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 Wickelgren Abstract We examine the influence of firms ability to target individualized pricing on the welfare consequences of horizontal mergers in location models with two and three firms, where each firm may have access to data profiles that identify consumers willingness to pay. We show that in a three-to-two merger the post-merger loss in consumer surplus can be substantially lower when firms can price discriminate based on individual preferences compared to when they cannot. In contrast, this reduction is absent in a two-to-one merger, leading to substantial anti-competitive effects of the merger. Therefore, the merger effects of access to consumer data depend on market structure. Keywords: Price discrimination, consumer privacy, data profiles, horizontal merger 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 1 Introduction Improvements in information technology have brought growing concerns about privacy intrusion in commercial marketplaces to the forefront of public debate. Nearly all US consumers now use online media to shop (BIA/Kelsey, 013), more than 60 percent of US consumers own smartphones (Deloitte, 013), and over two thirds of online adults in the US are now 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. The extent of such consumer profiling is illustrated by this quote: Of the nine data brokers, 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. 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. (FTC, 014) In response to growing privacy concerns, some policy commentators and consumer groups have urged the FTC to deal with privacy issues that arise in the context of mergers. Specifically, privacy advocates are concerned with the concentration of consumer data over and beyond the concentration of market power in mergers. 1 The aim of this paper is to provide 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 014. 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, forthcoming).

3 a theoretical analysis of the effects of consumer data on horizontal mergers, where firms compete in differentiated product markets such as Hotelling s linear city (199) and Salop s circular city (1979) models. With the proliferation of data brokers, downstream firms firms that may directly sell products and services to consumers can relatively easily access consumer data. It is the merger of direct-to-consumer downstream firms that are the focus of our analysis. To our knowledge, there are few formal economic analyses of merger incentives that take into account spillovers from the data-broker industry. It is the purpose of this paper to examine merger incentives and consumer welfare when firms have access to consumer data, and to provide contrast with the standard case, where relatively little data is available to firms. More specifically, we assume that the gain from having access to detailed consumer profiles is in facilitating the targeting of individualized pricing. This is largely because we seek to focus on the pricing implications of mergers that have a first-order effect on merger reviews; however, we note that mergers that facilitate more detailed consumer data may also have other welfare implications that we do not consider. For instance, amassing consumer data might enable product improvements or better product targeting (Wickelgren, 015). 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. We assume that firms can choose to collect (or purchase from data brokers at a sufficiently low cost) consumer data which reveals the location of individual consumers. Although the extent of business practices on individualized pricing has often been neglected in merger reviews, our analysis can be thought of as suggesting the upper bound on the effects of such practices on 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 monopoly are rarely approved even in the absence of individualized pricing, our more important result concerns the effect of individualized pricing on mergers in markets in which there is more 3

4 than one firm remaining after a merger. In these cases, we find that access to consumer data among all firms in the market may substantially lower the anticompetitive effects of a merger. 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. The remainder of the paper is organized as follows. Section discusses the relevant literature. Section 3 examines the pre-merger and post-merger equilibrium with two firms located at the edges of a linear city. Section 4 presents the pre-merger and post-merger equilibrium with three firms located equidistant in a circular city, and Section 5 concludes. Related Literature This paper aims to contribute to the intersection of consumer privacy and antitrust analysis. 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, 004; Villas-Boas, 004). Further, Shaffer and Zhang (00), Chen (006), Liu and Serfes (006), Taylor and Wagman (014), and Montes et al. (015) have studied models of perfect price discrimination through personalized pricing. While we build on these papers and they are complementary in nature, the difference is that none of these papers have direct implications with respect to the relationship between consumer data and mergers. The closest 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 There are potentially important factors that others have considered but are missing in our model. For instance, our model is static and does not endogenize consumer data acquisition; and we do not allow consumers to have access to anonymyzing technologies (Acquisti and Varian, 005; Conitzer et al., 01). 4

