A Dynamic Analysis of Cross-Category Innovation in Digital Platform Ecosystems with Network Effects

Abstract

Cross-category innovation in digital platform ecosystems is increasingly pivotal for competitive reconfiguration, and the value it generates for users primarily stems from the benefits of network effects. By extending the spatial competition framework of the Hotelling model through a four-stage sequential game comprising category competition, we formalize the strategic mechanism for expanding network effects governing benchmark competition and category dynamics. The cross-category innovation strategy proposed in this paper offers valuable insights in three key areas: investment in core technological advantages, reconstruction of user cognitive boundaries, and strengthening ecological dependency within the ecosystem. By transcending the limitations in the explanatory power of traditional management theories for cross-organizational boundary issues, this study integrates digital contexts into its analytical framework, thus providing a novel perspective for understanding the dynamic processes of cross-category innovation in digital platform ecosystems.

1. Introduction

Digital technologies have been revolutionizing traditional industries, leading to a profound transformation of industrial landscapes. This convergence has amplified the cross-category attributes of digital platform ecosystems, making cross-category innovation a pivotal strategy for market expansion [1]. Cross-category innovation breaks down industry barriers through such mechanisms as category emergence and category creation [2], enabling digital platform ecosystems to transcend the limitations of a single market or category. Instead, they exhibit significant characteristics of cross-category development through the scalability of technical architecture, user mobility, reusability of data resources, etc. [3,4]. Cross-category innovation, as a core strategy for digital platforms to break through growth bottlenecks and reconfigure competitive structures, has been validated by cases such as Amazon’s strategic diversification from e-commerce into cloud computing (AWS), alongside Google’s leveraging of search data to enter fields like smart home and autonomous driving [5]. The essence of such innovation is not simply business diversification, but rather using the platform’s existing resources and capabilities to create new value networks in unconnected markets. The key to success lies in the dynamic utilization and amplification of network effects [6].

As a core characteristic of digital platform ecosystems, network effects permeate the entire process of cross-category innovation. Direct network effects expand the user base by enhancing the intensity of interaction among users [7]; indirect network effects strengthen platform attractiveness through the richness of the ecology of complementary products [8]; and data network effects optimize service quality through continuous learning from user data [9]. Mastering the leverage of network effects for innovation has become pivotal to enhancing platform competitiveness, as it directly influences key performance dimensions like user retention, ecosystem scalability, and multi-side network cohesion. It can even break industry barriers through the migration of network effects, and the cross-market exploitation of network effects can be harnessed to promote ecosystem development. For example, platforms can integrate cross-category technologies based on modular technical architectures; data network effects can support the migration of cross-category data, such as the integration of supply chain data and financial risk control data, which helps make more forward-looking decisions in new fields, thereby entering new markets at low cost [10]. However, the role of network effects in cross-category innovation is not linear: user multi-homing behavior may weaken the lock-in effect; the rigidity of category cognitive boundaries may hinder the establishment of legitimacy for new categories; and strategic interactions among competing platforms, such as imitative innovation by followers, further increase dynamic complexity. Thus, how digital platform ecosystems leverage network effects to achieve cross-category innovation and the acquisition of market shares has become a critical issue.

To address this complex interplay comprehensively, this study focuses on the following interrelated research questions: How do we characterize the dynamic development process of cross-category innovation in digital platform ecosystems, driven by network effects? What specific roles do different types of network effects play in the stages of category emergence, category creation, and differentiation strategies? How do game equilibrium outcomes at each stage affect user scale expansion, profit growth, and social welfare optimization and ultimately enable cross-category innovation? This study will answer these questions through a four-stage sequential game model. It adapts the Hotelling model and employs a four-stage sequential game framework, methodologies well-suited for analyzing strategic interactions in multi-sided markets, and integrates numerical simulations to validate the theoretical deductions. These tools allow us to model the dynamic competition among platform ecosystems, decode the mechanisms through which network effects shape category expansion trajectories, and derive optimal cross-category innovation strategies. By integrating game-theoretic analysis with ecosystemic and social value goals, our approach aims to identify strategies that not only drive market dominance through network effect amplification but also contribute to long-term ecological and social value within platform ecosystems.

