Bundling, information and platform competition

Transcription

1 undling, information platform competition Keke Sun October 15, 201 bstract This paper studies duopolistic competition between two-sided platforms that connect consumers application developers. We propose a theoretical model in which one platform is allowed to decide whether to bundle with an in-house hset before price competition takes place. In this paper, bundling is a commitment to an aggressive pricing strategy; it is merely deployed to stimulate consumer dem. We introduce different levels of consumer information: developers some consumers are informed about all subscription prices hold responsive expectations, whereas the remaining consumers are uninformed about developer subscription prices form passive expectations. We find that bundling can be profitable when platforms engage in divide--conquer strategies, which involves subsidizing low-externality side (consumers) making profits on high-externality side (developers). We also find that a larger fraction of informed consumers intensifies price competition. Informed consumers respond to price changes by adjusting their own dem as well as their expectations of developer dem. This amplifies the effect of a discount on consumer subscription prices. Therefore, bundling is more effective to stimulate consumer dem when there are more informed consumers. undling is less likely to emerge when there is a larger fraction of informed consumers. Moreover, bundling a high level of consumer information improves consumer welfare. JEL classification: L11, L13, L2, D3, D8 Keywords: Two-sided platforms; undling; Passive expectations; Responsive expectations; Platform competition Universitat utònoma de arcelona arcelona GSE. kekesun.kk@gmail.com. I am thankful to Sjaak Hurkens for his guidance, advice, encouragement. I thank as well Roberto urguet, David Pérez-Castrillo, Xavier Martínez-Giralt, Pau Olivella, Javier Rodríguez Edgardo Lara for comments suggestions. ll errors are mine. Financial support from Spanish Ministerio de Economia y Competitividad is gratefully acknowledged. 1

2 1 Introduction smartphone operating system (OS) platform accommodates applications, makes the interactions between consumers application developers possible. Competition between smartphone platforms is relevant given the phenomenal growth of the smartphone market. This industry has certain features common to other two-sided markets: bundling practice information asymmetry across two sides of the platform. s one of the major competitor, pple s success in hardware has a significant bearing on its success in this industry (Kenney Pon, 2011). undling with a best-selling hset certainly adds to the platform s appeal for consumers 1. s a matter of fact, such bundling practice also exists in the video game industry, where major competitors such as Sony Microsoft bundle the OS platforms with their in-house consoles. lso, there is information asymmetry across two sides of the OS platform. Namely, developers are industry-insiders; they are usually informed about all subscription prices have good predictions of participation decisions on both sides of the platform. In contrast, consumers may not be aware of the fixed fees or royalties that platforms charge to developers. Even if consumers are aware of the developer subscription prices, they may be unable to adjust their expectations of developer dem as they may be uninformed about the structure of it. Similarly, newspaper readers may not be aware of how much the newspaper charges advertisers for listing advertisements. Inspired by the casual observations of bundling practice different levels of consumer information, the goal of this work is to develop a theoretical model to establish the bundling strategy for platforms when there is information asymmetry for users on different sides of the platform. We address two main research questions: 1. When does a platform practice bundling as a profit-maximizing strategy? 2. How does the level of consumer information affect platform competition bundling decision? We consider a two-stage game in which one of the platforms is allowed to make strategic decision, in addition to competing through adjustment of tactical variables. In the first stage, one of the platforms decides whether to bundle with its in-house hset 2, laying the groundwork for the competitive interactions down the line. In the second stage, the platforms make tactical decisions (subscription prices) simultaneously, competition takes place. We do not consider bundling to be an act of predation, but rather a commitment to an aggressive pricing strategy; it is merely a tool to stimulate consumer dem. Within the framework of the Hotelling model, two platforms compete for single-homed consumers 1 iphone has been the top-selling mobile phone in the U.S. Source: boston/blog/mass_roundup/2013/02/apple-top-selling-us-mobile-phone.html, accessed September, We consider pure bundling. Under pure bundling, the hset access to platform can only be purchased as a bundle. ccording to Tirole (2005), the difference between pure bundling tying is that, the tied good is still available on a st-alone basis under tying. Under tying, consumers on platform can still purchase the hset. 2

3 multi-homed developers. Departing from the stard setting of full information responsive expectations for all users, we assume that some consumers all developers are informed about all subscription prices hold responsive expectations, whereas the remaining consumers are uninformed about developer subscription prices hold passive expectations. We find that, when consumers are homogeneous with respect to the valuation of the hset, bundling emerges when platforms engage in divide--conquer strategies, where platforms subsidize low-externality side (consumers) make profits on high-externality side (developers). When consumers are heterogeneous with respect to the valuation of the hset, bundling can also be a tool to target certain types of consumers, i.e., attracting consumers with high valuation of the hset to join the platform. In this sense, bundling is more effective than tying to implement second-degree price discrimination. Our results further show that bundling improves consumer welfare. undling improves utility for the majority of consumers by lowering the subscription price offering more application variety; the remaining consumers also enjoy a lower subscription price when consumer prices are strategic complements. These effects dominate the utility loss caused by the additional aggregate transportation costs, less application variety a lower participation subsidy offered to the minority of consumers when prices are strategic substitutes. We also find that, a larger fraction of informed consumers intensifies price competition because these consumers respond to price changes by adjusting their own dem their expectations of developer dems accordingly. Therefore, bundling is more effective to stimulate consumer dem, hence developer dem through the dem shifting effect, when there are more informed consumers. Consumer surplus increases with the level of consumer information, because a higher level of consumer information leads to lower subscription prices more application variety. The level of consumer information also has an impact on the emergence of bundling: bundling is less likely to emerge when there is a larger fraction of informed consumers. This is because bundling only emerges when the competing platform reduces its consumer subsidy in response, which softens competition; but a higher level of consumer information intensifies competition. The remainder of the paper is organized as follows. Section 2 briefly discusses the related literature. In Section 3, we set up a duopoly model. Section reveals the bundling strategy of the platform by comparing two scenarios, depending on whether the platform practices or does not practice bundling. Section 5 offers an extension when consumers are heterogeneous with respect to the valuation of the hset. Section 6 concludes. 2 Relationship to the Literature Pure bundling is usually considered as an act of predation. Whinston (1990) shows that pure bundling reduces equilibrium profits of all firms; hence, it is usually adopted to deter 3