5 cost for targeting each consumer, which plays an important role in their analysis and findings. Matsumura and Matsushima assume that firms engage in marginal-cost reducing activities after deciding whether to employ personalized pricing. In order to focus on merger implications, both elements are absent in our model. Instead, we consider a potential marginal cost reduction following the merger. 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. 3 In an earlier work, Levy and Reitzes (199) consider multiple symmetric firms on a Salop circle and investigate a two-firm merger. They argue that price discrimination can deter or delay entry near the merging firms. Recently, Esteves and Vasconcelos (015) examine the implications of oligopolistic price discrimination on horizontal mergers. Specifically, building on the market segmentation literature mentioned above, they consider price discrimination based on purchase histories (e.g., old and new customers) and conclude that mergers with this form of price discrimination lead to an increase in profits at the expense of consumer welfare. Our findings are different from Esteves and Vasconcelos because we consider perfect price discrimination in location models, which yields more nuanced results that depend on the market structure (duopoly vs. tripoly). The spatial models we consider here have often been applied 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 are partially incomplete. 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 close one of their locations post merger. Our paper can thus provide some benchmark results of mergers in a spatial model with price discrimination. 3 Reitzes and Levy (1995) and Rothschild et al. (000) analyze mergers with spatial price discrimination; however, they consider models in which firms pay delivery costs that depend on the distance from a consumer s location while in our model consumers pay transportation costs that depend on the distance. 5

6 3 Linear City Model 3.1 Pre-Merger Analysis Consider 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 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 v c > 3t. In the first stage, if data is available, firms decide whether to purchase consumer data from data brokers. Data acquisition provides access to individualized consumer profiles, revealing consumers locations, denoted by α, to the acquiring firm. Given the competitive nature of the data broker industry, we assume that a firm s purchase price for consumer data is small taken as zero for simplicity. We emphasize that there is a range of fixed costs for acquiring data that are consistent with our equilibrium characterizations, because fixed costs do not affect firms pricing strategies. In the second stage, the firms compete in price No data available This is the textbook case. When firms have no information about consumers types, they set uniform prices to consumers. If the market is covered, the marginal consumer of type α is indifferent between purchasing from firm A and firm B if and only if v p A tα = v p B t(1 α ). Thus, α = 1 + p B p A. (1) t Taking α into account, firms maximize profits π A = α (p A c) and π B = (1 α )(p B c) by optimally setting p A and p B, respectively. As is well known in the literature, the following holds in equilibrium. 6

7 Lemma 1 (Hotelling, 199) Equilibrium prices are uniform and satisfy p A = p B = c + t. The marginal type is α = 1, profits are π A = π B = t 5t, and consumer surplus is v c. 4 Notice that for the market to be covered in equilibrium, the utility of the marginal consumer must be non-negative, which is satisfied when U(α = 1 ) = v c 3t assumed above. purchases from the nearest firm. > 0, as Moreover, the equilibrium outcome is efficient because every consumer 3.1. Data is available If both firms purchase data, and consumer types become common knowledge, then the two firms compete head-to-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 after some rearranging yields p A ; and similarly for p B. Lemma If firms set individualized prices, equilibrium prices are as specified above. The marginal type is α = 1, profits are π A = π B = t 3t, and consumer surplus is v c. 4 4 In comparison to the outcome with no consumer data, all consumers are better off with individualized price competition (to be precise, consumers located at the end-points, 0 and 7

8 1, are offered the same prices with and without firm access to data, and are thus indifferent, whereas all other consumers are strictly better off), which is illustrated in Figure 1. U( ) v-c-t/ v-c-t v-c-3t/ 1/ Figure 1: Consumer utilities pre-merger: with no data (solid, blue), with data (dotted, red), only B has data (dash-dot, green). The V-shaped solid line represents consumer utilities with uniform pricing while the inverse V-shaped dotted line represents utilities with individualized pricing. Given the area between the two curves, it is straightforward to see that individualized price competition transfers a surplus of t from firms to consumers (while total surplus remains unchanged). Thus, both firms are made worse off when competing with individualized price offers. Of course, this assumes that if data is available (for a low price) that both firms will use it. To show that this is the case, we derive the pricing equilibrium in the appendix when only one of the firms acquires consumer data. In this equilibrium, the firm with data can offer prices as low as its marginal cost to attract consumers closer to its rival while not sacrificing profits from the consumers closer to it. This enables it to expand its market share and to force its rival to charge lower prices. As a result, the firm with data has higher profits than in the no-data case, while the firm without data has lower profits than if both firms had data. This leads to the following result. 8

