ISSN (Print) 0473-453X

Discussion Paper No. 1108

ISSN (Online) 2435-0982

DATA-DRIVEN MERGERSANDPERSONALIZATION
Zhijun Chen
Chongwoo Choe
Jiajia Cong
Noriaki Matsushima

Revised August 2021
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¶
First draft: October 28, 2020
This version: June 22, 2021

Abstract
This paper studies tech mergers that involve a large volume of consumer data. The merger
links the markets for data collection and data application through a consumption synergy.
The merger-specific efficiency gains exist in the market for data application due to the consumption synergy and data-enabled personalization. Prices fall in the market for data collection due to the merged firm’s incentives to expand its outreach in the market for dataapplication. But in the market for data application, prices generally rise as the efficiency gains
are extracted away through personalized pricing, rather than being passed on to consumers.
When the consumption synergy is large enough, the merger can result in monopolization ofboth markets, with further consumer harm when stand-alone competitors exit in the longrun. We discuss policy implications including various merger remedies.
Key words: big data, personalization, tech mergers
JEL Classification: D43, L13, L41, K21∗

We thank the editor, Gary Biglaiser, and two anonymous referees for many valuable comments and suggestions. We are also grateful to Arthur Campbell, Greg Crawford, Jacques Crémer, Doh-Shin Jeon, Bruno Jullien,Paul Heidhues, Vai-Lam Mui, Patrick Rey, Susumu Sato, Greg Taylor, Tommaso Valletti, Chengsi Wang, Xiaojian
Zhao, and the audience at the Economics of Platforms seminar (TSE Digital Center), JEA 2021 Spring Meeting,Monash IO seminar, and Toulouse digital seminar for constructive comments and feedback. We gratefully acknowledge financial support from the Australian Research Council (grant number DP210102015), the Japan Society
for the Promotion of Science (KAKENHI grant numbers JP15H05728, JP17H00984, JP18H00847, JP18K01593,
JP19H01483, JP20H05631), Osaka University for its International Joint Research Promotion Program, and theprogram of the Joint Usage/Research Center for “Behavioral Economics” at the ISER, Osaka University. Cong
would like to acknowledge the financial support from National Natural Science Foundation of China (Project
number 72003035). 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
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 the cases cited above 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). After the first draft of this article wascompleted, the European Commission approved the Google/Fitbit merger on December 17, 2020 subject toconditions that pertain to the use of health data for Google ads, access to the Fitbit Web API, and competition in the market for wearable devices (https://ec.europa.eu/commission/presscorner/detail/en/ip 20 2484).
But similar undertakings were rejected by the Australian Competition and Consumer Commission. Despite the rejection, Google completed the transaction on January 14, 2021 so that the case has become an enforcement investigation of a completed merger (https://www.accc.gov.au/public-registers/mergersregisters/public-informal-merger-reviews/google-llc-proposed-acquisition-of-fitbit-inc). In the US, Google also
completed the transaction even though the case is still under review by the Department of Justice(https://www.bloomberg.com/news/articles/2021-01-14/google-closes-fitbit-deal-amid-ongoing-u-s-doj-review).

1

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 profileand 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. Access to richer sets of data can enable firms to tailor their products in a way that ismore personalized and better targeted for individual consumers. This can improve the quality ofmatching between firms and consumers. It can be also pro-competitive by allowing the merging
parties to enter a new market through data-driven innovation. But the positive feedback loop
discussed previously can harm competition and lead to market tipping. In addition, the flipside of personalization is the firm’s ability to engage in price discrimination and consumer
exploitation. Moreover, merging parties can extend market power to related markets, potentiallyleading to foreclosure and consumer exploitation there. For instance, Google could enter thehealth insurance market with highly personalized products by leveraging Fitbit’s data, massive
medical records Google has access to through Google Cloud and 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 (Choi et 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 and scope,
innovation incentives, incumbency advantage, and so on, are also relevant to non-tech mergers,
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albeit in varying degrees. Our specific focus in this paper is on the role of data since data
plays a uniquely important role in tech mergers. By doing so, we make a number of important
contributions to the growing body of literature on tech mergers reviewed below.
We start by sketching our model. Since Google/Fitbit serves as our motivating example, we
refer to this case whenever relevant. There are two related markets, A for data application suchas the digital health care 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. We consider a merger between a firm in market A, say A1 , and a firmin market B, say B1 , leading to a merged entity, say C. Stand-alone competitors are called A2
in market A and B2 in market B.
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 is called firm C’s target segment, and a consumer
in the target segment, a targeted consumer. By personalization, we refer to firm C’s ability tocharge a personalized price for a tailored product that better matches a targeted consumer’s taste
than the firm’s standard product, with the improved matching value increasing in the firm’s data
analytics quality. For non-targeted consumers, firm C offers the standard product at a uniform
price. Personalization in market B is too costly so we ignore that possibility. For example, inthe market for wearable devices, hardware reconfiguration necessary for personalization can be
too costly to be practicable.6 But the two markets are linked through some complementarity.
We model the linkage by assuming that consumers derive extra benefits from buying firm C’s
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 ecosystem,
which it can leverage to enhance user experience in the digital health sector.
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 extract much of these benefits
by using personalized prices except for those who are sufficiently far away from its locationand 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 consumers 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
outside firm C’s target segment, 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 firm A2 ’s product.
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

On balance, total consumer surplus in market A may increase or decrease depending on the
post-merger equilibrium. In what we call the accommodation equilibrium I, firm A2 remains
active after the merger and firm C serves some non-targeted consumers in addition to all targeted
consumers. This equilibrium arises when the consumption synergy is relatively small. In thiscase, the intensified competition for non-targeted consumers pushes down uniform prices, which
in turn reduces personalized prices. As a result, total consumer surplus increases after themerger. As the consumption synergy increases, firm C expands its target segment because
the larger consumption synergy implies more consumer surplus that can be extracted throughpersonalization. When firm C’s target segment is sufficiently large, firm C serves only targeted
consumers and firm A2 serves the rest of the market. We call this the accommodation equilibrium
II. In this equilibrium, the merger results in a higher uniform price charged by firm A2 mainly
because its market share is smaller than before the merger. The higher uniform price by firm
A2 allows firm C to raise all personalized prices above its pre-merger uniform price. As a result,consumers are worse off. When the consumption synergy is large enough, firm C monopolizes
market A, which we call the monopolization equilibrium. In this case, firm A2 , albeit inactive,
remains in the market, which makes the market contestable.
In market B, the market for data collection, competition intensifies unambiguously because of
firm C’s incentives to expand its target segment in market A. When the consumption synergy islarge enough, firm C chooses 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 in market B caused by below-cost pricing. Firm C’s incentives for below-cost pricing
increase in the consumption synergy, which eventually leads firm C to monopolize market B,
hence market A as well. Yet in both markets, monopolization does not mean immediate abuseof monopoly power by firm C, because the presence of competitors, albeit inactive, makes bothmarkets contestable. As a result, the merger increases total consumer surplus in market B in
the short run. But in the long run when competitors exit following monopolization, consumers
in both markets are worse off than before the merger.
A number of clear welfare implications of data-driven mergers emerge from our analysis.
First, thanks to the competitive edge derived from the consumption synergy and personalization, merging parties are better off at the cost of their stand-alone competitors. Second, inmarket B, consumers gain in the short run because of the intensified competition. Third, inmarket A, changes in consumer surplus depend on different equilibria: consumer surplus increases if firm C serves some non-targeted consumers after the merger, which is possible only
when the consumption synergy is relatively small; otherwise, it decreases. Fourth, the long-run
effect is unambiguously 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 turns into the monopoly equilibrium, making consumers in both markets worse off.
Thus there is a trade-off where potential dynamic costs can outweigh any static benefits.
In view of the above welfare implications, we examine some policy remedies relevant to data4

driven mergers. For example, in clearing the acquisition of Fitbit by Google in December, 2020,
the European Commission mentioned three main remedies that pertain to the use of healthdata for Google Ads, access to the Fitbit Web API, and competition in the market for wearable
devices.7 We discuss the second and third remedies as they are directly relevant to our paper.
First, we consider the case where firm C is compelled to share data with firm A2 . Such data
sharing reduces the value of data to firm C as it allows firm A2 to also use personalization. This
softens competition and hurts consumers in market B, but benefits consumers in market A.
In addition, data sharing makes monopolization less likely, hence mitigates the dynamic tradeoff. Second, we discuss the effect of banning below-cost pricing in market B. In the equilibria
where the ban becomes binding, prices rise and consumer surplus decreases in market B. In
market A, firm C’s target segment contracts after the binding ban. This allows firm A2 to serve
more consumers by charging a lower price, which in turn lowers firm C’s personalized prices,
benefiting consumers in market A. Thus the ban has differing effects on the markets for datacollection and data application, although both firms A2 and B2 are better off at the cost of firm
C. In addition, the ban prevents monopolization, hence also mitigates the dynamic trade-off.
A general conclusion we can draw is that these remedies 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 ofdata 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 datadriven tech mergers. Conventional merger assessments weigh possible costs due to lessening
competition against merger-specific efficiency gains that can be passed on to consumers, which
are often associated with lower prices.8 But lower prices are not a good indicator of consumer
7

https://ec.europa.eu/commission/presscorner/detail/en/ip 20 2484

8See, for example, the symposium on horizontal mergers and antitrust in the Journal of Economic Perspectives,
Fall 1987. The general guidelines for horizontal mergers extend to non-horizontal mergers such as Google/Fitbit
with suitably defined potential competition. For this, see Section 4 of the Department of Justice’s Merger
Guidelines (1984) in the US, Section 5 of the ACCC Merger Guidelines (2008) in Australia, or “Guidelines on
the assessment of non-horizontal mergers under the Council Regulation on the control of concentrations between
undertakings” (2008) in the European Union.

5

benefits in tech mergers because they can be transitory as the firm tries to increase market
penetration through price cuts.9 When the firm gains market dominance in the long run, allprices can rise. In addition, the price decrease is not due to efficiency gains passed on to
consumers; it is due to the merged firm’s incentives to expand data scale that it can leverage inthe market for data application. That is, although prices fall in the market for data collection,
they generally rise in the market for data application where the efficiency gains exist thanks
to the consumption synergy and product personalization. Thus, there is little sense in which
the efficiency gains are passed on to consumers. In sum, even based on the conventional merger
assessment, data-driven mergers do not present a convincing case. The case becomes even weaker
if one considers the dynamic trade-off.
If blocking the merger is not an option for whatever reasons, however, then competition
authorities need to look for policies that can help preserve consumer benefits, albeit temporary,while minimizing long-run consumer harm. The policies we discuss mitigate the dynamic tradeoff, implying that some sacrifice to short-term consumer benefits is inevitable. An alternative is
to allow consecutive mergers that can level the playing field. For instance, Apple’s expansion into
the digital health following the Google/Fitbit merger will have pro-competitive effects without
sacrificing the efficiency gains from data-enabled personalization. Needless to say, the success ofpolicy depends on effective monitoring and enforcement, which can be a daunting task in complex
digital industries. This presents a dilemma to competition authorities: blocking a merger can
prevent long-term harm, while also preventing potential benefits from being realized; approving
a merger 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 price discrimination by introducing a new innovation. The
existing literature considers either pure personalized pricing or perfect product 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 thesize of market segment in which the firm has consumer data, which we call the firm’s datascale. But the data scale alone does not allow the firm to tailor its product to better match anindividual consumer’s taste. To improve the matching value, the firm should be able to process
and learn from consumer data. We call this the firm’s data analytics. We allow the quality ofdata analytics to vary, with perfect product personalization possible only with the perfect data
analytics. Separating the data scale from the data analytics in this way generates new insight.
For example, the data scale has a non-monotonic effect on consumer surplus, but consumer
surplus is nondecreasing in the quality of data analytics.
The rest of the paper is organized as follows. After a review of the related literature below,
Section 2 presents our model. Section 3 analyzes the effect of personalization in market A.
Section 4 studies the cross-market effects from the merger. Section 5 discusses policy implications
9

This point is made emphatically by Khan (2017), Chair of the US Federal Trade Commission confirmed by
the US Senate on June 15, 2021.

6

and Section 6 provides the analysis of various extensions of the baseline model. Section 7
concludes the paper. Appendix provides proofs of results in Sections 3 and 4. Online Appendix
contains all other proofs, a brief account of Google’s interest in and expansion into health care,and some information on how big data and personalization are affecting the healthcare industry.

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 Morton et al. (“Stigler Report”, 2019). For reviews of the academic literatureon the digital economy, see Goldfarb and Tucker (2019), or Calvano and Polo (2021).
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 (Google,
Amazon, Facebook, Apple, and Microsoft) and find that most acquisitions are in areas where theacquirer’s and the target’s products and services are complementary to each other, a majorityof targets are young or start-up companies, and that “killer acquisitions” are not common.
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 (2021), Kamepalli
et al. (2020), Katz (2021), and Motta and Peitz (2021) 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.10 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.11
Although not related to mergers, several studies analyze how data can be used for learningand affect market dynamics.12 Hagiu and Wright (2020b) study a model of dynamic duopoly
where a firm’s data from past sales can be used for learning and augment the value of its productto current consumers. They analyze various types of data-enabled learning and their implications
10

For merger policy governing multi-sided platforms, see, for example, Jullien and Sand-Zantman (2021) andthe references therein.
11
Somewhat related to our cross-market effects, Condorelli and Padilla (2020) use a reduced-form approach to
study how a monopolist can use the data from one market for entry deterrence in another market.
12

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

7

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 network
effects 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).13 Zhang (2011) and Laussel andResende (2020) consider product personalization in addition to personalized pricing. Generalfindings from this literature can be summarized as follows. First, competition in personalized
pricing is more intense than competition in other types of price discrimination unless consumers
can take actions to bypass personalized pricing.14 Second, competition becomes increasingly
more intense as firms move from pure personalized pricing to personalized pricing combinedwith product personalization. Our work adds to this literature in several ways. First, unlike
most studies that focus on a symmetric duopoly, our model is in the context of merger where themerged firm can employ data-driven personalization while its stand-alone competitor cannot,
hence an asymmetric duopoly arises naturally. Second, we allow the merged firm to delink product personalization and personalized pricing, if it wishes to. Finally, we show how the merged
firm’s personalization strategy changes when cross-market effects are taken into account.

2

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
serve each market. In market A (B, resp.), firm A1 (B1 , resp.) is located at 0 and firm A2
13

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.
14

Choe et al. (2018) show competition is more intense when it is in personalized pricing than when it is inthird-degree price discrimination, as in Fudenberg and Tirole (2000). Chen et al. (2020) show consumers’ identity
management can soften competition in personalized pricing and even lead to a collusive outcome.

8

(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 > 3,
which simplifies analysis and also ensures that the market is fully covered even if it is served bya monopoly supplier. Before the merger, market A has a symmetric Hotelling equilibrium withprices α10 = α20 = 1, profits Π0A1 = Π0A2 = 1/2, and firm A1 ’s market share given by [0, 1/2].
Firms in market B are also symmetric but we allow sequential moves where firm B1 is thefirst mover.15 As in market A, a consumer located at x derives utility vB − x from firm B1 ’s
product and vB −(1 − x) from firm B2 ’s product, where vB > 3. Solving the sequential game, we
obtain equilibrium prices β10 = 3/2 and β20 = 5/4, hence firm B1 serves [0, x0 ] where x0 = 3/8.
Then firms earn profits equal to Π0B1 = 9/16 and Π0B2 = 25/32.
We consider the merger between firms A1 and B1 , leading to a merged entity to be calledfirm C. Alternatively, one may also consider the scenario in which firm B1 is acquired by adominant 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.16 Thus post-merger competition in market B continues to be in uniform price.
In market A, consumer data can be used for two types of personalization. Suppose firm
C knows exact locations of all consumers in [0, δA ]. We call this firm C’s target segment andδA , its data scale. Knowing each targeted consumer’s exact location enables firm C to offer apersonalized price to each targeted consumer. Moreover, firm C can utilize its data analytics
15
This is partly to reflect reality. For example, Fitbit sold its first fitness tracker at the end of 2009 whereas
the first Apple Watch was released in April 2015. In addition, assuming sequential moves in market B limits
possible deviations by the merged firm compared to the case with simultaneous moves, hence simplifies postmerger analysis. Having firm B2 as the first mover leads to similar qualitative results. That is, there are two
types of post-merger equilibria with monopolization more likely when the consumption synergy increases. In theprevious version of this paper (Chen et al., 2020), we considered simultaneous moves as well as asymmetric firms
in market B.
16

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and offer a personalized product that has a higher matching value for a targeted consumer thanits standard product. We parameterize this by φA ∈ (0, 1] such that consumer x derives utilityvA − (1 − φA )x from the personalized product, and call φA , firm C’s data analytics quality.17
For simplicity, we assume that firm C can offer a personalized product at no additional cost.
In this case, firm C will offer personalized products at personalized prices to all of its targeted
consumers, which we simply call personalization.18
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 andVives, 1988; Matsumura and Matsushima, 2015; Choe et al., 2018; Chen et al., 2020). In the firststage, firms simultaneously post uniform prices, which are publicly observed. In the second stage,
firm C makes private offers to 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 particular customer without adjusting the prices to other customers.19 Such flexibility inpricing gives firm C a second-mover advantage in responding to the rival’s pricing strategy.
We make several simplifying assumptions. First, consumer tastes are perfectly correlated in
the two 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. Second, firms’
locations remain the same before and after the merger so that firm C’s position in market A
remains at 0. Third, firms A2 and B2 remain independent so that firm C is the only merged
entity. Fourth, consumers are myopic in that when they make purchase decisions in market B,
they do not anticipate how their data will be used in market A.20 In Section 6, we relax someof these assumptions and show that our main insight pertaining to the implications of data andpersonalization remains robust.
17

We assume δA and φA are independent of each other. In reality, it is conceivable that there may be a positive
correlation between the two, for example, thanks to data-enabled learning (Hagiu and Wright, 2020b). A simple
way to model the positive correlation is to assume φA = h + (1 − h)δA , h ∈ [0, 1]. This modification does notchange our qualitative results, the details of which are available from the authors.
18

In the previous version of this paper (Chen et al., 2020), we considered the case where offering the personalized product incurs a unit cost c > 0. This leads to the segmentation of market in which firm C offers thestandard product at personalized pricing to targeted consumers close to its location, and personalized products at
personalized pricing to the remaining targeted consumers. Other than that, our main insight remains the same.
19

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.
20

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 to how their interaction with Facebook can be used byadvertisers and retailers. On the other hand, consumer myopia may be less plausible in our motivating example
of Google/Fitbit. In this sense, our assumption of consumer myopia is mainly to simplify analysis. That said,
the main change we expect from having forward-looking consumers is that competition in market B where datais collected will become more intense than when consumers are myopic. This is akin to the insight from theliterature on behavior-based price discrimination (Choe et al., 2018).

