Data brokers co-opetition

Abstract

1. Introduction

In today’s highly digitized economy, data have become particularly valuable and have attracted the attention of policymakers and institutions. To mention some examples, in 2018, the European Union (EU) General Data Protection Regulation (GDPR) to protect personal data was promulgated, and the State of California followed suit with the California Consumer Privacy Act. In 2020, the European Commission announced the EU Data Strategy (European Commission, 2020) to boost data sharing among firms and the recently proposed Digital Market Act includes mandatory data sharing as a crucial competition tool. The conventional view is that being non-rival, data can generate positive externalities, and the EU data strategy’s vision is that data sharing has to be incentivized or even mandated.

If data are considered the fuel of the digital economy, ‘data brokers’ are its catalyst.¹ These often unknown actors are ‘companies whose primary business is collecting personal information about consumers from a variety of sources and aggregating, analysing, and sharing that information’ (Federal Trade Commission, 2014) and engage mostly in business-to-business relations. As they do not usually have any contact with final consumers, the latter are often unaware of their existence. A defining characteristic of this sector is that data brokers (DBs) transact and exchange data with each other, and more information is obtained this way than from direct sources. The Federal Trade Commission (2014) reports that seven out of nine DBs were buying and selling consumer data to each other. For example, Acxiom has partnerships with other DBs, including Corecom (specialized in entertainment data) and Nielsen (a global data company).

Yet, these sharing practices might not necessarily be consistent with the positive social role envisioned in the current regulatory debate and, more worryingly, may hide anti-competitive behaviours. As little is known about the behaviours of these DBs, investigations worldwide are taking place. For instance, the French National Commission on Informatics and Liberty (CNIL) carried out an in-depth investigation in the period 2017–9 auditing 50 DBs and ad-tech companies (Financial Times, 2019).

In this context, our main research question is to identify the incentives of DBs to share data in some markets and compete with others and how these relate to the nature of the data a DB has. This is relevant as, on the one hand, these companies compete to provide customers with specialized data, analytics, and market research; on the other hand, they also cooperate through partnerships and data-sharing agreements. Moreover, DBs may be particularly strong in different areas and specialize in some services, rendering the nature and type of data crucial for their strategies. For example, Acxiom and Datalogix profile consumers for targeting purposes, collecting information such as demographics, sociographics, and purchasing behaviours. DBs like Corelogic and eBureau mostly sell in-depth financial and property data analytics.

To this end, we present a simple yet rather general model to analyse how the nature of data and merging costs shape DBs’ decisions. Our economy consists of two DBs and one data buyer. Throughout the article, we use ‘the (data) buyer’ and ‘the downstream firm’ interchangeably. The consumer-level information held by DBs potentially allows the downstream firm to increase its profits in its own market. For instance, a firm can use data to facilitate targeted advertising, to engage in price discrimination, or to adopt data-driven management practices.² DBs, on the other hand, can either share data and produce a consolidated report or compete to independently supply the downstream firm. If the DBs share data, they incur an upstream merging cost. If the DBs compete and the buyer acquires both datasets, then the buyer needs to merge them incurring a downstream merging cost.

We find that the underlying incentives to engage in either data sharing or competition crucially depend on whether the value of the merged dataset, net of the merging costs, shows forms of complementarities or substitutabilities. Indeed, data may be super-additive when combining two data sources, net of the merging costs, results in a more valuable dataset than the sum of the individual components. Combining the browsing history with email addresses, for example, would provide a detailed picture of the preferences of a certain consumer and enable targeted offers. In this example, data create synergies and become more valuable when merged.

Data are sub-additive when aggregating two datasets leads to a new value, net of the merging costs, that is lower than the sum of the two separate datasets. For example, datasets might present overlapping information, diminishing marginal returns of data, correlated data points, or high merging costs. Finally, when combining two different data sources is extremely costly, a sharp reduction in the merged dataset’s net value may occur. This represents a case of extreme sub-additivity and the value of the merged dataset is lower than the stand-alone value of its components.

Data sharing arises for two main reasons. First and foremost, to soften competition between DBs; secondly, to enable DBs to internalize potential merging cost inefficiencies on the buyer’s side. The balance of these two effects drives our results. The former contrasts with the pro-competitive vision of data sharing, whereas the latter is consistent with the socially valuable perspective permeating the regulatory debate.

Suppose DBs are more efficient than the buyer in handling data. Then, when the data structure is sub-additive or extreme sub-additive both effects favour sharing. By merging sub-additive datasets, DBs can avoid granting the buyer the discount that results from competition and reflects the overlapping information and the buyer’s merging cost. In the presence of an extreme sub-additive data structure resulting from a high merging cost, the mechanism is similar: as the buyer is only interested in one dataset, sharing avoids an intense, Bertrand-like, competition. When data complementarities are present, there exists a multiplicity of equilibria under competition and these render sharing less likely to occur: one DB may prefer to veto a sharing agreement when it expects to grab a larger share of the surplus than the sharing rule prescribes.

