Sustaining complementor engagement in digital platform ecosystems: Antecedents, behaviours and engagement trajectories

Digital platform ecosystems increasingly dominate the enterprise software domain, and the persistence of platforms depends on the sustained engagement of complementors. However, there is a limited understanding of its antecedents, complementors' evaluation of antecedents and the manifestations and dynamic changes of complementors' engagement. Therefore, we investigate complementors' engagement within platform ecosystems over time. We draw on actor and stakeholder engagement from service research to conceptualise complementor engagement (CE) and create an integrated empirical understanding of CE and its dynamics in digital platform ecosystems. Our embedded case study builds on 30 interviews with complementors in Anubis and Osiris enterprise software platform ecosystems. Inductive data analysis reveals five CE antecedents: platform resources and rules, platform value proposition, platform agents, customer needs and other complementors' value propositions. The antecedents are associated with three CE behaviours: generating, networking and synchronising. Further analysis of CE over time resulted in 26 different sequences representing stable and changing engagement trajectories, the latter comprising selective, growing and abating engagement as subcategories. We show how complementors' evaluations of antecedents lead to behaviour changes, providing a novel perspective on the dynamics underlying CE. Finally, we link complementors' evaluation outcomes to their (dis)satisfaction, contributing to the discussion on what drives and impedes CE. The findings implicate the debate on dynamic platform governance and inform platform owners about using cooperative and competitive approaches in the short and long term.

The concept of engagement from service research can inform research on CE and platform governance in IS. By contextualising the engagement concept towards CE (Hong et al., 2014), research on digital platforms can get unique insights into the dynamics of CE and its constituent elements. Furthermore, those dynamics can provide a deeper understanding of the antecedents implicating engagement and their changes, such as adjustments of governance mechanisms from competitive to cooperative strategies, to sustain CE over time (Huber et al., 2017;Jacobides et al., 2018). Hence we go beyond current conceptualisations of CE that reduce the concept to the mere contribution of complementarities and compliance with rules and processes (Saadatmand et al., 2019;Wang & Miller, 2019).
Ultimately, a better understanding of CE is integral for research on platform governance due to the interdependent nature of the two concepts (Chen et al., 2022). Therefore, this study has two objectives: 1. to contextualise CE from the engagement literature; and 2. to provide an integrated theoretical understanding and empirical evidence of dynamic CE in digital platform ecosystems.
First, we synthesise the literature on actor and stakeholder engagement, resulting in the service-researchinformed contextualisation of CE in the IS domain. We define CE as a complementor's state-based, partly volitional resource contribution in its interactions, activities, and relationships in a digital platform ecosystem. Hence, we use CE to (1) explain the antecedents and manifestations of complementors' engagement in digital platform ecosystems, (2) examine and relate changes in antecedents and manifestations, and (3) account for variations of CE in digital platform ecosystems over time.
Based on this contextualisation, we use CE as an analytical lens and conduct an embedded case study of two digital platform ecosystems in the enterprise software industry. The complexity and dynamics of this domain make it particularly suitable for investigating the dynamic changes in CE. Based on 30 interviews with complementors over 18 months, we identified five antecedents that lead to three main CE behaviours. Each evaluation phase and expressed behaviour constitutes one engagement stage. Our analysis further reveals how antecedent changes implicate behaviours in subsequent stages through complementors' evaluations and how those stages form CE trajectories. As a result, we further identify four types of engagement trajectories and describe 26 instantiations.
The results inform the discussion on dynamic CE and how platform governance as one antecedent can change those dynamics. First, we inform the literature on dynamic CE by revealing antecedents of CE and how they unfold as dynamic CE trajectories (Altman et al., 2022;Li & Kettinger, 2021). Furthermore, we describe how complementor (dis)satisfaction can increase or decrease their future engagement. Hence, we add to the literature on complementor participation strategies (Cenamor, 2021;Hurni et al., 2022) and how complementors shape their environments (Wang, 2021). As platform governance is one important antecedent, we also contribute to discussions on dynamic platform governance to manage CE over time (Foerderer et al., 2019;Hurni et al., 2022). Our findings suggest that cooperative and competitive governance approaches have different implications for CE in the short and long term.
Combining both approaches leads to sustained CE, enabling platform owners to build persistent platforms.
2 | LITERATURE REVIEW 2.1 | The engagement of complementors in digital platform ecosystems Digital platform ecosystems are semi-open collectives of actors around a (largely) stable platform core (Bonina et al., 2021;Tiwana et al., 2010). 1 The relevant stakeholders comprise the platform owner providing the platform, complementors offering complementary products and services, and customers using the platform and its 1 We will use the terms digital platform (ecosystem) and platform (ecosystem) interchangeably in the following. complements according to their needs . As autonomous third parties, complementors can choose whether and what resources to invest in a particular platform (Hurni et al., 2021(Hurni et al., , 2022Tan et al., 2020).
In this setting, platform owners want to attract and engage complementors sustainably. Nevertheless, complementors engage with varying intensity (i.e., resource contributions) over time, creating a dynamic and interactive context, which we will introduce below.

