Merchants vs. Two-Sided Platforms: Competing Intermediation Models

Transcription

1 erchants vs. Two-Sided latforms: Competing Intermediation odels Gary Biglaiser and Andrei Hagiu y RELIINARY AND INCOLETE - LEASE DO NOT CITE February 8, 014 Abstract We build and solve a model of competition between two intermediaries that can choose to o er a continuum of product categories in two modes. The "merchant" mode creates higher consumer willingness-to-pay but incurs higher xed costs relative to the "two-sided platform" (TS) mode. Consumers are heterogeneous in the willingness-to-pay di erential they perceive between a product o ered in the higher quality merchant mode and the same product o ered in the lower quality TS mode. We investigate four distinct competition scenarios which di er in two dimensions: i) consumers singlehome or multihome; ii) intermediaries can o er each product in one mode only or in both modes. In all scenarios, one intermediary acts as the Stackelberg leader by choosing its product mix before the Stackelberg follower. A rst key result is that the Stackelberg leader can completely foreclose the follower only when intermediaries are able to o er products in both modes. Second, we show that the follower always makes larger pro ts under multihoming relative to singlehoming. In contrast, the leader prefers multihoming when intermediaries are restricted to one mode per product, but prefers singlehoming when intermediaries can o er products in both modes. Third and in contrast with classical results in duopoly models with vertical di erentiation, we nd that in some cases the Stackelberg leader chooses a product mix of lower overall "quality" than the Stackelberg follower. Keywords: Competing Intermediaries, erchants, Two-Sided latforms, latform Competition. JEL Classi cations: L1, L, L8 1 Introduction any intermediaries (particularly online) can choose their business model along a spectrum ranging from pure "merchant" that buys goods from suppliers and resells them to buyers (e.g. supermarkets, Amazon with respect to products it sells in its own name, Zappos), to pure "two-sided platform" University of North Carolina, gbiglais@ .unc.edu y Harvard Business School, ahagiu@hbs.edu 1

2 that simply enables suppliers to sell directly to buyers (e.g. ebay, Amazon with respect to products sold by third-party sellers). The monopoly choice of the optimal intermediation model along this spectrum is driven by a series of tradeo s, which are analyzed in Hagiu and Wright (01, 014). In this paper, we investigate the equilibrium intermediation choices of two competing intermediaries by focusing on one speci c tradeo. Speci cally, the merchant mode allows an intermediary to create higher willingness-to-pay for buyers (e.g. by providing additional services, a uni ed buyer interface, more convenient and faster delivery, certi cation, etc.), but at higher xed costs, relative to the two-sided platform (TS) mode. For example, it is signi cantly cheaper for Amazon to expand into a new product category by allowing third-party sellers to o er it on its site. On the other hand, by incurring the higher xed cost necessary to build the capability of o ering the new product category itself, Amazon could create higher value for buyers. In our model, all consumers view a product o ered in the merchant mode as being of higher quality than the same product o ered in the TS mode, but consumers have di erent views of the quality di erence. Thus, the possibility for intermediaries to choose between two modes (merchant vs. TS) introduces a new dimension along which they can vertically di erentiate. At the same time, however, it also allows the intermediary that moves rst to pre-empt (and sometimes fully foreclose) its competitor. Indeed, in our duopoly model one rm (the Stackelberg leader or the incumbent) chooses which products to o er under each one of the two modes before its rival (the Stackelberg follower or the entrant). After the intermediaries have chosen their products line-ups, they simultanously choose prices for each of their products o ered in each mode. 1 We analyze di erent variants of this duopoly model, which di er in two important dimensions. First, we distinguish between two alternative scenarios of consumer behavior: multihoming - i.e. consumers can buy products from both intermediaries - or singlehoming - i.e. each consumer must make all their product purchases from the same intermediary. Second, we investigate two possibilities for rms: in one case, rms are restricted to o ering any given product in a single mode only; in the other case, rms can o er products in both modes. Consequently, there are four di erent duopoly competition scenarios. By comparing equilibrium outcomes between them, we derive several interesting results regarding the e ect of the nature of competition on foreclosure, incumbency advantage, equilibrium pro ts and product line-ups. First, we nd that foreclosure is only possible when rms are able to o er products in both modes ( and TS). In that case, the incumbent can introduce " ghting brands," i.e. products that are o ered in the lower quality TS mode solely in order to pre-empt the entrant from o ering 1 Our modeling approach is related to Champsaur and Rochet (18), where rms rst choose their product lines and then choose prices. There are, however, two important di erences. First, in Champsaur and Rochet (18) consumers only have demand for a single product, whereas in our model consumers are interested in all available product categories. Second, in order to capture the notion of an incumbent, we allow one rm to choose its product mix before the other. In Champsaur and Rochet (18) rms always move simultaneously.

3 the same products. The incumbent is then able to extract larger revenues by selling the merchant versions of the same products as a monopolist. A closely related result is that the two intermediary rms have opposite preferences regarding the ability to o er products in both modes: introducing that ability always increases the incumbent s pro ts and decreases the entrant s pro ts. Second, we nd that the two intermediary rms have di erent preferences regarding consumer singlehoming and multihoming. The entrant always prefers multihoming to singlehoming. The incumbent prefers multihoming when rms can o er each product in a single mode only, but prefers singlehoming when rms can o er products in both modes. The preference for multihoming is intuitive. Consumer multihoming tends to relax price competition: losing a consumer for one product does not preclude a rm from selling that same consumer a di erent product. In contrast, consumer singlehoming leads rms to engage in "winner-take-all" competition for each consumer s business - this creates stronger incentives for rms to try to steal consumers from each other. The reason this intuition fails to apply to the incumbent when rms can o er products in both modes is once again related to the possibility of foreclosure. When foreclosure is possible, more intense price competition (singlehoming) makes it easier for the incumbent to keep the entrant out. Third, a striking result is that in some cases the "quality" chosen by the incumbent in equilibrium is lower than the entrant s (although the incumbent always makes higher pro ts than the entrant). At a high level, this result seems to stand in stark contrast with the classic work of Shaked and Sutton (18): in a duopoly model with rms o ering a single product each, they show that the incumbent always chooses a higher product quality than the entrant. The key di erence is that in our model the notion of "quality" is not as straightforward: it is determined by the number of products sold in the merchant mode relative to products sold in the TS mode (the former are perceived as higher quality by consumers). The scenario with the incumbent o ering lower "quality" than the entrant occurs when consumers multihome and rms can o er each product in a single mode only. In that case, it is sometimes pro table for the incumbent to o er all products in the TS mode and force the entrant to o er a limited number of products in the merchant mode, which overall yields less competition than if the incumbent o ered some products in the merchant (higher quality) mode. The rest of the paper is organized as follows. In the next section, we present the modelling set-up. In section, we brie y analyze the monopoly benchmark. In section 4 we analyze the two duopoly scenarios corresponding to consumer multihoming, while section 5 focuses on the two duopoly scenarios corresponding to consumer singlehoming. We compare equilibrium pro ts and product mixes across the four duopoly settings in section 6, before concluding in section 7. At a high level, the use of " ghting brands" is similar to the mechanism formalized by Johnson and yatt (00), from whom we also borrow the terminology.