2. Literature Review

2.1. Network Effects of Digital Platform Ecosystems

Digital platform ecosystems are an organizational form formed around core platform technologies. Based on platforms, they connect multiple independent enterprises, users, and complementary products or services [11]. Through the flow of data and information, they realize value co-creation and sharing [12]. A distinctive feature of digital platform ecosystems is their network effects—the expansion of user scale and the enhancement of value mutually reinforce each other, thereby driving the growth of the platform’s commercial value [13]. Existing studies mainly focus on the direct network effects and the indirect network effects’ dual-dimensional characteristics. Direct network effects refer to the value that users obtain from the network derived from direct interactions among participants. For example, in social platforms, the higher the frequency of user interactions, the stronger the individual perceived value [14]. Indirect network effects are reflected in the positive feedback loop of “user scale-complementary ecosystem”: the more users there are, the stronger the platform’s attractiveness to complementary enterprises, which in turn promotes the improvement of complementary products in dimensions such as technological compatibility and service innovation, ultimately attracting more users to join [15]. The synergistic effect of these two effects leads to a mutually reinforcing dynamic relationship between the platform’s user scale and innovation networks, jointly driving the value upgrading of digital platform ecosystems [16]. In addition, the intensity of network effects—including factors such as the density of social relationships among users and the marginal contribution of new users to network value—has also been proven to affect the value brought by the expansion of the user base [17]. The stronger the motivation and contribution of complementors, the greater the diversity of platform content and complementary products, which in turn enhances the platform’s attractiveness to users [18].

With the deepening of research, Afuah [19] broke through the network size determinism and proposed that network structure and user behavior are important supplementary factors affecting the user value of multi-sided platforms. Data from digital platforms help optimize the accuracy and efficiency of matching user needs and assist users in achieving desired outcomes and making more rational decisions [20]. Based on the above research, Gregory et al. [9] put forward the concept of “data network effects”, which means that the more a platform learns from the user data it collects, the more its prediction speed and accuracy improve, and the more valuable the platform is to each user. Platforms leverage the economies of scale and scope from aggregating users’ transactional and interactive data, enabling societal benefits from the positive externalities of data collection, while their ability to learn from data to continuously improve products or services for each user generates new platform externalities; user utility depends on the scale of AI-enabled data-driven learning and improvement, which is reflected in more powerful product functions, higher platform quality, and better experiences, and such information asymmetry is utilized by platforms to facilitate interactions, enhance user welfare, and attract users to join. A typical example is Douyin, which optimizes its recommendation algorithms through user behavior data, significantly enhancing user perceived value [21]. Helfat and Raubitschek [22] proposed that the ability of digital platform ecosystems to coordinate multi-agent resources is reflected in three aspects: digital sensing, digital utilization, and digital reconfiguration. This includes using data to sense and act quickly, seize opportunities, avoid threats, and reconfigure internal and external resources [23]. The technological capabilities for cross-category innovation in digital platform ecosystems are rooted in the modular technological architecture of digital platforms [24], and data network effects are the key driving engine; that is, the platform’s ability to continuously improve its products and services by learning from data [25]. The core mechanism by which data network effects create user value is mining the value of user data, thereby promoting the value upgrading of the entire digital platform ecosystem [9].

Digital platform ecosystems strengthen the positive feedback loops of network effects by implementing strategies such as expanding the user base, enriching and innovating complementary product portfolios, and improving data analysis capabilities. These characteristics together constitute the unique competitive strategies of digital platform ecosystems, thereby realizing the coordinated development of economies of scale and scope, and ultimately forming differentiated competitive advantages.

2.2. Cross-Category Innovation Mechanism

As a fundamental framework of social structure, categories are regarded as partitioning organizational space and related organizational structural partitions with different meanings, thereby generating different departments, market boundaries, and division of labor orders [26]. Categories also simplify people’s understanding of surrounding things, enabling people to focus on limited dimensions or characteristics, which facilitates identification, judgment, and action-taking. This mechanism helps people discern complex social realities and conduct action navigation [27]. As an emerging organizational theory, category theory has been a hot topic in the field of organization and management over the past 3 decades [28]. Relevant research mainly focuses on the classification of cognitive laws and legitimization mechanisms for the stable development of organizations [29,30], as well as the classification strategic actions and classification processes that influence organizational restructuring and change [31,32]. Unlike traditional innovation, cross-category innovation research based on classification theory does not focus on breakthroughs in a single technology or model. Rather than conventional competitive forms, this phenomenon represents a strategic maneuver rooted in classification theory, aiming to construct legitimacy and achieve differentiated positioning. It establishes a synergetic mechanism among cognitive rules, resource integration, and dynamic evolution—one that fundamentally involves the reconfiguration of ecological niches and value leaps driven by the convergence of new technologies, business models, and ecosystem dynamics [33]. This process not only requires advantages in resources and scale but also demands continuous innovation in technological development and strategic actions [34].