However, not always are DBs more efficient than buyers in merging datasets. For example, as a former partnership between Facebook and Acxiom suggests, a tech company may acquire information from DBs, and the former can be more efficient in handling data, given its expertise and computational capabilities.³ In this case, the cost internalization incentive is clearly not present. However, an incentive to share data does exist when the value of the combined dataset is limited. Specifically, sharing avoids fierce competition when the datasets are extreme sub-additive. When instead the datasets are sub-additive, the two forces driving the incentives to share are now in contrast. On the one hand, DBs may be willing to share to soften competition and avoid discounting the overlapping component of the datasets. On the other hand, independent selling avoids the high merging cost facing the DBs.

Overall, depending on the nature of the data and merging costs, DBs may compete to supply a client firm in one market and, at the same time, cooperate and share data in another market. In this sense, our model successfully explains ‘co-opetition’ between DBs, a characterizing feature of the sector.

Our modelling of data intermediaries is consistent with some distinguishing characteristics of the data market. First, our model captures that the value of data is contextual. For example, the same two datasets can be substitutes or complements depending on their final use and downstream market circumstances (Sarvary and Parker, 1997). While our model abstracts away from the specifics of the downstream market and sheds light on both substitute and complementary data, it is compatible with a market where DBs repeatedly interact to supply downstream buyers in different sub-markets and with buyer-specific projects. Secondly, combining and sharing data sources can be substantially more costly than bundling other products. This highlights a crucial difference between data, which can be merged and disposed, and product bundling.⁴ For instance, merging datasets requires resource-intensive preparation of the data, and this may result in a very low net value of the final dataset. We highlight the importance of merging costs in shaping the data market outcome and characterize conditions for sharing to emerge in the unique subgame perfect Nash equilibrium. Finally, we discuss the possibility of data partitioning as, unlike many other products, a DB may be able to partly control the potential complementarity and substitutability when selling data.

1.1 Contribution to the literature

This article focuses on the market for data and the role of data intermediaries. The main contribution of our article is to capture the co-existence of competition and co-opetition between DBs, and identify the determinants of the transition between these. The closest papers to ours are Sarvary and Parker (1997), Bergemann et al. (2019), and Ichihashi (2021). Sarvary and Parker (1997) focus on the incentives of information sellers (e.g. consultancy, experts) to sell reports about uncertain market conditions to downstream firms, interested in finding the real state of the world. A crucial role is played by the reliability of information, data complementarity, or substitutability. In our framework, complementarity and substitutability are mediated by the presence of downstream and upstream merging costs, and data refer to individual characteristics rather than their reliability about the correct state of the world.

Instead, Bergemann et al. (2019) and Ichihashi (2021) analyse competition between DBs in obtaining data from consumers which can then be sold downstream. Similar to ours, Ichihashi (2021) considers a setting in which data intermediaries compete to serve a downstream firm with consumer data. However, he focuses on the welfare implications of data collection, whereas we explicitly study the incentives of data sharing and its implications for market actors.

Other studies have concentrated on related issues as privacy violations and anti-competitive practices stemming from access to data (Conitzer et al., 2012; Casadesus-Masanell and Hervas-Drane, 2015; Clavorà Braulin and Valletti, 2016; Choi et al., 2019; Gu et al., 2019; Montes et al., 2019; Belleflamme et al., 2020; Ichihashi, 2020; Bounie et al., 2021, and among others), strategic information sharing and signal jamming in oligopoly (Vives, 1984; Raith, 1996; Kim and Choi, 2010) and, more recently, the impact of data-driven mergers (Kim et al., 2019; Chen et al., 2020; De Cornière and Taylor, 2020; Prat and Valletti, 2021).

Our study also contributes to the recent law and economics literature on data sharing. In line with recent regulatory developments, this literature takes a mostly favourable view of the practice, based on the premise that, from a social perspective, there is not enough data sharing. For example, in Prüfer and Schottmüller (2021), data sharing might prevent tipping outcomes in data-driven markets. Graef et al. (2018) argue that the right to data portability, which enhances personal data sharing, should be seen as a new regulatory tool to stimulate competition and innovation in data-driven markets. Borgogno and Colangelo (2019) underline that data sharing via APIs requires a costly implementation process and to leverage their pro-competitive potential a regulatory intervention is necessary. Our results, instead, point to the possibility of excessive data sharing, through a harmful use of data to soften competition between data holding firms. This adds to other negative aspects of data sharing, as the overutilization of data pools or the reduced incentives for data gathering (Graef et al., 2019; Martens et al., 2020).

