Apparent Competition in Two- Sided Platforms

Transcription

1 Setember 2017 Aarent Cometition in Two- Sided Platforms Gokhan Guven, Eren Inci, Antonio Russo

2 Imressum: CESifo Working Paers ISSN (electronic version) Publisher and distributor: Munich Society for the Promotion of Economic Research CESifo GmbH The international latform of Ludwigs Maximilians University s Center for Economic Studies and the ifo Institute Poschingerstr. 5, Munich, Germany Telehone +49 (0) , Telefax +49 (0) , office@cesifo.de Editors: Clemens Fuest, Oliver Falck, Jasmin Gröschl grou.org/w An electronic version of the aer may be downloaded from the SSRN website: from the RePEc website: from the CESifo website: grou.org/w

3 CESifo Working Paer No Category 11: Industrial Organisation Aarent Cometition in Two-Sided Platforms Abstract We study a latform s design of membershi and transaction fees when sellers comete and buyers cannot observe the rices and features of goods without incurring search costs. The latform alleviates sellers cometition by charging them transaction fees that increase with sales revenue, and extracts surlus via membershi fees. It rices consumers membershi below its cost to encourage their search. Examles include malls and online marketlaces. Most malls do not charge for arking while most lease contracts include ercentage rents as well as fixed rents. Online marketlaces charge sellers for membershi and er transaction while letting consumers access website for free. JEL-Codes: D210, D400, D830, L130, R330. Keywords: consumer search, membershi fees, retail agglomeration, transaction fees, two-sided latforms. Gokhan Guven Sabanci University Faculty of Arts and Social Sciences, Orhanli Turkey Tuzla Istanbul gokhanguven@sabanciuniv.edu Eren Inci Sabanci University Faculty of Arts and Social Sciences, Orhanli Turkey Tuzla Istanbul ereninci@sabanciuniv.edu Antonio Russo KOF, ETH Zurich LEE G 126 Leonhardstrasse 21 Switzerland 8092 Zurich russo@kof.ethz.ch This version: Setember 2017 We would like to thank Jan Brueckner, Anna D Annunzio, seminar articiants at VU Amsterdam (2016), and session articiants at International Transortation Economics Association Annual Conference (2016) and the Meeting of the Turkish Academy of Sciences (2016) for useful comments. Inci would like to acknowledge financial suort from the Turkish Academy of Sciences (Outstanding Young Scientist Award, TUBA-GEBIP). Any remaining errors are our resonsibility.

4 1 Introduction A substantial share of economic activity takes lace in latforms that bring buyers and sellers together. Shoing malls and online marketlaces are rime examles of such latforms. 1 These latforms usually host several sellers that offer cometing goods. A longstanding literature studies why such cometing sellers colocate, ointing out a trade-off between centrietal and centrifugal forces (see., e.g., Wolinsky, 1983; Dudey, 1990; Fischer and Harrington, 1996; Anderson and Renault, 1999; Konishi, 2005). 2 The resence of multile stores in a marketlace signals consumers a higher chance of finding goods that match their taste. By increasing market size, this creates the centrietal force for agglomeration. Going against is the centrifugal force of rice cutting that stems from fiercer cometition between sellers in close roximity. Thus, when consumer search is costly, sellers may find it beneficial to colocate because they enjoy a larger market size although they may also need to cut down on rices. The crucial asect of cometition in a two-sided latform is that the latform s rofit deends on its ability to extract the surlus that buyers and sellers obtain as a result of transactions between them. Hence, the latform has an incentive to shae the cometitive environment according to its own benefit. Given that it caters to both sides of the market, its otimal strategy is not obvious. Should it foster cometition in order to increase the buyers willingness to ay for articiation, or should it soften cometition to extract higher surlus from sellers? What is the fee structure that imlements its desired outcome? Does agglomeration in a latform necessarily bring in lower rices? The objective of this aer is to shed some light on these questions. We develo a model of a two-sided latform that hosts retailers selling substitute goods. Consumers learn the rices and exact features of goods only after visiting the latform, which entails a search cost. 3 The latform can charge consumers and retailers lum-sum membershi fees. It can also charge transaction fees based on buyer-seller transactions. For the sake of concreteness, we refer to the latform as a shoing mall, but our model alies also to online marketlaces. 1 International Council of Shoing Centers (2014) reorts that more than half of the retail sales in the US took lace in shoing malls in The US Deartment of Commerce (2017) reorts based on quarterly data that on average 8 ercent of retail activity took lace in online marketlaces in As Murry and Zhou (2017) exlain in detail, the emirical evidence about this trade-off is mixed. 3 Consumers may have exectations about rices, but have virtually no chance to know ex ante the articular rice of each good on sale. Even for goods bought on a regular basis, imerfect recall revents a erfect knowledge of all rices. Moreover, in the case of goods such as latos, cars, or clothes, consumers tyically do not even know their exact willingness to ay for a articular good before hysically examining them. 2