4 entry or drive the rival out of the market. However, in two-sided markets, this may not be the case. Our paper fits this theme by considering bundling as a tool to stimulate consumer dem. The present work is closely related to Farhi Hagiu (2008) melio Jullien (2012). The former study shows that a subsidy on one side may lead to fundamentally new strategic configurations in oligopoly. Farhi Hagiu (2008) present the conditions upon which a cost-reducing investment by intermediaries may be a successful entry accommodation strategy may also benefit its rival. possible interpretation is that this reduction results from a tying strategy. Prices are not necessarily strategic complements in competition, the effects of cost-reducing investments on prices are ambiguous platforms may earn negative margin on one side. melio Jullien (2012) investigate the effects of tying of independent goods, with single-homing users non-negative pricing platforms. With a non-negative constraint, tying works as an implicit subsidy. In the monopoly case, the platform prefers tying as it is a way to subsidize users that have low network externality. Tying leads to higher participation, higher consumer surplus as well as profits. In the duopoly case, tying on one side makes a platform more or less competitive on the other side depending on externalities of the two sides. The impact of tying on platforms profits also depends on the relative levels of externalities. Total consumer surplus increases in case of high asymmetry in the network externalities between two sides. Tying is used to implement second-degree price discrimination to help a network to coordinate the customers participation. Instead of tying, we study the effect of pure bundling on platform competition. The key features differentiating our work from this line of literature are: firstly, we study the effect of information asymmetry, namely, the level of consumer information, on platform s bundling strategy; secondly, we allow consumers to be heterogeneous with respect to the valuation of the hset. We believe that these features bring our analysis close to reality. Our work is also about information asymmetry across two sides of the platform. The main characteristic of two-sided platforms is the bilateral indirect network externalities where one group s benefit from joining the platform depends on the size of the other group that joins the same platform, which gives rise to a chicken--egg problem (rmstrong, 2006; Hagiu, 2006). The majority of the existing literature on two-sided platform pricing usually assumes that all users have full information about all prices preferences, which implies that all users are able to perfectly predict other s participation decision. In reality, platform users, especially consumers, may not be able to observe all prices or perfectly anticipate the impact of price changes on dems. Hurkens López (201) suggest that passive expectation should be a plausible alternative for responsive expectation in a market with (direct or indirect) network externalities. Passive expectations, first introduced by Katz Shapiro (1985), are fulfilled in equilibrium. Consumers with passive expectations fixate their rational expectation of developer dem do not respond to any price changes on the other side of the platform. In the present work, we allow users on different sides to have different levels of information. We assume developers are always well-informed; they are aware of all prices hold responsive expectations of consumer dem. Consumers are not necessarily as well-informed as developers, not every consumer is aware of how much

5 the platforms charge developers for subscription. Therefore, we assume there is a fraction of consumers who are informed about developer subscription prices hold responsive expectations of developer dem, while the remaining consumers are uninformed about developer subscription prices hold passive expectations. In this spirit, the present paper is very close to Hagiu Ha laburda (201). They study the effect of different levels of information on two-sided platform profits, under both monopoly competition. They assume that developers always hold responsive expectations while all users hold passive or responsive expectations. They show that responsive expectation amplifies the effect of price reductions. monopoly platform can exploit the dem increases due to user s responsive expectation, so it prefers facing more informed users. While more information intensifies price competition, competing platforms are affected negatively when users are well informed. Our work reaches to the same conclusion that more information intensifies price competition regardless of bundling decision. There is one key difference between Hagiu Ha laburda (201) our analysis. They focus on impact of different user expectations on equilibrium allocations in monopoly duopoly contexts, whereas we are interested in the impact of the level of consumer information on platform s bundling decision in duopoly setting, because our work models the competition between smartphone OS platforms where bundling has a significant bearing. 3 The Model 3.1 Platforms Consider two platforms competing for market shares on both sides of the platform, indexed by T =,. Let p C T pd T denote the subscription prices platform T charges to consumers developers, respectively. We assume that the platforms have zero marginal cost of serving these two groups of users, which is consistent with the literature of information goods the reality of digital media industry, where large fixed costs very low marginal costs are observed 3. We allow for negative prices, as it is possible for platforms to subsidize one side of the market. The number of consumers developers on platform T are denoted by n C T n D T, respectively. We allow single-homing on one side multi-homing on the other side. To be more specific, we assume that each consumer decides in favor of only one platform while developers can design applications for both platforms. We extend the stard Hotelling model by allowing the duopoly to serve two groups of users on each side of the market. The unit transportation cost for consumers towards each end is t. It represents the competitiveness of the platforms for consumers. Platform 3 This assumption is made for calculation simplicity. ssuming platforms have marginal cost of c C c D of serving consumer s side developer s side complicates the calculations but do not change the qualitative results of the model. 5

