Platform Pricing Choice: Exclusive Deals or Uniform Prices

1 Introduction

Platforms, nowadays, host both exclusive and common content. For instance, two competing mobile operating software platforms, such as Apple’s App Store and Google’s Playstore, have applications that are exclusive to one platform as well as applications that are common on both platforms. One can notice similar trends in music streaming as well as in the video gaming platform market.^[1] The decision to single-home or multi-home by content providers is multidimensional. It can depend on the demographics being targeted, ease of coding as well as portability between platforms, among other things.

On the one hand, the decision to single-home by content developers could stem from their strong preferences to develop content for a particular platform. These platform specific preferences could arise from either technical difficulties or contractual terms that offer monetary or non-monetary benefits in exchange for exclusivity. Technical difficulties could be a result of different programming languages as well as platform idiosyncratic requirements like a lack of home button on the iOS platform necessitates that iOS developers create on-screen buttons.^[2] On the other hand, content developers like Facebook, Google, EA games etc., are present on both the platforms and prefer access to a larger pool of buyers. This homing behavior could arise due to lower development costs due to synergies as well as the ability to access a larger pool of buyers. Other additional benefits could include payoffs that are independent from being at a platform. This could comprise positive externalities in other independent markets due to overlap of buyers across these markets. For example, Microsoft offers the full suite of MS Office tools for free on both Android and iOS ecosystem so as to nudge buyers towards the windows ecosystem in the personal computing market.^[3] We call these benefits as “standalone benefits”, large standalone benefits suggest greater tendency to multi-home among content providers.

An exclusive deals regime is relevant if there is no possibility of arbitrage between the two types of agents. Fortunately, public observability of homing behavior is a realistic assumption for most platforms that we focus on like the online streaming services, mobile operating systems and the video gaming market. This is justified as the costs of verifying the deviation from contract terms for exclusive content on a competing platform are negligible.^[4] It is important to note that we abstract away from cloning and piracy of content on competing platforms.

We consider a model with two competing platforms. Buyers single-home on a platform, while content providers can multi-home or single-home. Platforms are horizontally differentiated a lá Hotelling for agents on both sides. Content providers endogenously sort themselves into multi-homers and single-homers. This endogenous homing behavior is a consequence of horizontal differentiation of the platforms. A larger standalone benefit obtained by content providers on a platform results in a greater proportion of multi-homing and a lower share of single-homing content providers.

We consider the pricing regime choice game and characterize the case when different pricing regimes are chosen. We find that for sufficiently large (small) values of standalone benefits exclusive deal strategy is chosen by the two platforms. An exclusive deals pricing policy provides an extra degree of freedom and hence higher profits compared to the uniform pricing regime for standalone benefits being sufficiently large or small. The intuition here is that when standalone benefits are either sufficiently large or small then respectively multi-homing or single-homing content provider proportions are relatively large compared to other type. Under these conditions, an exclusive deals strategy allows to better extract rent from the market than uniform pricing strategy. As a result, offering exclusive deals are a dominant pricing strategy regardless of any strategy chosen by the rival platform. Hence, exclusive deals regime is the unique equilibrium for sufficiently large or sufficiently small values of standalone benefits. Moreover, we find that, when standalone benefits are small, the exclusive deals equilibrium is also the industry profit maximizing strategy constellation of pricing strategy. In contrast, when standalone benefits are large, the exclusive deals equilibrium leads to a prisoner’s dilemma type of outcome. For intermediate levels of standalone benefits, we find that the symmetric uniform pricing strategy is the equilibrium pricing choice.

The remainder of this paper is organized as follows. In Section 2, we provide the literature review and compare our results to those known in the literature. In Section 3, we present the basic model. In Section 4, we provide the analysis for the different pricing subgames. In Section 5, we look at the equilibrium pricing policy choice and in Section 6 we discuss how our results differ from a traditional one-sided market. Finally, we conclude in Section 7 and proofs are available in Section A.

