The Impact of Access to Consumer Data on the. Competitive Effects of Horizontal Mergers

Transcription

1 The Impact of Access to Consumer Data on the Competitive Effects of Horizontal Mergers Jin-Hyuk Kim Liad Wagman Abraham L. Wickelgren Abstract The influence of firms ability to employ individualized pricing on the welfare consequences of horizontal mergers is examined in location models. In a two-to-one merger, the merger reduces consumer surplus more when firms can price discriminate based on individual preferences compared to when they cannot. However, the opposite holds true in a three-to-two merger, in which the reduction in consumer surplus is substantially lower with individualized pricing than with uniform pricing. Further, the three-to-two merger requires an even lesser marginal cost reduction to justify when an upstream data provider can make exclusive offers for its data to downstream firms. Keywords: Price discrimination, consumer privacy, data broker, horizontal merger JEL Classifications: K1, L11, L1 University of Colorado at Boulder. jinhyuk.kim@colorado.edu Illinois Institute of Technology. lwagman@stuart.iit.edu University of Texas at Austin. awickelgren@law.utexas.edu 1

2 Of the nine data brokers, one data broker s database has information on 1. 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. Most importantly, data brokers hold a vast array of information on individual consumers. For example, one of the nine data brokers has 3000 data segments for nearly every U.S. consumer. (Federal Trade Commission, 01) 1 Introduction Improvements in information technology have brought growing concerns about privacy intrusion in commercial marketplaces to the forefront of public debate. Nearly all U.S. consumers now use online media to shop (BIA/Kelsey, 013) and over two thirds of online adults in the U.S. are registered on social networks (Pew, 013). As recent reports by the Federal Trade Commission show, this has led to the proliferation of so-called data brokers. These brokers collect consumers personal, behavioral, and financial data from a wide range of sources, merge disparate elements of consumers offline and online footprints to form detailed individualized profiles, and sell this data as a critical input for a variety of marketing purposes across a number of sectors. In response to growing privacy concerns, some policy commentators and consumer groups have urged antitrust authorities to deal with privacy issues that arise in the context of mergers while others have disagreed. Specifically, privacy advocates are concerned with the concentration of consumer data over and beyond the concentration of market power in the product market. 1 This paper provides a theoretical analysis of the effects of consumer data on horizontal mergers and shows that its welfare implication may depend on the product 1 Center for Digital Democracy and Electronic Privacy Information Center have petitioned the FTC in such cases as the Google-DoubleClick merger in 008 and Facebook-WhatsApp merger in 01. The FTC allowed these mergers to proceed because privacy issues may not have been deemed relevant for competitive analysis (see, e.g., Ohlhausen and Okuliar, 015).

3 market structure, where downstream firms compete in differentiated product markets such as Hotelling s Linear City (199) and Salop s Circular City (1979) models. There is relatively little work on merger incentives that take into account spillovers from the data-broker industry. To be up front about our contribution, the most relevant work by Cooper et al. (005) analyzes the effect of price discrimination on post-merger average price, but they do not endogenize the decision to acquire the information and also do not demonstrate the differential impact based on whether the consumer data is supplied competitively or by a monopoly data-broker. This paper examines merger incentives and consumer welfare explicitly when firms can choose whether to access consumer data that facilitates individualized pricing, in comparison to the standard merger case which typically assumes uniform pricing. We also consider how this choice and the subsequent equilibrium are affected by the market structure in the upstream data-broker industry. Given that mergers with the potential to reduce competition involve at least two firms that sell related but not necessarily identical products, our model considers the role of individual consumer profiling in a market with horizontal differentiation. Firms that have access to the data can tailor their prices to each consumer s location. We consider two cases: (i) firms can purchase consumer data from competitive upstream data market at a sufficiently low price, and (ii) a monopoly data broker offers downstream firms contracts (including, possibly, exclusive contracts) to purchase consumer data to maximize its profit. Although the extent of business practices concerning consumer data acquisition and individualized pricing has been neglected in formal merger reviews, our analysis can shed some light on an upper bound on the effects of such practices on horizontal mergers. We find that in a merger to monopoly, access to consumer data exacerbates the anticompetitive effect (reduction in consumer surplus) of the merger. However, since mergers to One can think of the perfect price discrimination as the logical extreme of the impact of access to consumer data, which is assumed in most of the literature we discuss below. In reality, firms may not perfectly infer the individual s location parameter; however, the qualitative direction or implication of our results would be unaffected by this feature. 3