4 odel There is a continuum [0; N] of product varieties, each of which is supplied by an industry of perfectly competitive suppliers, whose cost we normalize to 0. There is a continuum of measure 1 of consumers, each of whom is interested in all product varieties. The only way consumers can have access to products is through one or two intermediary rms. Each product can be o ered by each intermediary in one of two modes. One mode is called the "merchant mode" or mode in short. The other is called the "two-sided platform mode" or TS mode in short. Each consumer has willingness to pay v for any of the N products acquired in the mode. On the other hand, consumers di er in their willingness to pay for products acquired in the TS mode. Speci cally, consumer derives utility v from acquiring any of the N products from an intermediary in the TS mode, where is uniformly distributed on [; 1] with density 1. We assume 1=. An 1 implication of this assumption is that a monopoly intermediary that only o ers a product in the TS mode will always price it at v so that all consumers buy the product. Also, there will be no scope for price discrimination by o ering both versions of the good: a rm always prefers that consumers purchase the good in the mode. Our formalization of the di erence between the two modes is meant to capture an important aspect of the di erence between merchant-type intermediaries and two-sided platform intermediaries (see Hagiu and Wright 01 for an overview). Speci cally, merchants (e.g. supermarkets, Amazon with respect to products it sells in its own name, Zappos) are able to create higher buyer willingness-to-pay by taking control over products from suppliers and providing additional services, e.g. uni ed and higher-quality buyer interface, more convenient and faster delivery, certi cation, etc. In contrast, two-sided platforms (e.g. ebay, Amazon with respect to products sold by third-party suppliers) get less involved in supplier-buyer transactions, which typically leads to a lower-quality buyer experience overall as individual suppliers are unable to match the level of additional services o ered by a merchant. Thus, in our model consumers are heterogenous in how much they care about the superior service implied by the mode. Higher consumers are those who care less about that di erence. In turn, we assume that the superior service of the mode is achieved by incurring higher costs per product variety relative to the TS mode. Speci cally, we assume that an intermediary o ering N products in the mode and N products in the TS mode incurs total xed costs equal to N + "N, where " > 0 is positive but small. Thus, there are diseconomies of scope in o ering product varieties in the mode due to the fact that scarce resources of the rm must be allocated across products categories in order to provide the necessary service. On the other hand, rms can o er products in the TS mode using a constant returns to scale technology (no additional services are necessary). arginal costs are normalized to 0 for both modes. 4

5 Finally, we assume that regardless of the mode chosen for a given product, the price charged to buyers is always chosen by the intermediary. Thus, in our model the di erence between the mode and the TS mode is entirely captured by di erences in cost structure and consumer willingnessto-pay. In particular, we abstract away from tradeo s between the two intermediation modes that are driven by di erences in the allocation of control rights - these are studied in Hagiu and Wright (014). Our assumption is not unrealistic: as pointed out by Hagiu and Wright (014), prices charged to buyers are most likely to be determined through contracts between suppliers and the intermediary. Furthermore, intermediaries hold all the bargaining power: recall we have assumed perfectly competitive suppliers for each product variety. There are two intermediaries: rm 1 and rm. The timing of the competition game we consider throughout the paper is as follows: 1. Firm 1 chooses which products to o er in each mode ( or TS) and incurs the corresponding xed costs.. Firm chooses which products to o er in each mode (having observed rm 1 s product line-up choices) and incurs the corresponding xed costs.. Firms simultaneously choose prices for their products o ered in each mode (possibly di erent prices for a product o ered in both modes). Consumers make their purchasing decisions. Consistent with this timing, we will sometimes refer to rm 1 as the "Stackelberg leader" or "incumbent" and to rm as the "Stackelberg follower" or "entrant". There are two reasons for our choice of Stackelberg timing for product line choices instead of simultaneous timing. First, one of the main objectives of our analysis is to determine how the incumbent s early mover advantage is a ected by the mode of competition. In particular, we wish to determine conditions under which rm 1 can foreclose rm. Second, from a methodological point of view, if rms make their product line choices simultaneously and before choosing prices (also simultaneously) then in general there may not be a pure strategy equilibrium in the product line selection stage. Our assumption that rms choose product line-ups (or "quality") rst and then prices, is reminiscent of the model in Kreps and Sheinkman (18), where rms choose capacities and then prices. Indeed, we view product line-ups as a long-run variable: it takes longer for rms to change products o ered in each mode, whereas prices can be changed more easily. We will examine a series of models that di er in two key dimensions. One is whether rms can o er their products in both modes ( and TS) or in one mode only. The second is whether consumers can make purchases from both rms - i.e. multihome - or must make all of their purchases 5

