Multihoming Alliances and Price Competition

Abstract

The over-the-top (OTT) subscription video streaming industry has witnessed significant growth and heightened competition in recent years, marked by the influx of new players. At the same time, competing services are forming new alliances that facilitate consumer multihoming. For instance, Amazon Prime Video has partnered with services such as HBO Max and Paramount+ to enhance the combined viewing experience for consumers through seamless integration. The authors build a game-theoretic model with horizontally differentiated services to examine how an alliance facilitating multihoming between two competing services affects price competition in the market. They find that the alliance's impact on price competition depends on the level of content differentiation in the market: Competition intensifies when differentiation is high but relaxes when differentiation is low. The alliance benefits the partnering services as long as the differentiation is not too high, and interestingly, it may increase the profitability of a third nonpartnering service when differentiation is sufficiently low. The authors show that consumer surplus increases under the alliance, even if price competition is relaxed. They also investigate a focal service's decision to partner with one of two competing services and find that it prefers to partner with a service that has high-quality content but a smaller loyal base. This research offers insights into the current landscape of the OTT video streaming market and provides implications for both managers and policymakers.

The over-the-top (OTT) subscription video streaming market is witnessing unprecedented growth globally (Patil 2023). It is projected to generate revenues of $119 billion in 2025, with an expected annual growth rate of 6.9% from 2025 to 2029 (Statista Market Insights 2025). OTT streaming services provide on-demand, flexible content to consumers to watch from the comfort of their homes. This convenience has notably diminished the appeal of traditional entertainment options like cinemas and television broadcasts. Consequently, major film studios like Disney and Paramount have launched their own streaming services, intensifying competition with established players like Netflix and Prime Video.

While competition is intensifying with the entry of new streaming services, an interesting aspect of this industry is that a significant proportion of consumers multihome—that is, hold subscriptions to multiple video streaming services. Forbes Home's market research shows that a staggering 86% of Americans pay for more than one such service (Glover 2023). Similarly, the Deloitte digital media trends survey reports that the average U.S. household has four different video streaming subscriptions (Westcott et al. 2021).

The reaction of key players in the subscription video streaming market to rising competition and consumer multihoming has been varied. While services like Netflix and Apple TV rely primarily on their own exclusive and licensed content, others, such as Amazon Prime Video and Hulu, have formed alliances with competing streaming services, such as HBO Max and Disney+, respectively. What is unique about these alliances is that they facilitate and enhance the multihoming experience for consumers. For instance, Prime Video subscribers can add a subscription to HBO Max and seamlessly view its content within the Prime Video interface. This integrated viewing experience offers numerous benefits to consumers. It eliminates any hassle of switching apps or websites and provides unified features like seamless playback, a consolidated watchlist and downloads library, personalized recommendations, and data management (Tech Desk 2021).

In the absence of an alliance, consumers can still subscribe to multiple services. However, they must navigate separate interfaces, missing out on the advantages of an integrated viewing experience. This multihoming cost for consumers has not gone unnoticed. Following the recent integration of Disney+ and Hulu, Disney Entertainment President Aaron LaBerge highlighted the enhanced value of multihoming services under an alliance: “We live in a world where people have multiple subscriptions. They’re in [HBO] MAX, they’re in Netflix, they’re in Hulu, they’re in Disney Plus, they’re in Prime Video. And they don’t know what's where. So we believe that for our content, putting it all in one place for you to easily find, applying personalization to recommend content you may like, and not having to send you into another app was really important” (McCracken 2023, emphasis added). ¹

In this article, we seek answers to the following questions. First, why have alliances between competing services in this industry become more common in recent years? In particular, what is the effect of these alliances, which facilitate multihoming, on price competition and profits? Second, how do these alliances affect the nonallied services? Third, given the plethora of streaming services, which should a focal service partner with? We observe an alliance between Amazon and HBO, but not with Netflix. Why is this the case? What are the strategic considerations when choosing one service over another?

To this end, we develop a theoretical framework to examine how a multihoming alliance between two services impacts price competition and profits in the industry. We consider a model with three symmetric services located on a unit circle, where consumers may subscribe to one or more services but incur a cost for multihoming. In the absence of an alliance, multihoming costs are high enough that consumers choose at most one service. ² This baseline serves as a benchmark to contrast prices and profits with the case where two services enter into an alliance to facilitate multihoming. Under the alliance, some consumers choose to multihome between the allied services. We find that price competition between the services is attenuated when the level of content differentiation is low. Interestingly, the alliance between the partnering services not only increases their profits relative to the baseline but also benefits the nonallied service.

The finding that an alliance mitigates price competition may be unsurprising. However, we find that when the services are sufficiently differentiated, the alliance actually intensifies price competition. Not only are prices under these market conditions lower than those in the baseline model, but the partnering services also charge a lower price than the nonallied service. Thus, the alliance actually has the opposite effect on price competition when content is sufficiently differentiated. Despite increased price competition, interestingly, the partnering firms’ profits are still higher than those in the baseline model as long as the content is not too differentiated. However, under these conditions, the partnership adversely affects the profits of the nonallied service. Therefore, the effect of the alliance on price competition and profitability depends on the level of content differentiation.

To address the question of which service to partner with, we relax the symmetry assumption by allowing the services to differ on two dimensions: the quality of their offerings and the size of their loyal consumer bases. We investigate a focal service's decision regarding which of two services it should partner with. We find that the focal service prefers to partner with the service that has a higher level of quality but a smaller loyal consumer base. The latter finding is counter to the idea that the firm may want to partner with a firm with a larger consumer base to leverage the eyeballs on that service.

Finally, we present two extensions. First, we consider an extension in which multihoming consumers get a bundle discount and demonstrate that our main findings remain robust. Interestingly, we also find that bundle discounts expand the region over which competition is relaxed and may serve as a strategic tool to compete more effectively with the nonallied service. Second, we examine whether our findings are sensitive to when consumers learn about the alliance. In this extension, the focal service offers an add-on subscription to its partnering service, but consumers can only learn about the alliance upon subscribing to the focal service. This extension mimics the real-world setting where Amazon subscribers can choose to subscribe to HBO once they have subscribed to Amazon, but not vice versa. Again, we find that the findings of our main model are robust to this extension.

While the video streaming services context is our motivating example, our model can also be applied to other digital services where consumers regularly multihome and alliances may improve the multihoming utility for consumers. For example, Mint, an Indian business and finance publication, has partnered with the Economist to offer a bundled subscription which allows Mint’s subscribers to read Economist articles on Mint’s interface (Marshall 2023). In keeping with the potential applicability of our model to other digital services, we refer to the players as simply “services” instead of “streaming services” when discussing our model and its findings.

Our findings offer implications for both managers and policymakers. We find that services should consider forming an alliance when the content market differentiation is low but should be wary of doing so when differentiation is high. We also shed light on how the alliance impacts nonallied firms, showing that even they may benefit when differentiation is sufficiently low. Furthermore, our findings provide guidance to services on which other services they should partner with. We show that a focal service should look to partner with a service that has high-quality content but a smaller loyal base. This finding is in line with the observation that Amazon partners with HBO but not Netflix. While HBO is known to have high-quality content (Hall 2022), it has a smaller loyal base than Netflix. As per one study, 80% of Netflix subscribers subscribe to only Netflix compared with 28.5% for HBO (Molla 2017). Lastly, our welfare analysis has implications for policymakers. We show that alliances that facilitate multihoming increase consumer welfare even if price competition is relaxed and consumers face higher prices.

Related Literature and Contribution

Our work builds on two related streams of literature: research on (1) multihoming and (2) partnerships between competing firms.

