Vertical and horizontal complementarities in platform ecosystems

ABSTRACT

We develop a framework of vertical and horizontal complementarities in platform ecosystems. Complementarity is a key theoretical construct for scholars investigating digital platforms and ecosystems, often mentioned in the context of complements, components, modularity, interdependence, and synergies. We shortly review the literature on complementarities in general strategy literature and then conceptualise complementarities in platform ecosystems. We distinguish between ‘vertical complementarity’ which signifies how complements (e.g., apps) increase the value of a platform (e.g., Android) and ‘horizontal complementarity’ which relates to the value creating complementarities between complements on a platform (e.g., an email and a calendar app). This distinction helps to clarify the notion of complementarities in platform ecosystems and has implications for our understanding of network effects, interdependence, generativity, platform governance, and platform strategy.

KEYWORDS:

• Platform
• ecosystem
• complement
• complementarity
• interdependence

Introduction

Platform value creation results from dynamic combinations of different resources, components, processes, and autonomous actors – most of which reside outside the focal platform firm and its hierarchical control (Parker, van Alstyne, & Jiang, 2017). These combinations are often complementary in nature (Baldwin, 2024; Cenamor et al., 2013; Ennen & Richter, 2010; Kapoor, 2018). Platform complementarities are studied most often in software-based platforms such as the platform ecosystems of Android or Apple, where complements (such as apps) provide complementary inputs to the value of the platform (e.g., Parker et al., 2017; Reuver, Sorensen, & Basole, 2018). However, in a similar vein, complementarity also takes place in data-based platforms such as Google Maps between the map database (platform core) and the complementary data about the locations added on top of it. Some scholars go as far to claim that a platform has no value without complements – and if the platform is unique in the market, then complements also have no value without the platform via which they are delivered to the platform user (Baldwin & Woodard, 2009).

However, complementarity also exists between complements, e.g., apps on a software platform, or between different content offered on a platform (Agarwal & Kapoor, 2022). For instance, there is complementarity in platform user value when calendar app and an email app are used together. Similarly, different data within Google Maps regarding a specific location complement each other, as do different entries in Wikipedia (Ritala & Karhu, 2023). As these examples show, complementarities can exhibit complex interdependencies in how they affect value creation on the platform (Baldwin, 2024; Hilbolling, Berends, Deken, & Tuertscher, 2020; Kapoor & Agarwal, 2017; Rietveld, Schilling, & Bellavitis, 2019), and, ultimately, drive network effects (Cenamor et al., 2013; Rietveld & Schilling, 2021).

While we know that complementarities clearly play a role in creating value in platform ecosystems, ‘the literature on complements is both confused and complex’ (Teece, 2018, p. 1373). An issue is that platform scholars have tended to interpret complementarities in a variety of ways, leveraging not only insights from multi-sided markets (e.g., Armstrong & Wright, 2007; Rochet & Tirole, 2006), but also from strategy (e.g., Harrison, Hitt, Hoskisson, & Ireland, 2001; Williamson, 1985) and the emerging ecosystem literature (e.g., Adner, 2017; Jacobides, Cennamo, & Gawer, 2018). Perhaps as a result, complementarities are discussed in parallel or in conjunction to complements and components (Burford et al., 2022), interdependencies (Kapoor, 2018), modularity (Jacobides et al., 2018), and synergies (Mantovani & Ruiz-Aliseda, 2016). The challenge of conceptualising complementarities is not new: many years ago, Samuelson (1974, p. 1255) noted that the ‘the time is ripe for a fresh, modern look at the concept of complementarity … this ancient preoccupation of literary and mathematical economists. The simplest things are often the most complicated to understand fully’. Therefore, it is crucially important to clarify complementarity as a theoretical construct in platform ecosystems to enable cumulative scholarship on this focal aspect of platform strategy.

There have been recent scholarly attempts to conceptualise complementarities. Jacobides et al. (2018; see also 2024) sought to clarify complementarities in ecosystems, differentiating between complementarity in production and consumption (cf. Teece, 2018), as well as introducing ‘supermodular’ complementarity (cf. Milgrom & Roberts, 1990). However, their concurrent consideration of business, innovation, and platform ecosystems means that their insights for platforms are potentially conflated with non-platform ecosystems, leaving the distinctive factors of different types of complementarities in platform ecosystems unaddressed. Agarwal and Kapoor (2022) studied ‘complementary technologies’ that help innovations on platforms create more value for their users, investigating the platform ecosystem of Apple’s iOS Appstore. In doing so, they found that complementarities between apps are both typical (90% of apps have interoperability with other apps in the app store) as well as beneficial (more connections between apps increases the chances of commercial success). More recently, Borner et al. (2023) distinguished between user pathways and producer pathways in establishing complementarity, and Baldwin (2024) theorised that complementarities reside in a spectrum which is directly related to the size of complementary surplus, which in turn shapes the forms of organisation likely to create the most value from the underlying technologies.

Platform ecosystem contexts have specific implications of how complementarities appear in practice and their conceptualisation and theorisation. Platforms are designed so that the participants in different sides of a multisided platform collectively create value (Autio & Thomas, 2020 Ceccagnoli et al., 2012), for example, by facilitating interactions and transactions, lowering the entry barriers to new markets, and scaling up collaboration and impact (Nambisan, Siegel, & Kenney, 2018; Ritala, 2023; Srinivasan & Venkatraman, 2020). To support complement-level innovation (also known as “generativity”, see: Thomas & Tee, 2022; Zittrain, 2006), platforms are designed to be malleable (Briel et al., 2018; Henfridsson & Bygstad, 2013), granular (Kallinikos, Aaltonen, & Marton, 2013; Tilson, Lyytinen, & Sørensen, 2010), and loosely coupled (Autio & Thomas, 2020 Yoo, Henfridsson, & Lyytinen, 2010).

While the platform and ecosystem literature has highlighted the focal role of complementarities in platform ecosystems, it remains ambiguous as to where and how exactly are complementarities formed between the platform and the complements – and between the complements – and how these complementarities affect platform value creation? Relatedly, which actors in platform ecosystems drive and govern the formation of such complementarities? What are the differences, if any, between interdependence and complementarity? To this end, we investigate the role of complementarity in platform ecosystems, building on the work of Jacobides et al. (2018) and others (e.g., Agarwal & Kapoor, 2022; Baldwin, 2024) with a specific platform ecosystem focus.