2 Related Literature

Seminal contributions to the topic of two-sided markets are Rochet and Tirole (2003), Armstrong (2006) and Parker and Van Alstyne (2005). In Rochet and Tirole (2003), platforms levy per-transaction charges with no fixed subscription fee. The two agents, buyers and retailers, are present on either sides of the platforms. Though retailers can ex-ante choose whether to multi-home or single-home, in equilibrium they are all multi-homers.^[5] They show that the share of total transaction charge borne by the either sides depends on how closely buyers view the two platforms as substitutes. Armstrong (2006), considers competition in two-sided markets in different market settings like multi-homing on both sides, competitive bottleneck models etc. This paper assumes content providers can either multi-home or single-home. Though platform choice is endogenous, homing choice (multi-homing or single-homing) is not. In contrast, we consider endogenous homing decision among content providers i.e., content providers can either be multi-homers or single-homers. Then we look at its impact on platform pricing policy choice.

We also contribute to the literature on price discrimination and exclusive deals in a two-sided setting. Armstrong and Wright (2007) look at the possibility of exclusive deals in a competitive bottleneck setting. They find that in the case when content providers do not have transportation costs, all the surplus in the market is appropriated by content providers when exclusive deals are offered. In our paper, we look at spatially differentiated content providers with endogenous homing behavior and hence our results are different. We find that under exclusive deals, platforms can extract surplus from the content providers more efficiently due to an extra degree of freedom in pricing. Liu and Serfes (2013) in an extension compare a uniform pricing regime to a regime with full price discrimination under endogenous homing decisions. In this extension, they make a simplifying assumption that cross-network externalities between the two groups are equal and obtain that price discrimination leads to higher profits. In contrast, we have asymmetric cross-network benefits which leads to richer results in our model. Moreover, we focus on the equilibrium pricing policy choice of platforms under endogenous homing decisions.^[6] Jeitschko and Tremblay (2020) is another work that is closely related to us. They also allow for endogenous homing behavior of agents on both sides of the market. They compare a setting with a monopolist platform to a competitive duopoly platform setting. In their model, providing exclusive deals can increase welfare. In contrast to them, we always focus on competition between platforms, and specifically look on the platform pricing choice between an exclusive deals or uniform pricing strategy.

We also contribute to the literature on endogenous multi-homing by sellers and pricing decision of platforms (Belleflamme and Peitz 2010, 2019; Choi 2010). The closest paper to our work is Belleflamme and Peitz (2019). Similar to our paper, they have endogenous decision on homing choice under a uniform pricing regime. Under uniform pricing, our results are qualitatively similar to their results. Nevertheless, we further extend their analysis by also considering the case when platforms can price discriminate between sellers contingent on their homing decisions along with the asymmetric pricing choice setting. In addition, our main focus is on the impact of endogenous homing choice by content providers on platform pricing policy decisions.

3 The Model

We consider a two-sided-market framework along the lines of Belleflamme and Peitz (2010) and Armstrong (2006) with two competing platforms denoted by i ∈ {1, 2}. The two sides served by these platforms are the consumer side and the content provider side. Our benchmark model is a competitive bottleneck where buyers only single-home, while content providers either single-home or multi-home. This market structure is very common in the mobile telephone industry and video game industry where buyers typically use only one mobile phone (and operating system such as Android/Google or iOS/Apple), or one gaming console. At the same time, platforms provide buyers access to common and exclusive content. The latter mirrors the fact that content providers’ side can both single-home and multi-home.

The two competing platforms orchestrate interactions between buyers and content providers. Each Platform i sets a price, p _i , to buyers for access to its content.^[7] Since content providers can multi-home or single-homer, platforms can choose between two pricing strategies — (i) exclusive deal pricing strategy (E) and (ii) the uniform pricing strategy (U). Under pricing strategy E, a platform charges different prices to a content provider depending on whether it single-homes or multi-homes where l i S is price for single-homing content providers and l i M is the price for multi-homing content providers. Thus, under regime E, a platform charges three prices p i , l i S , l i M . Under strategy U, the platform sets a uniform price to all content providers. Let the price offered to content providers in the uniform pricing case be denoted as l i U resulting in the platforms charging a pair of prices p i , l i U .