4 monopoly are rarely approved even in the absence of individualized pricing, more relevant results concern the effects of data access on mergers in a market in which there is more than one firm remaining after a merger. In these cases, easy access to consumer data with a competitive data broker industry may substantially lower the anticompetitive effects of a merger in equilibrium. The reason is that non-merging firms, through individualized price offers, can put a more effective restraint on the merging firms prices than in the absence of individualized pricing. While our analytical framework is similar to that of Cooper et al. (005), we show that the above result holds when access to data is endogenized and despite the fact that accessing such data lowers industry profits. More importantly, we establish the new result that with a competitive data-broker industry, while the adverse competitive effects (when they exist) of a three-to-two merger are always smaller when firms have access to consumer data, access to consumer data does not change the necessary efficiencies required to eliminate the adverse impact of the merger on consumer welfare. That is, the difference in the consumer welfare effect of the merger is decreasing in the magnitude of the marginal cost reduction from the merger and reaches zero exactly at the level of cost reduction in which the merger creates no decrease in consumer welfare with or without access to consumer data. Thus, our most novel and important finding is that when a data broker monopolizes the data market, the anticompetitive effect of a three-to-two downstream merger is smaller than in both the case of no data availability and the competitive data broker case. Moreover, unlike in the competitive data broker case, we find that with a monopoly data broker, access to consumer data can turn an anti-competitive merger into a pro-competitive merger. That is, the necessary efficiency gain for the merger to increase consumer surplus is substantially smaller (one-third the size) than it is without access to consumer data. Thus, when downstream firms face a monopoly data broker, antitrust authorities should be more willing to approve mergers for smaller efficiency gains than would be the case both if there were no consumer data available and if that data were available for very low cost. That is, access to

5 consumer data should make a consumer-welfare focused competition agency more permissive of these mergers if and only if this data is provided by a monopoly data-broker. The remainder of the paper is organized as follows. Section discusses the relevant literature. Section 3 examines the pre-merger and post-merger equilibria with two firms located in a linear city. Section presents the pre-merger and post-merger equilibria with three firms located in a circular city. Section 5 extends the analyses of Section 3 and Section to the case of a monopoly data broker, and Section 6 concludes. Related Literature This paper aims to contribute to the intersection of consumer privacy and antitrust policy. While we do not attempt to survey the fields, the literature on privacy has considered the possibility that past purchases allow firms to segment the market between old and new customers, facilitating some form of third-degree price discrimination (e.g., Fudenberg and Tirole, 000; Taylor, 00; Villas-Boas, 00). In particular, Thisse and Vives (1988), Shaffer and Zhang (00), Chen (006), Liu and Serfes (006), Taylor and Wagman (01), Matsumura and Matsushima (015), and Montes et al. (015) have studied models of perfect price discrimination through personalized pricing. While we build on these papers, the main difference is that none of these papers have direct implications with respect to the relationship between access to consumer data and horizontal mergers. 3 The most related papers to ours in this strand of the literature are Shaffer and Zhang (00) and Matsumura and Matsushima (015). Both consider Hotelling linear city models where firms can engage in personalized pricing. Shaffer and Zhang assume that there is a marginal cost for targeting each individual consumer, which plays an important role in 3 As previously noted, there are other potentially important dimensions that other papers have examined but are missing in our model. For instance, consumers in our model do not receive disutility from sharing their data; and we do not consider regulations that would require firms to obtain consumer consent to use their data (see Acquisti and Varian, 005; Conitzer et al., 01; Campbell et al., 015). See Acquisti et al. (016) for a recent survey of this literature. 5

6 their analysis. Matsumura and Matsushima assume that firms can engage in marginal-cost reducing activities after deciding whether to employ personalized pricing. Given our focus on merger implications, however, we abtract from endogenizing marginal costs in our model. Instead, we consider an exogenously given marginal-cost reduction following a merger and a fixed cost for obtaining consumer data, as consumer data may be packaged and brokers can sell bulk access packages rather than offer a per-profile transaction. On the antitrust side, there are surprisingly few papers that analyze horizontal mergers in the context of price discrimination, despite the fact that the 010 Horizontal Merger Guidelines highlight the relevance of price discrimination in merger analyses. Levy and Reitzes (199) analyze a two-firm merger on a Salop circle, which contains some implications of price discrimination on the entry near the merging firms location. Recently, Esteves and Vasconcelos (015) examine the implications of third-degree price discrimination (i.e., old vs. new customers) on horizontal mergers and find that the price discrimination reduces consumer welfare. Our findings are somewhat different from Esteves and Vasconcelos because we consider perfect price discrimination, which yields more nuanced results depending on market structure (duopoly vs. tripoly). The paper closest to ours in this literature is Cooper et al. (005). They analyze a three-to-two merger with personalized pricing, taking as given each firm s ability to price discriminate, and find that price discrimination based on consumer location lowers the postmerger average price. As mentioned above, our anlaysis adds to theirs by (i) showing that all firms acquiring data for price discrimination is an equilibrium; (ii) making precise the consumer welfare implications of access to data beyond the average price; and (iii) explicitly deriving the required marginal cost reduction for a merger to be approved and showing that it is identical to the marginal cost reduction that would be necessary in the no-data case. Reitzes and Levy (1995) and Rothschild et al. (000) also analyze mergers with spatial price discrimination; however, their focus is on the merger paradox or the issue of whether the proposed horizontal merger is more (or less) profitable for merging firms or non-merging firms, rather than comparing the merger implications per se when spatial price discrimination is available and unavailable. 6