10Remark 1. In our reference to Google/Fitbit, we refer to market A as the digital healthcare in general, and at times, the market for health insurance. We offer some justifications forour choice of Hotelling model for market A. The Hotelling model is often used in the analysis
of competition in healthcare markets.21 Health plans are highly differentiated for two reasons.
First, health plans cover a broad range of treatments for chronic or acute illnesses, and offerdifferent co-payment rates for different treatments. For instance, insurance plan A1 may cover
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 another consumer
with a knee problem but a good dental condition will prefer plan A1 . We choose the Hotellingmodel to capture differentiations described above. Thus market A captures one aspect of healthcare (product differentiation) but ignores other aspects such as different risk types that could
lead to adverse selection. As such, it can be best understood as a segment of the healthcare
market with customers of similar risk types. Our intention is to focus squarely on the effect of
personalization by abstracting away other issues. In Section 6.2, we discuss the case with tworisk types and show that focusing on a single risk type does not alter our main insight unlessthe costs of serving different risk types are sufficiently different.
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.22 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.23
21
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.
22

In the Online Appendix, we provide a more detailed account of how the healthcare sector is transformed by
big data and personalization.
23

https://www.clinicalomics.com/topics/oncology/multiple-myeloma/gns-healthcare/113Equilibrium Analysis of Personalization

We start by analyzing the equilibrium in market A. The only aspect of the merger relevant to our
focus is the consumer data harvested by firm B1 , which can be used by firm C for personalizationin market A. Denote firm C’s target segment by [0, δA ]. We treat δA as exogenous in this section,
but will endogenize it in the next section.
Targeted consumer x enjoys gross utility vA − (1 − φA )x from the personalized product andvA − x from the standard product. Since product personalization is costless, firm C will offer
personalized products to all its targeted consumers for any φA ≥ 0. Denote firm C’s personalized
price for targeted consumer x ∈ [0, δA ] by pA (x). For non-targeted consumers in [δA , 1], firm
C charges a uniform price, denoted by α1 . But firm A2 can only charge a uniform price forall consumers, denoted by α2 . We assume that firm C can prevent targeted consumers frompurchasing its standard product at uniform price α1 , for instance, by redirecting the productsearch from a targeted consumer, a practice dubbed steering or search discrimination.24 This
allows firm C to delink its choice of personalized prices and its choice of uniform price.25

3.1

Characterization of equilibria

Before characterizing the equilibrium, we define three cutoff values that will be used in our
analysis. First, competition for firm C’s non-targeted consumers is in uniform price. Given theuniform 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. Targeted consumer x prefers firm C’s personalized
offer to firm A2 ’s standard product if 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) = 1 − (2 − φA )x + α2 . Since firm C can adjust its personalized price foreach targeted consumer separately, it can reduce pA (x) down to 0. This defines the marginal
consumer x̄ as pA (x̄) = 0 = 1 − (2 − φA )x̄ + α2 , hencex̄ ≡1 + α2.
2 − φA(2)

Firm C can serve all targeted consumers x ≤ x̄ with personalization. In doing so, it will choose
24
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.
25

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.

12personalized prices that make all targeted consumers indifferent between its personalized offer
and its competitor’s standard offer. Note that x̄ ≥ x̂, which implies that personalization canserve as a more powerful weapon for firm C than uniform pricing in defending its target segment.
Finally, we define the maximum target segment that firm C can profitably serve. Notice firstthat firm C will never use the uniform price to serve its targeted consumers. The statement isclearly true for targeted consumers in [x̂, x̄]. So consider targeted consumer x ≤ x̂. Firm C canserve consumer x by choosing pA (x) = 1 − (2 − φA )x + α2 . Then x ≤ x̂ implies pA (x) ≥ 1 + α2 −2x̂ + φA x̂ = α1 + φA x̂ ≥ α1 . Thus personalization allows firm C to serve its targeted consumers
more profitably than uniform pricing. But the ability to use personalization is constrained byits data scale δA and data analytics quality φA . Even when δA = 1, firm C can serve consumers
only up to x̄ using personalization while competing for the remaining consumers in [x̄, 1] with
its rival. Given the marginal consumer’s location x̄ in (2), firm A2 can maximize profit α2 (1 − x̄)
by choosing α2 = (1 − φA )/2. This leads to x̄ = δ̄ where [0, δ̄] is the maximum market segmentthat firm C can serve, defined asδ̄ ≡3 − φA.
2(2 − φA )(3)

It is easy to see δ̄ increases in φA . Put differently, the above analysis shows how firm C can
expand its market reach through personalization. With uniform pricing, firm C can reach the
maximum market size [0, 3/4] by choosing α1 = 0. With personalization, this can be expanded
to [0, δ̄] where δ̄ ∈ [3/4, 1].
We now turn to the characterization of equilibrium. There are three cases to consider.
3.1.1

Equilibrium when δA < 3/4

First, on [δA , 1], competition is in uniform price with the marginal consumer’s location given byx̂ 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 prices
42α1∗ = 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, δA ], firm C offers personalization with price pA (x) that makes consumer x
indifferent between firm C’s personalized offer and firm A2 ’s standard product offered at priceα2∗ . Thus the equilibrium personalized price in this segment is given by2p∗A (x) = 1 − (2 − φA )x + α2∗ = 2 − δA − (2 − φA )x.
3
Then firm C’s total profit is Π∗C =

R δA
0

(5)

p∗A (x) dx + α1∗ (x̂ − δA ). Firm A2 serves consumers in[x̂, 1] with uniform price α2∗ , hence its profit is Π∗A2 = (1 − (2δA )/3)2 /2.
13

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 . Firm C serves all of its targeted consumers
in [0, δA ] with personalization, and 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.
3.1.2

Equilibrium when 3/4 ≤ δA < δ̄In this case, firm C cannot serve any of its non-targeted consumers. Competition in uniform
price on [δA , 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 to maximize profit
α2 (1 − x̂) subject to δA ≤ x̂. It is easy to see that, given vA > 3, firm A2 can maximize profit
by choosing α2 so that δA = x̂. This leads to the following equilibrium uniform prices:α1∗∗ = 0, α2∗∗ = 2δA − 1.

(6)

Given α2∗∗ , we can determined firm C’s personalized price as before.
p∗∗A (x) = 2δA − (2 − φA )x for x ∈ [0, δA ].
Given the above prices and market shares, firm C’s profit is Π∗∗
C =

R δA
0

(7)
p∗∗
A (x)dx, and firm A2 ’s

profit is Π∗∗
A2 = (2δA − 1) (1 − δA ) .
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 with personalization while firm A2 serves all consumers
not targeted by firm C. Thus the two firms’ market shares are exogenously determined by δA .
3.1.3

Equilibrium when δ̄ ≤ δA

In this case, firm C’s target segment is so large that firm A2 serves firm C’s targeted consumers
in [δ̄, δA ] in addition to all non-targeted consumers in [δA , 1]. As shown previously, we then havethe following equilibrium uniform prices:α1∗∗∗ = 0, α2∗∗∗ =1 − φA.
2(8)

Then firm C’s personalized prices are26
p∗∗∗
A (x) =

 3−φA − (2 − φ )x,

for x ∈ [0, δ̄].

≥ 0,

for x ∈ [δ̄, δA ].

A

2

26

(9)

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) ≥ 0, 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) < 0.

14

Profits are Π∗∗∗
C =

R δ̄

2
∗∗∗
∗∗∗
0 pA (x)dx and ΠA2 = (1 − φA ) / (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. We summarize the above discussions below.
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 serves all targeted
consumers with personalization at price p∗A (x), and chooses uniform price α1∗ to serve
non-targeted consumers in [δA , 1/2 + δA /3]. Firm A2 serves all remaining consumers withuniform price α2∗ . These prices are given in (4) and (5).
• When 3/4 ≤ δA < δ̄, there exists a unique equilibrium in which firm C serves all targeted
consumers with personalization at price p∗∗
A (x), and firm A2 serves all remaining consumers
with uniform price α2∗∗ . These prices are given in (6) and (7).
• When δ̄ ≤ δA , there exists a unique equilibrium in which firm C serves targeted consumers 
in [0, δ̄] with personalization at price p∗∗∗
(x),
while
firm
A
servesallconsumers
in
δ̄, 1
2
A
with uniform price α2∗∗∗ . These prices are given in (8) and (9).

3.2

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 close to firm C’s location since the benefit of improved matching value is small forthese consumers. On the other hand, firm C’s non-targeted consumers may benefit since more
intense competition in uniform price reduces uniform prices below the Hotelling benchmark. In
sum, personalization can lead to exploitation of 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 although, except for the casewith δA = φA = 1, firm A2 will continue to remain active in the market, albeit with reduced
profit and market share. But the market can turn into a monopoly in the long run if there aresome fixed costs of staying in the market, which are not covered by firm A2 ’s short-run profit.
With these observations in mind, let us examine how personalization following the merger
affects each firm’s profit and consumer surplus.
15

First, firm C is unambiguously better off after the merger. Given that firm C can always
revert to the Hotelling competition, the ability to use personalization at no additional costfollowing the merger cannot hurt it. This can be verified by checking that firm C’s profit in all
the three cases in Proposition 1 is larger than 1/2, its pre-merger profit. In contrast, firm A2 ’s∗∗
profit decreases unambiguously. 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.
Next, personalization harms some consumers but benefits others. Before the merger, atargeted consumer x receives utility vA − x − 1 given the Hotelling price equal to 1. After themerger, consumer x will be given a personalized offer from firm C that leaves her indifferent
between choosing firm C and firm A2 . The latter choice gives her 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 quarterof consumers including those in [0, 1/4] are worse off after the merger. But targeted consumers
in [α2 /2, δA ] benefit from personalization. In addition, all consumers outside firm C’s target
segment also benefit from the merger because of lower uniform prices than before the merger.
This suggests that personalization following the merger can decrease total consumer surplus if
firm C’s target segment is sufficiently large and firm C can exploit a large fraction of thesetargeted consumers through personalization. Otherwise, total consumer surplus increases.
Proposition 2 Suppose firm C’s target segment is given by [0, δA ]. Then personalization following the merger• increases firm C’s profit unambiguously;• reduces firm A2 ’s profit unambiguously;• increases total consumer surplus except when φA > 2/3 and δA ∈ (7/8, δ̄).
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 dependon δA . Consequently, an increase in δA affects neither firm’s profits, implying that an excessive
data scale beyond δ̄ has no effect on competition. In contrast, an increase in 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 ,16

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 may not be monotonic. It is easy to check Π∗C isconcave in δA and reaches a maximum at δA = δ ∗ ≡ 6/(14 − 9φA ) where δ ∗ ≤ 3/4 if and only if
φA ≤ 2/3. 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 onfirm 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 an increase in φA has no effecton consumer surplus as in the previous case.
Proposition 3 Suppose firm C’s target segment is given by [0, δA ].
• Firm C’s profit weakly increases in δA except when φA < 2/3 and δA ∈ [δ ∗ , 3/4] whereδ ∗ ≡ 6/(14 − 9φA ). 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 thereafter. 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.
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 firm C but only up to a certain
point, because its ability to serve additional targeted consumers is ultimately limited by its data
analytics. Insofar as firm C benefits from a larger data scale, its competitor inevitably loses due
to a decrease in its market share. In contrast, an improvement in data analytics can benefit
firm C without hurting its competitor since the benefit comes from the firm’s ability to extract
surplus from consumers that firm C already serves, rather than from poaching consumers fromits competitor. On the other hand, a further improvement in data analytics coupled with a large
data scale can hurt both firms by intensifying competition for consumers firm C cannot serve.
We close this section with a caveat. As our model is essentially static, Proposition 2 simply
reiterates the well-known point that data can generally benefit consumers in the short run
by intensifying competition. Of course, the effect can be only short-lived if the intensifiedcompetition leads to market tipping and drives the competitor out of the market in the long17

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 tothink about data externalities in our setting is that firm C can use the data from its target
segment [0, δA ] to infer information on the remaining segment. For example, firm C can expand
its target segment to [0, (1 + y)δA ] where 0 ≤ y ≤ (1 − δA )/δA . If y = (1 − δA )/δA , then firm C’s
target segment covers the entire market. This leads to the monopolization of market A by firm
C if φA = 1. Then firm C can use personalization to extract consumer surplus uninhibited bycompetition. This suggests a dynamic trade-off between short-term gains in consumer surplus
and possible long-term losses.

4

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 firm 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 somelinkages between the relevant markets. We model such linkages through two channels: data andconsumption synergy. First, we have already argued that firm C can use data it harvests inmarket B for personalization 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 > 0 by choosing firm C’s personalized product in market A. This extra value canbe interpreted as a consumption synergy, which may be due to several factors. First, there
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.27
Throughout this section, we assume perfect personalization, i.e., φA = 1, primarily to simplify analysis. Also recall our assumption that consumers are not forward looking, so that theirpurchase 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
27

The merger is not the only way to make data in market B available in market A. For example, firms A1 andB1 can sign a contract for trading data. In the absence of the consumption synergy, one can find non-linear tariffs
that can lead to the same outcome as that under the merger. But the consumption synergy is merger-specific in
the sense that it can be exploited only through the merger.

18

profit after the merger is larger than that before the merger. Without the merger, the status
quo is maintained. With the merger, we analyze market B first where firm C is the first mover.
This determines firm C’s target segment in market A. The timing of the pricing game in market
A is the same as before. That is, uniform prices are simultaneously chosen, after which firm C
makes personalized offers. We solve the game backward.