Buyers. Buyers are uniformly distributed on the unit interval as in Anderson and Coate (2005) with platforms being located on the opposite ends with platform 1 at x ₁ = 0 and platform 2 at x ₂ = 1.^[8] A consumer of preference type x with x ∈ [0, 1] that buys access to services on platform i, by paying a price p _i to the platform and incurring a preference mismatch cost t _b |x − x _i | with t _b being the constant transportation cost parameter, obtains the following utility.

where buyers derive a “stand-alone” utility of K _b > 0 from accessing content (and other services) on a platform, θ b ⋅ n i e stands for the utility buyers obtain from interacting with an expected mass of n i e content providers on platform i and θ _b being buyers’ value from interacting with each content provider.^[9] Using (1), we derive the indifferent consumer x ^⋆ and hence also consumer demands on the two platforms as a function of prices and buyers’ expectation on the mass of content providers active on the two platforms. The indifferent consumer is given as follows.

Notice that consumer demand on either platform depends on the difference in consumer prices on the two platforms and on the difference in the total mass of expected content providers on the two platforms. It is noteworthy that the difference between the mass of content providers matters and not the total mass of content providers on a single platform. Specifically, when some content providers multi-home and some single-home, this difference is essentially the difference in the mass of single-homing content providers on each platform. Accordingly, if all content providers are multi-homers, then the consumer demand will not be affected by the presence of content providers. Put differently, single-homing content providers are the driving force for consumer demand, while multi-homers have no impact in this regard.

Content Providers. Content providers can decide either to multi-home or single-home. They may have platform specific costs for development of content and for reasons not limited to technical preference, one platform may be strongly preferred by some content providers relative to the rival platform and content providers may choose to single-home.^[10] On the other hand, developing apps for both platforms allows these content providers access to a larger consumer base. As a result, some content providers have a strong preference to develop an app for a certain platform, while others do not have such preferences, and therefore, develop apps for both platforms. Similarly, in the video game industry, the presence of exclusive titles as well as common content is well known.^[11]

Content providers are uniformly distributed on a Hotelling line of unit length with platform 1 located at coordinate 0 and platform 2 located at coordinate 1. This modeling choice is made to take into account that content providers may have a strong preference towards a platform and single-home or they may prefer to port content on both platforms and multi-home. Content providers value the presence of buyers on a platform and obtain a marginal cross network benefit θ _c for an additional consumer at a given platform i and incur a transportation cost of affiliating with a platform. They choose an optimal strategy among multi-homing and single-homing given their location y and the pricing scheme. Specifically, the payoff of a content provider of type y from affiliating with only platform i and paying a participation fee l _i is given by

with y ₁ = 0 and y ₂ = 1 being the address of platform 1 and platform 2 respectively. We denote K _c as the standalone benefit of content providers from affiliating with a platform. This standalone benefit can be understood as the benefits content providers obtain from accessing a platform. The term θ c ⋅ D i e is the benefit a content provider gets from interacting with an expected mass of D i e buyers on platform i.^[12]

The payoff of a multi-homing content provider affiliating with both platforms and facing is given as follows.^[13]

Note that the payoff of multi-homers is simply the sum of the payoff of each single-homing content providers on the two platforms.^[14] We assume that the consumer side demand is covered and therefore D 1 e + D 2 e = 1 . Similarly, we assume that participation for developers is sufficiently attractive so that some context providers choose to multi-home. We invoke the following assumption, which ensures that both single-homing and multi-homing content providers coexist in equilibrium and sufficient second order conditions are satisfied.

Given the pricing regime which is either E or U, we analyze the following three-stage game: In the first stage, platforms simultaneously decide whether to offer exclusive deals or set uniform prices. In the second stage, platforms simultaneously choose the price they charge content providers and buyers for affiliating with their platform. In the third stage, content providers and buyers observe the fees and form expectations on the mass of content providers and buyers active on a platform. Then, content providers sort themselves into single-homers and multi-homers and buyers decide simultaneously which platform to join.

The equilibrium concept we employ is the subgame perfect rational expectations equilibrium.

