
data such as web server logs, network event logs, location data, etc. But firms also rely on
data brokers for additional data2 , or collect new sets of data through acquisition of other firms.
While data is relevant to almost all mergers involving tech firms, it is gaining growing importance, and played an especially salient role in several prominent merger cases such as Facebook/Instagram (2012), Google/Waze (2013), Facebook/WhatsApp (2014), Microsoft/LinkedIn(2016), Apple/Shazam (2018) and, more recently, the Google/Fitbit merger which is under regulatory probe at the time of writing this article.3
In the Google/Fitbit case, the main concern raised by regulators is that sensitive health data
held by Fitbit can be added to users’ personal profiles Google aggregates from its other services
such as emails, maps, and online searches. In a bid to alleviate these concerns, Google pledgedthat it would not use Fitbit data for advertising purposes. But this does not rule out Google’s
use of the data in other markets such as health care. By connecting Fitbit data with user datafrom Google’s Cloud Healthcare API, Google can build a more comprehensive patient profile
1“The world’s most valuable resource is no longer oil, but data”, The Economist, May 16, 2017.

2

The global data broker industry comprises thousands of firms and is estimated to generate US$200 billion in
annual revenue (https://pando.com/2014/01/08/surveillance-valley-scammers-why-hack-our-data-when-you-canjust-buy-it/). One of the largest data brokers, Acxiom (since renamed LiveRamp), claimed to have information
on 700 million consumers worldwide, and over 3,000 propensities for nearly every U.S. consumer (US Senate
Committee on Commerce, Science, and Transportation, 2013).
3

According to an OECD estimate, ‘big data related’ mergers and acquisitions rose from 55 in 2008 to
134 in 2012 (Stucke and Grunes, 2016). For the discussion of these cases except Google/Fitbit, see Argentesi et al. (2019). For Google’s bid for Fitbit, see, for example, “EU launches probe into Google’s $2 bn
bid for Fitbit”, Financial Times, August 5, 2020, and the related press release by the European Commission(https://ec.europa.eu/commission/presscorner/detail/en/ip 20 1446).

1and oﬀer more personalized health care. Indeed, Google’s bid for Fitbit is consistent with its
strategies to expand into health care, life sciences, and insurance.4
Mergers involving tech firms with a large volume of data can have both beneficial and harmful
eﬀects. On the one hand, access to richer sets of data can enable firms to tailor their products
in a way that is more personalized and better targeted for individual consumers. This canimprove the quality of matching between firms and consumers. It can be also pro-competitiveby allowing the merging parties to enter a new market through data-driven innovation. On theother hand, the positive feedback loop discussed previously can harm competition and lead tomarket tipping. In addition, the flip side of personalization is the firm’s ability to engage inprice discrimination and consumer exploitation. Moreover, merging parties can extend market
power to related markets, potentially leading to foreclosure and consumer exploitation there.
For instance, Google could enter the health insurance market with highly personalized productsby leveraging Fitbit’s data, massive medical records Google has access to through Google Cloudand Project Nightingale, and its own data analytics capabilities.5 Finally, data-driven mergers
can raise privacy concerns, which can be further exacerbated due to data externalities whereby
some consumers’ data can be used to infer personal information about other consumers (Choiet al., 2019).
Thus tech mergers warrant careful assessment of costs and benefits that are not often adequately addressed in the existing merger review. As a result, they can go under the radarof competition authorities. Indeed, the five largest tech firms have made over 400 acquisitions
globally over the last 10 years, but none was blocked and very few had conditions attached toapproval (Furman et al., 2019). As Tirole (2020) argues, since old-style regulation is impractical for tech firms, competition policy including merger review to “prevent the eggs from being
scrambled in the first place” may remain the main policy tool in the digital era.
The purpose of this paper is to study data-driven mergers and their implications for competition policy. Issues relevant to tech mergers such as network eﬀects, economies of scale andscope, innovation incentives, incumbency advantage, and so on, are also relevant to non-techmergers, albeit in varying degrees. Our specific focus in this paper is on the role of data inmergers since data plays a uniquely important role in tech mergers. By doing so, we make anumber of important contributions to the growing body of literature on tech mergers reviewed
in the next section.
We start by sketching our model. Since Google/Fitbit serves as our motivating example, wewill make reference to this case whenever relevant. There are two related markets, A for data
4

In the online appendix, we provide a brief account of Google’s expansion into health care. Sundar Pichai,
the CEO of Alphabet and its Google subsidiary, said health care oﬀers the biggest potential for Alphabet overthe next 10 years for using AI to improve outcomes (https://www.cnbc.com/2020/01/22/google-ceo-eyes-majoropportunity-in-health-care-says-it-will-protect-privacy.html). As of 2019, there are around 30 million active Fitbit
users worldwide (https://www.statista.com/topics/2595/fitbit/).
5

As explained in the online appendix, Google has already gained a foothold in the health insurance market with
its health tech subsidiary, Verily. But Google’s ambition in health care extends beyond health and life insurance.

2

application such as the digital health care market and B for data collection such as the market
for wearable devices. Each market is represented by a horizontally diﬀerentiated Hotelling
duopoly with the identical population of consumers. Market A is a symmetric duopoly while
we allow asymmetry in market B, partly motivated by the competitive landscape in the market
for wearable devices where Apple is a market leader. Allowing asymmetric firms also enables
us to identify interesting post-merger linkages between the two markets. We consider a merger
between a firm in market A, say A1 , and a firm in market B, say B1 , leading to a merged entity,
say C. This model also applies to the case where firm C acquires firm B1 and enters market A
in partnership with firm A1 .
Data is generated in market B and can be used in market A for personalization. The
set of consumers in market A whose data is available will be called firm C’s target segment,
and each consumer in the target segment, a targeted consumer. Personalization in market B
is too costly so we ignore that possibility. For example, in the market for wearable devices,
hardware reconfiguration that may be necessary for personalization can be too costly to bepracticable.6 But the two markets are linked through some complementarity. We model thelinkage by assuming that consumers derive extra benefits from patronizing firm C by buying its
product in market B and its personalized product in market A. We call this the consumption
synergy. In case of Google/Fitbit, Google can incorporate the wearable device into its powerful
ecosystem, which it can leverage to enhance user experience in the digital health sector.
By personalization, we refer to firm C’s ability to oﬀer a tailored product that better matchesa targeted consumer’s taste than the firm’s standard product, with the improved matching value
increasing in the firm’s data analytics quality. Naturally, firm C will oﬀer a personalized productat a personalized price, which we call collectively product personalization. When the firm oﬀers
a targeted consumer a standard product at a personalized price, we call it personalized pricing.
Although personalization generates extra surplus to a consumer, how much of the extra surplus
actually accrues to the consumer depends on the firm’s ability to extract it through a personalized
price, which in turn depends on competition. When the extracted surplus exceeds the cost ofdelivering a personalized product, firm C will choose personalization; otherwise, it will choose
personalized pricing. For non-targeted consumers, firm C oﬀers the standard product at a
uniform price. In our baseline model, we assume that firm C can prevent its targeted consumers
from having access to its standard product, for example, by search discrimination.
In market A, the market for data application, personalization following the merger has two
primary eﬀects. First, it has a potential to benefit targeted consumers thanks to the improved
matching value and the consumption synergy. But firm C can take away much of these benefits
by using personalized prices except for those who are suﬃciently far away from its location
6

Lausell and Resende (2020) provide examples of product personalization, which are predominantly throughsoftware reconfiguration in service industries such as e-commerce, hospitality, media and entertainment, andhealth. They also mention Tesla’s personalized dashboard. But this is also mainly through software interface,rather than through personalizing physical components of the automobile.

3

and for whom firm C has to compete hard. As a result, targeted consumers closer to firm C
can be worse oﬀ than before the merger, which may be called the consumer exploitation eﬀect.
Second, exploitation of targeted consumes has a salutary eﬀect of intensifying competition for
non-targeted consumers. It is because personalization allows firm C to delink its pricing policies
for targeted and non-targeted consumers. This shifts the battleground for Hotelling competition
away from firm C’s location, which intensifies competition in uniform price and benefits nontargeted consumers. This also limits firm C’s ability to exploit its targeted consumers, whosealternative option is to choose the competitor’s product.
On balance, total consumer surplus in market A may increase or decrease depending on
the post-merger equilibrium. In what we call the equilibrium with accommodation, firm C’s
competitor remains active after the merger. This equilibrium arises when the consumption
synergy is relatively small. In this case, the intensified competition for non-targeted consumers
not only pushes down uniform prices but also limits the increase in personalized prices. As aresult, total consumer surplus increases after the merger. But increased competition implies
that firm C’s stand-alone competitor is worse oﬀ after the merger, and may even choose toexit the market in the long run if the reduced profit does not cover its fixed cost. When the
consumption synergy becomes suﬃciently large, firm C can monopolize market A, reducing total
consumer surplus. We call this the monopolization equilibrium in which firm C’s competitor,
albeit inactive, remains in the market, which makes the market contestable.
In market B, the market for data collection, competition intensifies unambiguously sinceboth firms compete in uniform price and firm C has incentives to expand its market shareabove that in the Hotelling benchmark. When the consumption synergy is large enough, firm
C can engage in below-cost pricing. The large enough consumption synergy implies that firm C
can use personalization to extract surplus from market A that can more than oﬀset the loss inmarket B caused by below-cost pricing. Firm C’s incentives for below-cost pricing increase in the
consumption synergy, which can eventually lead firm C to monopolize market B. By extension,
this also leads to the monopolization of market A. Yet in both markets, monopolization does
not mean immediate abuse of monopoly power by firm C, because the presence of competitors,
albeit inactive, makes both markets contestable. As a result, the merger increases total consumer
surplus in market B regardless of whether firm C monopolizes the market.
Our analysis also shows how the merger links firm C’s competitors, firms A2 and B2 , thatare otherwise unrelated. First, the consumption synergy in market A is a source of value that
consumer data has for firm C. Thus the consumption synergy makes firm C more aggressive inmarket B than when there is no consumption synergy. This implies negative externalities running from market A to firm B2 through the consumption synergy. Second, firm B2 ’s competitive
advantage in market B increases firm C’s cost of expanding its customer based in market B,
and hence its target segment in market A. This implies positive externalities created by firm
B2 for firm A2 .
A number of clear welfare implications of data-driven mergers emerge from our analysis.
4First, thanks to personalization and the consumption synergy, the merging parties are better oﬀ
at the cost of their stand-alone competitors. Second, in market B, all consumers gain becauseof the intensified competition following the merger. Third, in market A, changes in consumer
surplus depend on diﬀerent equilibria: in the equilibrium with accommodation, consumer surplus
increases after the merger; in the monopolization equilibrium, it decreases. Which type ofequilibria is more likely depends on the size of consumption synergy. Fourth, the long-run
eﬀect is likely to be more detrimental to consumers than the short-run eﬀect. If stand-alone
competitors exit the market in the long run following monopolization, then the monopolization
equilibrium can turn into the monopoly equilibrium, making consumers in both markets worse
oﬀ. Thus there is a trade-oﬀ where potential dynamic costs can outweigh static benefits.
In view of the above welfare implications, we examine several policies often discussed andrelevant to data-driven mergers. First, we analyze the eﬀect of mandated data sharing between
firm C and its competitor in market A. Intuitively, data sharing reduces the value of data tofirm C as it allows the competitor to also use personalization. This softens competition andhurts consumers in market B, but benefits consumers in market A. It follows that firm C isworse oﬀ while its competitors in both markets are better oﬀ. In addition, data sharing makes
monopolization less likely, hence mitigates the dynamic trade-oﬀ. Second, we consider the eﬀectof prohibiting search discrimination in market A, which will allow targeted consumers access tofirm C’s standard product. Surprisingly, this can lead to a collusive outcome in which firm C
can extract maximum surplus from targeted consumers. Without search discrimination, firm C
chooses not to serve its non-targeted consumers, which allows its competitor to choose a highuniform price, which in turn allows firm C to increase its personalized prices. Prohibiting search
discrimination also makes monopolization more likely. Next, we discuss the eﬀect of banning
below-cost pricing. This softens competition in market B and, as a result, in market A as well.
Thus prices increase in both markets, benefiting firms at the cost of consumers. On the other
hand, the ban prevents monopolization, hence also mitigates the dynamic trade-oﬀ. Finally,
we consider the eﬀect of blocking the merger. Once again, this clearly benefits stand-alone
competitors. In market A, consumers benefit only if the merger were to lead to monopolization.
In market B, consumers lose in the short run, but can benefit in the long run if the merger wereto lead to monopolization. A general conclusion we can draw is that all of these policies except
the prohibition of search discrimination can mitigate the dynamic trade-oﬀ, although short-run
eﬀects on consumers vary depending on policies and markets.
Our paper makes several novel contributions to the literature on tech mergers and the literature on price discrimination. First, we develop a new model for the analysis of data-driven
mergers that captures two key features of such mergers: personalization and cross-market interaction due to complementarity. While there is a growing body of literature on personalizationand some new papers on conglomerate mergers such as Chen and Rey (2020), the combinationof these two features leads us to several novel findings relevant to tech mergers. For example,
the diﬀering eﬀects of the merger on consumer surplus in the two markets due to the role of5data have not been pointed out in the existing literature. Likewise, the mechanism whereby themerger creates externalities between stand-alone competitors across the two markets is novel.
Finally, our paper identifies the dynamic trade-oﬀ as one of the key issues in assessing techmergers and shows that the trade-oﬀ is at the heart of various merger remedies. To the best of
our knowledge, these issues are yet to be formally analyzed in published works.
Second, our paper provides a new perspective and clear policy implications relevant to techmergers. In the context of Google/Fitbit, personalizing health service by consolidating Fitbit’s data with the data from Google’s other services has a potential to generate benefits for
consumers, barring privacy concerns. On the other hand, if Google’s market power and data
externalities eventually lead the market to tip in Google’s favor, Google will be able to extract
these potential benefits through personalization. Blocking the merger can prevent the consumer
harm but also prevent the potential benefits from being realized. Thus competition authorities need to look for policies that can help realize potential benefits while minimizing consumer
harm. Banning below-cost pricing and other predatory practices can protect small competitors
and preserve the competitive landscape, thereby limiting Google’s ability to extract consumer
surplus. In addition, allowing consecutive mergers can also mitigate the trade-oﬀ. For instance,
approving Apple’s expansion into the digital health market following the Google/Fitbit merger
will have pro-competitive eﬀects while not sacrificing the potential benefits from data-enabled
personalization. Needless to say, the success of policy depends on eﬀective monitoring and enforcement, which can be a daunting task in complex digital industries. This presents a dilemma
to competition authorities. On the one hand, blocking a merger can prevent long-term harm,
while also preventing potential benefits from being realized. On the other hand, approving amerger with remedies presupposes an eﬀective system of monitoring and enforcement, without
which problems can be amplified after the merger has been approved and cannot be undone.
Third, we enrich the literature on personalization-based price discrimination by introducing
a new innovation. The existing literature considers either pure personalized pricing or perfectproduct personalization. Our key innovation is to distinguish between the firm’s ability to use
personalized pricing and its ability to process consumer data for product personalization. The
former depends on the size of market segment in which the firm has data on consumers. We callthis the firm’s data scale. But the data scale alone does not allow the firm to tailor its productto better match an individual consumer’s taste. To improve the matching value, the firm shouldbe able to process and learn from consumer data, which we call the firm’s data analytics. We
allow the quality of data analytics to vary, with perfect product personalization possible onlywith the perfect data analytics. Separating the data scale from the data analytics in this way
generates new insight. First, the firm uses a richer mix of pricing policies, pure personalized
pricing for some consumers, product personalization for other consumers, and uniform pricing
for consumers its data scale does not cover. Second, the data scale and the data analytics
have diﬀerent eﬀects on profits and consumer surplus. For example, the data scale has a nonmonotonic eﬀect on consumer surplus, but consumer surplus is nondecreasing in the quality of6

data analytics.
The rest of the paper is organized as follows. Section 2 contains a literature review. Section
3 presents our model, while Section 4 provides the analysis of personalization in market A.
Section 5 studies the cross-market eﬀects from the merger. Section 6 discusses policy implications
while Section 7 concludes the paper. Appendix provides selected proofs of the key results notprovided in the main text. The online appendix contains additional proofs, a brief account of
Google’s interest in and expansion into health care, and some information on how big data andpersonalization are aﬀecting the health industry.

2

Related Literature

While our work shares common interest with the large literature on the digital economy, we
review only those studies that are most closely related to the main focus of this paper, namely,
data-driven mergers and the use of data for personalization. For general discussions on the digital
economy and the relevant policy issues, see Australian Competition & Consumer Commission(2019), Crémer et al. (“EU Report”, 2019), Furman et al. (“Furman Report”, 2019), or Scott
Morten et al. (“Stigler Report”, 2019). For reviews of the academic literature on the digital
economy, see Goldfarb and Tucker (2019), or Calvano and Polo (2020).
There is a growing body of literature on mergers in digital industries. Evidence on the scaleand scope of tech mergers is documented in Argentesi et al. (2019) and Gautier and Lamesch(2020). They evaluate several hundred acquisitions made by the Big Five tech firms (GAFAM:
Google, Amazon, Facebook, Apple, and Microsoft) and find that most acquisitions are in areas
where the acquirer’s and the target’s products and services are complementary to each other,a majority of targets are young or start-up companies, and that “killer acquisitions” are notcommon.
In the digital economy, network eﬀects and economies of scale can lead to market tipping
so that a successful firm attains temporary market dominance until it is replaced by a more
successful entrant, with success crucially depending on innovation. Cabral (2020), Kamepalli
et al. (2020), Katz (2020), and Motta and Peitz (2020) study the eﬀects of merger policy on
innovation incentives by the incumbent and/or entrant. de Cornière and Taylor (2020) adopt
the competition-in-utility-space approach (Armstrong and Vickers, 2001) and study generalconditions for a data-driven merger to be pro- or anti-competitive.7 These studies adopt a
reduced-form approach and do not go into the details of how data is used by the merged firm.
In contrast, we provide a micro foundation by focusing on the specific use of data. We also
study cross-market eﬀects of data-driven mergers.8
7

For merger policy governing multi-sided platforms, see, for example, Jullien and Sand-Zantman (2020) andthe references therein.
8
Somewhat related to our cross-market eﬀects, Condorelli and Padilla (2020) use a reduced-from approach to
study how a monopolist can use the data from one market for entry deterrence in another market.