To a lesser extent, the issue we tackle shares similarities with patent pools (Lerner and Tirole, 2004, 2007) and how substitutability/complementarity might engender anti- or pro-competitive effects. In our framework, merging costs play an important role and interact with other forces in inducing data sharing. Moreover, a relevant difference between data and patent pools is that the latter can be considered as a structured combination of ideas whereas the former is a factor of production (Jones and Tonetti, 2020). Furthermore, unlike patents, data also have the characteristics of experience (Koutroumpis and Leiponen, 2013) and multipurpose goods (Duch-Brown et al., 2017). While data and DBs have distinctive features that characterize them in general, our framework may be applicable in other settings featuring substitutability or complementarity. For example, the two upstream firms might be patent holders deciding to pool their technologies or license them independently to a downstream firm.

1.2 Outline

The rest of the article is organized as follows. Section 2 outlines the model. Our main results are presented in Section 3. Section 4 explores several extensions to our main model and Section 5 concludes with final remarks. A microfoundation of the data structure and all proofs can be found in the Appendix.

2. The model

2.1 The DBs

Consider an economy with two DBs, k = 1, 2, who are endowed with data on different individuals and attributes. Each DB may have independent access to a subset of the attributes.⁵

To fix ideas, let $fk≥0$ be the extra surplus the buyer in question can generate by using the data owned by DB k, compared to a situation in which no data are available (i.e. $f(0)=0$⁠). The value function f can be interpreted as the monetary evaluation of the dataset from the perspective of the data buyer.

Data from different sources can be combined in a single dataset. This assembling process affects the value of the final dataset, depending on the underlying data structure, as defined below. In the absence of merging costs, a data structure is super-additive if $f12≥f1+f2$ and sub-additive if $f12<f1+f2$⁠, where $f12≥0$ is the value of the merged dataset to the buyer in question.⁶

The data structure identifies a continuum of cases depending on the value of the merged dataset. It is super-additive when datasets are complements and their combination returns a final output whose value is at least as large as the sum of the individual components. There are indeed synergies in the data which lead to the creation of a more informationally powerful dataset. This may happen when the interaction between different types of data plays a crucial role. For example, online purchasing history combined with credit card data collected offline can lead to data complementarity.

The data structure is sub-additive when the value of the merged dataset is lower than the sum of the values of individual datasets but is at least as large as either of the individual datasets. This happens when the two merging datasets have overlapping information.

The data structure is extreme sub-additive when the value of the merged dataset is lower than the value of an individual dataset. For instance, Dalessandro et al. (2014) suggest that, in some circumstances, adding additional data may be detrimental, and better predictions can be made with fewer data points. This is consistent with the seminal findings of Radner and Stiglitz (1984) who show theoretically that information can have a negative marginal net value. While a negative marginal value of information is caused by strictly positive information acquisition costs in Radner and Stiglitz (1984), in our framework the underlying force is the presence of non-negligible merging costs as we shall discuss below. Moreover, some customer attributes can be collinear or positively correlated (see, for example, Bergemann and Bonatti, 2019) and then lead to overlapping insights, whereas in other cases data can be difficult to integrate (see, e.g. health data in Miller and Tucker, 2014). Similar decreasing returns to scale are present in the recent literature on algorithms (Bajari et al., 2019; Claussen et al., 2019; Schäfer and Sapi, 2020).

2.2 The data buyer

2.3 Timing

The timing of the game is as follows. In the first stage, the two DBs simultaneously and independently decide whether or not to share their data. Data sharing arises if, and only if, both DBs choose to share data. In the second stage, DBs jointly or independently set the price(s) for the dataset(s). Then, in the third stage, the buyer decides whether or not to buy the offered dataset(s). The equilibrium concept is Subgame Perfect Nash Equilibrium (SPNE).

3. Analysis

Before the analysis is presented, we first need to define the data structure taking into account the merging cost, occurring either at the upstream (DBs) or the downstream (the buyer) level. That is, our definition focuses on the net value of the final dataset when two different data sources are combined.

Assume, without loss of generality, that $f2≥f1$⁠. We categorize the data structure as follows:

Definition 1. Under a given downstream merging cost c_b facing the buyer, the data structure is

• downstream super-additive, if $f12−cb≥f1+f2$⁠,

• downstream sub-additive, if $f2≤f12−cb<f1+f2$⁠, and finally

• downstream extreme sub-additive, if $f12−cb<f2$⁠.

The corresponding upstream data structure can be analogously defined by replacing c_b by c_db.

We note that the net benefit entailed by the combination of two datasets does not necessarily mirror the data structure in the absence of merging costs. For instance, a super-additive data structure without a merging cost may result in an extreme sub-additive data structure if the sharing activity takes place and its related cost is extremely high.

3.1 Independent data selling

We solve the game by backward induction. First, consider a second stage subgame where at least one DB has decided not to share data in the first stage and hence they simultaneously and independently set a price for their own data.

After observing the prices (p₁, p₂), the downstream firm decides whether to buy, and from whom, the dataset(s) so as to maximize its profit (3). This gives rise to the demand and revenue facing each DB for any given strategy profile (p₁, p₂).