7 That is, Cooper et al. show that a three-to-two merger with perfect price discrimination does not increase average prices as much as with uniform pricing given no merger efficiencies. We complement their analysis by showing that, contrary to what one would expect, this does not actually affect which mergers a consumer-surplus focused antitrust authority should approve or reject because the necessary merger efficiency to yield no loss of consumer surplus is identical with competitive access to data and with no consumer data. Moreover, we go beyond Cooper et al. by analyzing a monopoly data-broker and deriving very different and novel policy implications for this case; furthermore, it is this case that provides a justification for antitrust authorities to approve mergers that they would not have approved in the no price discrimination case. Finally, we note that the spatial models we consider here have often been proposed when interpreting empirical analyses of mergers. For instance, Gugler and Siebert (007) and Dafny (009) give theoretical justifications for their empirical findings, with three firms located on a Salop circle. However, their analyses seem partially incomplete. For instance, Gugler and Siebert assume the existence of pure-strategy interior equilibria post-merger, and Dafny considers a particular asymmetric location or assumes that merging firms shut down one of their locations post-merger. Our paper can thus provide benchmark results that are applicable to the interpretation of empirical merger analyses with spatial price discrimination by ensuring the existence of pure-strategy equilibria. 3 Linear City Model 3.1 Pre-Merger We begin with a standard linear city model represented by the unit interval, where firm A is located at 0 and firm B at 1. Both firms marginal costs of production are c, and consumers locations, α [0, 1], which specify their distances from 0, are assumed to be uniformly distributed. Consumers have unit demands with identical valuations, v, and incur 7

8 a transportation cost t per unit distance travelled. To focus on mergers between competing firms, we assume that the market is fully covered in equilibrium, which is ensured by assuming v c > 3t. In the first stage of the game, if data is available, firms independently decide whether to purchase consumer data from data brokers. Data acquisition provides access to information about individual consumers locations, α, to the acquiring firm. Initially, we consider a competitive data broker industry by assuming that the firm s purchase price for consumer data is sufficiently small taken as zero for simplicity. In the second stage of the game, the downstream firms compete in price. When data is not available, this is the well-known textbook case (Hotelling, 199). That is, lacking consumer data, firms set uniform prices, and as long as the market is covered, the marginal consumer type α is determined by v p A tα = v p B t(1 α ). Firms maximize profits π A = α (p A c) and π B = (1 α )(p B c), and equilibrium entails p A = p B = c + t. The market is fully covered as long as the utility of the marginal consumer is non-negative. When data is available, if both firms purchase data, then the two firms compete headto-head for each individual consumer. In equilibrium, the market will be covered because consumers are willing to pay at least v t, which is greater than each firm s marginal cost, c, given the running assumption v c > 3t. Competition then drives down prices as follows: p A (α) p B (α) α 0.5 c + t(1 α) c α 0.5 c c + t(α 1) For instance, for consumers located near firm A (i.e., α 0.5), firm B s price will be driven down to marginal cost, and firm A will sell at the price which makes consumers indifferent between the two firms, that is, v p A tα = v c t(1 α), which yields p A above (and similarly for p B ). In comparison to the outcome with no consumer data, all consumers are better off with individualized price competition, and both firms are made worse off. 8

9 Of course, this assumes that if data is available (for a low price), both firms will purchase it in equilibrium. In the following lemma, we show that this is the case. Note that both firms have lower profits when they have data than when neither does. This is consistent with the previous literature on spatial price discrimination in that there is a Prisoner s Dilemma (e.g., Thisse and Vives, 1988). In equilibrium, firms choose individualized pricing as long as the cost of acquiring data is sufficiently small, even though neither firm acquiring data would have been jointly optimal for the downstream firms. Lemma 1 In the unique equilibrium, both firms acquire consumer data and offer individualized pricing if consumer data is available for a sufficiently low price. Proof. See Appendix. 3. Post-Merger Consider now the same setup as above except that the two firms have merged, where the merged firm s marginal cost of production is c post-merger, with c c to allow for the possibility of efficiency gains from the merger. We assume that the merging firms product locations (A and B) remain unchanged post-merger but we allow for the possibility of shutting down a location. 5 Specifically, the game unfolds as follows: in the first stage, the merged firm (monopolist) decides whether to acquire customer data (at a sufficiently small fixed cost) to price discriminate. In the second stage, the monopolist sets the prices for active products. To be consistent with the pre-merger case, we maintain the assumption v c > 3t, which further implies v c > 3t. 5 By continuity of payoff functions, all our results continue to hold qualitatively, which we numerically verified, if both pre- and post-merger locations were to become slightly asymmetric; however, if the firms locations are sufficiently asymmetric, then there may not exist a pure-strategy equilibrium. Hence, we limit our attention to the symmetric locations for expositional simplicity. 9

10 When data is not available, if the merged firm does not shut down any location and the market is covered in equilibrium, then the marginal consumer α is indifferent between product A and product B; that is, v p A tα = v p B t(1 α ), which is the same as that of pre-merger. The difference from the pre-merger case is that the merged firm maximizes joint profits which results in higher prices. Now suppose data is available. In this case, the merged firm will obtain consumer data and offer individualized prices p A (α) and p B (α) for each product because it can extract the full consumer surplus by setting p A (α) = v tα and p B (α) > v t(1 α) to those consumers located in α [0, 1]; and p B(α) = v t(1 α) and p A (α) > v tα to those consumers located in α [ 1, 1].6 Proposition 1 In a merger to monopoly in which the market is fully covered, the availability of consumer data at sufficiently low costs increases the consumer surplus loss from merging relative to the case in which there is no consumer data. Proof. See Appendix. The intuition for this result is two-fold. First, data access facilitates individualized price competition under a duopoly, which pushes down pre-merger profits and provides more consumer surplus. Second, without competition, data access enables the monopolist to extract consumer surplus, increasing post-merger profits and eliminating consumer surplus. This finding echoes the concerns of privacy advocates: Because consumer surplus falls more with the merger when merging firms have access to consumer data, the required efficiencies have to be greater in order to approve such a merger than if firms do not have access to data. Since access to data enables firms to extract all the consumer surplus, there are no efficiencies that can make the merger increase consumer surplus. 6 There is a continuum of equilibria where the price of a product is set sufficiently high for those consumers who are not supposed to purchase that product; however, the equilibrium description, apart from the offthe-equilibrium prices, is essentially unique. 10