4 Analysis

We first analyze the subgame where both platforms choose uniform pricing, then the case where both platforms choose exclusive deals regime and finally, the asymmetric case where one platform chooses a uniform pricing regime and the other chooses an exclusive deals regime. We then move on to the first stage of the game where platforms decide simultaneously on their pricing strategy.

4.1 Uniform Pricing Subgame

In this subgame, both the platforms have chosen uniform pricing strategy. This strategy is very common to the mobile applications market, where public information suggests that prices are uniform regardless of homing choice.^[15] Hence, the prices charged by platform i are given as {p _i , l _i }. Consumer demands as a function of consumer prices and expectations on the mass of active content providers on each platform are presented in Eq. (3). Content providers can multi-home or single-home. Multi-homers are present only if the payoff from multi-homing is larger than from single-homing. Using (4) and (5), we find that this is the case if the following two conditions hold:

U M ( l 1 , l 2 ) ≥ U 1 l 1 , D 1 e , y ⇒ y ≥ y 1 ⋆ D 2 e , l 2 ≜ − K c + l 2 + t c − θ c ⋅ D 2 e t c

and

U M ( l 1 , l 2 ) ≥ U 2 l 2 , D 2 e , y ⇒ y ≤ y 2 ⋆ D 1 e , l 1 ≜ K c − l 1 + θ c ⋅ D 1 e t c .

This results in total content provider demand at platform 1 and 2 respectively as n 1 D 1 e , l 1 ≜ y 2 ⋆ D 1 e , l 1 and n 2 D 2 e , l 2 ≜ 1 − y 1 ⋆ D 2 e , l 2 . Note that Assumption 1 ensures that in equilibrium 0 < y ₁ < y ₂ < 1 holds. Figure 1 shows a possible constellation for how content providers may select into single-homers and multi-homers. There are three intervals with different types of agents. The interval on the left consists of single-homing content providers on platform 1, the interval in the middle represents the mass of multi-homing content providers and the interval on the right side depicts the mass of single-homing content providers on platform 2.

Figure 1:

Distribution of content providers.

The above figure shows that multi-homers are the ones that do not have strong preferences for either platform and therefore prefer to have access to a larger base of buyers. The total number of content providers on a platform includes both the multi-homers as well as the single-homers and is falling in the price charged to them and rising in the cross-network benefit.

Imposing rational expectations — D i ⋆ = D i e , n i D i ⋆ , l i = n i e for i = 1, 2 and solving, we get consumer demand and content provider affiliation with each platform as function of prices as presented below.

D i ⋆ ( p i , p − i , l i , l − i ) ≜ t b t c − t c ( p i − p − i ) − θ b ( l i − l − i + θ c ) 2 ( t b t c − θ b θ c )   for i = 1,2 , n i ⋆ ( l i , l − i , p i , p − i ) ≜ 2 ( K c − l i ) t b t c + θ c ( t c ( t b − p i + p − i ) − θ b ( 2 K c − l i − l − i ) ) − θ b θ c 2 2 t c ( t b t c − θ b θ c )   for i = 1,2 .

Platform pricing stage. Platforms choose prices on both sides of the market to maximize total profits. The profit of platform i is given as

(6) max l i , p i Π i U = p i ⋅ D i ⋆ ( ⋅ ) + l i ⋅ n i ⋆ ( ⋅ ) , for i ∈ 1,2 .

Differentiating the above profit expression with respect to p _i yields the following first order conditions

(7) ∂ Π i U ∂ p i = D i ⋆ ( ⋅ ) + p i ⋅ ∂ D i ⋆ ( ⋅ ) ∂ p i ︸ Margin  +  Volume effect + l i ∂ n i ( ⋅ ) ∂ D i e ∂ D i ⋆ ( ⋅ ) ∂ p i ︸ Content provider  effect ( − ) = 0 .

The effects presented in the above first order conditions determine the optimal prices to consumers and can be decomposed into two main effects. First, the classical trade-off between margins and volume due to a unit increase in consumer price. Second, the Content provider which enters the first order condition negatively and describes the effect of increased consumer prices on developer participation on the platform. A unit increase in price charged to consumers, lowers the expectation of content providers on the consumers affiliating with the platform. This lowers the volume of content providers active on the platform.