| Variations in the engagement of complementors
Complementors participate in platform ecosystems to co-create and capture value from their interactions with others (Ceccagnoli et al., 2012;Iansiti & Levien, 2004). The contributions of complementors (e.g., products and services) determine the platform ecosystem's innovative potential and generativity (Thomas & Tee, 2022) and address customer needs (Parker et al., 2017;Tan et al., 2020). They act autonomously and contribute or withdraw resources from one or more digital platform ecosystems (Engert et al., 2022;Hurni et al., 2022). However, this autonomy can be undermined by increased dependence on the platform, as with online marketplaces or mobile applications, forcing complementors into submission (Cutolo & Kenney, 2021;Hurni et al., 2022).
Generally, the autonomy of complementors leaves them to make strategic choices that affect their offerings and, thus, the entire platform ecosystem. For instance, Wang and Miller (2019) find that large publishers hold back their most important revenue-generating books from Amazon Kindle but offer them as physical prints, impacting Kindle's overall attractiveness to customers. As shown, complementors make strategic and operational decisions to create and maintain competitive advantages (Cenamor, 2021). Consequently, complementors are not always cooperative towards the platform owner but engage in competitive, even antagonistic behaviours (Eaton et al., 2015;Karhu et al., 2018).
Besides strategic choices and competitional aspects, complementors' engagement commitment may vary based on changes in customer demand or the underlying platform technology (Kapoor & Agarwal, 2017). For instance, Cennamo (2018) highlights the increased efforts for complementors to upgrade their complements to new platform generations in the video game industry.
In essence, CE in digital platform ecosystems takes many different forms. However, the literature on different forms of engagement, short-and long-term variations, and stimuli leading to changes in engagement is highly fragmented and underdeveloped (Altman et al., 2022;Li & Kettinger, 2021). For sustaining engagement, prior work has suggested different stimuli and orchestration capabilities for platform owners to motivate complementors to participate and continuously contribute to their platform ecosystems, ensuring sustainable growth (Blaschke et al., 2018;Schreieck et al., 2021).

| Sustaining CE for platform survival
From the perspective of platform owners, sustaining and increasing the engagement of complementors is essential for the survival of their platform ecosystem (Blaschke et al., 2018;McIntyre et al., 2021). To that end, platform owners, too, balance their value-co-creating and value-capturing activities to stimulate third-party contributions while ensuring value capture for themselves (Schreieck et al., 2021;Uzunca et al., 2022).
As the central actor in the ecosystem, platform owners provide and develop the technological base on which complementors build their value propositions (De Reuver et al., 2018;Hein, Weking, et al., 2019). In addition, platform owners continuously (re)create platform governance to manage complementors and their respective engagements (Wareham et al., 2014). Platform governance must balance individual and collective interests, spurring or halting complementors' dedication and engagement towards the platform ecosystem (Huber et al., 2017;Hurni et al., 2021). In its broadest sense, platform governance comprises the design and provision of the core technology, the platform boundary resources (e.g., Application Programming Interfaces [APIs]) Ghazawneh & Henfridsson, 2013;Petrik & Herzwurm, 2020), and the rules that determine interactions across the ecosystem (Song et al., 2018). Over time, platform owners adjust the governance, impacting value creation and distribution among complementors (Uzunca et al., 2022). Furthermore, platform owners must balance competitive and cooperative governance to stimulate and steer complementors' engagement (Eaton et al., 2015;Foerderer et al., 2019).
Despite the growing body of work on digital platform ecosystems, particularly from a platform owner perspective, answers to the intricate problem of understanding, systemizing and balancing the CE and its dynamics remain vague (Jacobides et al., 2018;Li & Kettinger, 2021;McIntyre et al., 2020). To advance this opportunity and inform IS research, we contextualise engagement from the adjacent stream of service research, which has received significant attention from service and marketing researchers and practitioners alike.

| The evolution of engagement in service research
Initially motivated by the insight that 'sustaining and nurturing the customer base may require the firm to look beyond repurchase behaviour alone', service researchers started to investigate customer engagement and engagement behaviours as their manifestations (Van Doorn et al., 2010, p. 253). Research on customer engagement argues that it can be understood as a dynamic, iterative process of different engagement levels comprising psychological and behavioural dimensions that result in co-created value (Brodie et al., 2011;Jaakkola & Alexander, 2014). Furthermore, research acknowledges that customer engagement comprises antecedents, manifestations, and outcomes and that the process ranges from short to long term, expressing variability over time (Brodie et al., 2011;Van Doorn et al., 2010).
Later, service research developed the notion of actor engagement by broadening the perspective beyond customers and considering any actor's ability to engage. Actor engagement is a micro-level concept, taking the perspective of an individual actor as part of a broader service ecosystem (Storbacka et al., 2016). Hence, in actor engagement, other actors and their value propositions are explicit or implicit antecedents to the focal actor to engage with them (Chandler & Lusch, 2015;L. P. Li et al., 2017).
As the most recent development, research has suggested overcoming shortcomings of actor engagement concerning sociopolitical tensions through stakeholder theory. To that end, Hollebeek et al. (2022) developed stakeholder engagement as 'a stakeholder's state-based, boundedly volitional resource endowment in his/her role-related interactions, activities and/or relationships' (Hollebeek et al., 2022, p. 9). The state-based nature of stakeholder engagement allows researchers to investigate and describe changes in engagement states in different temporal stages as part of an overarching engagement trajectory.
In the past decade, the evolution of engagement research from customer to actor and stakeholder engagement in service research resulted in a broad conceptual basis. However, in their recent study, Hollebeek et al. (2022) call for further research on stakeholder engagement and its constituent sub-concepts to account for the idiosyncrasies of different contexts. By contextualising insights on the engagement of complementors in light of the richness of engagement-related research, particularly stakeholder engagement, we put forward the concept of CE for the context of digital platform ecosystems.