4.1

Analysis of equilibria

Denote firm C’s target segment in market A by [0, x∗ ] where x∗ is the marginal consumer
who chose firm B1 ’s product in market B. Firm C sets personalized prices to leave all targeted
consumers indifferent between choosing either firm in market A. Thus vA +ω −pA (x) = vA −(1−x) − α2 , hence pA (x) = 1 + ω + α2 − x for all x ∈ [0, x∗ ]. This leads to the following observations.
First, since pA (1) = ω + α2 > 0, firm C can profitably serve all targeted consumers in market
A. Thus data scale has a positive marginal benefit in market A, which makes monopolization
an attractive option. Second, the consumption synergy ω increases the marginal benefit to datascale, 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 .
From the discussions above, we expect two types of equilibria. If ω is large enough, we expect
firm C to monopolize market B, which also implies the monopolization of market A. Otherwise,
firm C will accommodate competitors in both markets. In both types of equilibria, we expect
the merger to be an equilibrium outcome. This is because firm C obtains market power createdby the ability to use personalization and the consumption synergy only through the merger. We
now turn to the characterization of each type of equilibrium.
The analysis of market A is the same as that in Section 3 with δA replaced by x∗ . The only
differences are that we now have ω and φA = 1. Let us turn to market B. Given β1 , firm B2
chooses β2 to maximize β2 (1 − x∗ ) where x∗ = (1 − β1 + β2 )/2. This leads to firm B2 ’s best
response β2 = (1 + β1 )/2, hence x∗ = (3 − β1 )/4. Then firm C chooses β1 to maximize total
profit from both markets. Based on the analysis in Section 3, we consider two cases.
First, if x∗ ≤ 3/4, then, from Section 3.1.1, we have α1∗ = 1 − (4x∗ )/3, α2∗ = 1 − (2x∗ )/3,x̂ = 1/2 + x∗ /3, and p∗A (x) = 2 + ω − x − (2x∗ )/3. Firm C’s total profit in this case is∗

Z x∗

ΠC = β1 x +5p∗A (x)dx + α1∗ (x̂ − x∗ ) = − (x∗ )2 +
18

0




2
1
+ ω + β1 x∗ +
3
2

(10)

where x∗ = (3 − β1 )/4. Solving for firm C’s optimal uniform price β1∗ and substituting it backto β2 and x∗ , we obtainβ1∗ =99 − 36ω
88 − 18ω ∗ 33 + 9ω
, β2∗ =
, x =
.
77
77
77

19

(11)

Substituting x∗ into the prices in market A given above, we haveα1∗ =33 − 12ω
55 − 6ω ∗132 + 71ω93ω, α2∗ =, pA (x) =− x, x̂ =
+
.
77
77
77
14
77

(12)

The above prices constitute a local optimum if and only if x∗ = (33 + 9ω)/77 ≤ 3/4, henceω ≤ 11/4. We now verify that, given the above prices, firm C’s total profit is larger than thesum of the two firms’ pre-merger equilibrium profits. Before the merger, firm A1 ’s profit is 1/2
and firm B1 ’s profit is 9/16, hence the total profit 17/16. After the merger, firm C’s total profit
can be calculated from (10): Π∗C = 3(66 + 22ω + 3ω 2 )/154 > 17/16. In addition, Π∗C increases inω. In contrast, the merger hurts rival firms in both markets. Their post-merger profits can becalculated as Π∗A2 = α2∗ (1 − x̂) = (55 − 6ω)2 /11858 and Π∗B2 = β2∗ (1 − x∗ ) = 2(44 − 9ω)2 /5929.
It is easy to verify Π∗A2 < Π0A2 = 1/2 and Π∗B2 < Π0B2 = 25/32. Moreover, both profits decreasein ω; in particular, the consumption synergy in market A hurts firm B2 .
To summarize, if ω ≤ 11/4, then a candidate equilibrium exists in which firm C serves
non-targeted consumers in [x∗ , x̂] in addition to all targeted consumers in market A, but accommodates rivals in both markets. In this case, the merger allows firm C to increase its market
share from 3/8 to x∗ ≥ 3/7 in market B, and from 1/2 to x̂ ≥ 9/14 in market A. We call thisthe accommodation equilibrium I.
Second, if x∗ ∈ [3/4, 1], then, from Section 3.1.2, we have α1∗ = 0, α2∗ = 2x∗ − 1, andp∗A (x) = 2x∗ + ω − x. Firm C’s total profit in this case is∗

Z x∗

ΠC = β1 x +(1 − x + ω + (2x∗ − 1))dx =03(x∗ )2+ (β1 + ω)x∗2

(13)

where x∗ = (3 − β1 )/4. Solving for firm C’s optimal uniform price β1∗∗ and substituting it backto β2 = (1 + β1 )/2 and x∗ , we obtainβ1∗ =3 − 4ω
4 − 2ω ∗ 3 + ω, β2∗ =
, x =
.
5
5
5

(14)

Substituting x∗ into the prices in market A given above, we obtain
α1∗ = 0, α2∗ =1 + 2ω ∗6 + 7ω
, pA (x) =
− x.
5
5

(15)

The above prices constitute a local optimum if and only if x∗ ∈ [3/4, 1], hence 3/4 ≤ ω ≤ 2.
Once again, one can verify that, given the above prices, firm C’s total profit is larger than thesum of the two firms’ pre-merger equilibrium profits: Π∗C = (3 + ω)2 /10 > 17/16 since ω ≥ 3/4.
Likewise, both firms A2 and B2 have lower profits after the merger: Π∗A2 = (−2ω 2 +3ω +2)/25 <1/2 and Π∗B2 = 2(2 − ω)2 /25 < 25/32.
To summarize, if 3/4 ≤ ω ≤ 2, then a candidate equilibrium exists in which firm C serves
only targeted consumers in market A and accommodates rivals in both markets. In this case,the merger allows firm C to increase its market share to x∗ ≥ 3/4 in both markets. We call this20the accommodation equilibrium II.
The above analysis shows that there are two local optima when 3/4 ≤ ω ≤ 2. Thus we need
to identify a global optimum by comparing firm C’s profits given the two local optimal prices
β1∗ = (99−36ω)/77 and β1∗ = (3−4ω)/5. Comparing the profits for each case, one can verify that√β1∗ = (99 − 36ω)/77 is globally optimal if ω ≤ 3( 385 − 11)/16 ' 1.62. Thus the accommodation√
equilibrium I exists in this case. If 3( 385 − 11)/16 ≤ ω ≤ 2, then β1∗ = (3 − 4ω)/5 is globally
optimal, leading to the accommodation equilibrium II.
If ω ≥ 2, then it is optimal for firm C to monopolize market B by choosing β1∗ = −1, andhence market A as well.28 We call this the monopolization equilibrium. In this equilibrium,
firm C prices below cost in market B and serves all consumers in market A using personalized
prices p∗A (x) = 2 + ω − x, earning profit Π∗C = (1 + 2ω)/2.29 The monopolization equilibrium
can be described as the short-run predatory equilibrium in that firm C prices below cost andmonopolizes the market, but without fully utilizing its monopoly power. 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. This situation
is likely to prevail only in the short run, however. If competitors exit the market in the longrun, then the monopolization equilibrium will turn into the monopoly equilibrium, which will bemuch more profitable for firm C to the detriment of consumers.30 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]; in market B, it serves the entire market withmonopoly price β m = vB /2 > 3/2 = β10 > β20 = 5/4, resulting in consumer surplus lower thanthat in the pre-merger equilibrium.
Proposition 4 There exist three types of equilibria described below, in all of which firms A1
and B1 choose to merge.
√• If ω ≤ 3( 385 − 11)/16, then the accommodation equilibrium I arises with prices given in(11) and (12).
√• If 3( 385 − 11)/16 ≤ ω ≤ 2, then the accommodation equilibrium II arises with prices
given in (14) and (15).
• If ω ≥ 2, then the monopolization equilibrium arises.
28

When ω ∈ [2, 11/4], the accommodation equilibrium I is also possible. But it is easy to see that firm C’s
profit is higher when it monopolizes both markets.
29

In the monopolization equilibrium, firm A2 chooses an off-the-equilibrium price α2 . In this case, we use arefinement 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 monopolizationof market B, the only 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. Thus α2 = limε→0 α2 (ε) = 1.
30This is somewhat reminiscent of the dynamic leverage theory, in which an incumbent monopolist bundles
complementary products to extend its monopoly power into related markets by deterring entry of competitors(Carlton and Waldman, 2002; Choi and Stefanadis, 2001). But the main difference is the role of personalizationin our paper, without which firm C cannot monopolize market A even if it had acquired full information frommarket B. That is, data-enabled personalization, rather than tying, is a key to the monopolization of market A.

21

4.2

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 accommodation equilibria. Consider market A. Before the merger, priceis equal to 1 and firms share the market equally. After the merger, prices and firm C’s market
share are given in (12) in the accommodation equilibrium I, and they are given in (14) and(15) in the accommodation equilibrium II. Since α1∗ , α2∗ < 1, it is immediate that all consumers
in [x∗ , 1] are better off. On the other hand, firm C’s targeted consumers may or may not bebetter off. All of them pay personalized prices higher than 1 but they benefit from perfectly
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 threshold value of
taste parameter such that consumers are worse off if and only if their taste parameter is below
the threshold.31 Given the uniform distribution, one can show that total consumer surplus
in market A increases after the merger in the accommodation equilibrium I, but decreases in
the accommodation equilibrium II. The intuition is that consumers pay higher prices in theaccommodation equilibrium II than in the accommodation equilibrium I since firm A2 serves all
non-targeted consumers in the former.
In market B, all consumers are better off. Before the merger, prices are β10 = 3/2, β20 = 5/4,
and the market is divided at x0 = 3/8. After the merger, prices and the marginal consumer are
given in (11) and (14) for the respective accommodation equilibrium. It is worth noting that firm
C prices below cost, i.e., β1∗ < 0, for all values of ω that lead to the accommodation equilibrium
II. Since equilibrium prices are lower, all consumers in [0, x0 ] ∪ [x∗ , 1] are better off because they
pay less while choosing the same firm. For consumer x ∈ [x0 , x∗ ] who switches from firm B2 tofirm C after the merger, the change in consumer surplus is vB − x − β1∗ − vB − (1 − x) − β20 =1 − 2x − 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 since (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. On the other
hand, all consumers who purchased from firm A2 before the merger have the same consumer
surplus since (vA + ω − p∗∗
A (x)) − (vA − (1 − x) − 1) = 0. It follows that total consumer surplus
in market A decreases unambiguously after the merger. In market B, the merger benefits all
consumers thanks to below-cost pricing, although one needs to exercise caution in interpreting
The threshold value is given by vA − x − 1 = vA + ω − p∗A (x), hence x = (55 − 6ω)/154 in the accommodation
equilibrium I and x = (1 + 2ω)/10 in the accommodation equilibrium II.
31

22

this result. The comparison of consumer surplus in this case is in relation to the monopolization
equilibrium, rather than the monopoly equilibrium. If the merger leads to the latter in the longrun, then firm C will fully exploit its monopoly power. In market A, this implies that firm C
will extract entire consumer surplus thanks to data-enabled personalization. In market B, themonopoly price is β m = vB /2, hence total consumer surplus is equal to (vB − 1)/2. As discussed
earlier, this consumer surplus is smaller than that in the pre-merger equilibrium.
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. In the market
for data collection, consumers may gain in the short run thanks to intensified competition.
But consumers in the market for data application are better off if the consumption synergy
is not large enough so that the merged firm continues to serves some non-targeted consumers.
Otherwise, they are worse off since the merged firm uses personalized pricing to extract much of
the efficiency gains generated from the consumption synergy and the improved matching value
created by product personalization.
Proposition 5 The merger with cross-markets effects has the following welfare implications.
√• If ω ≤ 3( 385 − 11)/16 ' 1.62, then total consumer surplus is larger in both markets than
before the merger.
√• If ω ≥ 3( 385 − 11)/16, then total consumer surplus is smaller in market A but larger inmarket B than before the merger.
• If ω ≥ 2, when firms A2 and B2 exit in the long run following monopolization, total
consumer surplus is smaller in both markets than before the merger.
• In all three types of equilibria, firms A2 and B2 are worse off than before the merger andtheir profits decrease in ω while firm C’s profit increases in ω.

5

Policy Implications

In conventional merger assessments, possible costs due to lessening of competition are weighedagainst potential benefits from the merger-specific efficiency gains that can be passed on to
consumers. We have discussed two types of efficiency gains in data-driven mergers: consumption
synergy (ω) and product personalization (φA ) with the total efficiency gains for consumer x
measured by ω + φA x. As shown in Section 4, however, firm C can extract the efficiency gains
through personalized prices, pA (x) = 1 − 2x + α2 + ω + φA x. Thus possible consumers benefits
in the form of lower prices are not an indication that the efficiency gains are passed on to
consumers; rather, they are driven by firm C’s strategic motives for market dominance and,
therefore, are likely to be temporary. This also implies that firm C becomes more aggressive as
the efficiency gains increase: as Proposition 5 shows, the market is more likely to be monopolizedas ω increases. In short, the very source of potential benefits from the merger can be the reason

23

for the market to tip in the merged firm’s favor, and the efficiency gains cannot be a plausible
reason for approving a data-driven tech merger.
In addition, even if stand-alone competitors do not exit the market in the short run, there isrisk of market tipping in the long run due to data externalities and network effects, as we havediscussed previously. 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 effectsof specific practices.”
In view of these concerns, we consider possible remedies that are often discussed in relation
to tech mergers.32 Particularly relevant to the Google/Fitbit merger are remedies that relate to
the use of health data for Google Ads, access to the Fitbit Web API in relation to the digital
health, and competition in the market for wearable devices.33 As the first one is not directly
relevant to our model, we consider the other two. Specifically, we first analyze the effect of data
sharing between firms C and A2 . Then we examine the effect of banning below-cost pricing inmarket B. This is followed by a brief discussion on the case of blocking the merger. We continue
to assume φA = 1 and denote the marginal consumer in market B by x̃ to facilitate comparison
with x∗ in Section 4.

5.1

Data sharing

Suppose firm C is compelled to share data with firm A2 , based on which firm A2 can also makepersonalized offers. We assume firm A2 ’s personalization technology is identical to firm C’s.
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 collect consumer data, hence softens competition in market B. Thus the effectof data sharing in market B is clear: firm B2 is better off but consumers are worse off due tohigher uniform prices. But the effect in market A is more complex and we need to examine all
possible equilibria.
Before describing possible equilibria, we first note that, even with data sharing, firm C canserve all targeted consumers thanks to the consumption synergy, which firm A2 cannot offer toits consumers. With this in mind, we now describe 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 ≤ 3, there is an equilibrium in
32

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

33

These are discussed in the decision made by the European Commission in approving the Google/Fitbit
merger (https://ec.europa.eu/commission/presscorner/detail/en/ip 20 2484) and in the statement by the
ACCC in Australia (https://www.accc.gov.au/media-release/accc-rejects-google-behavioural-undertakings-forfitbit-acquisition).

24

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 has the same structure
as the accommodation equilibrium with accommodation I in Section 4, 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 bothmarkets because of (ii). Second, If ω ∈ [3, 5], then there is an equilibrium where firm C serves
only targeted consumers while firm A2 serves the rest, as in the accommodation equilibrium II.
Finally, if ω ≥ 5, then firm C monopolizes both markets.
Table 1: Equilibria with or without data sharingω[0, 2][2, 3][3, 5]

5≤ωNo data sharing
Data sharing

Accommodation I, II
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. 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 with accommodation for a wider range of valuesfor ω than without data sharing, as shown in Table 1. In this sense, data sharing can bepro-competitive. To summarize, 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. It can be also pro-competitive by intensifying
competition where data is used and by making monopolization harder to achieve. The following
proposition summarizes the key implications of data sharing.
Proposition 6 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 strictly smaller in all equilibria when ω < 5 than
without data sharing, but remains unchanged if ω ≥ 5.
• Monopolization is less likely with data sharing in the sense that the monopolization equilibrium arises for ω ≥ 5 whereas, without data sharing, the monopolization equilibrium
arises for ω ≥ 2.

5.2

Restriction on below-cost pricing

Our analysis in Section 4 shows that firm C will engage in below-cost pricing in market B in
the accommodation equilibrium II and the monopolization equilibrium. Clearly, the reason is toharvest a large set of consumer data that firm C can use in market A. If the benefit from market
25

A more than offsets the loss in market B, then below-cost pricing is profitable. What happens
if the competition authority bans below-cost pricing? We discuss its implications below.
Given the restriction β1 ≥ 0, firm C cannot monopolize the market and the accommodation
equilibria remain the only possibility. Consider first the accommodation equilibrium I, whichis possible when x̃ ≤ 3/4, hence ω ≤ 11/4. Since β1∗ ≥ 0 in this case as shown in (11), therestriction does not affect the accommodation equilibrium I. Consider next the accommodation
equilibrium II, which is possible when x̃ ≥ 3/4. In this case, we have β1∗ = (3 − 4ω)/5, as shownin (14). Thus the restriction is binding if ω ≥ 3/4, when firm C chooses β1 = 0, to whichfirm B2 ’s best response is β2 = 1/2. Since both accommodation equilibria are possible whenω ∈ [3/4, 11/4], we need to compare the profits to find the global optimum. It is easy to seethat firm C’s profit is higher in the accommodation equilibrium I. Thus we can conclude thatthe accommodation equilibrium I arises when ω ≤ 11/4 and the accommodation equilibrium
II arises when ω ≥ 11/4. The accommodation equilibrium I is the same as that without the
restriction. In the accommodation equilibrium II, we have β1∗ = 0, α2∗ = β2∗ = 1/2, different
from those without the restriction.
The analysis above shows that the restriction has two main effects. First, it expands the√range of ω that leads to the accommodation equilibrium I from [0, 3( 385 − 11)/16] to [0, 11/4].
Second, it eliminates the possibility of the monopolization equilibrium. Recall that, without the
restriction, we have the monopolization equilibrium when ω ≥ 2. Table 2 shows various typesof equilibria with or without the restriction for different ranges of ω.
Table 2: Equilibria with or without the restriction on below-cost pricingω√
0, 3( 385 − 11)/16 √
3( 385 − 11)/16, 2[2, 11/4]

11/4 ≤ ω

No restriction
Restriction

Accommodation I
Accommodation I

Accommodation II
Accommodation I

Monopolization
Accommodation I

Monopolization
Accommodation II√
From Table 2, we can make the following observations. When ω ≤ 3( 385 − 11)/16, therestriction has no effect. In all other cases, the restriction unambiguously hurts consumers inmarket B by raising prices, hurts firm C by decreasing its market share, and benefits firms A2
and B2 as a result. In what follows, we discuss only the comparison of consumer surpluses in√market A. When ω ∈ [3( 385 − 11)/16, 2], we compare the accommodation equilibrium I under
the restriction with the accommodation equilibrium II without the restriction. Firm A2 ’s priceis higher in the latter because firm C’s target segment is larger and firm C does not serve any
non-targeted consumers. This also means that firm C’s personalized prices are higher in thelatter. The combined effects from these dominate the lower uniform price charged by firm C
in the latter. As a result, total consumer surplus is higher in the accommodation equilibrium
I. When ω ∈ [2, 11/4], the comparison is between the accommodation equilibrium I under the
restriction and the monopolization equilibrium without the restriction. Since all prices decrease26

under the restriction, consumers are better off. The same argument applies when ω ≥ 11/4.
Proposition 7 Suppose firm C is not allowed to engage in below-cost pricing. The restriction√√
has no impact when ω ≤ 3( 385 − 11)/16. If ω ≥ 3( 385 − 11)/16, then• both firms A2 and B2 benefit at the cost of firm C;• consumer surplus increases in market A, but decreases in market B;• the ban prevents monopolization so all consumers can benefit in the long run compared towhen below-cost pricing is allowed.

