Data Brokers Co-opetition (Yiquan Gu, Leonardo Madio, and Carlo Reggiani)

Data Brokers Co-opetition
Yiquan Gu1 Leonardo Madio2 Carlo Reggiani3
1University of Liverpool
2CORE UCLouvain, CESifo Research Network, HEDG York
3University of Manchester
Annual Scientific Seminar on Media and the Digital
Economy, Florence
March, 2019
Gu, Madio, Reggiani (UoL, CORE, & UoM) Data brokers co-opetition 1 / 28

Motivation
• An expanding market: customer data market is highly lucrative.
• Expected grow annual rate of 11% by 2026 (Transparency Market
Research).
• Data are useful for a bunch of activities,
• risk mitigation, e.g., identity veriﬁcation and fraud detection;
• marketing, e.g. customer lists, reports;
• product costumisation;
• algorithm learning;
• price discrimination.

Motivation
• An expanding market: customer data market is highly lucrative.
• Expected grow annual rate of 11% by 2026 (Transparency Market
Research).
• Data are useful for a bunch of activities,
• risk mitigation, e.g., identity verification and fraud detection;
• marketing, e.g. customer lists, reports;
• product costumisation;
• algorithm learning;
• price discrimination.
• Evidence that data-driven decision making leads to
• higher profits (Brynjolfsson et al. 2011);
• personalised prices (Mikians et al. 2012, 2013; Hannak et al 2014;
Shiller 2014; Dubé and Misra 2017);
• search discrimination (Mikians et al. 2012).

Motivation: Where data come from?
• Where data come from?
• Data Brokers (DBs), “companies whose primary business is collecting
personal information about consumers from a variety of sources and
aggregating, analyzing, and sharing that information” (FTC 2014).
• Attention Brokers (FANG?), whose primary business is not data
collection.
DBs are less visible, hence more shady and even harder to track on what
they do with personal info.

Motivation: The Industry
• The FTC’s report. In 2014, the FTC released a report on data brokerage
highlighting several relevant features of the sector. For instance,
• Acxiom and Datalogix record transactions for trillions of dollars and
cover almost every US consumer.
• Corelogic and eBureau focus more on property and financial
information.
• Experian data are used by police authorities for eventual rehabilitation
programmes.
• Other companies specialise in profiling for background checks and
security purposes.
• DBs collect information from a large number of online and offline
sources.
• Key aspect: data sharing practices largely documented.

Motivation: Data Collection
Figure: FTC’s report on Data Brokerage

Motivation: FTC (2014)
Figure: FTC’s report on Data Brokerage

This Paper
Why do data brokers share data in some markets and compete in others?
• The answer comes from the type of information sold in the market.

This Paper
• Three types of data structure:
• sub-additive, e.g., when two datasets have signiﬁcant overlaps;
• additive, e.g., e.g., merging information of two independent segments
of the market;
• supra-additive, when synergies between two datasets (e.g., browsing
history with email addresses) generate additional value.

This Paper
• Three types of data structure:
• sub-additive, e.g., when two datasets have signiﬁcant overlaps;
• additive, e.g., e.g., merging information of two independent segments
of the market;
• supra-additive, when synergies between two datasets (e.g., browsing
history with email addresses) generate additional value.
• Intuitive interpretation? DBs would be more willing to share their data
when their joint value is larger than the sum of the parts.

Overview of the Results
Novel and counter-intuitive result:
• if data are additive or supra-additive, DBs (weakly) prefer to compete with
one another.
• if data are sub-additive, DBs compete fiercely to sell their dataset
independently. So, sharing would allow them to grab entirely the surplus of
the downstream firm.
• Data sharing also emerges when the firm faces some merging cost when
buying data from different sources. This avoids granting a discount to the
firm and soften competition.
The incentive for data sharing thus results from the opportunity of transitioning
from a competitive scenario to one of “co-opetition”.

Literature
• big data and privacy on firms’ competition (e.g., Conitzer et al. 2012,
Casadesus-Masanell and Hervas-Drane 2015, Belleflamme and Vergote 2016,
Belleflamme et al. 2017, Choi et al. 2018).
• data sales and downstream competition (e.g., Clavorá Braulin and
Valletti, 2016, Montes et al. 2018, Bounie et al. 2018).
• strategic information sharing (e.g., Shy and Stenbacka 2013, Liu and
Serfes 2006, Kraemer et al. 2018).
• mergers (e.g., Esteves and Vasconcelos 2015; Kim et al. 2018; Prat and
Valletti 2018).
To date, no analysis of the functioning of the upstream market and the behaviour
of “competing” DBs.