| Towards CE in digital platform ecosystems
Following stakeholder engagement (Hollebeek et al., 2022), we conceptualise CE as a complementor's state-based, partly volitional resource contribution in its interactions, activities and relationships in a digital platform ecosystem. Complementors make role-related decisions concerning the resources they give to the platform ecosystem (or individual actors). Differences in interests, such as platform entry into complementary markets, can create sociopolitical tensions. These tensions require additional resources to facilitate their effective resolution by, for example, negotiating, building trust and collaborating.
Based on the understanding of actor engagement (Brodie et al., 2019;L. P. Li et al., 2017), CE takes the microlevel perspective of complementors. CE is expressed as a state formed from CE antecedents and taking a concrete manifestation as a CE behaviour. Due to changing antecedents, the behaviours, and thus CE, changes over time across subsequent stages. As a result, CE varies along its trajectories.
CE serves as a contextualised, analytical lens to investigate the engagement of complementors. Thus, we extend the current understanding of CE, which only refers to the contribution of complementarities and compliance with rules and processes (Saadatmand et al., 2019;Wang & Miller, 2019). Instead, we focus our analysis on the unique antecedents that influence CE, adding to our understanding of the conditions that lead to CE as requested by extant work (Eckhardt et al., 2018;Jacobides et al., 2018). In addition, we aim to investigate CE behaviours, representing the manifestations of CE, which have been only described selectively. In addition, CE allows the investigation of changes in CE and the consequences of platform governance moves that affect antecedents and CE (Altman et al., 2022;Li & Kettinger, 2021).

| RESEARCH APPROACH
We follow an exploratory embedded-case study (Yin, 2018) to create a detailed, empirical understanding of CE. Case studies are suitable when the unit of analysis cannot be isolated from its surroundings, as is the case of complementors' interactions with the platform and the ecosystem of actors around it (Benbasat et al., 1987;Yin, 2018).
Based on interviews with complementors of two platform ecosystems, Anubis and Osiris, as our two units of analysis, we investigated the antecedents that influence CE and how CE behaviours subsequently manifest. As a starting point, we aimed to identify instances and commonalities concerning CE among complementors. Then, we linked subsequent stages of antecedents, the evaluation thereof, and behaviours as manifestations that result in CE trajectories. 2 The enterprise software industry is an intriguing setting to investigate how CE emerges and evolves. Complex and heterogeneous customer needs characterise this industry, requiring highly specialised and customised solutions to integrate existing infrastructures and processes. In addition, the subscription-based nature of cloud-based software requires ongoing interactions and close relationships with customers. The enterprise software industry is the largest segment within the global software market, with fierce competition among customers and complementors (Statista, 2021). From that industry, we choose two of the fastest-growing enterprise software firms, Anubis and Osiris, as our units of analysis: Anubis is a provider of a cloud-based platform in relationship management with 2000 applications in its marketplace. Osiris is a process management platform that integrates data sources into automated workflows with 700 applications. Hence, both case companies have attracted and engaged many complementors to provide applications (excluding connectors, system integrations and other third-party pieces of software for comparability), making them suitable objects for our study.

| Data collection
Our data collection concentrates on 30 semi-structured interviews with complementor organisations acting as independent software vendors (ISVs) in Anubis or Osiris (see Tables 1, 2, B1, B2, C1, D1, E1, and F1). For complementors to be eligible, they had to have at least one application in the respective application marketplace with at least three published customer reviews as a proxy for the complementor's active engagement in the ecosystem and to ensure they did not join the ecosystem just recently. Furthermore, we made sure that all complementors were small-tomedium-sized entities. This theoretical sampling strategy increased the probability that complementors' engagement is highly relevant to their business success and that resource contributions towards the platform are made according to their strategic goals.
We conducted the first set of interviews with 23 representatives of complementors. After evaluating the interviews, we contacted the respondents about 16 months later to conduct a second set of seven interviews with the same interviewees. 3 This step allowed us to take a longitudinal perspective towards CE and capture engagement over time in greater detail, giving the research team additional insights into unfolding engagement trajectories. The interviews are slightly skewed towards Anubis due to the size of the respective ecosystems and the resulting availability of interview partners. We switched from data collection to data analysis and back, adjusting the interview guidelines based on our findings (see Appendix B). When theoretical saturation of categories was reached while coding new interviews, we ended the first and second rounds of data collection.
We conducted all interviews with CEOs, C-level executives or high-ranking managers tasked with maintaining relationships with their respective platforms, attending events and meeting regularly with the respective platform owner (see Table B1). The interview data comprises 1214 min of recordings, which we transcribed. In addition, we used secondary data such as websites, blogs, whitepapers and the platform partner programmes to triangulate our findings.

| Data analysis
We applied different coding procedures for data analysis, allowing for a structured and transparent knowledgegeneration process and focusing on emerging themes (Glaser & Strauss, 1967). Thus, we iteratively applied open, axial and selective coding. The overarching aim to identify relevant aspects of CE and its underlying dynamics guided the data analysis process. Building on the concepts of CE, we considered CE antecedents, behaviours, and trajectories as analytical concepts. Therefore, we conducted three rounds of coding to identify engagement antecedents (round 1), behaviours (round 2) and trajectories (round 3) independently of each other as part of our inductive research approach.
In round 1, we openly coded the initial interviews to identify different CE antecedents. This step helped us gain an overview of the data and all aspects impacting CE. Next, we developed axial codes from all open codes and integrated them during a selective coding step, resulting in different concepts influencing complementors' engagement decisions. Finally, based on discussions among the research team, we refined the concepts until we reached the final categories, comprising five engagement antecedents (see Appendix C). In round 2, and similarly to round 1, we used open, axial and selective coding steps to identify the three main CE behaviours from the initial interviews. In addition, this iteration was guided by conceptualising CE behaviours as observable manifestations of resource contributions towards the platform ecosystem. Again, the three final engagement behaviours arose inductively from the data without any prior category (see Appendix D).
In round 3, we extensively analysed all initial interviews concerning the engagement trajectories described therein (see Appendix E). Two members of the research team first coded all engagement trajectories described in all first-round interviews openly, using the antecedents and behaviours specified in prior iterations to identify 81 engagement trajectories. Next, we compared trajectories and derived similarities and differences during axial cod-