5.3

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 and rapidly changing digital industries,
which may leave blocking the merger as the only alternative. As discussed in Proposition 5,
the key welfare implications of blocking the merger hinge on the consumption synergy, whichmakes the merging parties more aggressive. Thus, if the consumption synergy is significant,then allowing a merger is more likely to lead to monopolization of both markets. In this case,
blocking the merger is a convincing policy option to consider.

6

Extensions and Discussions

6.1

Imperfect preference correlation

One of our simplifying assumptions is that consumer preferences are perfectly correlated acrossthe two markets. We now discuss a case where preferences are imperfectly correlated. Imperfect correlation implies that consumer data collected in market B is less valuable in market A
than the case with perfect correlation. This reduces firm C’s incentives for data collection andhence softens competition in market B. This in turn softens competition in market A sincefirm C’s target segment is smaller and, in addition, firm C’s personalized prices cannot be precisely matched to its targeted consumers. Thus, compared to the case with perfectly correlated
preferences, we expect firm C to be worse off while its stand-alone competitors are better off.
Reduced competition in market B implies consumers are worse off whereas changes in consumer
surplus in market A depend on the way imperfect correlation is modelled.
We consider a simple case of imperfectly correlated preferences in Armstrong and Vickers(2010). Suppose that a fraction ρ ∈ [0, 1) of consumers in market B have exactly the same
preferences in market A whereas the remaining consumers have independent preferences, whichis common knowledge. The parameter ρ measures the preference link across the two markets,with ρ = 1 corresponding to our main model and ρ = 0 implying independent preferences. In
addition, we assume that, once firm C has collected data on the segment [0, x∗ ] in market B, it
can recognize the exact locations of the fraction ρ of these consumers in market A, for whom it
27can offer personalization. For the remaining fraction, it can offer only a uniform price based on
the belief that consumers are uniformly distributed on [0, 1].
With this modification, one can show that there continue to exist the accommodation equilibria and the monopolization equilibrium. But, compared to the case with ρ = 1, prices inmarket B in the accommodation equilibria are higher and the monopolization equilibrium ispossible for larger values of ω. This is intuitively clear since consumer data has now less value
than when ρ = 1. Thus competition is softened in market B and monopolization is less likely
as a result. This also means that firm C is worse off while firm B2 is better off. Imperfectpreference correlation also benefits firm A2 because firm C’s target segment is smaller and its
personalization is less effective than when ρ = 1. While consumers in market B are worse off
due to softened competition, the comparison of consumer surplus in market A is not as straightforward since it involves changes in equilibrium prices and consumers’ purchase decisions, where
only the fraction ρ of consumers in the target segment pay the personalized price.
As an example, denote firm C’s share of market B by [0, x(ρ)] and its uniform prices inmarket A by α1 (ρ) and α2 (ρ) in the accommodation equilibrium for some ω and ρ < 1. Suppose
the same ω leads to the accommodation equilibrium I when ρ = 1, with the corresponding
market share and prices denoted by x∗ , α1∗ , and α2∗ . In the Online Appendix, we show x(ρ) =(3(9 + 2ρ + 3ρω))/(72 + 9ρ − 4ρ2 ) < x∗ . Thus α1 (ρ) = 1 − (4ρx(ρ))/3 > α1∗ = 1 − (4x∗ )/3,and α2 (ρ) = 1 − (2ρx(ρ))/3 > α2∗ = 1 − (2x∗ )/3. In this case, consumer surplus in market A issmaller when ρ < 1. We can verify that the equilibrium prices in market B are also higher when
ρ < 1. In this sense, imperfect preference correlation softens competition in both markets. The
complete analysis is provided in the Online Appendix.
Proposition 8 Suppose a fraction ρ ∈ [0, 1) of consumers in market B have exactly the same
preferences in market A while the remaining consumers have independent preferences.
• Firm C is worse off but firms A2 and B2 are better off compared to when ρ = 1.
• The monopolization equilibrium arises when ω ≥ (15 − 16ρ + 5ρ2 )/(3ρ(1 − ρ)) > 2, hence
is less likely than when ρ = 1.
• Compared to when ρ = 1, consumer surplus in market B is larger, but consumer surplus√
in market A is smaller if ω < 3( 385 − 11)/16.

6.2

Heterogeneous consumer types in market A

We have represented each market in our model by a horizontally differentiated Hotelling line.
Given that our motivating example is Google/Fitbit, our choice of a Hotelling line for market A
was intended to capture one aspect of health care, namely, product differentiation, as we have
explained in Section 2. Nevertheless, this ignores other aspects of health care such as different
risk types into which consumers can be segmented into. In this section, we extend the model in
Section 3 by considering a simple case of two risk types with different costs of service, and showthat our analysis of the baseline model continues to be valid if the cost difference is not large.
28

We also show that, when the cost difference is large, cream skimming can arise where firm C
uses data to screen out some high-cost consumers, who are then served by firm A2 . Thus market
A in our baseline model can be best understood as representing a segment of health care where
the costs of serving different types of consumers are not very different.
Suppose there are two types of consumers in market A with equal proportion, indexed byθ = L (low-risk) or θ = H (high-risk). The cost of serving a type H consumer is c > 0 and thatof serving a type L consumer is normalized to zero. Each type is represented by a unit-length
Hotelling line, exactly the same as in our baseline model. For a targeted consumer x ∈ [0, δA ],firm C’s data covers (x, θ). Since types differ only in the cost of serving them, while personalized
prices depend on the rival’s uniform price and consumers’ locations only, firm C will continue
to choose the same personalized price for both types of consumers with the same location.
Assuming φA = 1, we then have pA (x) = 1 − x + α2 for all x ∈ [0, δA ] and θ = H, L. For all
consumers outside its target segment, firm C chooses a single uniform price α1 for both types.
Likewise, firm A2 chooses the same uniform price α2 for all consumers of either type.
With the above modification, it is easy to see that the equilibrium outcome of Section 3
continues to obtain for each type when c is not large enough. To see this, note that the Hotellingcompetition on [δA , 1] is now modified so that each firm has the expected cost c/2 of serving a
consumer. Thus firm C chooses α1 to maximize (α1 − c/2)(x̂ − δA ) and firm A2 chooses α2 tomaximize (α2 − c/2)(1 − x̂) where x̂ = (1 + α2 − α1 )/2. This leads to the equilibrium uniform
prices in Section 3 augmented by c/2. On the other hand, since firm C can identify consumer
types in its target segment, it will serve all type-H consumers in [0, δA ] if and only if pA (δA ) ≥ c.
In this case, we have qualitatively the same outcome for each type as in Section 3. But if
pA (ξ) = c for some ξ ∈ [0, δA ), then firm C will stop serving consumers in (ξ, δA ] since pA (x) < c
for all x ∈ (ξ, δA ]. Firm A2 cannot identify these consumers and will make a loss from these
consumers since α2 < c. In this cream-skimming equilibrium, firm C serves all type-L targeted
consumers, type-H targeted consumers in [0, ξ], and some non-targeted consumers. Thus theset of type-H consumers served by firm C is not contiguous. The following proposition provides
sufficient conditions for the two types of equilibria described above.34
Proposition 9 Suppose there are two types of consumers (H, L) in market A with equal proportion and only a type-H consumer incurs cost of service c.
• If c ≤ 3/2, then the equilibrium is qualitatively the same for each type as in Section 3.
• If c ∈ (3/2, 5] and δA ∈ [1/2, 4/5], then a cream-skimming equilibrium exists with ξ ∈(0, δA ) and x̂ ∈ (δA , 1) such that firm C serves all type-L consumers in [0, δA ], type-H
consumers in [0, ξ], and both types of consumers in [δA , x̂], while firm A2 serves type-H
consumers in [ξ, δA ] and both types of consumers in [x̂, 1].
34
Characterizing the complete set of equilibria in the context of merger is beyond the scope of the current
paper, which we leave for future work.

29

6.3

Successive merger

After firms A1 and B1 merge, would stand-alone competitors choose to merge if they have an
opportunity to do so? How does such a successive merger affect consumer surplus? Intuitively,
firms A2 and B2 have incentives to merge (and create, say, firm D) because the successive
merger can level the playing field. This will make market A more competitive as both merged
entities will use personalization in competition. But the effect on market B is less clear since
the successive merger makes it more difficult for firm C to monopolize the market, which may
soften competition. In this section, we analyze the firms’ incentives for successive merger andits welfare effect. To make the comparison with the baseline case meaningful, we assume firm C
moves first in market B after the successive merger, personalization is perfect and costless forboth firms C and D, but the consumption synergy exists only for firm C.
Let us analyze the equilibrium given the successive merger. First, in market A with firm C’s
target segment given by [0, x∗ ], firm D’s target segment is [x∗ , 1]. Each firm uses personalizationand serves all consumers in its target segment, which leads to equilibrium personalized prices
R x∗
R1
pC (x) = 1 − x + ω, pD (x) = x, resulting in profits πC = 0 (1 − x + ω)dx and πD = x∗ xdx.
Next, in market B, firm C chooses β1 to maximize ΠC = πC + β1 x∗ and firm D chooses β2
to maximize ΠD = πD + β2 (1 − x∗ ) where x∗ = (1 − β1 + β2 )/2. This leads to two possible
outcomes: (i) if ω ≤ 7, then we have an equilibrium with x∗ = (ω + 4)/11 ∈ (0, 1); (ii) if ω ≥ 7,then we have an equilibrium where firm C monopolizes the market by choosing β1∗ = −2.
The above shows that the successive merger has two main effects. First, it makes monopolization less likely since the monopolization equilibrium obtains when ω ≥ 2 without the successive
merger. Second, it makes monopolization more costly for firm C since the price it chooses tomonopolize market B is β1 = −2 instead of β1 = −1 as in the baseline model. As a result,consumers in market A benefit from the successive merger. But in market B, the effect is lessclear when ω ∈ (2, 7): without the successive merger, the market is monopolized by firm Cwith β1 < 0 but, with the successive merger, both firms are active, implying that prices canrise. Given that firm C chooses below-cost pricing in the accommodation equilibrium II in thebaseline model, we expect that the successive merger may decrease consumer surplus for somerange of ω that supports the accommodation equilibrium II. Comparing profits and consumer
surpluses with or without the successive merger, we obtain the following results.
Proposition 10 Suppose firms A2 and B2 can choose to merge following the merger between
firms A1 and B1 .
• If ω < 7, then they prefer merger to remaining independent.
• If ω ≥ 7, then they are indifferent between merger and remaining independent.
• Firm C’s profit is smaller after the successive merger.
• Consumer surplus is larger in market A after the successive merger. In market B, it is√√larger after the successive merger except when ω ∈ [3( 385 − 11)/16, (11 21 − 41)/2].
30

6.4

Personalization without personalized pricing

Although personalization can benefit consumers by increasing matching value, personalized pricing can be used as a tool to extract the improved matching value. Then, would consumers benefit
when firm C offers personalization but is not allowed to use personalized pricing? Clearly, thiswould hurt firm C by limiting its ability to extract surplus from its targeted consumers. On theother hand, firm C continues to enjoy a competitive advantage over firm A2 because only it canoffer personalized products. To analyze this problem, we consider a case where firm C uses two
uniform prices, one for its targeted consumers denoted by pC , and the other for non-targeted
consumers denoted by α2 as before. Consistent with the timeline in the baseline model, we
assume pC is chosen after the other uniform prices are chosen. To simplify analysis, we focus on
the case ω > 1.35
Although firm C cannot use personalized pricing, it can still serve all its targeted consumers
thanks to its competitive advantage. To see this, let xC ∈ [0, x∗ ] be the marginal consumer
defined by vA + ω − pC = vA − (1 − xC ) − α2 , hence pC = 1 + ω + α2 − xC . On [0, x∗ ], firm C
chooses pC to maximize pC xC . Given ω > 1, the solution obtains at the boundary, i.e., xC = x∗
and pC = 1 + ω + α2 − x∗ . Compared to the case without the restriction, firm C chooses thelowest personalized price that makes consumer x∗ indifferent, rather than choosing different
personalized prices for all targeted consumers. Thus the restriction limits firm C’s ability to
extract consumer surplus. Nevertheless, firm C continues to serve all its targeted consumers,
which implies that the equilibrium structure is the same as that in the baseline model. That is,
as ω increases, the equilibrium changes from accommodation to monopolization.
The main effect of the restriction is to soften competition in market B since consumer data
has less value in market A due to firm C’s reduced ability for surplus extraction. It thenfollows that the restriction benefits firm B2 but harms consumers in market B. In market A,
targeted consumers clearly benefit from the restriction. But the restriction reduces firm C’s
target segment, hence softens competition for non-targeted consumers. Thus the restriction
raises uniform prices and benefits firm A2 , but harms non-targeted consumers. But the first
effect dominates the second and, as a result, consumer surplus in market A increases after the
restriction. Finally, the restriction makes monopolization less likely than without the restriction.
Proposition 11 Suppose firm C can use only uniform pricing for its targeted consumers.
√• The accommodation equilibrium I arises when ω < 3( 129 − 5)/8 ' 2.384, the accom√
modation equilibrium II arises when 3( 129 − 5)/8 ≤ ω < 3, and the monopolization
equilibrium arises when ω ≥ 3.
• Compared to when firm C can use personalized pricing, firm C is worse off, but firms A2
and B2 are better off.
√
Since the equilibrium in the baseline model has cutoff values ω = 3( 385 − 11)/16 > 1 and ω = 2, thisassumption is innocuous for the purpose of comparison.
35

31

• Compared to when firm C can use personalized pricing, consumer surplus is larger inmarket A but smaller in market B.

6.5

Repositioning by the merged firm

In Section 4, we assumed that the merged firm continues to market the same standard productin market A. But the availability of customer data may help firm C to optimally reposition its
standard product. Since firm C can serve all consumers in its target segment given φA = 1, it
may have incentives to move the Hotelling battleground further to the right by repositioning
its standard product closer to firm A2 ’s location. This can allow firm C to serve more nontargeted consumers at a higher uniform price, which is the benefit from repositioning. But
such repositioning will intensify competition for non-targeted consumers and decrease firm A2 ’s
uniform price, which in turn decreases firm C’s personalized prices. Thus firm C’s profit fromits target segment decreases, which is the cost of repositioning. This discussion suggests thatfirm C’s repositioning decision hinges on its data scale δA . If δA is small, then the benefit from
repositioning can outweigh the cost. In this case, firm C will choose an interior location after
repositioning. If δA is large, then the cost of repositioning can outweigh the benefit, hence firm
C will choose not to reposition its standard product.
To elaborate on the above discussion, let x̂ be the marginal consumer given the uniform
prices (α1 , α2 ) when firm C does not reposition. Suppose now firm C chooses to reposition
at z ∈ (0, δA ] and denote the corresponding prices and marginal consumer by (α10 , α20 ) and x̂0 .
Since z > 0, we have α10 > α1 , α20 < α2 and x̂0 > x̂. Then the change in firm C’s profit can be
decomposed into the following three components.
∆πC =(α0 − α )δ| 2 {z 2 A}(-) targeted consumers+

α10 (x̂0 − x̂)| {z }(+) new non-targeted consumers+(α0 − α1 )(x̂ − δA )
| 1
{z
}

.