Cross-category innovation comes from organizational links to previously unmerged categories by adding different elements and business model components, which can lead to a reorganization of the symbols and perceptions of the elements, forming information about what the category is and should be. Durand and Khaire [35] distinguished two models of cross-category innovation based on whether the categories are formed by elements outside the existing classification system or by internal elements: category emergence and category creation. Category emergence refers to the valuable categories that form and evolve in the market using components and features outside the classification system. These categories are typically novel, attractive, and even disruptive, leading to winner-takes-all outcomes [36], such as the innovation in nanomaterials that has led to industry disruption. Category creation is a process of redesigning the cognitive boundary of an element subset in the existing classification system in the market, separating the created category from the current classification system, and giving new value to the category. The motivation of this process lies in the breeding of the new market order, which is a process in which the label changes precede the material changes. Organizations can break into the new market via cross-category innovation, which effectively broadens the scope for strategic planning [37]. These studies not only delve into internal organizational structures, cognitive activities, and adaptive behaviors but also cover the interaction between organizations and their external environment [38], enabling the tracking of long-term organizational operations and outcomes of organizational change. As organizations evolve from chaos to order in their development process, what is crossed is not just a simple sum of category elements [39]. Formulating differentiation strategies not only ensures that the organization has the capability to meet market development and audience needs while also promoting competitiveness in the complex environment [40].

In the process of platforms’ cross-category development into platforms in new fields, complementary enterprises and consumers may find it difficult to migrate to other competing platforms due to lock-in effects and switching costs, thus further amplifying the value of the platforms’ existing user bases. The digital platform ecosystem, through continuous learning from user behavior data, can not only improve the quality of services in the original categories but also support cross-category data migration. This data-driven breakthrough in the boundaries of user cognition, which enables the platform to transition from a single-category value network to a multi-category one, is essentially the synergistic result of the reusability of data resources and the scalability of technology. Platforms migrate network effects to cross-category markets and transform them into competitive advantages for cross-industry development through cross-category innovation strategies [41]. This migration breaks the restrictions of industry barriers in traditional markets, enabling platforms to enter new fields at low cost. When platforms reach a critical scale, the one with the largest user base will continue to attract high-quality resources through positive feedback mechanisms, forming a “winner-takes-all” market landscape [42]. This phenomenon is particularly evident in market environments where user multi-homing switching costs are high and differentiated functional needs are limited.

2.3. Theoretical Gaps and Research Questions

Digital platform ecosystems have reconfigured interdependencies at the platform level, blurred traditional market boundaries, and enabled cross-category innovation and creative reconfiguration. Therefore, digital platform enterprises need to continuously adjust their strategic choices to cope with increasing complexity and uncertainty [43]. Existing studies have discussed the network effects of digital platform ecosystems and the mechanisms of cross-category innovation, but there are still theoretical gaps in explaining the dynamic processes and strategies of cross-category innovation in digital platform ecosystems. First, traditional theories have limited explanatory power for cross-category innovation in digital platform ecosystems. Classic theories based on bureaucratic structures and traditional industry contexts are difficult to adapt to the particularities of digital platform ecosystems. For example, industrial organization theory struggles to explain the dynamic process of cross-category innovation, and transaction cost theory cannot fully account for the blurring of cross-category transaction boundaries driven by network effects [44]. Second, the interaction mechanism between network effects and cross-category innovation has not been clarified. Although existing studies have identified the multi-dimensional characteristics of network effects, they lack systematic analysis of their dynamic action paths in different stages of cross-category innovation. There is a lack of in-depth discussion on issues such as how network effects promote category boundary breakthroughs and how the intensity of network effects affects user migration and multi-homing behavior in cross-category innovation. Third, the complexity of cross-category innovation strategies from a game theory perspective is ignored. Existing game models mostly focus on price competition in two-sided markets or static analysis of single network effects, ignoring the complexity of “superposition of multiple network effects” and “dynamic interaction of cross-category strategies” in digital platform ecosystems [45]. Existing models have insufficient integration of factors such as digital technologies, data network effects, and reconstruction of user cognitive boundaries [46], resulting in limited explanatory power for strategic choices and equilibrium outcomes in cross-category innovation.