7

While not related to mergers, several studies analyze how data can be used for learning andaﬀect market dynamics.9 Hagiu and Wright (2020b) study a model of dynamic duopoly wherea firm’s data from past sales can be used for learning and augment the value of its product tocurrent consumers. They analyze various types of data-enabled learning and their implications
for competitive dynamics. Prüfer and Schottmüller (2020) study a dynamic duopoly where afirm’s cost of investment in quality of its product decreases in the amount of data or sales in theprevious period and the demand is an increasing function of quality. They show how networkeﬀects can lead to market tipping through a positive feedback loop. Farboodi et al. (2019) study
market dynamics in a competitive industry in which heterogeneous price-taking firms can use
data to improve eﬃciency.
The primary use of data in our model is for personalization of product and pricing. Personalized pricing has been the focus of many studies (Thisse and Vives, 1988; Chen and Iyer,
2002; Shaﬀer and Zhang, 2002; Choudhary et al., 2005; Ghose and Huang, 2009; Matsumura
and Matsushima, 2015; Choe et al., 2018; Chen et al., 2020).10 Zhang (2011) and Laussel andResende (2020) consider product personalization in addition to personalized pricing, hence iscloser to our study. But there are several key diﬀerences. First, they study a symmetric duopoly
while our focus is on the asymmetric case where the merged firm can employ data-driven personalization while its stand-alone competitor cannot. This is due to our focus on data-driven
mergers, from which asymmetry stems naturally. Second, we allow the merged firm to delink
product personalization and personalized pricing, if it wishes to. To the extent that productpersonalization is costly and may not suit every customer the firm has information on, this flexibility seems plausible. Finally, we show how the merged firm’s personalization strategy changes
when cross-market eﬀects are taken into account.

3

The Model

Consider two markets A and B with correlated demands. Consumer data is harvested in market
B and can be used in market A thanks to correlated demands. Since our model can be best
understood with help of a concrete example, we will refer to market B as the market for wearable
devices such as Fitbit watch and market A as the market for complementary services such as
the digital health care. Needless to say, our model applies to any pair of related markets wheredata is collected in one market for use in the other market. For example, market B can be
the market for professional services network and market A can be the market for productivity
software, as in Microsoft/LinkedIn merger.
Each market is represented by a Hotelling line with uniform distribution on [0, 1]. Two firms
9

For a non-technical discussion on various conditions for data-enabled learning to provide competitive advantage, see Hagiu and Wright (2020a).
10

For a comprehensive survey of the literature, see Fudenberg and Villas-Boas (2006, 2012). Ezrachi and Stucke(2016) provide discussions and examples of personalized pricing.

8

serve each market. In market A (B, resp.), firm A1 (B1 , resp.) is located at 0 and firm A2(B2 , resp.) is located at 1. We normalize the marginal cost of production to zero and treat
prices as profit margins. In each market, a consumer demands one unit of product and derives
gross utility vi (i = A, B) when the product in market i perfectly matches her taste. But a
consumer’s taste is private information, without which firms cannot oﬀer a perfectly matched
product to each consumer. In the absence of consumer information, firms can oﬀer only one
standard product. The utility consumers derive from the standard product varies depending on
the market and the consumer’s location, as explained below.
Firms are symmetric in market A. If both firms oﬀer a standard product, then a consumer
located at x derives utility vA −x from purchasing a product from firm A1 and utility vA −(1−x)
by patronizing firm A2 . Thus a consumer’s location is a taste parameter that represents thedegree of mismatch between her taste and each firm’s standard product. We assume vA > 2 to
avoid trivial equilibria, which also ensures that the market is fully covered even if it is served
by a monopoly supplier. Before the merger, market A has a symmetric Hotelling equilibrium
where each firm charges a uniform price equal to 1 and earns a profit equal to 1/2, with firm
A1 ’s market share given by [0, 1/2].
In market B, we allow asymmetry between firms, partly motivated by the competitive landscape in the market for wearable devices.11 Specifically, we assume that a consumer located at xderives utility vB − x from firm B1 ’s product and vB + γ − (1 − x) from firm B2 ’s product, where
vB > 2. Thus firm B1 has competitive advantage if γ < 0 and B2 has a competitive advantage if
γ > 0. Before the merger, market B has an asymmetric Hotelling equilibrium with prices givenby β10 = 1 − (γ/3) and β20 = 1 + (γ/3), hence firm B1 serves [0, x0 ] where x0 = (3 − γ)/6. Thenfirms earn profits equal to Π0B1 = (β10 )2 /2 and Π0B2 = (β20 )2 /2. We focus our analysis on the casewhere −3 < γ < 3 so that market B is not monopolized before the merger. Allowing asymmetricfirms enables us to identify interesting post-merger linkages between the two markets.
We are interested in the merger between firms A1 and B1 , leading to a merged entity to becalled firm C. Alternatively, one may also consider the scenario in which firm B1 is acquired bya dominant digital platform C that enters market A in partnership with firm A1 . The primary
use of consumer data collected in market B is for personalization in market A, which we will
explain shortly. We assume that the cost of using consumer data for personalization in market
B is prohibitively high. For example, personalizing hardware such as wearable devices can be
too costly.12 Thus post-merger competition in market B continues to be in uniform price.
11

As discussed in the online appendix, Fitbit’s global market share in wearable devices is less than 5%. Appleis a market leader with around 30% of market share, due possibly to stronger brand loyalty and the strength of
its ecosystem.
12

Allowing software customization may not be too costly. But our focus is on personalization rather thancustomization. The former is commonly defined as the practice whereby the firm decides what marketing mix issuitable for the individual customer, usually based on previously collected customer data. On the other hand,customization occurs when the customer pro-actively specifies one or more elements of his or her marketing mix(Arora et al., 2008; Zhang, 2011).

9

In market A, consumer data can be used for two types of personalization. Suppose firm C
has acquired data and knows exact locations of all consumers in [0, δA ]. We call this segment
firm C’s target segment and δA , its data scale. Knowing each targeted consumer’s exact location
enables firm C to oﬀer a personalized price to each targeted consumer. We call this personalized
pricing. Moreover, firm C can utilize its data analytics and oﬀer a personalized product that has
a higher matching value for a targeted consumer than its standard product. We parameterize
the higher matching value by ϕA ∈ (0, 1] such that consumer x derives utility vA − (1 − ϕA )xfrom the personalized product, and call ϕA , firm C’s data analytics quality. We assume thatoﬀering the personalized product incurs per-unit cost c. Thus it is socially desirable to oﬀer
personalized products to consumers if ϕA x > c. When firm C oﬀers a personalized product to
its targeted consumer, its price oﬀer is clearly personalized as well. Thus we call this priceproduct personalization simply product personalization.13
In market A, the merger allows firm C to oﬀer a mix of personalized and uniform prices.
The time line of the post-merger game is as follows, which is common in the literature (Thisse
and Vives, 1988; Matsumura and Matsushima, 2015; Choe et al., 2018; Chen et al., 2020). In
the first stage, firms simultaneously post uniform prices, which are publicly observed. In thesecond stage, firm C makes private oﬀers to targeted consumers. In doing so, firm C has an
option to choose between personalized pricing and product personalization, depending on thelocations of its targeted consumers. Consumers make purchasing decisions after observing all
available oﬀers. It is important to note that the private oﬀer of personalized prices gives firm C
the flexibility in adjusting prices. It can easily change a personalized price oﬀered to a particularcustomer without adjusting the prices to other customers.14 Such flexibility in pricing gives firm
C a second-mover advantage in responding to the rival’s pricing strategy.
We make two simplifying assumptions. First, consumer tastes are perfectly correlated in thetwo markets. That is, a consumer’s location is the same in both markets, implying that her
location data collected in market B perfectly reveals her location in market A. This is clearly astrong assumption. But allowing imperfect correlation significantly complicates analysis without
providing substantive additional insight. Second, we assume consumers are myopic in that when
they make purchase decisions in market B, they do not anticipate how their data will be usedin market A. In some cases, such myopia seems plausible: people leave a huge amount of data
by using various Google services (emails, maps, search, etc) on a daily basis without thinking
too much about how their data will be used; Facebook users may not be that forward-looking as
13

That the cost of personalization is constant at c is mainly to simplify analysis. In reality, the cost mayvary across products and customers. For instance, suppose the cost of personalization is proportional to thedegree of mismatch, say cx. Then the net benefit from personalization is (ϕA − c) x. When ϕA > c, firm C will
choose product personalization for all targeted consumers; otherwise, it will choose personalized pricing. It is
straightforward to check that our main results stay qualitatively the same in this case.
14
Pricing algorithms are becoming popular in digital industries. Personalized prices are generated by algorithms
rather than by managers, and algorithms can be designed to identify the best response to the rival’s prices. See
Brown and MacKay (2020) for the analysis of competition with pricing algorithms, and Calvano et al. (2020)
who demonstrate that algorithmic pricing can support tacit collusion.

10

to how their interaction with Facebook can be used by advertisers and retailers. On the other
hand, our motivating example of Google/Fibit will make consumer myopia less plausible. In
this sense, our assumption of consumer myopia is mainly intended to simplify analysis. Thatsaid, the main change we expect from having forward-looking consumers is that competition inmarket B where data is collected will become more intense than when consumers are myopic.
This is akin to the insight from the literature on behavior-based price discrimination (Choe etal., 2018).
Remark 1. In our reference to Google/Fitbit, we refer to market A as the digital healthmarket in general, and at times, the market for health insurance. We oﬀer some justifications
for our choice of Hotelling model for market A. The Hotelling model is commonly used in theanalysis of competition in healthcare markets.15 Health plans are highly diﬀerentiated for two
reasons. First, health plans cover a broad range of treatments for chronic or acute illnesses, andoﬀer diﬀerent co-payment rates for diﬀerent treatments. For instance, insurance plan A1 maycover 40% costs for the dental treatment and 60% costs for the treatment of knee problems,
whereas insurance plan A2 may cover 60% of dental treatment but 40% of knee treatment.
Second, consumers’ health conditions vary across individuals. A consumer with a serious dental
problem but a good knee condition will value plan A2 higher than plan A1 , whereas anotherconsumer with a knee problem but a good dental condition will prefer plan A1 . We choose theHotelling model to capture diﬀerentiations described above.
Remark 2. The key element of our model is the ability the merged firm has in oﬀering
personalization in market A. In the context of Google/Fitbit, this relates to the extent to which
healthcare services can be personalized, which warrants some elaboration. The healthcare sector is becoming a new battlefield for personalization due to the unprecedented accumulationof health data.16 In health and life insurance, the new concept Pay-As-You-Live (PAYL), introduced by Ernst & Young, is becoming popular. Wearable devices are developed to track apolicyholder’s health information, which is then used to perform risk assessments. Under PAYL,
consumers demonstrating healthy lifestyles receive premium discounts and other rewards. This
type of insurance model is adopted by not only a small start-up such as Health IQ, but also
one of the largest insurance companies such as John Hancock. It is worth noting that Google’s
subsidiary, Verily, entered the insurance market in 2019 in collaboration with John Hancock, as
we explain in the online appendix. Personalization based on the use of big data is also becoming
more prevalent in other areas of health care such as personalized cancer treatment.17
15

Olivella and Vera-Hernández (2007) employ the Hotelling model in studying competition among diﬀerentiatedhealth plans. Biglaiser and Ma (2003) incorporate vertical diﬀerentiation into the Hotelling model and study priceand quality competition in health care. Katz (2011) uses the Hotelling model to analyze the price and quality
competition in the U.S. hospital markets.
16

In the online appendix, we provide a more detailed account of how the healthcare sector is transformed by
big data and personalization.
17

https://www.clinicalomics.com/topics/oncology/multiple-myeloma/gns-healthcare/114Equilibrium Analysis of Personalization

We start by analyzing the equilibrium in market A following the merger. The only aspect of themerger relevant to our focus is the consumer data harvested by firm B1 , which can be used byfirm C for personalization in market A. Denote firm C’s target segment by [0, δA ]. We take δA as
exogenous in this section, but will endogenize it in the next section. Recall that we consider two
types of personalization: product personalization where the personalized product is oﬀered at apersonalized price; personalized pricing where the standard product is oﬀered at a personalized
price.
Targeted consumer x enjoys gross utility vA − (1 − ϕA )x from the personalized product andvA − x from the standard product. Since the cost of product personalization is c, it is sociallydesirable to oﬀer personalized products to consumers if and only if ϕA x ≥ c. That is, productpersonalization has social value for the subset of targeted consumers in [τ, δA ] where τ ≡ c/ϕA is
the cost-benefit ratio of personalization. For the rest of targeted consumers, firm C can exercise
personalized pricing since it has full information on their locations. Thus the choice between the
two types of personalization is driven by the trade-oﬀ between the cost and benefit of productpersonalization. Throughout this section, we make the following assumptions.
Assumption 1: (i) δA ≥ τ ≡ c/ϕA ; (ii) τ ≤ 1/2; (iii) ϕA ≤ min{1, (2 + 4c)/3}.
Assumption 1-(i) allows us to study an interesting case where product personalization arises
in equilibrium, without which firm C will use only personalized pricing for its targeted consumers.
Assumption 1-(ii) says that the cost of product personalization is not large relative to its benefit
so that product personalization is socially desirable for at least half of all consumers. Assumption
1-(iii) restricts the data analytics quality for a given cost of product personalization. It is atechnical assumption that simplifies analysis but it also prevents firm C from monopolizing themarket even if it had the full data scale, i.e., δA = 1. For example, if c = 0 and ϕA = 1, thenδA = 1 allows firm C to drive firm A2 out of the market, but Assumption A-(iii) rules out thispossibility by putting an upper bound of 2/3 on ϕA when c = 0.
Personalization changes the pricing game in market A by expanding firm C’s pricing arsenal.
Denote firm C’s personalized price for targeted consumer x ∈ [0, δA ] by pA (x) when it oﬀers
the personalized product, and by qA (x) when it oﬀers the standard product. In addition, firm
C chooses a uniform price for non-targeted consumers, denoted by α1 . But firm A2 can only
charge a uniform price for all consumers, denoted by α2 . We assume that firm C can engage
in search discrimination to prevent targeted consumers from purchasing its standard product at
uniform price α1 , for instance, by redirecting the product search from a targeted consumer, apractice dubbed steering or search discrimination.18 This allows firm C to delink its choice of18
Mikians et al. (2012) find that search discrimination is commonly used in online markets. Essentially, we
are assuming that firm C can successfully set access hurdles and execute its price discrimination strategy by
preventing arbitrage. In Section 6, we discuss the case where such search discrimination is prohibited.

12

personalized prices and its choice of uniform price.19

4.1

Characterization of equilibria

We now characterize the equilibria of the game. First, competition for firm C’s non-targeted
consumers is in uniform price. Given the uniform prices α1 and α2 , the marginal consumer’s
location denoted by x̂ is given by α1 + x̂ = α2 + (1 − x̂), hencex̂ ≡1 + α2 − α1
.
2

(1)

Firm C can serve all consumers x ≤ x̂ with uniform price.
Next, consider firm C’s target segment and suppose firm C chooses product personalization.
Targeted consumer x prefers the personalized oﬀer from firm C to firm A2 ’s standard productif pA (x) + (1 − ϕA )x ≤ α2 + (1 − x). Assuming that targeted consumers choose personalized
oﬀers when they are indiﬀerent, firm C’s best response to α2 is given by pA (x) = min{c, 1 −(2 − ϕA )x + α2 }. Since firm C can adjust its personalized price for each targeted consumer
separately, it can reduce pA (x) down to marginal cost, i.e., pA (x) = c. This defines the marginal
consumer x̄ as pA (x̄) = c = 1 − (2 − ϕA )x̄ + α2 , hencex̄ ≡1 + α2 − c.
2 − ϕA(2)

Firm C can serve all targeted consumers x ≤ x̄ with product personalization. In doing so, it will
choose personalized prices that make all targeted consumers indiﬀerent between its personalized
oﬀer and its competitor’s standard oﬀer. Note that x̄ ≥ x̂ due to Assumption 1-(i), implyingthat personalization can serve as a more powerful weapon for firm C than uniform pricing in
defending its target segment.
Finally, suppose firm C chooses personalized pricing instead of product personalization. Thenit can serve all consumers up to x such that qA (x)+x = α2 +(1−x), leading to qA (x) = 1−2x+α2 .
Once again, firm C can adjust its personalized price for each consumer, hence qA (x) = 0 for themarginal consumer. This implies that firm C can serve all consumers x ≤ (1 + α2 )/2 ≤ x̄ where
the second inequality is due to Assumption 1-(i). This implies that if firm C can serve a subset
of its targeted consumers with product personalization, it can always use personalized pricing
in serving a subset of consumers closer to its location.
While personalization is a more powerful weapon than uniform pricing, product personalization comes at an additional cost c. Thus firm C’s choice of pricing mix depends on thecomparison between pA (x) − c, qA (x) and α1 . Our first observation is that firm C will never
use the uniform price to serve its targeted consumers. The statement is clearly true for targeted
19

Although firm C’s personalized prices and uniform price can be delinked in this way, they are indirectly linked
through firm A2 ’s uniform price. That is, α1 aﬀects α2 in competition for non-targeted consumers, and α2 inturn aﬀects firm C’s personalized prices in competition for targeted consumers.