6 are exogenously located at x = 0 x = 1, respectively. Platform T s profit maximization problem is π T = p C T n C T + p D T n D T, where T =,. max p C T,pD T We assume one of the platforms (without loss of generality, platform ) has a killer inhouse hset with quality z marginal cost C, for instance, iphone by pple. For calculation simplicity, we normalize this marginal cost C = 0. Platform is a monopolist in the hset market, it can decide whether to bundle with this hset or not. 3.2 Consumers There is mass 1 of consumers uniformly distributed along the unit interval, each of whom chooses at most one platform to join. The consumers have identical intrinsic values of two platforms, equivalent to v, which is assumed to be large enough so that the whole market is covered. Consumers have a taste for application variety. Every consumer s utility of participating on a platform depends on the total number of developers on the same platform. Consumers have identical utility gain from application variety, we use parameter θ to capture this direction of network externalities. More specifically, the availability of each additional developer positively generates additional utility θ for consumers, i.e. θ>0. The consumer who locates at x decides joining platform or by comparing utilities v+θn De pc tx from platform v+θn De pc t(1 x) from platform. We assume there are two types of consumers: a fraction λ of consumers are informed about developer subscription prices hold responsive expectations on developer dem when choosing between two platforms, 0 λ 1. The expectations of these consumers match the realized developer dem, i.e., n De T = n D T. The remaining fraction 1 λ of consumers are uninformed about developer prices hold passive expectations. They do not adjust their expectation of developer dem in response to price changes. Therefore, the realized consumer dems of platform are respectively where T =,. n C T = pc T pc T + λθnd T λθnd T + (1 λ)θnde T (1 λ)θnde T, (1) For now, we assume consumers are homogeneous with respect to the valuation of the hset; they have identical marginal utility of the quality of platform s in-house hset φ=1, each buy at most one copy. To see a clear illustration of the difference between passive responsive expectations, see Hurkens López (201). 6

7 3.3 Developers There is mass 1 of potential developers; each developer lists one application on one platform. ssume that developers form responsive expectations of consumer dem. Developers are industry insiders, they are aware of consumer s preference, hence, can perfectly predict dem of the platforms. Developers differ in the cost of listing applications, denoted by y, are uniformly distributed along the segment [0, 1]. Each developer gains additional utility of β from each consumer who has access to its application. The revenue for a developer who lists on platform T is given by βn C T when the number of consumers who participate in platform T is n C T. The utility of developer y from joining platform T is u D T = βn C T p D T y. We assume that developers can multi-home 5 there are no economies of scope in multihoming. Therefore, the decision of joining a platform is independent of the joining decision of the other platform. That is, a y-type developer will join platform T if u D T (y) = βnc T pd T y 0. So, the developer dem of each platform is n D T = βn C T p D T, where T =,. Developers care more about the network benefits of reaching out with the widest population of consumers than they do about the cost of multi-homing since there is no stalone value for developers to join the platforms. We study a case of competitive bottlenecks (rmstrong, 2006): there is a high level of competition on consumer s side platforms make low profits on this side, but there is no competition for providing applications to consumers. We propose a two-stage game. The timing of the game is as follows: In Stage 1, platform makes the following strategic decision: whether to bundle with its in-house hset or not. The decision is publicly observable. In Stage 2, two platforms simultaneously decide on subscription prices for consumers developers, competition takes place. We compare the unbundling bundling scenarios to determine the bundling strategy for platform. Platform Competition.1 Symmetric Competition We first derive the competition outcomes when platform doesn t bundle with its in-house hset as the benchmark case. Platforms engage in symmetric competition.as they both 2013). 5 Some recent survey shows that on average mobile developers use 2.6 mobile platforms (VisionMobile, 7

8 make profits through subscription revenues. Platform T s profit function is given by max p C T,pD T π T = p C T n C T + p D T n D T, where T =,. Platform also has revenue z stemming from the in-house hset. fraction λ of consumers are informed about all subscription prices the structure of dem on both sides of the market; they make the participation decision upon subscription prices for both consumers developers. The remaining consumers are only informed about subscription prices on consumer s side, they make the participation decision upon consumer subscription prices their expectations on developer dems for each platform. Thus, the realized consumer dems for each platform are n C T = pc T pc T 2θβλ θ(1 λ)nde T + θ(1 λ)nde T 2θβλ + θλpd T θλpd T 2θβλ, (2) where T =,. Proposition.1. When two platforms engage in symmetric competition, the competition equilibrium outcomes are as follows: p C T = t β2 3θβλ, nc T = 1 2 p D T = β θλ n D T = β + θλ Proof. See ppendix π = t 2 θ2 λ θβλ β z π = t 2 θ2 λ θβλ β We need certain assumptions to guarantee the existence of a unique stable equilibrium. 1. β > 2θ. We assume developers care more about consumers than consumers care about developers. On the one h, a one-percent increase in the number of consumers increases developer s profit by one percent. On the other h, a one-percent increase in the number of applications makes not much difference to consumers once there are hundreds of thouss of applications available for each platform 6. This level of asymmetry between the two directions of network effect guarantees the existence of the situation where platforms engage in divide-conquer strategies. 2. t > α = β2 + θβ + θ2 λ + θβλ. With these assumptions, the Google Play offered 900, 000 available applications as of May 15th, Source: com/watch?feature=player_embedded&v=9pmpa_kxsm&t=5s, accessed July, pp Store offered 775, 000 available application as of January, Source: 07pp-Store-Tops-0-illion-Downloads-with-lmost-Half-in-2012.html, accessed July,