The Model
The economy is composed of
• Two DBs k = 1, 2;
• A downstream ﬁrm;
• N > 0 consumers and M > 0 attributes.
• Λk is the M × N logical matrix that represents DB k’s information
• λkij = 1(0) means DB k has (no) information about consumer j’s
attribute i.

The Model
The economy is composed of
• Two DBs k = 1, 2;
• A downstream firm;
• N > 0 consumers and M > 0 attributes.
• Λk is the M × N logical matrix that represents DB k’s information
• λkij = 1(0) means DB k has (no) information about consumer j’s
attribute i.
We assume
• The DBs have gathered information about consumers, which then can be
sold (exclusively) to a downstream firm, e.g. B2B.
• Data increase firm’s profitability, e.g., price discrimination, advertising,
data-driven management.
• DBs can either share their data and produce a consolidated report or
compete to independently supply the downstream firm.

The Data Structure
• Let f (·) be a function that maps M × N logical matrices to real numbers,
• f (Λ) ≥ 0 measures the extra proﬁt the ﬁrm can generate by using data in Λ.
The data structure can be of three types:

The Data Structure
• f (Λ) ≥ 0 measures the extra profit the firm can generate by using data in Λ.
The data structure can be of three types:
Definition
• additive, if f (Λk |Λ−k ) = f (Λk ) + f (Λ−k ),
• sub-additive, if f (Λk |Λ−k ) < f (Λk ) + f (Λ−k ), and
• supra-additive, if f (Λk |Λ−k ) > f (Λk ) + f (Λ−k ),
where | is the element-wise OR operator.

The Data Brokers
• Independent Selling: each DB sells its own data and obtains
Πk =
pk , if the firm buys k’s data,
0, if the firm does not buy k’s data,
where pk is DB k’s price for its own data.
• Data Sharing: the dataset is jointly sold and each DB obtains a share sk of
the joint profit
Πk = sk (Λk , Λ−k ) · PΛk |Λ−k
,
where PΛk |Λ−k
is the price for the merged dataset.

The Data Structure
• f (Λ) ≥ 0 measures the extra proﬁt the ﬁrm can generate by using the
information contained in Λ.
Three types of data structure:

The Data Structure
• f (Λ) ≥ 0 measures the extra profit the firm can generate by using the
information contained in Λ.
Three types of data structure:
Definition
• additive, if f (Λk |Λ−k ) = f (Λk ) + f (Λ−k ),
• sub-additive, if f (Λk |Λ−k ) < f (Λk ) + f (Λ−k ), and
• supra-additive, if f (Λk |Λ−k ) > f (Λk ) + f (Λ−k ),
where | is the element-wise OR operator.

The Data Structure
The value of incremental data for a downstream ﬁrm is contextual.
Example: the London butcher, Pendleton & Son (see e.g., Marr 2016; Claici
2018)
• In response to price competition from a large grocery chain, the butcher had
to rely on data to improve the product and service, e.g. with the assistance
of a DB.
• Data can generate a value f (·) for the butcher, whereas a value g(·) for the
supermarket.
• Data can also have diﬀerent value within and across industries. The same
butcher could obtain h(·) > f (·) in presence of an inelastic demand and only
f (·) if in direct competition with the grocery chain.

The firm
Data engender an extra surplus for the firm selling a product to final consumers.
• Independent Selling: the firm’s profits are
Πr
= π0
+
f (Λk ) − pk , if the firm only buys DB k’s data
f (Λk |Λ−k ) − p1 − p2, if the firm buys data from both DBs
,
where f (Λk |Λ−k ) is the value of the dataset. In this case, the firm can
merge datasets at no extra cost.
• This assumption is relaxed in the extension!
• Data Sharing: the firm’s profits are
Πr
= π0
+ f (Λk |Λ−k ) − PΛk |Λ−k
.