13

consumers in [x̂, x̄]. So consider targeted consumer x ≤ x̂. If x ∈ [0, τ ], then firm C can serve
consumer x by choosing qA (x) = 1 − 2x + α2 ≥ 1 − 2x̂ + α2 = α1 . If x ∈ [τ, x̂], then firm C canserve consumer x by choosing pA (x) = 1 − (2 − ϕA )x + α2 . Then x ≤ x̂ and x ≥ τ = c/ϕA implypA (x)−c = 1+α2 −2x+ϕA x−c ≥ 1+α2 −2x̂+ϕA x−c = α1 +ϕA x−c ≥ α1 . Thus personalization
allows firm C to serve its targeted consumers more profitably than uniform pricing.
Lemma 1 It is never optimal for firm C to serve targeted consumers using uniform pricing.
Firm C chooses personalized pricing to serve consumers in [0, τ ] and product personalization toserve consumers in [τ, δA ].
Lemma 1 establishes a clear result and simplifies analysis. When firm C can target someconsumers using big data, it will serve them with personalized oﬀers, starting with personalized
pricing followed by product personalization. But the ability to use personalization is constrainedby its data scale δA and data analytics quality ϕA . Even when firm C’s data set covers theentire market (δA = 1), whether or not firm C can monopolize the market depends on c and ϕA .
Suppose δA = 1. Since firm C can serve consumers only up to x̄ using personalization, it must
concede the remaining consumers in [x̄, 1] to its rival. Given the marginal consumer’s locationx̄ in (2), firm A2 can maximize profit α2 (1 − x̄) by choosing α2 = (1 − ϕA + c)/2. This leads tox̄ = δ̄ whereδ̄ ≡3 − c − ϕA.
2(2 − ϕA )(3)

Thus [0, δ̄] is the maximum market segment that firm C can serve. Even when δA = 1,
firm C has to concede the segment [δ̄, 1] to firm A2 . Note that δ̄ ≥ 3/4 due to Assumption
1-(ii), δ̄ ≤ 7/8 by Assumption 1-(iii), and δ̄ decreases in c and increases in ϕA . Suppose, forexample, c = ϕA = 0 so that δ̄ = 3/4. In this case, firm A2 can serve the segment [3/4, 1], but
its market share shrinks as firm C’s data analytics improves, although it cannot become smaller
than [7/8, 1].
Lemma 2 Firm A2 can always serve consumers in [δ̄, 1] regardless of firm C’s data scale ordata analytics quality, where δ̄ ∈ [3/4, 7/8] is given in (3).
Proof. When firm C uses personalization, the upper bound on the market segment it can serve
was shown to be δ̄. The remaining case to consider is when firm C uses uniform pricing. The
lowest uniform price it can charge is α1 = 0, in which case x̂ = (1 + α2 )/2. Solving for firm A2 ’s
optimal uniform price leads to α2 = 1/2, hence x̂ = 3/4. The lemma then follows since δ̄ ≥ 3/4
due to Assumption 1-(ii).
Put diﬀerently, Lemma 2 shows how personalization allows firm C to expand its market
reach. With uniform pricing, firm C can reach the maximum market size [0, 3/4] by choosing
α1 = 0. With product personalization, this can be expanded to [0, δ̄] when the personalized
price is set equal to the marginal cost of personalization.
We now turn to the characterization of equilibrium. There are three cases to consider.
144.1.1Equilibrium when δA < 3/4

First, in the segment [δA , 1], competition is in uniform price with the marginal consumer’s
location given by x̂ in (1). Thus firm C’s profit from this segment is α1 (x̂ − δA ) and firm A2 ’s
profit is α2 (1 − x̂). Solving for the Hotelling equilibrium, we obtain the equilibrium uniform
prices42α1∗ = 1 − δA , α2∗ = 1 − δA ,
3
3

(4)

which implies x̂ = 1/2+δA /3. For this equilibrium to exist, we need α1∗ ≥ 0, which is guaranteed
since δA < 3/4. Note also that δA < 3/4 implies x̂ > δA .
Next, for x ∈ [0, τ ], firm C chooses a personalized price qA (x) that makes consumer x
indiﬀerent between the two firms’ standard products. Thus2∗
qA(x) = 1 − 2x + α2∗ = 2 − δA − 2x.
3(5)

Finally, for x ∈ [τ, δA ], firm C chooses product personalization with price pA (x) that makes
consumer x indiﬀerent between firm C’s personalized oﬀer and firm A2 ’s standard productoﬀered at price α2∗ . Thus the equilibrium personalized price in this segment is given by2p∗A (x) = 1 − (2 − ϕA )x + α2∗ = 2 − δA − (2 − ϕA )x.
3(6)

These equilibrium prices are depicted in Figure 1.
— Insert Figure 1 here. —∫δ∫τ ∗(x) dx + τ A (p∗A (x) − c) dx + α1∗ (x̂ − δA ). Firm A2
Then firm C’s total profit is Π∗C = 0 qAserves consumers in [x̂, 1] with uniform price α2∗ , hence its profit is Π∗A2 = (1 − (2δA )/3)2 /2.

In sum, when firm C’s data scale is relatively small in that δA < 3/4, none of firm C’s
targeted consumers are contestable by firm A2 . Thus by Lemma 1, firm C serves consumers in[0, τ ] with personalized pricing, and those in [τ, δA ] with product personalization. In addition,
firm C serves some non-targeted consumers in [δA , x̂] with uniform price, while firm A2 serves
the rest. Thus the two firms’ market shares in this case are endogenously determined by x̂.
4.1.2

Equilibrium when 3/4 ≤ δA < δ̄In this case, firm C cannot serve any of its non-targeted consumers. Competition in uniform
price in the segment [δ, 1] would lead to prices given in (4). But 3/4 ≤ δA implies a negative
price for firm C. Thus firm C chooses α1 = 0, hence x̂ = (1 + α2 )/2. Firm A2 chooses α2 tomaximize profit α2 (1 − x̂) subject to δA ≤ x̂. It is easy to see that, given vA > 2, firm A2 canmaximize profit by choosing α2 so that δA = x̂. This leads to the following equilibrium uniform
prices:α1∗∗ = 0, α2∗∗ = 2δA − 1.

15

(7)

Given α2∗∗ , we can determined firm C’s personalized prices as before.

∫ δA
τ

∗∗
qA
(x) = 2δA − 2x, for x ∈ [0, τ ],

(8)

p∗∗
A (x)

(9)

= 2δA − (2 − ϕA )x, for x ∈ [τ, δA ].

∗∗ =Given the above prices and market shares, firm C’s profit is given by ΠC∗∗(p∗∗
A (x) − c) dx. Meanwhile, firm A2 ’s profit is ΠA2 = (2δA − 1) (1 − δA ) .

∫τ∗∗
0 qA (x) dx +In sum, when firm C’s data scale is in the intermediate range in that 3/4 ≤ δA < δ̄, firm
C can serve only its targeted consumers, again with personalized pricing for those in [0, τ ] andwith product personalization for those in [τ, δA ]. Firm A2 serves all consumers not targeted byfirm C. Thus the two firms’ market shares are exogenously determined by δA .
4.1.3

Equilibrium when δ̄ ≤ δA

In this case, firm C’s target segment is so large that targeted consumers in [δ̄, δA ] are served byfirm A2 in addition to all non-targeted consumers in [δA , 1]. Following the discussion leading up
to Lemma 2, we then have the following equilibrium uniform prices:α1∗∗∗ = 0, α2∗∗∗ =1 − ϕA + c
.
2

(10)

Then firm C’s personalized prices are20
3 − ϕA + c− 2x,
for x ∈ [0, τ ] , 2
 3−ϕA +c − (2 − ϕ )x, for x ∈ [τ, δ̄].
A
2
p∗∗∗
(x)
=
A
≥ c,
for x ∈ [δ̄, δ ].
∗∗∗
qA
(x) =

(11)
(12)

A

Firm C’s profit in this case is Π∗∗∗C =∫ δ̄ ∗∗∗∗∗∗
0 qA (x) dx+ τ (pA (x) − c) dx while firm A2 makes∫τ2
profit equal to Π∗∗∗A2 = (1 − ϕA + c) / (4(2 − ϕA )).

To summarize this case, when firm C’s data scale is large in that δ̄ ≤ δA , firm C can serve
its targeted consumers only up to δ̄. Firm A2 poaches firm C’s targeted consumers in [δ̄, δA ] inaddition to serving all non-targeted consumers. In this case, the two firms’ market shares areendogenously determined by δ̄.
In the discussions so far, we have only characterized a candidate equilibrium in each casewithout checking its uniqueness. In the proof of the following proposition, we show that noother equilibria exist.
20

Firm C cannot profitably serve targeted consumers in [δ̄, δA ]. So the only restriction we have on these oﬀthe-equilibrium prices is p∗∗∗A (x) ≥ c, based on a refinement using trembling-hand perfection. That is, suppose
firm A2 ‘trembles’ and increases its price so that some consumers in [δ̄, δA ] choose firm C. This will cost firm C
if it had chosen p∗∗∗A (x) < c.

16

Proposition 1 Suppose firm C’s target segment is given by [0, δA ].
• When δA < 3/4, there exists a unique equilibrium in which firm C chooses personalized∗ (x) for all consumers in [0, τ ], product personalization with prices p∗ (x) for all
pricing qAA

consumers in [τ, δA ], and uniform price α1∗ for consumers in [δA , 1/2 + δA /3], whereas firm
A2 serves the rest of consumers with uniform price α2∗ . These prices are given in (4), (5),and (6).
• When 3/4 ≤ δA < δ̄, there exists a unique equilibrium in which firm C chooses personalized∗∗ (x) for all consumers in [0, τ ], product personalization with prices p∗∗ (x) for
pricing qAA

all consumers in [τ, δA ], and uniform price α1∗∗ = 0, whereas firm A2 serves consumers in[δA , 1] with uniform price α2∗∗ . These prices are given in (7), (8), and (9).
• When δ̄ ≤ δA , there exists a unique equilibrium in which firm C chooses personalized∗∗∗ (x) for all consumers in [0, τ ], product personalization with prices p∗∗∗ (x) for
pricing qAA[ ]all consumers in τ, δ̄ , and uniform price α1∗∗∗ = 0, whereas firm A2 serves consumers in[ ]δ̄, 1 with uniform price α2∗∗∗ . These prices are given in (10), (11), and (12).

Proof. See Appendix.

4.2

Welfare implications of personalization

Based on the equilibrium characterization in Proposition 1, we now turn to the discussions of
how firm C’s ability to use personalization following the merger aﬀects welfare. We start bymaking two observations on how personalization can increase firm C’s market power, which canbe used to exploit a subset of targeted consumers and harm its stand-alone competitor.
That personalization can lead to consumer exploitation seems intuitive given that firm C
can tailor its pricing strategy for each targeted consumer. This is especially true for targeted
consumers in [0, τ ] since they are oﬀered personalized prices without the benefit of improved
matching value. For targeted consumers in [τ, δA ], the benefit of improved matching value needs
to be weighed against the cost of potentially higher personalized price. On the other hand, firm
C’s non-targeted consumers benefit since more intense competition in uniform price reduces
uniform prices below the Hotelling benchmark. In sum, personalization can lead to exploitationof some consumers while benefiting others.
The ability to use personalization expands firm C’s pricing arsenal, making it a more eﬀective
defender of its target segment and a more aggressive competitor outside of it. The end result
is that firm C will be able to enlarge its market share above the Hotelling benchmark. Thisis true for any value of δA since having a target segment [0, δA ] shifts the battleground forHotelling competition from [0, 1] to [δA , 1]. This hurts firm A2 . On the other hand, firm C
cannot monopolize the market since δ̄ ≤ 7/8. Thus firm A2 will continue to remain in themarket, albeit with reduced profit and market share. But the market can turn into a monopoly
in the long run if there are some fixed costs of staying in the market, which are not covered byfirm A2 ’s short-run profit.
17

With these observations in mind, let us examine how personalization following the merger
aﬀects each firm’s profit and consumer surplus.
First, firm A2 ’s profit decreases unambiguously. In all the three cases in Proposition 1, it isstraightforward to verify that firm A2 ’s profit is less than 1/2, its pre-merger profit. Moreover,∗∗
one can check Π∗∗∗A2 < ΠA2 < 1/8. Thus the merger can reduce firm A2 ’s profit to less than 25%

of its pre-merger profit if firm C’s data set covers more than three quarters of consumers. As
discussed previously, this could force firm A2 to exit the market in the long run if it has a fixed
cost greater than 1/8.
Second, firm C’s profit increases when δA ≤ δ̄, but can decrease when δA > δ̄ and ϕA becomes
suﬃciently large. This follows from comparing the second and third equilibria in Proposition 1.
Having a larger data scale benefits firm C by allowing it to use personalization, but only up toδA = δ̄. Beyond that, firm C cannot serve additional targeted consumers. But a higher valueof ϕA intensifies competition and decreases firm A2 ’s uniform price, as can be seen from (10).
This in turn reduces firm C’s personalized prices, which are strategic complements to firm A2 ’s
uniform price. This can make firm C’s profit less than 1/2, its pre-merger profit. To see this,notice that, when ϕA = 1, firm C’s profit is equal to (4 − 4c + 5c2 )/8, which is less than 1/2
since c ≤ ϕA /2 ≤ 1/2 where the first inequality is due to Assumption 1-(ii). Therefore, as ϕA
increases to 1, firm C’s profit monotonically decreases to less than 1/2, implying that there is a
threshold value of ϕA above which firm C’s profit is less than 1/2.
Third, personalization harms some consumers but benefits others. Before the merger, atargeted consumer with taste parameter x receives utility vA − x − 1 given the Hotelling priceequal to 1. After the merger, consumer x will be targeted with either personalised pricing
or product personalization. But in either case, firm C adjusts its personalized oﬀer so that
consumer x will be indiﬀerent between accepting firm C’s personalized oﬀer or choosing firm
A2 ’s standard product. That is, consumer x will receive utility equal to vA − (1 − x) − α2 . Thus
consumer x is worse oﬀ after the merger if vA − (1 − x) − α2 < vA − x − 1, or x < α2 /2. Thisimplies that consumers closer to firm C are more likely to be exploited through personalization.
In the equilibrium with δA < 3/4, we have α2∗ /2 = 1/2 − δA /3 > 1/4. Thus at least one
quarter of consumers including those in [0, 1/4] are worse oﬀ after the merger. But targeted
consumers in [α2 /2, δA ] benefit from personalization. Needless to say, all consumers outside firm
C’s target segment also benefit from the merger because competition in uniform price becomes
more intense, leading to lower uniform prices than before the merger. Under our assumptionthat x is uniformly distributed, total consumer surplus increases after the merger.
Proposition 2 Suppose firm C’s target segment is given by [0, δA ]. Then personalization following the merger• reduces firm A2 ’s profit unambiguously;• increases firm C’s profit if δA < δ̄, but reduces it if δA > δ̄ and ϕA is suﬃciently large;• harms some consumers but benefits others, but increases total consumer surplus.
18

Proof. See Appendix.
Next, we discuss the comparative statics of profits and consumer surplus with respect to δA
and ϕA . First, suppose firm C has a large data scale in that δA ≥ δ̄. In this case, the two
firms’ market shares are determined by δ̄, which is independent of δA ; nor do equilibrium prices
depend on δA . Consequently, an increase in δA aﬀects neither firm’s profits, implying that an
excessive data scale beyond δ̄ has no eﬀect on competition and welfare. In contrast, an increasein ϕA intensifies competition and reduces firm A2 ’s uniform price, which in turn reduces firm
C’s personalized prices. Thus an increase in ϕA reduces both firms’ profits but benefits all
consumers.
Consider next the case 3/4 ≤ δA < δ̄, when firm C can serve all its targeted consumers whilefirm A2 serves the rest. In this case, an increase in δA benefits firm C simply because it allows
firm C to serve more consumers, but hurts firm A2 for exactly the same reason. Consumer
surplus decreases in δA since an increases in δA increases firm A2 ’s uniform price. As for ϕA ,its increase benefits firm C by allowing it to increase its personalized prices pA (x), thereby
extracting the eﬃciency gain from the improved matching value. But it has no eﬀect on firm
A2 ’s profit since neither firm A2 ’s market share nor its equilibrium uniform price depends on
ϕA . Likewise, it has no eﬀect on consumer surplus since the improved matching value is fully
extracted by firm C through personalized pricing.
When δA < 3/4, firm C serves some non-targeted consumers in addition to all of its targeted
consumers. An increase in δA in this case has two countervailing eﬀects: it allows firm C to serve
more consumers but it also intensifies competition for non-targeted consumers. As a result, theimpact of an increase in δA on firm C’s profit is not monotonic. Firm C’s profit Π∗C increasesin δA for δA < δ ∗ , after which it decreases where δ ∗ ≡ (6 − 9c)(14 − 9ϕA ) ≤ 3/4, the inequality
being due to Assumption 1-(iii). In contrast, an increase in δA unambiguously reduces firm A2 ’s
profit. On the other hand, an increase in ϕA benefits firm C by allowing it to increase pA (x)but it has no eﬀect on firm A2 ’s profit. As for consumer surplus, an increase in δA benefits
consumers since it decreases uniform prices, and therefore, personalized prices as well. But anincrease in ϕA has no eﬀect on consumer surplus as in the previous case.
Proposition 3 Suppose firm C’s target segment is given by [0, δA ].
• Firm C’s profit increases in δA up to δA = min{δ ∗ , 3/4} where δ ∗ ≡ (6 − 9c)(14 − 9ϕA ),after which it is non-increasing in δA . Firm C’s profit increases in ϕA when δA < δ̄, but
decreases in ϕA when δA ≥ δ̄.
• Firm A2 ’s profit decreases in δA up to δA = δ̄, but is independent of δA after that. Firm
A2 ’s profit is independent of ϕA when δA < δ̄, but decreases in ϕA when δA ≥ δ̄.
• Consumer surplus increases in δA up to δA = 3/4, decreases in δA for δA ∈ [3/4, δ̄], but
is independent of δA after that. Consumer surplus is independent of ϕA when δA < δ̄, but
increases in ϕA when δA ≥ δ̄.
19

Proof. See Appendix.
The main thrust of Proposition 3 is diﬀerential eﬀects of data scale vis-à-vis data analytics
relevant to personalization. Increasing data scale can benefit the firm but only up a certain
point, because the firm’s ability to serve additional targeted consumers is ultimately limited byits data analytics. As the firm benefits from a larger data scale, its competitor inevitably loses
due to a decrease in its market share. On the other hand, an improvement in data analytics
that benefits the firm has no eﬀect on its competitor. This is because the benefit comes fromthe firm’s ability to extract surplus from consumers that the firm already serves, rather thanfrom poaching consumers from its competitor.
We close this section with a caveat. As our model is essentially static, Proposition 2 simply
reiterates the well-known point that data can benefit consumers in the short run by intensifying
competition. Of course, the eﬀect can be only short-lived if the intensified competition leads tomarket tipping and drives the competitor out of the market in the long run. Data externalities
can further expedite this process. Relevant to Google/Fitbit, Google can correlate health data on
Fitbit users with its own data from other Google services, and infer health-related information on
Google users even if they do not use Fitbit devices. One way to think about data externalities inour setting is that firm C can use the data from its target segment [0, δA ] to infer information on
the remaining segment [δA , 1]. In the extreme case, firm C can expand its target segment to theentire market. This, coupled with improved data analytics that can relax the restriction δ̄ ≤ 7/8,
can result in the monopolization of market A by firm C. Then firm C can use personalization
to extract consumer surplus uninhibited by competition. This suggests a dynamic trade-oﬀ
between short-term gains in consumer surplus and possible long-term losses.