5 We first focus on the mall s role in shaing cometition between retailers. We show that the mall has retailers charge rices above what they would actually charge if they were cometing with each other indeendently. That is, the mall virtually acts as a tacit-collusion device, and thus, cometition between stores is only aarent. The mall achieves this outcome by imosing a fee on the retailers transactions, which in ractice takes the form of a ercentage rent clause in the rental lease contract. 4 The ercentage rent is chosen to maximize retailers joint rofits. The mall can extract this surlus by imosing a high enough membershi fee, which in ractice takes the form of a base (fixed) rent. Because consumers cannot observe the rices of goods rior to visiting, the mall anticiates that raising retail rices has little effect on the number of consumers who visit the mall, while it increases the surlus extracted from those who do. Therefore, it has an incentive to alleviate retailers rice cometition. Next, we take a broader look at the structure of fees charged by the latform. In rincile, in addition to taxing transactions between consumers and retailers with ercentage rents, the mall can charge either side for membershi. In reality, malls do charge retailers membershi fees in the form of base rents. 5 However, they tyically do not charge consumers for visiting the mall. Almost every mall rovides free arking. 6 Similarly, online marketlaces charge transaction and membershi fees to sellers, but do not charge membershi fees to consumers. A riori, it is not obvious why choosing such fee structures is otimal. An alternative strategy would be encouraging cometition among retailers for the benefit of consumers, and then recovering consumer surlus through high arking fees (or other membershi charges). However, this strategy is actually dominated when consumers are imerfectly informed about the rices of goods rior to visiting. The mall anticiates that lowering retail rices cannot exand the market size (nor can it increase the arking fee revenue) when consumers do not observe retail rices rior to their search. Yet, consumers tyically know the arking fee rior to visiting the mall. Hence, lowering the arking fee does exand the market size. In fact, given high retail rices, raising the arking fee has a high 4 Unlike traditional rental contracts, rental lease contracts between shoing malls and retailers often require the latter to ay a ercentage of their sales revenue in addition to a fixed rent. Gould et al. (2005) and Wheaton (2000) show that a large number of retailers in malls have a clause secifying a ercentage rent. Online marketlaces levy similar fees. Although the rates may vary by category, Amazon and ebay charge sellers between 3 to 15 ercent on each transaction in addition to membershi fees. We rovide additional details on these fees in Section 2. 5 Some excetions exist. For instance, 73 ercent of anchor stores ay no rent (Gould et al., 2005). In Section 6.2, we analyze the case of anchor stores and exlain why they may be asked to ay no rent. 6 The International Council of Shoing Centers and Urban Land Institute (2003) reort that arking is free in 94 ercent of the US malls. 3

6 imlicit cost for the mall because losing the marginal consumer means a substantial loss in exected retail revenue. This means that the mall generally refers charging low or no fees for arking. Our results highlight the role of consumer uncertainty in shaing the latform s fee structures. Because consumers are imerfectly informed about retail rices, the mall follows a logic similar to, yet at the same time oosite of, a standard two-art tariff. This tariff maximizes consumer surlus and extracts it via a membershi fee (Oi, 1971). In our setting, the mall maximizes the roducer surlus by making retailers charge high rices, and recovers their surlus by charging a base rent. However, the fli side is that the mall minimizes the surlus of consumers who visit, although it subsidizes their search by roviding arking below cost. 7 If we assumed, rather unrealistically, that consumers observe all rices ex ante, the standard two-art tariff result would emerge: the mall would then actually boost retailer cometition by charging negative ercentage rents (i.e., subsidizing transactions) combined with a high arking fee. This ricing strategy is the oosite of what is commonly observed in reality, imlying the relevance of our assumtion of consumer uncertainty. Finally, we analyze the relationshi between the number of retailers in the latform and the equilibrium rices. We show that, quite surrisingly, agglomeration does not necessarily result in lower rices. The mall s incentive is to soften cometition between retailers, which means that having more of them may not make the marketlace more cometitive. In fact, when retailers sell substitute goods and consumers are uncertain about their tastes rior to visiting the mall, a higher number of retailers means a higher chance of finding a good that fits one s taste. Thus, a higher number of consumers visits the mall. As a result, the aggregate demand faced by the mall becomes less elastic, which imlies that retail rices increase with the number of retailers at the mall. We argue that this result is context-deendent and more likely to hold for certain tyes of goods than for others. It alies more reasonably to goods that consumers tyically buy in single units and when taste uncertainty is relevant (e.g., TVs, latos, or shoes) than to goods tyically bought in multile units with well-known characteristics (e.g. groceries). Previous literature recognizes that latforms maniulate the cometitive environment that they host. Armstrong (2006) argues that a latform may limit the number of cometing sellers if it 7 Nonetheless, the fact that arking fees are below their marginal cost does not mean that consumers do not actually ay for arking. They do ay for arking in the form of higher retail rices. 4