9 Lemma 3 If consumer data is available for a low enough price, in equilibrium both firms acquire consumer data and offer individualized pricing. Proof. See Appendix. Notice, however, that both firms have lower profits when both have data than when neither does. This is consistent with the previous literature on spatial price discrimination (e.g., Thisse and Vives, 1988); there is a Prisoner s Dilemma, and in equilibrium both firms choose individualized pricing as long as the fixed cost of acquiring data is sufficiently small, even though neither firm acquiring data is jointly optimal for the firms. Figure 1 also depicts consumer utilities under asymmetric access to consumer data. Specifically, consumer utilities when firm B employs individualized pricing are represented by the downward-sloping dash-dot line. Hence, the nearer a consumer is to B s location, the worse off the consumer is in equilibrium. Firm B captures more surplus and a larger customer base than firm A, and there is an efficiency loss since consumers in [ 1, 1] inefficiently 4 purchase from firm B. 3. Post-Merger Analysis 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, c c, to allow for the possibility of efficiencies from the merger. We assume that the merging firms product locations remain unchanged post merger (at least in the short run). 4 On the other hand, we allow for the merging firms to drop one firm s product, but this never happens in equilibrium. The game unfolds as follows: in the first stage, the merged firm (monopolist) decides whether to drop one of the products (i.e., the product of firm A or firm B) as well as whether to acquire customer data to price discriminate (at a sufficiently small fixed cost). 4 The merged firm can potentially re-position its locations, which means changing existing products and/or introducing new products; however, such actions may involve fixed development costs and take some time. For benchmark comparisons, we hold fixed the location of each product. 9

10 In the second stage, the firm sets prices. To be consistent with the above, we maintain the assumption v c > 3t, which further implies v c > 3t No data available First, suppose that the merged firm continues to sell both A s and B s products. Since there is no consumer data, the firm sets uniform prices. If the market is covered in equilibrium, the marginal consumer α is indifferent between purchasing product A and product B if and only if v p A tα = v p B t(1 α ), which yields α = 1 + p B p A. () t The difference from the pre-merger case is that the merged entity maximizes overall profits π M = α (p A c ) + (1 α )(p B c ) by setting p A and p B. Would the merged firm have an incentive to drop one of the products? Intuitively, since marginal costs are the same, offering only one product would necessitate a price reduction in order to attract those consumers who are located closer to the removed product. On the other hand, if the monopolist drops one product, then it can lessen market cannibalization. We summarize our findings in the following lemma. Lemma 4 If the merged firm sets uniform prices, equilibrium prices are p M = v t and the marginal type is α = 1. Profit is π M = v c t, consumer surplus is t, and the merged 4 firm has no incentive to drop one of the products. Proof. See Appendix. 3.. Data is available The merged firm will obtain consumer data and offer individualized prices p A (α) and p B (α) for the two products. In this case, the monopolist can extract the full surplus from consumers 10