5

Data-Driven Mergers with Cross-Markets Eﬀects

One of the concerns that competition authorities have in cases like Google/Fitbit merger is how
a dominant digital platform like Google can leverage advantages from its powerful ecosystem
into related markets through the merger. Of course, such concerns make sense only when there
are some linkages between the relevant markets; in pure conglomerate mergers without any
linkages, there is no sense in which firms can extend market power to other markets through amerger.
We model such linkages through two channels: data and consumption synergy. First, we havealready argued that firm C can use data it harvests in market B for personalization in market A.
In this section, we endogenize firm C’s target segment: consumer x’s taste parameter is known
to firm C if she chooses firm B1 in market B, which, by our assumption of perfect correlation, isalso her taste parameter in market A. But data alone establishes only a one-way linkage. So we
introduce another element. Specifically, a consumer who purchases firm B1 ’s product receives
extra value ω by choosing firm C’s personalized product in market A. This extra value canbe interpreted as the consumption synergy, which may be due to several factors. First, there20may be “one-stop shopping” benefits such as reduced transactions costs. Second, there may bebenefits from consuming the two products together. For example, some add-on features in the
personalized product may have value only when consumed together with firm B1 ’s product. In
case of Google/Fitbit, incorporating the wearable device into Google’s ecosystem and packaging
it with other existing applications and services can enhance user experience in the market for
digital health. Third, the extra value ω may capture a bundling discount in reduced form. Our
aim in this section is to understand how data and the consumption synergy aﬀect competition
in both markets. Throughout this section, we use the following assumptions.
Assumption 2: (i) ω ≥ γ ≥ 1; (ii) ϕA = 1, c = 0.
Assumption 2-(i) says firm B2 has a competitive advantage in market B (i.e., γ > 0) but theconsumption synergy in market A is larger. It allows us to explore the possibility the merged
firm may price below-cost in market B when the consumption synergy is suﬃciently large. The
assumption γ > 0 may reflect the current market for wearable devices where Apple is a dominant player. Assumption 2-(ii) is intended primarily to simplify analysis since, with additionalparameters ω and γ and the two linked markets, analysis becomes considerably more complicated. The implication of Assumption 2-(ii) is that firm C will now use product personalizationand oﬀer perfectly matched products to all of its targeted consumers. There will not be any
substantive changes to the main insight from this section when we incorporate ϕA and c withϕA ≥ 2c as we did in the previous section. As before, we assume that firm C can prevent targeted
consumers from purchasing its standard product. Also recall our assumption that consumers are
not forward looking, so that their purchase decisions in the two markets are separately made.
In addition, neither consumers nor firms discount future.
The timing of the game is as follows. First, firms A1 and B1 decide whether they should
merge and create firm C. They choose to merge if and only if their total profit after the merger
is larger than that before the merger. Without the merger, two firms in each market play asimultaneous pricing game in uniform price. With the merger, we analyze market B first, which
determines firm C’s target segment, based on which we study market A. The timing of thepricing game in market A is the same as before. That is, uniform prices are simultaneouslychosen first, after which firm C makes personalized oﬀers. We solve the game backward.

5.1

Analysis of equilibria

Let us start with market A. Denote firm C’s target segment by [0, x∗ ] where x∗ is the marginal
consumer who purchased firm B1 ’s product in market B. By Assumption 2-(ii), firm C uses
product personalization for all consumers in [0, x∗ ]. In doing so, firm C chooses personalized
prices to leave all targeted consumers indiﬀerent between choosing either firm. Thus vA + ω −pA (x) = vA − (1 − x) − α2 , hence pA (x) = 1 − x + ω + α2 for all x ∈ [0, x∗ ].
We make several observations. First, since pA (1) = ω + α2 > 0, firm C can profitably serve
all targeted consumers in market A, unlike in Section 4 where firm C’s maximum market share21was capped at δ̄ ≤ 7/8. Thus data scale has a positive marginal benefit in market A, whichmakes monopolization an attractive option. Second, the consumption synergy ω increases themarginal benefit to data scale in market A, which makes firm C more aggressive in market B
than without the consumption synergy. Thus ω plays two roles: it adds market power to firm C
in market A; it links the two markets by creating negative externalities for firm B2 . Third, firm
B2 ’s competitive advantage γ increases firm C’s cost of expanding its target segment in market
A, implying that γ also links the two markets by benefiting firm A2 . Therefore, the merger links
not only firms A1 and B1 but also the two competitors, firms A2 and B2 , that are otherwise
unrelated.
From the discussions above, we expect two types of equilibria. If ω is significantly large
relative to γ, we expect firm C to monopolize market B, which also implies the monopolizationof market A. Otherwise, firm C will accommodate competitors in both markets. In both typesof equilibria, we expect the merger to be an equilibrium outcome. This is because firm C obtains
market power created by the ability to use personalization and the consumption synergy only
through the merger. We now turn to the characterization of each type of equilibrium.
5.1.1

Equilibrium with accommodation

When the consumption synergy ω is not large enough, monopolizing market B can be costly
to firm C as it would require aggressive competition against the rival that has competitive advantage (recall, γ > 0). In this case, firm C will accommodate its competitor in both markets.
We derive such an equilibrium in this section. As we show below, the equilibrium with accommodation is possible only when x∗ ≤ x̂ where we recall that [0, x∗ ] is firm C’s target segmentin market A endogenously determined in market B, and x̂ = (1 + α2 − α1 )/2 is the marginal
consumer in market A when competition is in uniform price.
In market A, this case corresponds to the case with δA < 3/4 in Section 4.1.1. The only
diﬀerences are c = 0, ϕA = 1, and the presence of ω. Thus substituting δA by x∗ , we obtain
α1∗ = 1 − (4x∗ )/3, α2∗ = 1 − (2x∗ )/3, and x̂ = 1/2 + x∗ /3. For this equilibrium to exist, weneed α1∗ ≥ 0, hence x∗ ≤ 3/4. This also implies x̂ = 1/2 + x∗ /3 ∈ [x∗ , 3/4]. Given α2∗ , firm C’s
personalized prices are p∗A (x) = 2 + ω − x − (2x∗ )/3.
In market B, firm C chooses β1 to maximize total profit from both markets∗∫ x∗

ΠC = β1 x +0p∗A (x)dx +

(

4x∗
1−
3

)(

1 2x∗
−
2
3

)

5
= − (x∗ )2 +
18

(

)
1
2
+ ω + β1 x∗ + ,3
2

where x∗ = (1 − β1 + β2 − γ)/2. This leads to the best response function defined by β1 =(23x∗ − 9ω − 6)/9. Firm B2 ’s profit is ΠB2 = β2 (1 − x∗ ), hence its best response is given by
β2 = (1 + γ + β1 )/2. Solving them for the equilibrium uniform prices in market B, we obtainβ1∗ =45 − 23γ − 36ω
52 + 18γ − 18ω ∗ 33 + 9ω − 9γ
, β2∗ =
, x =
.
59
59
59

22

(13)

Since this equilibrium is possible when x∗ ≤ 3/4, we must have ω ≤ 5/4 + γ. Substituting x∗
into the equilibrium prices in market A given above, we obtainα1∗ =37 + 6γ − 6ω ∗96 + 6γ + 53ω
15 + 12γ − 12ω, α2∗ =, pA (x) =
− x.
59
59
59

(14)

The equilibrium prices in both markets are depicted in Figure 2.
— Insert Figure 2 here. —We now show that the merger is an equilibrium outcome by showing that firm C’s total
equilibrium profit is larger than the sum of the two firms’ pre-merger equilibrium profits. Before
the merger, firm A1 earns profit equal to 1/2 and firm B1 ’s profit is (1 − γ/3)2 /2. So the total
pre-merger profit is less than 1. By substituting the best response function β1 into ΠC , firm
C’s total equilibrium profit can be expressed in terms of x∗ as Π∗C = 1/2 + (41(x∗ )2 )/18. Sincex∗ > 1/2 because ω ≥ γ by Assumption 2-(i), we have Π∗C > 1, implying that the merger is anequilibrium outcome. In addition, Π∗C increases in ω but decreases in γ, as does x∗ . Thus themerger is more likely when the consumption synergy is stronger, but less likely when there is astronger competitor in the market where consumer data is harvested.
In contrast, the competitors’ profits are Π∗B2 = β2∗ (1 − x∗ ) = 2(26 + 9γ − 9ω)2 /3481 andΠ∗A2 = α2∗ (1 − x̂) = (37 + 6γ − 6ω)2 /6962. Both profits increase in γ but decrease in ω. Thus
firm B2 ’s competitive advantage not only benefits itself but also creates positive externalities
for firm A2 . Likewise, the consumption synergy in market A hurts both firms A2 and B2 . But
both firms are worse oﬀ after the merger. Consider firm B2 first. Before the merger, firm B2
serves more than half of the market, charging price β20 = 1 + (γ/3) > 1. But after the merger,
it charges price β2∗ < 1 to serve less than half of the market since 1 − x∗ < 1/2. Similarly, firm
A2 ’s pre-merger profit is 1/2, being from serving half of the market at price equal to 1. Afterthe merger, it serves less than half of the market, charging price less than 1/2.
To summarize, the equilibrium with accommodation is possible when ω ≤ 5/4 + γ. In thisequilibrium, firms A1 and B1 choose to merge, following which firm C’s market share increases
to [0, x∗ ] in market B where 33/59 < x∗ ≤ 3/4. In market A, firm C’s market share increases
further to [0, x̂] where x∗ ≤ x̂. Firm C serves all consumers in [0, x∗ ] using personalized oﬀers,
serves additional consumers in [x∗ , x̂] with uniform price, while firm A2 serves the rest withuniform price.
There are several notable cross-market eﬀects arising in this equilibrium, which we discuss
here. First, β1∗ < 0, hence firm C engages in below-cost pricing in market B. But this allows
firm C to increase the size of target segment in market A above 1/2, its pre-merger market
share. Second, there is cross subsidization in that firm C’s loss in market B due to below-cost
pricing is more than oﬀset by the profit gain in market A. Thus below-cost pricing in the market
for data collection is driven by the firm’s incentives to engage in consumer exploitation throughpersonalization in the market for data application. Clearly, such incentives become stronger
as the consumption synergy becomes stronger, hence β1∗ decreases in ω. Third, firm B2 suﬀers
23

negative externalities from market A due to the consumption synergy. As ω increases, firm C
becomes more aggressive in market B, which intensifies competition and harms firm B2 . Finally,
firm A2 benefits from positive externalities from firm B2 . Firm B2 ’s competitive advantage isa countervailing force that constrains firm C’s expansion in market B, hence in market A byextension. As γ increases, x∗ decreases and, as a result, both uniform prices increase in market
A. We summarize below the discussions so far. The proof follows the same step used in the
proof of Proposition 1, so is omitted.
Proposition 4 Suppose ω ≤ γ + 5/4. Then there is a unique equilibrium in which firms A1
and B1 choose to merge and create firm C.
• Subsequent equilibrium prices are as given in (13) and (14).
• Firm C engages in below-cost pricing in market B to increase market share to [0, x∗ ], andincreases its market share in market A to [0, x̂] where x∗ is given in (13) and x∗ ≤ x̂ ≤ 3/4.
• Firm B2 ’s equilibrium price decreases in ω, hence the consumption synergy in market A
creates negative externalities and hurts firm B2 .
• Firm A2 ’s equilibrium price increases in γ, hence firm B2 ’s competitive advantage creates
positive externalities and benefits firm A2 .
The equilibrium with accommodation can be sustained when the consumption synergy is not
too large, which limits firm C’s target segment in market A. As we have discussed previously,
however, data externalities can allow firm C to expand its target segment and monopolize market
A, although market B remains as a duopoly. On the other hand, firm C will monopolize bothmarkets when the consumption synergy becomes suﬃciently large, as we discuss below.
5.1.2

Monopolization

When the consumption synergy ω is considerably large relative to γ, firm C can be tempted tomonopolize both markets. A necessary condition for this is x∗ ≥ x̂, as shown in Proposition 4.
In this case, firm C’s target segment in market A includes the marginal consumer x̂. Then, as in
Proposition 1, one may ask if an equilibrium may exist in which firm C serves all of its targeted
consumers only and concedes the rest to firm A2 . We show below that such an equilibrium is
not possible, which leaves x∗ = 1 as the only possibility.
Suppose there is an equilibrium with x̂ ≤ x∗ < 1. Then following the argument in Section
4.1.2, firm A2 chooses uniform price α2 = 2x∗ − 1 and serves all consumers in [x∗ , 1]. Suppose
now firm C deviates to increase its target segment to [0, x′ ] with x′ > x∗ . This allows firm C touse personalization for additional consumers in [x∗ , x′ ]. The cost of expanding its market share
can be intensified competition in uniform price, leading to a lower uniform price by firm A2 ,which in turn compels firm C to cut its personalized prices. However, as shown above, firm A2 ’s
uniform price is α2 = 2x∗ − 1 when x̂ ≤ x∗ < 1, which increases in x∗ . Thus firm C does not
face any trade-oﬀ in expanding its target segment, implying that its deviation to x′ is profitable.
24

This implies that there cannot be an equilibrium with x̂ ≤ x∗ < 1. Then the only possibility iswhen x∗ = 1, i.e., monopolization.21
Proposition 5 Suppose ω > γ + 5/4. Then there is a unique equilibrium in which firms A1
and B1 choose to merge and create firm C.
• Firm C monopolizes both markets with prices p∗∗
A (x) = 2 + ω − x for all x ∈ [0, 1] in market
A and β1∗∗ = −1 − γ in market B.
• Firm C’s equilibrium profit is Π∗∗
C = (1 + 2ω − 2γ)/2 > 1.
Proof. See Appendix.
Once again, firm C engages in below-cost pricing in market B to squeeze its competitor. The
equilibrium in Proposition 5 can be described as the short-run predatory equilibrium in thatfirm C prices below cost and monopolizes the market, but without fully utilizing its monopoly
power. For example, in market A, firm C is not able to extract full consumer surplus eventhough it can in principle exercise perfect price discrimination. Of course, this is because firm
A2 is lurking in the background, waiting to counter any price increase by firm C. Thus thepresence of firm A2 , albeit inactive in equilibrium, makes the market contestable.
The above situation is likely to prevail only in the short run, however. If competitors exit
the market in the long run, then the monopolization equilibrium can turn into the monopoly
equilibrium, which will be much more profitable for firm C, and hence to the detriment ofconsumers. In the monopoly equilibrium, firm C can extract full consumer surplus from each∗∗consumer in market A with personalized prices pm
A (x) = vA + ω > pA (x) for all x ∈ [0, 1]; inmarket B, it serves the entire market with monopoly price β m = vB /2 > 1.

5.2

Welfare implications of the merger

Our analysis so far has shown that the merger benefits firm C at the cost of its competitors
in both markets. The benefits are derived from data-enabled personalization that allows firm
C to extract surplus from its targeted consumers, and to expand its market power against thecompetitor in the market for data application, supported by firm C’s aggressive pricing in themarket for data collection. To complete the analysis, we now examine how consumer surplus
changes after the merger.
Let us start with the equilibrium with accommodation. Consider market A. Before themerger, price is equal to 1 and firms share the market equally. After the merger, prices are givenin (14) and the market is divided at x̂ = 1/2 + x∗ /3. Since α1∗ , α2∗ < 1, it is immediate that
When x∗ = 1, firm A2 chooses oﬀ-the-equilibrium price α2 . In this case, we use a refinement in which
α2 = limε→0 α2 (ε) where α2 (ε) is optimally chosen when x∗ (ε) = 1 − ε. This refinement is in the same spirit as
trembling-hand perfection that allows firm C’s tremble in market B. Given the monopolization of market B, theonly meaningful tremble is when firm C increases its price slightly. This leads to x∗ (ε) < 1, whence α1 (ε) = 0
and α2 (ε) = 2x∗ (ε) − 1.
21

25

all consumers in [x∗ , 1] are better oﬀ. On the other hand, firm C’s targeted consumers may or
may not be better oﬀ. All of them pay personalized prices higher than 1 but they benefit fromperfectly matched products and the additional consumption synergy. Since personalized prices
are higher for consumers whose taste parameter is closer to 0, it follows that there is a thresholdvalue of taste parameter such that consumers are worse oﬀ if and only if their taste parameteris below the threshold.22 Given the uniform distribution, one can show that total consumer
surplus in market A increases after the merger. On the other hand, all consumers in market B
are unambiguously better oﬀ. Before the merger, prices are β10 = 1 − γ/3, β20 = 1 + γ/3, andthe market is divided at x0 = (3 − γ)/6. After the merger, prices and the marginal consumer
are given in (13). Since x∗ > x0 , β1∗ < 0 < β10 , and β2∗ < β20 , all consumers in [0, x0 ] ∪ [x∗ , 1]
are better oﬀ since they pay less while choosing the same firm. For consumer x ∈ [x0 , x∗ ]who switches from firm B2 to firm C after the merger, the change in consumer surplus is)(vB − x − β1∗ − vB + γ − (1 − x) − β20 = 1 − 2x − γ − β1∗ + β20 > 0. Thus all consumers in market
B are better oﬀ after the merger.
In the monopolization equilibrium, changes in consumers surplus are clearer. In market A,
consumer x ∈ [0, 1/2] is worse oﬀ after the merger because (vA + ω − p∗∗
A (x)) − (vA − x − 1) =2x − 1 ≤ 0. Thus all consumers who purchased from firm A1 before the merger are worse oﬀ.
Similarly, consumer x ∈ [1/2, 1] is better oﬀ after the merger if (vA + ω − p∗∗
A (x)) − (vA − (1 −x) − 1) = 1 − 2x ≥ 0, implying that all consumers who purchased from firm A2 before the merger
are also worse oﬀ. It follows that total consumer surplus in market A decreases unambiguously
after the merger. In market B, it is obvious that the merger benefits all consumers thanks
to below-cost pricing, although one needs to exercise caution in interpreting this result. The
comparison of consumer surplus in market B is in relation to the monopolization equilibrium,
rather than the monopoly equilibrium. If the merger leads to the latter in the long run, then themerger hurts all consumers in both markets. In the monopoly equilibrium, consumer surplus iszero for all consumers in market A and, in market B, it is lower than the pre-merger consumer
surplus since vB > 2 implies β m = vB /2 > 1 − γ/3 = β10 , i.e., the monopoly price is higher thanthe pre-merger price.
Put together, these results show clear welfare implications of data-driven mergers. The
merging parties are better oﬀ at the cost of their stand-alone competitors. Consumers as awhole gain in the market for data collection because competition intensifies in that market. On
the other hand, consumers in the market for data application are better oﬀ if the consumption
synergy is not large enough so that the merged firm does not monopolize the market. Otherwise,
they are worse oﬀ despite data-enabled personalization made possible by the merger. It isbecause monopolization allows the merged firm to extract from all consumers the additional
surplus generated from the consumption synergy and the improved matching value created bypersonalization.
22

The threshold value is given by vA − x − 1 = vA + ω − p∗A (x), hence x = (37 + 6γ − 6ω)/118.