(16)

(+) old non-targeted consumers

That firm C chooses z > 0 implies ∆πC ≥ 0, which in turn can be shown to imply z ≥ 14δA − 6.
Moreover, ∆πC is increasing in z when z ≥ 14δA − 6. The main reason for this is that the lossesin (16) are linear in z while the gains are quadratic in z. Thus we can conclude that firm C
will optimally reposition at z = δA if 14δA − 6 ≤ z ≤ δA , or if δA ≤ 6/13. Clearly, firm C’s
repositioning hurts firm A2 . But consumers benefit because both firm C’s personalized prices
and firm A2 ’s uniform price decrease, although firm C’s uniform price increases. The following
proposition formalizes our discussions above.36
Proposition 12 Suppose firm C can reposition its standard product in market A at z given its
target segment [0, δA ].
36

We only present the analysis of market A. The full analysis of both markets does not alter the main insightprovided in Proposition 12. But it is rather messy and available from the authors.

32• If δA ≤ 6/13, then firm C chooses z = δA , which decreases firm A2 ’s profit but increases
consumer surplus.
• If δA > 6/13, then firm C does not reposition its standard product, i.e., z = 0.

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 the Google’s acquisition of Fitbit, werecapitulate 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 we have provided
justification and evidence.
First, the merger harms stand-alone competitors in both markets. Second, the merger intensifies competition and, in the short run, benefits consumers in the market for wearable devices.
These benefits stem from lower prices due to Google’s incentives to gather a large amount of consumer data that it can leverage in the digital health market. Third, in the digital health market,
the merger can increase consumer surplus if the consumption synergy is not large enough, but
decreases it otherwise. The increase in consumer surplus is not driven by efficiency gains thatare passed on to consumers since the efficiency gains are extracted away through personalized
pricing; rather, it is the result of intensified competition for consumers for whom Google does
not have data. Fourth, markets can tip in Google’s favor when the consumption synergy is
sufficiently large, which harms consumers in both markets in the long run. In sum, data-driven
tech mergers may generate short-term consumer benefits in the form of lower prices. But they
are driven not by the efficiency gains being passed on to consumers but by Google’s pricing
strategies to increase its data scale. Consequently, the long-term consumer harm due to market
tipping is likely to be more substantial than short-term benefits.
We have examined the effects of blocking the merger as well as policy remedies such as data
sharing 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, theeffectiveness of merger remedies assumes the effectiveness of monitoring and enforcement, which
can be a tall order in complex digital industries. We have also shown that allowing consecutive
mergers can benefit consumers. For example, if the Google/Fitbit merger is approved, thenallowing Apple’s expansion into the digital health market can have pro-competitive effects.37
37

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

Finally, we have assumed away issues such as adverse selection, moral hazard, and privacy
concerns in health care, which we have chosen as the market for data application. Personalizationin this market can help screen consumers and ameliorate adverse selection, although it could
amplify privacy concerns. Competition between firms with asymmetric information and the useof personalization by a better informed firm may also lead to cream skimming, as we have briefly
touched upon in Section 6.2. 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 α2 given in Proposition 1 isuniquely optimal for firm A2 , hence firm A2 has no incentive for unilateral deviation. 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 choice of α1 is its best
response to the equilibrium α2 , hence there is no reason for unilateral deviation. Finally, 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 the uniform and personalized prices. In
what follows, we show that firm C cannot benefit from the global deviation.
Let us start with the case δA < δ̄. Then firm C serves all targeted consumers in [0, δA ] withpersonalized 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. Thus the only possible deviation isin uniform price, which 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 0, and so is its uniform
price, 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
Let us start with firm C. Recall that firm A1 ’s pre-merger profit is 1/2. First, when δA < 3/4,
2 + 2 δ + 1/2 > 1/2. When 3/4 ≤ δ < δ̄, firm C’s
firm C’s profit is Π∗C = − ((14 − 9φA )/18) δA
A
3 A

34

2
∗∗
profit is Π∗∗
C = ((2 + φA )/2) δA . It is easy to see that ΠC increases in δA for δA > 3/4. Thus∗∗
we have Π∗∗
C (δA ) > ΠC (3/4) = 1/2 + (9φA + 2)/32 > 1/2. Finally, when δA ≥ δ̄, firm C’s
2∗∗∗
profit is Π∗∗∗C = (3 − φA ) /(8(2 − φA )). Differentiating ΠC with respect to φA , we can show
∗∗∗
∗∗∗
∂Π∗∗∗
C /∂φA < 0. Moreover, we have ΠC = 1/2 when φA = 1. Thus ΠC ≥ 1/2 always holds.

Consider next firm A2 . When δA ≤ 3/4, Π∗A2 = (1 − (2δA )/3)2 /2 < 1/2, and the profit
2
is decreasing in δA . When 3/4 < δA < δ̄, firm A2 ’s profit is Π∗∗
A2 = 3δA − 1 − 2δA , which isdecreasing in δA and is less than Π∗∗A2 (3/4) = 1/8. Finally, when δA > δ̄, it is straightforward2
to check Π∗∗∗A2 = (1 − φA ) /(4(2 − φA )) < 1/2. Thus firm A2 is worse off after the merger.
R 1/2
We now turn to the total consumer surplus. Before the merger, it is given by S0 ≡ 0 (vA −R1
x − 1)dx + 1/2 (vA − (1 − x) − 1)dx = vA − 5/4. After the merger, targeted consumers receive

the same surplus as when they choose firm A2 , hence vA − (1 − x) − α2 . First, when δA < 3/4,Rδ
we have α2∗ = 1 − (2δA )/3, hence the post-merger total consumer surplus is S1 ≡ 0 A (vA −R x̂
R1
2 )/9 > S .
(1 − x) − α2∗ )dx + δA (vA − x − α1∗ )dx + x̂ (vA − (1 − x) − α2∗ ) dx = vA − 5/4 + (4δA
0
Next, when 3/4 ≤ δA < δ̄, we have α2∗∗ = 2δA − 1, so the post-merger consumer surplus
R1
is S1 = 0 (vA − (1 − x) − α2∗∗ ) dx = vA + 1/2 − 2δA . Thus S1 ≥ S0 if δA ≤ 7/8. Noticethat δ̄ ≤ 7/8 if and only if φA ≤ 2/3. It then follows that S1 < S0 only if φA > 2/3 andδA ∈ (7/8, δ̄). Finally, when δA > δ̄, we have α2∗∗∗ = (1 − φA )/2, and the total consumer surplus
R1
is S1 = 0 (vA − (1 − x) − α2∗∗∗ ) dx = vA − 1/2 − (1 − φA )/2 > vA − 5/4.

Proof of Proposition 3
We make use of the expressions derived in the proof of Proposition 2. Consider first firm C.
When δA < 3/4, Π∗C is concave in δA and reaches a maximum when δA = δ ∗ = 6/(14−9φA ) whereδ ∗ ≤ 3/4 if and only if φA ≤ 2/3. Differentiating Π∗C with respect to φA , we have ∂Π∗C /∂φA =2 /2 ≥ 0. When 3/4 ≤ δ < δ̄, one can verify that ∂Π∗∗ /∂δ ≥ 0 and ∂Π∗∗ /∂φ ≥ 0. When
δA
A
A
A
C
C
∗∗∗
δA > δ̄, Π∗∗∗C is independent of δA , but one can verify ∂ΠC /∂φA ≤ 0. Consider next firm A2 .
∗∗∗Clearly, both Π∗A2 and Π∗∗
A2 are decreasing in δA but independent of φA . But ΠA2 is decreasingin φA but independent of δA . Finally, consider consumer surplus. When δA < 3/4, the consumer
2 )/9. Clearly, S increases in δ but is independent of φ . Whensurplus is S1 = vA − (5/4) + (4δA
1AA

3/4 ≤ δA < δ̄, we have S1 = vA − 2δA + 1/2, which is decreasing in δA but independent of φA .
When δA > δ̄, we have S1 = vA − 1/2 − (1 − φA )/2, which is increasing in φA but independentof δA .

Proof of Proposition 5
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.
Consider first the pre-merger equilibrium. In market A, the prices are α10 = α20 = 1 and
R 1/2
0 =
the marginal consumer is at 1/2. The resulting consumer surplus is CSA
0 (vA − x −351)dx +

R1

1/2 (vA − (1 − x) − 1)dx

= vA − 5/4. In market B, the prices are β10 = 3/2 and0 =β20 = 5/4 and the marginal consumer is at 3/8. The resulting consumer surplus is CSB

R 3/8
R
1
0
0
0 (vB − x − β1 )dx + 3/8 vB − (1 − x) − β2 dx = vB − 103/64.

It is straightforward to see that total consumer surplus in market B after the merger is larger
than that before the merger in all post-merger equilibria. This follows largely from the fact that
post-merger prices are lower than pre-merger prices. So we consider only market A. In theaccommodation equilibrium I, using (11) and (12), one can calculate the consumer surplus in
I = v +(36ω 2 )/5929+(24ω)/539−229/196. In the accommodation equilibrium
market A as CSAA
II = v −(2ω)/5−7/10. In the monopolization equilibrium,
II, from (14) and (15), we obtain CSAA
M = v − 3/2. From these follow max{CS II , CS M } ≤ CS 0 ≤ CS I . Finally, in the
we have CSA
A
A
A
A
A

monopoly equilibrium when ω > 2, total consumer surplus is zero in market A. In market B,
0 since v > 3.
total consumer surplus is (vB − 1)/2, which is smaller than CSB
B

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39

Online Appendix for Data-Driven Mergers and Personalization
 Proof of Proposition 6
We use notation pC (x) to denote firm C’s personalized price to distinguish it from pA (x) used in
Section 4. We also denote the marginal consumer in market B by x̃ to facilitate comparison withx∗ in the previous section. Given firm C’s target segment [0, x̃], let x̂ be the marginal consumer
in market A when competition 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) =1 + ω + α2 − x, 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.
1. Analysis of market A
We divide analysis to two cases. First, suppose 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.
Next, suppose x̂ < x̃ ≤ 1. 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. It
is easy to check that firm C has no incentive to deviate and firm A2 has no incentive to deviate
to a lower price. Suppose now firm A2 deviates by raising its price to α2d > 2x̃ − 1. Then its
deviation profit is α2d 1 − (1 + α2d )/2 . Thus the deviation is not profitable if 2x̃ − 1 ≥ 1/2, orx̃ ≥ 3/4. Thus this equilibrium is possible if x̃ ≥ 3/4.
2. Analysis of market B
Based on the analysis of market A, we consider two separate cases. First, consider the casex̃ ≤ 3/4. Then firm C chooses β1 to maximize profit
Z x̃





4x̃
1 x̃
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 + β2 ) β1 + (1 + β2 ) +ω−(1 + β2 ) + .
36
2 3
9
9
2
3
2
Firm B2 chooses β2 to maximize its profit ΠB2 = β2 (1 − x̃). This leads to the best response
β2 = (1 + β1 )/2, hence x̃ = (3 − β1 )/4. The condition 0 ≤ x̃ ≤ 3/4 is equivalent to 0 ≤ β1 ≤ 3.
Substituting firm B2 ’s best response to ΠC and solving for firm C’s optimal β1 , we obtain
β1 = 9(3 − ω)/14 if ω ≤ 3, and β1 = 0, otherwise.
Consider next the case x̃ ≥ 3/4. As before, firm B2 ’s best response is β2 = (1 + β1 )/2 andx̃ = (3 − β1 )/4. Thus the condition 3/4 ≤ x̃ ≤ 1 is equivalent to −1 ≤ β1 ≤ 0. Firm C chooses
β1 to maximize

Z x̃
ΠC = β1 x̃ +pC (x) dx = (β1 + ω) x̃.
01This gives us β1 = 0 if ω ≤ 3, β1 = (3 − ω)/2 if ω ∈ [3, 5], and β1 = −1 if ω ≥ 5.
Comparing profits from the two cases to find a global optimum for the given range of ω, we
obtain the following. If ω ≤ 3, then the equilibrium prices areβ1∗ =9(3 − ω)41 − 9ω
15 + 9ω
9 − 3ω
23 − 3ω
33 + 3ω, β2∗ =, x̃ =, α1∗ =, α2∗ =, x̂ =
.
14
28
56
14
28
56

This is the accommodation equilibrium I. Profits in this case are9ω 2 + 30ω + 81
1
, Π∗A2 =
112
2

Π∗C =



23 − 3ω
28

2, Π∗B2 =12

41 − 9ω
28

2.

If 3 ≤ ω ≤ 5, then the equilibrium prices are
β1∗ =

3−ω
5−ω
3+ω
ω−1
, β2∗ =, x̃ =, α1∗ = 0, α2∗ =
.
2
4
8
4

This is the accommodation equilibrium II where profits areΠ∗C =(ω − 1)(5 − ω)
(5 − ω)2(3 + ω)2, Π∗A2 =, Π∗B2 =
.
16
32
32

When ω ≥ 5, we have the monopolization equilibrium with prices β1∗ = −1 and β2∗ = 0, andprofits Π∗C = ω − 1, Π∗A2 = Π∗B2 = 0.
From the profits derived above, it is straightforward to verify that firm C’s profit with data
sharing is smaller than that without data sharing, and firms A2 and B2 have larger profits underdata sharing for all values of ω ≤ 5. When ω ≥ 5, then both markets are monopolized with orwithout data sharing, so the profit comparison is trivial.
3. Comparison of consumer surpluses
Total consumer surplus without data sharing can be calculated as as follows. When ω ≤

143
81
180
2
98 − 5929 ω − 539 ω where√3( 385−11)
N SI = v + 36 ω 2 + 24 ω − 229 , CS N SI = v −
, CSA
A
B
B
16
5929
539
196

√

the superscript “NSI” indicates “no sharing accommodation I”. When 3( 385−11)≤ ω < 2,
16

2
7
47
1 2
16
N
SII
N
SII
CSA
= vA − 5 ω − 10 , CSB= vB − 50 − 25 ω − 25 ω where the superscript “NSII”
N SM = v − 3 , CS N SM = v + 1
indicates “no sharing accommodation II”. When ω ≥ 2, CSA
A
B
B
2
2

where the superscript “NSM” indicates “no sharing monopolization”.
With data sharing, total consumer surplus can be calculate as follows. When ω ≤ 3,
DSI
CSA
=

Z 1 + x̃Z x̃2(vA + ω − pC (x))dx +03(vA − x − α1∗ )dx +

x̃

13 2
5
(x̃) + 2x̃ −
18
4
117 2
813
4805
= vA −
ω +
ω−
,
6272
3136
6272

= vA −

2

Z 1
1
+ x̃3
2

(vA − (1 − x) − α2∗ )dx

DSI
CSB
=

Z x̃

(vB − x − β1∗ )dx +Z 1(vB − (1 − x) − β2∗ )dx

x̃

0




Z 15+9ω 
Z 156
9(3 − ω)41 − 9ω=dx +dxvB − x −vB − (1 − x) −
15+9ω
14
28
0
56

81 2
639
5935
= vB +
ω +
ω−
,
3136
1568
3136
where the superscript “DSI” indicates “data sharing accommodation I”. When 3 ≤ ω ≤ 5,
DSII
CSA
=

Z 1

Z x̃
(vA + ω − pC (x))dx +

x̃

0

Z 3+ω
8

=

Z 1
(vA + ω − ω)dx +0= vA +

DSII
CSB
=

Z x̃

(vB − x − β1∗∗ )dx +(vA − (1 − x) −

ω−1
)dx
4

Z 1

(vB − (1 − x) − β2∗∗ )dxx̃

Z 3+ω 
8

0

3+ω
8

3 2
7
5
ω − ω−
,
128
64
128

0

=

(vA − (1 − x) − α2∗∗ )dx3−ω
vB − x −
2




Z 1 
5−ω
dx +
vB − (1 − x) −
dx
3+ω
4
8

1
11
103
= vB + ω 2 + ω −
,
64
32
64
where the superscript “DSII” indicates “data sharing accommodation II”. When ω ≥ 5,
DSM
CSA
=

Z 1

DSM
(vA + ω − pC (x))dx = vA , CSB
=

0

Z 1

1
(vB − x − β1∗∗∗ )dx = vB + ,20where the superscript “DSM” indicates “data sharing monopolization”.
Based on the above, we can verify that data sharing always increases total consumer surplus
in market A. In market B, total consumer surplus strictly decreases when ω < 5, but does notchange when ω ≥ 5 when the market is monopolized with or without data sharing.