9 condition for unique stable equilibrium (t > β2 ) second order condition 3 (t > θβλ) are satisfied, both platforms make positive profits in equilibrium, so that they remain active in the market. s we are interested in seeing the impact of bundling the level of consumer information on platform competition where both platforms remain active in the market, our assumptions rule out corner solutions. + θ2 λ 2 + 2θβλ 6 6 The equilibrium consumer subscription price is the stard Hotelling price with zero marginal cost (t) adjusted downwards by β2 + 3θβλ. The adjustment factor, which measures the benefits to the platform from attracting an extra consumer, can be decomposed into two parts β( β + 3θλ ). The term β means the platform attracts additional β developers when it has an additional consumer. The term β + 3θλ is the profit that the platform can earn from an additional developer. The extra developer pays a subscription price β θλ to the platform, also attracts θλ informed consumers because only informed consumer adjust their expectations of developer dem according to price changes. The larger network externalities (β θ) are, the lower subscription price is charged on the consumer s side. The equilibrium developer subscription price is the monopoly pricing β 7 adjusted downwards by θλ, where θλ is the extra benefit that an extra developer brings to the platform from attracting informed consumers. When β is large, developers attach a high value to consumer participation, platforms have an incentive to lower the subscription price or even subsidize consumers for participation. So that the platform can charge a higher subscription price on developer s side. The equilibrium developer price increases with developer s network externalities. When θ is large, consumers attach a high value to developer participation, platforms have an incentive to lower developer subscription price to encourage participation, the equilibrium developer price decreases with consumer s network externalities. Corollary.1.1. The subscription prices on both sides of the platform are negatively affected by the fraction of informed consumers, while developer participation is positively affected by it. The platform profits decrease with the fraction of informed consumers. When informed consumers are offered a lower price, they anticipate that consumer dem would increase developer dem would increase accordingly. This intensifies price competition (Hagiu Ha laburda, 201). Indeed, the intensity of competition increases with the fraction of informed consumers. 7 If all consumers are uninformed about developer subscription prices hold passive expectations on developer dem, platforms exploit monopoly power on developer s side charge developer subscription price β 2 pc T, the equilibrium developer subscription price is β. 9

10 The best response function on consumer s side is p C T (p C T ) = (t β2 3θβλ)(t θ 2 λ 2 3θβλ) p C T γ + (t β2 3θβλ)(t 2 + θ 2 β 2 λ 2 5tθβλ) γ + (t β2 3θβλ)θ(1 λ)(t 3θβλ)(n De T γ nde T ), (3) where γ = 3 2 tθ 2 λ 2 tθβλ tβ 2 + 3θ 3 βλ 3 + 1θ 2 β 2 λ 2 + 3θβ 3 λ. We further discuss this scenario in the following two cases, depending on the consumer subscription prices are either strategic complements ( pc T (pc T ) > 0) or strategic substitutes p C T ( pc T (pc T ) p C T < 0)..1.1 Case I. Strategic Complements When t > β2, the transportation cost is larger than the benefits to the platform from attracting an extra consumer. The best response curves on consumer s side are upwardsloping, the consumer subscription prices of the two platforms are strategic complements. y definition, the consumer subscription price of one platform increases as the rival s price increases. In this case, both platforms set positive prices on both sides of the market make profits from both sides. Without network externalities, when two consumer subscription prices are strategic complements, the platform raises its consumer price in response to the rival s raising price. The existence of network effects gives the platform two-fold incentives to lower its subscription price on consumer s side. For one thing, the platform charges lower prices to attract all consumers, hence, developers through developers network effects (β). For another, the platform would even lower the consumer prices further as the informed consumers hold responsive expectations on developer dems, hence affecting consumer dem. When the transportation cost is high, the tendency of increasing price prevails. Therefore, the platform would follow the rival s pricing movement, which is the same as the one-sided market, but the price increment would not be as much as in the stard one-sided market, since the price increment on the consumer s side leads to opportunity cost on the other side of the platform. + 3θβλ.1.2 Case II. Strategic Substitutes When α < t < β2, the transportation cost is small relative to the benefits to the platform from attracting an extra consumer. The best response curves on consumer s side are downward-sloping, the consumer subscription prices of the two platforms are strategic substitutes. y definition, the consumer subscription price of one platform increases as + 3θβλ 10