Several papers have studied consumer multihoming and its impact within content/media markets in recent years. Jiang, Tian, and Zhou (2019) analyze a setting where competing distributors decide whether to acquire content from an upstream content creator. They show that, in contrast to single-homing, multihoming leads to only one distributor acquiring the creator's new content. Furthermore, when the distributors are not highly differentiated, the creator decreases content production, reducing profits for both the content creator and the distributors. Amaldoss, Du, and Shin (2023) examine competing firms’ pricing strategies—uniform and tiered (no ads on the higher tier)—and find that symmetric firms may adopt asymmetric pricing strategies when consumers’ multihoming valuation is large. They also show that tiered pricing strategies need not improve the firms’ profits when consumers multihome. Ambrus, Calvano, and Reisinger (2016) show that consumer multihoming induces media platforms to strategically increase the level of advertising to reduce the body of multihoming consumers and increase profits. Athey, Calvano, and Gans (2018) show that consumer multihoming incentivizes advertisers to single-home, increasing competition between advertisers and reducing advertising prices. Anderson, Foros, and Kind (2018) also consider the impact of consumer multihoming on firms’ competition for advertisers and find that the entry of new firms decreases advertisement prices, while a merger increases them.

This body of work considers how the presence of consumer multihoming impacts the content/advertising side of the market and, in turn, how that impacts firms’ decisions. However, it does not speak to the effects of multihoming in a context where competing firms may form an alliance to enhance the value of multihoming between the partnering firms, and the effect that has on price competition in an oligopoly. In this article, we take the content strategies as given and focus on studying the alliances that facilitate multihoming and their impact on price competition and ensuing profits.

The second stream of literature relates to alliances, partnerships, or coopetition between firms (e.g., Amaldoss et al. 2000; Bucklin and Sengupta 1993; Cai and Raju 2016; Kuksov, Prasad, and Zia 2017; Luo, Rindfleisch, and Tse 2007; Nalebuff and Brandenburger 1997). While this body of literature is large and examines the role of partnerships between firms in various contexts, we limit our focus to partnerships in content markets. Weeds et al. (2016) examine the incentives of a vertically integrated operator to supply its “premium” content to a rival distributor. They find that while in a static setup, the integrated operator supplies this content to the rival to soften competition, in a dynamic setting with switching costs, it may keep the content exclusive to gain a market share advantage. Adner, Chen, and Zhu (2020) examine the compatibility decisions of two competing firms and find that they may cooperate by offering one-way compatibility when the difference in their standalone values is high. Wu, Han, and Chiu (2023) consider the impact of multihoming on a firm's decision to keep its newly developed content exclusive or license it to (and hence cooperate with) a rival firm. They find that, under single-homing, the firms license content when the licensing fees are high enough. However, under multihoming, the content-creating firm maintains exclusivity. Hence, they find that cooperating with the rival is not an equilibrium outcome in the presence of multihoming.

This literature views licensing arrangements, content sharing, and compatibility decisions between competing firms as forms of partnerships/alliances or coopetition. In this study, the alliance between competing firms that we explore is distinct from any of these arrangements. Specifically, the alliance in our setting does not affect the overlap in the content provided by the competing services but rather enhances the value of multihoming by, for example, offering an integrated viewing experience.

We see our work contributing to the existing literature by combining elements of both these streams and addressing questions of managerial relevance that, to the best of our knowledge, have not been addressed before. First, we bring together the idea of multihoming with the decision of whether to form an alliance. How the alliance affects the multihoming utility of consumers in this article is distinct from any that we are aware of in the extant literature. Specifically, in this study, when two competing services enter into an alliance, the value of multihoming is enhanced due to the integrated viewing experience, which is not available without the alliance. This is distinct from partnerships in the extant literature, where a service may license its exclusive content to a rival and/or a downstream player for a fee. Such an alliance would actually decrease the value of multihoming. Second, we consider an oligopoly setting, which allows us to speak to not only how the alliance affects the partnering services but also how it impacts the nonallied service. Third, in addition to the question of whether to form an alliance, we also address the important question of which service to form an alliance with. Thus, our analysis sheds light on the issue of whether Amazon should partner with HBO or Netflix, the market conditions under which that partnership is mutually beneficial, and the impact that, in turn, has on the nonallied firm's profits. We also consider several extensions to our model and find that our qualitative results remain robust.

The rest of the article is organized as follows. We begin by presenting the model details and analyzing the alliance's impact on competition, profits, and welfare. Next, we address the question of which service to partner with. We then extend our model to incorporate bundle discounts and ex post awareness of the alliance. Finally, we conclude with a discussion of our key results and identify areas of future research.

Model and Analysis

We contemplate a model in which three services N, A, and H compete to deliver content to consumers. Consumers in our model are distributed uniformly on a unit circle, and the three services, N, A, and H, are located symmetrically on this circle at 0, 1/3, and 2/3, respectively. It is helpful to think of the location of the consumer on the circle as the ideal content they prefer and the location of the service as the kind of content they offer. So, for instance, service N may offer content that may appeal more to families that have young children, and consumers located in the neighborhood of N should be seen as those who prefer family-oriented content. Similarly, service H may offer more adult-oriented content relative to N, and consumers located in the neighborhood of H should be seen as those who prefer adult-oriented content more than family-oriented content.

Consumers value the subscription of their ideal content at V, and the disutility per unit distance away from their ideal content is t. ³ The parameter t in our model should be seen as a measure of how differentiated the content market is with higher (lower) values of t representing markets where the content is more (less) differentiated. The utility that a consumer derives from subscribing to service $\mathrm{i}\in \{\mathrm{N},\mathrm{A},\mathrm{H}\}$ located d_i units away from their ideal point at price p_i is:

$${\mathrm{U}}_{\mathrm{i}}=\mathrm{V}-\mathrm{t}{\mathrm{d}}_{\mathrm{i}}-{\mathrm{p}}_{\mathrm{i}}.$$

(1)

We allow for the possibility of multihoming. If consumers choose to multihome, then they have the option of subscribing to any two of the three services: {N, A}, {A, H}, or {H, N}. We assume that no consumer in our model subscribes to all three services, which captures the institutional reality that few consumers (if any) subscribe to all the services in the marketplace. We assume that consumers, at their ideal point, value subscribing to a second service at V − c, which is lower than their valuation of subscribing to the first service (V). This reduction in value by c may be attributed to the hassle caused by having to manage content across two different services. Each service makes it convenient for consumers to manage the content on its own service by making it easier to resume paused content, watch next episodes of TV shows, and discover newer content based on past viewing history. However, upon subscribing to two services, consumers have to incur both the time and psychological costs involved in tracking content across the two services. The parameter c also captures any decrease in the marginal utility of subscribing to one more service. This decrease in marginal utility may also result for other reasons, such as overlapping or similar content across the two services (Jiang, Tian, and Zhou 2019) or limited viewing time or attention span of the consumers (Amaldoss, Du, and Shin 2023). In effect, while subscribing to one service at their ideal location provides consumers utility V, subscribing to the second service provides them a lower additional utility V − c.

Given our interest in how alliances affect competition, we distinguish between the cases where consumers choose to multihome allied services versus where they choose to multihome nonallied services. For instance, if Amazon and HBO are in an alliance, the integrated viewing experience resulting from multihoming these two services must be modeled differently relative to multihoming Netflix and Amazon, which are not in alliance. Formally, if two services (say A and H) enter into an alliance to facilitate multihoming for consumers, it increases the valuation of the second partnering service from V − c to V + κ − c. However, the valuation of another nonpartnering service remains the same at V − c. The partnering services achieve this increase (κ) in multihoming valuation by consolidating the watch lists, providing better recommendations, unifying the download library, and simplifying data management for content from both their services (Tech Desk 2021). We label the arrangement where the alliance increases the multihoming valuation between the partnering firms as subhoming. Given our utility specification, if a consumer's ideal point is located d_i and d_i′ units away from services i and ${\mathrm{i}}^{\mathrm{\prime }}\in \{\mathrm{N},\mathrm{A},\mathrm{H}\}$ , respectively, and they decide to multihome the two services at prices p_i and p_i′, they derive a utility of:

$$\begin{array}{cc}{\mathrm{U}}_{\mathrm{i}{\mathrm{i}}^{\mathrm{\prime }}}& =2\mathrm{V}+\kappa {\mathbb{I}}_{\{\mathrm{i},{\mathrm{i}}^{\mathrm{\prime }}\}}-\mathrm{c}-\mathrm{t}{\mathrm{d}}_{\mathrm{i}}-\mathrm{t}{\mathrm{d}}_{{\mathrm{i}}^{\mathrm{\prime }}}-{\mathrm{p}}_{\mathrm{i}}-{\mathrm{p}}_{{\mathrm{i}}^{\mathrm{\prime }}},\end{array}$$

(2)

where $\mathbb{I}$ _{{i, i′}} is equal to 1 if services i and i′ are in alliance and 0 otherwise.