The Timing
1 Sharing Decision: The two DBs simultaneously and independently decide
whether or not to share their data. The two DBs share their data if, and
only if, both of them choose to share data.
2 Pricing Decision: With data sharing DBs jointly set a price for the firm.
Else, they simultaneously and independently set a price for their own dataset.
3 Purchasing Decision: The firm decides whether or not to buy the offered
dataset(s).

Independent Data Selling: additive and supra-additive data
• In these cases, the DBs can independently set their own prices.

• In equilibrium, the prices are such that p∗
1 + p∗
2 = f (Λ1|Λ2) and
p∗
k ≥ f (Λk ) for k = 1, 2.

1 + p∗
2 = f (Λ1|Λ2) and
p∗
k ≥ f (Λk ) for k = 1, 2.
• DB 1’s best response function when data are supra-additive.
BR1(p2) =



f (Λ1) if p2 ≥ f (Λ1|Λ2) − f (Λ1)
f (Λ1|Λ2) − p2 if f (Λ2) ≤ p2 < f (Λ1|Λ2) − f (Λ1)
f (Λ1|Λ2) − f (Λ2) if p2 < f (Λ2)

1 + p∗
2 = f (Λ1|Λ2) and
p∗
k ≥ f (Λk ) for k = 1, 2.
• DB 1’s best response function when data are supra-additive.
BR1(p2) =



f (Λ1) if p2 ≥ f (Λ1|Λ2) − f (Λ1)
f (Λ1|Λ2) − p2 if f (Λ2) ≤ p2 < f (Λ1|Λ2) − f (Λ1)
f (Λ1|Λ2) − f (Λ2) if p2 < f (Λ2)
• Firm’s profits are Πr
= π0
.
• Prices have two properties:
(i) firm buys the data, and
(ii) extract the highest value from the firm.

Independent Data Selling: sub-additive data
• The data market is more competitive.
• The unique pair equilibrium prices is
p∗
k = f (Λk |Λ−k ) − f (Λ−k ) < f (Λk ).

p∗
k = f (Λk |Λ−k ) − f (Λ−k ) < f (Λk ).
• DB 1’s best response function when data are sub-additive.
BR1(p2) =



f (Λ1) if p2 > f (Λ2)
∅ if f (Λ1|Λ2) − f (Λ1) < p2 ≤ f (Λ2)
f (Λ1|Λ2) − f (Λ2) if p2 ≤ f (Λ1|Λ2) − f (Λ1)
.
(1)

p∗
k = f (Λk |Λ−k ) − f (Λ−k ) < f (Λk ).
BR1(p2) =



f (Λ1) if p2 > f (Λ2)
∅ if f (Λ1|Λ2) − f (Λ1) < p2 ≤ f (Λ2)
f (Λ1|Λ2) − f (Λ2) if p2 ≤ f (Λ1|Λ2) − f (Λ1)
.
(1)
• The proﬁts are Πk = p∗
k , and
Πr
= π0
+ f (Λ1) + f (Λ2) − f (Λ1|Λ2) > π0
, so the ﬁrm is being left
with some positive surplus.

p∗
k = f (Λk |Λ−k ) − f (Λ−k ) < f (Λk ).
BR1(p2) =



f (Λ1) if p2 > f (Λ2)
∅ if f (Λ1|Λ2) − f (Λ1) < p2 ≤ f (Λ2)
f (Λ1|Λ2) − f (Λ2) if p2 ≤ f (Λ1|Λ2) − f (Λ1)
.
(1)
• The profits are Πk = p∗
k , and
Πr
= π0
+ f (Λ1) + f (Λ2) − f (Λ1|Λ2) > π0
, so the firm is being left
with some positive surplus.
• Paradoxically, the firm would rather prefer to have redundant, imperfect or
less powerful information when buying from both DBs than more powerful
information.

Data Brokers’ Sharing Decision
Consider the subgame where the DBs have agreed to share their data.
• The total proﬁts the DBs can extract is f (Λk |Λ−k ) and individual proﬁts are
Πk =
f (Λk )
f (Λk ) + f (Λ−k )
f (Λk |Λ−k ).
that is, sharing rule follows relative bargaining power.