11 the rival s price decreases. This is the case where platforms engage in divide--conquer strategies: platforms subsidize consumers, which is the side with low network externalities (divide) earns a positive margin on developer s side, which is the side with high network externalities (conquer)(caillaud Jullien, 2003). Without network externalities, the platform raises its consumer price in response to the rival s raising price. The existence of network effects gives platforms incentives to lower the subscription prices on consumer s side to attract all consumers, hence, developers, to further lower its price to attract informed consumers. s the transportation cost is relatively small, consumer dem is sensitive to price changes. It turns out to be more profitable to lower the consumer price in response to the rival s raising price, resulting in larger market share on consumer s side greater profits from developers when network externalities are strong..2 undling We assume platform sets p as the price for the bundled products, then p C = p z is the implicit subscription price for consumers. Under pure bundling, neither the in-house hset nor the access to platform would be available on a stalone basis. Platform would now charge a lower price for the bundled products, relative to selling them separately. Under bundling, platform has more incentives to lower the consumer subscription price, a fall of p C not only encourages consumer participation, but also stimulates dem of the hset. The marginal consumer at location x derives utility v+z (p C +z) tx+θnde from purchasing the bundle v p C t(1 x) + θnde from joining platform. lso, there is a fraction λ of consumers are informed about developer subscription prices hold responsive expectations, i.e., n De T = n D T ; the remaining consumers are uninformed about developer subscription prices hold passive expectations. Therefore, the consumer dems of each platform are the same as Eq. (1). Platform s profit maximization problem evolves to max p C,pD π = p n C + p D n D = (p C + z)n C + p D n D. Platform s profit maximization problem is unchanged. The following proposition characterizes the equilibrium prices allocations in the bundling scenario. Proposition.2. When platform bundles with its in-house hset consumers are homogeneous with respect to the valuation of the hset, the equilibrium outcomes are as follows. p C = t β2 3θβλ p C = t β2 3θβλ z(8t 2θβ β2 2θ 2 λ 3θβλ), 12(t α) 11 z(t β2 3θβλ), 12(t α)

12 p D p D n C = z 6(t α), nc = 1 2 z 6(t α), = ( β θλ )( z ), nd 6(t α) = ( β θλ )( z ), nd 6(t α) = ( β + θλ )( z 6(t α) ), = ( β + θλ )( z 6(t α) ), π = 8t β2 θ 2 λ 2 6θβλ (6(t α) + 2z) (t α) 2 π = 8t β2 θ 2 λ 2 6θβλ (6(t α) 2z) (t α) 2 s we are interested in the effect of bundling on platform competition, we assume platform s bundling decision cannot drive its rival out of the market, 3. 0 < z < z = 3t 3α. When z z, platform would always bundle with the hset in order to push the rival out of the market. Under bundling, only consumers on platform would purchase the killer hset. Platform has to drop its consumer subscription price to stimulate the dem for the bundled products. Thus, it manages to steal some consumers from its rival. However, the cut on platform s consumer subscription price dominates the increment on its consumer dem. Hence, platform suffers a loss on consumer s side. Yet, the direction of change on platform s consumer subscription price is ambiguous, depending on the strategic relationship between consumer subscription prices. When consumer prices are strategic complements (resp. substitutes), platform s consumer price goes down (resp. up). The directions of changes on profits from developer s side for both platforms are clear. s a fall on p C shifts the consumer dem toward platform, platform (resp. ) becomes more (resp. less) attractive on developer s side through network effects. This effect increases with β, which determines the sensitivity of developer dem to the dem on consumer s side. Corollary.2.1. When platform bundles with its in-house hset, its implicit consumer subscription price decreases with the fraction of informed consumers while both its consumer dem developer dem increase with it. Platform s developer subscription price, dems on each side of the platform total profits are negatively affected by the fraction of consumer dem. This corollary has significant empirical implications. It indicates that bundling is a more effective tool to stimulate consumer dem, hence developer dem, when there are more informed consumers. The effect of a discount on platform s consumer price is amplified. Platform s dems on each side of the market reach the highest levels when all consumers are informed. higher level of consumer information also intensifies competition as both 12

13 platforms lower subscription prices on both sides. Platform suffers the largest loss when all consumers are informed. The system of best response functions on consumer s side is as follows. p C (p C ) = (t β2 3θβλ)(t θ 2 λ 2 3θβλ) p C γ + (t β2 3θβλ)(t 2 + θ 2 β 2 λ 2 5tθβλ) γ + (t β2 3θβλ)θ(1 λ)(t 3θβλ)(n De γ nde ) 16t2 tθ 2 λ 2 20tθβλ + 3θ 3 βλ 3 + 5θ 2 β 2 λ 2 z, γ () p C (p C ) = (t β2 3θβλ)(t θ 2 λ 2 3θβλ) p C γ + (t β2 3θβλ)(t 2 + θ 2 β 2 λ 2 5tθβλ) γ + (t β2 3θβλ)θ(1 λ)(t 3θβλ)(n De γ θ2 λ 2 (t β 2 3θβλ) z. γ nde ) (5) Compared to Eq. (3), there are two effects determining the movements of the best response curves. The terms proportional to z represent the impact of bundling on consumer prices. undling has a direct impact on consumer prices: all consumers observe the changes on consumer prices. It also has an indirect impact on consumer prices: informed consumers anticipate the impact of bundling on developer s participation decisions. The terms proportional to n De nde represents the impact of bundling on perceived platform quality (application variety) for uninformed consumers. Following melio Jullien (2012), we separate the impact of p C changing on the derivative of platform profits as follows: p C ( π ) = nc p D p D + nd p C θλ = 2θβλ β 2θβλ (6) p C ( π ) = nd p D p C = β 2θβλ. (7) β The term in Eq. (6) captures the fact that a fall of 2θβλ pc shifts the consumer dem towards platform. s a result, platform becomes more attractive for developers. The 13