Based on the above theoretical gaps, this study seeks to integrate the perspective of network effects with game-theoretic analytical methods, thereby shedding light on the strategic mechanisms underlying cross-category innovation in digital platform ecosystems. By adapting the Hotelling model and employing a four-stage sequential game framework well-suited for capturing dynamic competitive interactions in multi-sided markets. This research aims to formalize the processes through which network effects drive category expansion, clarify the distinct roles of different network effects across stages of category emergence, creation, and differentiation, and unravel how game equilibrium outcomes at each stage influence user scale expansion, profit growth, and social welfare optimization. This approach intends to transcend the limitations of traditional theories in explaining cross-category innovation dynamics, integrate digital contextual factors into the analytical framework, and ultimately provide a novel theoretical lens for understanding the complexities of this research. In doing so, this study not only aims to fill theoretical voids in management research but also to offer actionable strategic insights for platform enterprises and policymakers navigating the evolving landscape of digital competition.

3. Model Setup

3.1. Model and Parameter Setting

To address the research questions, this chapter constructs a four-stage sequential game model grounded in the theoretical foundations of network effects and cross-category innovation mechanisms. By explicitly linking model parameters, stages, and equilibrium outcomes to the theoretical constructs, the model systematically unpacks the strategic mechanisms of cross-category innovation in digital platform ecosystems. To study such strategies, this research introduces a Hotelling model to construct a platform competition game model [47], as well as the extended model based on network effects proposed by Ma Lin et al. (2019) [48]. It is determined that the demand of platform users is affected by network effects and establishes corresponding models for cross-category innovation strategies and differentiated countermeasures of digital platform ecosystems, further analyzing user scale and market share expansion strategies under different market equilibrium states. The model also explores the impact of pricing mechanisms and benefit levels on cross-category innovation behavior and analyzes the corresponding competitive strategies and market game outcomes. Parameters are defined to reflect the core theoretical concepts with the literature on network effects and cross-category innovation. The platform in this study specifically refers to digital platform ecosystems, and users are defined as complementary enterprises, specifically referring to third-party sellers that provide goods or services for the supply side of the platform. The research makes the following assumptions:

Platform attribute setting: consider a duopoly market where there are two digital platform ecosystems providing homogeneous services to users. The users of digital platform ecosystems are diverse complementary enterprises, including manufacturers, developers, and service providers. Platform i $\in [A, B]$ are located at the two ends of the Hotelling model [0, 1] respectively. The service level of digital platform ecosystems is represented by the user’s belonging utility u, where it is the initial belonging utility. When a user chooses platform i, they receive the corresponding utility of that platform. Following Armstrong and Wright [49], we assume the initial utilities of the two platforms are equal. By making this assumption, potential differences in user preferences for specific platforms can be eliminated. Thus, the initial utility is $u=u_A=u_B>0$, enabling the accurate identification of the impact caused by different platform strategies. Similar to Zhang et al. [50], the platforms provide users with services having different competitive advantages j $\in \{m, c\}$. Here, m represents digital technology services (e.g., big data analysis, AI-driven recommendations, cloud computing), and c denotes efficiency services (e.g., supply chain responsiveness, system integrity capability, after-sales service standardization). The two form the initial service difference parameters $t=t_m+t_c$, where $t_m$ is the difference in intensity of digital technology services and $t_c$ is the difference in intensity of efficiency services. The two types of services can be compatible on the platforms.

User behavior setting: A user with coordinate $x\in [0, 1]$ chooses a platform according to their needs and preferences for services. The movement of users towards platform A or B represents an increase in their preference degree and recognition of service differentiation, while moving toward the opposite end of the platform indicates the generation of negative utility. The service difference parameter t is equivalent to the matching cost for a user at position x choosing platform i, which is $t\left|x-x_i\right|$, which reflects the degree of deviation from their service preference. Similar to Rochet & Tirole [8] and Hagiu & Wright [51], when users choose platform i, they need to pay the basic service fee $p_i$ and the commission ${\gamma }_i$, which is settled according to the transaction ratio. If a user belongs to multiple platforms, the user can enjoy the services of digital technology and efficiency advantages and needs to pay the fees and commissions for multiple affiliations simultaneously. In the competition of digital platform ecosystems, information is relatively transparent, technology is compatible, and data migration is convenient, so users will not incur transfer costs [52].