Proposition 1

• If the data structure is downstream super-additive, any pair of $(p1*,p2*)$⁠, such that $p1*+p2*=f12−cb$ and $pk*≥fk$⁠, for k = 1, 2, constitutes a Nash equilibrium in this subgame. The downstream firm buys both datasets and merges them.

• If the data structure is downstream sub-additive, there exists a unique Nash equilibrium in this subgame in which $pk*=f12−cb−f−k$⁠, for k = 1, 2. The downstream firm buys both datasets and merges them.

• If the data structure is downstream extreme sub-additive, there exists a unique Nash equilibrium in this subgame in which $p1*=0$ and $p2*=f2−f1$⁠. The downstream firm does not merge the two datasets even when it buys both.

Proof: See Appendix.

The rationale of the above results is as follows. First, consider the data structure is downstream super-additive. In this case, the two datasets are characterized by strong synergies and complementarities persist even when considering merging costs c_b. This implies that rather than trying to price the rival out, each DB prefers the rival to sell its dataset too. This way, each DB hopes to appropriate some of the (positive) externalities the datasets produce downstream. As a result, in equilibrium, the buyer acquires data from both DBs and merge them on its own.

We note that in this case of downstream super-additivity, there is a continuum of competitive equilibria in which the DBs always extract the entire surplus from the buyer, that is, $Πk*+Π−k*=f12−cb$⁠. This leaves the buyer 0 net benefit. Note also that the merging cost that the downstream firm faces is passed upstream because, in any equilibrium, the downstream firm will pay no more than $f12−cb$ in total.

Consider now the case where merging two datasets leads to downstream sub-additivity. In contrast to the super-additivity case, the DBs prefer undercutting the rival than accepting its own marginal value to the rival’s dataset, an observation common in Bertrand-type price competition models. As a result, the unique equilibrium in (ii) emerges. Note that even if the downstream merging cost was negligible, the prices set by the DBs are limited by the substitutability of the datasets when the structure is sub-additive (e.g. overlapping information or high correlation between datasets).

In equilibrium, the buyer purchases from both DBs and pays a composite price of $p1*+p2*=2f12−f1−f2−2cb$⁠, with a net benefit of $f1+f2−f12+cb>0$⁠. As a result, the buyer is better off: in competition, DBs have to discount the merging costs, which are incurred by the buyer only once, and also the overlapping component.

Finally, merging costs can be large for the buyer such that the data structure gets extreme sub-additive. This implies that combining different data sources becomes less appealing and the buyer would only need the most valuable dataset. Under the assumption of $f2≥f1$⁠, only DB2 sells its data in equilibrium for sure. Its equilibrium price in this case equals the difference in the datasets’ intrinsic values, whereas the rival is forced to set a zero price, as a result of competition. The buyer obtains a net benefit of f₁.

The following corollary summarizes the downstream firm’s surplus and, for comparison, the industry profit of the DBs.

Corollary 1

• If the data structure is downstream super-additive, $Πb=π0$ and $Π1c+Π2c=f12−cb$⁠.

• If the data structure is downstream sub-additive, $Πb=π0+f1+f2−f12+cb$ and $Π1c+Π2c=2f12−f1−f2−2cb$⁠.

• If the data structure is downstream extreme sub-additive, $Πb=π0+f1$ and $Π1c+Π2c=f2−f1$⁠,

where $Πkc$ denotes DB k’s profit under competition.

Figure 1 illustrates the buyer’s surplus in relation to the gross value of the merged dataset, f₁₂. It is clear from the figure that the buyer is weakly worse off as the value of the merged dataset increases. It starts off with a positive net benefit of f₁ when the datasets are downstream extreme sub-additive and ends up with zero net surplus in the case of downstream super-additivity. The more synergy between the individual datasets, the worse it is for the downstream firm.

Fig. 1

The data buyer’s surplus and the value of the merged dataset in the absence of a merging cost, f₁₂.

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3.2 Data sharing

We now analyse DBs’ decision on data sharing. Figure 2 presents the normal form representation at the first stage of the game. To simplify the presentation, we assume $|cb−cdb|≤f1$⁠. That is, we exclude the less relevant cases where the cost difference is larger than the value of DB1’s dataset.⁸

Fig. 2

The normal form game at the first stage. (a) DBs are more efficient (⁠$cb>cdb$⁠). (b) The buyer is more efficient (⁠$cdb−f1/2≤cb<cdb$⁠). (c) The buyer is much more efficient (⁠$cb<cdb−f1/2$⁠).

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For data sharing to occur as an SPNE, the joint profit of the DBs when sharing their data has to be no less than those under competition, that is, $Π1s+Π2s≥Π1c+Π2c$⁠. Otherwise, sharing cannot be a mutual best response at the first stage.

Proposition 2 (Joint Profits)

• Suppose $cb≥cdb$⁠. The joint profits of the DBs under data sharing are no less than those under independent selling, irrespective of the nature of the data structure.