11 However, any merger to monopoly is likely to be blocked by regulators regardless of access to consumer data, making the above merger scenarios of limited practical importance for merger policy. Once we move to a market with more than two firms, we find that the effects of access to data drastically change the welfare implications of a merger, because access to data intensifies the remaining competition. Circular City Model.1 Pre-Merger For our three-firm case, we consider a standard circular city model. Let A, B, and C be three firms located equidistant on a three-unit circular city. That is, we assume that there is a unit measure of consumers uniformly distributed between any two firms locations. Let α A [0, 1] denote a consumer s location counter-clockwise from firm A s location, α B [0, 1] from firm B s location, and α C [0, 1] from firm C s location. 7 The remainder of the game remains unchanged: consumers incur a transportation cost t per unit distance, and the market is assumed to be covered in equilibrium, which is satisfied using the same parameter restriction as before, v c > 3t. In the pre-merger analysis that follows, we restrict attention to interior equilibria, without loss of generality, in which the marginal consumer types are located on the market segment between a given pair of firms. We begin with the textbook case, where data is not available. The following results are well known (Salop, 1979): when firms set uniform prices, the marginal consumer types are α A = 1 + p B p A t, αb = 1 + p C p B, and α t C = 1 + p A p C, and firm A maximizes π t A = α A (p A c) + (1 α C )(p A c) by choosing p A, and similarly for firms B and C. When data is available, it is intuitive that for any pair of firms, the equilibrium pricing and outcome in each segment of the market would look the same as in the linear city model 7 Most often, the circular city model assumes that the entire circle is unit length. We assume a three-unit circle because it allows us to use our results from the linear city model in a straightforward manner. Notice that the circle length is a free parameter given the transportation cost parameter t. 11

12 analyzed in Section 3.1 when all three firms use consumer data to set individualized prices. What is less clear is whether symmetric access to the data would be an equilibrium. To give some intuition on asymmetric data access cases, Figure 1(a) shows the equilibrium when only firm B has access to consumer data. In the region where firm B competes with A, the change from the linear city model in Section 3.1 is that firm B s market segment expands from α A [ 1, 1] to α A [ 1, 1]. The reason is that firm A has another market between its 6 own location and firm C s location, and this market is effectively shielded from firm B s competition in equilibrium. Since the other firm (firm C) does not offer individualized prices, firm A need not price as aggressively as it did in the linear city model. Figure 1(b) depicts the equilibrium when both firms A and B have access to consumer data. Compared to the previous case where only firm B had access, the market size of A (or B) decreases in competition with firm C. This is because C no longer faces another market in which its rival sets a uniform price. Hence, firm C prices more aggressively and thus gains more market share from A and B. Lemma In the unique equilibrium, all three firms purchase data and engage in individualized price competition if consumer data is available for a sufficiently low price. Proof. See Appendix.. Post-Merger We now consider a three-to-two firm merger. Suppose that firms A and B have merged and maintain their previous locations (this is in fact satisfied in equilibrium since the merged firm has no incentive to shut down a location). Thus, we have two firms in the market, firm AB and firm C, where firm AB can coordinate the pricing of its two products A and B. Notice that the consumer segment α A [0, 1] is not a captive market of the merged firm because consumers in this segment may yet choose to buy from firm C. Firm AB s marginal cost of production is c < c, while the nonmerging firm s marginal cost remains at c. 1

13 Suppose data is not available. Under uniform pricing, the merged firm AB has an incentive to raise prices to extract additional surplus from consumers located between A and B, although doing so trades off a reduction in its market share vis-à-vis firm C. That is, firm C will capture a larger share of the competitive market and can subsequently also increase its price. One important technical difference from the linear city case is that with more than two firms in the circular city model, there is a discontinuity in the firm s demand function, to which Salop (1979) originally referred as the supercompetitive region. What happens in this region is that a firm undercuts the price of the rival by the transportation costs associated with the distance between them, hence capturing the rival s whole market. While Salop showed that in a symmetric equilibrium (i.e., without a merger), the supercompetitive behavior is not profitable, it turns out that with mergers the non-merging firm s supercompetitive behavior is in fact profitable given the locations, unless there is a sufficient reduction in the marginal cost of the merged firm. The equilibrium is characterized as follows where we denote p AB p A = p B and c c c. Lemma 3 If firms AB and C set uniform prices, an interior equilibrium exists if and only if c (3 3 5)t 0.196t, where for v c 13t 6 equilibrium prices are p AB = 5t+c +c 3, p C = t+c +c; marginal types are α 3 A = 1, α B = 1 α C = 1 t c ; profits are π 6t AB = (5t+ c), 9t π C = (t c) 9t ; and consumer surplus is 3v + c (13c+1c )t 193t 36t. Proof. See Appendix. It follows from this lemma that as long as v is sufficiently high, (i) firm AB sets a higher price than firm C, and (ii) the combined market share of AB shrinks relative to its premerger market share if and only if its marginal cost reduction ( c) is less than the unit transportation cost t. However, if the marginal cost reduction is larger than t, then AB s combined market share increases relative to its pre-merger level, and AB captures the entire market (i.e., C s market share is zero) if c t. 13