11 by offering 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].5 It is straightforward to see that the merged firm has no incentive to drop one of its products. That is, if the monopolist drops, e.g., product B, then it only has product A with which to extract the full surplus by offering p A (α) = v tα. However, consumers located near α = 1 incur larger transportation costs, which lower their willingness to pay for product A. Hence, the following holds: Lemma 5 If the merged firm sets individualized prices, equilibrium prices are given as above and the marginal type is α = 1. Profit is π M = v c t, consumer surplus is 0, and the 4 merged firm has no incentive to drop one of the products. By comparing the monopoly profits in the case where data is available with the no-data case, it follows that the merged firm will sell both products, acquire consumer data, and set individualized prices in the post-merger equilibrium. We can now compare the pre-merger and post-merger equilibria in both the no-data and data cases to determine the impact of consumer data availability on the merger s effect on consumer surplus, as shown in the following proposition. Proposition 1 In a two firm linear city model in which the market is fully covered (v c > 3t), the availability of consumer data at sufficiently low costs both increases the firms profit from merging and increases the consumer surplus loss from merging relative to the case in which there is no consumer data. Proof. This follows directly from the prior lemmas. 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 5 There is a continuum of equilibria where the price of a good is set sufficiently high for those consumers who are not supposed to purchase that good; however, the equilibrium description, apart from the off-theequilibrium prices, is essentially unique. 11

12 consumer surplus. Second, without competition, data access enables the monopolist to extract consumer surplus, increasing post-merger profits and eliminating consumer surplus. This finding seems to echo the concerns of privacy advocates: Because consumer surplus falls more with the merger when merging firms have access to consumer data, the required efficiencies would be greater in order to warrant approving such a merger than if firms do not have access to data. In fact, in this model, since access to data enables firms to extract all the consumer surplus, there are no efficiencies that can make the merger increase consumer surplus. Due to greater increases in profits, data access may also drive firms to seek mergers even when facing lower probabilities of regulatory approval. Therefore, in a merger to monopoly, merger review should be stricter when firms have access to consumer data. 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 relevance for merger policy. Once we move to a market with more than two firms, as we do in the next section, we can see that the effects of access to data drastically change the welfare implications of a merger, precisely because access to data intensifies the remaining competition. 4 Circular City Model 4.1 Pre-Merger Analysis For our three firm case, we use Salop s (1979) circular city model, a workhorse oligopoly model in the literature. Let A, B, and C be three firms located equidistant on a threeunit 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] 1

13 from firm C s location. 6 The remainder of the game remains the same. That is, 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 any pair of firms No data available Without consumer data, the textbook case, the three firms set uniform prices for their respective products. The marginal type is determined by the usual indifference conditions which yield the following: αa = 1 + p B p A, (3) t αb = 1 + p C p B, (4) t αc = 1 + p A p C. (5) t Taking α into account, firm A maximizes π A = α A (p A c) + (1 α C )(p A c), and similarly for firm B and firm C. 7 Lemma 6 (Salop, 1979) If firms set uniform prices, equilibrium prices are p A = p B = p C = c + t and the marginal types are α A = α B = α C = 1. Profits are π A = π B = π C = t, and consumer surplus is 3(v c 5t 4 ). 6 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. 7 Notice that between each pair of firms, the equilibrium looks exactly the same as that of the linear city model considered above. It also follows that the marginal consumer s utility is U(α = 1 ) = v c 3t, whereby v c > 3t ensures market coverage. 13

14 4.1. Data is available We now analyze the case in which data is available to all three firms and all three firms use that data to engage in price competition towards individual consumers. Notice that for any pair of firms, the equilibrium outcome in each segment of the market is exactly the same as in the linear city model analyzed in Section 3.1. Hence, we have the following result. Lemma 7 If all three firms engage in individualized pricing, the marginal type is α A = αb = α C = 1; profits are π A = π B = π C = t 3t, and consumer surplus is 3(v c ). 4 Next, we have to show that, if data is available, in equilibrium all three firms will acquire and use the data if its acquisition cost is sufficiently low. We prove this in the appendix. The following lemma provides the result. Lemma 8 If data is available for a sufficiently low price, all three firms will purchase data and engage in individualized price competition. Proof. See Appendix Figure (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 Subsection 3.1 is that firm B s market segment expands from α A [ 1, 1] to α 4 A [ 1, 1]. The reason is 6 that firm A has another market between its location and firm C s, which is 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 (b) depicts the equilibrium when 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 14