7 cannot charge buyers for membershi. Hagiu and Jullien (2011, 2014) show that a latform may divert consumer search to generate more revenue on the seller side of the market even when cometing with other latforms. 8 Dukes and Liu (2015) show that latforms may increase consumers search costs in order to mitigate cometition. Emirical evidence on the latform s imact on cometition between retailers is mixed. Scott Morton et al. (2001) consider an online referral latform connecting customers to car dealers and find that, although online customers ay about 2 ercent less for a car than offline ones, dealers realize higher margins er sale on the online latform. 9 Iyer and Pazgal (2003) study internet shoing agents that allow consumers to comare CD rices at online retailers. They find that, although consumers are generally able to find a better deal when using the shoing agent, the average rice charged by retailers on the latform increases with the number of retailers in the latform. These mixed results are ossibly due to the fact that joining latforms allows retailers to realize some cost savings (e.g., lower labor costs er transaction), which are artly assed through to consumers. Furthermore, these studies focus on latforms as information gatekeeers in that they only refer consumers to retailers but do not kee track of buyer-seller transactions. Thus, they cannot really charge transaction fees. Baye and Morgan (2001) rovide a theoretical treatment of such latforms. By roviding a novel exlanation for the role of transaction fees in alleviating cometition in latforms, we contribute to different strands of literature. The real estate literature studies rovisions of ercentage rents in mall lease contracts. Using data from aroximately 2500 stores in 35 US malls, Gould et al. (2005) find that rents ositively vary with retailers sales revenue underlining the relevance of ercentage rents. As a matter of fact, 99 ercent of the rental contracts of non-anchor stores in their samle has a clause secifying a ercentage rent. 10 Gould et al. (2005) interret these rovisions as the mall s resonse to its own inability to commit to costly actions that benefit the retailers (e.g., renovations, cleanliness of communal areas, etc.). In a similar vein, 8 They rovide some anecdotal evidence of this behavior. For examle, Netflix sometimes leads viewers towards movies that generate higher revenues (Shih et al., 2007). Shoing malls and stores are often designed to increase the distance consumers have to walk to reach the most oular stores or roducts (Petroski, 2003). 9 It is worth ointing out that the latform take measures to limit cometition between its members, assigning them exclusive territories. 10 Although almost all non-anchor stores have a ercentage rent clause, the threshold over which ercentage rents aly is usually high. Only 18 ercent end u aying these additional rents in ractice. We show in Section 6.1 that our results continue to hold even if only one of the retailers is charged a ercentage rent. We further show in Aendix B that having a two-art tariff structure rather than three-art is without loss of generality. 5

8 Wheaton (2000) argues that ercentage rents serve as commitments for the mall not to alter the tenant mix in ways that may damage existing tenants. Brueckner (1993) argues that ercentage rents internalize inter-store externalities, but obtains negative ercentage rents as otimal. Our results stem from exlicitly modeling the ricing decisions of the retailers in the mall, which this literature ignored. The fee structures have also been studied in the literature on two-sided latforms (Rochet and Tirole, 2006). Nevertheless, very few aers actually model the transactions between buyers and sellers. Bedre-Defolie and Calvano (2013) study the design of membershi and transaction fees by a ayment network, showing that the network subsidizes consumers transactions because, contrary to merchants, they can decide which means of ayment to use. Wang and Wright (2017) consider a latform hosting cometing sellers and show that ad valorem transaction fees are an effective form of third-degree rice discrimination in the resence of heterogeneous roduct categories. Hagiu (2009) shows that transaction fees solve a commitment roblem of the latform, which is unable to commit not to bring in otential cometitors of existing sellers. Finally, Gans (2012) shows that a digital latform relies on revenue sharing agreements with alication develoers, rather than charging consumers directly, when the latter observe the rices set by develoers only after joining. Although revenue sharing is equivalent to transaction fees, these agreements have no effect on the rices of alications in Gans (2012) model. Furthermore, there is no cometition among develoers. 11 Another related strand of the literature concentrates on the ricing of arking sace at shoing malls, but simlifies the roblem by taking the mall and stores as a single entity (Hasker and Inci, 2014; Ersoy et al., 2016). Our setting differs by modeling these entities as searate layers. Molenda and Sieg (2017) allows for two cometing shoing malls located at the end oints of a Hotelling line while treating the relationshi between the mall and retailers in a reduced form. Last but not least, we contribute to the literature that exlores retail ricing strategies (see, among others, Konishi and Sandfort, 2002; Rhodes, 2015) and agglomeration forces that lead to the concentration of cometing sellers in the resence of imerfectly informed consumers (see, e.g., 11 A related literature (e.g., Foros et al., 2014; Gaudin and White, 2014; Johnson, 2017) studies revenue-sharing agreements between a retailer latform and suliers in the so-called agency model. The focus of this literature is not on the latform s incentives to alleviate cometition among suliers. Shy and Wang (2011) comare ad valorem and unit transaction fees, showing that a monoolist latform refers the former when sellers have market ower. 6

9 Konishi and Sandfort, 2003; Konishi, 2005). This literature neglects the strategic behavior of latforms. Our model extends Konishi and Sandfort (2002, 2003) by incororating such interactions, which is the driving force behind our results. We argue that latforms have strong incentives to distort retail rices in order to weaken cometition. This restrains rice cutting, which is considered to be one of the most imortant benefits of agglomeration of cometing retailers for consumers. The aer is organized as follows. Section 2 resents our base model. Section 3 reorts our findings on the role of the latform in distorting cometition between retailers. Section 4 shows the imortance of our assumtion of unobservability of rices on the fee structures imosed by the latform. Section 5 analyzes the relationshi between agglomeration and rices. Section 6 makes a robustness check by introducing heterogeneous retailers in the model. Section 7 briefly discusses the case of cometing latforms. Section 8 concludes. Aendices contain generalizations of our base model, and roofs of some of the results and claims. 2 The model We resent a model of a latform that brings sellers and buyers together. Although the model alies also to other kinds of latforms, such as online marketlaces, for the sake of concreteness, we refer to the latform as a shoing mall, to sellers as retailers and to buyers as consumers. We build on the framework of Konishi and Sandfort (2002, 2003). There is a monoolist mall, M, and two retailers, indexed by i = 1, Each retailer sells a single good, also indexed by i = 1, 2, at a constant marginal cost m < 1. The marginal cost is assumed to be less than one because a consumer s maximum willingness to ay will be normalized to one. Retailers comete by choosing rices. Because we are not interested in the decision to locate at the mall but rather in the mall s ricing, we assume that a retailer makes an exogenous rofit if it locates outside the mall and normalize this rofit to zero. 13 There is a unit mass of risk-neutral consumers. Each buys at most one good from at most one retailer. Consumers learn the rice of each good, i, and their willingness to ay for it, v i, 12 Section 7 allows for cometing malls and Aendix A allows for n 2 retailers. 13 Section 6.1 shows that allowing for heterogeneous outside otions would alter the distribution of surlus between the retailers and the mall, but it would not change the main insights of the aer. Section 6.2 shows that allowing one of the retailers to charge an exogenous rice (erhas due to being a subsidiary of a chain whose rices are determined at the regional or national level) does not change the main insights, either. 7