• Suppose instead $cb<cdb$⁠. The joint profits of the DBs under data sharing are no less than those under independent selling if $f12≤f^12$⁠, where

  $f^12={f1+f2+2cb−cdbif cdb−f1/2≤cb<cdbf1/2+f2+cbif cb<cdb−f1/2.$

  (6)

Proof: See Appendix.

Figure 3 provides a graphical representation of the findings presented in Proposition 2. Figure 3a focuses on the more natural case in which the buyer is less efficient than the DBs in merging the datasets, $cb>cdb$⁠. One illustration could be an insurance company that wants to access several potential clients’ characteristics for credit scoring and profiling. For example, browsing history can be used to know an individual’s habits and can be obtained through a DB specializing in marketing. Differently, data related to income and wealth can be accessed through a financial DB. These DBs routinely handle the latter data, whereas merging and cleaning separate databases may considerably be a harder task for the insurance company. The solid line (joint profits under sharing) is always above the dashed line (joint profits under competition). As a result, DBs are collectively better off when sharing data as it helps internalize downstream inefficiencies and avoid competition when their datasets overlap.

Figure 3(b, c) considers the cases where the buyer is more efficient than the DBs, $cb<cdb$⁠. For example, a dot com company, particularly effective in handling data, acquires new information from the DBs. Sharing in such cases is only an option if $f12<f^12$⁠, that is, when the value of the merged datasets is sufficiently small. Intuitively, without the benefit of internalizing downstream merging inefficiencies, sharing only helps to increase joint profit when information overlapping is sufficiently severe.⁹ The graphs also illustrate how the cut-off value $f^12$ is derived in these two scenarios, that is, when the downstream merging cost is relatively high or low compared to $cdb−f1/2$⁠.

Fig. 3

DBs’ joint profits from sharing (solid line) and from individual sales (dashed line), and the joint value of the datasets.

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3.2.1 Proportional sharing rule

In this way, we capture all possible equilibria, ranging from the one in which the extra-surplus is allocated equally across DBs (⁠$α=0.5$⁠) to the ones characterized by a very asymmetric surplus reallocation (α = 1 or α = 0).

We are now ready to present the main result of our analysis.

Proposition 3 (Equilibrium Sharing)

• Suppose $cb≥cdb$⁠. Data sharing emerges in the unique Subgame Perfect Nash Equilibrium of the game, if and only if, $f12<f˜12$ where

  $f˜12=f1+f2+cb+{(cb−cdb)f1(1−α)f2−αf1if α<f2f1+f2∞if α=f2f1+f2 and cb>cdb0if α=f2f1+f2 and cb=cdb(cb−cdb)f2αf1−(1−α)f2if α>f2f1+f2.$

  (7)
• Suppose instead $cb<cdb$⁠. Data sharing emerges in the unique Subgame Perfect Nash Equilibrium of the game, if and only if, $f12<f12≈$ where

  $f12≈=f1+cb+{f22f1+f2if cdb−cb<f12f1+f2f2−f2f1(cdb−cb)if cdb−cb>f12f1+f2.$

  (8)

Proof: See Appendix.

Consider the case where DBs are more efficient than the buyer in handling data, that is, $cb≥cdb$⁠. Suppose first that the data structure features some complementarities. The previous proposition established that sharing could be industry-efficient, but this does not necessarily arise. As under competition, DBs may make very asymmetric profits (given the multiplicity of equilibria), and sharing would make one of them better off but penalize the other. In other words, for either a large or a small α, one DB vetoes a sharing agreement provided that the joint profits are sufficiently large. Only in the special case where the expected competitive profit shares are exactly in line with the sharing rule, do both brokers agree to share their data for any value of the joint dataset. To obtain the unique result, we differentiate whether $cb>cdb$ or $cb=cdb$ as in the latter case for any $f12≥f1+f2+cb$⁠, competition can also be an equilibrium outcome. The above discussion is reflected in the critical value of $f˜12$ and in the conclusion that data sharing arises for $f12<f˜12$ as defined by (7).

Turning to a sub-additive data structure, data sharing allows for a surplus extraction that they would otherwise fail to implement fully with independent selling. Because competition leads DBs to provide a discount to the buyer (equal to downstream merging cost and the overlapping component of the datasets), sharing data can restore full surplus extraction. This way, DBs can soften competition and internalize downstream inefficiencies. A similar argument applies to an extreme sub-additive data structure. In this case, data sharing is optimal for DBs as it always allows them to coordinate on ‘throwing away’ DB1’s dataset and extract all surplus generated by the most valuable dataset. Importantly, both DBs are better off with sharing under the assumed sharing rule than under competition.

Suppose now that the buyer is more efficient than the DBs. Note that in this case, the benefit of internalizing inefficient merging costs through sharing is absent and hence, at least one DB objects sharing when the data structure is super-additive.