Regardless of whether or not there is an alliance, each service sets the price of its subscription independently and simultaneously. We start by assuming that each consumer pays the sum of the prices of all services they subscribe to. Said differently, subscribing to multiple services does not entitle consumers to a price discount (with or without an alliance), which is consistent with the institutional reality. A consumer who subscribes to both Amazon and HBO, for example, ends up paying the sum of the subscription fees incurred upon subscribing to only Amazon and only HBO, even with the alliance between the two firms (Cohen, Blanchet, and Rogers 2022). We investigate the possibility of offering a bundle discount to multihoming consumers in an extension and show the robustness of our findings. The outside option of consumers is normalized to zero, so consumers (single-homing or multihoming) subscribe only if the subscription yields a nonnegative surplus.

It is reasonable to ask, what information do consumers possess at the time of making their homing decision? We assume that the prices set by the three services are common knowledge and that consumers know the valuation of subscribing to an additional service ex ante. If an alliance between two services—say, A and H—facilitates subscribers of A to subscribe to H as well, consumers also know that they will value the additional partnering service higher relative to the case where there is no alliance. However, we must address the issue of whether consumers know about the existence of the alliance before they make their homing decision. For instance, we could imagine situations where the alliance between Amazon and HBO is known to all consumers. It is also possible that consumers do not know ex ante but learn about the alliance only after they subscribe to Amazon or HBO. In the former case, where the existence of the alliance is known ex ante, there is no issue of which service is subscribed to first. ⁴ However, if the existence of the alliance (and hence the opportunity to have an integrated viewing experience with HBO) is known to consumers only after they subscribe to Amazon, we would need to treat that scenario differently. Initially, we assume that the existence of the alliance is common knowledge. In an extension, we will examine the case where consumers learn about the alliance only after subscribing to one service. ⁵

On the service side, we assume that the marginal cost of the content offered is zero. Hence, the profit of service $\mathrm{i}\in \{\mathrm{N},\mathrm{A},\mathrm{H}\}$ is given by π_i = p_iD_i, where D_i is the total demand of the service. We envision the game unfolding in the following stages: Stage 1: the services simultaneously set prices p_i; Stage 2: consumers make their homing decision and choose the service(s) that yield(s) the highest utility. For ease of exposition, we define $\tilde{\mathrm{V}}=\mathrm{V}-\mathrm{c}+\kappa$ . We assume that $\mathrm{V}+\kappa >\mathrm{c}>\mathrm{V}$ , $\mathrm{c}>\kappa$ , and $\mathrm{t}\in (\underset{\_}{\mathrm{t}},\overline{\mathrm{t}})$ , where $\underset{\_}{\mathrm{t}}=207\tilde{\mathrm{V}}/182$ and $\overline{\mathrm{t}}=\min \{42\tilde{\mathrm{V}}/17,2\mathrm{V}\}$ , to ensure the consistency and stability of our proposed equilibria. Please see the proofs of Lemma 1 and Lemma 2 in the Appendix for more details.

Discussion of Some Key Model Assumptions

1. An alliance is formed between only two services: We assume that the focal firm may only form an alliance with one other firm. This assumption is made exogenously, given the focus of our study, which is to examine the effect of an alliance on the nature of competition (and ensuing profits) in the industry. Given this focus, we study the simplest possible setting where two services form an alliance and examine how a third service, representing the “rest of the industry,” reacts to the alliance. In practice, the reason firms choose to not enter into an alliance may be varied (e.g., a firm may seek to protect its brand) and we do not attempt or claim to rationalize this decision. ⁶

2. Generality/specificity to the streaming services market: The following features of the model make it relevant to the streaming services market:

3. The alliance is between services that otherwise compete in the same market and operate at the same level in the channel.

4. The alliance increases consumers’ incentive to multihome. This feature is distinct from licensing arrangements, where if the exclusive content of one service is licensed to another, the incentive to multihome decreases.

We see these features present mainly in the streaming services industry. However, our findings should generalize to other industries (e.g., news subscriptions) that exhibit similar features (Marshall 2023).

Baseline Model: No Alliance

We assume c > V, which implies that subscription to the additional service will yield negative utility (V − c < 0) and no consumer will multihome in the absence of an alliance. Hence, in this benchmark case, each consumer subscribes to just one service. For any given p_N, p_A, and p_H, the consumer indifferent between services N and A is located at x_NA = (t − 3p_N + 3p_A)/(6t), and the consumer indifferent between services A and H is located at x_AH = (t − p_A + p_H)/(2t). Consequently, consumers located in the interval $\mathrm{x}\in ({\mathrm{x}}_{\mathrm{NA}},{\mathrm{x}}_{\mathrm{AH}})$ will subscribe to A. More generally, the demand of service i competing with i′ and i″ is given by:

$${\mathrm{D}}_{\mathrm{i}}={\displaystyle \frac{1}{3}+{\displaystyle \frac{{\mathrm{p}}_{{\mathrm{i}}^{\mathrm{\prime }}}+{\mathrm{p}}_{{\mathrm{i}}^{\mathrm{″}}}-2{\mathrm{p}}_{\mathrm{i}}}{2\mathrm{t}}.}}$$

(3)

We illustrate the demands of all services in Figure 1. Optimizing π_i = p_iD_i with respect to p_i, and invoking symmetry, we obtain the following lemma. Not surprisingly, given the symmetry, firms charge the same price and make identical profits.

Figure 1.

Illustration of the Demands of the Services Under the Baseline Model.

Lemma 1.

In the baseline model, where there is no alliance and all consumers single-home, all services charge p^BASE = t/3, resulting in profits of π^BASE = t/9 in equilibrium.

Subhoming Model: Alliance Between Two Services

We next explore the setting in which two services, the focal firm (say A) and H, enter into an agreement to facilitate multihoming. The alliance increases consumers’ valuation of the additional partnering service to the point that they consider adding a subscription to that service. Specifically, with the alliance, consumers who want to multihome the pair {A, H} derive utility 2V + κ − c but continue deriving utility 2V − c to multihome between the other possible pairs of services. We maintain the assumption that c > V but consider the case where c < V + κ, so that consumers may find it worthwhile to multihome {A, H} but not the other pairs. With the assumption c > V, consumers do not find it optimal to multihome services that are not in alliance. This assumption is not critical to our findings but does allow us to clearly delineate the alliance's effect on competition. ⁷ As noted previously, we assume that this alliance is known to consumers ex ante. Hence, it is useful to think of consumers who end up multihoming {A, H} as making a simultaneous choice of subscribing to both services.

To make the game explicit, without any loss of generality, we assume that services A and H enter into an arrangement to facilitate multihoming between {A, H}. All services set their prices p_i, $\mathrm{i}\in \{\mathrm{N},\mathrm{A},\mathrm{H}\}$ in Stage 1, and then consumers make their homing decision in Stage 2 based on which service(s) yield(s) the highest subscription utility. Since c > V, multihoming between pairs {N, A} or {H, N} is dominated by single-homing. The identity of the marginal consumers indifferent between subscribing to N and A (or H) is given by x_NA (or x_HN) and can be obtained by setting U_N = U_A (or U_N = U_H). The identity of the marginal consumers indifferent between multihoming {A, H} and single-homing A (or H) is given by x_OA (or x_OH) and can be obtained by setting U_AH = U_A (or U_AH = U_H). It is worth noting that while x_NA is a function of p_N and p_A and x_HN is a function of p_H and p_N, x_OA is only a function of p_H and x_OH is only a function of p_A.