Data Brokers’ Sharing Decision
Consider the subgame where the DBs have agreed to share their data.
• The total proﬁts the DBs can extract is f (Λk |Λ−k ) and individual proﬁts are
Πk =
f (Λk )
f (Λk ) + f (Λ−k )
f (Λk |Λ−k ).
that is, sharing rule follows relative bargaining power.
Proposition
A strictly positive incentive to share data by both DBs only exists when the data
structure is sub-additive. In all other cases, there is no Pareto improvement for
the DBs to share data.
Remark: Sharing would allow the DBs to soften competition and grab entirely
the surplus created.

Extension: Costly Data Processing
• In the real world, DBs have a comparative advantage in handling data
and merging databases as well as data analytics.
• Suppose that the firm incurs a fixed merging cost c > 0 when buying
the data from different sources while this is not the case for DBs.

Extension: Cost Asymmetry (2)
• When DBs compete and the ﬁrm buys from both, the combined price is
p∗
1 + p∗
2 =2f (Λ1|Λ2) − f (Λ1) − f (Λ2) − 2c if sub-additive data
p∗
1 + p∗
2 =f (Λ1) + f (Λ2) − 2c if additive data
p∗
1 + p∗
2 =f (Λ1|Λ2) − 2c if supra-additive data

• When DBs compete and the firm buys from both, the combined price is
p∗
1 + p∗
2 =2f (Λ1|Λ2) − f (Λ1) − f (Λ2) − 2c if sub-additive data
p∗
1 + p∗
2 =f (Λ1) + f (Λ2) − 2c if additive data
p∗
1 + p∗
2 =f (Λ1|Λ2) − 2c if supra-additive data
• When data are sub-additive, the firm’s profits are
Πr
= π0
+ f (Λk ) + f (Λ−k ) − f (Λk |Λ−k )
Overlaps
+ c
Discount
• When data are additive or supra-additive, the firm’s profits are
Πr
= π0
+ c
• By sharing, they can grab entirely the surplus.
• Interestingly, incentive to pump up costs to get larger discounts.

• Discount effect: the competitive disadvantage of the firm is passed onto
the DBs, who in turn compete more fiercely.
• Overlap effect: the fact that with sub-additive data (only!), DBs compete
more fiercely by charging their marginal contribution to the final DB.
• Very similar to Prat and Valletti (2018) with mergers with significant
overlaps (e.g., Instagram/Facebook).
• All in all, data sharing emerges also in other circumstances.

Furrther Extensions
• Different sharing rules. Main results confirmed.
• Sequential Pricing: Main results confirmed.
• Sequential Data Selling:
• Second-mover advantage when data are supra-additive;
• First-mover advantage when data are sub-additive,
• Data sharing emerges with sub-additive data when decision on moving
first is endogeneous. Else, sharing never arises.

Discussion
• We delve into the nature of the “co-opetition” between DBs and link their
strategic incentives to different types of data structures.
• Simple yet general model with two DBs and a firm. It then embeds any
asymmetry between DBs in how they collect and process personal data.
• Data sharing arises
• First, to soften competition when data are sub-additive (e.g., overlaps).
• Second, to avoid granting a discount to the firm when this has a
competitive disadvantage, regardless of data structure.
• Perhaps less intuitive explanation to the sharing practice observed by
the FTC.

Policy implications
• So far, emphasis on privacy and individual rights. No attention devoted to
anti-competitive nature of data trading. Instead,
• anti-competitive behaviour of sharing does not generate ineﬃciency in
the present model sans consumer surplus (but losses may arise in richer
environments).
• regulators may be concerned about the reallocation of surplus across
sides of the market.

Policy implications
• So far, emphasis on privacy and individual rights. No attention devoted to
anti-competitive nature of data trading. Instead,
• anti-competitive behaviour of sharing does not generate ineﬃciency in
the present model sans consumer surplus (but losses may arise in richer
environments).
• regulators may be concerned about the reallocation of surplus across
sides of the market.
Given a parallel between sharing and data brokers mergers,
• antitrust enforcers should carefully take into account the nature of the
data structure when scrutinising merger proposals (see e.g., Wu 2017;
Prat and Valletti 2018).

Food for thought
• Should we expect a pro-competitive (unintended) eﬀect of the EU
GDPR?

Thank you!
Comments - very welcome.
yiquan.gu@liv.ac.uk
leonardo.madio@uclouvain.be
carlo.reggiani@manchester.ac.uk

Data Brokers Co-opetition (Yiquan Gu, Leonardo Madio, and Carlo Reggiani)

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