Differentiating the profit expression as presented in Eq. (6) with respect to l _i yields the following first order conditions

(8) ∂ Π i U ∂ l i = p i ⋅ ∂ D i ⋆ ( ⋅ ) ∂ l i ︸ Consumer  demand effect  ( − ) + n i ⋆ ( ⋅ ) + l i ⋅ ∂ n i ( ⋅ ) ∂ D i e ∂ D i ⋆ ( ⋅ ) ∂ l i ︸ ( − ) + ∂ n i ( ⋅ ) ∂ l i ︸ ( − ) ︸ content providers’ Margin   +  Volume effect  = 0 .

The above first order condition describes effects that determine the content provider prices. First, there is the classical content providers margin and volume effect due to an increase in participation fee charged to developers. Second, the Consumer demand effect which describes how consumers demand is affected by an increase in the participation fee charged to content providers. An increase in the participation fee lowers consumers expectation on the mass of content providers active on the platform which also lowers their participation on the platform. The optimal prices are obtained after solving simultaneously these system of first order conditions. Substituting these prices in the demands and profits, we present our results in the following lemma.

Lemma 1

In the uniform pricing regime, prices and platform profits are l ⋆ ≜ 2 K c + θ c − θ b 4 , p ⋆ ≜ t b − θ c ( 2 K c + θ c + 3 θ b ) 4 t c and Π U , ⋆ ≜ t b 2 − θ c 2 + θ b 2 + 6 θ b θ c − 4 K c 2 16 t c respectively. The total mass of buyers and content providers on platform i = 1, 2 are given by D i ⋆ ≜ 1 2 and n i ⋆ ≜ ( 2 K c + θ c + θ b ) 4 t c , respectively.

These optimal values are the same as in Belleflamme and Peitz (2016). As in Belleflamme and Peitz (2016), if platforms focused only on the content providers they would charge a price equal to 2 K c + θ c 4 . We can notice that these prices are downward adjusted by θ b 4 , when the cross-group effect that content providers exert on buyers is taken into account. Similarly, on the buyers’ side, platform charge the Hotelling price, t _b , less a term that depends on the size of the cross group network effects and transportation costs.

The total mass of content providers is rising in K _c . The increase in multi-homers outweighs the fall in single-homers with a rise in K _c . Interestingly, the price charged to content providers is also rising. Although the price charged to content providers is rising, the mass of total content providers on each platform rises as the increase in value due to an increase in standalone value K _c outweighs the price increase effect and hence platform profits are also rising.

5 Platform Pricing Strategy Choice

In this section, we look at the pricing regime choice. This is the first stage of the game where platforms simultaneously choose pricing strategy vis-á-vis content providers which can be either exclusive deals, E, or uniform pricing, U. This pricing policy stage is similar as in Thisse and Vives (1988). Figure 2 shows the payoff matrix for the simultaneous regime choice of the two platforms.

Figure 2:

Payoff matrix for different pricing regime constellations.

For simplicity, let us define the difference in platform profits between the case when both platforms choose exclusive deals and profits when a platforms chooses uniform prices in asymmetric pricing outcome as λ ≜Π^E,⋆ − Π^u,⋆. Similarly, define the difference between the profits a platform obtains when setting exclusive deals in the asymmetric pricing subgame and in the uniform pricing subgame as γ ≜Π^e,⋆ − Π^U,⋆. When the signs of the two differences are positive i.e., λ > 0 and γ > 0, we have a unique symmetric equilibrium denoted (E, E). If both λ and γ are negative, we get (U, U) as equilibrium. If the signs are opposite, i.e., λ < (>)0 and γ > (<)0, we obtain multiple equilibria that can result in either symmetric pricing strategies or asymmetric pricing strategies.

To simplify the analysis, we first look at the properties of λ and γ in K _c .