26

Proposition 6 The merger with cross-markets eﬀects has the following welfare implications.
• Firm C’s total profit is larger than the sum of the two firms’ pre-merger profits.
• Both firms A2 and B2 are worse oﬀ than before the merger.
• In market A, total consumer surplus is larger in the equilibrium with accommodation but
smaller in the monopolization equilibrium than before the merger.
• In market B, total consumer surplus is larger in both equilibria.
• In the long run when firms A2 and B2 exit following monopolization, consumers are worse
oﬀ in both markets than before the merger.
Proof. See Appendix.

6

Policy Implications

Our analysis in Section 5 has established that the data-driven merger can be pro-competitivein the market for data collection. In the market for data application, total consumer surplus
can also increase after the merger if the consumption synergy is not large enough. As we havestressed, however, these are short-term benefits that could be outweighed by long-term costs if
the merger eventually leads to market tipping. Indeed, digital markets often face a trade-oﬀ
where the potential dynamic costs of concentration outweigh any static benefits (Furman et al.,2019). This trade-oﬀ has been one of the main concerns for competition authorities. To quote
Crémer et al. (2019, p. 76), “Because of the innovative and dynamic nature of the digital world,and because its economics are not yet completely understood, it is extremely diﬃcult to estimate
consumer welfare eﬀects of specific practices.”
In view of these concerns, we discuss several possible remedies that are often discussed inrelation to tech mergers.23 First, we analyze the eﬀect of mandated data sharing between themerged firm and its competitor. Second, we have assumed so far that the merged firm canprevent its targeted consumers from having access to its standard product oﬀered at a uniform
price. We ask what happens if the firm cannot employ such a discriminatory practice. Third,
we examine the eﬀect of banning below-cost pricing. Finally, we briefly discuss the eﬀect ofblocking the merger altogether. Throughout this section, we continue to maintain Assumption
2 and use notation pC (x) to denote firm C’s personalized price for consumer x to distinguish itfrom pA (x) used in the previous section. We also denote the marginal consumer in market B byx̃ to facilitate comparison with x∗ in the previous section.

6.1

Data sharing

Suppose firm C is compelled to share data with firm A2 , based on which firm A2 can also
make personalized oﬀers. Needless to say, firm A2 benefits from such one-way data sharing. We
23

For example, see Bourreau et al. (2020).

27

assume firm A2 ’s personalization technology is identical to firm C’s. But only firm C can leverage
the consumption synergy since firm A2 continues to be a stand-alone competitor. Given data
sharing, firms C and A2 compete under symmetric information, which intensifies competition in
the target segment and reduces the value of data. This dampens firm C’s incentives to collectconsumer data, hence softens competition in market B and benefits firm B2 . An immediate
consequence is that consumers in market B are worse oﬀ due to higher uniform prices. But theeﬀect in market A is more complex and we need to examine all possible equilibria.
Before describing possible equilibria, we note first that, even with data sharing, firm C
can serve all targeted consumers thanks to the consumption synergy. This is because, for any
personalized price pA2 (x) chosen by firm A2 , firm C can choose personalized price pC (x) ≥ 0such that vA + ω − pC (x) ≥ vA − pA2 (x). Bertrand competition for consumer x will lead topA2 (x) = 0, hence firm C will choose pC (x) = ω to serve consumer x. Clearly pC (x) = ω is lower
than all personalized prices without data sharing, the latter given by pA (x) = ω + α2 + 1 − x.
Thus firm C can continue to serve all its targeted consumers despite data sharing, but at lower
personalized prices than without data sharing.
Based on the above observation, we can identify three possible equilibria given data sharing.
Let [0, x̃] be the target segment and x̂ be the marginal consumer in market A when competition
is in uniform price. First, when ω is relatively small in that ω ≤ γ + 3/2, there is an equilibrium
in which firm C serves all consumers in [0, x̃] with personalization, those in [x̃, x̂] with uniform
price, while firm A2 serves the rest with uniform price. This equilibrium, called the equilibriumwith accommodation I, has the same structure as the equilibrium with accommodation in theprevious section, but with several key diﬀerences: (i) personalized prices are lower due to more
intense competition in the target segment; (ii) the target segment is smaller because of (i); (iii)
uniform prices are higher in both markets because of (ii). Second, If ω ∈ [γ + 3/2, γ + 3], thenthere is an equilibrium where firm C serves only targeted consumers while firm A2 serves therest, to be called the equilibrium with accommodation II. Finally, if ω > γ + 3, then firm C
monopolizes both markets.
Table 1: Equilibria with or without data sharingω

[1, γ + 54 ][]γ + 54 , γ + 32[]
γ + 23 , γ + 3

γ+3≤ωNo data sharing
Data sharing

Accommodation
Accommodation I

Monopolization
Accommodation I

Monopolization
Accommodation II

Monopolization
Monopolization

Table 1 shows various types of equilibria with or without data sharing for diﬀerent rangesof ω, where the first row indicates the range of ω. Comparing the equilibria for the given
range of ω, we can show that total consumer surplus in market A increases after data sharing,primarily because of lower personalized prices. In addition, data sharing sustains equilibria withaccommodation for a wider range of values for ω than without data sharing, as shown in Table28

1. In this sense, data sharing can be pro-competitive.
A general observation we can make is that data sharing benefits stand-alone competitors at
the cost of merging firms, and in the process, hurts consumers in the market for data collection
but benefits consumers in the market for data application. Finally, data sharing can be procompetitive by intensifying competition where data is used and by making monopolization harderto achieve. The following proposition summarizes key implications of data sharing.
Proposition 7 Suppose firm C is compelled to share data with firm A2 .
• Firm C is worse oﬀ but both firms A2 and B2 are better oﬀ than without data sharing.
• In market A, total consumer surplus is larger in all equilibria than without data sharing.
• In market B, total consumer surplus is smaller in all equilibria than without data sharing.
• Monopolization is less likely with data sharing in the sense that the monopolization equilibrium arises for ω ≥ γ + 3 whereas, without data sharing, the monopolization equilibrium
arises for ω ≥ γ + 5/4.
Proof. See Online Appendix.

6.2

Prohibition of search discrimination in market for data application

Suppose firm C is prohibited from engaging in search discrimination that prevents its targeted
consumers from having access to its standard product oﬀered at a uniform price.24 This implies that firm C’s targeted consumer x can choose firm C’s standard product in addition to
its personalized product and firm A2 ’s product. Thus the problem consumer x faces now is
max{vA − (pC (x) − ω), vA − (α1 + x), vA − (α2 + 1 − x)} where the terms inside the rounded
brackets represent the ‘eﬀective price’ consumer x pays for each choice.
The extra choice given to targeted consumers implies that personalization is less eﬀective
in extracting consumer surplus, if firm C serves non-targeted consumers. In this case, firm C’s
personalized prices are constrained by its own uniform price. That is, given α1 , its personalized
price pC (x) needs to satisfy pC (x) − ω ≤ α1 + x; otherwise, targeted consumers will choose thestandard product. On the other hand, if firm C chooses not to serve any of its non-targeted
consumers, then its choice of personalized prices is no longer constrained by its own uniform
price, but by firm A2 ’s uniform price as before. This presents an opportunity for the two firms
to achieve a collusive outcome.
To see how a collusive outcome is possible in market A, let [0, x̃] be firm C’s target segment.
Consider the following outcome. Firm C chooses suﬃciently high α1 that is not accepted by
24This corresponds to the case in Chen et al. (2020) where consumers are active in identity management, except
one key diﬀerence that we consider product personalization while Chen et al. (2020) consider only personalized
pricing for the standard product. Product personalization generates an extra value ω + x for consumer x but thestandard product does not. Thus in Chen et al. (2020), the firm cannot use a mix of personalized prices anduniform price (on the equilibrium path), but it is possible in our case.

29

any non-targeted consumers. For example, α1 > vA is suﬃcient for this. In response, firm A2chooses the maximum uniform price to serve all non-targeted consumers, i.e., α2 = vA − (1 − x̃).
Given α2 , firm C can extract full surplus from each one of its targeted consumers by choosing
personalized price pC (x) = vA + ω, which is accepted by consumer x as she would be worse oﬀ
by choosing either α1 or α2 . We call this a collusive outcome since it is supported by firm C’s
choice of a collusive uniform price, which allows firm A2 to extract the maximum surplus fromall non-targeted consumers and firm C to extract full surplus from its targeted consumers.25
The possibility of the collusive outcome makes firm C more aggressive in market B thanwhen search discrimination is allowed. This hurts firm B2 but benefits consumers in market B.
In addition, firm C’s personalized price in the collusive outcome increases in ω and vA . Thisimplies that firm C is likely to monopolize both markets when ω or vA is large enough. In thiscase, firm C can exercise perfect price discrimination in market A, which is in contrast to themonopolization equilibrium when search discrimination is allowed.26 Thus firm C’s monopolization of market B, hence market A, is also more likely than when search discrimination isallowed in the sense that monopolization obtains for a larger set of values for (ω, vA ).
To summarize, prohibiting search discrimination can be used as a collusive device, which
benefits firm C, and firm A2 as well insofar as it remains active in the market. But it reduces
total consumer surplus in market A. In market B, total consumer surplus (weakly) increases
thanks to intensified competition, which in turn hurts firm B2 . Finally, prohibiting search discrimination does not mitigate the dynamic trade-oﬀ; on the contrary, it worsens it by rendering
monopolization more likely than when search discrimination is allowed.
Proposition 8 Suppose firm C is not allowed to prevent its targeted consumers from having
access to its standard product oﬀered at a uniform price.
• When vA < 3 and ω < 3 + γ − vA , the collusive equilibrium exists. In market A, firm
C serves [0, x̃] with pC (x) = vA + ω, and firm A2 serves the rest with α2 = vA − (1 − x̃)
where x̃ = (3 − γ + vA + ω)/6. In market B, prices are β1 = (3 − γ − 2vA − 2ω)/3 andβ2 = (3 + γ − vA − ω)/3.
• When vA < 3 and ω ≥ 3 + γ − vA , or when vA ≥ 3, the monopolization equilibrium
exists. Firm C charges pC (x) = vA + ω in market A, and prices in market B are given by
β1 = −1 − γ and β2 = 0.
• Firm C is better oﬀ but firm B2 is worse oﬀ, while firm A2 is better oﬀ as long as it
remains active in the market.
• Total consumer surplus is smaller in market A but larger in market B.
25

Note that firm C’s oﬀ-the-equilibrium price here is restricted to α1 > vA . This is diﬀerent from our discussion
in Section 5.1.2 where firm C’s oﬀ-the-equilibrium price is α1 = 0.
26
In the monopolization without search discrimination, the oﬀ-the-equilibrium prices that satisfy tremblinghand perfection are such that α1 > vA and α2 = vA − (1 − x̃(ε)) where x̃(ε) < 1 follows firm C’s tremble in market
B.

30

• Monopolization is more likely in the sense that monopolization is possible for a larger setof values for (ω, vA ) than when search discrimination is allowed.
Proof. See Online Appendix.
Table 2 shows various types of equilibria with or without search discrimination for diﬀerent
ranges of (ω, vA ). In the table, the first row indicates the range of ω and we note ω ≥ γ ≥ 1 byAssumption 2 and γ + 5/4 > 3 + γ − vA since vA > 2.
Table 2: Equilibria with or without search discrimination(ω, vA )[1, 3 + γ − vA ]vA < 3[]3 + γ − vA , γ + 45
vA < 3Discrimination
No discrimination

Accommodation
Colluision

Accommodation
Monopolization

6.3[

3 + γ − vA , γ + 54
vA ≥ 3
Accommodation
Monopolization]

γ + 5/4 ≤ ωvA ≥ 3
Monopolization
Monopolization

Restriction on below-cost pricing

We have seen in Section 5 that firm C will engage in below-cost pricing in market B with a viewto harvesting a large set of consumer data that can be used in market A. What happens if thecompetition authority bans below-cost pricing? We discuss its implications below.
Given the restriction β1 ≥ 0, the equilibrium with accommodation remains the only possibility. In this equilibrium, firm C chooses β1 = 0 since its total profit increases in its market
share in market B, denoted by x̃. Then, from firm B2 ’s best response, β2 = (1 + γ + β1 )/2, we
obtain firm B2 ’s equilibrium price as β2 = (1 + γ)/2. Given β1 = 0 and β2 = (1 + γ)/2, we
can solve for firm C’s equilibrium market share as x̃ = (3 − γ)/4. Comparing x̃ with x∗ in (13),
we have x∗ > x̃. Thus firm C’s market share decreases when below-cost pricing is not allowed.
Meanwhile, the equilibrium in market A is precisely the same as in the equilibrium with accommodation in Section 5, with the only diﬀerence that x∗ is replaced by x̃, hence α1 = 1 − (4x̃2 )/3,
α2 = 1 − (2x̃2 )/3, and pC (x) = ω + α2 + 1 − x. Consequently, all prices in market A increase
when x̃ decreases due to the ban on below-cost pricing. Thus banning below-cost pricing reduces
consumer surplus in both markets. On the other hand, the ban prevents firm C from monopolizing the market, which can benefit consumers in the long run. This suggests a trade-oﬀ between
short-terms losses from the ban and the long-term gains from preventing monopolization.
Proposition 9 Suppose firm C is not allowed to engage in below-cost pricing.
• Both firms A2 and B2 benefit at the cost of firm C.
• In both markets, all prices increase, hence all consumers are worse oﬀ as a result of theban.
• The ban prevents monopolization so consumers can benefit in the long run compared towhen below-cost pricing is allowed.
31

6.4

Blocking the merger

Merger remedies require continuous and eﬀective monitoring and enforcement to have intended
eﬀects. But this can be a daunting task in complex digital industries, which may leave blocking
the merger as the only alternative. We discuss briefly what happens if the competition authority
blocks the merger altogether. The eﬀects of blocking the merger on profits and consumer surplus
depend on the counterfactual equilibrium that would prevail if the merger were allowed. Basedon the analysis in Section 5 and Proposition 6, we can summarize the eﬀects as follows.
Proposition 10 Suppose the merger is blocked.
• The sum of profits for firms A1 and B1 is smaller than that if the merger were allowed.
• Both firms A2 and B2 earn larger profits than if the merger were allowed.
• In market A, total consumer surplus is smaller if ω ≤ γ + 5/4, and larger if ω > γ + 5/4
than if the merger were allowed.
• In market B, total consumer surplus is smaller in the short run than if the merger wereallowed, but larger in the long run if ω > γ + 5/4 and firm B2 exits the market following
the merger.

7

Conclusion

This paper has studied data-driven tech mergers where data-enabled personalization and theconsumption synergy are two key elements that link the market for data collection and themarket for data application. As our motivating example is Google’s proposed acquisition of
Fitbit, we recapitulate our main findings in that context. In doing so, we choose the two
relevant markets as the market for wearable devices and the digital health market, for which wehave provided justification and evidence.
First, the merger harms stand-alone competitors in both markets. Second, the merger intensifies competition and benefits all consumers in the market for wearable devices. Third, inthe digital health market, the merger increases total consumer surplus when stand-alone competitors continue to remain active, but decreases it when the market is tipped in Google’s favor.
Fourth, market tipping is more likely when the consumption synergy is suﬃciently large, which
can harm consumers in both markets in the long run. Fifth, the presence of a strong competitor
such as Apple in the market for wearable devices generates positive externalities for stand-alone
competitors in the digital health market, making market tipping less likely.
We have also examined the eﬀects of blocking the merger as well as several remedies suchas data sharing, prohibition of search discrimination, and a ban on below-cost pricing. A general conclusion we can draw is that these remedies can reverse short-run eﬀects of the merger
on firms and mitigate the dynamic trade-oﬀ, although short-run eﬀects on consumers vary depending on policies and markets. Needless to say, the eﬀectiveness of merger remedies assumes

32the eﬀectiveness of monitoring and enforcement, which can be a tall order in complex digitalindustries. While not modelled in this paper, allowing consecutive mergers can also mitigate thedynamic trade-oﬀ. For example, if the Google/Fitbit merger is approved, then allowing Apple’s
expansion into the digital health market can have pro-competitive eﬀects.27
Our use of the stylized Hotelling model is mainly for simplicity of analysis. But we think the
economic insight and qualitative results should continue to be valid in a generalized setting withdiscrete choices. But the comparison of consumer surplus depends on our assumption of uniform
distribution, and may not generalize to diﬀerent distributions. Thus empirical studies are neededfor quantitative analysis of consumer welfare in the assessment of the merger. Likewise, empiricalstudies on the size of consumption synergy can help competition authorities in assessing whenthe merger is more or less likely to lead to the significant lessening of competition. Finally, we
have assumed away issues such as adverse selection, moral hazard, and privacy in health care,which we have chosen as the market for data application. Personalization in this market can help
screen consumers and ameliorate adverse selection, although it could amplify privacy concerns.
Competition between firms with asymmetric information and the use of personalization by abetter informed firm may also lead to cream skimming. We leave these issues for future research.