15 A *=1/6 A A C *=1/ A *=1/ C *=1/4 B C B C (a) B *=5/6 (b) B *=3/4 Figure : (a) Only firm B has access to consumer data; (b) Both firms A and B have access to consumer data. which its rival sets a uniform price. Hence, firm C prices more aggressively and thus gains more market share from A and B. Nonetheless, as we show in the appendix, a Prisoner s Dilemma situation takes place once again, with each firm acquiring data despite the fact that the resulting equilibrium is less profitable than if no firm acquired data. As figure indicates, when some firms have data and others do not, the firms without data lose market share and profits relative to the no-data case, making it more profitable to acquire data. This reduces the profits of their rivals and leads to lower prices for consumers. 4. Post-Merger Analysis We now consider a three-to-two firm merger. Without loss of generality, suppose that firms A and B have merged while maintaining their previously held locations in the product space (i.e., no product repositioning.) The merged firm, denoted by AB, may drop one of the two products; however, it follows from Section 3. that the merged firm has no incentive to do 15

16 so, independent of access to consumer data. 8 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 < c, while the nonmerging firm s marginal cost remains at c. We also maintain the running assumption, v c > 3t Data is not available First, suppose both firm AB and firm C do not have access to consumer data, so each product is offered at a uniform price. The merged firm 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 with linear transportation costs, the supercompetitive behavior is not profitable (without merger considerations), it turns out that with mergers the non-merging firm s supercompetitive behavior is profitable given symmetric 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 A = p B p AB ). 8 That is, suppose the merged firm were to drop product A. Since we know dropping product A is not profitable for the market between A and B, and it is irrelevant between B and C, it follows that firm AB has no incentive to drop product A. 16

17 Lemma 9 If firms AB and C set uniform prices, an interior equilibrium exists if and only if c c c (3 3 5)t 0.196t, where for v c 13t 6 equilibrium prices are p AB = 5t+c +c 3, p C = 4t+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 = (4t+ c) 9t ; and consumer surplus is 3v + c 4(13c+14c )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, where AB captures the entire market (i.e., C s market share is zero) if c 4t. 4.. Data is available First, suppose that 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, α C ]; and similarly C sets p C (α C) = c + t(1 α C ) for α C [0, α C ] 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), 17

18 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]. Lemma 10 If both firms AB and C set individualized prices, equilibrium prices are as specified above and the marginal types are αa = 1 and α B = 1 α C = 1 + c c. Profits are t πab = ( 3t+c c )(t + c c ), π t C = (t c+c ), and consumer surplus is 3v c c (c c ) 11t. t t 4 Of course, it is possible that even though data is avaiable, one or both of firms AB and C will choose not to acquire it. As in the previous cases, however, the next lemma establishes that in equilibrium both firms will acquire data. Lemma 11 In the unique equilibrium, both firms AB and C will acquire data and engage in individualized pricing if the cost of doing so is sufficiently low. Proof. See Appendix. In the proof of Lemma 11, we calculate firm profits if either firm AB alone or firm C alone acquires consumer data. We show that for firm C, acquiring data is a dominant strategy, and that if C has data, AB s profits increase if it also has consumer 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 losses, thereby reducing its profits. If firm C acquires data as well, however, then it can charge more to its nearby consumers and maintain its market share among the consumers that are closer the midpoint between it and A or B. 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 18

19 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 merger case to the pre-merger equilibrium in the previous subsection, we can now state the effect of consumer data (hence price discrimination) on the consumer welfare consequences of the three-to-two merger in the circular city model. Proposition Assume c is large enough for an interior equilibrium to exist. Without consumer data, a merger in the three firm market reduces consumer surplus by CS nodata = 3(v c 5t) (3v + (c c ) 4(13c+14c )t 193t ) = (t (c c ))(c c +9t) 4 36t 18t which is equal to 9t 18 when c = c c = 0 and 0 when c = t. With consumer data, a merger in the three firm market reduces consumer surplus by CS Data = 3(v c 3t) (3v c 4 c (c c ) t 11t 4 ) = (t (c c )) t which is equal to t d CS nodata = 14 c d c 9 9t c t, while d CSData d c when c = 0 and 0 when c = t. Furthermore, < 0; therefore, the rate of the decrease in CS nodata increases as = 1 + c t decreases as c c t, as in Figure 3. < 0; therefore, the rate of the decrease in CS Data Figure 3: The decrease in consumer surplus following the merger of firms A and B, when all three firms do and do not have access to consumer data. 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 19