We first review extant theoretical understanding of complementarities and apply this to platform ecosystems. We then theoretically describe the important difference between vertical and horizontal complementarities, which are usually conflated or not distinguished from each other in the literature, as well as their interactions. ‘Vertical complementarity’ signifies how a complement (e.g., a software application) increases the value of a platform (e.g., Android) on which it is built giving rise to a cross-side network effect. In contrast, ‘horizontal complementarity’ signifies the increased value of a platform stemming from complementarities between these complements (e.g., an email app and a calendar app), which may greatly amplify the same network effect. We identify four enablers of horizontal complementarity – platform design, open standards, peer-to-peer integration, and portfolio integration – which feature varying modes of integration, interoperability, and interdependence between complements.

Clarifying and conceptualising the two types of complementarities in platform ecosystems helps explain what drives platform value for platform users and for platform complementors, and ultimately, how complementarities help to create and amplify network effects in platform ecosystems. We conclude with implications for future research on network effects, interdependence, generativity, platform governance, and platform strategy. We also discuss how the role of horizontal complementarities is likely to be increased as users seek to utilise different platform functionalities and contents together, such as in the case of Zapier (Hagiu & Wright, 2022) or in the emerging metaverse environments.

Conceptual foundations of complementarity

In general, complementarity refers to the relationship between two entities, where the value of one entity is increased through its relationship with the other (Baldwin, 2024; Ennen & Richter, 2010; Milgrom & Roberts, 1990).¹ As noted by Baldwin (2024), complementarity is different to dependence, with the former coming from economics and the latter from engineering. While complementarity relates to value, dependence occurs when X depends on Y if, when Y changes, X needs to change as well. Entities are interdependent if a change in either may trigger a necessary change in the other.² Teece (1986, p. 289) was addressing this when he highlighted the importance of co-specialisation, defined as ‘assets … for which there is a bilateral dependence’. Furthermore, co-specialised assets are complementary when their value increases when they are used or consumed together (Jacobides et al., 2018).

Complementarity has a valence, that is, strength, which is derived from the dependence relationship. A one-way strong complementarity exists when the value of X depends and does not realise without Y and applies to specific and unique goods where their value have become inseparable, e.g., through some technological transformation or linkage (Baldwin, 2024). Similarly, a two-way strong complementarity occurs if X and Y are interdependent on each other in a similar manner. A weak complementarity occurs when X will still be valuable without Y, and applies when there are substitutes so that withdrawal does not destroy the value of the other (Baldwin, 2024). Thus, weak complementarity occurs when there is only little (inter)dependence between X and Y, even if there is value created when used together.

The directionality and valence of a complementarity has important implications for organisations (Baldwin, 2024; Hart & Moore, 1990; Helfat & Lieberman, 2002; Jacobides, Knudsen, & Augier, 2006; Teece, 1986). For instance, Hart and Moore (1990) consider complementarity to be strong when two assets are unproductive unless they are used together; for this reason they argue that coordination of investments in the two assets is critical to maximise the marginal return on investment. When a component or an asset has weak complementarity due to standardisation, firms have little concern for governance structures or risks of misappropriation when using them due to low dependence (Teece, 1986). For this reason, weak complements are an important and common way to facilitate production while safeguarding against contractual hazards (Helfat & Lieberman, 2002), and firms often strategise to turn weak complementarities into strong ones, and vice versa (cf. Jacobides et al., 2006).

Complementarity in platform ecosystems

In platform ecosystem research, an important but sometimes neglected aspect of complementarities has been the difference between the complement and the complementor. Following McIntyre and Srinivasan (2017), we consider a complement a component that relies on the platform for value creation. Thus, for instance, in mobile phone platforms apps are complements. They extend the functionality of the iOS or Android platform and also rely on the respective operating systems. A complementor, in turn, is an actor that develops and deploys a complement in a platform ecosystem. To continue to use our mobile phone ecosystem example, the developers of the apps (complements) are complementors. This relationship is represented through the dotted lines between complementors and complements in Figure 1 (which also depicts our overarching framework which is discussed in the remainder of this article). The distinction between complementors and complements is vital as it distinguishes between what is consumed by the users of the platform, i.e., the complements, and who creates those specific complements, i.e., the complementors.

Figure 1. Vertical, horizontal, and collective complementarities in platform ecosystems.

Distinguishing between complements and complementors helps to distil the role of complementarities. To this end, we reinterpret the ‘complementarity in production’ and ‘complementarity in consumption’ of Jacobides et al. (2018) for platform ecosystems.

First, complementarities of production comprise the complementarities between complementors (‘Items … can be produced’, p. 2266), as they consider the nature of the production process. Complementarities of production have been a major theme in general management literature, and complementarity has been considered from a variety of levels of analysis, including specific assets and resources (e.g., Hart & Moore, 1990), productive processes (Bharadwaj et al., 2007) and organisations (Harrison et al., 2001).

In terms of specific productive assets, the original transaction cost economics (TCE) framework focused on unique complementarities that arise as a result of asset specificity between different organisations (Argyres & Zenger, 2012; Williamson, 1985). Consequently, as they were seeking a ‘theory of the firm’, these theories considered strong intra-firm complementarities of production. Furthermore, the resource-based view (RBV) literature has considered the important role of complementary resources in acquisitions (Hitt, Harrison, Ireland, & Best, 1998) and complementarities as the main source of creating value in alliances (Harrison et al., 2001).³ The alliance, network, and ecosystem literatures broadly link the motivation for value creation to complementary resources and capabilities accessed and acquired through inter-firm ties (Das & Teng, 2000; Grant & Baden-Fuller, 2004; Ireland, 2002). Such complementary resources and capabilities are seen to create unique and valuable synergies, facilitate learning, and generate new knowledge and innovation (Dyer & Singh, 1998; Dyer et al., 2018; Harrison et al., 2001). As these theories were looking at complementarities outside the firm, they are implicitly focused on (mostly) weak, inter-firm complementarities of production.