When the data structure is sub-additive or extreme sub-additive, sharing can help DBs to appropriate some surplus otherwise left because of the overlapping component between their datasets. However, this appealing strategy constitutes an equilibrium only when the loss from the higher merging cost outweighs each DB’s loss under competition. When the value of the merged dataset is sufficiently low, meaning substantial overlapping information, then sharing would be optimal for both DBs. As a result, there exists a critical value such that only for lower values of the joint dataset both DBs agree to share and to take on the higher upstream merging cost. This critical value is denoted by $f12≈$⁠.

An interesting result emerges from the above discussion. At first, one may expect that an incentive to share would emerge when complementarities between data are strong. For instance, combining email addresses (or postal codes) with the browsing history would provide the two DBs with powerful information to be sold in the market for data. Similarly, when data partially overlap or their joint use leads to quality deterioration, the incentive to share would decrease as the incremental benefit of the rival’s database decreases too. On the other hand, joint selling may soften competition when data are substitutes, rendering sharing more appealing. Our model indicates that data sharing is most likely to arise when datasets present forms of substitutability and DBs are more efficient than buyers in handling data. On the contrary, competition arises more often when datasets are complements and there are upstream inefficiencies in merging data.

As noted previously, the value of data is often contextual. The same datasets held by the brokers can have different data structures, depending, for example, on the data already possessed by the downstream buyer. Suppose there are three units of data, A, B, and C.¹⁰ DB DB1 has data A and B while DB2 has B and C. Suppose further that the downstream buyer possesses A and C. With slight abuse of notation, it is easy to verify that $f1=f2=f12=f(A,B,C)−f(A,C)$⁠. Consequently, the upstream data structure is almost always sub-additive, and hence DBs face fierce competition in independent selling. As a result, in this example, data sharing between the DBs is very likely to emerge. Note also that the buyer’s data make those of the DBs completely overlapping with each other although, on their own, they are complements. In this sense, the buyer’s data substantially enhance the DBs’ incentive to share data upstream.

Suppose the downstream buyer possesses data B instead. In this case, $f1=f(A,B)−f(B), f2=f(B,C)−f(B)$ and $f12=f(A,B,C)−f(B)$⁠. In the absence of merging costs, it is easy to check that the upstream data structure can be either super- or sub-additive depending on the sign of $f(A,B,C)≶f(A,B)+f(B,C)−f(B)$⁠. Thus, the same data held by the DBs can have different data structures depending on the context. Moreover, in this example, data B is available to all parties from the outset. By letting $f(A)=f(A,B)−f(B), f(C)=f(B,C)−f(B)$⁠, and $f(A,C)=f(A,B,C)−f(B)$⁠, our baseline model can capture the same strategic situation without explicitly referring to B. In this sense, the buyer’s data do not substantially alter the sharing incentives of the DBs.

Finally, consider the welfare implications of our analysis. Note that we abstract from explicitly modelling consumers, and this greatly simplifies the analysis. In fact, as prices are just transfers between DBs and the buyer, if datasets are merged under both regimes (competition and data sharing), welfare corresponds to the value of the data, f₁₂, net of the merging costs (c_b and c_db, respectively). As a result, the welfare gain of sharing vis-à-vis competition is simply the cost differential, $ΔW=Ws−Wc=cb−cdb$⁠. For example, if $cb≥cdb$ then data sharing is welfare enhancing. Hence, according to Proposition 3, Part (i), for the values of f₁₂ above the threshold $f˜12$ the equilibrium featuring competition is inefficient.

Inefficiency in the opposite direction can take place when DBs are less efficient than the buyer (⁠$cb<cdb$⁠). In fact, competition is welfare enhancing when $f12≥f2+cb$⁠.¹¹ However, the market outcome features socially inefficient sharing if f₁₂ is between $f2+cb$ and the threshold $f12≈$ of Proposition 3, Part (ii). In case neither the buyer nor the DBs merge the two datasets, that is, if f₁₂ is very low, then only a reallocation of surplus across parties occurs regardless of the scenario. In turn, $ΔW=0$ and no choice is strictly socially efficient. The previous discussion can be summarized as follows:

Proposition 4 (Welfare)

• Suppose $cb≥cdb$⁠. In equilibrium, welfare decreasing competition takes place for $f12≥f˜12$⁠. Otherwise, the equilibrium outcome is (weakly) socially efficient.

• Suppose instead $cb<cdb$⁠. In equilibrium, welfare decreasing data sharing takes place for values of $f12∈[f2+cb,f12≈)$⁠. Otherwise, the equilibrium outcome is (weakly) socially efficient.

Proof: See Appendix.

4. Extensions

4.1 Alternative sharing rules

The sharing rule adopted in the previous section is just one among several possible alternatives. For example, s_k can follow the Shapley value implementation. Unlike the proportional rule, the Shapley value captures the average marginal contribution of a DB to a given coalition, that is, in our context, a data-sharing proposition. Indeed, the literature on the Nash implementation of the Shapley value demonstrates that it can be the equilibrium outcome of a properly constructed non-cooperative bargaining game (Gul, 1989).