| RESULTS
The case study analysis results in a conceptual model comprising antecedents and behaviours of CE in digital platform ecosystems (see Figure 1), describing the basic building blocks of one engagement stage. Moreover, complementors (often implicitly) evaluate the antecedents and derive motives that lead to different behaviours. Those motives are transient states that describe the evaluation of upsides and downsides based on antecedents. Through engagement behaviours, complementors contribute resources to the platform ecosystem and influence their environment, affecting antecedents and the evaluation in later stages. This process results in interlinked stages of repeated evaluations of antecedents, enactment of behaviour and resource contribution represented as an engagement trajectory.
Across several stages, complementors' engagement trajectories can either be stable or change, reflecting an iterative and dynamic CE process. The following sections present the identified CE antecedents, manifestations of CE behaviours and the resulting CE trajectories using examples of specific sequence instantiations of stages inferred from our empirical evidence.

| Antecedents of CE
The interviews revealed five engagement antecedents, which are associated with the platform owner (value proposition, agents, resources and rules), customers (needs) and other complementors (value proposition) influencing CE behaviours subsequently.

Platform owner
The platform owner is the central actor and leading business partner of complementors within proprietary platform ecosystems, with its value proposition, agents, resources and rules determining CE. The platform value proposition The platform owners' agents (Platform Agents), embodied as partner managers, account managers, sales managers or solution engineers, are key interaction points with complementors, impacting CE. According to IP9, 'human contact is the most critical thing in any engagement', and building and maintaining good relationships 'is the best way to work'.
The platform resources and rules (Platform Resources and Rules), such as platform boundary resources (e.g., APIs, the application marketplace, events) and control rules (e.g., app security checks), provide structural support and guardrails for CE. Several interview partners mention that the platform marketplace serves as an information channel or store window and initial point of contact for customers, facilitating engagement [IP1; IP4; IP5; IP12; IP13].

Customers
The motivation for complementors to engage with the platform ecosystem depends on existing and emerging customer needs (Customer Needs), such as customers that want to automate their IT-related processes. Complementors cater to the needs of their potential customers in the enterprise segment more effectively when engaging with a platform ecosystem since customers demand integrated end-to-end solutions instead of single products [IP2; IP4; IP9; IP13; IP17; IP20].

Other complementors
Complementors compete and collaborate with other complementors. They collaborate by connecting their applications once a clear path towards added value is apparent. In these cases, the other complementors' value proposition

| CE behaviours
The interviews show that complementors engage with platform ecosystems through observable CE behaviours. We identify generating, networking and synchronising behaviours from our case study. Each behaviour enacted by the complementor also results in a change in resource endowment towards the platform ecosystem.

Generating behaviour
The core of a complementor's engagement in platform ecosystems is generating and delivering applications and services (Generating Behaviour). Complementor 7, for instance, extends the platform by offering an application that automates customer incentive programmes: 'We bring our core functionality, which does not exist in that way in the Anubis environment' [IP7]. Furthermore, as customer problems and out-of-the-box solutions in enterprise settings regularly diverge due to the specificity of customer needs, there is a constant need for customisation and consulting services [IP19].

Networking behaviour
Complementors build networks across platform ecosystems through personal relationships (

Synchronising behaviour
Complementors continuously ensure the fit and alignment between their offering, the platform's value proposition and other complementors they collaborate with (Synchronising Behaviour). For instance, complementors synchronise with the platform owner to sell to customers jointly, as exemplified by Complementor 8, which collaborates with Anubis to replace a competitive system for a large 'number of accounts in Japan, [being an] initiative driven by Anubis that is very fruitful' [IP8]. Ultimately, synchronising behaviour increases alignment between actors, resolves tensions and fosters collaboration. Thus, it creates advantages for both parties in the short term, sometimes leading to long-term strategic partnerships.

| CE trajectories
By integrating CE stages of antecedents, evaluation, behaviours and changes in resource contribution into sequences over time, our data reveal two major engagement trajectories: stable (i.e., stable resource contribution) and changing engagement (i.e., changing resource contribution). For instance, sequence S1 describes a stable engagement trajectory, which we found eight times in our data. Further analysis of changing engagement resulted in selective, growing and abating engagement as its constituent subcategories. Figure 2 shows the engagement trajectories, including exemplary sequences and an illustration of each trajectory based on a complementor's resource contributions towards the platform ecosystem over time. In addition, we identified variants of some sequences, such as S13.1 and S13.2 of S13.
Along engagement trajectories, a complementor evaluates antecedents that can lead to changes in their engagement. The evaluation of upsides and downsides is often an implicit reaction to changing antecedents, resulting in transient motives and implicating subsequent engagement behaviours. Contrasting prior assumptions, our findings stress that CE does not require complementors' satisfaction (positive evaluation) but can also result from dissatisfaction (negative evaluation). Moreover, CE does not per se increase the alignment with the platform ecosystem but may drive operational and strategic divergence or opposition.

| Stable engagement
The first CE trajectory is stable engagement and follows a steady trajectory across stages with minor changes concerning resource endowment. It represents complementors' baseline engagement with the platform ecosystem and their ongoing and steady resource contributions.
A prototypical example (S4)  We capture these instances as changing engagement trajectories.

| Changing engagement
The second CE trajectory is changing engagement and describes adjustments to the resources contributed to the platform ecosystem over time. A detailed analysis of the changes in complementors' resource contributions across stages resulted in three manifestations: selective engagement, growing engagement and abating engagement.