In contrast, complementarities of consumption are the complementarities between the complements that are consumed by platform users (‘joint consumption generates … utility’, page 2266). Put differently, it is not complementors that are consumed by the platform users, but the complements that the complementors produce.⁴ Complementarities of consumption only really became apparent to scholars with the publication of Gawer and Cusumano’s (2002) seminal book ‘Platform Leadership’.⁵ Since then, research on value creation in platform ecosystems has generally considered the number and variety of complements (e.g., Agarwal & Kapoor, 2022; Cennamo & Santaló, 2019; Kapoor & Agarwal, 2017; Rietveld et al., 2019). Further, the research focusing on complementors has considered, e.g., their role in producing new complements (e.g., Boudreau, 2012) and on the effect on complementor performance within a platform ecosystem (e.g., Ceccagnoli et al., 2012), particularly as one of the defining characteristics of platform value is the presence of network effects (Rietveld et al., 2019). In the language of Jacobides et al. (2018, p. 9), platforms exhibit ‘supermodular complementarity of consumption’ – that is, more complements make the platform more valuable.⁶

In summary, in the context of platforms and network effects, it becomes increasingly important to consider the complementarities in consumption in addition to complementarities in production.

Vertical complementarity

Vertical complementarity is the relationship between the platform and the complements (and by extension, complementors). Vertical complementarity is the enabler for complements to create value within a platform ecosystem (solid black lines marked A in Figure 1),⁷ and reflects interoperability between the platform and the complements. This is by far the most commonly discussed type of platform complementarity, and the classic example is Wintel (Gawer & Phillips, 2013). Wintel was a hardware-software platform that allowed both third-party peripheral manufacturers and software developers to produce value-adding complements on top of Intel hardware and Windows operating system. Similarly, modern smartphone platforms, such as Apple iOS or Google Android, prominently feature vertical complementarities between platform and apps. Often unnoticed, a similar vertical complementarity also exists in data-based platforms. For example, a map database can be considered a platform (cf. operating system) and the business information added on top of it (cf. apps) are the complements. Vertical complementarity is two-way; complements are dependent on a platform (Ci→P) in order to create value, and a platform depends on complements (and by extension complementors) to create value (P→Ci). However, the valence of these complementarities differs.

For C_i→P, if the platform is unique, then there is a strong complementarity between any individual complement and the platform, because the complement has no value unless used together with the platform. Put differently, there is a high dependence between the complement and the platform, as the complement needs the platform to function. In instances where the platform has a de facto monopoly position over a certain market segment, then this high-dependence relationship would result in a strong complementarity. However, if a platform is not unique, i.e., complementors can multihome at a reasonable cost, then complements are less dependent on the platform. Thus, the valence of vertical complementarity can be weaker if it is affected by multihoming.

For P→C_i, regardless of whether the platform is unique, the platform does not need any specific individual complement to function as complements are optional (cf. Baldwin, 2024).⁸ Thus, there is a weak complementarity between the platform and any given complement (or complementor). Put differently, there is a low dependence between the platform and any given complement.⁹ However, beyond the weak complementarity between the platform and any individual complement, there is a stronger complementarity between the platform and the collection of complements as a whole (P→C_n), what we call collective vertical complementarity. This is due to platform value being driven by the network size (cf. Rietveld & Schilling, 2021), also been described as a supermodular complementarity (Jacobides et al., 2018, p. 2263). This is indicated in Figure 1 by the dot-dash lines marked as F.

When a platform has multiple sides (cf. Hagiu & Wright, 2015), each side can be considered an additional vertical. For example, in contrast to iOS, Android broke the vertical integration between the hardware and the operating system and opened another vertical complementarity by attracting third-party hardware manufacturers. In addition, the valence may differ for distinct types of complements. For example, the multihoming costs are significantly higher for hardware manufacturers than for app developers, suggesting a stronger complementarity.

Vertical complementarity is enabled by platform design and boundary resources (Baldwin & Woodard, 2009; Ghazawneh & Henfridsson, 2013; Karhu, Gustafsson, & Lyytinen, 2018). Platform design is necessarily modular and loosely coupled: by definition, every complement is an option. Boundary resources, such as application programming interfaces (APIs), serve as the interface between the platform and the complements (and complementors). For instance, vertical complementarity allows complementors to exploit standardised data collection and analysis to develop more advanced complements (Huang, Henfridsson, Liu, & Newell, 2017). In doing so, platform design and boundary resources enable the ‘transfer [of] design capability to users’ (Hippel, 2005), stimulating complement production (Eaton et al., 2015), but ensuring a level of control over the platform (Ghazawneh & Henfridsson, 2013; Karhu et al., 2018).

Horizontal complementarity

Beyond the dominant vertical complementarity and the related collective vertical complementarity, we argue that there is another type of complementarity – horizontal complementarity – between individual complements (C_i→C_i). Each individual complement, by definition, makes some contribution to the platform value (thus enabling vertical complementarity). However, horizontal complementarities enable combinations of specific complements to create additional value over and above their independent value.

Horizontal complementarities exist between individual complements and are realised in different ways (as detailed with the short-dash lines in Figure 1 marked as B, C, D and E).¹⁰ Horizontal complementarity reflects interoperability between the various complements within the platform ecosystem, and occurs when a platform user consumes different complements together. At its most basic, horizontal complementarity can arise from a selection of groceries (complements) bought online from a platform, which are complementary in making a meal, for example. Such complementarities are weak, as each component can most likely be substituted, as well as each complement maintaining value as they are not (inter)dependent (although there may be interdependencies from the perspective of a specific recipe). On mobile phone platforms various office productivity apps, such as the email and the calendar apps, typically offer complementary value if used together. Similarly, related Wikipedia entries are horizontally complementary to each other. In these examples, horizontal complementarities create additional value in consumption and are weak, in that each complement is not dependent on the other for their operation, but which provide additional and sometimes even significant value for individual users and use cases.

An example of a strong horizontal complementarity is the open-source statistical platform R and the add-on packages built on top of it. While R add-on packages can be built independently without any reliance on other packages, most packages depend on and reuse existing packages (i.e., other platform complements). Interestingly, in such open-source platforms, as the complements it depends upon are available through open-source licencing terms, individual complements can cease to be separate options as they all can be made available as a single bundle.¹¹

While horizontal complementarity is often designed into complements (such as R case above), horizontal complementarity can also be leveraged by users themselves. In particular, many platform ecosystems platform allow users to select between different complements and identify a combination of different complements that are more valuable when consumed together than separately (Borner et al., 2023). An explicit example of platform user’s deliberate selection of complements is Zapier, a platform that allows end users to integrate the web applications they use and automate workflows. In other words, Zapier allows users to create technical compatibility between complements they identify as complementary in their own use (Borner et al., 2023). As noted by Hagiu and Wright (2022), on Zapier the ‘more apps to integrate with … increases the value of the app in the eyes of its users [as] … there is almost no limit to the number of ways different apps could work together’. Thus, in the Zapier case, end user platform value is driven in substantial part by horizontal complementarity between the complements.

