Selling Strategic Information in Digital Competitive Markets 

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Selling Strategic Information in Digital Competitive Markets

Introduction

The digital economy is driven by consumer information, what analysts have called ’the new oil’ of the twenty rst century.1 Digital giants such as Face-book, Apple, Amazon and Google, base their business models on traces left by Internet users who visit their online websites. In a race to information domi-nance, these large companies also acquire information from data brokers that gather information about millions of people.2
Data brokers collect all sorts of information on consumers from publicly available online and o ine sources (such as names, addresses, revenues, loan default information, and registers). They are major actors in the data economy, as more than 4000 data brokers operate in a market valued around USD 156 billion per year (Pasquale (2015)). In a study of nine data brokers from 2014,3 the Federal Trade Commission found that data brokers have information « on almost every U.S. household and commercial transaction. [One] data broker’s database has information on 1.4 billion consumer transactions and over 700 billion aggregated data elements; another data broker’s database covers one trillion dollars in consumer transactions; and yet another data broker adds three billion new records each month to its databases. »4 Data brokers therefore possess considerable amounts of information that they can sell to help rms learn more about their customers to better target ads, tailor services, or price discriminate consumers.
Competition between rms is thus in uenced by how much consumer infor-mation rms can acquire from data brokers. On the one hand, more information allows rms to better target consumers and price discriminate. They can ex-tract more consumer surplus, which increases their pro ts. On the other hand, more information means that rms will ght more ercely for consumers that they have identi ed as belonging to their business segments. This increased competition lowers the pro ts of the rms. Overall, there is an economic trade-o between surplus extraction and increased competition. This article analyzes this trade-o when a data broker strategically combines consumer segments in order to maximize its pro ts.
Understanding how the quantity of information available on a market in u-ences competition is a central question in economics, dating back to Hayek’s seminal work (Hayek, 1945). The emergence of data brokers adds a strategic dimension to the literature that assumes that information is exogenously avail-able on the market.5 Braulin and Valletti (2016) study vertically di erentiated products, for which consumers have hidden valuations. The data broker can sell to rms information on these valuations. Montes et al. (2018) consider informa-tion allowing competing rms to rst-degree price discriminate consumers. In both articles, the data broker sells either information on all consumers, or no information at all.
We build a model where a data broker can sell information that partitions consumer demand into segments of arbitrary sizes to one or to two competing rms. The data broker can strategically sell consumer segments of information to rms competing on the product market, and can weaken or strengthen the intensity of competition by determining the quantity of information available on the market. In other words, the data broker has the choice to sell information on all available consumer segments, on a subset of consumer segments, or no information at all. By acquiring information from the data broker, rms can identify the most pro table consumer segments, on which they set speci c prices.
Using this setting, we show that the data broker sells information on consumers with the highest willingness to pay, which allows rms to extract more consumer surplus. Information on low-valuation consumers is not sold to rms in order to soften competition. In other words, it is not optimal for the data broker to sell all consumer segments, as doing so would reduce the pro ts of the rms, and hence their willingness to pay for consumer information.
This paper contributes to the fast growing literature on customer informa-tion acquisition by allowing a data broker to sell any combination of consumer segments. Data brokers can strengthen or weaken competition between rms by choosing the amount of consumer information that they sell. Thus, the strategies of data brokers can have con icting policy implications for competi-tion authorities and data protection agencies. On the one hand, competition authorities could encourage industry practices that increase information and competition on the market. On the other hand, more information available on the market allows rms to extract more consumer surplus, which can harm consumers. Data protection agencies could be wary of such practices.
The remainder of the article is organized as follows. In Section 2.2 we de-scribe the model, and in Section 2.3 we characterize the optimal structure of information. In Section 2.4, we provide the equilibrium of the game, and we discuss the e ects of information acquisition on welfare. We conclude in Section 2.5.