Given the identities of the marginal consumers, we can write down the demands of the different services. ⁸ Consumers in the interval $\mathrm{x}\in ({\mathrm{x}}_{\mathrm{OA}},{\mathrm{x}}_{\mathrm{OH}})$ multihome and subscribe to {A, H}. The rest of the consumers single-home and subscribe to only H if $\mathrm{x}\in ({\mathrm{x}}_{\mathrm{OH}},{\mathrm{x}}_{\mathrm{HN}})$ , only A if $\mathrm{x}\in ({\mathrm{x}}_{\mathrm{NA}},{\mathrm{x}}_{\mathrm{OA}})$ and only N if $\mathrm{x}\in ({\mathrm{x}}_{\mathrm{HN}},1)\cup (0,{\mathrm{x}}_{\mathrm{NA}})$ . We illustrate these intervals and the correspondingly chosen service(s) in Figure 2, Panels A and B. Recalling that $\tilde{\mathrm{V}}=\mathrm{V}+\kappa -\mathrm{c}$ , the total demands facing the three services are given by:

$$\begin{array}{ccc}{\mathrm{D}}_{\mathrm{N}}({\mathrm{p}}_{\mathrm{N}},{\mathrm{p}}_{\mathrm{A}},{\mathrm{p}}_{\mathrm{H}})& ={\displaystyle \frac{1}{3}+{\displaystyle \frac{{\mathrm{p}}_{\mathrm{A}}+{\mathrm{p}}_{\mathrm{H}}-2{\mathrm{p}}_{\mathrm{N}}}{2\mathrm{t}},}}& \\ {\mathrm{D}}_{\mathrm{A}}({\mathrm{p}}_{\mathrm{N}},{\mathrm{p}}_{\mathrm{A}})& ={\displaystyle \frac{\mathrm{t}+6\tilde{\mathrm{V}}}{6\mathrm{t}}+{\displaystyle \frac{{\mathrm{p}}_{\mathrm{N}}-3{\mathrm{p}}_{\mathrm{A}}}{2\mathrm{t}},}}& \\ {\mathrm{D}}_{\mathrm{H}}({\mathrm{p}}_{\mathrm{N}},{\mathrm{p}}_{\mathrm{H}})& ={\displaystyle \frac{\mathrm{t}+6\tilde{\mathrm{V}}}{6\mathrm{t}}+{\displaystyle \frac{{\mathrm{p}}_{\mathrm{N}}-3{\mathrm{p}}_{\mathrm{H}}}{2\mathrm{t}}.}}& \end{array}$$

(4)

Figure 2.

Illustration of the Demands of the Services Under Subhoming.

We obtain the equilibrium prices by optimizing the profits of the services π_i = p_iD_i with their respective prices. The prices and profits of the three services are given in Lemma 2.

Lemma 2.

In the setting where A and H enter into an alliance to facilitate multihoming, the prices charged by the three services are ${\mathrm{p}}_{\mathrm{N}}^{\mathrm{SUB}}=(7\mathrm{t}+6\tilde{\mathrm{V}})/33$ and ${\mathrm{p}}_{\mathrm{A}}^{\mathrm{SUB}}={\mathrm{p}}_{\mathrm{H}}^{\mathrm{SUB}}=(\mathrm{t}+4\tilde{\mathrm{V}})/11$ , and the corresponding profits are ${\pi }_{\mathrm{N}}^{\mathrm{SUB}}={(7\mathrm{t}+6\tilde{\mathrm{V}})}^2/(1,089\mathrm{t})$ and ${\pi }_{\mathrm{A}}^{\mathrm{SUB}}={\pi }_{\mathrm{H}}^{\mathrm{SUB}}=3{(\mathrm{t}+4\tilde{\mathrm{V}})}^2/(242\mathrm{t})$ .

Note that because of symmetry, the allied services, A and H, charge the same price ${\mathrm{p}}_{\mathrm{A}}^{\mathrm{SUB}}={\mathrm{p}}_{\mathrm{H}}^{\mathrm{SUB}}$ , and the nonallied service, N, charges a different price ${\mathrm{p}}_{\mathrm{N}}^{\mathrm{SUB}}$ .

Effect of the Alliance on Prices and Profits

Next, we compare the prices of the three services in this equilibrium with the prices in our baseline model to highlight the effect of the alliance between A and H on the intensity of competition between the services.

Proposition 1:

If t < t*, then $({\mathrm{p}}_{\mathrm{A}}^{\mathrm{SUB}}={\mathrm{p}}_{\mathrm{H}}^{\mathrm{SUB}})>{\mathrm{p}}_{\mathrm{N}}^{\mathrm{SUB}}>{\mathrm{p}}^{\mathrm{BASE}}$ and if t ≥ t*, then $({\mathrm{p}}_{\mathrm{A}}^{\mathrm{SUB}}={\mathrm{p}}_{\mathrm{H}}^{\mathrm{SUB}})\le {\mathrm{p}}_{\mathrm{N}}^{\mathrm{SUB}}\le {\mathrm{p}}^{\mathrm{BASE}}$ , where $\mathrm{t}*=3\tilde{\mathrm{V}}/2$ .

Proposition 1 highlights that the alliance between A and H mitigates price competition if the content differentiation is low (t < t*) but intensifies price competition if the content differentiation is high (t ≥ t*). We plot the prices for the three services under the subhoming equilibrium in Figure 3. The y-axis represents the price and the x-axis represents the misfit cost parameter t, which captures how differentiated the content is across the services.

Figure 3.

Comparison of the Subhoming Equilibrium Prices with the Baseline Equilibrium Price.

We find, interestingly, that when t < t*, both A and H's prices are higher than N's price (and all prices are higher than the baseline price), whereas when t ≥ t*, A and H's prices are lower than N's price (and all prices are lower than the baseline price). The intuition for this finding is the following. We begin by noting that when t = t*, ${\mathrm{p}}_{\mathrm{i}}^{\mathrm{SUB}}={\mathrm{p}}^{\mathrm{BASE}}=\mathrm{t}/3$ , $\mathrm{\forall }\mathrm{i}=\{\mathrm{A},\mathrm{H},\mathrm{N}\}$ , and the demand from multihomers equals 1/3, as all consumers in the interval $\mathrm{x}\in [1/3,2/3]$ multihome. However, when t < t*, the demand from multihomers exceeds 1/3, as some consumers located at x < 1/3 and x > 2/3 also prefer to multihome (see Figure 2, Panel B). This is because when t is smaller, a larger segment of consumers finds value in multihoming under the alliance, as the misfit cost (t), and hence the disutility from consuming nonideal content is lower. We find that when t < t*, the allied firms’ marginal benefit of increasing price above the baseline (t/3) exceeds the marginal cost of reduced demand as a result of the higher price. In other words, they prefer to harvest the rather large base of multihoming consumers by increasing price (above the baseline). Conversely, when t ≥ t*, the set of consumers who multihome are within the interval [1/3, 2/3] (depicted in Figure 2, Panel A). In this case, the firms prefer to reduce price to increase the demand from multihomers at the expense of reduced margins.