Beyond individual horizontal complementarity between any individual complements, there is also a collective horizontal complementarity between an individual complement and the collection of complements as a whole (C_i→C_n), indicated in Figure 1 by the dot-dash lines marked as F. Collective horizontal complementarities are the value that the collection of the complements represents to an individual complement. The valence of collective horizontal complementarities is weak, as while no individual complement is dependent on the collection of complements for its value, the value of a complement is dependent to some extent on the overall value of the other complements. Similar to vertical collective complementarity, horizontal collective complementarity is a supermodular complementarity (Jacobides et al., 2018) as it is due to platform value being driven by network size (cf. Rietveld & Schilling, 2021).

Thus far, horizontal complementarities have not been theorised and clearly differentiated from vertical complementarities, although they have been foreshadowed and identified by some scholars both conceptually and empirically. For instance, in the context of linear value chains Amit and Zott (2001) differentiated between vertical complementarities provided by the focal firm, such as after-sales services, and horizontal complementarities provided by partner firms, such as one-stop shopping, or cameras and films. Teece (2018) differentiated between vertical, horizontal and lateral complementarity, but did not develop this line of thought much further. Subramanian, Iyer and Venkatraman (2019) note the wide-scale possibilities of connecting complementary products in digital ecosystems during consumption by users. More recently, Aversa et al. (2021) began to consider complementarities between customers in business model portfolios, and Cenamor (2021) specifically notes that complementors can have interdependencies with other complementors and platform users.

Perhaps, the most direct identification of horizontal complementarity are the recent empirical studies of Agarwal and Kapoor (2022) and Borner et al. (2023). Agarwal and Kapoor (2022) demonstrated how platform-specific complementary assets and complementary technologies (that include but are not limited to complements) facilitate greater value creation, and that technological interdependencies may also introduce performance bottlenecks and governance issues. Agarwal and Kapoor (2022) provide a strong empirical demonstration of the relevance of horizontal complementarities in Apple’s app store ecosystem, finding that 90% of apps involve references and/or interoperability to other apps, and that these complementarities are a driver of apps’ commercial success. In their multi-method case study, Borner et al. (2023) described how users can identify complementary combinations between complements and build the technical compatibility necessary to unlock the complementary value when the complements have not been initially designed to work together.

Horizontal complementarity is an important form of platform complementarity as it means that, if present, using specific complements together (i.e., that are horizontally complementary to each other) further increases platform value beyond the ‘baseline’ vertical complementary value between the platform and the complements. This echoes notions of ‘recombination in use’, where the consumption of complements is no longer a discrete act, but instead comprises users ‘actively selecting resources of an offering and configuring them with other resources, or even rethinking their usages and purpose’ (Henfridsson, Nandhakumar, Scarbrough, & Panourgias, 2018, p. 91). While vertical complementarity in platform ecosystems features a strong dependence of the complement on the platform and a weak dependence of the platform on any given complement, dependencies within horizontal complementarities in platform ecosystems are more nuanced as we will discuss in the following.

Enabling horizontal complementarities

The value that results from horizontal complementarities is enabled through technical means of interoperability: platform design, open standards, peer-to-peer integration, and portfolio integration, each of which has a different enabling actor (see Table 1). Each of platform design, open standards, peer-to-peer integration, and portfolio integration shape how a complement can be technically combined with others to create additional value over and above its independent value.

Table 1. Comparison of horizontal complementarity enabler.

Enabler	Interoperability	Actor	Example
Platform Design	Interoperability through platform features such as boundary resources, proprietary functions or protocols, or access to 3^rd party protocols.	Platform	Wikipedia-specific functions (types of boundary resources), such as links and anchors, so that individual articles (and parts of articles) can be linked together or with external web pages, forming valuable cross-references across different content items.
Open Standards	Interoperability between complements independently of the platform design using open standards.	Standards organisations	Hypertext Markup Language (HTML) and Really Simple Syndication (RSS).
Peer-to-Peer Integration	Specific integration, using APIs or custom code, enabling originally unrelated complements to be interoperable with each other.	Complementors	Security software provided by Symantec supports integration to networking applications provided by Cisco on the Amazon Web Services (AWS) platform.
Portfolio Integration	Systematically designed interoperability by a complement provider (who can be the platform owner or an otherwise dominant player)	Complementors	Integration between Microsoft apps (Office, Teams, OneDrive, and so on) in mobile phone platforms, as well as the suite of services that Apple and Google provide on their mobile phone platforms.

Platform design, including the boundary resources, is controlled by the platform sponsor (Table 1). In Figure 1, complements 1 and 2 exhibit horizontal complementarity (short-dash line B) enabled by the platform design rules that enable interoperability (long-dash line B from the platform). One approach is for the platform itself to provide the interoperability. For example, Wikipedia is a platform that offers the ability for contributors (complementors) to create articles (complements). To do so, it offers various kinds of Wikipedia-specific functions (types of boundary resources), such as wikilinks and anchors, so that individual articles (and parts of articles) can be linked together or with external web pages, forming valuable cross-references across different content items. The horizontal complementarity is weak as an individual article itself still delivers value to the platform user.

Platform design can also be used to influence which third-party interoperability protocols are available for complements to interact with each other within the platform. For instance, some platform designs may make it difficult for complements to interoperate with others, effectively creating a ‘sandbox’ for each complement, while others may open specific interoperability methods for complements to interact.¹² These horizontal complementarities are also weak as there are low dependencies with other complements; however, if these interoperability pathways are used, this increases the dependence of the complement on the platform (vertical complementarity). Boundary resources – as part of the platform design – can be also designed to make it easier or more difficult to enable particular interoperation between complements (cf. Thomas & Tee, 2022). For example, Zapier provides boundary resources that make it easier for developers of apps to build connections to Zapier’s integration platform (to make their apps available for integrations to other apps on, and via, Zapier). Similarly, the R platform provides interoperability mechanisms through with R add-on-packages can reuse functionality from other packages.