Selective engagement
Complementors engage in selective engagement by selectively contributing resources to the platform ecosystem in one stage but reducing their engagement in subsequent stages.
For instance (S7), complementors of Anubis that offer applications via the platform sometimes encounter potential customers (Antecedent: Customer Needs), which first need to instal the platform before getting the application in a 'downstream project' [IP13]. Complementors then invest resources ad-hoc to understand the customer's needs (Behaviour: Synchronising) and work with platform owner representatives (Antecedent: Platform Agents) to convince customers to use Anubis. After that, they deliver their application to the customer (Behaviour: Generating) before their engagement recedes: We often get requests for our system, then make a discovery call with customers. According to IP13, only 'about 5%' of customer requests require these situational resource investments.
Another instance (S8) of selective engagement prevalent in the Osiris ecosystem relates to the spontaneous development of applications: 'We did a custom development for a customer and said: "Well, this is a great product, let's develop it further and distribute it"' [IP16]. In the first stage, complementors work with customers (Antecedent: Customer Needs) in consulting projects (Behaviour: Generating). Seeing a long-term business opportunity in offering applications through the app store (Antecedent: Platform Resources and Rules), they generalise these custom solutions to more generic applications. For instance, Complementor 23 published an application for dispatching letters directly from Osiris as a generic application for the marketplace (Behaviour: Generating). Once the application is developed and published, complementors' resource contributions towards the application again receded.
In addition to situational engagements, we observe changes to resource contributions resulting in higher or lower engagement levels in subsequent stages.

Growing engagement
Correlated with the growth of Anubis's and Osiris's ecosystem, we encountered growing engagement as an increase in complementors' resource contributions towards the platform ecosystem as the prevailing CE trajectory. In its initial stage, this trajectory starts at a low (or zero) level of engagement and increases over time until it reaches an elevated engagement level. Prototypical examples describe increasing alignment and collaboration with other ecosystem actors, such as the platform owner or other complementors. In contrast to suggestions by prior work, CE is not dependent on complementors' satisfaction. Dissatisfaction and tensions among actors can be strong drivers for complementors, motivating them to engage and change things in their favour by, for instance, seeking to strengthen their alignment.
We find three variants of growing engagement based on the respective complementor's market success (S13), the ease of technological and cultural alignment (S13.1), and the intensity of their networking (S13.2). Under variants (S13) and (S13.1), complementors that leverage the platform (Antecedent: Platform VP) to develop an application (Behaviour: Generating) in an initial stage get little attention from platform owner representatives (Antecedent: Platform Agents): Typically, an Anubis customer will ask their salesperson, account manager, or customer success manager when looking for a technical solution. And usually, [these] people don't know all the applications […] We try to position ourselves so that they know us so that they don't just know us from [the app store], but also know our service. [IP13] In (S13), with increasing market success (Behaviour: Generating) in the second stage, the awareness of representatives grows (Antecedent: Platform Agents). As IP8 put it: 'If we generate revenue, then there will be more focus. It's very simple: Money talks'. In the third stage, complementors started to pitch their products to customers with the platform owner as a part of a joint go-to-market strategy: Later on, we started cracking deals. So, we came into the limelight of Anubis that these guys bring value to pharma customers so that customers are interested in looking at the solution. And that is the primary reason that in the last 1.5 years, we were able to define a joint go-to-market with Anubis […].

We […] keep evolving and keep working closely with Anubis. [IP6]
The collaboration is then elevated towards a strategic partnership once the platform owner understands the value a complementor brings to the platform (Behaviour: Synchronising): The relationship with Anubis has matured, […] one and a half years ago, I think the awareness of [Complementor 8] was not that great, but today, most people within Anubis know who we are, and Nevertheless, complementors keep intensifying their efforts by pitching and demoing their application to even more platform agents (Antecedent: Platform Agents). That way, they continuously grow their network within the platform owner (Behaviour: Synchronising). As a result, in subsequent stages, the awareness of platform representatives increases (Antecedent: Platform Agents), ultimately resulting in more joint deals (Behaviour: Generating) and long-term complementors' satisfaction: We also do demos, lunch and learn sessions, and other things. So, when [Anubis representatives] are asked by customers whom they know [to solve a particular problem], they automatically say: 'Yes, you just call the guys from [Complementor 13]'. That is a very easy approach to going to market today. [IP13] While all these trajectories (S13 and variants) resulted in increased CE, complementors' evaluation of antecedents can be negative. However, also negative evaluation outcomes and tensions among actors can spur engagement in the next stage: As a result, complementors have to spend additional resources regularly to educate new platform agents on their solutions and rebuild a trusted relationship.
Moreover, our case study revealed that platform owners invest in complementor businesses (S15). In the early stages, Anubis's market-leading position (Antecedent: Platform VP) motivated IP3 to expand its Anubis-related business by deepening its collaboration with Anubis. Frequent exchanges (Behaviour: Synchronising) increased Anubis agents' awareness of Complementor 3's solution (Antecedent: Platform Agents). Getting an offer for Anubis's investment, IP3 accepted the offer (Behaviour: Synchronising): We do get a lot of attention and strategic direction from Anubis. We do have a lot of executive engagement. We do have an executive sponsor since we are part of the Anubis investment portfolio.