14 best response curve of platform shifts upwards because its perceived quality has improved β for consumers. Similarly, the term in Eq. (7) indicates that a fall of 2θβλ pc makes platform less attractive for developers. The term θλ in Eq. (6) captures the other direction of the dem shifting effect. 2θβλ fall of p D increases the developer dem for platform, which improves platform quality by increasing application variety. Therefore, the consumer dem shifts upwards. Note that this direction of effect is discounted because only informed consumers adjust their expectations of developer dem according to the price change. The sensitivity of this direction of dem shifting effect depends on both consumer s network externality the fraction of informed consumers. The higher fraction of informed dem there is, the more sensitive this direction of dem shifting effect is. In the same fashion as before, we further discuss the impact of bundling decision when consumer subscription prices are either strategic complements or strategic substitutes..2.1 Case III. Strategic Complements When t > β2, the best response curves are again upward-sloping; thus the consumer subscription prices are strategic complements. The best response curves are shown in Figure 1(a). Compare to the dashed lines in Figure 1(a), we see that, under bundling, the response curve of platform moves downwards the curve of platform shifts to the left. Through bundling, platform offers a discount on consumer subscription price, so the response curve of platform moves downwards, but this effect is dampened by consumer s expectations of more application variety on platform. Under bundling, platform has a higher consumer dem, the dem shifting effect indicates that it also has a higher developer dem. The fraction 1 λ of uninformed consumers expect platform to offer more application variety than platform, the perceived quality of platform increases the perceived quality of platform decreases, platform s best response curve has the tendency to move upwards. lso, when consumer prices are strategic complements, platform follows the rival s movement to lower its consumer subscription price. + 3θβλ Following Farhi Hagiu (2008), we investigate the effect z on platform profits. We decompose the overall effect on platform s own profits into a direct effect strategic effects on both sides of the platform. dπ dz = π z + π p C dp C dz + π p D dp D dz Note that the direct effect is π z of bundling on consumer s side: = n C. The first term of strategic effect concerns the effect π p C dp C dz = (pc + z + βp D ) nc p C ( t β2 3θβλ ) < 0. 12(t α) 1

15 The intuition behind this is that bundling drives the rival to set the subscription price low, it intensifies competition on consumer s side. The second term of strategic effect concerns the effect of bundling on developer s side: π p D dp D dz = (p C + z + βp D ) nc ( β θλ p D 12(t α) ) < 0. Notice that nc p D θλ =. 2θβλ undling has a strategic effect on developer s side because informed consumers adjust their expectations of developer participation due to bundling. undling makes the competing platform less attractive for developers through the dem shifting effect. Therefore, the competing platform has to lower its developer subscription price. In this case, bundling intensifies competition on both sides of the platform, bundling would not be profitable for platform under such circumstances. s bundling has no direct effect on platform s profits, we only check the strategic effects: dπ dz = π + π dp C }{{} z p C dz + π dp D p D dz. =0 The first term of strategic effect also conserns the effect of bundling on consumer s side: π p C dp C dz = n C (pc p C + p D β nc p C )( 8t β2 2θβ 2θ 2 λ 3θβλ ) < 0, 12(t α) Under bundling, platform sets a low subscription price, platform has to lower its price in response. Platform s bundling decision leads to a more competitive environment on consumer s side. On developer s side, the strategic effect of bundling is: π p D dp D dz = (p C n C p D + p D β nc )( β θλ p D 12(t α) ) > 0. undling makes platform more attractive for developers, it would increase its developer subscription price. Thus, there is room for platform to increase its developer subscription price as well. undling softens competition on this side of the platform. The over all effect of z on platform s profits are as follows. dπ dz = nc ( 8t β2 2θβ 2θ 2 λ 3θβλ ) + θλn C 12(t α) ( β θλ 12(t α) ). s platform suffers a loss on consumer dem under the rival s bundling strategy, the higher the value of the hset is, the less profits platform makes. 15

16 .2.2 Case IV. Strategic Substitutes When α < t < β2, the best response curves are downward-sloping consumer subscription prices are again strategic substitutes. oth platforms engage in divide--conquer strategies. The changes on equilibrium is shown in Figure 1(b). Compare to the dashed lines in Figure 1(b), the response curve of platform shifts downwards under bundling. Through bundling, platform increases subsidy for consumer participation, so the response curve of platform moves downwards. In response, platform raises its consumer price as prices are strategic substitutes. Platform s best response curve moves upwards. The dem shifting effect indicates that platform has higher developer participation under bundling. The fraction 1 λ of uninformed consumers expect more application variety on platform, the perceived quality of platform increases, platform increases subsidy for consumer participation to compete very fiercely for consumer dem to make a large profits through the strong network effect as the benefit of attracting one developer dominates the transportation cost. The best response curve of platform moves downwards further. Uninformed consumers expect platform to offer less application variety, the perceived quality of platform drops. The dem shifting effect indicates that platform is less attractive for developers. Platform cuts subsidy for consumer participation further, its best response curve moves upwards further. + 3θβλ We further investigate the impact of z on platform s profits. dπ dz = π z + π p C dp C dz + π p D dp D dz. Now the strategic effect on consumer s side is positive. platform s response to bundling is to reduce its consumer subsidy, which softens competition on this side of the platform. This effect dominates the negative effect it generates on developer s side. s both the direct effect the strategic effects are positive, the overall effect of z on π is positive. lthough the hset is only sold to consumers on platform under bundling, platform s profit increases in the value of the hset faster than n C when consumer prices are strategic substitutes. Therefore, bundling can be profitable. The effect of z on platform s profit is the same as the case where consumer prices are strategic complements. The overall effect of z on platform s profits is negative, platform cannot gain any profits from the rival s bundling practice. 16