20 when they do not. The 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 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 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, in this simple model, the differences between the data and the nodata case converge to zero exactly at the 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, 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. That said, the precise cutoff is likely very model specific. In particular, the assumption of unit demands for each consumer is particularly important for generating the specific impact of efficiencies on consumer surplus in this model. The larger intuition provided by the model, that consumer data that permits individualized pricing can reduce the amount of market power generated by a merger, is surely more robust. Thus, if anything, these results suggest a somewhat looser standard for mergers short of mergers to monopoly may be optimal when firms have access to consumer data than when they do not. 5 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 0

21 argument is not robust to the presence of non-merging firms, such as in the tripoly case we analyzed. This is because the non-merging firm can exert pricing pressures on the merged entity as long as it also has access to the data post merger. Thus, it seems important to ensure that non-merging firms can have access to consumer data when such concerns arise in merger reviews. More specifically, our analysis shows that the merger to monopoly in the linear city model reduces consumer surplus more when firms have access to data; however, with a three-totwo merger in the circular city model this implication is reversed. The three-to-two merger reduces consumer surplus to a lesser extent when firms have access to data. Since a merger to monopoly is likely to be blocked independent of data considerations, the latter implication seems to weigh more in favor of mergers in oligopoly markets where firms have access to detailed consumer profiles. We caution that the above does not entail that mergers should receive less scrutiny or generate no privacy concerns when firms have access to detailed consumer data. In particular, a direct implication of our study is that serious antitrust concerns arise if a merger imposes on the non-merging firm s access to data. Overall, our analysis suggests that the level of cost-reducing efficiencies required so that a merger does not reduce consumer surplus is likely no higher (and may be lower) when firms have access to consumer data and the merger does not eliminate all competition. Appendix Proof of Lemma 3. We first establish the equilibrium if only one of the firms, without loss of generality say this is 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 ). 1

22 That is, α = 1 + c p A. (6) t Then, firm A maximizes its profit 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 p A into () yields α = 1. Given 4 p A, firm B sets individualized prices p B (α) for those with α 1 4 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 4 ; and p B (α) = c for α 1 4. We have now proved the following claim. Claim 1 If only firm B sets individualized prices, equilibrium prices are given as above and the marginal type is α = 1. Profits are 4 π A = t and 8 π B = 9t, and consumer surplus is 16 v c t. Claim 1 together with the first two lemmas establish that in the first stage of the game, the firms face the following payoff matrix: Firm B No Data Data Firm A No Data t/, t/ t/8, 9t/16 Data 9t/16, t/8 t/4, t/4 The only equilibrium of this payoff matrix is for both firms to acquire consumer data. Proof of Lemma 4. Suppose that the market is not fully covered in equilibrium 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.

23 Substitution yields π M = v p A (p t A c ) + v p B (p t B c ). 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 t contradicts the assumption that market is not fully covered. > 3 4 which 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 is pinned down by driving the marginal consumer s utility to zero, that is, U( 1 ) = v p M t = 0. Profits and consumer suplus throughout this paper are standard. Here, they are π M = 1 0 [v t c ]dα = v c t, and CS = 1 0 [v v + t tα]dα = t 4. To see that the merged firm has no incentive to drop one of the products, suppose that the monopolist drops product B and only sells product A. Then there are two sub-cases to consider. First, 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. Second, 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. Given α, the monopolist t 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 4t π M = v c t for v c t and π M = (v c ) 4t for t > v c > 3t. 3