So, we definitely get insight in terms of product direction, [and] sales direction. [IP3]
In subsequent stages, Complementor 3 and the platform owner turned from frequent exchanges to deepening their development and sales efforts to provide innovative functionalities to customers together (Antecedent: Customer Needs). Similarly, Complementor 8 became a strategic partner for the manufacturing industry after getting an investment from Anubis. Hence, the success of the previous engagement led to even closer alignment on a strategic level (Behaviour: Synchronising).
Finally, changes in engagement across stages may also result from complementors' abating resource contributions towards the platform ecosystem across stages.
Abating engagement CE trajectories that start at a high(er) level of engagement and decrease over time (i.e., withdraw resources) until they reach a lower (or zero) level are abating engagement trajectories. Notably, our case study revealed only four different abating engagement trajectories with only one example each. Due to the growth of the enterprise software industry in the recent decade, most complementors only infrequently lower their engagement. One example (S24) is Complementor 17, which ceased to update its application in the marketplace: In the first stage, Complementor 17 started from a high level of engagement, motivated by Osiris's growth and strong customer base (Antecedent: Platform VP). Aiming to expand, they soon developed and maintained a certified resource management application in the application marketplace (Behaviour: Generating): 'When we became an Osiris partner, we were very enthusiastic about the store. And we also developed solutions for it' [IP17].
Importantly, however, in the context of business software, applications often require extensive sales cycles.
These include cold-calling, demos, discovery calls and subsequent implementation and customisation projects. IP

| Antecedent evaluation and dynamics of CE
Our results reveal how complementors explicitly and implicitly evaluate antecedents and derive short-term motives, which serve as transient states that spur their subsequent engagement behaviours. Moreover, these evaluations comprise weighing upsides against downsides arising from the respective antecedents. Hence, we add further nuance to complementors' re-assessment of their engagement (H. Li et al., 2022;Selander et al., 2013) and answer the call to investigate the underlying criteria by Li and Kettinger (2021).
In particular, the results highlight the need to refine assumptions from prior work that complementors' satisfaction based on a positive evaluation of antecedents is a prerequisite for CE (Hurni et al., 2021;Petrik & Herzwurm, 2020). Our study counterintuitively shows that negative evaluation outcomes and the associated dissatisfaction can increase CE. At the same time, positive evaluations can lead to abating engagement, depending on their short-term or long-term occurrence. The following discussion focuses on counterintuitive findings (e.g., abating engagement despite short-term satisfaction).
First, CE can grow despite complementors' short-term dissatisfaction, extending the literature on CE (Petrik & Herzwurm, 2020). Consider, for instance, Complementor 6, dissatisfied with the awareness and support from Anubis's platform agents, which led it to ramp up its networking engagement (S13.2). When complementors face unfavourable conditions in the short term (e.g., sparse support by platform agents), they can be motivated to engage and invest more resources that benefit the platform. However, engagement after dissatisfaction is not always positive, as studies on complementors jailbreaking iPhones have shown (Eaton et al., 2015). Hence, dissatisfaction can elicit antagonistic engagement (jailbreaking iPhones) and constructive engagement, as in the case of Complementor 6's networking. These examples emphasise that even if engagement increases, not every engagement is good (Karhu et al., 2018), which needs consideration when designing platform governance.
In addition, the results help to explain other studies' findings. For example, Google applied competitive governance and increased CE after entering the photography application market of the Android platform (Foerderer et al., 2018). While complementors negatively evaluated the increase in competition in the short term, many decided to increase their innovation efforts (i.e., CE) momentarily to address additional customer needs and change antecedents in their favour during the next stage. Many third-party photography apps, however, perished subsequently. This example shows that long-term dissatisfaction leads to abating engagement when complementors' attempts to influence antecedents are insufficient, leading them to reduce or redirect their resources.
Again, this observation helps to explain findings from quantitative studies on digital platforms. For instance, platform awards represent a cooperative governance mechanism. They have been found to increase the winners' likelihood of multihoming in the short term (Foerderer et al., 2021), which is associated with a decrease in CE with the original platform. Hence, despite the positive evaluations of winning an award and gaining additional customer attention, complementors decided to reduce their engagement in the short term and focus on other platforms instead.
These insights implicate how we theorise short-term incentives for complementors, such as subsidies (Rochet & Tirole, 2006) or exclusivity agreements (Parker et al., 2017), as they may decrease subsequent engagement. At the same time, long-term satisfaction often leads to growing engagement or motivates complementors to stabilise their engagement on a certain level.
Overall, the study contributes to understanding dynamics within platform ecosystems and the performance outcomes of complementors. First, we identify and structure antecedents of CE in enterprise software platforms, answering recent calls to provide the criteria influencing the sustained CE (Altman et al., 2022;Li & Kettinger, 2021).
Second, we shed light on the interplay of antecedents and behaviours underlying dynamic CE, through which complementors seek to influence antecedents and the platform ecosystem in the next stage. This CE process illustrates the ongoing, recursive process of shaping and reshaping digital platform ecosystems (Li & Kettinger, 2021;Wang, 2021). For instance, we uncover how antecedents shape CE and how CE shapes the generativity of platform ecosystems through generative behaviours. In turn, the platform ecosystem's generativity shapes antecedents, such as intra-platform competition, that need to be continuously governed by the platform owner. These insights illustrate platform ecosystems' recursive dynamics and contribute to recent calls for further inquiry into generativity in this context (Thomas & Tee, 2022).
Moreover, we add more nuance to complementors' participation strategies in platform ecosystems (Cenamor, 2021;Hurni et al., 2022;McIntyre et al., 2021). Based on their respective evaluation, complementors balance different CE trajectories over time. Through CE, complementors can influence and determine their performance outcomes. Thus, we add to the discussion on complementor performance, emphasising the individual's contribution to their respective performance and standing (Cenamor, 2021;Floetgen et al., 2021;Li & Kettinger, 2021). Our proposed model provides an empirical framework for the processes underlying these dynamics, and the identified trajectories demonstrate the repeated interplay of antecedents and behaviours over time.