Network effects setting: There are network effects μ between users on the same platform, which are positively correlated with the market share of services on the platform. Digital technology services generate data network effects ${\mu }_m$, which derive from continuous technological upgrading and value mining of user data. Efficiency services generate network effects ${\mu }_c$, which arise from the richness and coordination of complementary services. Similar to Ma et al. [48], the intensity of the network effects of service is ${\mu }_b={\mu }_m+{\mu }_c>0$. μ represents a more comprehensive integration of effects, particularly relevant in the differentiation stage when exclusive complementary products strengthen user stickiness. Based on the rational assumption, it needs to satisfy $\mu <t$, and it follows the core logic of Hotelling model that product difference is transformed into selection cost.

Cross-category innovation strategies setting: The user scale is standardized to 1, selling homogeneous products, and is uniformly distributed along the straight line from [0, 1]. Basic service demand $q_i$ equals market share $n_i$, that is $q_i=n_i$. Innovation category demand $q_a$ is bundled with basic services, therefore ${q_a=q}_i$; commission income $\gamma q_a$ is directly related to basic service demand. Set ${\epsilon }_i$ as the exclusive utility for cross-category innovation strategies, where platform A implements category emergence ${\epsilon }_A=\delta$, $\delta$ increases the user bases of digital technology services [53], platform B implements category creation to reduce the multi-homing cost ${\epsilon }_B=-c$ for users, and when implementing a differentiation strategy, the exclusive value of complementary products is represented by ε, indicating that complementary products enhance the retention utility for single-homing users [54].

Table 1. Model Parameters and Description.

Parameters	Description	Parameters	Description
$U$A	Consumer utility of platform A	$q_i$	The service requirements of the platform
$U$B	Consumer utility on platform B	$n_i^j$	The market share of platform i service j
$t_j$	Platform service differentiation parameters	ε	Differentiation strategy exclusive value
$x$	The position coordinates of the user on Hotelling line	$\delta$	Category emergence market expansion effect
$p_i$	The basic service pricing of platform i	c	Multi-homing cost reduction factor for category creation
${\gamma }_i$	Platform’s settlement commission rate	$\Delta CS$	Consumer surplus variation
${\mu }_j$	The intensity of the network effects for service j	$\Delta W$	Changes in social welfare benefits

summarizes the notations utilized throughout this paper.

This paper assumes the consumer group is defined as having homogeneous characteristics, with its bargaining power set to 0. The service has a marginal production cost set to 0. The service prices provided by the platform are exogenous market prices, with a standardized setting of 1 and a marginal production cost set to 0. The moderating effect of consumer behavior heterogeneity on the interaction relationship between digital platform ecosystems and complementary enterprises is not yet considered in order to focus the research on constructing the core interaction mechanism between digital platform ecosystems and their complementary partners.

3.2. Model Formulations

We study the process of implementing the cross-category innovation strategy in four stages. Stage 1: In the baseline competition, the two platforms provide homogeneous services. Stage 2: One platform initiates the category emergence strategy, launching cross-category digital technology services, thus becoming the industry leader. Stage 3: The other platform implements the category creation strategy, launching services of the same category. Stage 4: The category emergence platform responds to the category creation platform by offering more differentiated complementary products. The process diagram of cross-category innovation in digital platform ecosystems is shown in Figure 1.

3.2.1. Benchmark Competition Model

In the early stage of the industry, limited to the constraints of technical resources, the two leading digital platform ecosystems in the duopoly market provide products with highly homogeneous content and have not yet implemented cross-category innovation. Users can freely choose a single-homing or multi-homing. In this stage, the platform service presents the characteristics of low digital level and strong homogenization. The core strategy of the enterprise is to attract industry practitioners through pricing competition so as to seize the first-mover advantage. In constructing the benchmark user utility function, this study systematically integrates the action mechanism of network effects under the framework of two-sided market theory. The competition model of the two platforms at this stage is as shown in Figure 2a benchmark competitive model diagram. Based on Armstrong and Wright’s foundational bilateral platform competition from Hotelling model [49], and Ma et al.’s [48] extended formulation, we posit that platform users’ utility is inherently shaped by network effects. Further incorporating Rochet and Tirole’s non-neutral core perspective on price structure [8], set the user $x\in [0,x^e]$ in platform A, the user $x\in [x^e,1]$ in platform B, and the utility function of the user single-homing platform i is:

$$U_A=u+{\mu }_m{n}_A-tx-p_A$$

(1)

$$U_B=u+{\mu }_c{n}_B-t(1-x)-p_B$$

(2)