14 Let us now suppose that data is available and both AB and C obtain access to consumer data. Since firms compete for individual consumers, the market between A and C is unaffected by the presence of product B. Similar to the duopoly competition described in Section 3.1, but with asymmetric marginal costs, AB sets individualized prices p A (α C) = c + t(α C 1) for α C [αc, 1] and p A (α C) = c for α C [0, αc ]; and similarly C sets p C (α C) = c + t(1 α C ) for α C [0, αc ] and p C (α C) = c for α C [αc, 1] in the market between A and C. The marginal consumer type α C is indifferent between products A and C, that is, v c t(1 α C ) = v c tα C, from which it follows that α C = 1 c c t < 1 since c > c. Thus, the merged firms market share increases due to the marginal cost reduction relative to the pre-merger equilibrium. If c c t, then AB captures the entire market, leaving C a market share of zero. On the other hand, firm C s marginal cost pricing constrains AB s individualized prices in the market between A and B. Specifically, p A (α A) satisfies v p A (α A) tα A = v c t(α A +1), so p A (α A) = c + t for α A [0, 1]; and similarly p B (α A) = c + t for α A [ 1, 1]. It is easy to verify that profits are πab = ( 3t+c c )(t + c c ) and π t C = (t c+c ) ; and consumer surplus is t 3v c c (c c ) t 11t in this case. Lemma In the unique equilibrium, both firms AB and C acquire data and offer individualized pricing if the cost of doing so is sufficiently low. Proof. See Appendix. In the proof of Lemma, we derive firm profits if either firm AB alone or firm C alone acquires consumer data. We find that for firm C, acquiring data is a dominant strategy, and that if C has data, AB s profit increases if it also has data. The intuition for this is that if AB has data, it can encroach on C s market share without sacrificing its own profits from the consumers close to A and B. Without data, firm C can only lower its price to limit its 1

15 losses, thereby reducing its profits. If firm C acquires data as well, however, it can charge more to its nearby consumers and maintain its market share among the consumers that are closer to the midpoint between its own location and A s or B s. If AB does not have data, then by acquiring data C can take advantage of AB s incentive to keep prices high to the consumers in between A and B it can do so by charging higher prices to its nearby consumers and stealing market share from AB by undercutting the merged firm for consumers closer to A or B in the segments between C and A or B. Once AB recognizes that C will acquire data, it can increase its profit by acquiring data as well to limit C s ability to steal its market share without sacrificing the ability to charge consumers between A and B higher prices. Comparing the above post-merger outcome to the pre-merger equilibrium, we can summarize the effect of consumer data (hence price discrimination) on the consumer welfare consequences of the three-to-two merger as follows: Proposition Assume c 0.196t, so that an interior equilibrium exists. Without consumer data, a three-to-two merger in the three firm market reduces consumer surplus by CS nodata = (t c)( c+9t). With consumer data, a three-to-two merger reduces consumer 18t surplus by CS Data = (t c) t. Figure depicts how CS nodata and CS Data change as a function of c. Specifically, the rate of the decrease in CS nodata ( CS Data ) increases (decreases) as c t because d CS nodata d c = 1 9t < 0 while d CS Data d c = 1 t > 0, and eventually CSnoData = CS Data = 0 when c = t. Hence, Proposition establishes that, contrary to the merger to monopoly case, the decrease in consumer surplus in a three-to-two merger is smaller when firms have access to data than when they do not. The intuitive reason for this is that when firms engage in individualized pricing, the remaining competitors can provide a stronger constraint on the merged firm, especially for 15

16 consumers closer to the merged firm s locations. In the circular city model, a merger reduces consumer surplus only because it makes some consumers second choice more distant. With individualized pricing, this is the only effect that leads to reduced consumer surplus. With uniform pricing, however, there is an additional strategic effect due to the fact that each firm assumes that the other firm will charge higher prices after a merger. This effect is absent with individualized pricing, making the merger less anti-competitive. On the other hand, the above result shows that with a competitive data broker industry the differences between the data and the no-data case converge to zero exactly at the same point where the efficiencies from the merger become sufficient to eliminate any consumer surplus loss from the merger. So, if the legal standard is that the merger may not reduce consumer surplus at all, then our results show that whether or not firms have access to consumer data should not affect merger analysis at all in a world of perfect information. 5 Monopoly Data Broker Importantly, we have assumed thus far that the upstream data market is competitive, so that the downstream firms can buy consumer data at a zero (or sufficiently small) cost. In this section, we show how our results change when a monopoly data broker can extract profits from the downstream firms, whereby the implications for merger policy can vary across pertinent data markets. When the upstream data broker can sell consumer data to maximize its profit, the timing and the nature of the sales become relevant. Following the literature on exclusionary contracting (e.g., Rasmusen et al., 1991; Segal and Whinston, 000), we consider both the cases of simultaneous and sequential offers by the data broker. Specifically, we assume that in the first stage the data broker can either make nonexclusive offers to downstream firms simultaneously or sequentially, or it can make sequential exclusive offers that will allow only 16