| Cooperative and competitive platform governance for sustained CE
CE differs across complementors and dynamically varies based on changing antecedents. Hence, CE can rapidly fluctuate, and platform owners must take a flexible stance. Nevertheless, its variability makes CE malleable and thus manageable for platform owners via their governance. Essentially, platform governance allows platform owners to influence CE antecedents and steer engagement: Platform owners may govern strategic adjustments of resources and rules (Ghazawneh & Henfridsson, 2013;Song et al., 2018), the platform value proposition (Miric et al., 2021) or of platform agents (Huber et al., 2017). In addition, they may impact relations among complementors by, for example, steering intra-platform competition (Tiwana, 2015) and customer needs by entering complementary markets (Foerderer et al., 2018). As such, platform governance allows platform owners to steer antecedents, complementors' evaluations, and their subsequent engagement.
The outcomes of complementors' antecedent evaluation (i.e., positive or negative) correspond to the two modes of platform governance (Foerderer et al., 2019;Parker et al., 2017). The cooperative mode reflects positive evaluations by complementors, while the competitive mode is associated with negative evaluation outcomes (Gawer & Henderson, 2007). Our empirical evidence suggests that either mode can incite and deter CE.
First, our results emphasise the importance of cooperative governance in stabilising and growing engagement in the long term. Most of the identified growing engagement trajectories build on increasing alignment with platform agents, which are vital to operationalising cooperative governance (Huber et al., 2017;Hurni et al., 2021). Our results resonate with prior work stating that platform agents are fundamental in cooperative approaches by transferring knowledge (Foerderer et al., 2019) and aligning complementors with the platform owner (Huber et al., 2017). Nevertheless, we find occasional instances where cooperative approaches are associated with short-term abating engagement (e.g., S24), providing cautionary tales for platform owners.
Overall, we see increases in CE in light of cooperative governance when complementors see immediate shortterm value in their engagement, such as new customer demand. In contrast, the lack of an immediate short-term value lowers CE despite complementors' satisfaction. Therefore, platform owners must communicate and highlight immediate benefits for complementors when using cooperative governance approaches to trigger increases in CE.
Second, competitive governance approaches in the long-term lead to abating engagement trajectories. For instance, IP12 described Anubis's development of features similar to their application without prior announcement decreased their synchronising activities (S23). The negative, long-term, and short-term impact of competitive approaches has been documented by extant work (Foerderer et al., 2018;Hurni et al., 2022). However, we find that, situationally, competitive approaches can act as short-term stimuli for increasing CE. For example, Complementor 16 is synchronising with Osiris to change the incentive schemes of platform agents towards ISV partners (S14).
Again, these insights expand our understanding of platform governance and its interplay with CE. Platform owners that opt for competitive approaches are advised to consider long-term effects, which may be clouded by short-term increases in CE as complementors respond and rally to compete or adjust. These insights follow findings from early work on platform ecosystems that moderate levels of intra-platform competition spur innovation while intensive competition risks crowding out innovation (Boudreau & Jeppesen, 2015). We advance this understanding of platform owner competition by introducing a temporal and dynamic element of intra-platform competition (i.e., short-and long-term effects) besides the intensity of competition considered by prior work (Cennamo & Santalo, 2013).
Generally, our study shows that platform owners can and should integrate cooperative and competitive governance approaches to steer CE across multiple stages. These insights add to the literature on dynamic platform governance and power dynamics (Foerderer et al., 2019;Huber et al., 2017;Hurni et al., 2022). Furthermore, cooperative governance has a positive, long-term impact on CE, while competitive governance has negative long-term consequences. Notably, long-term satisfaction of complementors is essential to grow, stabilise and sustain engagement.
However, cooperative governance can also lead to abating engagement in the short term. Platform owners are cautioned to monitor such instances, ready to react if the trend persists. Similarly, competitive governance can increase CE in the short term, motivating complementors to overcome barriers or change antecedents in their favour.
Platform owners may use these insights to stimulate complementor investments (i.e., CE) in the platform as part of a well-balanced 'carrot-and-stick' approach that integrates cooperative and competitive governance. As a result, to sustain CE long-term, platform owners must couple their competitive moves, such as releasing competitive applications, with cooperative ones. Our study shows that short-term competition and subsequent cooperation combinations are strong drivers of growing engagement. Hence, using competitive actions to stimulate CE adds a new tool to platform owners' governance toolbox.