Multi-homing users $x\in [x_1, x_2]$, its utility function is:

$$U_{AB}=2u+{\mu }_m{n}_A+{\mu }_c{n}_B-t-p_A-p_B$$

(3)

The profit of the platform is divided into two parts: basic service and settlement commission, which is the product of unit price and market share. Its profit function is as follows:

$${\pi }_i=\left(p_i+\gamma \right)n_i (i=A, B)$$

(4)

Platform services include basic services and innovative services b, and the two services are provided for bundling. The difference in the service level of the platform leads to users’ unequal demand for the platform. However, when users choose the basic service of platform i, they need to pay the corresponding innovative service fee. Therefore, the market share of the platform shall be subject to the maximum service value:

$$n_i=\mathrm{m}\mathrm{a}\mathrm{x}\{n_i^m, n_i^c\}$$

(5)

When the competitive equilibrium is reached, the no-difference condition is $U_A=U_B$, $U_A=U_{AB}$, there are two points of no difference in user utility ${x_1=n}_A$ and ${x_2=1-n}_B$, $x_1<x_2$ represents that there is no difference between single-homing and multi-homing of the platform, and the equilibrium point is $p_A=p_B={\displaystyle \frac{t-\mu }{2}}$, $n_A=n_B={\displaystyle \frac{1}{2}}$.

Thus, the consumer surplus can be derived as:

$$CS={\int }_0^{1/2}\left(U_A-1\right)dx+{\int }_{1/2}^1\left(U_B-1\right)dx+{\int }_{x_1}^{x_2}\left(U_{AB}-1\right)dx={\displaystyle \frac{{(t-\mu )}^2}{12t}}+\gamma$$

(6)

Social welfare function is:

$$W={\pi }_A+{\pi }_B+CS={\displaystyle \frac{{(t-\mu )}^2}{6t}}+2\gamma$$

(7)

3.2.2. Category Emergence Model

The essence of category emergence is to break through the cognitive boundaries of existing classification systems, as discussed in this study is the dual driver of technology and cognition. When digital platform ecosystems provide value that existing categories cannot accommodate through technological innovation, such as digital twin emerging as a new category, the new category will capture the full new share of the market [24]. The data network effects from digital technology innovation result from the combined action of market expansion and user transfer: they stem from continuous technological upgrading and value mining of user data. As an innovative strategy that transcends existing cognitive boundaries, category emergence is driven by data network effects μₘ. Here, δ denotes the market expansion effect generated by launching novel digital technology services, such as Alibaba’s extension from e-commerce into cloud computing, leveraging its accumulated e-commerce data, thus capturing how data reusability facilitates entry into previously unconnected markets. This drives market expansion by attracting new users. Because the success of the emergence of digital platform ecosystems categories is not only dependent on technological innovation but also limited by the categorical imperative of the existing classification system, the dependence on the prototype platform services will produce a cognitive lock to users. This dynamic process unfolds as follows: User segments with pronounced preferences for technological novelty act as early adopters of emerging categories, driven by their intrinsic motivation to engage with cutting-edge digital solutions [36]. Digital platform ecosystems implement the category emergence strategy and launch cross-category innovative digital technology services, further shaping and changing the utility perception of users, and increasing the number of consumers that associated users can contact. These factors are intertwined and jointly affect users’ value experience and decision-making process on the platform. The category emergence model of the two platforms at this stage is as shown in Figure 2b category emergence model diagram. Therefore, the utility gain of the new digital technology innovation users of the single-homing platform A is:

$${\overline{U}}_A=u+{\mu }_m{(\overline{n}}_A+\delta )-t\overline{x}-{\overline{p}}_A$$

(8)

Since the new settlement commission generated by digital technology innovation is only obtained by platform A, only the profit function of Platform A is changed accordingly to:

$${\overline{\pi }}_A={(\overline{p}}_A+\gamma \left)\right({\overline{n}}_A+\delta )$$

(9)

$${\overline{\pi }}_B={(\overline{p}}_B+\gamma ){\overline{n}}_B$$

(10)