 Proof of Proposition 8
As described in the main text, a fraction ρ ∈ [0, 1) of consumers in market B have exactly thesame preferences in market A whereas the remaining fraction of consumers have independent
preferences, which is common knowledge. In addition, once firm C has collected data on [0, x∗ ]in market B, it can recognize the exact locations of the fraction ρ of these consumers in market
A, for whom it can offer personalized prices. For the remaining fraction, it can offer only auniform price.
1. Analysis of market A

3

As before, let x̂ = (1 − α1 + α2 )/2 be the marginal consumer when competition is in uniform
price. We divide the analysis into two cases: x̂ > x∗ and x̂ ≤ x∗ . For its targeted consumers,
firm C’s personalized prices are given by pA (x) = 1 − x + ω + α2 . Clearly, firm C can serve allof its targeted consumers since pA (x) > 0 when α2 = 0. We proceed as follows. For each case,
we first identify the candidate equilibrium by solving best response functions simultaneously.
This candidate equilibrium prescribes locally optimal prices for each firm within each case only.
Thus we check the possibilities of deviations across the two cases.
(i) x̂ > x∗
Firm C chooses α1 to maximize α1 [(1 − ρ)x∗ + x̂ − x∗ ], which leads to the best response
α1 = (1 + α2 )/2 − ρx∗ . Firm A2 chooses α2 to maximize ΠA2 = α2 (1 − x̂), hence the best
response is α2 = (1 + α1 )/2. Solving them together gives us uniform prices
42α1∗ = 1 − ρx∗ , α2∗ = 1 − ρx∗ ,
3
3

(1)

and the marginal consumer x̂ = 1/2 + (ρx∗ )/3. The resulting profits for firms C and A2 are(3 − 4ρx∗ )2 /18 and (3 − 2ρx∗ )2 /18 respectively. For this equilibrium to exist, we need α1∗ ≥ 0
and x̂ > x∗ , which are equivalent to
x∗ <

3
.
6 − 2ρ

(2)(ii) x̂ ≤ x∗
In this case, firm C chooses α1 to maximize α1 (1 − ρ)x̂, which leads to the best response
α1 = (1 + α2 )/2. Firm A2 chooses α2 to maximize ΠA2 = α2 [(1 − ρ)(x∗ − x̂) + (1 − x∗ )], hence
its best response is α2 = (1 − ρx∗ )/(1 − ρ) − (1 − α1 )/2. Solving them together gives us uniform
prices38α1∗∗ = 1 +4ρ(1 − x∗ )2ρ(1 − x∗ ), α2∗∗ = 1 +,
3(1 − ρ)3(1 − ρ)(3)and the marginal consumer x̂ = (1 − ρx∗ )/(3(1 − ρ)) + 1/6. The resulting profits for firms C
and A2 are (3 − ρ − 2ρx∗ )2 /(18(1 − ρ)) and (3 + ρ − 4ρx∗ )2 /(18(1 − ρ)) respectively.
3−ρThe condition x̂ ≤ x∗ is equivalent to x∗ ≥ 6−4ρ. We also need the marginal consumer toobtain non-negative utility, i.e., vA − x̂ − α1∗∗ ≥ 0, which is equivalent to x∗ ≥ 1+2ρ3ρ −(vA − 76 )(1−ρ)
.
ρ

A −9
We focus on the case ρ ≤ 6v
6vA −3 so that this condition always holds, which is reproduced below:

x∗ ≥

3−ρ
.
6 − 4ρ

(4)

We now check deviation incentives across the two cases, starting from deviations from case38

When ρ = 1, firm C cannot serve any consumers with uniform price. Firm A2 ’s profit function becomesΠA2 = α2 (1 − x∗ ). Then the equilibrium uniform prices are α1 = 0 and α2 = 2x∗ − 1 and x̂ = x∗ . Thus theequilibrium prices are discontinuous at ρ = 1.

4

(i) to case (ii). First, we check the condition that firm C does not deviate from α1∗ in (1) to the
locally optimal α1 in case (ii). Given α2∗ in (1), the optimal deviation price is α1d∗ = 1 − ρx∗ /3,
which satisfies x̂d ≤ x∗ if and only if x∗ > 3/(6 + ρ). The resulting deviation profit for firm
C is π1d∗ = (1 − ρ)(3 − ρx∗ )2 /18, which is smaller than (3 − 4ρx∗ )2 /18 if and only if x∗ <√(3(3 + ρ − 3 1 − ρ))/(ρ(15 + ρ)). Second, we check the condition that firm A2 does not deviate
from α2∗ in (1) to the locally optimal α2 in case (ii). Given α1∗ in (1), the optimal deviation priceis α2d∗ = (3 − ρ(5 − 2ρ)x∗ )/(3(1 − ρ)), which satisfies x̂d ≤ x∗ if and only if x∗ > 3/(6 − 5ρ + 2ρ2 ).
The resulting deviation profit for firm A2 is π2d∗ = (3−ρ(5−2ρ)x∗ )2 /(18(1−ρ)), which is smallerpthan (3 − 2ρx∗ )2 /18 if and only if x∗ > (3(3 − 9 − 21ρ + 16ρ2 − 4ρ3 ))/(ρ(21 − 16ρ + 4ρ2 )).
The latter is satisfied whenever x̂d ≤ x∗ holds.
From the above discussion, we can conclude that the prices in (1) constitute equilibrium if
and only if∗

x < min√√
33(3 + ρ − 3 1 − ρ)
3(3 + ρ − 3 1 − ρ),=.
6 − 2ρ
ρ(15 + ρ)ρ(15 + ρ)(5)Then firm C’s personalized prices are given by p∗A (x) = 2 − (2ρx∗ )/3 − x + ω. Firm C’s profit
in market A is
∗
πC
=ρ

Z x∗

p∗A (x)dx + α1∗ [(1 − ρ)x∗ + x̂ − x∗ ].

0

Next, we check the possibilities of deviations from case (ii) to case (i). First, we check thecondition that firm C does not deviate from α1∗∗ in (3) to the locally optimal α1 in case (i).
Given α2∗∗ in (3), the optimal deviation price is α1d∗∗ = (3 − ρ − ρ(5 − 3ρ)x∗ )/(3(1 − ρ)), which
satisfies x̂d ≥ x∗ if and only if x∗ < (3 − ρ)/(6 − 7ρ + 3ρ2 ). The resulting deviation profit for firm
C is π1d∗∗ = (3 − ρ − ρ(5 − 3ρ)x∗ )2 /(18(1 − ρ)2 ), which is smaller than (3 − ρ − 2ρx∗ )2 /(18(1 − ρ))√
if and only if x∗ > (3 − ρ)(3 − ρ − 3(1 − ρ) 1 − ρ)/(ρ(21 − 26ρ + 9ρ2 )).
Second, we check the condition that firm A2 does not deviate from α2∗∗ in (3) to the locally
optimal α2 in case (i). Given α1∗∗ in (3), the optimal deviation price, denoted by α2d∗∗ , can be
described as follows. When ρ ≤ 3/4, we have α2d∗∗ = (3 − 2ρ − ρx∗ )/(3(1 − ρ)), which satisfiesx̂d ≥ x∗ if and only if x∗ < (3 − 4ρ)/(6 − 7ρ)s. In this case, firm A2 ’s deviation profit is
π2d∗∗ = (3 − 2ρ − ρx∗ )2 /(18(1 − ρ)2 ). This deviation profit is smaller than firm A2 ’s equilibrium√
profit (3+ρ−4ρx∗ )2 /(18(1−ρ)) if and only if x∗ < (9−6ρ−4ρ2 −9(1−ρ) 1 − ρ)/(ρ(15−16ρ)),which holds whenever x̂d ≥ x∗ holds.
When ρ > 3/4, we have α2d∗∗ = ((6 − 8ρ)x∗ + 2ρ)/(3(1 − ρ)), which makes x̂d = x∗ . In thiscase, firm A2 ’s deviation profit is π2d∗∗ = ((6 − 8ρ)x∗ + 2ρ)(1 − x∗ )/(3(1 − ρ)). The deviation
profit is always smaller than firm A2 ’s equilibrium profit.
From the above discussion, we can conclude that the prices in (3) constitute equilibrium if
and only if∗

x ≥ max√√(3 − ρ)(3 − ρ − 3(1 − ρ) 1 − ρ)
3 − ρ (3 − ρ)(3 − ρ − 3(1 − ρ) 1 − ρ)
,
=
. (6)
6 − 4ρ
ρ(21 − 26ρ + 9ρ2 )ρ(21 − 26ρ + 9ρ2 )5

6vA −9and ρ ≤ min{ 43 , 6v
}.
A −3
∗∗
Firm C’s personalized prices are p∗∗
A (x) = 1 − x + ω + α2 and its profit in market A is
∗∗
πC
=ρ

Z x∗

∗∗
p∗∗
A (x)dx + α1 (1 − ρ)x̂.

0√√√(3−ρ)(3−ρ−3(1−ρ) 1−ρ)
1−ρ)3(3+ρ−3 1−ρ)<Notice that 3(3+ρ−3
holds
for
any
ρ
∈
(0,
1).
When
ρ(15+ρ)ρ(15+ρ)ρ(21−26ρ+9ρ2 )√(3−ρ)(3−ρ−3(1−ρ) 1−ρ)∗<x <, we do not find a pure-strategy equilibrium in market A.
ρ(21−26ρ+9ρ2 )(iii) Mixed strategy equilibrium
Since a pure strategy equilibrium does not exist if√√
3(3 + ρ − 3 1 − ρ)
(3 − ρ)(3 − ρ − 3(1 − ρ) 1 − ρ)∗<x <,ρ(15 + ρ)ρ(21 − 26ρ + 9ρ2 )we solve for a mixed strategy equilibrium below.
The non-existence of pure strategy equilibrium stems from firm C’s deviation incentives. So
we examine firm C’s best response in more detail. Firm C prefers choosing (1+α2 )/2 to choosing√(1 + α2 )/2 − ρx∗ if α2 ≤ ᾱ2 = −1 + 2(1 + 1 − ρ)x∗ ; it prefers choosing (1 + α2 )/2 − ρx∗ tochoosing (1+α2 )/2 if α2 ≥ ᾱ2 . This implies that both α1 = (1+ ᾱ2 )/2−ρx∗ and α1 = (1+ ᾱ2 )/2
are firm C’s best response to α2 = ᾱ2 . So, we consider the following mixed strategy: firm C
chooses α1 = (1 + ᾱ2 )/2 − ρx∗ with probability g and α1 = (1 + ᾱ2 )/2 with probability 1 − g.
We solve for g such that α2 = ᾱ2 is firm A2 ’s best response to firm C’s mixed strategy (g, 1 − g).
Given (g, 1 − g), there are three possibilities for α2 : (i) α2 satisfies x̂ < x∗ regardless of
the realized α1 ; (ii) α2 satisfies x̂ ≥ x∗ if the realized α1 is α1 = (1 + ᾱ2 )/2 − ρx∗ and α2satisfies x̂ < x∗ if the realized α1 is α1 = (1 + ᾱ2 )/2; (iii) α2 satisfies x̂ ≥ x∗ regardless of the√realized α1 . Thus we can consider α2 in three cases: (i) α2 < −1 + (3 − ρ + 1 − ρ)x∗ , (ii)√√√
−1 + (3 − ρ + 1 − ρ)x∗ ≤ α2 < −1 + (3 + 1 − ρ)x∗ , (iii) −1 + (3 + 1 − ρ)x∗ ≤ α2 .
The A2 ’s profit for the three cases can be calculated as
1 − ((1 + ᾱ2 )/2 − ρx∗ ) + α2∗
) + ρ(1 − x )gα2 (1 − ρ)(1 −


2






1 − ((1 + ᾱ2 )/2) + α2∗+(1 − g)α2 (1 − ρ)(1 −) + ρ(1 − x )in case (i),


2








1 − ((1 + ᾱ2 )/2 − ρx∗ ) + α2
 gα2 1 −2

1 − ((1 + ᾱ2 )/2) + α2
∗


+(1
−
g)α
(1
−
ρ)(1
−
)
+
ρ(1
−
x
)
in case (ii),
2


2








1 − ((1 + ᾱ2 )/2 − ρx∗ ) + α2
gα2 1 −


2







1 − ((1 + ᾱ2 )/2) + α2+(1 − g)α2 1 −in case (iii).
2
6

From the above, it is easy to find α2 = ᾱ2 = −1 + 2(1 +√1 − ρ)x∗ in case (ii). First, we checkthe optimal α2 in case (ii). Then we find g that makes the optimal α2 equal to ᾱ2 . Solving thefirst-order condition, we have√√
1 + ρ + (1 − 3ρ + (1 − ρ) 1 − ρ)x∗ + ρ(−1 + (2 + 1 − ρ)x∗ )gα2 =.
2(1 − ρ + ρg)
Then setting α2 derived above equal to ᾱ2 , we can derive√√
3 − ρ − (3(1 + 1 − ρ) − ρ(1 + 3 1 − ρ))x∗√.
g=
ρ(−1 + (2 + 3 1 − ρ)x∗ )It is easy to check that firm A2 ’s profit monotonically increases in α2 in case (i) and monotonicallydecreases in α2 in case (iii). Thus firm A2 does not deviate from α2 derived above. In sum, we
have found the following mixed strategy equilibrium: Firm C chooses
 1 + ᾱ2− ρx∗ with probability g ∗



2

 1 + ᾱ2∗∗∗with probability 1 − g ∗ , where
α1 =
2

√
√



3 − ρ − (3(1 + 1 − ρ) − ρ(1 + 3 1 − ρ))x∗ g∗ =√;
ρ(−1 + (2 + 3 1 − ρ)x∗ )(7)

Firm A2 chooses
α2∗∗∗ = ᾱ2 = −1 + 2(1 +p
1 − ρ)x∗(8)

with probability 1. This equilibrium exists, i.e., g ∗ ∈ [0, 1], if and only if√√
3(3 + ρ − 3 1 − ρ)
(3 − ρ)(3 − ρ − 3(1 − ρ) 1 − ρ)∗≤x ≤.
ρ(15 + ρ)ρ(21 − 26ρ + 9ρ2 )The threshold values perfectly coincide with the threshold values for which there is no purestrategy equilibrium. By the nature of mixed strategy, the firm C’s expected profit is equivalent
to that when firm A2 chooses α2∗∗∗ with probability 1 and firm C chooses α1 = (1 + ᾱ2 )/2 withprobability 1. Therefore, firm C’s equilibrium profit of is√(1 − (1 + α2∗∗∗ )/2 + α2∗∗∗ )(1 − ρ)(1 + 1 − ρ)2 (x∗ )2(1 + α2∗∗∗ )(1 − ρ)
=
.
2
2
2
∗∗∗
In addition, firm C obtains profits from personalized prices, p∗∗∗A (x) = 1 − x + ω + α2 :

Z x∗
ρ

√

ρx∗ (2ω + (3 + 4(1 − x + ω + α2∗∗∗ )dx =201 − ρ)x∗ ).

Notice that firm C’s profit is continuous in x∗ ∈ [0, 1]. This can be checked by substituting thethreshold value of x∗ in (5) (resp. x∗ in (6)) into the profit functions in cases (i) and (iii) (resp.
(ii) and (iii)) and verifying that their values are the same.
7

2. Analysis of market B
Firm C chooses β1 anticipating firm B2 ’s best response β2 (β1 ) = (1 + β1 )/2. We proceedwith analysis in the following sequence: i) x̂ > x∗ , (ii) mixed strategy equilibrium, (iii) x̂ ≤ x∗ .
√(i) x̂ > x∗ , or equivalently, x∗ < (3(3 + ρ − 3 1 − ρ))/(ρ(15 + ρ))
Firm C chooses β1 to maximize total profit from both markets
Z x∗p∗A (x)dx + α1∗ [(1 − ρ)x∗ + x̂ − x∗ ]ΠC = β 1 x + ρ
0




2 2 1
2
1
∗ 2
=
ρ − ρ (x ) + β1 + ρ + ρω x∗ + .
9
2
3
2
∗

Differentiating ΠC with respect to β1 , we obtainβ1 =3(36 + ρ − 4ρ2 − 12ρω),
72 + 9ρ − 4ρ2(9)

90 + 6ρ − 8ρ2 − 18ρω,
72 + 9ρ − 4ρ2

(10)

β2 =

and the marginal consumer’s location related to the above β1x∗ =3(9 + 2ρ + 3ρω).
72 + 9ρ − 4ρ2(11)

One can check that the above uniform prices are higher than their counterparts when ρ = 1(β1∗ = (99 − 36ω)/77 when x∗ < 3/4; β1∗∗ = (3 − 4ω)/5 when 3/4 < x∗ < 1). Thus, pricecompetition in market B is softened when consumers preferences are imperfectly correlated,which benefits firm B2 .

√Firm C’s price β1 given in (9) is the local optimum when x∗ < 3(3+ρ−3 1 − ρ)/(ρ(15+ρ)),which is equivalent to√2(36 − 6ρ − 7ρ2 − ρ3 ) − (72 + 9ρ − 4ρ2 ) 1 − ρω<≡ ω̂1 ,
ρ2 (15 + ρ)

(12)

√

otherwise, the corner solution, β1 = 3(12 1−ρ−(1−ρ)(12+ρ))is the local optimum in case (i).
ρ(15+ρ)To summarize case (i), the equilibrium prices and the marginal consumer in market B aregiven by (9), (10), and (11). In market A, the equilibrium prices are given by (1) and the marginal
consumer is x̂ = 1/2 + (ρx∗ )/3. Firm C’s personalized prices are p∗A (x) = 2 − (2ρx∗ )/3 − x + ω.

8Then the equilibrium profits are
Π∗C =






2
1
2 2 1
∗ 2
∗
ρ − ρ (x ) + β1 + ρ + ρω x∗ + ,92
32

Π∗B2 = β2∗ (1 − x∗ ),Π∗A2 = α2∗ (1 − x̂) =

(13)
(14)



2
1 − ρx∗
3



ρx∗

1
−
2
3


.