24 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 ) 4t > 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 5. 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. The market is fully 4 covered in equilibrium even with one product 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 4. Proof of Lemma 8. To establish that all firms will acquire data if it is available for sufficiently low cost, we need to derive the equilibria for the subgames in which only one or two firms have data. First, say only one firm, firm B, has access to consumer data while the other firms do not. The nature of competition between firm B and firm A (or firm C) is similar to that considered in Section 3.1, where firm B is willing to offer p B (α A ) = p B (α B ) = c to attract the marginal consumers in each segment of the market vis-à-vis firms A and C, respectively. The difference is that there is a market segment between firm A and firm C, not directly competing with firm B. Hence, firm A maximizes a concave profit function π A = αa (p A c)+(1 α C )(p A c), where α A is from (4) and α C is from (6). Using the first-order condition and symmetry, it can be shown that p A = p C = c + t 3, and α A = 1 6, α B = 5 6, and α C = 1. Firm B s individualized prices are then determined by the marginal consumer s indifference condition, that is, v p B (α A) t(1 α A ) = v p A tα A for consumers located in α A [0, 1], which implies p B (α A) = p A + t(α A 1) = c + t(α A 1 3 ) for α A 1 6, and p B (α A) = c for α A 1 6. Similarly, p B (α B) = p C + t(1 α B) = c + t( 5 3 α B) for α B 5 6, 4

25 and p B (α B) = c for α B 5 6. If 5t 3 3t v c, then firm A and firm C s pricing does not constrain firm B s monopoly power near B s location. For instance, if v c = 3t, then a consumer s utility from purchasing A s product is negative for α A 5. Clearly, these consumers would not buy from A when 6 offered a price of p A = c+ t 3. Instead, firm B would set p B (α A) = v t(1 α A ) for α A [ 5 6, 1] to extract the full surplus. Thus, when the valuation v is not sufficiently high, firm B can have a monopoly region for consumers located near B. We now establish the following claim. Claim If only firm B sets individualized prices, for v c 5t, equilibrium prices are 3 specified as above and the marginal types are α A = 1 6, α B = 5 6, α C = 1. Profits are π A = π C = 4t 9 and π B = 5 18 t, and consumer surplus is 3(v c) 13 4 t. Proof. Over the market segment between B and A (or C), the worst-off consumer is the one located at α B = 0 given the pricing schedules p B (α A) and p B (α B), where U(α B = 0) = v c 5t 3 5t. Hence, for the market to be covered, this requires v c >. Between A and C, the 3 worst-off consumer s utility is U(α C = 1) = v c 7 t, which is positive by the assumption 6 v c > 3t. Notice that A (or C) has indeed no incentive to undercut C s (or A s) price by t to capture C s entire market because p C t < c; hence, the equilibrium is in the interior. Profits are given by πa = π C = p A c + p A c = 4t, π 6 9 B = [c + t(α ) c]dα = t, and 18 consumer surplus satisfies CS = [v p A tα A]dα A [v p B (α A) t(1 α A )]dα A [v p C tα C]dα C = 3(v c) 13 4 t. Now, consider the case in which two firms, A and B, have access to consumer data while the remaining one, C, does not. It follows that firm A would offer p A (α C ) = c to the marginal consumer located between A and C, and firm B would similarly offer p B (α B ) = c to the marginal consumer located between B and C. Evaluating (5) and (6) at these marginal types, firm C then chooses p C to maximize its profit π C = α C (p C c) + (1 α B )(p C c). 6 5