The indifference point moves left towards platform A, and the market share is:

$${\overline{n}}_A={\displaystyle \frac{1}{2}}+{\displaystyle \frac{\delta }{2t}}$$

(11)

$${\overline{n}}_B={\displaystyle \frac{1}{2}}-{\displaystyle \frac{\delta }{2t}}$$

(12)

As the price remains unchanged, the new market expansion effect and commission income are $\gamma \delta$, and the consumer surplus is:

$$\overline{CS}=CS+{\int }_0^{n_A}\delta dx={\displaystyle \frac{{(t-{\mu }_m)}^2}{12t}}+\gamma +{\displaystyle \frac{{\delta }^2}{8t}}$$

(13)

Social welfare function is:

$$\overline{W}={\overline{\pi }}_A+{\overline{\pi }}_B+\overline{CS}={\displaystyle \frac{{(t-{\mu }_m)}^2}{6t}}+2\gamma +{\displaystyle \frac{{\delta }^2}{4t}}$$

(14)

3.2.3. Category Creation Model

Category creation is a “concept first” market-driven process, centered at the cross-level integration of existing category elements, that reshapes rather than disrupts existing cognitive boundaries and market order [55]. This reconfigurative approach is driven by network effects ${\mu }_b$, leveraging the coordination of launching digital technology and data analysis services similar to those of platform A to reduce users’ multi-homing costs—a dynamic captured by parameter c, which quantifies the cost reduction from such integration. Network effects here integrate both initial efficiency services and digital technology services, reinforcing the feedback loop between ecosystem coordination and user stickiness. The process of category creation usually does not disrupt the existing classification system and market order. When platform A launches new digital technology services, platform B responds by redefining category boundaries, combining differentiated labels with familiar category elements to align with evolving user needs. Drawing on its existing ecosystem user base, platform B leverages coordinated development to lower transfer costs, such as JD.com, which added digital services and data analysis services, gradually locking users into its similar services and reducing their ownership costs. This strategic maneuver allows the platform to acquire new identities and positional power without upending the existing classification system, in turn reshaping consumer cognition and value orientations. Over time, this not only enhances user retention in the category creation stage but also expands the platform’s existing market size and drives higher profits. The multi-homing user utility at this stage thus reflects these dynamics, as captured in the category creation model. The category creation model of the two platforms is as shown in Figure 2c category creation model diagram. Therefore, the multi-attribution user utility is:

$${\widehat{U}}_{AB}=2u+{\mu }_b{(\widehat{n}}_A+{\widehat{n}}_B)-t-{\widehat{p}}_A-{\widehat{p}}_B+c$$

(15)

The profit function is:

$${\widehat{\pi }}_B=({\widehat{p}}_B+\gamma )({\widehat{n}}_B+c)$$

(16)

The indifference equilibrium point moves to the direction of platform B, and the market share of the platform is:

$${\widehat{n}}_A={\displaystyle \frac{1}{2}}+{\displaystyle \frac{c}{2t}}$$

(17)

$${\widehat{n}}_B={\displaystyle \frac{1}{2}}-{\displaystyle \frac{c}{2t}}$$

(18)

Platform B price is ${\widehat{p}}_B={\displaystyle \frac{t-\mu -c}{2}}$, substitute for consumer surplus:

$$\widehat{CS}={\displaystyle \frac{{(t-{\mu }_b-c)}^2}{12t}}+\gamma +{\displaystyle \frac{c(t-{\mu }_b)}{4t}}$$

(19)

Social welfare function is:

$$\widehat{W}={\widehat{\pi }}_A+{\widehat{\pi }}_B+\widehat{CS}={\displaystyle \frac{{(t-{\mu }_b-c)}^2}{6t}}+2\gamma +{\displaystyle \frac{c(t-{\mu }_b-c)}{4t}}$$

(20)

Figure 2. Competitive Model Diagram of Cross-category Innovation in Digital Platform Ecosystems.

Figure 2. Competitive Model Diagram of Cross-category Innovation in Digital Platform Ecosystems.