Appendix: Proofs
Proof of Proposition 1
In the main text leading up to Proposition 1, our argument establishes that the outcome statedin Proposition 1 characterizes the only possible equilibrium for each case. This takes care ofuniqueness. So it suﬃces to show that there are no profitable deviations by either firm from theequilibrium outcome characterized in Proposition 1.
First, since firm A2 chooses only a uniform price, it is clear that the equilibrium α2 given
in Proposition 1 is uniquely optimal for firm A2 , hence firm A2 has no incentive for unilateraldeviation. Second, firm C’s choice of personalized prices is subgame-perfect given the equilibrium
α2 , hence there is no reason for deviation when firm A2 does not deviate. Third, firm C’s choiceof α1 is its best response to the equilibrium α2 , hence there is no reason for unilateral deviation.
Finally, Lemma 1 shows that firm C will never use a uniform price to serve targeted consumers.
Putting all these together, we only need to consider a global deviation that includes both theuniform and personalized prices. In what follows, we show that firm C cannot benefit from theglobal deviation.
27

Apple’s ambition in health care is commonly known, as shown by the development of various software
frameworks such as HealthKit, ResearchKit, and CareKit. In 2016, the ResearchKit apps began incorporating genetic data, via a module designed by the consumer genetics company, 23andMe. The Google/Fitbit
merger can increase the likelihood of Apple’s expansion into the healthcare industry. For more details, see
https://www.apple.com/healthcare/. Sharon (2016) provides detailed discussions on Google’s and Apple’s interest in health care.

33

Let us start with the case δA < δ̄. In this case, firm C serves all targeted consumers in[0, δA ] with personalized prices optimally chosen in response to firm A2 ’s equilibrium uniform
price. Insofar as firm C serves all its targeted consumers and firm A2 ’s equilibrium uniform
price remains fixed, no deviation can benefit firm C in its target segment. Then it follows thatthe only possible deviation is in uniform price, but this was ruled out already. So there is no
profitable global deviation.
Next, when δ̄ ≤ δA , firm C concedes some of its targeted consumers in [δ̄, δA ] to its rival.
Since firm C’s personalized price for its marginal consumer δ̄ is equal to c, and its uniform priceis zero, firm C cannot profitably deviate by reducing these prices. The only way it may deviate
is to increase personalized prices and/or the uniform price. But the increase in the uniform
price does not have any eﬀect since firm C does not serve any non-targeted consumers. Then,
as discussed previously, an increase in personalized prices alone cannot be profitable given firm
A2 ’s equilibrium uniform price. Once again, there is no profitable global deviation.

Proof of Proposition 2(i) Comparison of firm A2 ’s profits()2
When δA ≤ 3/4, Π∗A2 = 12 1 − 23 δA < 21 , and the profit is decreasing in δA . When2
3/4 < δA < δ̄, firm A2 ’s profit is Π∗∗
A2 = 3δA − 1 − 2δA , which is decreasing in δA and is less than)((1−ϕA +c)2
1
3
1
∗∗∗
Π∗∗
A2 4 = 8 . Finally, when δA > δ̄, it is straightforward to check ΠA2 = 4(2−ϕA ) < 2 . Thus

firm A2 is worse oﬀ after the merger.
(ii) Comparison of the merged firm’s profits
Recall that firm A1 ’s pre-merger profit is 1/2. First, when δA < 3/4, firm C’s profit is∗
2 + ((2 − 3c)/3) δ + 1/2 + c2 /(2ϕ ) > 1/2.
ΠC = − ((14 − 9ϕA )/18) δAAA∗∗
2 − cδ + c2 /(2ϕ ). It is
When 3/4 ≤ δA < δ̄, firm C’s profit is ΠC = ((2 + ϕA )/2) δA
A
A
∗∗
∗∗
∗∗
easy to see that ΠC increases in δA for δA > 3/4. Thus we have ΠC (δA ) > ΠC (3/4) =1/2 + (16c2 − 24cϕA + 9ϕ2A + 2ϕA )/(32ϕA ). To show Π∗∗C (3/4) > 1/2, it suﬃces to show22
Φ (ϕA ) ≡ 16c − 24cϕA + 9ϕA + 2ϕA > 0. Given Assumption 1-(i), ϕA > 2c, we have Φ′ (ϕA ) > 0.
Thus Φ (ϕA ) > Φ (2c) = 4c + 4c2 > 0.
Finally, when δA ≥ δ̄, firm C’s profit is Π∗∗∗= (3 − c − ϕA )2 /(8(2 − ϕA )) + c2 /(2ϕA ).
C∗∗∗
Diﬀerentiating Π∗∗∗C with respect to ϕA , we can show ∂ΠC /∂ϕA < 0. Moreover, when ϕA = 1,
2
we have Π∗∗∗C = (5c )/8 − c/2 + 1/2 < 1/2 since c ≤ ϕA /2 ≤ 1/2 by Assumption 1-(ii). On
9∗∗∗the other hand, Π∗∗∗C = 16 > 1/2 when ϕA = c = 0. Thus, for a fixed value of c, ΠC > 1/2
when ϕA is small enough, but Π∗∗∗C < 1/2 when ϕA becomes suﬃciently large. Thus there is a
threshold value of ϕA above which Π∗∗∗C < 1/2.
(iii) Comparison of consumer surplus
Before the merger, the total consumer surplus is S0 ≡

∫ 1/2
0

(vA − x − 1)dx +∫1

1/2 (vA − (1 −x) − 1)dx = vA − 5/4. After the merger, targeted consumers receive the same surplus as when
they purchase firm A2 ’s standard product, hence vA − (1 − x) − α2 .
34

First, when δA < 3/4, we have α2∗ = 1 − 23 δA , hence the total consumer surplus after the
∫δ
∫ x̂
∫1
merger is given by S1 ≡ 0 A (vA −(1−x)−α2∗ )dx + δA (vA −x−α1∗ )dx + x̂ (vA − (1 − x) − α2∗ ) dx
2 )/9 > S .
= vA − 5/4 + (4δA
0

Next, when 3/4 ≤ δA < δ̄, we have α2∗∗ = 2δA − 1, so the post-merger consumer surplus is∫δ∫1
S1 = 0 A (vA − (1 − x) − α2∗∗ ) dx + x̂ (vA − (1 − x) − α2∗∗ ) dx = vA − 5/4 + (7/4 − 2δA ) ≥ S0
where the last inequality follows from Assumption 1-(iii) since ϕA ≤ (2 + 4c)/3 implies δ̄ ≤ 7/8.
Finally, when δA > δ̄, we have α2∗∗∗ = (1 − ϕA + c)/2, and the total consumer surplus is∫1
S1 = 0 (vA − (1 − x) − α2∗∗∗ ) dx = vA − 1/2 − (1 − ϕA + c)/2 > vA − 5/4. Thus the merger
increases total consumer surplus in all cases.

Proof of Proposition 3
We will make use of the expressions derived in the proof of Proposition 2. Let us start with firm∗∗∗
A2 ’s profit. Clearly, both Π∗A2 and Π∗∗
A2 are decreasing in δA but independent of ϕA . But ΠA2

is decreasing in ϕA but independent of δA .
Consider next firm C’s profit. When δA < 3/4, Π∗C is concave in δA and reaches maximum
when δA = δ ∗ = (6 − 9c)/(14 − 9ϕA ) where δ ∗ ≤ 3/4 by Assumption 1-(iii). Diﬀerentiating Π∗C
2 − τ 2 )/2 ≥ 0 where the inequality is by Assumption
with respect to ϕA , we have ∂Π∗C /∂ϕA = (δA∗∗
1-(i). When 3/4 ≤ δA < δ̄, one can verify that ∂Π∗∗C /∂δA ≥ 0 and ∂ΠC /∂ϕA ≥ 0. When δA > δ̄,∗∗∗Π∗∗∗C is independent of δA , but one can verify ∂ΠC /∂ϕA ≤ 0.

Finally, consider consumer surplus. When δA < 3/4, the consumer surplus is S1 = vA −2 )/9. Clearly, S increases in δ but is independent of ϕ . When 3/4 ≤ δ < δ̄,(5/4) + (4δA
1AAA

S1 = vA − 2δA + 1/2, which is decreasing in δA but independent of ϕA . When δA > δ̄, S1 =1/2 − (1 − ϕA + c)/2, which is increasing in ϕA but independent of δA .

Proof of Proposition 5
Consider market A first. Given x̂ ≤ x∗ , firm C cannot serve any consumers in [x∗ , 1]. Thus itchooses uniform price α1 = 0, implying x̂ = (1 + α2 )/2. Firm A2 chooses α2 to maximize profit
α2 (1 − x̂) subject to x̂ ≤ x∗ . This leads to α2∗∗ = 2x∗ − 1 with firm A2 serving all in [x∗ , 1],
hence pA (x)∗∗ = 1 + ω + α2∗∗ − x = ω + 2x∗ − x.
Consider now market B. Firm C’s total profit is given by ΠC = β1 x∗ +

∫ x∗
0

p∗∗
A (x) dx =(β1 + ω) x∗ + (3(x∗ )2 )/2. Firm C maximizes ΠC subject to x∗ − 1 ≤ 0. Given β2 , this problem
is equivalent to firm C’s problem of choosing x∗ to maximize ΠC = (1 − γ + β2 − 2x∗ + ω) x∗ +(3(x∗ )2 )/2 subject to x∗ ≤ 1, where we substituted β1 = 1−γ +β2 −2x∗ . Diﬀerentiating ΠC withrespect to x∗ , we obtain ∂ΠC /∂x∗ = ω − γ + β2 + 1 − x∗ ≥ 0 since ω ≥ γ and β2 ≥ 0. Thus, theconstraint x∗ = 1 must be binding. This leads to β1∗∗ = −1−γ, β2∗∗ = 0, x∗ = 1. Then we have
∫ 1 ∗∗∗∗p∗∗
A (x) = 2 + ω − x, so the resulting profit is ΠC = (−1 − γ) + 0 pA (x)dx = (1 + 2ω − 2γ)/2 > 1
since ω > 5/4 + γ. Thus the merger is profitable.
We now check possible deviations. Clearly there is no profitable deviation for firm B2 .

35

Thus the only meaningful deviation is for firm C to increase its price. First, suppose firm C
deviates to β1d > β1∗∗ , which leads to x̂ ≤ x̃d < 1. But, as we have already shown above,
β1∗∗ is the best response to β2∗∗ when x̂ ≤ x̃d . So such a deviation cannot be profitable. It
remains to check if there is a profitable deviation β1d that leads to x̃d < x̂. Following thedeviation, competition in market A leads to α1 = 1 − (4x̃d )/3, α2 = 1 − (2x̃d )/3, and x̂ =1/2 + x̃d /3. Then x̃d < x̂ is equivalent to x̃d < 3/4. Given firm C’s personalized prices
pdA (x) = 2+ω−x−(2x̃d )/3, firm C chooses β1d to maximize its total profit ΠdC = 1/2−5(x̃d )2 /18+
(2/3 + ω + β1d )x̃d , subject to x̃d < 3/4. Given β2∗∗ = 0, the optimal deviation price can be foundas β1d = (11 − 23γ − 18ω)/41 when ω < γ + 7/4, which implies x̃d = (15 − 9γ + 9ω)/41 < 3/4.
d
Substituting(β1d back to the deviation profit,) we obtain ΠC = (3ω − 3γ + 5)/82. Then we have2
ΠdC − Π∗∗C = 9 (ω − γ) − 52 (ω − γ) + 25 /82 < 0 for γ + 5/4 < ω < γ + 7/4. Thus there is no

profitable deviation. When ω ≥ γ + 7/4, the optimal deviation price is β1d = −γ − 1/2, which
implies x̃d = 3/4. Then the deviation profit is ΠdC = (24ω − 24γ + 15)/32, hence ΠdC − Π∗∗C =−(8ω − 8γ + 1)/32 < 0. Thus there is no profitable deviation either when ω ≥ γ + 7/4.

Proof of Proposition 6
In the main text, we have already explained how profits change after the merger. It remains toshow changes in consumer surplus. For completeness, we provide full comparison of consumer
surplus in both markets.
First, consider the pre-merger equilibrium. In market A, the prices are α1 = α2 = 1 and∫ 1/2
the marginal consumer is at 1/2. The resulting consumer surplus is CSA = 0 (vA − x −∫11)dx + 1/2 (vA − (1 − x) − 1)dx = vA − 5/4. In market B, the prices are β1 = 1 − γ/3 andβ2 = 1 + γ/3 and the marginal consumer is at 1/2 − γ/6. The resulting consumer surplus is∫1∫ 1/2−γ/6(vB − x − β1 )dx + 1/2−γ/6 (vB + γ − (1 − x) − β2 ) dx = vB + γ/2 + γ 2 /36 − 5/4.
CSB = 0
Second, consider the equilibrium with accommodation after the merger. In market A, givenx∗ , the prices are p∗A (x) = 2 + ω − x − 2x∗ /3, α1 = 1 − 4x∗ /3, and α2 = 1 − 2x∗ /3, with themarginal consumer x̂ = 1/2 + x∗ /3. In market B, the prices are β1 = (45 − 23γ − 36ω)/59 andβ2 = (52 + 18γ − 18ω)/59 and the marginal consumer x∗ = (33 + 9ω − 9γ)/59. Thus we have
∫ ∗
∫
∫
∗
M A = x (v + ω − p∗ (x))dx + 1/2+x /3 (v − x − α )dx + 1
CSA
1
A
A
A
1/2+x∗ /3 (vA − (1 − x) − α2 )dx =
x∗
0
∫
∫
∗
1
x
MA =
vA − 5/4 + 4(x∗ )2 /9 and CSB
0 (vB − x − β1 )dx + x∗ (vB + γ − (1 − x) − β2 )dx =2vB − 5/4 − (5γ )/36 + (21 + 54ω + 5γ)(1083 + 54ω + 241γ)/125316 + γ(26 − 9ω + 9γ)/59 where
the superscript ‘MA’ denotes ‘merger accommodation’.
Third, consider the monopolization equilibrium after the merger. In market A, the prices arep∗A (x) = 2 + ω − x for all x ∈ [0, 1]. In market B, the prices are β1 = −1 − γ and β2 = 0. Thus we∫∫
M M = 1 (v + ω − p∗ (x))dx = v − 3/2 and CS M M = 1 (v − x − β )dx = v − 5/4 −have CSA
1
A
A
B
B
A
B
0
0
(5γ 2 )/36 + (3 + γ)(21 + 5γ)/36 where the superscript ‘MM’ denotes ‘merger monopolization’.
M M ≤ CS ≤ CS M A and CS ≤ CS M A , CS M M .
From the above, it follows CSA
A
B
A
B
B

36

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39

Figure 1: Equilibrium Prices under Personalization

Figure 2: Prices in the Equilibrium with Accommodation

Online Appendix for Data-Driven Mergers and Personalization
1. Proof of Proposition 7
Let [0, x̃] denote firm C’s target segment, and x̂ the marginal consumer in market A whencompetition is in uniform price. Given data sharing, Bertrand competition for each x ∈ [0, x̃]leads to pA2 (x) = 0, whence pC (x) = ω. Clearly pC (x) = ω < pA (x) = 2 + ω − x − (2x∗ )/3,
the latter being firm C’s personalized price without data sharing. So all targeted consumers
benefit from data sharing. For non-targeted consumers, we need to consider diﬀerent types of
equilibria.
(i) Equilibrium when x̃ < x̂ < 1
In this case, competition in uniform price in the segment [x̃, x̂] is identical to the case without
data sharing. Thus we have α1⋆ = 1 − (4x̃)/3, α2⋆ = 1 − (2x̃)/3, and x̂ = 1/2 + x̃/3. As before,
we need α1⋆ ≥ 0, hence x̃ ≤ 3/4.
Firm C’s optimization problem in market B is to choose β1 to maximize its total profit
)(
(
)
1 x̃
4x̃
ΠC = β1 x̃ +pC (x)dx + 1 −+ − x̃
3
2 3
0
[
]
(
)
10 2 1 4
1
2
1
4
1
2
= − β1 +− ω + (1 − γ + β2 ) β1 + (1 − γ + β2 ) +ω−(1 − γ + β2 ) + .
36
2 3
9
9
2
3
2
∫ x̃

Firm B2 chooses β2 to maximize its ΠB2 = β2 (1 − x̃). Solving the two firms’ best response
problems simultaneously, we obtain the equilibrium uniform prices and the marginal consumer
in market B asβ1⋆ =27 − 18ω − γ
23 − 9ω + 9γ
15 + 9ω − 9γ
, β2⋆ =, x̃ =.
19
19
38

Substituting x̃ into α1⋆ , α2⋆ , and x̂, we obtainα1⋆ =9 − 6ω + 6γ
14 − 3ω + 3γ
72 + 9ω − 9γ
, α2⋆ =, x̂ =.
19
19
114

The condition x̃ ≤ 3/4 is equivalent to ω ≤ γ + 3/2. This equilibrium, to be called theequilibrium with accommodation I, corresponds to the equilibrium with accommodation in theabsence of data sharing. Recall that the equilibrium with accommodation is possible whenω ≤ γ + 5/4. Thus the set of ω that admits the equilibrium with accommodation I is larger. Put
diﬀerently, the value of ω that induces the monopolization equilibrium in the absence of data
sharing can lead to the equilibrium with accommodation I given data sharing. This implies thatdata sharing makes monopolization more diﬃcult.
We compare the above with case without data sharing. The above equilibrium is possible
when ω ≤ γ + 3/2. Since the same range of ω admits both types of equilibria without data
sharing, we make comparison in two separate cases.