17 p C R p C 0 R R R 0 p C p C (a) Strategic Complements (b) Strategic Substitutes Figure 1: est response curves on consumer side when platform bundles Platform would bundle with its killer hset iff π = z ( 16t+θ2 λ 2 θ 2 λ 6θβλ θβ 3β 2 (8t θ 2 λ 2 6θβλ β 2 )z (6t 6α) 2 6t 6α ) 0. The following lemma reveals platform s bundling strategy. Lemma.3. When consumers are homogeneous with respect to the valuation of platform s in-house hset, (i). platform always chooses to bundle with the hset for all z < z when α < t t = 3β 2 +θβ+6θβλ+θ 2 λ θ 2 λ 2 ; 16 (ii). platform bundles if the value of the hset is high, i.e., (6t 6α)(16t+θ2 λ 2 θ 2 λ 6θβλ θβ 3β 2 ) = 8t θ 2 λ 2 6θβλ β 2 z z < z, when t < t t = 5β2 +8θβ+6θβλ+8θ 2 λ 3θ 2 λ 2 ; 2 (iii). platform never practices bundling when t > t. undling always hurts the rival. Proof. See ppendix. It is worth commenting that when competition for consumers is intense (the market power element t is small relative to the network externalities), a small extra consumer dem can lead to significant profits on developer s side, so platform is willing to bundle with the hset even if it can only steal small consumer dem from the rival (a small value z is associated with a small additional consumer dem). When the transportation cost is medium, in order to recoup the loss on consumer s side due to bundling, platform needs to have a larger consumer dem. Therefore, platform would practice bundling only when bundling can steal large consumer dem from the rival, that is to say, the value of bundled hset needs to be significant. When the transportation cost is very high relative to the network externalities, platform can never recoup the loss on consumer s side given a fixed-sized consumer market; bundling never occurs. s platform makes lower profit 17

18 once platform practices bundling, bundling can also be deployed as an entry deterrence strategy in the presence of a significant fixed cost. The following corollary reveals the impact of the level of consumer information on the bundling strategy. Corollary.3.1. The set of parameters upon which bundling emerges shrinks as the fraction of informed consumers increases. undling emerges only when the platforms engage in divide--conquer strategies, where the competing platform reduces its consumer subsidy in response to bundling. However, a larger fraction of informed consumers intensifies competition, pushing the competing platform to increase its consumer subsidy. In Figure 2, the grey area represents the region in which bundling would emerge. undling is less likely to occur when there is a large fraction of informed consumers. t t t t z t t z α 0 z z (a) undling strategy: low λ α α z (b) undling strategy: high λ z Figure 2: The impact of consumer information on bundling strategy.3 Tying If platform practices tying, it still sells the hset to consumers on platform extracts full surplus of the hset from them. Platform s maximization problem now evolves to max p C,pD π = (p C + z)n C + p D n D + n C z = p C n C + p D n D + z. Lemma.. When consumers are homogeneous with respect to the valuation of platform s in-house hset platform extracts full surplus from the fixed-sized hset market, tying makes no difference from untying. 18

19 . Welfare nalysis Now we address the issue how platform s bundling practice affects consumer surplus. The consumer surplus in two scenarios are as follows. CS symmetric = n C 0 (v + θn D tx p C )dx n C = v 5t + β2 + θβ + θ2 λ + 3θβλ. (v + θn D t(1 x) p C )dx CS bundling = n C 0 (v + θn D tx + z z p C )dx n C = v 5t + β2 + θβ + θ2 λ + 3θβλ + z 2 + tz 2 (6t 6α) 2 (v + θn D t(1 x) p C )dx Lemma.5. Consumer surplus is positively affected by the fraction of informed consumers. Under bundling, consumer surplus is positively affected by the value of the hset. higher level of consumer information leads to lower subscription prices higher developer participation, resulting in higher consumer surplus. lso, both consumer developer participation on platform is positively affected by the value of the bundling hset while platform s consumer subscription price is negatively affected. The surplus of the majority of consumers increases with the value of the hset. Therefore, in general, consumer surplus increases with it. undling has indeed one negative two positive effects on consumer welfare. On the one h, the unequal-split of consumer dem between two platforms increases total transportation cost, which reduces consumer welfare. The larger the consumer dem differential between the two platforms, the larger adverse welfare effect of bundling. On the other h, there are two positive welfare effects of bundling coming from the fact that the majority of consumers enjoy a lower subscription price more application variety. Consumers on platform also enjoy a lower subscription price when consumer prices are strategic complements suffer a loss as platform subsidizes less when consumer prices are strategic substitutes. The change on consumer surplus due to platform s bundling decision is CS = CS bundling CS symmetric = z 2 + tz 2 (6t 6α) 2 > 0 19