Open standards enable horizontal complementarity by providing interoperability between complements independently of the platform design using open protocols (Henfridsson et al., 2018; Yoo et al., 2010; Table 1). In Figure 1, complements 2 and 3 exhibit horizontal complementarity (short-dash line C) with open standards enabling their interoperability (long-dash line C). Many of the open internet protocols, such as Hypertext Markup Language (HTML) and Really Simple Syndication (RSS) enable horizontal complementarity between complements. For example, HTML and RSS technologies enable web content such as blog posts and web pages to be linked together on a variety of different services. In such examples, the open standards provide the interoperability that creates horizontal complementarity when complements are consumed. Open standards-based horizontal complementarity is hence weak, as open standards, prima facie, do not require a dependence between the complements. However, (inter)dependence can exist if it is created through deliberate integration choices.

Peer-to-peer integration also enables horizontal complementarity (see also Table 1). These integrations are usually developed by the complementor(s) and go beyond the use of interoperability enabled by pre-existing platform design, or open standards. In Figure 1, complements 3 and 4 exhibit horizontal complementarity (short-dash line D) enabled by peer-to-peer integration (long-dash lines D emanating from complementors 3 and 4). Peer-to-peer integration occurs when two originally unrelated complements are made interoperable with the other. Interoperability usually occurs through APIs to support easier integration; this means that one-way dependencies can occur through deliberate integration choices of the complementor using the API, although it can also be achieved through specific custom integration. For instance, on the Amazon Web Services (AWS) platform, a complement such as security software provided by Symantec supports integration to networking applications provided by Cisco (Agarwal & Kapoor, 2022). Given the nature of the integration, the level of (inter)dependence between the complements is dependent on the deliberate integration choices of the complementors (see, for e.g., Borner et al., 2023).

Peer-to-peer integration is often driven by a dominant complement, provided by marquee or operationally significant complementors, such as Adobe. At times, the platform owner themselves may provide a dominant complement that enable peer-to-peer integrations. Such ‘first-party complements’ (see also Böhmer-Horländer & Kretschmer, 2020) can only be truly perceived as complements when they feature the same vertical complementarity as any other complements and they increase the user value of the platform but are not required for using the platform.¹³ For instance, both Google and Apple provide complements, such as navigation apps, and specific interoperability APIs for them that third party complements can integrate with. Thus, navigation functionality between apps is an example of a horizontal complementarity; for example, a platform user clicks a location link in app X and navigates using app Y.¹⁴ Interoperability between apps has the effect of creating two types of dependence for an integrated complement; a strong dependence on the platform through the vertical complementarity, and another dependence, driven by the nature of the specific integration, with the complement provided by the platform owner.

Portfolio integration occurs when two or multiple complements are related to each other via deliberate and strategic integration choices (see also Table 1). In the case of Figure 1, complements 4 and 5 exhibit horizontal complementarity (short-dash line E) enabled by portfolio integration (long-dash line E from complementor 4 who provides both complements). Portfolio integration differs from peer-to-peer integration in the sense that it has not emerged spontaneously between two initially unrelated complementors or encouraged by an API on a dominant complement. Instead, portfolio integration features systematically designed interoperability by single complementor (who is often the platform owner or otherwise dominant player). An example of such horizontal complementarity are the integrations between Microsoft apps (Office, Teams, OneDrive, and so on) in mobile phone platforms, as well as the suite of services that Apple and Google provide on their mobile phone platforms. The level of dependence between the portfolio complements is a strategic choice by the complementor (Lee, Venkatraman, Tanriverdi, & Iyer, 2010). Indeed, since the complementor in such cases is often the platform owner, they can be a major source of platform value from the user perspective.

Interactions between horizontal and vertical complementarities

Vertical and horizontal complementarities are not independent of each other. At its most basic, the platform owner can shape which complements are available through their control over the vertical complementarities, or what is known as membership (Tiwana, Konsynski, & Bush, 2010; Wareham, Fox, & Cano Giner, 2014). For example, through its control of the iOS Appstore, Apple can choose which apps are available for any horizontal complementarity.

Vertical complementarities generally shape how horizontal complementarities function. For instance, in many cases, vertical complementarity between the complements and the platform is strong (C_i→P), meaning complements are highly dependent on the platform, and typically do not function without the platform. This means that any change to the platform design may also affect the complements, and by extension, both horizontal and vertical types of complementarities. For example, in platforms that enable data sharing and analysis, such as in bioinformatics contexts, the database schema affects both how individual complements (such as algorithms) operate on top of the platform (i.e., whether they can establish a vertical complementarity) and how these complements interoperate with each other (i.e., whether they can establish a horizontal complementarity).

In any case, any generational update or other change to the platform technology potentially affects all vertical complements that rely on the platform unless the platform takes steps to make the update backward compatible with existing complements (see, e.g., Eisenmann et al., 2009; Karhu et al., 2018). In particular, updates to the platform technology can introduce trade-offs between facilitating value creation through complementarities (and maintaining the vertical and horizontal collective complementarity) and managing the technological interdependencies (Agarwal & Kapoor, 2022). This is likely to be the case if many complements have horizontal complementarities between them. Any change in the platform technology can necessitate both a change in each of the complements individually to maintain compatibility with the platform, as well as all of the ‘connections’ that underpin the horizontal complementarities of any particular complement (if the change in the platform technology affects the basis of these connections). This means a complementor might need to change both the complement with respect to the platform and make additional changes to maintain all existing connections to other complements it has horizontal complementarities with, an especially salient point for a complementor with a set of horizontally complementary complements through portfolio integration (Lee et al., 2010).

Horizontal complementarity and network effects

Platform literature to date has mainly focused on discussing network effects from the vertical complementarity perspective (Corts & Lederman, 2009; Gregory, Henfridsson, Kaganer, & Kyriakou, 2021; Jacobides et al., 2018; McIntyre & Srinivasan, 2017). For instance, Corts and Lederman (2009) investigated how the nature of the vertical relationship between the platform and the complements influences indirect network effects. Jacobides et al. (2018) present supermodular complementarity, e.g., between an operating system and its apps, as the basis for cross-side network effects. The recent work of Gregory et al. (2021) on ‘data network effects’ considers the collection of data from a vertical perspective (such as through complements that improve the platform’s offering via providing continued learning based on data), rather than through horizontal relationships between platform actors.