1Comparing the above with the equilibrium with accommodation, it is easy to verify β1⋆ > β1∗ ,β2⋆ > β2∗ , α1⋆ > α1∗ , α2⋆ > α2∗ , and x̃ < x∗ . Thus data sharing softens competition in uniform
price in both markets, hurting all consumers in market B and all non-targeted consumers inmarket A. On the other hand, it benefits firm C’s competitors in both markets due to thesoftened competition and smaller market share firm C can obtain. Finally, competition fortargeted consumers intensifies given data sharing. Put together, we conclude that data sharing
unambiguously hurts firm C.
(ii) Equilibrium when x̂ ≤ x̃ ≤ 1
Consider market A first. In this case, firm C cannot serve any non-targeted consumers,
implying α1 = 0. This leads to x̂ = (1 + α2 )/2, and firm A2 serves all [x̃, 1] with α2 = 2x̃ − 1.
Then in market B, firm C chooses β1 to maximize∫ x̃ΠC = β1 x̃ +pC (x) dx = (β1 + ω) x̃.
0subject to x̃ − 1 ≤ 0, while firm B2 chooses β2 to maximize ΠB2 = β2 (1 − x̃). This leads to thefollowing two cases depending on whether the constraint x̃ − 1 ≤ 0 is binding.
Case 1: γ + 32 ≤ ω < γ + 3
In this case, the equilibrium prices and the marginal consumer in market B are given byβ1⋆⋆ =

3 − 2ω − γ
3−ω+γ
ω−γ+3
, β2⋆⋆ =, x̃ =.
3
3
6

Since x̃ = (ω − γ + 3)/6 < 1, monopolization does not arise in this equilibrium, to be called
the equilibrium with accommodation II. Then α2⋆⋆ = 2x̃ − 1 = (ω − γ)/3 < 1. For the samerange of ω, no data sharing leads to the monopolization equilibrium. Thus it follows that all
consumers in market B are worse oﬀ when data sharing is in place. In market A, consumer x
pays pA (x) = 2 + ω − x without data sharing. Then it is easy to see that all consumers pay
less in market A after data sharing. Needless to say, data sharing benefits both stand-alone
competitors at the cost of firm C.
Case 2: ω ≥ γ + 3
In this case, the equilibrium uniform prices in market B are
β1⋆⋆⋆ = −1 − γ, β2⋆⋆⋆ = 0.
Thus this equilibrium also features monopolization as in the case without data sharing. The
only diﬀerence is that consumers in market A now pay personalized prices pC (x) = ω, insteadof pA (x) = 2 + ω − x. Thus consumers in market A are better oﬀ given data sharing.
In the main text, we have already established that data sharing hurts firm C, benefits bothcompetitors, increases total consumer surplus in market A if ω ≥ γ + 5/4, decreases total
2

consumer surplus in market B in all equilibria, and leads to the monopolization equilibrium forlarger values of ω than without data sharing. Thus it only remains to show that total consumer
surplus in market A with data sharing is larger than that without data sharing when ω ≤ γ +5/4.
When there is no data sharing, total consumer surplus in market A in the equilibrium withaccommodation was already calculated in the proof of Proposition 6 as
∫ x∗
MA
CSA

=

(vA + ω − p∗A (x))dx +0= vA −∫ 1/2+x∗ /3x∗(vA − x − α1 )dx +∫ 1
1/2+x∗ /3(vA − (1 − x) − α2 )dx

5 4(x∗ )2+,
4
9

where x∗ = (33 + 9ω − 9γ)/59. With data sharing, total consumer surplus in market A in theequilibrium with accommodation I can be calculated as
M DI
CSA
≡

∫ x̃

(vA + ω − pC (x))dx +

0

∫ x̂

(vA − x − α1⋆ )dx +

x̃

∫ 1

(vA − (1 − x) − α2⋆ )dx

x̂

13
5
=vA − (x̃)2 + 2x̃ − ,184where x̃ = (15 + 9ω − 9γ)/38. Comparing the two, we have
M DI
MA
CSA
− CSA
=

1
4
(5 + 3ω − 3γ)(391 − 39ω + 39γ) −2 × 3829(

33 + 9ω − 9γ
59

)2
.

M DI > CS M A . Thus total consumer surplus is larger in all
Using ω ≤ γ + 5/4, we can verify CSA
Aequilibria with data sharing.

2. Proof of Proposition 8
1. Analysis of market A
We start with market A. With prohibition on search discrimination, firm C’s personalized
prices are constrained by its own uniform price if it serves any non-targeted consumer; otherwise,
it is constrained by firm A2 ’s uniform price, as before. Denote the personalized price for targeted
consumer x in the first case by pC (x), and that in the second case by pA (x). Then we havepA (x) = min{ω + α2 + 1 − x, vA + ω},
pC (x) = min{ω + α1 + x, vA + ω}.
Let [0, x̃] be firm C’s target segment in market A and x̂ be the marginal consumer when competition is in uniform price, hence x̂ = (1 − α1 + α2 )/2. Note that firm C can serves all its targeted
consumers thanks to Assumption 2-(ii). We divide analysis into two cases based on the relative
locations of x̂ and x̃.
(i) x̃ ≥ x̂3

In this case, firm C can serve all consumers in [0, x̃] with personalized prices while firm A2serves the rest. Unlike the case with search discrimination, firm C’s uniform price in [x̃, 1] cannot
be α1 = 0 since, then, all targeted consumers will also choose firm C’s standard product. Thus,
when firm C does not serve any non-targeted consumers, it sets α1 suﬃciently high (α1 > vA ,to be exact) so that it is not accepted by any consumers, both targeted and non-targeted. Thenfirm A2 ’s profit is ΠA2 = α2 (1 − x̃). Firm A2 chooses its uniform price to extract maximum
surplus from the segment [x̃, 1], leading to α2∗ = vA − (1 − x̃) and x̂ = (vA + x̃ − α1 )/2. Given
α2∗ = vA − (1 − x̃), firm C’s personalized prices are given by pA (x) = vA + ω. Thus firm
C can extract full consumer surplus from each of its targeted consumers. Thus profits are∗ = (v + ω)x̃ and Π∗ = (v − (1 − x̃))(1 − x̃). Here we use lower-case π for firm C’s profit
πC
A
A
A2

in market A, to distinguish it from firm C total profit ΠC .
For the above to be an equilibrium outcome, we need to check conditions that guarantee no
profitable deviations exist. Clearly, firm A2 does not have incentives to deviate from the above.
Then the only meaningful deviation is for firm C to cut its uniform price to α1d that leads tox̂d > x̃, charge pC (x)d = ω + α1d + x for all consumers in [0, x̃], and charge α1d for consumers in[x̃, x̂d ]. Firm C’s profit from this deviation is
∫ x̃
d
πC
=
0

1
pC (x)d dx + α1d (x̂d − x̃) = x̃2 + ωx̃ + α1d2(vA + x̃ − α1d2).

d < π ∗ , if and
One can show that the deviation profit is lower than the equilibrium profit, i.e., πC
C

only if 1 vA ,√x̃ ≥vA − 1 − v 2 − 4vA + 5,A5

if vA < 10
3 ,

(8.1)

if vA ≥ 10
3 .

We omit the derivation of (8.1) since it is long and tedious, but it is available upon request.
In sum, given (8.1), there can be a collusive outcome in market A in which firm C extracts
full surplus from each of its targeted consumers by charging pA (x) = vA + ω, and firm A2 serves[x̃, 1] with uniform price α2∗ = vA − (1 − x̃) which leaves consumer x̃ zero surplus. This outcome
is supported by firm C’s choice of a high enough uniform price (α1 > vA ) that is not acceptedon the equilibrium path.
(ii) x̃ < x̂
In this case, firm C can serve some non-targeted consumers in [x̃, x̂] through Hotellingcompetition, hence its personalized prices are constrained by its own uniform price. That is,
firm C charges pC (x) for consumers in [0, x̃] and α1 for consumers in [x̃, 1]. This leads to firm
C’s profit
∫ x̃
πC =
0

1
pC (x)dx + α1 (x̂ − x̃) = x̃2 + ωx̃ + α124(

1 − α1 + α22).

Then firm C’s best response is α1 = (1 + α2 )/2. Firm A2 ’s profit is ΠA2 = α2 (1 − x̂) =α2 (1 + α1 − α2 )/2, hence its best response is α2 = (1 + α1 )/2. This gives us equilibrium prices,∗∗ = x̃2 /2 + ωx̃ + 1/2
α1∗∗ = α2∗∗ = 1, pC (x) = ω + 1 + x, hence x̂∗∗ = 1/2. Then profits are πCand Π∗∗
A2 = 1/2. Since this equilibrium is possible when x̃ < x̂, we need x̃ < 1/2.
Next, we derive conditions that ensure there are no profitable deviations. Once again, firm
A2 has no reason to deviate. Nor can firm C profitably decrease its uniform price. The only
possible deviation is for firm C to increase its uniform price and serve only targeted consumers
with personalized prices pA (x) = ω + 2 − x > pC (x) = ω + 1 + x for all x ≤ x̃ < 1/2. Firm C’s
profit from the deviation is
∫ x̃
d
πC
=

1
(2 + ω − x)dx = (2 + ω)x̃ − x̃2 .
20d − π ∗∗ = −x̃2 + 2x̃ − 1/2. Thus the deviation is not profitable if and only if
Note that πC
C

√
2− 2
x̃ <
.
2

(8.2)

In sum, given (8.2), there is a partial Hotelling outcome in market A in which firm C serves
all of its targeted consumers charging pC (x) = ω+1+x, additional consumers in [x̃, 1/2] charging
uniform price α1∗∗ = 1, and firm A2 serves consumers in [1/2, 1] with uniform price α2∗∗ = 1.
Before moving onto the analysis of market B, we note that we have not fully solved the gamein market A. We have only characterized possible equilibrium outcomes under conditions (8.1)
and (8.2). We are agnostic about other possible outcomes when these conditions are not met.
2. Analysis of market B
In market B, x̃ is given by x̃ = (1 − β1 + β2 − γ)/2. When market A has the collusive
outcome, firm C’s total profit is ΠC = (ω + vA + β1 )x̃. Substituting β1 from x̃, we haveΠC = (ω+vA +1−γ +β2 −2x̃)x̃. Then an interior optimal value of x̃ is x̃ = (ω+vA +1−γ +β2 )/4.
Since β2 ≥ 0 and ω ≥ γ, it follows that x̃ ≥ 1 if vA ≥ 3. That is, vA ≥ 3 is a suﬃcient condition
for monopolization by firm C. Based on this and our analysis in market A, we now consider thefollowing three cases.
(i) vA < 3
Then from (8.1), firm C’s profit when market A has a collusive outcome is(ΠC = β1 x̃ + (vA + ω)x̃ = (β1 + vA + ω)

1 − γ + β2 − β12).

Firm C maximizes the above profit subject to vA /5 ≤ x̃ ≤ 1. Firm B2 ’s profit is ΠB2 =5

β2 (1 − x̃) = β2 (1 + γ − β2 + β1 )/2. When ω < 3 + γ − vA , the equilibrium prices in market B areβ1∗ =3 − γ − 2vA − 2ω
3 + γ − vA − ω, β2∗ =
.
3
3

(8.3)

This leads to the marginal consumer x̃∗ = (3 − γ + vA + ω)/6, which satisfies vA /5 ≤ x̃ ≤ 1
given ω < 3 + γ − vA . We call this the collusive equilibrium, as it leads to the collusive outcome
in market A.
When ω ≥ 3 + γ − vA , the equilibrium prices in market B are
β1∗ = −1 − γ, β2∗ = 0.

(8.4)

Then the marginal consumer is x̃∗ = 1. We call this the monopolization equilibrium, as itleads to the monopolization of market A. Note that this equilibrium is diﬀerent from themonopolization equilibrium in Section 5, where firm C cannot extract full consumer surplus
because oﬀ-the-equilibrium uniform prices in market A that satisfy trembling-hand perfection
are α1 = 0, α2 = 2x̃−1 for x̃ < 1. In the current monopolization equilibrium, oﬀ-the-equilibrium
uniform prices in market A are given by α1 > vA and α2 = vA − (1 − x̃) for x̃ < 1. This allows
firm C to extract full consumer surplus in market A.
(ii) vA ≥ 3
As we have seen above, this case admits only the monopolization equilibrium.
(iii) Partial Hotelling outcome in market A when x̃ < x̂
We now show that there cannot be an equilibrium in which market A has a partial Hotellingoutcome. In this case, firm C chooses β1 to maximize its total profit
11ΠC = β1 x̃ + x̃2 + ωx̃ +
2
2
(
)
3
1
1
1 − γ + β2
1
= − β12 + (1 − γ + β2 − 2ω)β1 + (1 − γ + β2 )2 + ω
+ ,
8
4
8
2
2
subject to x̃ < (2 −√2)/2. As before, firm B2 ’s profit is ΠB2 = β2 (1 − x̃), leading to the best

response β2 = (1 + γ + β1 )/2. Then the equilibrium prices in market B are√√
β1∗∗ = 2 2 − 1 − γ, β2∗∗ = 2,√

and the marginal consumer is x̃∗∗ = 2−2 2 < x̂∗∗ = 12 . Firm C’s profit in this case is
(
(
√ )2
√
√ )
1
2− 2 1 2− 2
2− 2
+
+
+ω
ΠC = (2 2 − 1 − γ)
2
2
2
2
2
√
√
7 2− 2=2 2− +
(ω − γ).
4
2
√

6

(8.5)

But given β2∗∗ =√2, firm C has incentives to deviate to a lower price that leads to the casewhere x̃d > x̂d so that the collusive outcome obtains in market A. This deviation gives firm
C much higher profit in market A than the partial Hotelling outcome, which more than oﬀsets
the loss from the deviation in market B. That is, firm C has a profitable deviation, and hence
the partial Hotelling outcome in market A cannot be sustained in equilibrium. The detailed
analysis is quite long, hence omitted, but is available upon request.
Putting together the results we have obtained so far, we have
Lemma A. (i) When vA < 3 and ω < 3 + γ − vA , there exists a collusive equilibrium in which
equilibrium prices in market B are β1∗ = (3−γ −2vA −2ω)/3 < 0 and β2∗ = (3+γ −vA −ω)/3 > 0with the marginal consumer given by x̃∗ = (3 − γ + vA + ω)/6 ∈ (vA /5, 1). In market A, firm C
extracts full surplus from each of its targeted consumers by charging pA (x) = vA + ω, and firm
A2 serves [x̃∗ , 1] with uniform price α2∗ = vA − (1 − x̃) which leaves consumer x̃ zero surplus.
This outcome is supported by firm C’s choice of a high enough uniform price (α1 > vA ) that is
not accepted on the equilibrium path. Firms’ total profits are(3 − γ + vA + ω)2,18(3 + γ − vA − ω)2Π∗B2 = β2∗ (1 − x̃∗ ) =,18

Π∗C = (β1∗ + vA + ω)x̃∗ =Π∗A2 = α2∗ (1 − x̃∗ ) = (vA − (1 − x̃∗ ))(1 − x̃∗ ) =(7vA − 3 − γ + ω)(3 − γ + vA + ω).
36(ii) When vA ≥ 3, or vA < 3 and ω ≥ 3 + γ − vA , there exists the monopolization equilibrium
arises in which prices in market B are given by β1∗ = −1 − γ and β2∗ = 0. In market A, firm C
charges pA (x) = vA + ω to extract full surplus from all consumers. Thus firm C’s total profit isΠ∗C = vA + ω − 1 − γ.
3. Welfare implications
Using Lemma A, Propositions 4 and 5, we can derive the following welfare implications of
the prohibition on search discrimination. Note that, when search discrimination is allowed,
there are two possible equilibria: the equilibrium with accommodation when ω ≤ γ + 5/4 andthe monopolization equilibrium when ω > γ + 5/4. Note also that firm C’s market share in
the collusive equilibrium is larger than that in the equilibrium with accommodation: x̃∗ =(3 − γ + vA + ω)/6 > 5/6 > x∗ = (33 + 9ω − 9γ)/59.
First, firm C benefits from the prohibition on search discrimination. Clearly, its profit
is larger in the collusive equilibrium than in the equilibrium with accommodation. Also its
profit is larger in the monopolization equilibrium when search discrimination is prohibited.
Note that monopolization is supported by a wider range of γ when search discrimination isprohibited: with search discrimination, monopolization arises when ω > γ + 5/4; without search
discrimination, monopolization arises for any value of ω when vA ≥ 3 and, when vA < 3, it arises
7

for ω ∈ [3 + γ − vA , 5/4 + γ]. It follows that firm C is better oﬀ when search discrimination is
not allowed.
Second, firm B2 is worse oﬀ unambiguously. Comparing the equilibrium with accommodationand the collusive equilibrium, firm B2 ’s market share is smaller in the latter. Moreover, pricesin (8.3) are lower than those in the equilibrium with accommodation. In addition, as argued
previously, monopolization is supported by a wider range of γ when search discrimination isprohibited.
Third, firm A2 ’s profit is higher in the collusive equilibrium than in the equilibrium withaccommodation thanks to the higher uniform price α2∗ despite the smaller market share, x̃∗ . On
the other hand, monopolization can kick in for lower values of ω when search discrimination is
not allowed. Thus firm A2 is better oﬀ only if it remains active in the market.
Fourth, total consumer surplus in market A is unambiguously smaller than when search
discrimination is allowed. This follows since, when search discrimination is not allowed, targeted
consumers have zero surplus in both equilibria while non-targeted consumers end up paying
higher uniform prices in the collusive equilibrium than in the equilibrium with accommodationthat would arise with search discrimination.
Finally, total consumer surplus in market B depends on diﬀerent pairs of equilibria with orwithout search discrimination. We consider three cases. (i) If vA ≥ 3, then we have the monopolization equilibrium without search discrimination. When search discrimination is allowed, we
have the equilibrium with accommodation if ω ≤ γ + 5/4. In this case, direct comparison showsthat total consumer surplus is larger when search discrimination is prohibited. When search
discrimination is allowed, we have the monopolization equilibrium if ω > γ + 5/4, in which casethe total consumer surplus is the same. (ii) If 2 < vA < 3, there are three cases to consider.
When ω < 3 + γ − vA , we have the collusive equilibrium without search discrimination and theequilibrium with accommodation with search discrimination. Note that prices in (8.3) are lower
than those in the equilibrium with accommodation. So even though some consumers shift fromfirm B2 to firm C without search discrimination, the price eﬀect dominates. As a result, total
consumer surplus is larger when search discrimination is prohibited. The same is true when3 + γ − vA ≤ ω < γ + 5/4. When ω > γ + 5/4, the monopolization equilibrium arises in bothcases, hence total consumer surplus is the same.