| Practical implications
Our findings also have concrete implications for platform owners and complementors in enterprise software platform ecosystems from a managerial perspective. First, we provide rich empirical evidence on the dynamics of CE for platform owners. Platform governance allows them to control or manipulate virtually all CE antecedents and, thus, CE. While platform owners are generally advised to follow collaborative governance approaches, this study encourages the deliberate and situational use of competitive elements to stimulate CE. In addition, we caution platform owners to consider short-and long-term effects on CE when designing governance mechanisms. In sum, platform owners must pay close attention to complementors' engagement and their repeated evaluations of antecedents.
Second, managers of complementor companies are advised to carefully and regularly assess antecedents concerning their upsides and downsides and to be willing to act accordingly. Complementors individually and collectively possess considerable power in platform ecosystems (Hurni et al., 2022). This study shows that complementors can further their positions by influencing antecedents through their engagement. Furthermore, complementors should consider calibrating their engagement to their situation and explore options such as strategically lowering their engagement in light of long-term dissatisfaction and pursuing alternative options.
Finally, complementors should accurately evaluate platform owners' competitive actions and identify their associated opportunities.

| Limitations and future research
First, we study two well-established digital platform ecosystems in the enterprise software domain as units of analysis as part of a qualitative, exploratory approach. While descriptive, we are confident that the emerging theoretical abstractions (e.g., the CE model and its underlying categories and the four types of CE trajectories) are applicable in other contexts. Nevertheless, future research should investigate CE in contexts that require fewer upfront investments by complementors, such as mobile applications, creating an even more volatile environment to examine CE and its trajectories. Notably, reporting additional instantiations and variants of engagement trajectories will broaden our understanding of CE, particularly how combinations of antecedents influence subsequent engagement behaviours and the resulting trajectories.
Second, our analysis focused on sequences of two to four stages due to the available data and our study's goal to conceptualise CE and gain the first empirical evidence. However, sequences could span across a large number of stages when analysing expanded periods. Hence, we encourage future work to use longitudinal study designs to investigate long-term CE trajectories comprising multiple stages. Moreover, different configurations of antecedents can lead to different CE outcomes, and qualitative comparative analysis methods will be suitable to investigate such configurations and the implications for platform governance.
Third, since the current study sampled only active complementors as interview partners, we cannot report why complementors disengage and leave (potentially thriving) platform ecosystems. Similarly, complementors whose applications have zero or few downloads are likely to engage differently, posing a necessary extension to our study.
This further links to complementors' autonomy in hierarchical contexts such as digital platform ecosystems and how complementors can leverage their autonomy vis-à-vis top-down control.
Finally, our data collection focuses on complementors, excluding other relevant actors such as customers, partnering complementors and platform owner representatives. Thus, we encourage future work to broaden the perspective on CE by focusing on the ecosystem as the unit of analysis when further investigating CE and its effects.

| CONCLUSION
Sustaining the engagement of complementors in digital platform ecosystems is a significant success factor in creating persistent platforms (McIntyre et al., 2021). This study investigates CE dynamics and their interplay with platform governance.
To that end, we conceptualise CE based on service research's recent concept of stakeholder engagement (Hollebeek et al., 2022) and borrow antecedents and behaviours as building blocks of CE from actor engagement (Brodie et al., 2019; L. P. Li et al., 2017). We then explore CE and its variations over time in digital platform ecosystems in the enterprise software context. To understand how CE unfolds, we select Anubis and Osiris as two units of analysis in an embedded case study taking the complementor perspective. Our findings reveal five CE antecedents, which complementors repeatedly evaluate and determine subsequent CE behaviours. Analysing the temporal dimension, we differentiate four types of engagement trajectories and 26 instantiations thereof. Our findings illustrate the dynamics and variations of CE in digital platform ecosystems as a result of complementors' evaluations of upsides and downsides. Hence, the current study informs research on CE dynamics and the underlying decision-making by complementors. We refine earlier assumptions that CE depends on complementors' satisfaction (i.e., positive evaluations) by showing that dissatisfaction (i.e., negative evaluations) can stimulate CE in the short term. These insights add further nuance to the temporal perspective of CE.
Furthermore, platform owners' governance may impact all CE antecedents, illustrating their power to influence and steer CE over time. Finally, we shed light on the interplay of CE and platform governance, focusing on short-and long-term effects and cooperative and competitive governance approaches. Our results suggest that combinations of cooperative and competitive governance approaches can effectively increase CE, adding a new tool to the governance toolbox and informing the ongoing discussion on dynamic governance approaches.

ACKNOWLEDGMENT
The authors want to thank the students from Technical University of Munich that contributed to data collection and analysis of this research project. Open Access funding enabled and organized by Projekt DEAL.

DATA AVAILABILITY STATEMENT
Research data are not shared.
Each stage comprises one engagement antecedent and an engagement behaviour that directly follows from the antecedent. Changes in antecedents and/or behaviours mark the beginning of a new stage. Hence, an engagement trajectory includes a sequence of at least two stages of engagement, that is, at least two distinct points in time associated with a particular context or theme. In the example, a complementor attended platform owner events (antecedent) to network with various customers, necessitating resources to visit the different events (behaviour) represented by engagement stage 1. Later, the complementor visited industry-specific events organised by the platform owner (change in antecedent), facilitating access to relevant customers and intensifying the complementor's networking activities (change in behaviour) in stage 2. Finally, in stage 3, the platform owner started to offer industry-specific platform features (change in antecedent), which the complementor included in its application, aligning even closer with the platform roadmap (change in behaviour). Thus, the complementor's resource contributions towards the platform ecosystem increase across the sequence, resulting in a growing engagement trajectory. The overarching context is the increasing industry focus of the platform owner, which drives the engagement of the example complementor.

Antecedent Behavior
Industry specific event(s)