Model set-up

The model involves a data broker, two rms (noted = 1; 2), and a mass of consumers uniformly distributed on a unit line [0; 1]. The data broker collects information about consumers who buy products from the competing rms at a cost that we normalize to zero. Firms can purchase information from the data broker to price discriminate consumers.6
The two rms are located at 0 and 1 on the unit line and sell competing products to consumers. A consumer located at x derives a gross utility V from consuming the product, and faces a linear transportation cost with value t > 0. A consumer buys at most one unit of the product, and we assume that the market is fully covered, that is, all consumers buy the product. Let p1 and p2 denote the prices set by Firm 1 and Firm 2, respectively. A consumer located at x receives the following utility:  U(x) = V t(1 x) p2; if he buys from Firm 2;
In the following sections, we de ne the information structure, the pro ts of the data broker and of the rms, and the timing of the game.

Information structure

Firms know that consumers are uniformly distributed on the unit line, but with-out further information, they are unable to identify their locations. Therefore, rms do not know the degree to which consumers value their products and cannot price discriminate them.7
Firms can acquire an information structure from a monopolist data broker at cost w. The information structure consists of a partition of the unit line into n segments of arbitrary size. These segments are constructed by unions of elementary segments of size k1 , where k is an exogenous integer that can be interpreted as the quality or the precision of information. Although the data broker can sell any such partition, it is useful to de ne a reference partition Pref , which includes k segments of size k1 .
Figure 4.1 illustrates the reference partition that includes all segments of size k1 . All existing models in the literature assume that the data broker can only sell the reference partition Pref to competing rms, or no information at all. A major contribution of the present article is to demonstrate that the optimal partition sold by the data broker is not the reference partition Pref .
Fig. 2.1: Reference partition Pref
We introduce further notations. We denote S the set comprising the k 1 endpoints of the segments of size 1 : S = f 1 ; ::; i ; ::; k 1 g. Consider the mapping that associates to any subset f k ; ::; k ; ::; k g 2 S, a partition f[0; k ]; [ k ; k ]; :
:; [ sn 1 ; 1]g, where s1 < :: < si < :: < sn 1 are integers lower than k. We write P as the target set of the mapping: M : S ! P; this set includes all possible partitions of the unit line generated by segments of size k1 . Thus, P is the sigma-eld generated by the elementary segments of size k1 . In particular, Pref and ; are included in P.
The data broker can sell any partition P in the set of partitions P: for instance, a partition starting with one segment of size k1 , and another segment of size k2 , and so on, as illustrated in Figure 4.4.
A rm that has information f[0; sk1 ]; [ sk1 ; sk2 ]; ::; [ snk 1 ; 1]g will be able to identify whether consumers belong to one of the segments of the set, and charge them a corresponding price. Namely, the rm will charge consumers a price p1 on [0; sk1 ], a price pi+1 on [ ski ; sik+1 ], and so forth for each segment. Firms thus practice third-degree price discrimination. We show in Section 4 that rst-degree price discrimination is a limit case of our model when k ! 1.
Finally, to keep the analysis as simple as possible, we rule out elements of the partition P that consist of several disjoint intervals, and that add uncertainty on the location of consumers, such as [ ski ; sik+1 ] [ [ ski0 ; si0k+1 ] (with i0 > i + 1).