20 Lemma.6. When consumers are homogeneous with respect to the valuation of the bundling hset, platform s bundling decision unambiguously improves consumer welfare. Proof. See ppendix Recall Lemma.3., as long as platform practices bundling, it improves consumer welfare. 5 Extension: Heterogeneous Consumer Valuation of the Hset Now we modify our setting regarding consumer s valuation of the hset. Let consumer s location on the unit interval be x the marginal utility of the quality of platform s inhouse hset be φ. The pair (x, φ) defines a consumer type. oth x φ are distributed independently uniformly on [0, 1]. Type-φ consumer s utility from the hset is U hs = φz p hs. Without bundling, platform would sell the hset at monopoly price p hs = z, the 2 dem for this hset is D(p hs ) = 1. Consumers with high marginal utility φ φ = would purchase (Figure 3(a)). Platform earns revenue π hs = z from the unbundled hset. gain, we assume platform sets p as the price for the bundled products, p = p C + z. 2 Consumers with heterogeneous marginal utility of the hset quality derives different levels of utility from purchasing the bundled products (Figure 3(b)). Now, consumer (x, 0) derives utility v p + θn De tx from purchasing the bundle v pc + θnde t(1 x) from joining platform, the marginal consumer with 0 marginal utility for the hset quality is x 0 = pc pc z t + λθnde λθnde + (1 λ)θnde (1 λ)θnde. Similarly, consumer (x, 1) derives utility v p + z + θn De tx from purchasing the bundle v p C + θnde t(1 x) from joining platform, the marginal consumer with highest marginal utility of the hset quality is x 1 = pc pc + z t + λθnde λθnde + (1 λ)θnde (1 λ)θnde. The realized consumer dems of each platform are the same as Eq. (1). 20

21 1 1 x 1 a b φ = 1 2 φ = 1 2 d c 0 x 0 x 0 (a) No undling (b) Platform bundles Figure 3: Consumers are heterogeneous with repsect to the valuation of the hset Platform s profit maximization problem evolves to max p C,pD π = p n C + p D n D = (p C + z 2 )nc + p D n D. Proposition 5.1. When platform bundles with its in-house hset consumer s marginal utility of the quality of the hset is uniformly distributed over [0, 1], the equilibrium outcomes are as follows. p C = t β2 3θβλ z(8t 2θβ β2 2θ 2 λ 3θβλ), 2(t α) p D p D p C = t β2 3θβλ z(t β2 3θβλ), 2(t α) n C = z 12(t α), nc = 1 2 z 12(t α), = β θλ ( z ), nd 12(t α) = β θλ ( z ), nd 12(t α) = β + θλ ( z 12(t α) ), = β + θλ ( z 12(t α) ), π = 8t β2 θ 2 λ 2 6θβλ (6t 6α + z) 2 16 (6t 6α) 2 π = 8t β2 θ 2 λ 2 6θβλ (6t 6α z) (6t 6α) 2 21

22 Proof. See ppendix. We use the following lemma to reveal the bundling strategy for platform when consumer s valuation of the hset is uniformly distributed along [0, 1]. Lemma 5.2. When consumer s marginal utility of the quality of platform s in-house hset is uniformly distributed over [0, 1], (i). platform chooses to bundle with the hset for all z < z when α < t 2θβ+β2 +2θ 2 λ θ 2 λ 2 ; (ii). platform practices bundling iff (6t 6α)(8t θβ 2β2 θ 2 λ+2θ 2 λ 2 ) 8t β 2 θ 2 λ 2 6θβλ z < z when 2θβ+β2 +2θ 2 λ θ 2 λ 2 < t < 8θβ+3β2 +8θ 2 λ 5θ 2 λ 2 6θβλ 8 ; (iii). platform never practices bundling when t > 8θβ+3β2 +8θ 2 λ 5θ 2 λ 2 6θβλ 8. undling always hurts the rival. The set of parameters upon which bundling emerges is strictly larger than the case where consumers are homogeneous with respect to the valuation of the hset. Notice that bundling can be profitable even when consumer subscription prices are strategic complements. Indeed, the overall effect of z on platform s profit is: dπ dz = nc + (p C + z 2 + βpd ) nc p C ( t β2 3θβλ 12(t α) ) + (p C + z 2 + βpd ) nc ( β θλ p D 2(t α) ). When consumer prices are strategic substitutes, the strategic effects are positive, dπ > n C dz, platform s profit increases in value of the hset at a rate faster than n C, also bundling exps consumer dem (n C > 1 ), bundling is profitable. When consumer prices are 2 strategic complements, although platform s profit increases in value of the hset at a rate slower than n C, given the exped consumer dem for the bundle, bundling still can be profitable. From Figure 3(b), we see a difference in consumer dem between consumers with high valuation of the hset the ones with lower valuation. In fact, under bundling, more consumers with high valuation of the hset join platform than the ones with lower valuation ( n C = nc (φ φ) nc = z ), the difference increases with the value of (φ<φ) 8t the hset. Through bundling, platform targets consumers with high valuation of the hset for participation. 5.1 Welfare nalysis We also investigate how the bundling decision affects consumer surplus when consumers are heterogeneous with respect to the valuation of the hset. s depicted in Figure 3(b), some consumers are made better off while others are made worse off. asically, consumers with high marginal utility of the quality of the hset (φ φ = 1 ) increase their utility 2 by consuming the hset at price p hs = z. Under bundling, consumers in area a are 2 22