The results obtained prove robust. Also in this context, data sharing arises for relatively low values of the combined dataset, whereas competition prevails if combining datasets generates high values. Moreover, sharing is more likely if DBs are relatively more efficient in handling the data and if the competitive equilibrium share of profits is expected to be balanced, that is, when α is close to the Shapley sharing rule. Overall, compared to a proportional rule, a Shapley value sharing rule contributes to realigning the choices of DBs with industry efficiency.

Still, both the proportional and the Shapley sharing rules may lead to a loss of surplus and inefficiency from the perspective of the DBs. Indeed, if c_b is larger than c_db, the joint profits always increase through sharing, but it is often the case that a proposed agreement is vetoed by one of the parties. These sharing rules have been considered so far as exogenously given. The sharing rule could be endogenized in several ways, and a take-it-or-leave-it offer by one of the DBs is a natural one. In such a setup, if the industry surplus is higher under sharing than competition, the proposer will make sure that the receiver will not veto industry efficient data sharing. Similarly, if the DBs engage in Nash bargaining with their profits in independent selling as their respective outside option, the outcome will also be efficient for them.

There are reasons to believe that both types of sharing rules (exogenous or endogenous as an outcome of a bargaining process) may characterize what happens in reality. In fact, given DBs’ repeated interactions over time, a fixed sharing rule may act as a sort of (flexible) commitment, to be adjusted on a case-by-case basis. Indeed, whereas an endogenous rule leads to industry efficiency, always negotiating an endogenous agreement may be in itself overly costly for the involved parties.

4.2 Data can be partitioned

A key feature of data is its divisibility. That is, a dataset containing information regarding N consumers and M attributes can be ‘repackaged’ to contain information on alternative sets $N^$ of consumers and $M^$ of attributes. One may wonder whether DBs have an incentive to operate strategically such partitions when competition occurs. A rationale for partitioning might be that DBs try to soften the very harsh competition that occurs when data are sub-additive. In other words, if the original datasets feature some overlaps or correlation, the data may be restructured prior to competition in a way that eliminates or minimizes such issues.

We note, however, that this would not affect the conclusions of our previous analysis for two reasons. First, as Part (ii) of Proposition 1 demonstrates, the DB that considered removing some overlapping information from its own dataset still obtains a profit equal to its net marginal contribution, whereas the other DB would now obtain a higher profit. Secondly, selectively repackaging some information can be particularly costly. For example, identifying specific variables and observations to remove can be time-consuming for a DB. This suggests that absent anti-competitive side-transfers, a DB may not have incentives to unilaterally reduce overlaps.

4.3 Sequential pricing

We also investigate whether DBs’ incentive to share data changes when they set their prices sequentially. The timing is changed as follows. DB k first sets p_k and then DB—k sets $p−k$ after observing p_k. Given the resulting prices, the downstream firm decides whether to buy the dataset(s) and from which DB. Regardless of the order of moves, our main findings and intuitions remain qualitatively similar: data sharing emerges as a tool to soften the competition between DBs. However, as compared to the case in which prices are set simultaneously, sharing arises less often.

The intuition is as follows. A first-mover advantage is identified with a downstream super-additive data structure, which leads to the possibility of naturally selecting one equilibrium from the multiplicity identified in the benchmark. Formally, this implies selecting the equilibrium with $α={0,1}$ from the benchmark model with $cdb≤cb$⁠, and, hence, the most asymmetric surplus divisions. As a result, the first-mover has an incentive to veto any sharing agreement, rendering competition the most likely scenario.

5. Conclusion and discussion

This article sheds light on the quite obscure and relatively underexplored market for data. We present a model of data intermediaries and study their role as suppliers of valuable information to downstream firms. A distinctive aspect of the sector, prominently transpiring from the Federal Trade Commission’s (2014) report, is the exchange and trade of data between brokers and how this relates to the particular properties of data, as compared to other products (contextual value, merging costs, and complementarities).

Our framework is compatible with a market for data in which DBs repeatedly interact to supply buyers in different sub-markets, and in which projects are buyer-specific. We highlight how the incentives for data sharing are crucially related to the nature of the data held by the brokers. Specifically, we find that data sharing can arise for two reasons. First, DBs can soften competition when data present some form of substitutability. Secondly, it allows DBs to internalize downstream inefficiencies, as buyers may be less efficient than DBs in merging multiple datasets. In turn, we identify a possible trade-off between the positive effects of cost internalization, consistent with the spirit of the EU Data Strategy (European Commission, 2020), and the negative effects of data sharing linked to reduced competition in this opaque market.

In particular, our analysis highlights the importance of the sub- or super-additive data structures, the data merging costs, and the selection of the competitive equilibrium for their decisions to cooperate on a shared project. These insights are also partly consistent with the literature on co-opetition, which has long held that companies may be collaborators with respect to value creation but become competitors when it comes to value capture (e.g. Nalebuff and Brandenburger, 1997). In the context of our model, collaboration may go beyond situations of value creation (efficiency savings) and can soften competition between DBs at the expense of their clients.