10 only after visiting the mall (i.e., searching). 14 However, consumers have rational exectations. We assume that v i is indeendently and identically distributed across consumers and goods. Let G (v i ) be the cumulative distribution function for v i. To ease exosition, we assume that this distribution is uniform with suort on the [0, 1] interval. 15 Given our assumtions, consumers are ex-ante (i.e. rior to visiting M) identical, excet for a (sunk) search cost s, which is also uniformly distributed on the unit interval [0, 1]. Following our interretation of M as a shoing mall, it is natural to think of s as a transortation cost, but it can also be interreted broadly to include the oortunity cost of the time sent searching for the good. We normalize the surlus of consumers who decide not to visit the mall to zero. The references distributions, search costs, and the number of retailers at the mall are common knowledge. The mall charges a rent R i to the retailers occuying its floor sace. This rent is comosed of a fixed ayment (or base rent), a i, and an additional ayment r i er each dollar of sales (the ercentage rent). Thus, denoting the retailer s sales revenue by S i, the rental contract has the form of a two-art tariff: 16 R i = a i + r i S i i = 1, 2. (1) We assume the consumers do not observe the rental contracts between the mall and the retailers. There is a fee f 0 that consumers ay to enter the mall. To fix ideas, we interret this fee as a arking charge (the imlicit assumtion is that all consumers travel to the mall by car). We assume that consumers observe this fee before visiting the mall. 17 It costs c for the mall to rovide each arking sace. Although we maintain the shoing mall interretation throughout the analysis, our model alies to other latforms hosting cometing sellers. In online marketlaces, consumers incur search costs because browsing through different listings and checking the features of the goods 14 Anderson and Renault (1999), Konishi and Sandfort (2002, 2003), and Konishi (2005) make similar informational assumtions. 15 Aendix A generalizes the model to a broader range of reference distributions. 16 As Wheaton (2000) describes in deth, retail lease contracts in malls actually have a three-art-tariff structure. The ercentage rent (or the overage rent as Gould et al., 2005 and Baek and Brueckner, 2015, call it) alies only if the sales revenue exceeds a threshold. Aendix B shows that there is no loss of generality in restricting attention to two-art tariffs. Desite being less flexible, in our model, a two-art tariff is sufficient to imlement the rofit-maximizing equilibrium that the mall can imlement with a three-art tariff. 17 Although this fee is not crucial for our main result, having an ex-ante observable rice hels to highlight the imortance of the unobservability of retail rices. 8

11 are time consuming. These latforms generally do not charge consumers for access while the fee structure that they charge to retailers is similar to the one shown in equation (1). 18 Therefore, while going through the analysis, one should kee in mind the analogy between equation (1) and the fees tyically encountered in other tyes of latforms. The base rent a i is a membershi fee levied on sellers and the ercentage rent r i is an (ad valorem) fee on transactions between sellers and buyers, and the arking fee f is a membershi (or access) fee on buyers. 19 The assumtion that retailers are single-roduct firms is due to our main objective of studying the role of the latform. Given this focus, there is little loss in ignoring that retailers sell multile roducts. In fact, as it will later become clear, the mall itself can be thought of as a multiroduct firm, because it has the extensive ability to influence the retailers ricing decisions. With our assumtion, we abstract from some of the comlexities of multiroduct ricing (see, e.g., Rhodes, 2015). Our model is is more suitable for goods that consumers tyically buy in single units er shoing tri (e.g. TVs, comuters, or furniture) than for goods tyically bought in multile units (e.g. groceries). 3 Equilibrium The sequence of the events in the model is as follows. First, the mall offers each retailer a takeit-or-leave-it rental contract, R i, and sets f. Retailers simultaneously decide whether to accet. They then simultaneously choose the rices of their goods i. If there is only one retailer that acceted the contract, it chooses the rice on its own. Consumers decide whether to visit the mall by incurring the search cost s. They learn i and v i once they arrive at the mall. Finally, each consumer who visits the mall decides whether to buy (at most) one good from (at most) one retailer. Our equilibrium concet is Subgame Perfect Nash Equilibrium. Therefore, we solve the model by backward induction. We concentrate on the interior ure strategy equilibria of this game. 18 For instance, Amazon charges rofessional sellers a monthly fixed fee lus a referral fee er each item sold, equal to a ercentage of the selling rice (htts://sellercentral.amazon.com). Likewise, ebay offers several lans to rofessional sellers, which involve a monthly base fee and a final value fee comuted as a ercentage of the rice of each good sold (htt://ages.ebay.com/seller-center/stores/subscritions.html). TMall.com charges sellers an annual technology and service fee in addition to commission fees on each transaction. 19 The fact that the ercentage rent is formally charged to retailers is immaterial. Due to the standard tax incidence arguments, the effect of r i on transactions does not deend on to which grou it is levied (Weyl and Fabinger, 2013). 9