(15)

One can verify that firm C’s total profit is smaller than when ρ = 1. But both firms B2 andA2 benefit when preferences are imperfectly correlated since their prices are higher and market
shares are larger.
√(ii) Mixed strategy equilibrium, or equivalently, (3(3 + ρ − 3 1 − ρ))/(ρ(15 + ρ)) ≤ x∗ ≤ (3 −√ρ)(3 − ρ − 3(1 − ρ) 1 − ρ)/(ρ(21 − 26ρ + 9ρ2 ))Firm C chooses β1 to maximize total profit from both markets∗

Z x∗

ΠC = β 1 x + ρ(1 − ρ)(1 +p∗∗∗
A (x)dx +√1 − ρ)2 (x∗ )22√(ρ(3 + 4 1 − ρ) + (1 − ρ)(1 + 1 − ρ)2 ) ∗ 2∗= (ρω + β1 )x +(x ) .
20√

Differentiating ΠC with respect to β1 , we obtain√
6 − 3ρ2 − 6(1 + ρ) 1 − ρ − 4ρω√,
β1 =6 − ρ2 − 2(1 + ρ) 1 − ρ(16)√
2(3 − ρ2 − 2(1 + ρ) 1 − ρ − ρω)√,
6 − ρ2 − 2(1 + ρ) 1 − ρ

(17)

β2 =

and the marginal consumer’s location related to the above β1x∗ =3 + ρω
6 − ρ2 − 2(1 + ρ)

√

1−ρ

.

(18)

√
The requirement x∗ ≥ (3(3 + ρ − 3 1 − ρ))/(ρ(15 + ρ)) is equivalent to√3(3 − ρ − ρ2 − (5 + 2ρ) 1 − ρ)√ω≥≡ ω̂2a .
ρ(3 + ρ + 3 1 − ρ)

(19)

√

If this inequality does not hold, then the corner solution, β1 = 3(12 1−ρ−(1−ρ)(12+ρ)), is the local√ρ(15+ρ)∗
optimum in case (ii). Also, the requirement x ≤ (3−ρ)(3−ρ−3(1−ρ) 1 − ρ)/(ρ(21−26ρ+9ρ2 ))is equivalent to√
9 − 3ρ − 3ρ2 + ρ3 − (15 − 5ρ − 2ρ2 ) 1 − ρ√ω≤≡ ω̂2b .
ρ(3 − ρ + 3(1 − ρ) 1 − ρ)

9

(20)

If this inequality does not hold, then the corner solution
β1 =√−3 + ρ + 9(1 − ρ) 1 − ρ√
3 − ρ + 3(1 − ρ) 1 − ρ(21)is the local optimum in case (ii), when the marginal consumer in market B is√
(3 − ρ)(3 − ρ − 3(1 − ρ) 1 − ρ).
x =ρ(21 − 26ρ + 9ρ2 )∗(22)Firm C’s price β1 given in (16) is the local optimum in case (ii) if and only ifω̂2a ≤ ω ≤ ω̂2b .

(23)

To summarize case (ii), the equilibrium prices and the marginal consumer in market B aregiven by (16), (17), and (18). In market A, the equilibrium uniform prices are given by (7) and∗

1−ρx(8), and the marginal consumer is x̂ = 3(1−ρ)+ 16 with probability g ∗ and x̂ = 1/2 + (ρx∗ )/3√∗
with probability 1 − g ∗ . Firm C’s personalized prices are p∗∗∗A (x) = −x + ω + 2(1 + 1 − ρ)x .
√(iii) x̂ ≤ x∗ , or equivalently, (3 − ρ)(3 − ρ − 3(1 − ρ) 1 − ρ)/(ρ(21 − 26ρ + 9ρ2 )) ≤ x∗ ≤ 1

Firm C chooses β1 to maximize total profit from both markets
∗

Z x∗

∗∗
p∗∗
A (x)dx + α1 (1 − ρ)x̂
11ρ2 + 9ρ ∗ 2−4ρ2 + 12ρ
1 1 − ρ ρ(3 − ρ)=−(x ) + β1 + ρω +x∗ + ++.
18(1 − ρ)
9(1 − ρ)3
6
9(1 − ρ)ΠC = β 1 x + ρ0Differentiating ΠC with respect to β1 , we obtainβ1 =108 − 129ρ + 49ρ2 − 36ρ(1 − ρ)ω
,72 − 63ρ + 11ρ2

(24)

β2 =

6(15 − 16ρ + 5ρ2 − 3ρ(1 − ρ)ω),72 − 63ρ + 11ρ2

(25)

and the marginal consumer’s location related to the above β1x∗ =27 − 15ρ − 4ρ2 + 9ρ(1 − ρ)ω
.
72 − 63ρ + 11ρ2

(26)

√

1−ρ)
The requirement x∗ ≥ (3−ρ)(3−ρ−3(1−ρ)
is equivalent toρ(21−26ρ+9ρ2 )√2(6ρ5 + 7ρ4 − 113ρ3 + 261ρ2 − 261ρ + 108) − (3 − ρ)(1 − ρ)(11ρ2 − 63ρ + 72) 1 − ρω≥≡ ω̂3 .
3ρ2 (1 − ρ)(21 − 26ρ + 9ρ2 )
(27)
√

1−ρ
√
If this inequality does not hold, then the corner solution, β1 = −3+ρ+9(1−ρ), is the local
3−ρ+3(1−ρ) 1−ρ10optimum in case (iii). Also, the requirement x∗ ≤ 1 is equivalent toω ≤ (15 − 16ρ + 5ρ2 )/(3ρ(1 − ρ)) ≡ ω̂M .
If this inequality does not hold, then the corner solution, β1 = −1, is the local optimum in case(iii). Thus, this case holds if and only ifω̂3 ≤ ω ≤ ω̂M .

(28)

To summarize case (iii), the equilibrium prices and the marginal consumer in market B
are given by (24), (25), and (26). In market A, the equilibrium uniform prices are given by∗

1−ρx(3) and the marginal consumer is x̂ = 3(1−ρ)+ 16 . Firm C’s personalized prices are p∗∗
A (x) =∗)
2 + 4ρ(1−x3(1−ρ) − x + ω.
2

As mentioned before, when ω ≥ 15−16ρ+5ρ
3ρ(1−ρ) , the equilibrium prices are
β1∗∗∗ = −1, β2∗∗∗ = 0.

(29)

In this case, we have x∗ = 1, i.e., firm C monopolizes both markets. It is straightforward to2

check that 15−16ρ+5ρ
> 2, implying that accommodation is possible for larger values of ω under3ρ(1−ρ)imperfect preference correlation. In market A, firm C serves a fraction ρ of all consumers withpersonalized prices p∗∗∗A (x) = 2 + ω − x. For the remaining fraction 1 − ρ of consumers, theequilibrium uniform prices are α1∗∗∗ = α2∗∗∗ = 1, and the marginal consumer is x̂ = 1/2.
In Figure 1, we plot the range of (ω, ρ) that leads to different equilibria. The figure on the lefthand side summarizes the threshold values of ω̂ that correspond to the various cases discussed
above with interior local optima. The figure on the right-hand side shows these threshold values
for global optima.
3. Welfare implications
For each pair of equilibria corresponding to ω, it is straightforward to check that firm C has
smaller profit but firms A2 and B2 have larger profits when ρ < 1. Given that the equilibrium
uniform prices are higher in market B when ρ < 1, imperfect correlation reduces consumer
surplus in market B.
The comparison of consumer surplus in market A is not as straightforward since it involveschanges in equilibrium prices and consumers’ purchase decisions, where the fraction 1 − ρ ofconsumers in the target segment pay the uniform price when ρ < 1. So we calculate consumer
surplus directly. In case (i), i.e., x̂ > x∗ , consumer surplus in market A is(i)

CSA = vA −55
+ ρ − ρ2 (x∗ )2 ,49where x∗ is given in (11) and the superscript (i) indicates case (i). In case (ii), i.e., mixed
11

ω
12

ω
12

Mono.

10

10

M
ω

(iii)

8
6

M
ω

(iii)

8
6

3
ω

Corner between (ii) and (iii)

4

Mono.

3
ω

Corner between (ii) and (iii)

4

1
ω

1
ω

2

2
2b
ω

(i) or `Corner between (ii) and (iii)'

0.0

0.2

0.4

0.6

(i) or (ii)

0.8

2a
ω
(i)

1.0

2b
ω

Corner between (ii) and (iii)

(i)

(ii)
(i)

ρ

0.0

0.2

Candidates for the optimal outcome

0.4

0.6

0.8

2a
ω
(i)

1.0

ρ

Optimal outcome

Figure 1: The threshold values of ω
strategy equilibrium, expected consumer surplus in market A isp
(1 − ρ)(2 − ρ + 2
1(ii)
CSA = vA + − 2(1 + 1 − ρ)x∗ +2√

1 − ρ + 4ρg ∗ )4(x∗ )2 ,where g ∗ and x∗ are as in (7) and (18) and the superscript (ii) indicates case (ii). In case (iii),
i.e., x̂ ≤ x∗ , or the corner case between cases (ii) and (iii), consumer surplus in market A is
(iii)

CSA

= vA −

45 − ρ2
ρ(9 + ρ)x∗ + ρ2 (x∗ )2+.
36(1 − ρ)
9(1 − ρ)where x∗ is given in (22) in the corner case and in (26) in case (iii). In the monopolization
equilibrium, consumer surplus in market A is
(M )

CSA

= vA −

5 1
− ρ.
4 4

Comparing the above with consumer surplus in market A when ρ = 1, one can show that√imperfect preference correlation decreases consumer surplus in market A when (a) ω < 3( 385−√
11)/16 or (b) 3( 385 − 11)/16 ≤ ω and ρ is larger than a threshold value that depends on ω.
The threshold value is smaller than 3/10 for ω ≤ 5.

 Proof of Proposition 9
In Hotelling competition on [δA , 1], firm C chooses α1 to maximize (α1 − c/2)(x̂ − δA ) and firm
A2 chooses α2 to maximize (α2 − c/2)(1 − x̂) where x̂ = (1 + α2 − α1 )/2. This leads to the12following equilibrium uniform prices: α1∗ = 1 − (4δA )/3 + c/2, α2∗ = 1 − (2δA )/3 + c/2 if δA ≤ 3/4;α1∗ = c/2, α2∗ = (2δA − 1) + c/2 if δA > 3/4. Then firm C’s personalized prices are given byp∗A (x) = 1 − x + α2∗ . Clearly, firm C serves all type-L targeted consumers since p∗A (x) ≥ 0.
Firm C will also serve all type-H targeted consumers if p∗A (δA ) ≥ c. First, if δA ≤ 3/4, thenp∗A (δA ) = 2 − (5δA )/3 + c/2. So we have p∗A (δA ) ≥ c if c ≤ 3/2. Second, if δA ≥ 3/4, thenp∗A (δA ) = δA + c/2 ≥ c if c ≤ 3/2. Thus if c ≤ 3/2, then the equilibrium is qualitatively thesame for each type as that in Section 3.
Next, suppose pA (ξ) = 1 − x + α2 = c for some ξ ∈ (0, δA ). Then pA (x) < c for all x ∈ (ξ, δA ].
Below we find sufficient conditions for an equilibrium in which firm C serves all type-L consumers
in [0, δA ], type-H consumers in [0, ξ], and both types of non-targeted consumers in [δA , x̂], whilefirm A2 serves type-H consumers in [ξ, δA ] in addition to both types of consumers in [x̂, 1]. In
this equilibrium, firm C chooses α1 to maximize (α1 − c/2)(x̂ − δA ) and firm A2 chooses α2 tomaximize π2 = (α2 − c/2)(1 − x̂) + (α2 − c)(δA − ξ)/2 where x̂ = (1 + α2 − α1 )/2. Solving
them for an interior solution, we obtain α1∗ = 4/7 − δA + (9c)/14, α2∗ = 1/7 + (11c)/14, hence∗ . These pricesx̂∗ = 2/7 + δA /2 + c/14, ξ ∗ = 8/7 − (3c)/14, and firm A2 ’s profit denoted by πA2∗ ≥ 0. One can verify that all of these
constitute equilibrium if 0 < ξ ∗ < δA < x̂∗ < 1 and πA2inequalities are satisfied if c ∈ (3/2, 5] and δA ∈ [1/2, 4/5].

 Proof of Proposition 10
1. Equilibrium following the successive merger
Let us start with market A. Let firm C’s target segment be [0, x∗ ] so that firm D’s target
segment is [x∗ , 1]. It is easy to see each firm serves all its targeted consumers using personalized
prices p∗C (x) = ω + 1 − x + α2 and p∗D (x) = x + α1 . Given that they cannot serve non-targeted
consumers, we can set uniform prices α1 = α2 = 0. This leads to each firm’s profit in market A
R1
R x∗
given by πC = 0 (ω + 1 − x)dx and πD = x∗ xdx.
In market B, firm D chooses β2 to maximize ΠD = πD + β2 (1 − x∗ ) where x∗ = (1 − β1 +β2 )/2, leading to its best response β2 (β1 ) and x∗ (β1 ). Then firm C chooses β1 to maximize
ΠC = πC + β1 x∗ (β1 ). From this, we obtain the following. First, if ω < 7, then we have anaccommodation equilibrium withβ1∗ =13 − 5ω
10 − 3ω ∗ 4 + ω, β2∗ =
, x =
.
11
11
11

Second, if ω ≥ 7, then we have a monopolization equilibrium with β1∗ = −2 and β2∗ = −1. Total
profits are then
(4 + ω)25(7 − ω)2, ΠSM=
in the accommodation equilibrium,
D
22
242
3
ΠSM
= ω − , ΠSMC
D = 0 in the monopolization equilibrium,
2
ΠSM
=
C

13

where the superscript ‘SM’ denotes the successive merger.
2. Merger decision and profits
Without the successive merger, we have the following total equilibrium profits:√37−6ω 2+2
59

9
• When ω ≤ 3( 385−11), Π∗C = 154
ω 2 + 37 ω + 97 , Π∗A2 + Π∗B2 = 1216√26−9ω 2
.
59
2

2

+3ω+2
1
• When 3( 385−11)≤ ω < 2, Π∗C = 10
(ω + 3)2 , Π∗A2 + Π∗B2 = −2ω 25+ 2(2−ω).
16
25• When ω ≥ 2, Π∗C = ω + 12 , Π∗A2 + Π∗B2 = 0.
Comparing the profits above, we find that Π∗A2 + Π∗B2 < ΠSM
when ω < 7, and Π∗A2 + Π∗B2 =D
ΠSM= 0, otherwise. Thus firms A2 and B2 prefer merger to remaining independent whenD
ω < 7, and are indifferent, otherwise. It is easy to see ΠSM< Π∗C is always true.
C
3. Consumer surplus
Without the successive merger, consumer surplus in each market is given by
√

2

2

24ω
229
81ω
180ω
143
, CSA = vA + 36ω
• When ω ≤ 3( 385−11)165929 + 539 − 196 , CSB = vB + 5929 + 539 − 98 .
√

2

7
ω
16ω
47
• When 3( 385−11)≤ ω < 2, CSA = vA − 2ω16
5 − 10 , CSB = vB + 25 + 25 − 50 .

• When ω ≥ 2, CSA = vA − 23 , CSB = vB + 21 .
After the successive merger, consumer surplus can be calculated as follows. First, consider
the equilibrium with accommodation that arises when ω < 7. In market A, consumers [0, x∗ ]pay p∗C (x) = ω + 1 − x and consumers [x∗ , 1] pay p∗D (x) = x where x∗ = (4 + ω)/11. So total
consumer surplus in market A is
Z x∗
CSA =

(vA + ω − p∗C (x))dx +

0

Z 1
x∗

(vA − p∗D (x))dx = vA +

1 2
3
177
ω −
ω−
.
121
121
242

In market B, total consumer surplus is
Z x∗
CSB =

(vB − x − β1∗ )dx +

0

Z 4+ω
11

=
0

= vB +Z 1x∗(vB − (1 − x) − β2∗ )dx

13 − 5ω(vB − x −
)dx +
11

Z 1
4+ω
11

(vB − (1 − x) −10 − 3ω
)dx
11

1 2
41
309
ω +
ω−
.
121
121
242

Next, consider the monopolization equilibrium when ω ≥ 7. In market A, all consumers payp∗C (x) = ω + 1 − x and in market B, all consumers pay β1∗ = −2. Thus hence
Z 1
CSA =
0

1
(vA + ω − p∗C (x))dx = vA − , CSB =
2

14

Z 1

3
(vB − x − β1∗ )dx = vB + γ + .
20Based on the above, we can verify the following. First, for all values of ω, consumer surplus
in market A without the successive merger is smaller than under the successive merger. Second,√
consumer surplus in market B is smaller under the successive merger if and only if 3( 385 −√
11)/16 ≤ ω ≤ (11 21 − 41)/2.