Horizontal complementarity and its impact on network effects have so far received little direct attention, even if it is clearly important for platform value (cf. Agarwal & Kapoor, 2022; Cenamor, 2021). Baseline platform value has largely been equated with the number of different platform users and complements (i.e., network size) and any stand-alone value from the platform (Cennamo, 2021; McIntyre & Chintakananda, 2014). However, by definition, the existence of horizontal complementarity amplifies platform’s value.

While vertical complementarity provides a platform user a range of different valuable complements, horizontal complementarities bring additional value due to the extra value unlocked when the complements are consumed together. Some platform ecosystems are able to deliver both types of complementarity value, differentiating them from the competition. As noted by Hagiu and Wright (2022): ‘ Zapier also enjoys a same-side network effect between the apps themselves, given they have to work together. An app is more likely to join Zapier, the more other (complementary) apps are on Zapier, because that means there are more apps to integrate with, which in turn increases the value of the app in the eyes of its users.’ Thus, the value of the platform for a platform user increases as more complementary value is unlocked by bundling specific complements together.

The additional value of horizontal complementarities can turn out to be substantial, since theoretically all complements may be complementary with each other, resulting in a Metcalfe’s Law-type quadratic increase in value (Swann, 2014), similar to user value growing in a telephone network that gains more connections. Theoretically, even Metcalfe’s Law understates the potential value of horizontal complementarity because complementary groups include not just groups of 2, but groups of any size between 2 and N.¹⁵

In summary, horizontal complementarity between specific complements adds value to the platform over and above the vertical collective value of the complements. Just as connections between clusters of participants in a social network increase its value to those participants, horizontal connections between groups of complements increase the value of the platform to specific users, reducing their incentives to switch to another platform. Therefore, we argue that horizontal complementarity is an important consideration for any analysis of network effects in platform ecosystems.

Implications for platform ecosystems

In this article, we have differentiated between vertical complementarity that takes place between the platform and its complements (e.g., an operating system and applications), and horizontal complementarity between complements on one side of the platform (e.g., between different applications such as an email and office apps, or between different entries in information platforms such as Wikipedia). This differentiation provides important contributions to our understanding of platforms, in particular network effects (as discussed above), interdependence, generativity and platform innovation, governance, and strategy.

Technical interdependence and economic complementarities

An important contribution of our study are conceptual clarifications and distinctions to both complementarities and interdependencies in platform ecosystems. In platform ecosystems, vertical complementarity is typified by a dependence of the complement on the platform (C_i→P); the complement is dependent on the platform in order to create value, but the platform itself does not depend on any specific complement (P→C_i). This means that for vertical complementarities, dependence is one-way: a change in any complement does not entail changing the platform, whereas a change in the platform’s design rules will generally require a change in a complement’s design. However, vertical collective complementarity means that the value of the platform is dependent on the availability of the overall system of complements for user consumption on the platform (P→C_n). This differentiation between vertical complementarities and vertical collective complementarities highlights that these are two different types of dependencies. One derives from the technology and design, and hence is a technical dependence, and the other from the way economic value is created in a complex system, and hence is an economic complementarity. Treating the two as interchangeable risk conflating different types of causal relations.

Furthermore, we have argued that if the platform is unique (i.e., it occupies a unique position in the markets so that multihoming is difficult), vertical complementarity between the complements and the platform is strong (C_i→P). In contrast, horizontal complementarities are generally weak (C_i→C_i). For interdependence to occur, the complements would need to rely on each other for necessary functionalities. In these cases, if the dependence develops to become very strong, the complements cease to be separable and collapse de facto into a single complement. This is generally a deliberate choice of the complementor that designed that specific complement. Maintaining weak complementarity (low dependence) means that most complements are able to be consumed alone. This enables platform users to select and consume in personal consumption bundles to reap the benefits of customised horizontal complementarities (cf. Dattée et al., 2023).

Studying the relationship between technical (inter)dependence and economic complementarities is an important theme for further research (see Agarwal & Kapoor, 2022). One important aspect is considering how the technical interdependencies of platform design, open standards, peer-to-peer integration, and portfolio integration lead to economics predictions about value. In particular, the prevalence, nature, value impact, and strategic implications of the technical interdependencies between complements that enable economic horizontal complementarity is much less understood and studied.

Generativity and platform innovation

Generativity – unprompted innovation by autonomous heterogeneous audiences (Zittrain, 2006; 1980) – is an increasingly important aspect of complementor innovation and platform value (Cennamo & Santaló, 2019; see Thomas & Tee, 2022 for a review). Generativity involves combinatorial innovation, a process of combining and recombining complements in platform ecosystems to create new complements, and hence is a consequence of technological interoperability in platform ecosystems. The resulting combinational innovation feeds back into the platform ecosystem enhancing the platform system as a whole (Eaton et al., 2015; Henfridsson & Bygstad, 2013; Henfridsson et al., 2018; Thomas & Tee, 2022).

To date, complementarity in generative platform ecosystems has mostly been assumed (or implied through references to modularity). While vertical complementary is a requirement for any new complement to have value on a generative platform, horizontal complementarities further increase the innovation potential of a platform by providing additional means for innovative recombination. Furthermore, as horizontal complementarity is weak, additional complements are ‘cumulative’ (Hill & Monroy-Hernandez, 2013), and enable both ‘continual reinterpretations, expansions and refinements’ (Yoo et al., 2010) and ‘assembly, extension and redistribution’ (Nambisan, 2017) of platform functionality. For example, on iOS and Android, augmented reality apps have stimulated the development of new apps (e.g., the IKEA app allows the virtual placement of furniture in a user’s living room). However, such platform-specific and co-specialised interdependencies could limit innovation opportunities for platform owners (Hilbolling et al., 2020) and complementors over time. Research is required to understand the distinctive role of vertical and horizontal complementarities in shaping the generative potential of platforms.

While our analysis has focused on the roles of platform owner and complementors in creating horizontal complementarities, Borner et al. (2023) have shown how users can both identify horizontal complementarities and implement them technically. This provides an interesting avenue for research on how users can be harnessed to foster generativity via their creation of horizontal complementarities. Indeed, how users can contribute to value creation in platform ecosystems merits further attention in general.

Platform governance

Our differentiation between horizontal and vertical complementarities has implications for understanding platform governance. Platform governance – the policy, technical, and design decisions that shape value creation within a platform ecosystem (Tiwana et al., 2010; Wareham et al., 2014) – is a driver of complementarity, as it permits the specific platform design elements and open standards that enables interoperability, and hence vertical and horizontal complementarity.