6 from one rm only - i.e. singlehome. We thus examine four di erent competition scenarios in order to test how the incumbency advantage changes as the rms strategy space and consumers ability to purchase from multiple rms change. onopoly Before turning to the competition settings, we rst determine the optimal choices for a monopoly intermediary in terms of prices and product line choices. The monopoly case will serve as a useful benchmark when we turn to analyzing the four competition scenarios. First, it is never optimal for the monopolist to o er the same product in both modes. Indeed, if both modes are available for a given product, it is always a dominant strategy for the monopolist to only sell the version of the product at a price equal to v (slightly below), which extracts the entire consumer surplus. Selling both the and the TS version at any combination of prices will necessarily result in revenues less than v. Thus, it would not make sense to o er the TS mode (which incurs a positive xed cost) for any product also carried in the mode. Second, the monopolist always covers the entire product range. Any product can be o ered in the TS mode only and generate positive net pro ts v " (recall that the xed cost " of selling products in the TS mode is small). Suppose then without loss of generality that the monopolist o ers products [0; N ] in the mode and products [N ; N] in the TS mode. The rm optimally charges v for products and av for TS products. The resulting monopoly pro ts are then (N ) = vn N + v (N N ) " (N N ). The optimal number of products o ered in the mode is leading to optimal pro ts: 8 >< = >: vn + (v(1 v (1 ) + " N = min ; N, vn N if N v (1 ) + " )+") "N if N v (1 ) + " Thus, if is su ciently small then the rm is a pure merchant, i.e. o ers all products in the mode. When passes a certain threshold, the optimal monopoly intermediation model is a hybrid, All products are identical so their ordering is immaterial. 6

7 with the number of products o ered in the mode decreasing in. 4 Competition with multihoming consumers Let us now turn to the rst set of duopoly scenarios. Throughout this section, we assume that consumers can buy products from both rms (i.e. they multihome) and rms cannot condition their prices on where consumers have made other purchases. Consumer multihoming is likely to prevail in markets in which search costs are low or consumers do not perceive a large inconvenience from browsing multiple intermediaries. Consumer multihoming implies that in Stage (price setting) rms compete for consumers on a product-by-product basis ultihoming with one mode per product In this subsection we assume that rms are restricted to o er each product in one mode only - either TS or (or not at all). This may be because an intermediary having chosen the TS mode does not want to compete with its suppliers by also o ering products in the mode. Or because the intermediary derives exogenous bene ts (not modeled here) from committing to a "pure mode" strategy. 4 The following lemma is helpful in the derivation of the full equilibrium. Lemma 1 In any equilibrium with consumers multihoming and rms restricted to one mode per product, every product n [0; N] is either o ered by rm 1 only in the TS mode or by both rms, one in the TS mode and the other in the mode. Every product that belongs to the rst category yields revenues v for rm 1 in stage. Every product that belongs to the second category yields revenues (1 ) v= for the rm that o ers it in the TS mode and 4 (1 ) v= for the rm that o ers it in the mode. roof. If a product n [0; N] is not o ered by either rm, one of them could deviate (in stage 1 for rm 1 or stage for rm ) by o ering that product in the TS mode. This would bring in additional pro ts v " > 0. Furthermore, if both rms o ered product n in the same mode, they would derive negative pro ts from that product (counting xed costs), which cannot be part of an equilibrium. Finally, suppose that rm i o ers product n in the mode at price p, while rm j o ers it as a TS at price p, where fi; jg = f1; g. Consumer buys the product from rm i if and only if v+p v p v p, which implies that rm i s stage revenues from product n are p, 1 v while rm j s stage revenues from that product are p 1 1 v+p p v. The stage equilibrium is then p = (1 ) v= and p = (1 ) v=, yielding revenues 4 (1 ) v= for rm i and (1 ) v= for 4 One such reason might be fending o antitrust investigation. p 7

8 rm j. Thus, if rm 1 o ers product n in the mode in equilibrium, it must be that rm o ers the same product in the TS mode. Note however that the converse is not necessarily true: if rm 1 o ers product n in the TS mode, then in equilibrium rm either o ers it in the mode or not at all (if the xed cost of the products that rm already o ers in the mode is too high). Finally, note that it is a dominated strategy for rm 1 to not o er all products: it can guarantee positive pro ts for any product by o ering it in the TS mode. Using Lemma 1, we can derive the equilibrium for the entire game (the proof is in the appendix): roposition 1 When consumers multihome and rms are restricted to at most one mode per product, the equilibrium product line-ups and pro ts are as follows: If N (1 )v + " then rm 1 o ers all products [0; N] in the mode, while rm o ers all products in the TS mode. ro ts are: If (1 )v + " N 1 = = (71+1)(1 )v + 18(10 1) h (1 )v 4 (1 ) vn (1 ) vn "N N "(6v(1 )+") then rm 1 o ers products v(10 1) i + " ; N h i (1 )v 0; + " in the mode and products in the TS mode, while rm o ers products h i h i (1 )v 0; + " in the TS mode and products (1 )v + " ; N in the mode. ro ts are: 1 = = (1 ) vn 7 (1 ) vn + (1 ) v 18 (1 ) v 6 " N N (1 ) v (1 " ) v " N + " If N (71+1)(1 )v "(6v(1 )+") + 18(10 1) while rm only o ers products then rm 1 o ers all products [0; N] in the TS mode, v(10 1) h i 0;, all in the mode. ro ts are: 4(1 )v 1 = vn = 8 (1 ) v 81 4 (10 1) (1 ) v 81 "N Several observations are in order. First, consider the third parameter region de ned in the proposition above, where N (71+1)(1 )v "(6v(1 )+") +. Here, the Stackelberg leader rm 1 18(10 1) v(10 1) 8