12 3.1 Consumers A consumer who visits M learns the rice of both goods and his ersonal valuations v i. He then buys the good that maximizes his net surlus, rovided that it is ositive. He makes no urchase if no good gives him a ositive surlus. Formally, the consumer buys good i if and only if v i i max[v j j, 0], where i, j = 1, 2. Let e = ( e 1, e 2 ) be the vector of exected rices at the mall, which will coincide with the vector of equilibrium rices in the end due to rational exectations. The exected utility of a consumer who visits the mall is EU ( e, f) =E (max [0, v 1 e 1, v 2 e 2]) = (v 1 e 1) G (min [v 1 e 1 + e 2, 1]) dv 1 + (v 2 e 2) G (min [v 2 e 2 + e 1, 1]) dv 2 e 1 e G ( e 1) G ( e 2) f, (2) where G ( ) is the cumulative distribution function of the valuations v i. This exression excludes the search cost s, which is sunk once the consumer visits the mall. It will however be relevant in the consumer s decision to visit, which we analyze below. Each line of equation (2) can easily be understood from Figure 1, which shows on the x axis (y axis) the level of the rice of the good sold by retailer 1 (retailer 2) in the distribution of the consumer s valuation of the good. This figure concentrates on the case where 1 < 2, but the oosite case can easily be analyzed by interchanging the two axes. The two goods are imerfect substitutes, and thus, the consumer does not necessarily buy the cheaest one. He may buy the more exensive one if his valuation for it is high enough. To understand the second line in equation (2), recall the condition for urchasing good i described above, and that the distribution of valuations for each good does not exceed one. Thus, assuming a ositive surlus from the urchase, the consumer buys from retailer i with robability G(min[v i e i + e j, 1]), in which case he gets v i e i. The first term on the third line of equation (2) exresses the case in which the consumer does not buy any good. With robability G( e 1 ), his valuation is below the rice of good 1 (similarly for good 2). Given our assumtions, these events haen jointly with robability G( e 1 ) G(e 2 ). Finally, the second term on the third line says that, conditional 10

13 2 1 1 = Buy from Retailer 2 2 Buy from Retailer Figure 1: Consumer s decision when 1 < 2 on visiting the mall, the consumer ays the arking fee f whether he buys a good or not. Because all consumers are ex-ante identical with resect to their references (as a consequence of v i being i.i.d.), they obtain the same exected utility from visiting the mall. However, they still differ with resect to their search costs. A consumer visits M if and only if his exected utility in equation (2) is weakly higher than his search cost, i.e. EU( e, f) s. Thus, the marginal consumer, who is indifferent between visiting M and not, is such that EU( e, f) = s. Hence, given our assumtions, the mass of consumers who visits, in other words the mall s market size, µ( e, f), satisfies µ ( e, f) = EU ( e, f). (3) It is imortant to note that the market size is a function of the exected rices, not the actual ones. The reason is that consumers make their decision to visit before observing the rices. 3.2 Retailers Consider now the retailers ricing decision. Equation (2) states that a mass µ( e, f) of consumers atronizes the mall. Each shaded area in Figure 1 is the robability that a consumer buys from retailer i. Given our assumtions on the distribution of references, these robabilities actually reresent the share of consumers who buy from retailer i, θ i (), where = ( 1, 2 ) is the vector of 11

14 actual rices at the mall. Using Figure 1, it is straightforward to calculate θ i () for each i = 1, 2: θ i () = 1 j + i i (v i i + j ) dv i + dv i 1 j + i if i j (v i i + j ) dv i if i > j. i 1 j + i 1 (4) We can now derive a retailer s rofit. A mass θ i ()µ( e, f) of consumers buys from retailer i and ays i. Thus, retailer i s total revenue is S i = i θ i ()µ( e, f), while its total cost (excluding the rental ayment) is mθ i ()µ( e, f). Given equation (1), the retailer also ays a rent a i + r i S i to the mall. Hence, its net rofit, π i, is given by π i = ( i (1 r i ) m) θ i () µ ( e, f) a i i = 1, 2. (5) The key oint to realize here is that the retailer knows that consumers do not observe the rices before they visit. Hence, it treats the market size µ( e, f) as given. This assumtion catures the fact that consumers cannot have erfect information about the rices and the quality of the goods available in the mall before actually visiting it. 20 Simultaneously maximizing the rofits of the retailers, we find the rice i as follows: i = 2 ( 1 + m ) 1 i = 1, 2. (6) 1 r i This rice is unique and symmetric. 21 The comarative static roerties of this rice equation are of interest. As exected, the higher the marginal cost m, the higher the equilibrium rice. The arking fee f, which is ex-ante observable and ex-ost sunk, does not affect i. It only affects the market size µ( e, f), which retailers take as given. Because the base rent is a fixed cost for the retailer, it does not have an imact on ricing, either. However, the ercentage rent does matter: the higher it is, the higher the rice. The ushot is that the mall is able to influence the retail rices by aroriately designing the rental contract. Hence, it can soften the cometition between the retailers. 20 This is a standard assumtion in the literature on consumer search. Ellison (2005) describes a similar mechanism where, for examle, hotels announce low base rices for rooms while charging higher rices for add-ons, such as minibar items, meals, etc. 21 We rovide a formal roof of the uniqueness of the equilibrium in Aendix A in a more general setting. 12