17 one firm to access the data. 8 We show below that if the data broker offers a non-exclusive contract, then it has an incentive to sell to all downstream firms. This means that the downstream firms equilibrium behavior (and therefore the resultant consumer welfare change) remains the same. However, the data broker has a strict incentive to sell an exclusive contract to one of the downstream firms, which changes not only the equilibrium behavior of the downstream firms but also the consumer welfare implications of horizontal mergers. 5.1 Linear City Model Suppose, pre-merger, the monopoly data broker makes nonexclusive offers to firm A and firm B. Formally, let P i, i {A, B}, denote the amount of money each downstream firm has to pay the upstream monopolist in order to have access to the consumer data. We allow the upstream broker to price discriminate (P A P B ) wherein the nondiscriminatory access price is a special case. The analysis starts from the duopoly payoff matrix (see the proof of Lemma 1), not accounting for the cost of data: Firm B No Data Data Firm A No Data t/, t/ t/8, 9t/16 Data 9t/16, t/8 t/, t/ It is straightforward that if P i > t 8 then not purchasing the data is the dominant strategy for both firms. Thus, the most the data broker can extract when it offers nonexclusive contracts is capped at t. The question that remains is whether P A = P B = t 8 can be sustained as a subgame perfect equilibrium (we assume that as a tie-breaking rule whenever a downstream firm is indifferent between purchasing and not purchasing data it purchases data). The answer is a qualified yes because with simultaneous offers of P A = P B = t 8, there 8 We do not consider simultaneous exclusive offers because simultaneous acceptance of exclusive offers that only one downstream can accept does not make much sense. 17

18 are two pure-strategy equilibria wherein both firms either purchase or do not purchase the data. One might think that it is more reasonable in this case that the two downstream firms would coordinate on the uniform pricing equilibrium which yields higher profits. If we apply this refinement criterion, then it can be shown that the most the data broker can extract is reduced to 3t 16 when it offers t 16 to one firm and t 16 to the other. Price discrimination is the dominant strategy for the firm that is offered a lower price, which induces the other firm to price discriminate as well. In a sequential game, however, P A = P B = t 8 is the unique equilibrium because the threat of offering the second firm the data for t/16 if the first firm refused would induce the first firm to accept t/8. On the other hand, if the monopolist offers exclusive contracts pre-merger, then it can exploit the fact that with asymmetric data access the firm without data performs significantly worse than if it had access to the data as well. Without loss, suppose the monopoly broker first approaches A, and if A rejects the offer it will then turn to B for signing an exclusive contract. It can be easily shown that the subgame perfect equilibrium entails that A accepts the offer and pays the broker 7t 16 (because A knows that if it rejects, then the broker will offer the data to B for t/16 and B will accept). Thus, the upstream broker will choose to contract exclusively in equilibrium. Lemma 5 In the pre-merger (duopoly) equilibrium, the data broker sells an exclusive contract to one of the downstream firms for 7t, and consumer surplus is v c t. In the 16 post-merger (monopoly) equilibrium, the data broker sells the data for t, and consumer sur- plus is zero. By comparing the consumer surplus pre- and post-merger with and without an exclusive contract, it follows that the merger between A and B reduces consumer surplus less with an exclusive contract than it had previously without exclusive contracting because consumer surplus is lower in the pre-merger case with a monopoly data broker offering an exclusive 18

19 contract. However, the consumer surplus reduction with an exclusive access to data (v c t) is still larger than that with no data (v c 3t ). Thus, the qualitative conclusion from Section 3 remains unchanged there is a greater reduction in consumer surplus from a merger to monopoly with access to data than without. 5. Circular City Model First, consider the pre-merger tripoly equilibrium. The analysis when the data broker makes nonexclusive offers P i, i {A, B, C}, starts from the payoff matrix (see the proof of Lemma ), not accounting for the cost of data: B B No Data Data No Data Data A No Data t, t, t t, 5t, t t Data, t, t 3t, 3t, t C plays No Data A No Data t, t, 5t t Data, t, 3t C plays Data t, 3t, 3t t, t, t Here, the most the data broker can extract is by offering to sell the data to all three firms at P = t. To see this, suppose P i = t. Then purchasing data is a dominant strategy for each downstream firm. If P > t, then any one firm has a profitable deviation from the proposed equilibrium, whether the offers are sequential or simultaneous. The equilibrium (of either a sequential or a simultaneous offer game) must either have the broker sell to only one or two firms. If the broker sells to only one firm, then the price can be at most 7t 18 because otherwise the downstream firm is better off by not purchasing the data. Similarly, if P > t and the broker sells to two firms, then the most each firm is willing to pay is 11t. Each of 36 these two cases yields a lower profit for the data broker than if it had sold to all three firms at P = t 3t. Thus, the upstream monopolist generates nonexclusive contracts. in equilibrium when it can only offer Now, consider exclusive offers. Without loss, suppose the data broker makes an exclusive 19