Our theoretical analysis rationalizes the large heterogeneity in the contractual arrangements and collaborations in this market, as also illustrated by the Federal Trade Commission (2014). For a client, our results provide two rather counter-intuitive implications. First, a firm may prefer to buy ‘lower quality’ (e.g. sub-additive, with overlapping information) data. This happens because competition between brokers intensifies and the firm can retain some of the surplus produced through the data. Secondly, downstream cost inefficiencies may prove to be an advantage as competition leads DBs to grant a discount to a downstream firm. This suggests that downstream firms may have less incentive to develop their digital skills when there is a functioning data market.

The sector is not particularly transparent and reliable information to conduct a proper empirical analysis of DBs’ strategies is not easy to access. If data were available, however, our model delivers testable predictions. For example, the probability that DBs may exchange a dataset required by a buyer should positively relate to their relative efficiency in handling data compared to the buyers. The probability should also increase in the data homogeneity, and decrease when composite information from a variety of sources is usually in demand. At the same time, it might be inferred from highly asymmetric revenues in competitive segments of the market that data sharing has failed due to the profitable firm anticipating its dominant role.

Moreover, we shall note that the EU and the USA have followed different regulatory approaches on how data should be managed by intermediaries, third parties, and retailers. The EU has tackled the issue of privacy more strictly. More specifically, the EU GDPR has strengthened the conditions for consent by consumers, who need to be explicitly informed about the final use of the data collected.

In other words, data sharing among different DBs without prior authorization of consumers is deemed illegal, to the point that such regulation is often emphatically evoked as the ‘death of third-party data’.¹² In the light of our analysis, the EU GDPR may have some unintended pro-competitive effect in the upstream data market. Specifically, the need for the explicit consent of the consumers to data sharing should reduce the prevalence of this practice, with the further consequence of enabling downstream firms to partially retain some of the data-generated surplus.

Additionally, most of the attention of the policymakers has been devoted to the final use of data and on how data sharing might create positive externalities and pro-competitive effects. Nevertheless, little attention has been given to data as an input, produced, managed, and traded by DBs. Our analysis highlights that the co-opetitive practices of DBs might require additional scrutiny from a regulator.

Finally, we conclude with a few possible extensions for future work. First, it is important to note that in our model we have assumed perfect information about buyer’s evaluation. Related to the case of patent pools (e.g. Lerner and Tirole, 2004), incorporating uncertainty about the buyer’s evaluation could create an additional incentive for DBs to share data in the presence of super-additive data structures. Secondly, for tractability, we have also assumed that there are only two DBs. We conjecture that our results in the spirit of Proposition 3, that is, data sharing emerges as the unique equilibrium outcome when the merged value of individual datasets falls below a (possibly more demanding) critical level, are likely to hold with more DBs. However, data structures become more involved in the presence of several individual datasets, as complementarity and substitutability have to be specified among all possible merging decisions. This is akin to the specification of a characteristic function in a cooperative game. We leave this extension for future work where one can further explore the conditions under which data sharing only takes place among a strict subset of the DBs. Last but not least, our model is also parsimonious in the downstream and does not directly model consumers. A welfare analysis encompassing consumers would be of particular interest in this context as, besides the effect of data on product prices, data transfers, and sharing could affect the risks of data leakages and, more generally, influence consumers’ privacy.

Supplementary material

Supplementary material is available on the OUP website. This consists of the online appendix.

Funding

This work was supported by the ‘MOVE-IN Louvain’ Incoming Fellowship Programme of the Université Catholique de Louvain to LM.

Footnotes

Acknowledgements

We are grateful to Alan Beggs (the Associate Editor) and two anonymous referees for insightful comments that have improved the paper. We also thank Paul Belleflamme, Nina Bobkova, Federico Boffa, Marc Bourreau, Emilio Calvano, Bruno Carballa-Smichowski, Elias Carroni, Alexandre de Cornière, Flavio Delbono, Antoine Dubus, Néstor Duch-Brown, Luca Ferrari, Juan-José Ganuza, Axel Gautier, Andreas Hervas-Drane, Alberto Iozzi, Johannes Johnen, Yassine Lefouili, Jan Krämer, Fabio Manenti, Andrea Mantovani, Bertin Martens, David Ronayne, Lorien Sabatino, Daniel Schnurr, Tommaso Valletti, John Van Reenen, Wouter Vergote, and Patrick Waelbroeck, alongside participants at the IX IBEO Workshop on Media Economics (Alghero), 45th EARIE Conference (Athens), 11th TSE Digital Economics Conference, X NERI Workshop (Rome), 9th Florence School of Regulation Seminar on Media and the Digital Economy, 2019 EEA-ESEM Conference (Manchester), 2019 IIOC (Boston), 2020 MACCI/EPoS Virtual IO Seminars, and seminar participants at different universities, for useful comments and suggestions. The usual disclaimer applies.

References