26 It is easy to show that p C = c+ t, which then implies α C = 1 4 and α B = 3 4. Given p C, firm A s individualized prices for consumers located between firm A and firm C can be determined from v p A (α C) t(1 α C ) = v p C tα C, which yields p A (α C) = p C + t(α C 1) = c + t(α C 1 ) for α C 1 4 and p A (α C) = c for α C 1 4. Similarly, p B (α B) = c + t( 3 α B) for α B 3 4 and p B (α B) = c for α C 3 4. Notice, however, that the competition from B constrains A s pricing towards consumers located in α C [ 3, 1], and similarly for α 4 B [0, 1 ]. Because B and A are only one unit 4 apart from each other and can offer individualized pricing, neither A nor B can offer a price that exceeds c + t to any customer since then either B or A would offer a price above c and steal that customer. The constraint that p A (α C), p B (α B) c + t binds for A for α C [ 3 4, 1] and for B for α B [0, 1 ]. Hence, while the outcome between A and B is the same as in the 4 linear city, the outcome between C and A (or B) is slightly different from that of Section 3.1. We now establish the following claim. Claim 3 If firms A and B set individualized prices, equilibrium prices are as specified above and the marginal types are α A = 1, α B = 3 4, and α C = 1 4. Profits are π A = π B = 3t 4 and π C = t 4, and consumer surplus is 3(v c) 1 8 t. Proof. Over the market segment between C and A (or B), the worst-off consumer is the one located at α C = 3 4 given the pricing schedules p A (α C) and p B (α B), where U(α C = 3 4 ) = v c 5t 4 3t, which is positive by the assumption v c >. Notice that between A and B, the equilibrium looks exactly the same as in the linear city model, and purchase prices are p A (α A) = c+t(1 α A ) for those located at α A 1 and p B (α A) = c+t(α A 1) for α A > 1. Thus, the worst-off consumer s utility is U(α A = 0) = v c t, which is positive too. Profits are given by πa = π B = 1 0 [c+t tα A c]dα A [c+t c]dα C [c+tα C t c]dα C = 3t, and consumer surplus satisfies CS = 1 0 [v p A (α A) tα A ]dα A [v p A (α C) t(1 α C )]dα C [v p C tα C]dα C = 3(v c) 1 8 t. We can now describe the pre-merger equilibrium of the circular city model. Specifically, 6 4

27 if v c 5t, then Claim, Claim 3, Lemma 6, and Lemma 7 establish that the firms face 3 the following payoff matrices in the first stage of the game: B B No Data Data No Data Data A No Data t, t, t 4t, 5t, 4t t Data, 4t, 4t 3t, 3t, t C plays No Data A No Data 4t, 4t, 5t t Data, t, 3t C plays Data t, 3t, 3t t, t, t It is straightforward to see that, as in the case of the linear city model, each firm in the circular city model has a unilateral incentive to acquire data in a Prisoner s Dilemma game and thus employ individualized pricing in equilibrium. Proof of Lemma 9. Suppose that the market is fully covered in equilibrium. Then, firm AB chooses p A and p B to maximize π AB = α A (p A c )+(1 α A )(p B c )+(1 α C )(p A c ) + α B (p B c ), which is a concave function of p A and p B. Substituting in for (4), (5), (6), the first-order condition yields t+p C p AB +c = 0. On the other hand, firm C maximizes π C = α C (p C c)+(1 α B )(p C c), where the first-order condition yields t+p AB p C +c = 0. Solving this system of equations, we have p AB = 5t+c +c 3 and p C = 4t+c +c 3. By substitution, the marginal consumers are α A = 1 and α B = 1 α C = 1 t+c c 6t. For market to be covered, U(α A ) = v 5t+c +c 3 t 0 and U(α B ) = v 5t+c +c 3 t + t+c c 6 0 are required. The former condition is sufficient for the latter. Given c < c, U(αA 13t ) > v c. Thus, a sufficient condition to guarantee 6 U(α 13t A ) 0 is v c. Profits 6 are given by π AB = (α A + 1 α C )(p AB c ) = (1 t+c c 6t )( 5t+c +c 3 c ) = (5t+c c ) 9t, π C = αc (p C c) = ( 1 + t+c c)( 4t+c +c c) = (4t+c c), and consumer surplus is calculated as 6t 3 9t CS = α C[v p 0 C tα C]dα C + 1 [v p α AB t(1 α C)]dα C + α A[v p C 0 AB tα A]dα A. Note that if C were to deviate by undercutting p AB by t, then its profit is 3(p AB t c) = t+c c. Thus, for the interior solution to hold, (4t+c c) 9t t+c c. This is satisfied 7