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Strategies and timing

We present the strategies and pro ts of the data broker and of rms, and then the timing of the game.
The data broker maximizes its pro ts by choosing a pair of partitions noted P1; P2 in the set P that are respectively proposed to Firm 1 and Firm 2. These partitions, or information structures, can be potentially di erent for Firm 1 and Firm 2. Finding the optimal partitions is a complex optimization problem given that the cardinality of P can be very large, and that we do not impose restrictions on the total number k of segments of the reference partition.
We denote whether a rm and its competitor are informed (I) or uninformed (N I) by the couple (x; y) where x; y 2 fI; N Ig, and (I; N I) refers to a situation in which Firm is informed and Firm is uninformed. We note x;y(P1; P2) the pro t of Firm with information P1 whereas Firm has information P2 in situation (x; y). For instance, 1I;I (P1; P2), is the pro t of Firm 1 when both rms are informed.8 For any information structure, we need to compute the pro ts in four possible con gurations: f NI;NI ; I;NI ; NI;I ; I;I g.
The data broker decides to sell information to one rm only or to both rms. In both cases, information is sold through an auction mechanism with negative externalities as in Jehiel and Moldovanu (2000). Before the auction takes place, the data broker proposes partition P1 to Firm 1 and partition P2 to Firm 2. When the data broker sells information to only one rm, we assume that it is Firm 1, without loss of generality.
The data broker extracts all surplus from competing rms and maximizes the value of information, which is the di erence between the pro ts of an informed rm and those of an uninformed rm. The pro t function of the data broker can be written as: P1; P2) = 1I;NI(P1; 😉 1NI;I(;; P2)  if the data broker sells information to Firm 1;  2(P1; P2) = 1 (P1; P2) 1 (;; P2) + 2 (P2; P1) 2 (;; P1)  I;I NI;I I;I NI;I
The rst part of Eq. (3.3.3), 1, is the pro t of the data broker when selling partitions P1 to Firm 1 only; the second part of Eq. (3.3.3), 2, is the pro t of the data broker when selling partitions P1 and P2 to Firm 1 and Firm 2 respectively.9
In order to compute the pro ts of the rms, we need to compute demand and prices on each consumer segment. When a rm has no information, it sets a uniform price on the whole interval [0; 1]. However, when a rm has a partition P1, it sets a price on each segment of the partition. There are two types of segments to analyze: segments on which both rms have a strictly positive demand, and segments on which a rm is a monopolist. We assume that Firm sets prices in two stages.10 First, it sets prices on segments where it shares consumer demand with its competitor. Then, on segments where it is a monopolist, it sets a monopoly price, constrained by the price proposed by its competitor. Each rm knows whether its competitor is informed, as well as the structure of the partition acquired by its competitor.

Table of contents :

Introduction 
1. Information Goods and Strategic Gatekeepers 
1.1 Introduction
1.2 Shaping of downstream competition
1.2.1 Selling information to a subset of rms
1.2.2 Lowering the quality of information and innovations
1.3 The Arrow eect
1.4 Payo uncertainty
1.5 Conclusion
2. Selling Strategic Information in Digital Competitive Markets 
2.1 Introduction
2.2 Model set-up
2.2.1 Information structure
2.2.2 Strategies and timing
2.3 Optimal information structure
2.3.1 Information is sold to only one rm
2.3.2 The data broker sells information to both rms
2.3.3 Competitive eects of information acquisition
2.4 Model resolution
2.4.1 Stages 2 and 3: rms set prices
2.4.1.1 The data broker does not sell information
2.4.1.2 The data broker sells information to one rm
2.4.1.3 The data broker sells information to both rms
2.4.2 Stage 1: prots of the data broker
2.4.3 Characterization of the equilibrium
2.4.4 Welfare analysis
2.4.4.1 Prots of the rms in equilibrium
2.4.4.2 Consumer surplus
2.4.4.3 First-degree price discrimination
2.5 Conclusion
2.6 Appendix
3. Selling Mechanisms and the Market for Consumer Information
3.1 Introduction
3.2 Model
3.2.1 Consumers
3.2.2 Data intermediary
3.2.2.1 Collecting data
3.2.2.2 Selling information
3.2.3 Firms
3.2.4 Timing
3.3 Selling mechanisms
3.3.1 Take it or leave it
3.3.2 Sequential bargaining
3.3.3 Auction
3.4 Number of segments sold in equilibrium
3.4.1 Number of segments sold in equilibrium
3.4.2 Independent data contracts
3.5 Collecting data in equilibrium
3.6 Extension: alternative selling mechanisms
3.7 Conclusion
3.8 Appendix
4. Collecting and Selling Consumer Information: the Two Faces of Data Brokers
4.1 Introduction
4.2 Description of the model
4.2.1 Consumers
4.2.2 Data brokers
4.2.2.1 Collecting information
4.2.2.2 Selling information partitions
4.2.2.3 Pricing information
4.2.3 Firms
4.2.4 Timing
4.3 Collecting and selling information
4.3.1 Stages 3 and 4: prots of the rms in equilibrium
4.3.2 Stage 2: Selling information
4.3.2.1 Selling information in monopoly
4.3.2.2 Selling information under competition
4.3.2.3 Competing gatekeeper eect
4.3.3 Stage 1: Collecting information with competing data brokers
4.3.3.1 Prots of the data brokers in equilibrium
4.3.3.2 Rent-extraction eect
4.4 Consumer surplus
4.5 Discussion
4.6 Appendix
Conclusion

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