To see this more formally, consider the marginal change in profit for the focal firm A for a change in price p_A from the baseline price (p^BASE = t/3):

$$\begin{array}{rl}& {\displaystyle \frac{\mathrm{\partial }{\pi }_{\mathrm{A}}}{\mathrm{\partial }{\mathrm{p}}_{\mathrm{A}}}={\mathrm{p}}_{\mathrm{A}}{\displaystyle \frac{\mathrm{\partial }{\mathrm{D}}_{\mathrm{A}}}{\mathrm{\partial }{\mathrm{p}}_{\mathrm{A}}}+{\mathrm{D}}_{\mathrm{A}}.}}\\ & \Rightarrow {{\displaystyle \frac{\mathrm{\partial }{\pi }_{\mathrm{A}}}{\mathrm{\partial }{\mathrm{p}}_{\mathrm{A}}}}|}_{\begin{array}{c}{\mathrm{p}}_{\mathrm{i}}=\mathrm{t}/3\\ \mathrm{\forall }\mathrm{i}\in \{\mathrm{N},\mathrm{A},\mathrm{H}\}\end{array}}=-{\displaystyle \frac{1}{2}+\left(-{\displaystyle \frac{1}{6}+{\displaystyle \frac{\tilde{\mathrm{V}}}{\mathrm{t}}}}\right).}\end{array}$$

The first term represents the marginal cost of reduced demand from increasing price and the second term represents the marginal benefit from increased margins. It is easy to see that ${\frac{\mathrm{\partial }\pi \mathrm{A}}{\mathrm{\partial }\mathrm{pA}}|}_{{\mathrm{p}}_{\mathrm{i}}=\mathrm{t}/3}>0$ , when $\mathrm{t}<3\tilde{\mathrm{V}}/2$ and ${\frac{\mathrm{\partial }\pi \mathrm{A}}{\mathrm{\partial }\mathrm{pA}}|}_{{\mathrm{p}}_{\mathrm{i}}=\mathrm{t}/3}\le 0$ when $\mathrm{t}\ge 3\tilde{\mathrm{V}}/2$ , where $3\tilde{\mathrm{V}}/2=\mathrm{t}*$ . Consequently, the firms in the alliance charge prices above the baseline when t < t* and below the baseline when t ≥ t*. Since prices are strategic complements, the nonallied firm also charges above or below the baseline depending on whether t < t* or t ≥ t*, respectively.

Furthermore, N's price is always between the baseline price and the allied services’ price (A and H's price). The intuition for this result is that with multihoming, A and H essentially do not have to compete (in prices) for the marginal consumer indifferent between multihoming and subscribing only to the partnering service. Consider, for example, the demand of service A. The relevant marginal consumer on the circle toward its partnering service H is given by x_OH, which depends only on p_A (see Figure 2). In contrast, the relevant marginal consumer toward N is given by x_NA, which depends on both p_A and p_N. This is not the case with N, since the marginal consumer indifferent between N and H (or A) depends on both p_N and p_H (or p_A). Because N is competing with both A and H, its response both above (when t < t*) and below (when t ≥ t*) the baseline price is muted.

We next compare the profits of the three services under the alliance between A and H with the profits in our baseline model.

Proposition 2:

Comparing the profits under the arrangement where A and H enter into an alliance to facilitate multihoming with the benchmark model,

if t ≤ t*, $({\pi }_{\mathrm{A}}^{\mathrm{SUB}}={\pi }_{\mathrm{H}}^{\mathrm{SUB}})>{\pi }_{\mathrm{N}}^{\mathrm{SUB}}\ge {\pi }^{\mathrm{BASE}}$ ,

if t* < t < t⁺, $({\pi }_{\mathrm{A}}^{\mathrm{SUB}}={\pi }_{\mathrm{H}}^{\mathrm{SUB}})>{\pi }^{\mathrm{BASE}}>{\pi }_{\mathrm{N}}^{\mathrm{SUB}}$ ,

if t ≥ t⁺, ${\pi }^{\mathrm{BASE}}\ge ({\pi }_{\mathrm{A}}^{\mathrm{SUB}}={\pi }_{\mathrm{H}}^{\mathrm{SUB}})>{\pi }_{\mathrm{N}}^{\mathrm{SUB}}$ ,

where ${\mathrm{t}}^{+}=\frac{12\left(9+11\sqrt{6}\right)}{215}\tilde{\mathrm{V}}$ .

We find that not only are the prices charged by services higher when t < t*, but the demands and therefore the profits of all services are also greater relative to those in the baseline model (please see Figure 4). As noted previously, when t = t*, the prices charged by the three services are equal to the price in the baseline model (t/3). Furthermore, all consumers in the interval [1/3, 2/3] subscribe to both A and H. Given the symmetry in prices, N serves 1/3 of the market. However, the demand of A and H is greater than 1/3, as all consumers in the interval [1/3, 2/3], a measure 1/3, subscribe to both A and H plus a measure 1/6 of the consumers located between the respective service and N subscribe only to them, for a total demand of 1/3 + 1/6 = 1/2. Therefore, when t = t*, N's profit is ${\pi }_{\mathrm{N}}^{\mathrm{SUB}}=1/3\times \mathrm{t}/3=\mathrm{t}/9$ , which is equal to its profit in the baseline model, while the profits of A and H, ${\pi }_{\mathrm{A}}^{\mathrm{SUB}}={\pi }_{\mathrm{H}}^{\mathrm{SUB}}=1/2\times \mathrm{t}/3=\mathrm{t}/6$ , are strictly greater than their profits in the baseline model. When t < t*, the prices of both A and H are strictly greater than that of N and all prices are greater than the prices in the baseline model. As a result, N's demand is strictly greater than 1/3 and profits are greater than t/9. Even though A and H lose some demand to N, they are compensated by the increased demand from multihoming consumers, resulting in higher profits than in the baseline model. Therefore, when t < t*, the alliance between A and H benefits all services.

Figure 4.

Comparison of the Subhoming Equilibrium Demands and Profits with the Baseline Equilibrium.

When t > t*, given that prices of A and H are lower than that of N, the demand of N is less than 1/3. Since the price of N is also strictly lower than that in the baseline model, its profit is also lower than its baseline profit. Conversely, the demand for A and H is higher than that for the baseline model, thanks to both the influx of demand from multihoming consumers and their prices being lower than that of N. This higher demand more than compensates for the lower price when t < t⁺ and the profits of both A and H are higher than the baseline. However, as t increases further, the number of multihoming consumers decreases, and since the services are more differentiated, it reduces the ability of A and H to steal consumers from N via price reduction. Therefore, when t > t⁺, the additional demand no longer compensates for the drop in price, leading to lower profits for A and H relative to the baseline model.

Effect of the Alliance on Social Welfare

We also analyze the impact of the alliance between A and H on the consumer and social welfare. We summarize our findings in the following proposition.

Proposition 3:

Comparing the alliance with the benchmark model,

consumer surplus is always higher,

social welfare is higher if and only if $\mathrm{t}<\hat{\mathrm{t}}$ , where $\hat{\mathrm{t}}=\frac{6\left(137-11\sqrt{110}\right)}{53}\tilde{\mathrm{V}}$ and $\hat{\mathrm{t}}>{\mathrm{t}}^{+}$ .

Interestingly, Proposition 3 demonstrates that the alliance always increases consumer surplus. This is true even when the alliance relaxes price competition between the services. The intuition behind this result is that the alliance has a direct impact on the utility of consumers—it increases the multihoming utility by κ. As a result, while some consumers have a lower utility owing to higher prices, other consumers gain a higher utility by multihoming despite paying higher prices. The net effect is an increase in consumer surplus. Since consumer surplus always increases and all firms are better off when t < t*, the social welfare also increases when differentiation is low. However, when differentiation is very high ( $\mathrm{t}>\hat{\mathrm{t}}$ ), the social welfare may be lower, owing to reduced profits for all three firms at high $\mathrm{t}$ (please see Figure 4b). Since $\hat{\mathrm{t}}>{\mathrm{t}}^{+}$ , the social welfare is always higher under the alliance when it increases the allied firms’ profits.

In summary, in this subhoming setup, we focus on how an alliance between two services affects price competition, profits, and welfare. We have identified market conditions where competition is relaxed and the alliance exerts a positive externality on, and benefits, the nonpartnering firm as well. We also show that the alliance need not always relax price competition, but despite more intensified price competition, the alliance can still benefit the partnering services so long as the content market is not too differentiated. We are also able to show that the consumer surplus is higher (relative to the baseline) even when price competition is relaxed. Thus, our results show that the alliance's impact on price competition is nuanced and highlight the effect of the interplay between the alliance and content differentiation on price competition and ensuing profits and welfare.

In the next section, we relax the symmetry assumption and allow firms to be asymmetric both in how consumers value their content and the size of their loyal consumer bases. In our main model, since firms are symmetric, the question of which firm to partner with is moot. Relaxing the symmetry assumption allows us to shed light on the question of which to partner with.