20 offer to A, B, and C in that order, who either accept or reject the offer. Given the finite horizon, it is straightforward to see that the subgame perfect equilibrium entails A accepting the offer immediately and the broker can charge up to 17t. To see this, notice that if A and 18 B were to reject, then the broker would get C to accept for 7t. Thus, if A were to reject the 18 offer, its continuation value is only t 5t. If it accepts, it obtains P 9 18 A. Since 17t > 3t, the 18 monopolist data broker will choose to sell an exclusive contract to one of the downstream firms pre-merger. Second, consider the post-merger duopoly equilibrium. The analysis starts from the payoff matrix (see the proof of Lemma ), not accounting for the cost of data: Firm C Firm AB No Data (5t+c c ) No Data, (t+c c) 9t 9t Data (7t+c c )(3t+c c ), (t c+c ) 8t t Data (t+c c ), (t c+c ) t 8t ( 3t+c c )(t + c c ), (t c+c ) t t Here, the payoffs are asymmetric between firm AB and firm C and they also depend on the size of the marginal cost reduction (c c ). We show that when the data broker sells nonexclusive contracts it sells to both firms at different prices. However, the data broker can do better by selling an exclusive contract to AB (rather than C). The following lemma establishes the equilibrium characterization. Lemma 6 In the pre-merger (tripoly) equilibrium, the data broker sells an exclusive contract to one of the downstream firms for 17t 18 13t, and consumer surplus is 3(v c). In the post- merger (duopoly) equilibrium, the data broker sells an exclusive contract to merged firm AB for 13t +(c c )(t (c c )), and consumer surplus is 3v 3(c+c +5t) for c c [0, t]. 8t Proof. See Appendix. Comparing the post-merger equilibrium where AB has an exclusive access to the data with the pre-merger equilibrium where one of the downstream firms has an exclusive access 0

21 to the data, we can state the effect of consumer data (hence price discrimination) on a horizontal merger. In particular, by comparing the change in consumer surplus due to a merger with a competitive data broker market (in Section ) to that with a monopoly data broker, we can examine the robustness of the merger policy implication to the presence of market power in the upstream data market. Proposition 3 The reduction in consumer surplus as a result of the three-to-two merger is CS Comp = (t (c c )) with a competitive data market while it is CS Mono = t 3(c c ) t with a monopoly data broker and exclusive contracts. The merger reduces consumer surplus less in the latter (i.e., CS Comp > CS Mono ). Furthermore, the merger increases consumer surplus if the marginal cost reduction exceeds t 3 with a monopoly data broker, while the required marginal cost reduction must be at least t if data is supplied competitively. Proposition 3 establishes that, consistent with the previous result (in a competitive data broker market), the decrease in consumer surplus in a three-to-two merger is smaller when firms have access to data than when they do not. Additionally, the merger causes an even smaller reduction in consumer surplus when the monopoly data broker can offer exclusive contracts to the downstream firms. The reason for this is that while consumer surplus is lower both pre- and post-merger with exclusive contracts (because there is less intense competition when only one firm has access to data), this effect is smaller post-merger for two reasons: First, post-merger half the firms have access to consumer data, as opposed to only onethird pre-merger. Second, the fact that the merged firm obtains the data is better for consumers than the third firm having the data. This is because the merged firm is the one that would otherwise have a greatly diminished incentive to reduce its price to attract C s customers, since that would sacrifice its high profits from the customers between A and B. Because it has access to data, it can continue to compete very aggressively for C s customers, forcing C to charge a relatively low uniform price. 1

22 This result gives a rigorous justification for treating a merger of downstream firms less harshly when there is upstream market power for access to consumer data. Furthermore, this result has actual policy implications for merger review given the lower threshold for efficiencies ( c) necessary to make the merger consumer-surplus enhancing; that is, it is possible that a three-to-two merger could improve consumer surplus when there is a monopoly data broker even if such a merger would reduce consumer surplus either without access to data or with competitive access to data. 6 Conclusion A common refrain among consumer advocacy groups is that mergers can be especially harmful to consumers when merging firms have access to detailed consumer data profiles. In this paper, we have shown that this argument has validity in a duopoly market; however, this argument is not robust to the presence of non-merging firms, such as in the tripoly case we have analyzed. This is because the non-merging firm can exert pricing pressures on the merged entity regardless of whether the upstream data broker sells nonexclusive or exclusive access to the consumer data. Moreover, when there is a monopoly data-broker that can offer exclusive access to data, the required efficiencies for a three-to-two merger to not reduce consumer surplus are substantially less than in either the uniform pricing case (no data available) or the competitive data-broker case (all firms have data). Both of these latter cases require the same marginal cost reduction for a merger to not reduce consumer surplus. In contrast, in the monopoly data broker case, the required marginal cost reduction is only one third as much. This suggests that there are important merger policy implications for how mergers are treated in the presence of consumer data when data brokers have substantial market power. Given the importance of the issue, we nonetheless caution that our findings do not imply that mergers should receive less scrutiny or generate no privacy concerns when firms have