9 does not o er any products in the mode; instead, it chooses to only o er lower quality products as a pure TS. This is a counter-intuitive result, especially since the marginal cost for rm 1 to add one product in the mode is 0. The logic of the result is as follows. If rm 1 chooses to deviate by o ering a product in the mode, then rm s best response will be to o er that same product in the TS mode, so rm 1 makes pro ts 4 (1 ) v= from selling that product. If instead rm 1 o ers the product as a TS then rm s best response is not to o er the product at all in this parameter region. This is because rm is already o ering too many products in the mode, so the xed cost of selling an additional product is high enough that rm prefers not to compete on it. In this scenario, rm 1 is a monopolist TS on the product in question, so it makes pro ts v from selling it. For rm 1 to prefer this outcome, v must exceed 4 (1 ) v=. Furthermore, rm must prefer not to o er the product at all when rm 1 o ers it as a TS. In other words, the revenue from o ering the product in the mode when rm 1 o ers it in the TS mode, 4 (1 ) v=, must be less than or equal to the marginal cost of o ering an additional product in the mode, 4(1 )v = 4 (1 ) v=. The desired inequality clearly holds. Second, as increases, rm 1 o ers fewer products in the mode: it goes from N to (1 )v )v 18(10 1)N and then down to 0. In particular, at = (71+1)(1 N 1 = (1 )v + " "(6v(1 )+") + vn(10 1) + ", rm 1 goes from o ering > 0 products in the mode to o ering no products. At that point, the trade-o mentioned above kicks in: rm 1 drops the mode entirely and o ers all products in the TS mode, knowing that mode xed costs are too high for rm to o er all products in the mode. Thus, there is a positive measure of products that rm 1 prefers to o er as a TS monopolist, rather than o er them in the mode and face competition. Third, rm 1 s pro ts are decreasing in in the rst two regions and increasing in on the third region. This is simply because in the rst two regions, rm 1 o ers some positive measure of products in the mode, hence the higher the xed cost of products, the lower rm 1 s pro ts. On the other hand, in region, rm 1 does not o er any products in the mode, but rm does, so that a higher hurts rm by inducing it to lower the number of products it o ers. This in turn bene ts rm 1, who becomes a monopolist TS for more products. 4. ultihoming with multiple modes per product Suppose now that rms can o er each product in both the mode and the TS mode (they can still o er products in a single mode as well). Again, we start with a lemma. Lemma In any equilibrium with consumers multihoming and rms allowed to o er products in both modes, rm 1 always o ers all N products in the TS mode and rm o ers no products in the TS mode.

10 roof. First, suppose rm 1 o ers products [0; N 1 ] in the mode only. Then rm s best response is to o er products [0; N 1 ] in the TS mode, which yields revenues 4v (1 ) N 1 = for rm 1 on products [0; N 1 ]. But rm 1 could do strictly better by also o ering products [0; N 1 ] in the TS mode. Indeed, this would ensure that rm makes negative pro ts on products [0; N 1 ] no matter in which mode it o ers them, so rm s best response is to not o er products [0; N 1 ] at all. This means that rm 1 would be able to derive revenues vn 1 from products [0; N 1 ], in exchange for an increase in xed costs equal to "N 1 - clearly a pro table deviation if N 1 > 0. Second, for any given product, rm 1 makes higher pro ts by o ering it in the TS mode than by not o ering it at all. Indeed, if rm 1 o ers a product in the TS mode then rm will either o er the product in the mode or not at all (o ering the product in the TS mode is a dominated strategy due to Bertrand competition). This implies that by o ering a product in the TS mode, rm 1 can make pro ts of at least (1 ) v= " > 0. Thus, rm 1 always o ers all products in the TS mode. Consequently, rm would lose money on any product o ered in the TS mode. In accordance with the lemma, suppose (without loss of generality) that in equilibrium rm 1 o ers products [0; N 1 ] in both modes and products [N 1 ; N] in the TS mode only, while rm only o ers products [N 1 ; N ] in the mode, where N N. In a sense, the products [0; N 1 ] o ered by rm 1 in the TS mode serve as " ghting brands," i.e. a credible commitment which dissuades rm from o ering them and thereby allows rm 1 to extract maximum mode pro ts from them. The following proposition (proven in the appendix) completes the characterization of the equilibrium. roposition When consumers multihome and rms are allowed to o er products in both modes, rms product choices and equilibrium pro ts are as follows: If N (1 ) v 1 + q (1 ) rm is foreclosed (it does not o er any product). ro ts are: If N (1 products h (1 ) v 1 + i )v ; N q then rm 1 o ers all products [0; N] in both modes and 1 = vn N (1 ) the mode only. ro ts are: "N and = 0 then rm 1 o ers products h 0; i (1 )v in the TS mode only, while rm o ers products in both modes and i in h (1 )v ; 1(1 )v 1 = vn + (1 ) (8 161) v 16 "N and = 8 (1 ) v 81 10

11 Thus, for low, rm 1 nds it pro table to fully foreclose rm by o ering all products in both modes. This is simply because a lower reduces rm 1 s cost of o ering products in the mode (it already o ers everything in the TS mode) and any product o ered by rm 1 in both modes e ectively forecloses rm from o ering it. As increases, rm 1 no longer nds it pro table to o er all products in the mode, which opens the door for rm to enter by o ering in the mode some of the products that rm 1 only supplies as a TS. 5 Competition with singlehoming consumers In this section we analyze the duopoly scenarios in which consumers can only visit one rm for all of their product purchases, i.e. they singlehome. Consumers are most likely to singlehome when it is costly or inconvenient to browse multiple intermediaries for the products they are looking for. Furthermore, although not captured in our model, consumers may receive bene ts from buying more products from the same rm. Just like in the previous section, we examine two cases: (i) each rm can o er a given product in one mode only ( or TS); (ii) rms can o er products in both modes. 5.1 Singlehoming with one mode per product Denote by Ni the number of products that rm i o ers in the mode and by Ni the number of products that rm i o ers in the TS mode, for i = 1;. When products can only be o ered in a single mode, Ni + Ni N. The next lemma (proven in the appendix) determines the Stage equilibrium as a function of product line choices Ni ; Ni, i = 1;. Lemma Suppose N > N1. Then there exists y [; 1] such that in the Stage equilibrium all consumers [; y] go to rm 1 and all consumers [y; 1] go to rm. There are three cases: If ( 1) N N1 N 1 N ( ) N N1 then Stage equilibrium revenues are 1 = v N1 N ( 1) N N1 (1 ) (N N1 ) = v N N1 + ( ) N N1 (1 ) (N N1 ) If ( 1) N N 1 N 1 N then rm 1 makes 0 revenues in Stage. If N 1 N ( ) N N 1 then rm makes 0 revenues in Stage. 11