Knowing that λ and γ are convex in K _c , we solve for K _c when the two differences are zero. Solving for λ = 0 with respect to K _c , we obtain two solutions {k ₁, k ₂} where k 1 ≔ 1 2 ( − 3 θ b + 4 t c − θ c ) and k 2 ≔ 5 ( 2109 θ b + 2398 t c ) − 9350 θ c − B − C 4840 .^[20] Similarly, γ = 0 has two solutions in K _c given by {k ₁, k ₃} where k 3 ≔ ( 2116 t c − 997 θ b − 1495 θ c + D ) 1058 .^[21] The sign of the slope of ∂ λ ∂ K c | K c = k 1 and ∂ γ ∂ K c | K c = k 1 is positive (negative) if θ _c > (<) θ _b .^[22] The proposition below describes results for the parameter constellation of {t _S, θ _b , θ _c } where solutions k ₂ and k ₃ are in the relevant parameter ranges of K _c i.e., K c ∈ [ 2 t S − θ b − θ c 2 , k ̄ ] .

Figure 3 graphically depicts that both λ and γ are convex in K _c . One can see that the point at which λ and γ intersect denoted by k ₁ is smaller than k ₂ and k ₃. We can then divide the above graph into regions where different pricing constellations are offered to content providers. The blue regions in the graph depict the case when both the platforms offer exclusive deals to content providers. The green region depicts the case when both platforms offer uniform pricing to content providers, while the pink region depicts the case when there exist multiple symmetric pricing strategies between (U, U) and (E, E).

Figure 3:

λ (dotted blue line) and γ (red) for parameter values θ _b = 2, θ c = 1 2 and t _c = t _b = 3.

The following proposition characterizes the pricing regime choice for the case, θ _b ≤ θ _c . When θ _b ≤ θ _c , the parameter constellation of {θ _b , θ _c , t _c , t _b } is such that the solutions k ₂ and k ₃ are in the relevant range of K _c .

From the above proposition, it is easy to see that both the platforms choose to offer exclusive deals when either K _c is sufficiently large or sufficiently small. In particular, when K _c < min{k ₂, k ₃} and K _c > k ₁ both platforms choose to offer exclusive deals to content providers. There exists a prisoner’s dilemma in the pricing strategy choice when choosing (E, E) for K _c > k ₁ large enough. While for K _c < min{k ₂, k ₃}, pricing strategy (E, E) provides the highest industry profit and is efficient. For intermediate levels of K _c , we can have the asymmetric pricing regime, where one platform chooses to offer exclusive deals, while its competitor offers uniform prices, as well as the symmetric pricing regime where both the platforms offer uniform prices.

Figure 4 provides a graphical representation of the results in proposition 2. We can notice the point where the two convex curves meet k ₁ is larger than max{k ₂, k ₃}. As in the previous figure, the blue shaded regions are the cases when a unique symmetric equilibrium occurs and platforms offer exclusivity deals to content providers. The region shaded in green is the case when a unique symmetric pricing strategy occurs on equilibrium and platforms offer uniform prices to both types of content providers.

Figure 4:

λ (dotted blue line) and γ (red) for parameter values θ b = 1 2 , θ _c = 2 and t _b = t _c = 3.

The intuition behind the result that for sufficiently large or small levels of K _c , exclusive deals strategy is chosen by both the platforms is that exclusive deals afford an extra degree of freedom to the platform in pricing to extract surplus. For instance, low (high) levels of K _c imply that there is a greater proportion of single (multi)-homers. An exclusive deals strategy allows platforms to better exploit this market configuration to extract more from the market regardless of what pricing regime the rival platform chooses. Hence, exclusive deals are offered. Nevertheless, having an extra degree of freedom also implies greater competition. Interestingly when K _c > k ₁, platforms are in a prisoner’s dilemma where both platforms choose exclusive deals while it is jointly profitable for them to choose uniform pricing. The intuition behind this result is that for large K _c , the mass of single-homers is low as the value from multi-homing is relatively high. Recalling that consumer demand is affected only by the presence of single-homing content providers, to attract a higher mass of single-homing developers, platforms must lower their prices to attract single-homers which lowers their profits.