23 access to detailed consumer data. Our study has shown that antitrust authorities should pay attention to the upstream data market structure when analyzing the competitive effects of mergers in downstream markets that use this consumer data. However, mergers that facilitate concentration of consumer data may have other welfare implications that we did not consider in this paper. 9 Appendix Proof of Lemma 1. Suppose only one of the firms (say firm B) acquires consumer data while the other does not. Firm B can offer individualized prices p B (α) while firm A can only set a uniform price p A. Because firm B is willing to offer prices as low as its marginal cost in order to attract individual consumers, the marginal consumer type α is determined by v p A tα = v c t(1 α ). That is, α = 1 + c p A. Then, firm A maximizes its profit t π A = α (p A c) by choosing p A, and firm B, where feasible, sets individualized prices p B (α) to just undercut A. To be precise, it follows from firm A s first-order condition that p A = c+ t. Substituting in for p A yields α = 1. Given p A, firm B sets individualized prices p B (α) for those with α 1 by equating consumers utilities from purchasing the two products (indifferent consumers are assumed to purchase from B); that is, v p A tα = v p B(α) t(1 α), which yields p B (α) = p A + t(α 1) = c + t(α 1) for α 1; and p B (α) = c for α 1. Thus, if only firm B sets individualized prices, profits are given as πa = t and 8 π B = 9t, and consumer 16 surplus is v c t. On the other hand, it can be readily verified that firms profits are π A = π B = t, and consumer surplus is v c 5t, when data is not available; and that profits are π A = π B = t, and consumer surplus is v c 3t, if both firms set individualized prices. It can be easily 9 For instance, concentration of consumer data makes it more important to safeguard individuals privacy from breaches while it can also enable product improvements and consumer targeting (see, e.g., Wickelgren, 015). 3

24 verified that the unique equilibrium of the payoff matrix constructed from these quantities is for both firms to acquire consumer data. Proof of Proposition 1. First, if the merged firm AB sets individualized prices, then equilibrium prices are given as in the text and the marginal type is α = 1. With both products being offered, the monopoly profit equals total surplus, which is given by πm = 1 0 [v tα c ]dα = v c t, and consumer surplus is 0. On the other hand, the market is fully covered even with one product, say, A because it is profitable to sell to the most remotely located consumer (α = 1), i.e., v t c > 0. The monopoly profit would then be π M = 1 0 [v tα c ]dα = v c t, which is smaller than v c t. Second, if the merged firm AB sets uniform prices, then there are a few things to consider. Suppose that the market is not fully covered post merger, so that there are two captive markets served by the monopolist with no overlap. Then the monopolist maximizes π M = γ A (p A c ) + (1 γ B )(p B c ), where γ A and γ B are measured from 0 and determined by v p A tγa = 0 and v p B t(1 γb ) = 0, respectively. Given separability and concavity, it follows that p A = p B = v+c. By substituting in p A for γ A (and similarly p B for 1 γ B ), we obtain γa = 1 γ B = v c. However, given our assumption v c > 3t, t γ A = v c > 3 t which contradicts the assumption that market is not fully covered. If the market is covered, then the marginal consumer type must be α = 1. To see this, suppose α (0, 1) is the marginal type in equilibrium. Then the optimal monopoly prices are determined by making the marginal consumer s utility zero for both products, that is, v p A tα = 0 and v p B t(1 α ) = 0, which in turn yields p A = v tα and p B = v t(1 α ). Thus, the monopolist s profit given α is π M (α ) = α (v tα c )+(1 α )(v t(1 α ) c ) which is concave in α and attains its maximum value at α = 1. Since p A and p B effectively determine α, any choice of prices for which α 1 is suboptimal. Because in a symmetric equilibrium p A = p B p M, which implies π M = p M c, the monopolist s optimal price p M = v t is pinned down by driving the marginal consumer s

25 utility to zero, that is, v p M t = 0. Profits and consumer suplus are π M = 1 0 [v t c ]dα = v c t, and CS = 1 0 [v v + t tα]dα = t. Then Lemma 1 establishes the claim in the proposition. To see that the merged firm has no incentive to shut down a location, suppose that the monopolist drops product B and only sells product A. Then there are two sub-cases: i) the market is covered with product A. In this case, the optimal price drives down the marginal consumer s utility to zero, i.e., the utility of the consumer who is located at α = 1 satisfies U(1) = v p A t = 0. Thus, p A = v t, and the monopoly profit is π M = v c t. ii) the market may not be fully covered with only product A. Then, the marginal consumer type is determined by v p A α t = 0, hence, α = v p A t. Given α, the monopolist maximizes π M = α (p A c ), and it follows that p A = v+c, which in turn implies α = v c t and πm = (v c ). Because α < 1, this requires t > v c. Thus, the monopoly profit is t π M = v c t for v c t and π M = (v c ) t for t > v c > 3t. Notice that v c t is always smaller than the merged firm s profit, π M = v c t, when it offers both products. Further, (v c ) t > v c t if and only if v c < ( )t or v c > ( + )t. However, the first range, v c < ( )t, is ruled out by our assumption v c > 3t, and the second range, v c > ( + )t, violates the parameter restriction for partial market coverage, i.e., v c < t, hence, irrelevant. Proof of Lemma. If firms set uniform prices, the marginal types are determined by αa = 1 + p B p A, (1) t αb = 1 + p C p B, () t αc = 1 + p A p C. (3) t It is straightforward to verify that the equilibrium prices are p A = p B = p C = c + t; the marginal types are α A = α B = α C = 1 ; profits are π A = π B = π C = t; and consumer surplus 5