12 Results for the case N < N 1 are obtained by symmetry. A key result in the proof of the lemma is that in any Stage equilibrium only the total prices charged by each rm matter. This is intuitive: given that each consumer has the same valuation for all products and she makes all of her product purchases at the same rm (singlehoming), consumers make their rm choice based on the total price they expect to pay at each rm. Note that N > N 1 implies N 1 > N if both rms are to make positive revenues in Stage (interior equilibrium). Using Lemma, we can derive the equilibrium product line choices and pro ts for the entire game. roposition When consumers singlehome and rms are restricted to at most one mode per product, there exists a unique equilibrium, determined as follows: 4v(1 ) If N +" then rm 1 chooses N 1 = N and N1 = 0, while rm chooses N = 0 and N = N. Equilibrium pro ts are 1 = 4v (1 ) N N and = v (1 ) N "N If N 4v(1 ) + " then rm 1 chooses N 1 = 4v(1 ) chooses N = 0 and N = N. Equilibrium pro ts are 1 = 8v (1 ) 81 " N 4v (1 ) " + " and N 1 = N N 1, while rm and = 4v (1 ) 81 "N Thus, when the xed cost of products is small, we essentially obtain maximum di erentiation between the two rms: rm 1 o ers all products in the mode (higher "quality"), while rm o ers all products in the TS mode (lower "quality"). This is the exact same outcome as with multihoming consumers, single mode per product and low ( rst region in roposition 1). As 4v(1 ) N increases past + ", the two rms remain di erentiated but the "quality" di erential is N decreasing because rm 1 starts substituting products for TS products in order to lower its xed costs, whereas rm keeps o ering all products in the TS mode. 4v(1 ) (71+1)(1 )v "(6v(1 )+") Let us now focus on the parameter range + " N +, so that 18(10 1) v(10 1) we are in the second region of roposition (singlehoming, single mode) and the second region of roposition 1 (multihoming, single mode). Firm 1 behaves very similarly in both cases: it o ers some products in the mode and the rest in the TS mode, with the number of products declining in. Firm behaves quite di erently: it covers the entire product space in both cases, 1

13 but under multihoming (roposition 1) it o ers some products in the mode, whereas under singlehoming (roposition ) it only o ers TS products. This di erence in behavior by rm can be explained as follows: under multihoming, rm aims to di erentiate product by product, whereas under singlehoming, competition is in terms of total utility (cf. comment after Lemma ), so di erentiation is also achieved in terms of total utility. Thus, in order to di erentiate under singlehoming, rm chooses the lowest possible total "quality" conditional on o ering all products (as the rst mover, rm 1 never allows rm to be the higher "quality" rm and thereby derive larger pro ts). Furthermore, note that roposition does not exhibit the discontinuity in the number of products o ered by rm 1, which occurs at N = (71+1)(1 )v "(6v(1 )+") + in roposition 1. 18(10 1) v(10 1) Indeed, under singlehoming rm never considers o ering in the mode products that rm 1 only o ers in the TS mode. Again, this is because rms compete in total utility only, so rm always achieves maximum di erentiation (conditional on being the lower quality rm) by o ering all products in the TS mode. Finally, note that as grows very large, we approach Bertrand competition, with rm o ering all products in the TS mode and rm 1 o ering almost all products in the TS mode Singlehoming with multiple modes per product Suppose now that rms can o er each product in both the mode and the TS mode (they can still o er products in a single mode as well). The following proposition (proven in the appendix) establishes that in this scenario the incumbent ( rm 1) always forecloses the entrant ( rm ). roposition 4 If consumers singlehome and rms can o er products in both modes then rm 1 always forecloses rm by o ering all products in the TS mode and N1 = min (1 )v ; N products in the mode. ro ts are: 1 = 8 >< >: = 0 vn N "N if N v (1 ) vn + v (1 ) "N if N v (1 ) Thus, we obtain the rather striking result that rm 1 can foreclose entry by rm simply by adding the TS mode to all products o ered in the mode in the monopoly product line-up. 6 5 The only reason we do not get all the way to perfect Betrand competition is " > 0. 6 N1 is very similar to the monopoly choice of products in the mode. The di erence is that here rm 1 always o ers all products in the TS mode. 1

14 Note that these TS products are never purchased in equilibrium: as a de facto monopolist in Stage, rm 1 prefers selling the version only. Thus, just like in the case when consumers multihome, foreclosure is only possible when rms can o er products in both modes. The di erence is that now foreclosure occurs all the time, whereas it only occurred for low enough when consumers multihomed (cf. roposition ). This is understood by noting that singlehoming generally creates more intense price competition than multihoming. Under multihoming, in order to foreclose rm, rm 1 had to o er all products in both modes, which becomes too costly for large. In contrast, under singlehoming, rm 1 already makes it very di cult for rm to enter by o ering all products in the TS mode. By adding the monopoly number of products, rm 1 can then ensure that rm cannot hope to make positive pro ts by entering, due to intense price competition. 6 Comparison of equilibria We now turn to the comparison of rm pro ts and product line choices across the four di erent competition scenarios that we have studied. 6.1 Equilibrium pro ts First, we compare the pro ts of both rms using ropositions 1,,, and 4. We obtain the following results (all comparisons involve straightforward calculations in, N and v). roposition 5 i) Firm 1 (Stackelberg leader) always makes higher pro ts than rm (Stackelberg follower). ii) Firm 1 makes higher pro ts, whereas Firm makes lower pro ts when rms can o er products in multiple modes relative to the case when they must o er each product in a single mode. iii) If rms can o er each product in a single mode only then both rms always makes higher pro ts when consumers multihome relative to the case when they singlehome. iv) If rms can o er each product in multiple modes then rm 1 makes higher pro ts when consumers singlehome, whereas rm makes higher pro ts when consumers multihome. Regarding result (i), recall than in a traditional duopoly context, the Stackelberg leader makes larger pro ts than the Stackelberg follower in a Cournot setting, but lower pro ts in a Bertrand setting. Our modeling set-up with rms rst choosing product line-ups and then prices is similar in spirit to the Kreps and Sheinkman (18) set-up, in which rms choose capacities and then prices - the outcome in that model is the Cournot equilibrium. In other words, capacity investments 14