15 Suose the mall was not charging any ercentage rent (i.e., r i = 0). Then, the equilibrium rice would have been 0 = 2 (1 + m) 1, (7) which is lower than any i in equation (6) for any r i (0, 1]. We call 0 the cometitive rice. In sum, our first result is that ercentage rents make the market less cometitive. The following roosition records this result. Proosition 1 (Percentage rents alleviate cometition). The equilibrium rices charged by the retailers are increasing in the ercentage rent charged by the mall: i / r i > 0. The ercentage rent is essentially a fee that the mall levies on each transaction. As such, it is akin to an ad valorem sales tax (Wang and Wright, 2017). As we are now going to show, it is in the mall s interest to tax the transactions between buyers and sellers. 3.3 The mall Consider now the mall s roblem. Its rofit, π M, is comosed of rents aid by the two retailers and the arking revenue left by the consumers: π M = 2 R i + (f c) µ ( e, f). (8) i=1 The mall maximizes this rofit by choosing a base rent of a i, a ercentage rent of r i, and a arking fee of f. Because the retailers outside otion is exogenous, the mall can extract their entire net rofits. It can do so by setting a base rent of a i = ( i (1 r i ) m)θ i ()µ( e, f). Therefore, the mall-otimal rental contract must satisfy R i = ( i m) θ i () µ ( e, f) i = 1, 2. (9) Hence, the mall s rofit function reduces to π M = after relacing for the base rent. ( 2 ) ( i m) θ i () + f c µ ( e, f) (10) i=1 13

16 Consider now the mall s choice of the ercentage rent r i. Maximizing π M with resect to r i yields the equilibrium value of the ercentage rent, r i : r i = 1 ( ( m 3 (m + 3) m )) m m 2 + 4m + 2 i = 1, 2. (11) Because m is less than one, the second term in this equation is always strictly less than one, thus we have 0 < r i < 1. As a result, the mall charges a ositive ercentage rent, which we record in the following roosition. Proosition 2 (Percentage rent). The mall charges a ositive ercentage rent: 0 < r i < 1. Recall from Proosition 1 that retail rices increase with the ercentage rent. Hence, ositive ercentage rents mean that the mall induces the retailers to charge a rice that exceeds the cometitive rice 0 shown in equation (7). The mall wants to alleviate cometition between the retailers because it can recover their entire rofit by aroriately charging a fixed rent a i. Hence, it wants the joint rofit of retailers to be as high as ossible. Like retailers, it knows that consumers do not observe the actual retail rices before visiting. As a result, it treats the market size µ( e, f) as invariant to the actual rice vector,. From its ersective, cometition decreases the rofits that can be extracted from the retailers without exanding the market. Using ri in (6), we obtain the equilibrium rice, i : i = m + m i = 1, 2. (12) This equilibrium rice is in fact what a monoolist firm, owning both retailers, would choose. This roerty is striking because the retailers seemingly comete, and one would exect a more vigorous cometition due to agglomeration within the mall. However, this reasoning ignores the incentives of the latform that hosts the sellers. By taxing buyer-seller transactions using a ercentage rent, the mall discilines retailers cometitive behavior and maximizes their joint surlus. In other words, the rental contract acts as a coordination device to alleviate cometition. This finding leads to the following roosition. Proosition 3 (Aarent cometition). The equilibrium rice that retailers charge, i, is the 14

17 rice that a monoolist firm, owning both retailers, would charge. Although the retailers aear to be cometing, the outcome is a monooly outcome. This result shows that two-sided latforms that bring sellers and buyers together adot transaction fees in order to induce seller coordination on a desired vector of rices. We now turn to the determination of the arking fee by maximizing π M with resect to f. The arking fee cannot be negative because a arking subsidy is hard to imlement in reality. Hence, if the maximization roblem yields a negative f, we shall set it to zero. The first-order condition with resect to f is given by π M f = ( 2 ) ( i m) θ i () + f c i=1 µ f + µ(e, f) = 0. (13) After relacing for the equilibrium rice i from equation (12) and solving for f, we obtain [ c ] f = max 2 A, 0, (14) where A = 1 6 ( ) 2 m m + ( m + ) 2 ( m m 4 m ). (15) It can be shown that A is strictly ositive for all m [0, 1]. Hence, the equilibrium arking fee f is strictly lower than the variable cost of roviding arking. In fact, because this marginal cost is close to zero in reality, the mall does not charge any arking fee in most circumstances, which is in line with emirical observations. In any case, arking is a loss leader, being riced below its marginal cost. The mall can then embed some of the costs of arking in the retail rices. The arking fee can be interreted as an additional comonent of the search cost. Hence, the mall effectively subsidizes consumer search by ricing arking below cost. We summarize our findings in the following roosition. Proosition 4 (Loss-leader ricing of arking). The arking fee is below the marginal cost of roviding a arking sace, c. If c is small enough, arking is rovided for free. According to the International Council of Shoing Centers and Urban Land Institute s survey (2003), 94 ercent of shoing malls in the US do not charge any arking fee. The ractice is 15