3. Google’s Ambition in Health Care
Google and its parent company Alphabet have made significant investments in life sciences andhealth care. Alphabet started two independent subsidiaries in these areas: Verily was foundedin 2015 with focus on research in life sciences; Calico was founded in 2013 with focus on health,well-being, and longevity. Alphabet’s venture capital arm, GV, invested $21 billion or 36% of its
funds in health care and life sciences in 2014, up from 9% in 2012 and 2013.28 Since its founding28

https://money.cnn.com/2014/12/16/smallbusiness/google-ventures-funding/index.html

8

in 2009, GV has invested in nearly 60 life sciences companies.29 In 2018, Google re-established
Google Health as an integrated health department, reporting to Google AI. Google’s $2.1 billion
bid for Fitbit is in continuation of this strategic direction. Sundar Pichai, the CEO of Alphabet
and Google, said health care oﬀers the biggest potential for Alphabet to use artificial intelligenceto improve outcomes over the next five to ten years.30
Google Health
Google’s interests in health care date back to 2006, when it started a repository of health records
and data. Google Health, back then, aimed to link doctors and hospitals and help consumers
aggregate their medical data.31 But the early experiments failed and Google terminated the“Google Health” product in 2012. Google’s new health service projects were re-organized in2018, under the lead of David Feinberg, the former CEO of Geisinger Health System. Under
Feinberg, a major task of Google Health is to develop a specific search engine for medical records
and improve the quality of health-related search results.32
Project Nightingale and Google’s access to health data
Project Nightingale is Google’s attempt to gain a foothold in the healthcare industry on alarge scale.33 It is a joint project secretly initiated in 2018 by Google Cloud and Ascension,
one of the largest private healthcare systems in the U.S. The two companies signed the Health
Insurance Portability and Accountability Act (HIPAA) business associate agreement, underwhich Ascension would transfer patient data to Google Cloud, and Google would be barred fromusing this data for purposes other than providing services to Ascension. The data sharing would
allow Google access to almost complete electronic health records on millions of Americans.34 The
partnership is currently under investigation by the Department of Health and Human Services
for its implications for patient privacy under the HIPAA.
In September 2019, Google announced a ten-year deal with Mayo Clinic to store the hospitalsystem’s genetic, medical and financial records.35 In 2019, Google also made a generous proposal
to Cerner Corp, a health-data company, for a storage of 250 million health records, although
Cerner eventually chose Amazon. According to a report in The Wall Street Journal, Google has
29https://www.cnbc.com/2018/03/30/alphabet-gv-life-sciences-and-health-investments-going-public.html

30

https://www.cnbc.com/2020/02/11/google-health-has-more-than-500-employees.html

31

https://www.cnbc.com/2020/02/11/google-health-has-more-than-500-employees.html

32

https://www.cnbc.com/2019/11/02/google-healths-david-feinberg-focus-on-search-for-doctorsconsumers.html
33

https://en.wikipedia.org/wiki/Project Nightingale

34

https://www.wsj.com/articles/google-s-secret-project-nightingale-gathers-personal-health-data-on-millionsof-americans-11573496790
35
https://www.wsj.com/articles/google-s-secret-project-nightingale-gathers-personal-health-data-on-millionsof-americans-11573496790

9struck partnerships with some of the largest hospital systems and most-renowned healthcare
providers in the U.S., and it is able to view or analyze tens of millions of patient records in atleast three-quarters of the U.S. states.36
Google/Fitbit merger
The global market for wearable devices was worth $23 billion in 2018, and is projected to
grow to $54 billion by 2023 (“Wearable Technology in Healthcare, August 2019, GlobalData).37
According to a Gallup poll in 2019, about one in three Americans report at some point having
worn a fitness tracker such as a Fitbit or smartwatch (34%) or having tracked their healthstatistics on a phone or tablet app (32%).38 The growing adoption of mobile platforms, increasing
adoption of AI and 5G, and the growing awareness and preference for home health care is
expected to boost the growth of the market.39 While wearable technologies have been employedin various fields, they have the greatest potential in healthcare field. Combined with AI andmachine learning, the market for wearable technologies is becoming more personalized anddisease-specific (“Wearable Technology in Healthcare, August 2019, GlobalData).
Fitbit was founded in 2007 and filed an IPO in 2015. If oﬀers a suite of fitness trackers,
smartwatches, and wristbands. Fitbit’s revenue in 2019 was $1.42 billion with profit $234 million.
Google’s $2.1 billion bid for Fitbit is under regulatory probe in multiple jurisdictions at the timeof writing this article. If successful, the acquisition will enhance Google’s ability to produce
wearable devices and enable Google to have access to personal health tracking data of around30 million Fitbit users.40
According to the IDC Worldwide Quarterly Wearable Device Tracker, Fitbit’s global market
share in wearable devices market was 4.7% in 2019, down from 7.8% in 2018.41 Although Google
will be initially a minor player in the fitness-tracker/wearable device market after the acquisitionof Fitbit, “the concern is Google would use this data to help reinforce its dominance in othersegments,” said Maurice Stucke, an antitrust law professor at the University of Tennessee, aconcern shared by the European Competition Commission.42
An ostensible reason for Google’s bid for Fitbit is Google’s intention to gain a toehold in the36

https://www.wsj.com/articles/paging-dr-google-how-the-tech-giant-is-laying-claim-to-health-data11578719700
37
Wearable devices include earwear, basic watch, smartwatch, wristband, clothing and others. According to
IDC (https://www.idc.com/promo/wearablevendor), smartwatch accounts for 20% to 30% of the market, while
wristband has around 22% to 30% of the market share.
38

https://news.gallup.com/poll/269096/one-five-adults-health-apps-wearable-trackers.aspx

39

https://www.marketsandmarkets.com/Market-Reports/wearable-medical-device-market-81753973.html

40

https://www.bloomberg.com/news/articles/2020-02-10/google-fitbit-deal-poses-test-for-merger-cops-eyeingdata-giants
41

https://www.idc.com/getdoc.jsp?containerId=prUS46122120

42

https://www.bloomberg.com/news/articles/2020-02-10/google-fitbit-deal-poses-test-for-merger-cops-eyeingdata-giants

10market for wearable devices. But the merger would also allow Google to add sensitive health data
to users’ personal profiles it aggregates from other services, which can then be used to improve
its online advertising. In a bid to allay these concerns raised by antitrust regulators in Australia
and Europe, Rick Osterloh, senior vice president for Google’s devices and services, said the deal
was “about devices, not data”, and that Fitbit data would not be used for Google ads.43 On theother hand, Google will be able to harvest users’ detailed health data 24/7 by selling wearable
devices. Indeed, Fitbit users and the European Commission express concern that the healthdata tracked by Fitbit would be combined with Google’s other data and can be used to exploit
consumers. “This takeover is likely to be a worrying game changer for how consumers’ healthand wellness data is used,” Monique Goyens, the director general of the European Consumer
Organization, said in a statement.44
With Google Health (medical search engine), Google Cloud and Project Nightingale (massive
medical records), Fitbit (wearable devices tracking health data), and Google AI (data analytics),
Google will be in a formidable position to become a major player in the digital health industry.
Although Google has not oﬀered many healthcare products directly in the market, its subsidiary,
Verily, has already begun to venture into health care and insurance, which we discuss below.
Verily’s business in health care and insurance
Verily was established in 2015 as an independent subsidiary of Alphabet with focus on researchin health care and life sciences. In 2017, Verily initiated an ambitious four-year health project,called Project Baseline, to comprehensively study human health around the globe. In doingso, Verily created its own smartwatch, called Study Watch, with electrocardiogram technology
built-in to track participants’ health data. The eventual goal, according to Jessica Mega, Verily’s
chief medical oﬃcer, is to “create a map of human health”.45 Over the past few years, Verily has
been quietly expanding in healthcare and insurance industries leveraging its strength in digital
health technology. The overarching theme for its new business is opportunities in the cross fieldof the health and technology sectors.
Verily has collaborated with various health systems, including Atrius Health, the Palo Alto
Veterans Aﬀairs healthcare system, and other providers on initiatives to tackle major healthchallenges. Verily has also partnered with Blue Cross Blue Shield Association and Walgreensfor diabetes care.46 Its main role in these collaborations is to analyze medical data for datadriven prescriptions. For example, in the cooperation with Atrius, Verily will analyze patient
health information to better detect the interventions that might work for heart failure patients.
43

https://www.nytimes.com/2020/08/04/business/google-fitbit-europe.html

44

https://www.nytimes.com/2020/08/04/business/google-fitbit-europe.html

45

https://www.cnbc.com/2017/04/18/alphabet-verily-project-baseline-longitudinal-health-study.html

46

https://www.fiercehealthcare.com/tech/verily-and-onduo-collaborating-john-hancock-to-oﬀer-life-insurancedisease-management-for11Verily entered the insurance market in 2019 by collaborating with life insurer John Hancock.
The two companies cooperate to oﬀer a life insurance solution and digital wellness programs
to help people with diabetes manage and improve their condition.47 Brooks Tingle, president
and CEO of John Hancock Insurance, said the company saw an opportunity to work with
Google to leverage a personalized approach to disease management and make life insurance
more personalized and engaging.48
In August 2020, Verily and Swiss Re Corporate Solutions, the commercial insurance unitof the Swiss Re Group, established a new subsidiary, called Coeﬃcient Insurance Company,
with a focus on employer stop-loss health insurance, a market valued approximately $20 billion.
Departing from the traditional stop-loss health insurance, the partnership would leverage Verily’s
core strengths integrating hardware, software and data science to provide a data-driven solution
to self-funded employers for more predictable protection and cost control.49 “We’re hoping to
be more personalized in the way we oﬀer health solutions,” said Vivian Lee, Verily’s President of
Health Platforms.50 Once Coeﬃcient Insurance finds its footing, Verily would want to integrate
its suite of health devices in tracking employees’ health to provide tech-driven interventions.
Given the smartwatch Verily already used in its Project Baseline and the pending acquisition of
Fitbit, it is plausible to expect that Verily would be able oﬀer more personalized health insurance
products that utilize health/fitness tracking and data analytics.

4. Big Data and Personalization in Health Care
The global digital health market is estimated to reach $505 billion by 2025, up from $86 billion
in 2018.51 . This is a new battlefield for big-data applications. According to an estimate by the
McKinsey Global Institute, big-data applications could generate up to $100 billion in value annually across the US healthcare system.52 We give a brief review on the trend of personalization
and use of big data in health care.
Data processing has always been the core of insurance business. With more data emerging from digitization, new datasets, including internet of things (IoT) data, online footprints
and mobile devices data, and new data analytics tools (e.g., machine learning and artificial
intelligence) are increasingly incorporated into insurance business. According to the survey of47

https://www.fiercehealthcare.com/payer/alphabet-s-verily-breaks-into-stop-loss-health-insurance-marketbacked-by-swiss-re48

https://www.fiercehealthcare.com/tech/verily-and-onduo-collaborating-john-hancock-to-oﬀer-life-insurancedisease-management-for49
https://www.fiercehealthcare.com/payer/alphabet-s-verily-breaks-into-stop-loss-health-insurance-marketbacked-by-swiss-re50

https://www.cnbc.com/2020/08/25/alphabet-verily-enters-stop-loss-insurance-market.html

51https://www.statista.com/statistics/1092869/global-digital-health-market-size-forecast/

52

https://www.mckinsey.com/industries/pharmaceuticals-and-medical-products/our-insights/how-big-datacan-revolutionize-pharmaceutical-r-and-d

12European Insurance and Occupational Pensions Authority (EIOPA), many insurance companies have developed their own big data analytics (BDA) strategies or have included many BDA
projects in their business plans. Among the 222 insurance companies in the survey, 50 companies already use IoT data and another 75 companies anticipate to use it within the next three
years. A smaller number of health insurers in the survey use wearable devices and smartphone
apps to track their customers’ real-time health information.53
Insurance companies typically pool customers with similar risk profiles, and premiums are
based on the average risk across the pool. The insurer’s ability to distinguish the riskiness of
diﬀerent customers determines the size of the pool. BDA significantly improves the insurer’s
ability to segment customers based on their risk profiles and fine-tune insurance premium accordingly. Out of the 222 insurers that participated in EIOPA’s survey, most of them consider
that BDA has had a biggest impact in the pricing and underwriting stage of the insurance value
chain, and many of them have begun to adopt more sophisticated BDA-driven pricing models
in order to optimize profits.54
Usage-based insurance (UBI) in motor and health insurance are the most common productsthat apply BDA. The UBI products measure a consumer’s behavior and environment to perform
risk assessments, based on which premiums and discount rewards are determined.55 In healthinsurance, Pay-As-You-Live (PAYL) is gaining popularity. It uses wearable devices tracking
the policyholder’s health information such as blood pressure, glucose level, number of steps
walked, calories consumed, etc., and the tracking data is used to perform risk assessments
and determine insurance premium. Under PAYL, policyholders demonstrating healthy lifestyles
receive premium discounts and other types of rewards.
South African insurance company Discovery’s Vitality program is considered the pioneerof personalized wellness program and PAYL product. With the help of wearable devices andsmartphone apps, Vitality creates mini challenges related to shopping for healthy food, sporting
activities, medical checkups, and motivates clients to accomplish these challenges with rewards(e.g., cash-back, discounts) or other types of incentives. The use of connected devices gives
Discovery precious data on people’s lifestyle and health condition.56
A leading insurance company John Hancock employs the wealth of data collected by wearable devices, including Fitbit bands and Apple Watch, to reward their customers with healthy
lifestyle. In April 2015, John Hancock cooperated with Vitality to launch a new PAYL life
53

See EIOPA report ”Big Data Analytics in Motor and Health Insurance: A Thematic Review”, page 12.

54

Figure 11 in EIOPA report ”Big Data Analytics in Motor and Health Insurance: A Thematic Review”.

55

There are two main types of UBI products in motor insurance. The first kind is Pay-As-You-Drive (PAYD)
product in which the premiums are based on the number of kilometers driven by the consumer. The other kind is
Pay-How-You Drive (PHYD) product. The consumer receives a driving score based on his/her driving behavior
and the score directly aﬀects the premium paid by the consumer. In either product, drivers that show safe driving
behavior receive lower premium. The UBI motor insurance, in most cases, requires the tracking data of telematics
devices.
56

https://www.discovery.co.za/vitality/how-vitality-works

13insurance product that oﬀers up to a 15% premium discount to clients who track their healthy
habits and share the information with the company. New clients even get free Fitbit bands orother wearable devices to begin tracking.57 In 2018, John Hancock announced it would stopoﬀering traditional life insurance altogether, and only sell interactive life insurances that track
fitness and health data through wearable devices and smartphones.58 In 2020, John Hancock
further announced it would streamline the life insurance buying experience through cooperation
with Human API, a leading health data platform, oﬀering a simple, digital way consumers canshare access to their electronic health records in real time.59
Similar strategies are adopted by Oscar Health, an insurance technology startup. In August
2014, the company announced that it would begin oﬀering members a free Misfit fitness wearable
plus Amazon gift-card rewards for those who met individualized, algorithmically determined
step-targets. Since discriminatory pricing is illegal under the Patient Protection and Aﬀordable
Care Act 2010 (Obama Care), Mario Schlosser, the co-founder of Oscar, said the investment inwearable devices and clients’ information is for risk reduction. As an another example, Health
IQ, an American insurance startup, rewards clients with healthy lifestyles. The company workwith partners in healthcare, pharmaceuticals and medical devices to collect clients’ current
health condition, health literacy and lifestyle. The clients get personalized pricing discounts up
to 41%.60
In addition to the insurance industry, more personalized products/services are emerging inother health-related industries. The GNS healthcare, a precision medicine company leveraging
artificial intelligence to model individual patients’ response to drug treatment, utilizes a rangeof data streams including the EHR (electronic health record) clinical data, claims data, and lab
results to better match therapeutics or procedures to individual patients. In 2020, GNS unveiled the in silico patient called Gemini, the world’s most accurate computer model of multiple
myeloma disease progression and drug response. Gemini leverages broad datasets of molecular,
genomic, and clinical and include the most common drug types used to treat multiple myeloma.
“We are reaching a tipping point where patient data is becoming rich and multi-layered enoughto power AI models that can help predict patient response at the individual level. [...] a true
step forward in personalizing cancer treatment,” said Dr. Ravi Parikh, an Oncologist at the
University of Pennsylvania.61 The use of big data is becoming more prevalent in personalized
health care at all stages of prevention, diagnosis, and treatment.

57

https://www.the-digital-insurer.com/dia/john-hancock-redefines-life-insurance-with-vitality-program/

58

https://www.reuters.com/article/us-manulife-financi-john-hancock-lifeins/strap-on-the-fitbit-john-hancockto-sell-only-interactive-life-insurance-idUSKCN1LZ1WL
59

https://www.prnewswire.com/news-releases/john-hancock-and-human-api-join-forces-to-transform-the-lifeinsurance-purchase-process-300986166.html
60Everis report “Rethinking Healthcare for 2030” available at http://insurtechnttdata.everis.com/dist/ resources/vlarrosa/insurtech/Insurtech Insight Health Data final compressed.pdf
61https://www.clinicalomics.com/topics/oncology/multiple-myeloma/gns-healthcare/14