15 (quantity in Kreps and Sheinkman 18 and product "quality" in our model) serve as credible commitment devices that provide an advantage to the Stackelberg leader. Result (ii) is understood by noting that the ability to o er products in multiple modes allows the leader, rm 1, to establish the TS modes of some products as " ghting brands" that serve solely to reduce competition by pre-empting (and sometime fully foreclosing entry of) rm. The follower ( rm ) naturally has the opposite preference. A similar logic applies to result (iv). Conditional on o ering products in multiple modes, rm 1 s ability to foreclose rm is enhanced when moving from multihoming to singlehoming consumers, because price competition is more intense under singlehoming. As a result, the two rms have once again opposite preferences: rm 1 prefers singlehoming, whereas rm prefers multihoming. Result (iii) says that the two rms have the same preference over consumer homing behavior when they are restricted to o er each product in a single mode: both rms make higher pro ts under multihoming than under singlehoming. This is because multihoming relaxes price competition between the two rms. Indeed, when consumers multihome, competition occurs product by product: losing a consumer for one product does not preclude a rm from selling that same consumer a di erent product. On the other hand, if consumers singlehome then rms engage in "winner-takeall" competition for each consumer s business - this creates stronger incentives for rms to try to steal customers from each other. Note the contrast with result (iv): with a single mode per product, foreclosure is not possible so rm 1 also prefers less intense price competition. 6. Equlibrium average product "quality" We now turn to the comparison of equilibrium "quality" choices, i.e. the total consumer utilities created by the equilibrium product mixes of each rm. Speci cally, denote by qi m1 () the total willingness-to-pay of consumer [; 1] for rm i s products in the multihoming equilibrium with one mode per product, where i = L; F (L stands for the Stackelberg leader, i.e. rm 1; F stands for the Stackelberg follower, i.e. rm ). Similarly, de ne qi m () for the multihoming equilibrium with multiple modes, qi s1 () for the singlehoming equilibrium with one mode, and qi s () for the singlehoming equilibrium with multiple modes. For simplicity, we refer to these willingnesses-to-pay as "qualities" chosen by the two rms. Comparing quality choices across the four duopoly equilibria, we obtain: roposition 6 i) All consumers view the equilibrium quality of rm 1 (Stackelberg leader) as higher than that of rm (Stackelberg follower), except when consumers multihome, rms can o er each product in a single mode only and 4(1 )v (71+1)(1 )v 4(1 )v N. In that case, consumers < 18(10 1) N view rm s quality as higher than rm 1 s. ii) For the Stackelberg leader, q m1 L () qs1 L () qs L () qm 1 () for all and all parameter 15

16 values. iii) For the Stackelberg follower, 0 = qf s parameter values. () qm F () min fqm1 () ; qs1 ()g for all and F F Result (i) indicates that in most cases, rm 1 s product mix if of higher quality than rm s for all consumers. This is in line with the Shaked and Sutton (18) result that the rst mover in a duopoly with vertical di erentiation achieves higher pro ts by always choosing a higher quality. However, our model produces an interesting exception to this broad principle, which occurs when consumers i multihome, rms can o er each product in a single mode only and N. h (71+1)(1 )v ; 18(10 1) 4(1 )v Recall from our discussion of roposition 1 that in this parameter range rm 1 only o ers TS products because is large enough that rm does not react by covering the entire product range with products in the mode. Thus, rm 1 is actually a monopolist on some products, which yields higher pro ts than competing as the higher quality producer for the same products. This scenario provides an important di erence between our set-up and traditional vertical di erentiation models like Shaked and Sutton (18). Speci cally, the scenario in which the Stackelberg leader o ers lower "quality" than the Stackelberg follower can only occur when rms compete product by product (consumer multihoming) and rms can choose di erent qualities for each product. In contrast, the Shaked and Sutton (18) model is closest to the scenario with singlehoming and single mode per product in our model. A nal important di erence between our model and the Shaked and Sutton framework is that higher quality is more costly in our model, while in their model it is costless to increase the quality of a rm s o ering. Result (ii) indicates that the quality chosen by rm 1 is higher when rms are allowed to o er each product in both modes relative to the case when they are restricted to one mode per product - this holds under both singlehoming and multihoming. The reason is as follows. Firm 1 uses multiple modes to engage in pre-emption (and possibly complete foreclosure) of rm : speci cally, rm 1 can use the TS mode as a " ghting brand" to pre-empt rm from o ering a given product, which then liberates rm 1 to extract maximum pro ts with the version of that product, which in turn means rm 1 is able to o er more products in the mode, leading to higher overall quality. Just like pro ts in roposition 5, the respective qualities chosen by rm behave in the opposite way: result (iii) says that rm chooses higher quality when rms are restricted to o er each product in a single mode (both under singlehoming and multihoming). The reason is similar: since rm 1 increases quality by o ering more products (when going from single mode to multiple modes), rm is forced to reduce the number of products it o ers in favor of TS products, in order to di erentiate. Another interesting part of result (ii) is that when rms can o er each product in one mode only, rm 1 chooses higher quality under singlehoming relative to multihoming, although single- 16