18 similar in other countries. Past work rovides various exlanations for this observation. In Hasker and Inci (2014), consumers are risk averse and find their desired good at the mall only with some robability. The mall thus rovides free arking as a form of insurance to consumers. In Ersoy et al. (2016), the mall is accessible by both car and bus, and the latter can get crowded. The mall charges high rices for goods to internalize crowding externalities, but subsidizes arking in order not to enalize car users. We rovide an exlanation for free arking different from the rior literature. Our exlanation is based on the ex-ante observability of arking fees and ex-ante unobservability of rices of goods. The mall anticiates that decreasing the rices of goods does not exand the market size (and the arking fee revenue, µ( e, f)f). In contrast, decreasing the arking fee does exand the market size because consumers know it rior to their visit. As a matter of fact, given high retail rices, raising the arking fee has a high imlicit cost for the mall because losing the marginal consumer imlies a substantial loss in exected retail revenue. As a result, the mall is better off charging a arking fee below its cost. An additional imlication of the analysis is that the rovision of free arking in shoing malls is second-best efficient from a social welfare ersective. It is straightforward to see it. First, note that it is usually not ossible to regulate neither the rice of goods within the mall nor the rental contracts between the mall and retailers. Given that the mall has retailers set rices above the cometitive level, it is socially otimal to exand the market size by subsidizing arking. 4 Information and the structure of fees Taken together with the results of Section 3.3, Proosition 4 highlights the role of information in shaing the fees charged by a latform. Because consumers are imerfectly informed about retail rices, the mall adots a fee structure with a logic similar to, yet at the same time oosite of, a standard two-art tariff. A firm charging a conventional two-art tariff maximizes consumer surlus by making consumers ay for usage at marginal cost, and extracts this surlus via a membershi fee (Oi, 1971). In a similar vein, we find that the mall maximizes the roducer surlus by inducing higher retail rices to be charged, and extracts this surlus by imosing base rents. To highlight the relevance of consumer uncertainty, assume for the moment that consumers er- 16

19 fectly observe the rices of goods before visiting the mall. This is rather an unrealistic assumtion. As Aendix C shows in a more general setting, when rices are ex-ante observable, the mall s best strategy drastically changes. Because it recognizes that changes in the rice of goods affect the market size, the mall now has retailers to rice goods at marginal cost by adoting negative ercentage rents. That is, it subsidizes the transactions between buyers and sellers in order to maximize the visiting consumers exected surlus. The arking fee is then used to recover this surlus. Hence, we get: i = m, r i < 0, f = c + EU( m, f), (16) where m = (m, m) is the vector of retail rices, and EU( m, f) is the exected utility from visiting the mall as defined in equation (2). This exercise highlights that the structure of fees chosen by the mall hinges critically on consumers information. When they are imerfectly informed about the rices of goods rior to visiting the mall, the mall refers to tax buyer-seller transactions while subsidizing consumer search by loss-leader ricing of arking. In contrast, in the rather unrealistic case where consumers erfectly observe rices without searching, the mall wants to subsidize transactions while charging a high arking fee to recover surlus. Proosition 5 (Information and the structure of fees). If consumers cannot observe the rices of goods rior to visiting the mall, the ercentage rents are ositive (i.e., the mall taxes buyerseller transactions) and the arking fee is below cost (i.e., the mall subsidizes consumer search). However, if consumers can observe all rices ex ante, the ercentage rents are negative (i.e., the mall subsidizes buyer-seller transactions) but the arking fee is high. Negative transaction fees and high membershi fees charged to consumers are the oosite of what is commonly observed in reality. This means that consumer uncertainty is in fact quite relevant in determining the fee structure chosen by a latform. Nevertheless, the latform and retailers can decrease the uncertainty by advertising. If consumers can be made erfectly informed rior to visiting, then the latform has an incentive to induce lower retail rices. We do not exect advertising to fundamentally change our results. In ractice, advertising does not comletely eliminate uncertainty, at least not for all consumers. Even if retailers advertise, it is reasonable 17

20 to exect that some consumers remain imerfectly informed. Then, as long as there are some consumers with uncertainty, the latform has an incentive to induce high retail rices. Thus, aarent cometition revails although we do not necessarily get the strict monooly outcome. In addition, as Konishi and Sandfort (2002) and Rhodes (2015) argue in detail, sellers do not always find advertising advantageous, and if they do, they usually end u advertising only a small subset of goods in their roduct range. 5 Agglomeration and retail rices We now investigate the relationshi between the number of retailers in the mall and the equilibrium rices. In light of our revious results, we can say that it is not obvious that increasing the number of retailers at the mall leads to lower rices. To illustrate this result, we now comare the case in which there is only one retailer at the mall with the case in which there are two retailers, which we have already analyzed above. This comarison suffices to show the first-order intuition. Aendix A generalizes the result by allowing for n 2 retailers. Suose there is a single retailer at the mall and let denote the rice of its good. A consumer visiting the mall buys the good if and only if v. Given our assumtions on references, this haens with robability θ s () = g(v)dv = 1. (17) We use subscrit s to denote the single-retailer case. We retain the assumtion that consumers cannot observe before visiting the mall, so the market size µ ( e, f) deends on the exected rice e. Thus, the retailer s rofit is π s = ( (1 r) m) θ s () µ ( e, f) a, (18) where r is the ercentage rent and a is the base rent. The market size µ ( e, f) is given by µ ( e, f) = EU ( e, f) = E (max [0, v e s]) = (v e s) dg(v). (19) e s 18