To date, most of the literature has focused on managing vertical complementarities, by balancing the tensions between the conflicting goals of maintaining ecosystem-level coherence in the value proposition, and allowing freedom for participant-level experimentation in component innovation and value appropriation (Kretschmer, Leiponen, Schilling, & Vasudeva, 2022; O’Mahony & Bechky, 2008; Tiwana et al., 2010; Wareham et al., 2014). This ranges from governing the ease with which participants can enter and exit the platform ecosystem (Nambisan & Sawhney, 2011; Tiwana et al., 2010) as well as the space within which complements operate, thereby regulating the overall platform ecosystem dynamics (Gulati, Puranam, & Tushman, 2012; Thomas & Tee, 2022).

While the platform owner has strong control over vertical complementarity through their control of the platform design (including boundary resources such as APIs) which shape complement interoperability with the platform, they have more limited control over horizontal complementarities. While horizontal complementarities can be encouraged via particular platform design choices that enable formation of different interoperability between complements, horizontal complementarity also arises independently through the use of open standards, peer-to-peer integration, and portfolio integration. This suggests that platform owners need to think of orchestrating differing dynamics of value creation-one that is driven by vertical complementarities, another by horizontal complementarities, and a third by both collective vertical and horizontal complementarities. Furthermore, as noted above, actions on shaping vertical and collective complementarity can shape horizontal complementarity. Yet, to date there is limited research on how governance decisions affect horizontal complementarities on the platform and vice versa.

Furthermore, horizontal complementarity may also affect which complements and complementors platform owner should potentially favour or selectively promote on the platform (Rietveld et al., 2019). Consideration of horizontal complementarity therefore adds to the complexity of trade-offs platform owners need to consider. Currently, we do not know how existing or potential new customers value horizontal complementarity when they decide whether to adopt the platform or continue use. However, horizontal complementarity is likely a more relevant factor for existing customers than for prospective customers as it is unlocked in use during consumption. Further, the volume of complements is easier to grasp ex ante than potential horizontal complementary connections between available complements.

Another governance issue relates to openness of digital platforms (see, e.g., Karhu et al., 2018). A complement that offers horizontal complementarity within one platform could potentially offer integration to complements on a second platform, which may lead to governance and competition issues for the second platform owner. For instance, Hilbolling et al. (2020) describe how apps on the Phillips owned Hue platform enabled integrations of smart lightbulbs and switches (complements) made by also other manufacturers. This cannibalised sales and introduced hardware issues affecting the system integrity. Phillips tried to protect its platform by banning 3rd party products (i.e., closing its platform, see Karhu, Gustafsson, Eaton, Henfridsson, & Sørensen, 2020) but had to rapidly reverse the decision due to customer backlash. The customer clearly saw the added connections as valuable, while Phillips saw a risk for their platform integrity arising from the new and difficult-to-anticipate complementarities. Similar issues might arise from the intermediary toolkits identified in (Borner et al., 2023) that may enable integrations across platform ecosystems. More research is required into understand the complexity horizontal complementarities bring to the governance of platform openness.

Platform strategy

The differentiation between horizontal and vertical complementarities also provides additional insight into platform strategy, in particular the chicken-and-egg problem, platform owner entry to complement markets, and within platform competition.

Seeding a platform with initial complements has been suggested as a way to counteract the chicken-and-egg problem, either attracting early complementor entry or by providing first-party complements developed by the platform owner (see, e.g., Boudreau, 2012; Cenamor et al., 2013; Gawer & Henderson, 2007; Parker & van Alstyne, 2016). As horizontal complementarities between complements unlock further value in consumption, it would seem preferable if complements used to seed the platform early on would have horizontal complementarities between them and/or if the seeded complements would facilitate potential connections with horizontal complementarity to them by future complements. Arguably, when the number of complements is necessarily small at launch and early stages of the platform lifecycle, the boost received from horizontal complementarity may be relatively more prominent early on than later in the platform lifecycle. Complements that are horizontally complementary could be seeded by the platform owner, or the platform owner could seek for such complements from capable and resourceful complementors. Here, a deliberate portfolio integration strategy would mean developing interoperable in-house, first-party complements readily available on the platform (such as Google’s native apps on Android) or by collaborating with a strong complementor (such as Microsoft). Future research is needed on the question of how horizontal complementarities help in platform launch and emergence phases as opposed or in addition to more well-known vertical complementarities (i.e., number of complements in the platform).

Entry into complementor market within platforms is a tactic that can bear benefits for the platform owner but also introduce negative responses from complementors (Gawer & Henderson, 2007; Huang, Lyu, & Xu, 2022). The entry can be seen as generally competitive, i.e., as a mark of the platform owner showing willingness to exercise its power to capture value in the complementor space, or directly competitive when the owner provides a complement that is a substitute for complement(s) already available on the platform (Gawer & Henderson, 2007). If the owner enters with a complement that is horizontally complementary to other complements, it could be perceived less negatively in general (apart from the point of view of those complementors already providing substitute complements). This could be viewed differently if the platform owner enters with a strongly integrated portfolio of its own complements that are not open for combinations with complementor complements. Further, platform owner entry may increase the risk that a complementor that provides a complement with numerous horizontal complementarities would abandon offering that complement, leading to negative compounding effects to other complements.¹⁶ Platform envelopment is a related strategy, where a platform owner enters another platform market, and combines its own functionality with that of the target in a multi-platform bundle that leverages shared user relationships (Eisenmann et al., 2011). All in all, platform market entry dynamics in the context of horizontal complementarities offers many intriguing further research directions.

Horizontal complementarity can also play a role in competition between platform complementors as well, and could affect their currently identified strategic options (Cenamor, 2021; Hukal, Kanat, & Ozalp, 2022). A complement with more horizontal complementarities should prevail in competition if both stand-alone value (from features) and network value (from users) of the complement (Cenamor, 2021) are comparable and added benefits from horizontal complementarities are higher than the cost of establishing and maintaining them. Horizontal complementarities may also form a basis for establishing coopetitive networks between the complementors; in this regard, Cenamor (2021) suggested that such networks represent a potential source of competitive advantage for the complementor that becomes more significant as the platform ecosystem matures. While these insights begin to provide some insight into competition between platform complementors, we know little about how the use of different horizontal complementarity – enabling strategies shape the dynamics of competition between complementors.