Which Firm Should You Partner With?

In this section, we study the question of with which firm focal firm A should partner. In the main model, since both neighboring firms N and H are symmetric, the focal firm is indifferent between partnering with firm N or H. In this extension, we introduce asymmetry between the two neighboring firms in two ways: (1) we allow the two firms to have different levels of content quality and (2) we allow the sizes of their loyal consumer bases to be different. Differences in the quality of content should be viewed as distinct from the spatial differentiation in content formalized in our main model. As noted previously, it is helpful to think of spatial differentiation in content across services arising from the difference in the type of the content they offer, while quality differentiation (for the same content type) can arise based on the quality of the cast, production, direction, budget, and so on.

Formally, we allow each service $\mathrm{i}\in \{\mathrm{N},\mathrm{A},\mathrm{H}\}$ to have different base valuations for their content: A subscriber derives consumption utility V + Δ_i instead of V from subscribing, where Δ_i ≥ 0 represents the boost in valuation from the quality of service i. Next, we allow each service to have a loyal consumer base of size μ ≥ 0. Loyalty to a specific service may arise because consumers view its content as their ideal content, with no other substitute. These loyal consumer bases only subscribe to the service that they are loyal to and are not interested in multihoming. They are separate from the unit mass of consumers distributed over the Salop circle. Hence, the mass of consumers in this setup is 1 + μ_A + μ_H + μ_N. It is easy to normalize the size of the market to one, but this formulation allows us to make statements about how a change in one loyal segment size affects outcomes while holding other segment sizes constant. ⁹ We compute the optimal prices and profits analogously under two scenarios: (1) when there is no alliance and (2) when the focal firm i partners with i′ (without loss of generality). We summarize them in Lemma W.1 in the Web Appendix. ¹⁰

We find that the profit of each service increases as the size of the loyal consumer base of a competing firm increases, and it decreases as the base valuation of a competing firm increases. The intuition behind this finding is that price reductions are costlier for the competing firm when it has a larger loyal segment because the price reductions needlessly subsidize sales to its loyal consumers. Consequently, its incentive to decrease price is reduced, which in turn relaxes price competition, lifting profits. In contrast, when the base valuation of the rival firm increases, the firm has to compete more aggressively to maintain share, which adversely affects profits.

We also find that, in the presence of an alliance, the profit of each firm in the alliance is more sensitive to the size of the loyal segment and the base valuation of the nonallied firm rather than the allied firm. Consequently, a firm would prefer to partner with a firm that has a small loyal base and high base valuation. The intuition for this follows directly from the discussion in the previous paragraph. Once an alliance is formed, the partnering firms no longer compete for the marginal consumer. Therefore, the allied services’ direct competition is solely with the service outside the alliance. The question then essentially boils down to whether the focal firm wants the nonallied service to be a strong or a weak competitor. For reasons mentioned previously, the service with the relatively larger loyal segment and lower base valuation poses a lower competitive threat and is best left out of the alliance. To demonstrate this, we compare the profit of the focal firm A upon partnering with N to its profit upon partnering with H to obtain the following proposition.

Proposition 4:

The focal service A prefers to partner with the service N over H if $({\mathrm{\Delta }}_{\mathrm{N}}-{\mathrm{\Delta }}_{\mathrm{H}})>\frac{10\mathrm{t}}{9}({\mu }_{\mathrm{N}}-{\mu }_{\mathrm{H}})$ and with H over N otherwise.

Proposition 4 suggests that the focal firm prefers to partner with a firm that has a higher level of quality and/or a smaller loyal segment (relative to the other firm). The firm with a higher level of quality and a smaller loyal base poses a more serious competitive threat, and hence, partnering with it is optimal. This is akin to “sleeping with the enemy” or “keeping your enemies close.” We tabulate the different scenarios and the corresponding partner of choice in Table 1. If, for instance, service H has higher quality (Δ_H > Δ_N) but a smaller loyal base (μ_H < μ_N) as compared with service N (bolded cell in Table 1), then the focal firm A prefers partnering with H over N. This result is in line with the observation that Amazon has allied with HBO but not with Netflix. As noted previously, Netflix has a larger loyal base as compared with HBO: 80% of Netflix subscribers subscribe only to Netflix, compared with 28.5% for HBO (Molla 2017). HBO, however, is considered to produce and carry more high-quality content (Hall 2022). Hence, our results indicate that Amazon should prefer forming an alliance with HBO over Netflix.

Table 1.

Optimal Partner Choice of the Focal Firm A.

		Who Has High Quality (Δ)?
		H	N
Who has more loyal customers (μ)?	H	Depends	Partner with N
	N	Partner with H	Depends

Similarly, if Δ_H < Δ_N and μ_H > μ_N, then A would prefer partnering with N over H. However, if the same service has higher quality and a larger loyal base (cells labeled “Depends” in Table 1), then the decision of which firm to partner with depends on whether the inequality identified in Proposition 4 is satisfied. While Proposition 4 addresses the issue of which firm to partner with, it does not clarify whether partnering with N or H results in higher profits than the baseline (for the partnering firms). To address this issue, we take the partner of choice of the focal firm as N or H depending on whether the condition in Proposition 4 is satisfied and compare the profits of the partnering firms conditional on entering into an alliance with their baseline profits (with no alliance). A detailed analysis of this can be found in the Web Appendix.

Extension: Bundle Discount

In our main model, we assume that consumers who multihome are not entitled to a discount—that is, they end up paying the sum of the prices of the two services they subscribe to. The goal of this extension is to demonstrate the robustness of our findings by relaxing this assumption. We extend our main subhoming model by allowing the allied services to offer a bundle discount to consumers who subscribe to both services. Without loss of generality, we assume that services A and H enter into the alliance. Consumers pay price p_B = p_A + p_H − γ to subscribe to both A and H and receive utility ${\mathrm{U}}_{\mathrm{AH}}=\mathrm{V}+\tilde{\mathrm{V}}-{\mathrm{td}}_{\mathrm{A}}-{\mathrm{td}}_{\mathrm{H}}-{\mathrm{p}}_{\mathrm{B}}$ . The parameter γ represents the discount offered to multihoming consumers. We assume that γ is set by one of the two allying services, say H. The rationale for this is that in practice, one of the services in the alliance (say A) acts as the focal service and hosts other services on it (in this case, H). Hence, it is reasonable to assume that the hosted service makes the discount decision and bears the cost of it. We also note that while both the discount γ and the higher consumption utility κ from the alliance positively affect the multihoming utility, their cost side implications differ. Offering a discount to multihomers imposes a marginal cost equal to γ per user. In contrast, increasing the multihoming valuation—by offering a more integrated experience—imposes no additional marginal cost. However, it may involve a fixed cost of developing and maintaining the integrated viewing experience, which we assume to be zero. ¹¹

The profits of the three services are given by π_N = p_ND_N, π_A = p_AD_onlyA + p_AD_{{A, H}}, and π_H = p_HD_onlyH + (p_H − γ)D_{{A, H}}. The game unfolds in the following stages: Stage 1: the services simultaneously set prices p_i, $\mathrm{i}\in \{\mathrm{N},\mathrm{A},\mathrm{H}\}$ ; Stage 2: H sets the bundle discount γ; and Stage 3: consumers make their homing decision and choose the service(s) that yield(s) the highest utility. All other assumptions of the main model are maintained. Additionally, we assume $\mathrm{t}\in (207\tilde{\mathrm{V}}/182,min\{2\mathrm{V},138\tilde{\mathrm{V}}/43\})$ to ensure that the characterized equilibria are consistent and stable. We summarize our findings in the following proposition.