21 Maximizing π s leads to the following equilibrium rice: s = 1 2 ( 1 + m ). (20) 1 r As in the two-retailer scenario, the ercentage rent increases the rice charged by the retailer. Consider now the mall s roblem. As we argue above, the mall is better off setting a such that π s = 0. Hence, we can write its rofit as π M,s = (( m) θ s () + f c) µ ( e, f). (21) The comarison of this exression with equation (18) suggests that, when r = 0, the retail rice that maximizes the retailer s rofit also maximizes the mall s rofit. Therefore, the mall sets no ercentage rent, r = 0. The intuition is simle: because there is no cometition, the mall has no reason to distort rices. Hence, we have s = 1 + m. (22) 2 Let us now comare this rice with equation (12). Because m < 1, we conclude that s = 1 + m 2 < i = m + m (23) 3 Therefore, the equilibrium retail rice when there are two retailers at the mall is higher than the rice when there is one retailer. Proosition 6 (Number of retailers and rices). The equilibrium rice of goods is increasing in the number of retailers. Why do we get this result? A first reason is that the mall has an incentive to soften cometition, which results in higher retail rices. The second reason is related to the market-exansion effect associated with a higher robability of finding a good that fits one s references when we increase the number of retailers at the mall. To see this effect formally, comare the market size in the case in which there are two retailers at the mall (see equation (2)) with the case in which there is only one retailer (see equation (19)), at a given level of retail rices. It is straightforward to see that the 19

22 market size with two retailers is larger. As a result, the demand faced by the mall on the consumer side of the market becomes less elastic when the number of retailers increases. Then, the mall finds it otimal to have the retailers set even higher rices when their number increases. In other words, as a two-sided latform, the mall exloits the ositive externality that the availability of retailers exerts on consumers (Rochet and Tirole, 2006). It extracts this additional surlus by having the retailers themselves charge higher rices, which it then extracts via base rent, rather than charging consumers directly via arking fees. These results suggest that agglomeration does not necessarily result in lower rices. The ast literature shows that agglomeration exands the market size of stores at the mall, but it also reduces the rice they charge in equilibrium because of intense cometition (see. e.g., Konishi, 2005). This last finding in the ast literature stems from the fact that the mall has no means to influence the retailers ricing decisions because it is allowed to charge only base rents. To see this transarently, we now comare the retail rice in the single-retailer case with the retail rice in the two-retailer case again, but this time by setting the ercentage rents to zero in equation (7). In that case, we have s = 1 + m 2 > 0 = 2 (1 + m) 1. (24) Therefore, if the mall does not adot transaction fees, cometition does indeed decrease rices. However, once we incororate the mall s incentives, the relationshi between the number of stores and the equilibrium rices is reversed. A caveat concerning Proosition 6 is that it artly deends on our assumtion that consumers buy at most one good from at most one retailer er visit. In a model in which consumers can buy multile goods er visit, Rhodes (2015) shows that a retailer charges lower rices when roduct range in the mall increases. The reason is that the demand by consumers who buy multile goods is more elastic with resect to rices. Our model does not feature this effect. However, Rhodes (2015) assumes that consumers are not uncertain about their taste for goods, which is robably a better assumtion for grocery shoing. We instead assume that this variable is realized only after the consumer visits the mall. Thus, a broader roduct range actually reduces the elasticity of demand erceived by the mall, leading to our rice-increasing result. That is why we argue that Proosition 6 is more likely to aly for goods that consumers buy in single units er visit and 20

23 that are difficult to evaluate without incurring substantial search costs. This descrition is more likely to be a good fit for such goods as TVs, comuters, furniture, or cars, but less for groceries. 6 Retailer heterogeneity We have so far assumed that the retailers in the mall are symmetric. However, malls contain various retailers that differ in certain imortant dimensions. To bolster confidence in our results, we now introduce heterogeneity to our model in two ways. First, in Section 6.1, we assume that the retailers have different bargaining owers so that the mall is able to charge a ercentage rent only to one of them. We show that the other one is still charged a ositive ercentage rent. Thus, the mall continues to distort cometition between the retailers even in that case. Second, in Section 6.2, we assume that one of the retailers is an anchor store. In line with emirical observations reorted in Gould et al. (2005), we find that the mall charges no ercentage rent (and ossibly no fixed rent) to the anchor store, but still charges a ositive ercentage rent to the other retailer. 6.1 Heterogeneity in rental lease contract This section entertains the ossibility that some retailers have higher bargaining ower or better outside otions than others, so that they must be given better contractual terms by the mall. This extension is motivated by emirical evidence (e.g., Gould et al., 2005), which shows that, although ercentage rent rovisions are extremely common in rental contracts, some retailers are able to negotiate overage thresholds large enough that they only ay the base rent in equilibrium. Accordingly, suose now that one of the retailers, say retailer 1, is not charged a ercentage rent (i.e., r 1 = 0). 22 We are going to establish that the mall still charges a ositive ercentage rent to the other one, thereby distorting cometition. Although introducing heterogeneity is simle, equilibrium exressions get quite comlicated. In equilibrium, we may have either 1 2 or 2 > 1. We first assume that the equilibrium rices satisfy 1 2 and show that this condition, in fact, holds in the end. We then assume 2 > 1, but show that there are no such equilibria. We do not reort the details of this second case for 22 This retailer may also be able to negotiate a lower base rent, but this would not change the analysis that follows. Indeed, we could imose a lum-sum discount on the base rent a 1 (see equation (25) below). Clearly, this additional term affects neither the retailer s ricing decisions nor the mall s fees. 21