17 homing yields lower pro ts (cf. result (iii) in roposition 5). This is understood by recalling that foreclosure is not possible when only a single mode is allowed per product. In this case, rm 1 must seek to maximize vertical di erentiation from rm, which is a more pressing imperative under singlehoming, because this is when price competition is more intense. This result is reversed when rms can o er each product in multiple modes. In that scenario, rm 1 does not have to seek vertical di erentiation under singlehoming because it can completely foreclose rm. As a result, rm 1 s chosen quality is higher under multihoming. Finally, note that, with one possible exception, the ranking of qualities chosen by rm is the reverse of that of qualities chosen by rm 1. This plays into the idea that the rms qualities are strategic substitutes, just like capacities are strategic substitutes in the Kreps and Scheinkman (18) model. 7 Conclusion We have analyzed a duopoly model with competing intermediaries choosing to o er products under one or two modes - merchant or two-sided platform. We have shown that the ability to o er products under multiple modes leads to the possibility of foreclosure. We have also derived several results regarding equilibrium intermediary pro ts and product mixes that stand in contrast with the traditional literature on vertically di erentiated duopolies. Our analysis can be extended in a number of ways. First, one could introduce strategic suppliers that maintain decision rights in the TS mode. This would enrich the factors that drive the intermediaries to choose one mode or the other. Second, one could introduce demand di erences across products, i.e. some products having a larger and/or more elastic demand than others. Again, this would introduce additional factors that drive equilibrium choices of intermediation modes. References [1] Biglaiser, G. (1) iddlemen as Experts, Rand Journal of Economics, 4, 1. [] Casadesus-asanell, R. and F. Zhu (010) "Strategies to Fight Ad-Sponsored Rivals," anagement Science, 56(), [] Champsaur,. and J.C. Rochet, (18), ultiproduct Duopolists, Econometrica, 57, [4] Hagiu, A. and J. Wright (01) "Do You Really Want to Be an ebay?" Harvard Business Review, 1(),

18 [5] Hagiu, A. and J. Wright (014) "arketplace or Reseller?" Harvard Business School working paper, No [6] Johnson, J. and D. yatt (00) "ultiproduct Quality Competition: Fighting Brands and roduct Line runing," American Economic Review, 7 (), [7] Kreps, D. and J. Scheinkman (18) "Quantity recommitment and Bertrand Competition Yield Cournot Outcomes," Bell Journal of Economics, 14, 6-7. [8] Rochet, J.-C. and J. Tirole (006) Two-Sided arkets: Where We Stand, Rand Journal of Economics, 7 (), [] Rysman,. (00) The Economics of Two-Sided arkets, Journal of Economic erspectives,, [10] Shaked, A. and J. Sutton (18) "Relaxing rice Competition Through roduct Di erentiation," Review of Economic Studies, 4, -1. [11] Stone, B. (01) The Everything Store - Je Bezos and the Age of Amazon, New York, NY: Little, Brown and Company. 8 Appendix 8.1 roof of roposition 1 From Lemma 1, we know that rm 1 covers the entire range of products categories [0; N]. Thus, in any equilibrium rm 1 o ers products [0; N 1 ] in the mode and products [N 1 ; N] in the TS mode (without loss of generality). Lemma 1 then implies that rm necessarily o ers products [0; N 1 ] as a TS and no other products as a TS. Thus, assume without loss of generality that rm o ers products [N 1 ; N ] in the mode and does not o er products [N ; N] at all, where N 1 N N. Firm pro ts are therefore: 1 = 4 (1 ) vn 1 N 1 + (1 ) v (N N 1 ) + v (N N ) " (N N 1 ) = (1 ) vn 1 "N (1 ) v (N N 1 ) Firm 1 chooses N 1, then rm chooses N having observed N 1. We have: N (N 1 ) = min N (1 18 ) v ; N (N N 1 )

19 This implies: d 1 dn 1 = 4 (1 ) v N 1 + " ( v if N1 N (1 )v if N 1 N 4(1 )v 4(1 )v 4(1 )v Thus, d 1 dn 1 < 0 for all N 1 N (since 1= and " is small). If N 7(1 )v + " then d 1 dn 1 < 0 for all N 1, so N1 = 0 and N = 4(10 1)(1 )v 1 = vn "N and 81 = 8(1 ) v h 81 If N 4(1 )v then N = N and N1 = min (1 )v + i. " ; N Thus: 4(1 )v < N. This leads to If N (1 )v + " then 1 = If (1 7(1 )vn )v + " 4(1 )vn 4(1 )v N then 1 = (1 ) v 6 N " (1 )v N + " N and = (1 )vn "N N (1 )vn + (1 ) v " 18 (1 )v " and = Suppose now 4(1 )v N one yields higher pro ts to rm 1: 7(1 )v. Then either N 1 = 0 or N 1 = (1 )v + ", depending on which If N 1 = 0 then N = 4(1 )v and therefore 1 = vn If N 1 = (1 )v + " then N = N and therefore 1 = and = 7(1 )vn (1 ) v 6 N " (1 )v N + " 4(10 1)(1 )v "N and 81 = 8(1 ) v 81 (1 )vn + (1 ) v " 18 N (1 )v Comparing the last two pro t expressions for rm 1, we have N1 = 0 (respectively, N1 = (1 )v + " ) if and only if N (71+1)(1 )v "(6v(1 )+") (71+1)(1 )v "(6v(1 )+") + (respectively, N + ). 18(10 1) v(10 1) 18(10 1) v(10 1) " 8. roof of roposition Given the discussion before roposition in the text, we know that in equilibrium rms 1 o ers products [0; N 1 ] in both modes and products [N 1 ; N] in the TS mode only, while rm o ers products [N 1 ; N ] in the mode only, where N 1 N N. ro ts are therefore: 1 = vn 1 N 1 = 4 (1 ) v (N N 1 ) + (1 ) v (N N 1 ) + v (N N ) "N (N N 1 ) Thus, we must have: 4 (1 ) v N = min 1 + N 1 ; N