Proposition 5:

In the setting where A and H enter into an alliance to facilitate multihoming and multihoming consumers get a discount of γ:

If t < t⁰, H sets γ* = 0, and if t ≥ t⁰, $\gamma *=\frac{89}{312}\mathrm{t}-\frac{21}{52}\tilde{\mathrm{V}}$ ,

If t < t*^DISC, ${\mathrm{p}}_{\mathrm{i}}^{\mathrm{DISC}}>{\mathrm{p}}^{\mathrm{BASE}}$ and if t ≥ t*^DISC, ${\mathrm{p}}_{\mathrm{i}}^{\mathrm{DISC}}\le {\mathrm{p}}^{\mathrm{BASE}}$ ,

If $\mathrm{t}<{\mathrm{t}}_{\mathrm{i}}^{+\mathrm{DISC}}$ , ${\pi }_{\mathrm{i}}^{\mathrm{DISC}}>{\pi }^{\mathrm{BASE}}$ , and if $\mathrm{t}\ge {\mathrm{t}}_{\mathrm{i}}^{+\mathrm{DISC}}$ , ${\pi }_{\mathrm{i}}^{\mathrm{DISC}}\le {\pi }^{\mathrm{BASE}}$ ,

where ${\mathrm{t}}^0=\frac{18(104\sqrt{30}-69)}{6,269}\tilde{\mathrm{V}}$ , ${\mathrm{t}}^{*\mathrm{DISC}}=2\tilde{\mathrm{V}}$ , ${\mathrm{t}}_{\mathrm{N}}^{+\mathrm{DISC}}={\mathrm{t}}^{*\mathrm{DISC}}$ , ${\mathrm{t}}_{\mathrm{H}}^{+\mathrm{DISC}}=\frac{6\left(805-52\sqrt{106}\right)}{673}\tilde{\mathrm{V}}$ and ${\mathrm{t}}_{\mathrm{A}}^{+\mathrm{DISC}}=\frac{18\left(85+52\sqrt{5}\right)}{1,259}\tilde{\mathrm{V}}$ .

Proposition 5 demonstrates the robustness of our main findings even in the presence of an endogenously set bundle discount. We plot the prices and the profits of the three services with and without the alliance in Figure 5. The service H sets discount to be zero when the content differentiation (t) is low. The discount is nonzero and increases with differentiation (t) when it is high. Recall that in our main model when content is sufficiently differentiated t > t*, price competition is intensified. The bundle discount allows the firms to decouple the multihoming price and the single-homing price. While in our main model, the multihoming price is the sum of the single homing prices of the allied services, in this model, the multihoming price is equal to the sum minus a discount (γ). By offering a discount selectively to the multihoming consumers, the allied services are able to compete less intensely. A few observations are noteworthy when the discount is endogenously determined:

Recall that, in our main model, competition is relaxed when t < t* and intensified when t ≥ t*. In this extension, the same is true depending on whether t < t*^DISC or t ≥ t*^DISC, respectively. Also note that t*^DISC > t* (see Figure 5, Panel A). Therefore, when the discount is set endogenously, the region over which competition is relaxed is expanded. Because prices are strategic complements, this exerts a positive externality on the nonallied partner (N), which is also able to make higher profits relative to baseline over a larger region.

Furthermore, the ability to offer a discount selectively to multihomers serves as a strategic tool and allows the allied partners to compete more effectively with the nonallied service. In the region where competition is intensified, the single-homing prices are not as low as in our main model. In other words, the ability to offer a discount selectively dampens the intensity with which price competition is intensified and is a win-win for both the allied partners and the nonallied service.

In our main model, the prices and profits of the allied partners (A and H) are symmetric. However, in this extension, since H sets and bears the cost of the discount, the prices and profits of A and H are no longer the same (refer to Figure 5, Panels A and B, to note the difference). In our main model, the profits of the allied partners are higher as long as t < t⁺. Note that, in this extension, ${\mathrm{t}}_{\mathrm{N}}^{+\mathrm{DISC}}<{\mathrm{t}}_{\mathrm{H}}^{+\mathrm{DISC}}<{\mathrm{t}}_{\mathrm{A}}^{+\mathrm{DISC}}$ . This implies that the alliance is profitable for both partners only if $\mathrm{t}<{\mathrm{t}}_{\mathrm{H}}^{+\mathrm{DISC}}$ , even though for $\mathrm{t}\in ({\mathrm{t}}_{\mathrm{H}}^{+\mathrm{DISC}},{\mathrm{t}}_{\mathrm{A}}^{+\mathrm{DISC}})$ , the focal firm A 's profits from the alliance are higher than its baseline profits.

Figure 5.

Comparison of the Equilibrium Prices and Profits Under a Bundle Discount with the Baseline Equilibrium (for V = .5, c − κ = .2).

In summary, this extension offers insights on how discounts may be used as a strategic tool to compete more effectively with the nonallied service. Furthermore, we show that the key results of our main model are robust to relaxing the assumption in our main model that multihomers are not entitled to a bundle discount.

Extension: Alliance Revealed Ex Post

In this extension, consumers are ex ante unaware of the alliance and only learn about it after having subscribed to the focal service. Consumers in this model make their first and second subscription decisions sequentially. Additionally, we distinguish between the two services that enter into the alliance. Only one of them, which we call the focal service, offers an integrated experience of the other service's content on its website. ¹² For example, if A and H enter into the alliance and A is the focal service, subscribers of A can add H's subscription and view its content on A's website, but the reverse is not true. Consequently, only the subscribers of the focal service can benefit from the alliance. These assumptions mimic the setting wherein Amazon subscribers can choose to subscribe to HBO once they have subscribed to Amazon but not vice versa. If consumers are ex ante aware of the alliance, as in our main model, then they can anticipate their multihoming preference and pick the subscription order accordingly. Hence, in our main model, the distinction between who offers the integrated experience does not affect consumers’ homing decisions and hence the services’ demands. However, if consumers are ex ante unaware of the alliance, then this distinction becomes relevant.

Formally, we assume, without loss of generality, that A is the focal service that allies with service H. The game unfolds in the following stages: Stage 1: the services simultaneously set prices p_i, $\mathrm{i}\in \{\mathrm{N},\mathrm{A},\mathrm{H}\}$ ; Stage 2: consumers make their first subscription decision by choosing the service that yields the highest utility; and Stage 3: consumers learn about the alliance if they subscribe to the focal service A and decide whether to add a second subscription (to service H). We maintain the assumption that V < c < V + κ and c > κ. Additionally, we assume that $\mathrm{t}\in \left(\frac{6(13-2\lambda )\tilde{\mathrm{V}}}{35-6\lambda },\min \left\{\frac{6(55-7(1-\lambda )\lambda )\tilde{\mathrm{V}}}{305-(47-17\lambda )\lambda },2\mathrm{V}\right\}\right)$ to ensure the consistency and stability of the proposed equilibrium.

Since consumers are initially unaware of the alliance, their ex ante expected utility of adding a second subscription is V − c, which is negative for all possible sequences of pairs of services. Hence, all consumers make their first subscription decision (in Stage 2) with the expectation of not multihoming, similar to our baseline model. In Stage 3, consumers who chose to subscribe to A learn about the alliance and decide whether to multihome and subscribe to H. As in our main model, the profits of the services are given by π_i = p_iD_i. We obtain the equilibrium prices by optimizing the profits with respect to their respective prices. We summarize them in Lemma W.3 in the Web Appendix. The results on prices and profits of the allied partners and the nonallied service in this setup are summarized in Proposition 6.

Proposition 6:

In the setting where only the focal service A allows add-on subscriptions to H and consumers are ex ante unaware of their alliance:

If t ≤ t*, then ${\mathrm{p}}_{\mathrm{i}}^{\mathrm{EXP}}\ge {\mathrm{p}}^{\mathrm{BASE}}$ , and if t > t*, then ${\mathrm{p}}_{\mathrm{i}}^{\mathrm{EXP}}<{\mathrm{p}}^{\mathrm{BASE}}$ , where $\mathrm{t}*=3\tilde{\mathrm{V}}/2$ .