 Proof of Proposition 11
1. Equilibrium in market A
Denote firm C’s uniform price for consumers in its target segment [0, x∗ ] by pC . Given firm
A2 ’s price α2 , the marginal consumer xC ∈ [0, x∗ ] is defined by vA + ω − pC = vA − (1 − xC ) − α2 ,or xC = 1 + ω + α2 − pC . On [0, x∗ ], firm C chooses pC to maximize pC xC . Suppose we have aninterior solution so that the first-order condition is satisfied with equality, 1 + ω + α2 − 2pC = 0.
This leads to xC = (1 + ω + α2 )/2. But this would imply xC > 1 if ω > 1, an impossibility. Thus
the boundary solution is the only possibility, xC = x∗ . In sum, on [0, x∗ ], firm C chooses uniform
price pC (α2 ) = 1 + ω + α2 − x∗ to serve all its targeted consumers and earns profit pC (α2 )x∗ .
On [x∗ , 1], firms choose α1 and α2 . But we have already solved this problem in Section 3. The
equilibrium prices and profits areα1
3 − 4x∗


3
=

 0

α2


3 − 2x∗3=
 2x∗ − 13
if x∗ < ,43
if x∗ ≥ .
43
if x∗ < ,4
3∗
if x ≥ .
4
(3 − 4x∗ )2


18
πC =

 0

3
if x∗ < ,43
if x∗ ≥ .
4


(3 − 2x∗ )23
if x∗ < ,
18
4
πA2 =

 (2x∗ − 1)(1 − x∗ ) if x∗ ≥ 3 .
4

Putting together, firm C’s profit in market A isπC,A
9 + 6(2 + 3ω)x∗ − 14(x∗ )2


18
=

 (ω + x∗ )x∗3
if x∗ < ,4
3∗
if x ≥ .
4

2. Equilibrium in market B
Given firm B2 ’s best response β2 (β1 ) = (1 + β1 )/2, firm C chooses β1 to maximize ΠC =β1 x∗ + πC,A , which can be expressed as



1
2
7
3

 + β1 + ω +x∗ − (x∗ )2 if x∗ < ,

2
3
9
4
ΠC =

3

 (β1 + ω + x∗ )x∗
if x∗ ≥ ,415

1
where x∗ = 1+β2 (β21 )−β1 = 3−β
4 . The first-order derivative is given by
9(7 − 2ω) − 43β1


dΠC
72
=

dβ1
 3 − 2ω − 3β1
83
if x∗ < ,43
if ≤ x∗ ≤ 1.
4

Solving for the equilibrium prices, we obtain three different types of equilibria, the same as in
the baseline model except for the parameter regions.
First, the accommodation equilibrium I is possible when x∗ < 3/4. The interior solution
from the first-order condition, β1∗ = 9(7 − 2ω)/43, is optimal if ω < 7/2. In this case, firm
C’s total profit is Π∗C = 3(69 + 22ω + 3ω 2 )/172 with x∗ = (9ω + 33)/86, and firm B2 ’s price is
β2∗ = (53 − 9ω) /43. Second, the accommodation Equilibrium II is possible when 3/4 ≤ x∗ < 1.
The optimal price is the interior solution β1∗ = (3 − 2ω)/3 when 3/2 ≤ ω ≤ 3. Firm C’s profit2∗is Π∗∗C = (3 + ω) /12 with x = (3 + ω)/6, and firm B2 ’s price is β2 = (3 − ω)/3. Third, themonopolization equilibrium obtains when ω ≥ 3. In this case, firm C will optimally set β1 = −1
and its equilibrium profit is Π∗∗∗C = ω.
From the above, both accommodation equilibria are possible when ω ∈ [3/2, 3] and the accommodation equilibrium II and the monopolization equilibrium are possible when ω ∈ [3, 7/2].
For each case, we need to compare firm C’s profits to find firm C’s global optimum. This√∗∗∗∗
leads to Π∗C > Π∗∗C if and only if ω < 3( 129 − 5)/8 ' 2.384, and ΠC < ΠC if and only if√ω ≥ (53 − 946)/9 ' 2.471. Thus we can conclude that the accommodation equilibrium I exists√√
when ω < 3( 129−5)/8, the accommodation equilibrium II exists when 3( 129−5)/8 ≤ ω < 3,
and the monopolization equilibrium arises when ω ≥ 3.
The equilibrium prices in market B are summarized as follows

β1

β2

√

3( 129 − 5)9(7 − 2ω)
if ω <
,



43
8

√
3 − 2ω
3( 129 − 5)=if≤ ω < 3,



3
8



−1
if 3 ≤ ω.
√
53 − 9ω3( 129 − 5)
if ω <
,



43
8

√
3−ω
3( 129 − 5)=if≤ ω < 3,



3
8



0
if 3 ≤ ω.

16This leads to the following equilibrium profits

ΠC

πB2

πA2

√

3( 129 − 5)
3(69 + 22ω + 3ω 2 )
if ω <
,



172
8

√
(3 + ω)2
3( 129 − 5)=if≤ ω < 3,



12
8



ω
if 3 ≤ ω.
√2
129 − 5)
3(
(53
−
9ω)


if ω <
,



3698
8

√
(3 − ω)2
3( 129 − 5)=if≤ ω < 3,



18
8



0
if 3 ≤ ω.
 √23( 129 − 5)
1 32 − 3ωif ω <
,


2
43
8

 
√


9ω − 1053 − 9ω3( 129 − 5)=if≤ ω < 3,



43
86
8




0
if 3 ≤ ω.

Based on the above, the comparison of profits is straightforward. Given the restriction, firm C
is worse off while firms A2 and B2 are better off than without the restriction.
3. Comparison of consumer surpluses
Recall that firm C’s market share without the restriction is given by
33 + 9ω





77

3+ω
x∗ =



5



1

√
3( 385 − 11)if ω <' 1.617,16√
3( 385 − 11)if≤ ω < 2,16
if 2 ≤ ω,

whereas the market share given the restriction becomes (subscript R for “restriction”)
9ω + 33





86

∗
3+ω
xR =



6



1

√
3( 129 − 5)if ω <' 2.384,
8√
3( 129 − 5)if≤ ω < 3,8
if 3 ≤ ω.

17Without the restriction, consumer surplus in market A can be written as
√3( 385 − 11)
5 4 ∗ 2
 vA − + (x ) if ω <
,


4 9
16

√

1
3( 385 − 11)
CSA =vA + − 2x∗if≤ ω < 2,


2
16




 vA − 3
if 2 ≤ ω,2whereas, given the restriction, consumer surplus in market A is√3( 129 − 5)
5 17 ∗ 2
if ω <,
vA − + (xR )



4 18
8

√
R
1
3( 129 − 5)
1CSA=
≤ ω < 3,vA + − 2x∗R + (x∗R )2 if



2
2
8



vA − 1
if 3 ≤ ω.
Comparing the total consumer surpluses given above, we obtain

41 625(3ω + 11)2 > 0


87
701
768




153 2 17 597
30 393



ω +
ω−
>0


36 98073 960 14 792
R
153 2
561
5 755
CSA
− CSA =ω +ω+>0

 14 792
7 396
14 792 (9 − ω)2

>0



72




 1 >02√
3( 385 − 11)if ω <,
16√
3( 385 − 11)
if
<ω< 2
16
√
3( 129 − 5)
if 2 ≤ ω <8√
3( 129 − 5)
if
<ω< 3
8
if 3 ≤ ω.

Thus consumer surplus in market A increases after the restriction.
In market B, the restriction softens competition and reduces total consumer surplus in theaccommodation equilibria, but it does not affect the consumer surplus in the monopolization
equilibrium. Without the restriction, consumer surplus in market B can be expressed as
√53( 385 − 11)

∗ 2
∗


vB − + (x ) + 2x if ω <
,


2
16

√

5
3( 385 − 11)
CSB =vB − + (x∗ )2 + 2x∗ if≤ ω < 2,


2
16




 vB + 1
if 2 ≤ ω.
218

Under the restriction, total consumer surplus in market B is given by√3( 129 − 5)
5

∗ 2
∗

 vB − + (xR ) + 2xR if ω <
,


2
8

√

R
5
3( 129 − 5)
CSB=
vB − + (x∗R )2 + 2x∗R if≤ ω < 3,


2
8




 vB + 1
if 3 ≤ ω.
2Comparing the total consumer surpluses given above leads to27(11 + 3ω)(18623 + 1467ω)



<0
−


43 850 884(93 + 41ω)(1283 + 131ω)


<0
−



184 900
R
3(97 + 3ω)(53 − 9ω)CSB− CSB =
<0
−



7 396




 − (21 + ω)(3 − ω) < 0



36




0

√
3( 385 − 11)if ω <,
16√
3( 385 − 11)
if
<ω< 2
16 √
3( 129 − 5)
if 2 ≤ ω <8√
3( 129 − 5)
if
<ω< 3
8
if 3 ≤ ω.

Thus the restriction reduces consumer surplus in market B.

 Proof of Proposition 12
Given firm C’s target segment [0, δA ], let z be the location chosen by firm C. Then the consumer
who is indifferent when competition is in uniform price is given by x̂ = (1 + z + α2 − α1 )/2. To
find firm C’s optimal choice of z, we consider two cases.
1. x̂ ≤ δA
Since φA = 1, firm C serves all consumers in [0, δA ] using personalization, and firm A2 serves
all consumers in [δA , 1] by the definition of x̂. This leads to equilibrium uniform prices α1 = 0
and α2 = 2δA − 1 − z. Given that firm C’s profit is entirely from its targeted consumers and its
personalized prices increase in α2 , firm C’s optimal choice of z is z = 0. Thus, this case leads
to z = 0, α1∗ = 0, α2∗ = 2δA − 1, and x̂ = δA .
Given the above prices, firm C has no incentives for deviation. But firm A2 may deviatethat leads to x̂d > δA . The deviation price is α2d = 2x̂d − 1 with the deviation profit given
by α2d (1 − x̂d ). Such a deviation is not profitable if and only if δA ≥ 3/4, when we have an
equilibrium described above.
2. x̂ > δA
When δA < x̂, firm C serves non-targeted consumers in [δA , x̂] in addition to all its targeted
consumers. Notice that we cannot have z > x̂ by the definition of x̂. Thus we only need to19consider z ≤ x̂. Solving for the equilibrium uniform prices, we obtainα1∗ =3 + z − 4δA
3 − z − 2δA
3 + z + 2δA, α2∗ =, x̂ =
3
3
6

and firm C’s personalized prices, p∗A (x) = 1 + ω + α2∗ − x. Thus firm C’s profit in market A is
Z δAp∗A (x)dx + α1∗ (x̂ − δA )
0



2


1 2
2
4
1 7
1
1
2
= z +
1 − δA− δA z + 2 − δA + ω δA − (δA ) +
18
3 9
3
2
2
3

 z   z 7δA
= πC +−+ 1 ≡ πC + F (z)363πC (z) =where πC is firm C’s profit in market A when its location is 0, hence is independent of z.
Firm C’s problem is to choose z to maximize F (z) subject to z ≤ x̂, or equivalently, z ≤(3 + 2δA )/5. Solving the problem, we obtain the following: (i) when δA ∈ [0, 6/13], we havez = δA with α1∗ = α2∗ = 1 − δA and x̂ = (1 + δA )/2; (ii) when δA ∈ (6/13, 3/4], we have z = 0
with α1∗ = 1 − (4δA )/3, α2∗ = 1 − (2δA )/3 and x̂ = (3 + 2δA )/6. Combining these with the casewhere x̂ ≤ δA proves the derivation of optimal z.
It remains to show that firm A2 ’s profit is smaller but consumer surplus is larger whenz = δA . Clearly, firm A2 ’s profit decreases because it serves less consumers at lower uniform
price when firm C chooses z = δA . The consumer surplus when z = δA is given by
R
CSA
=

Z δA

[vA + ω − p∗A (x)]dx +0= vA −Z x̂

[vA − α1∗ − (x − z)]dx +

δA

Z 1

[vA − α2∗ − (1 − x)]dx

x̂

2
5 δA
δA
+
+
.
4
4
2

2 )/9. It is straightforward to check CS R > CS .
When z = 0, it is CSA = vA − 5/4 + (4δAAA

 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 2013.39 Since its foundingin 2009, GV has invested in nearly 60 life sciences companies.40 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
39

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

40

https://www.cnbc.com/2018/03/30/alphabet-gv-life-sciences-and-health-investments-going-public.html

20

and Google, said health care offers the biggest potential for Alphabet to use artificial intelligenceto improve outcomes over the next five to ten years.41
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.42 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.43
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.44 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.45 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.46 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
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.47
41

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

42

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

43

https://www.cnbc.com/2019/11/02/google-healths-david-feinberg-focus-on-search-for-doctorsconsumers.html
44

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

45

https://www.wsj.com/articles/google-s-secret-project-nightingale-gathers-personal-health-data-on-millionsof-americans-11573496790
46
https://www.wsj.com/articles/google-s-secret-project-nightingale-gathers-personal-health-data-on-millionsof-americans-11573496790
47

https://www.wsj.com/articles/paging-dr-google-how-the-tech-giant-is-laying-claim-to-health-data-21

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).48
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%).49 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.50 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.51
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 2018.52 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.53
An ostensible reason for Google’s bid for Fitbit is Google’s intention to gain a toehold in themarket 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
11578719700
48

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.
49

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

50

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

51https://www.bloomberg.com/news/articles/2020-02-10/google-fitbit-deal-poses-test-for-merger-cops-eyeingdata-giants
52

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

53

https://www.bloomberg.com/news/articles/2020-02-10/google-fitbit-deal-poses-test-for-merger-cops-eyeingdata-giants22was “about devices, not data”, and that Fitbit data would not be used for Google ads.54 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.55
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”.56 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.57 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.
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.58 Brooks Tingle, president
54

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

55

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

56https://www.cnbc.com/2017/04/18/alphabet-verily-project-baseline-longitudinal-health-study.html

57

https://www.fiercehealthcare.com/tech/verily-and-onduo-collaborating-john-hancock-to-offer-life-insurancedisease-management-for58

https://www.fiercehealthcare.com/payer/alphabet-s-verily-breaks-into-stop-loss-health-insurance-marketbacked-by-swiss-re23

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.59
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.60 “We’re hoping to
be more personalized in the way we offer health solutions,” said Vivian Lee, Verily’s President of
Health Platforms.61 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.

 Big Data and Personalization in Health Care
The digital health sector can be defined as the segment of health care heavily reliant on digitaltechnologies, including wireless health, mobile health, electronic health record, telehealth, etc.
The global digital health sector is estimated to be worth around $100 billion in 2019, and ispoised to grow at 28.5% annually.62 It is becoming a new battlefield for personalization due
to the unprecedented accumulation of health data. According to an estimate by the McKinsey
Global Institute, big-data applications could generate up to $100 billion in value annually acrossthe US healthcare system.63 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 ofEuropean Insurance and Occupational Pensions Authority (EIOPA), many insurance companies have developed their own big data analytics (BDA) strategies or have included many BDA
59

https://www.fiercehealthcare.com/tech/verily-and-onduo-collaborating-john-hancock-to-offer-life-insurancedisease-management-for60

https://www.fiercehealthcare.com/payer/alphabet-s-verily-breaks-into-stop-loss-health-insurance-marketbacked-by-swiss-re61

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

62https://www.statista.com/statistics/1092869/global-digital-health-market-size-forecast/

63

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

24

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.64
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 ofdifferent 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.65
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.66 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.67
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
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 or64

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

65

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

66

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.
67

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

25other wearable devices to begin tracking.68 In 2018, John Hancock announced it would stop
offering traditional life insurance altogether, and only sell interactive life insurances that track
fitness and health data through wearable devices and smartphones.69 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.70
Similar strategies are adopted by Oscar Health, an insurance technology startup, which announced in 2014 that it would begin offering members a free Misfit fitness wearable 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 in wearable devices and clients’ information is forrisk reduction. As an another example, Health IQ, an American insurance startup, rewards
clients with healthy lifestyles. The company works with 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%.71
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.72 The use of big data is becoming more prevalent in personalized
health care at all stages of prevention, diagnosis, and treatment.

68

https://www.the-digital-insurer.com/dia/john-hancock-redefines-life-insurance-with-vitality-program/69

https://www.reuters.com/article/us-manulife-financi-john-hancock-lifeins/strap-on-the-fitbit-john-hancockto-sell-only-interactive-life-insurance-idUSKCN1LZ1WL
70

https://www.prnewswire.com/news-releases/john-hancock-and-human-api-join-forces-to-transform-the-lifeinsurance-purchase-process-300986166.html
71

Everis report “Rethinking Healthcare for 2030” available at http://insurtechnttdata.everis.com/dist/ resources/vlarrosa/insurtech/Insurtech Insight Health Data final compressed.pdf
72

https://www.clinicalomics.com/topics/oncology/multiple-myeloma/gns-healthcare/26