20 If N 1 N 4(1 )v then N = N and rm 1 s pro ts are (taking into account rm s best response): vn 1 N 1 + (1 ) v (N N 1) "N increasing for N 1 (8+)v If N 1 N best response): and decreasing for N 1 (8+)v 4(1 )v then N = vn 1 N 1. 4(1 )v + N 1 and rm 1 s pro ts are (taking into account rm s + 4 (1 ) v 81 increasing for N 1 (1 )v and decreasing for N 1 Since 1=, we always have (1 Suppose rst N N 1 N pro ts: 4(1 )v )v (8+)v, i.e. N + v N (1 )v. < (8+)v. (1 )v 4(1 )v, therefore the equilibrium is N 1 = Second, suppose N N 1 N pro ts: 1 = vn + 4(1 )v (1 ) (8 161) v 16 (1 )v, i.e. N 4 (1 ) v N 1 "N. In this case, rm 1 s pro ts are decreasing for (1 )v < N and N = 1(1 )v "N and = 8 (1 ) v 1(1 )v 4(1 )v, therefore the equilibrium is N 1 = min Third, suppose 1(1 )v 1 = vn N < (8+)v N 81 < N, leading to. Then rm 1 s pro ts are increasing for = N and N = N, leading to (8+)v ; N "N and = 0 (1 )v. Then rm 1 chooses between: option 1: N 1 = (1 )v, which results in N = for rm 1 (same as the rst case above) 1(1 )v (1 )(8 161)v and yields pro ts vn + "N 16 option : N 1 = (8+)v, which results in N = N and yields pro ts (8+) v (1 )vn "N for rm It is straightforward to verify that option 1 dominates for N (8+)v. Thus, the equilibrium is the same as in the rst case above. Fourth and nally, suppose 1(1 )v N (8+)v < (1 )v. Then rm 1 chooses between: option 1: N 1 = (1 )v, which results in N = for rm 1 (same as the rst case above) 1(1 )v (1 )(8 161)v and yields pro ts vn + "N 16 0

21 option : N 1 = N, which results in N = N and yields pro ts vn N the second case above) (1 )(8 161)v "N for rm 1 (same as Let (N) (1 ) vn N the di erence between option and option 1 16 as a function of N. Note that is strictly decreasing in N for N 1(1 )v (1 )v >. And it is straightforward to verify that 1(1 )v > 0 (8+)v. The unique solution to (N) = 0 h i q 1(1 on the interval is N = ( Thus, rm 1 chooses option for )v ; (8+)v N N and option 1 for N N. )v (1 ) 8. roof of Lemma For each rm i, let us order the products it o ers in the TS mode, n 0; Ni, such that the price charged, p i (n), is increasing in n. Similarly, denote by p i (n) the price charged for products n N i ; Ni + Ni, which are o ered in the mode. Clearly, p i (n) v for all n Ni ; Ni + Ni. Thus, for any consumer [; 1], the net utility from going to rm i is u i () = Z N i 0 max v p i (n) ; 0 dn + Z N i +N i N i v p i (n) dn. Note that u 0 i () is increasing (possibly discontinuously) for all. Let then p i p i Ni denote the highest price charged by rm i for a good sold in the TS mode. We will show that if these prices are part of a stage II equilibrium then only the total price i R Ni p 0 i (n) dn + R Ni +N i Ni Case I: p 1 p. p i (n) dn charged by each rm i = 1; matters. Suppose u p 1 =v u 1 p 1 =v. Since u 0 1 () = vn 1 < vn = u 0 () for all p 1 =v, this would then imply that no consumer p 1 =v comes to rm 1, so that rm 1 makes 0 sales on its products priced at p 1. This cannot be an equilibrium: rm 1 could lower its price on all of these products until either it increases its pro ts or the price becomes equal to the next highest price (and then we can restart the same reasoning). Thus, we must have u p 1 =v < u 1 p 1 =v - But this implies that there exists > 0 such that all consumers p 1 =v ; p 1 =v come to rm 1 but do not buy the products priced at p 1. Let then rm 1 decrease p 1 by very small such that p 1 remains its highest price. The resulting loss is lower than (1 p =v) 1, while the resulting gain is 1 p greater than 1 v(1 ). The net e ect is strictly positive if p 1 > v (since > 1=), therefore we must have v p 1 p. This implies that any consumer that goes to any of the two rms buys all products available, so that only the total price matters for both rms in equilibrium. Case II: p 1 < p. 1

22 If u 1 p =v < u p =v then u 1 () < u () for all p =v (again, recall u 0 1 () < u 0 () for all p =v).. In this case, if p > v then rm could slightly decrease p and increase pro ts. Thus, we must have u p =v < u 1 p =v and u () crosses u 1 () exactly once, from below, for p =v. Denote that point of intersection by y (i.e. u (y) = u 1 ()). Suppose u p 1 =v < u 1 p 1 =v In this case, if p 1 > v then, by the same reasoning as above, rm 1 could pro tably decrease p 1. If p 1 v then u 1 () is linear and u () < u 1 () for all ; p =v. This implies that for each rm only the total price matters for demand and rm pro ts. Suppose then u p 1 =v u 1 p 1 =v. Since u p =v < u 1 p =v, u 1 () is linear and u 0 () is increasing for all p 1 =v, there exists a unique x [p 1 =v; p =v[ such that u (x) = u 1 (x). All consumers with [x; y] go to rm 1 while all consumers with [y; 1] go to rm. Let then N min n such that p (n) xv. Any given TS product n N o ered by rm is only bought by consumers [y; 1], who in fact buy all TS products n N (because v > p ). Thus, we can assume without loss of generality (i.e. without changing anything to demands and pro ts) that all TS products n N are priced at p, where N N p = R N p N (n) dn. Clearly, x and y remain unchanged and p =v ]x; p =v], so u p =v < u 1 p =v. Thus, we are now in a scenario in which: u () = ( u 1 () = u 1 (x) + v ( x) N 1 for all x p 1 =v u (x) + v ( x) N for x; p =v u (x) + p vx N + v p =v N for p =v; 1 Since u 1 () > u () for ]x; p =v] we must have N < N 1 (recall N 1 < N since u 1 (y) = u (y), we have: dy dp = N N v (N N1 ) > 1 v ). Furthermore, Let now rm deviate by slightly lowering p by " > 0. The loss due to this deviation is approximately equal to "(N N )(1 y), which is smaller than "(N N )(1 p =v). The gain is at least N 1 1 N p dy dp which is greater than "(N N )p, which in turn is greater than "(N N )(1 p =v) whenever p v(1 ) 1 v > v=. The deviation is therefore pro table whenever p v > v=, so the initial prices can only be part of an equilibrium if p < v. This implies that all rm prices for TS products are lower than v, so that only the total prices matter for each rm (recall that all rm prices for products are lower than v). Thus, for any consumer [; 1] the respective utilities from going at either rm are: " 1, u i () = vn i + vn i i