If t ≤ t*, then ${\pi }_{\mathrm{H}}^{\mathrm{EXP}}>({\pi }_{\mathrm{A}}^{\mathrm{EXP}}={\pi }_{\mathrm{N}}^{\mathrm{EXP}})\ge {\pi }^{\mathrm{BASE}}$ ; if $\mathrm{t}*<\mathrm{t}<{\mathrm{t}}_{\mathrm{EXP}}^{+}$ , then ${\pi }_{\mathrm{H}}^{\mathrm{EXP}}>{\pi }^{\mathrm{BASE}}>({\pi }_{\mathrm{A}}^{\mathrm{EXP}}={\pi }_{\mathrm{N}}^{\mathrm{EXP}})$ ; and if $\mathrm{t}\ge {\mathrm{t}}_{\mathrm{EXP}}^{+}$ , then ${\pi }^{\mathrm{BASE}}\ge {\pi }_{\mathrm{H}}^{\mathrm{EXP}}>({\pi }_{\mathrm{A}}^{\mathrm{EXP}}={\pi }_{\mathrm{N}}^{\mathrm{EXP}})$ , where ${\mathrm{t}}_{\mathrm{EXP}}^{+}=\frac{18\left(17\sqrt{6}+15\right)}{503}\tilde{\mathrm{V}}$ .

We plot the equilibrium prices and profits under this model in Figure 6. We find that since the two partnering firms are no longer symmetric, the price and profit of A and H are not the same in this extension. In fact, the price and profit of A are the same as that of N. Since the entire revenue from add-on subscriptions goes to H, A has no incentive to change its price to impact the demand of this add-on subscription. In contrast, H would want to change its price to maximize its profit coming from both first and second subscriptions. Similar to our main model, H charges a higher price (as compared with the baseline price) to leverage the multihomers when t < t* and a lower price to attract multihomers when t > t*. Both A and H respond by increasing and decreasing their price, though to a lower extent, respectively, due to strategic complementarity. We find that all services, including N, are better off with the alliance between A and H when the level of differentiation is sufficiently low (t < t*). When the level of differentiation is sufficiently high (t > t*), both A and N are no longer better off under the alliance. Hence, in contrast to our base model, the alliance is feasible only when competition is relaxed. We provide further details of this analysis in the Web Appendix.

Figure 6.

Prices and Profits Under the Ex Post Awareness Equilibrium Compared with the Baseline Equilibrium.

It is reasonable to ask why A would enter into the alliance if the primary beneficiary of the alliance is going to be H. Can the focal firm A extract additional rents from H through a revenue-sharing arrangement? This would be similar to the institutional setting wherein Amazon takes a cut of the revenue for add-on subscriptions to other partnering services (James 2022). We explore this issue in an extension in the Web Appendix and identify market conditions where a revenue sharing arrangement can be profitable for both partners. We show that an alliance between A and H can be profitable with revenue sharing even when competition is intensified.

Concluding Remarks

This research is motivated by the changes that have occurred in the OTT subscription video streaming market in recent years. Once dominated by major players like Netflix and Amazon Prime Video, the industry has seen a mushrooming of many smaller video streaming services and the late entry of major players like HBO Max and Disney+, making the market extremely competitive. While there is no doubt that competition is intensifying with the entry of newer services, the majority of U.S. households multihome (i.e., subscribe to multiple streaming services). We are also witnessing an increase in the number of partnerships between competing streaming services such as Amazon and HBO, Hulu and Disney, and so on, to name a few.

The goals of this study are to examine the effect of partnering with a competitor on competition in a context in which consumers may multihome and to shed light on the question of which competitor to partner with. To do this, we develop a game-theoretic framework in which three services are symmetrically located on a unit circle. In the baseline model, where there is no alliance, the services set prices simultaneously, and consumers single-home and choose the service that yields the highest utility. This model provides a benchmark to compare with when two of the services partner to form an alliance that facilitates multihoming between the partnering firms. Some consumers in this setting multihome, and we find that price competition between the services is attenuated if the services are not too differentiated. Under these market conditions, the prices charged by all the services are higher than those in the baseline model. Interestingly, the alliance between the partnering services not only increases their profits relative to the baseline but also benefits the nonpartnering service. Counter to intuition, the alliance intensifies price competition when the services are sufficiently differentiated. Not only are the prices under these market conditions lower than those in the baseline model but the partnering services charge lower prices than the nonpartnering service. We find that the profits of the partnering firms can still be higher than that in the baseline model so long as the content is not too differentiated, but the partnership adversely affects the profits of the nonpartnering service.

Next, we consider a setting where content services are asymmetric in terms of their quality and the size of their loyal consumer base, which enables us to investigate the focal service's decision of which competitor to partner with. We find that the focal firm prefers to partner with a service that has a higher level of quality but, counter to intuition, a relatively smaller loyal consumer base. The intuition behind this result is that while a competitor with high quality poses a higher competitive threat, a competitor with a larger consumer base is less likely to indulge in price competition. We also show that the alliance can only benefit the partnering firms when the market is not too differentiated.

We also analyze two extensions of our main model. In the first extension, multihoming consumers receive a bundle discount. We find that the results from our main model on the interplay between content differentiation and the intensity of price competition remain robust under this extension. We also show that bundle discounts expand the region over which competition is relaxed and can be used as a strategic tool to compete more effectively with the nonallied service. In the second extension, we relax the assumption that the existence of the alliance is common knowledge. Consumers only become aware of the existence of the alliance after subscribing to a focal service and then add the subscription to the partnering service if it yields a nonnegative surplus. With this extension, we demonstrate that the findings of our main model are robust and not sensitive to the assumption on the timing of when consumers become aware of the alliance. We also identify the market conditions where a mutually beneficial revenue-sharing arrangement is feasible.

Our findings build on and contribute to extant work on multihoming, partnerships, and strategic decisions in the content market. Our analysis offers insights into market considerations that impact strategic decisions for both managers and policymakers interested in consumer welfare. Our findings suggest that services should consider forming an alliance when the content market is not too differentiated. We also shed light on the impact of such an alliance on nonpartnering firms and demonstrate that even they may be better off when the content differentiation is sufficiently low. We show that revenue-sharing arrangements may be necessary to justify the alliance when the market is moderately differentiated if consumers learn about the alliance only after first subscribing to the focal firm. The exit and subsequent return of HBO Max on Amazon Prime Video may highlight the importance of these arrangements (James 2022). Furthermore, our findings provide guidance to services regarding which other services they should partner with. We show that a focal service should aim to partner with services that have relatively higher-quality content but a smaller loyal base. This finding may help explain why Amazon chose to partner with HBO, which is known to have higher-quality content but a smaller loyal consumer base compared with Netflix. Lastly, our findings also have implications for policymakers interested in consumer welfare. We find, interestingly, that consumer welfare is always higher with alliances even if price competition is relaxed and consumers end up paying higher prices relative to the baseline. Our analysis suggests that policymakers interested solely in consumer welfare should not be opposed to such alliances, even if they relax price competition. However, social welfare can be lower under alliances if content is sufficiently differentiated.

We conclude with a discussion of some avenues for future research. In this article, we take the content strategies as given to isolate and focus on studying the impact of alliances that facilitate multihoming on price competition. Future work may consider incorporating firms’ investment decisions in original/licensed content and studying how those decisions may shed light on alliances that facilitate multihoming. Furthermore, while our analysis explores the case where firms cater only to the consumer side of a multisided market, future work could consider how advertisers and/or content creators (with cross-sided network effects) may moderate the impact of alliances that facilitate multihoming on price competition and profits. In an extension, we model the case where the subhoming arrangement is asymmetric—that is, while subscribers of one service are able to sign up for the partnering service and enjoy the integrated viewing experience, the reverse is not true. Future work may explore strategic considerations that may rationalize such an arrangement. Another avenue of future research is to study how streaming alliances of services that are independent and competitors compare with a setting where a monopolist owns all services and can offer bundles of different services.

Supplemental Material

sj-pdf-1-mrj-10.1177_00222437251381805 - Supplemental material for Multihoming Alliances and Price Competition

Supplemental material, sj-pdf-1-mrj-10.1177_00222437251381805 for Multihoming Alliances and Price Competition by Abhinav Uppal, Nanda Kumar and Manish Gangwar in Journal of Marketing Research