Looking forward

We believe that horizontal complementarities will grow significantly more important for platform ecosystems and their participants in the future. As digital technology continues to evolve and become embedded into everyday life (Yoo, 2010), increasing standardisation and technologies for interconnection will lead to new opportunities to harness complementarities within and across different platforms. For instance, the development and standardisation of the technologies underlying blockchains will enable additional horizontal complementarities, which some have suggested have outsize effects on generativity and governance (Leiponen, Thomas, & Wang, 2022). Furthermore, emerging technologies such as the metaverse will increase the relevance of horizontal complementarities as integration of content, digital artefacts, and payment capabilities from different providers is expected to be accessible across multiple interfaces (Ball, 2022).

Further, the recognition that vertical and horizontal complementarities also exist in data-based platforms calls for research focusing on data complementarities (Ritala & Karhu, 2023) and data-based innovation to complement the dominant software-based innovation research stream. The increasing use of, and sharing of, data in platform ecosystems offers in particular potential for horizontal complementarities through combinations of different data sets into actionable and meaningful data goods, objects, and artefacts (Alaimo & Kallinikos, 2022; Ritala & Karhu, 2023). However, the ambitious visions of market leaders in blockchain and metaverse contexts (and in many other novel digital contexts that provided connectivity and exchange between actors) are likely not realised until meaningful and well-functioning horizontal complementarities are formed between complements.

Understanding vertical and horizontal complementarities will also be important for our understanding of platform hierarchies. Platform hierarchies arise when the complement of a platform is in turn a platform to a group of subsidiary complements. For example, smartphone applications (complements) are installed on operating systems (platforms) through intermediate platforms (called app stores) controlled by the operating system sponsor. Indeed, creating subsidiary platforms is often the technical means of implementing horizontal complementarities through peer-to-peer integration and portfolio integration (see Figure 1): the would-be integrators create an API ‘abstraction layer’ between the platform and the complements. Given that no digital platform operates in isolation, a deeper understanding of the dynamics of platform hierarchies is vital to understand value creation in platform ecosystems.

Conclusion

In this article, we have identified two types of complementarities in platform ecosystems: vertical complementarity, the relationship between the platform and the complements, and the horizontal complementarity that exists between individual complements. While the former are much better known, theorised, and studied, horizontal complementarities are less recognised, despite their relevance for platform value. We have shown how horizontal complementarities are enabled by platform design, open standards, peer-to-peer integration and portfolio integration, and which have important insights for our understanding of network effects, interdependence, generativity and platform innovation, platform governance, and platform strategy. Distinguishing between vertical and horizontal complementarities in platform ecosystems provides scholars with more accurate theoretical tools to analyse how and why complementarities are formed in platforms, and how platform owners, complementors and users can utilise and manage such complementarities. We hope that other scholars will pick up on the challenge to explore further the distinctive role of vertical and horizontal complementarities, and how these types of complementarities interact in platform ecosystems.

Acknowledgments

Our deepest thanks to Carliss Baldwin for her exceptionally helpful comments on earlier drafts of this paper, as well as to the two anonymous reviewers for their insightful advice. We also thank attendees for their insightful comments at Bayes (previously Cass) Business School, the Berkeley Open Innovation Seminar Series, DIEM Brown Bag Seminar at Aalto University, and the AIS SIG DITE (Digital Innovation, Transformation, and Entrepreneurship) Digital Research Seminar.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1. For a review of complementarities in platform and ecosystem contexts, see Baldwin (2024).

2. The conditional ‘may’ is used here purposefully to indicate that X and Y are not typically fully dependent on each other; for this reason, a change is triggered only when the change occurs in such part that the other specifically depends on.

3. Relational view of the firm (Dyer & Singh, 1998) combines arguments from both TCE and RBV. Relational view demonstrates how relation-specific assets (argument that follows TCE logic) coupled with complementary resources and capabilities (argument that follows RBV logic) in interfirm relationships are drivers of ‘relational rents’. The other drivers of relational rents are knowledge-sharing routines and effective governance.

4. Even in the case of Uber, it is not the driver (complementor) that is consumed, but the service they provide. From the perspective of the Uber platform, this means the complement is actually their listing (see Parker, van Alstyne, & Choudary, 2016 for a full discussion).

5. We thank Carliss Baldwin for pointing this out to us.

6. It is for this reason that platform examples in Figure 2 of Jacobides et al. (2018) only appear in the final column (‘supermodular complementarities of consumption’); see their paper for a fuller discussion of supermodularity.

7. For the sake of exposition, we have assumed in Figure 1 that all complementarities are two-way.

8. A platform by definition cannot depend on its complements: if it did, then the complements would not be optional but would be part of the platform. See Saltzer et al. (1984) for a thorough discussion on this design principle.

9. This principle does not naturally rule out that a specific complement could be very valuable to the platform and its users.

10. For clarity of exposition, we only consider horizontal complementarities to occur between the complements in a single side of a platform, such as between apps on a mobile phone platform. However, we do not discount that horizontal complementarities can emerge between complements in different sides.

11. Note that it is only the package that depends on another that ceases to be independent, as the other package can still be independently downloaded and used (unless it depends on some other package).

12. However, even if a platform design has been set up to create a ‘sandbox’, it still may be possible for complements to interact through off-platform custom integrations (such as server to server).

13. The competitive and governance implications for the platform owner-provided first-party complements are naturally distinctive from those provided by 3^rd party complementors.

14. In contrast, implementing navigation functionality in an app using the platform APIs is an example of a vertical complementarity.

15. However, from a practical perspective, groups of two are probably sufficient for modelling purposes. This is also indicated by recent empirical research that estimated a strength of horizontal complementarity somewhat below Metcalfe’s Law in the case of Wikipedia (Karhu & Jokinen, 2023). Further, Borner et al. (2023) reported cases where combinations of two products were much more popular than combinations with three or more, and combinations of more than five much rarer than with fewer.

16. On the other hand, it may be more difficult for the platform owner to dislodge an established complement with numerous horizontal complementarities with its own substitute. For the owner substitute to provide the same benefits to users would require all those complementors that have built the connections underlying the horizontal complementarity to the existing complement to implement all those connections anew to the owner substitute. For a complementor, building and fostering horizontal complementarities is not without costs but may lower risk of envelopment or direct competition from the platform owner, at least if its complement can provide comparable stand-alone value to the substitute owner complement.