3.2.4. Differentiation Strategy Model

The core of the differentiation strategy is to seek a balance between category legitimacy and uniqueness, aiming to establish a competitive edge distinct from similar platforms while ensuring the services of digital platform ecosystems gain recognition within a specific category [54]. This strategy relies on comprehensive network effects μ manifested through exclusive complementary products, which strengthen user interaction intensity and thereby promote single-homing behavior. Here, the parameter ε represents the exclusive utility for single-homing users. When platform A faces competitive pressure from latecomer platform B, it needs to establish heterogeneity through complementary product innovation, such as adding exclusive services and providing more attractive terms, so that users can obtain certain benefits and value-added and may choose single-homing. For example, Alibaba has offered single-homing users unique services such as intelligent personalized recommendations and exclusive business analytics tools. It has implemented measures like reducing commission rates for long-term partnered merchants and providing customized digital operation training to retain more merchants. The condition chosen is that under the differentiated strategy, the user surplus is greater than the non-differentiated strategy state, ${CS}_M^{*}\left(x^{*}\right)\ge {\widehat{CS}}_{AB}\left(\widehat{x}\right)$. The differentiation strategy model of the two platforms at this stage is as shown in Figure 2d differentiation strategy model diagram. The utility of the single-homing user through complementary products is as follows:

$$U_i^{*}=u+\mu n_i+\epsilon -t\left|x-x_i\right|-p_i$$

(21)

Profit comes from basic services and new complementary services, and the profit function is:

$${\pi }_i^{*}=(p_i^{*}+\gamma )n_i^{*}$$

(22)

In the symmetric equilibrium state, the platform price and market share are solved as follows $p_A=p_B=t-\mu -\epsilon$, $n_A=n_B={\displaystyle \frac{1}{2}}$. At the same time, complementary products enhance the utility of single-homing, so the consumer surplus is:

$${CS}^{*}={\displaystyle \frac{{(t-\mu -\epsilon )}^2}{8t}}+\gamma$$

(23)

Social welfare is:

$$W^{*}={\displaystyle \frac{{(t-\mu -\epsilon )}^2}{4t}}+2\gamma$$

(24)

4. Analysis of Competitive Equilibria and Strategic Implications

In this section, we systematically analyze the four-stage sequential game model to explicitly address the research questions. By linking equilibrium outcomes to network effects dynamics, stage-specific strategies, and performance metrics, this study analyzes how cross-category innovation strategies and multi-homing user behavior reshape digital platform ecosystems market share. The specific research paths are as follows: First, the emerging platform A analyzes the optimal strategy of digital technology innovation and category boundary breakthrough in different stages. Secondly, for the platform B implementing category creation, it analyzes the digital technology of establishing a similar category, analyzes the market balance when reconstructing the cognitive boundary of category, and makes category creation strategies. Thirdly, it evaluates the impact of differentiation strategy on market structure and analyzes whether it leads to monopoly patterns or promotes differentiated competition patterns with better social welfare. Finally, by comparing the market equilibrium results under different strategies, the influence path of strategy differences on user selection and the overall market benefit is revealed. Using the explanatory function of Hotelling model on differentiated products, Bertrand-Nash equilibrium is introduced to analyze, and the demand function of bilateral platform i is deduced: $q_i=q_i(p_i, p_{-i})$, so ${\pi }_i=p_i{q}_i^p\left(p_i, p_{-i}\right)+\gamma q_i^p\left(p_i, p_{-i}\right)$, $i\in \{A, B\}$. Under the Bertrand-Nash equilibrium condition, the first-order condition for profit maximization is ${\displaystyle \frac{\partial {\pi }_i}{\partial p_i}}=0$, ${\displaystyle \frac{{\partial }^2{\pi }_i}{\partial {p_i}^2}}<0$, which can obtain equilibrium price, market share, and profit. For easy analysis and without loss of generality, the hypothesis ${\mu }_m={\mu }_c={\displaystyle \frac{\mu }{2}}$, $t_m=t_c={\displaystyle \frac{t}{2}}$.

4.1. Benchmark Competitive Equilibria and Strategies

When the benchmark model reaches the competitive equilibrium state, there are two points of user utility indifference, $n_A=n_B={\displaystyle \frac{1}{2}}$. Interval (0, ${\displaystyle \frac{1}{2}} )$ users are more likely to prefer platform A, while users in the interval (${\displaystyle \frac{1}{2}}, 1)$ are more likely to prefer platform B. There is no difference between the single-homing and multi-homing of the platform. From Formulas (1)–(7), the following conclusions are drawn.

Lemma 1.

When $2\gamma <t-\mu <2t$, single-homing and multi-homing yield identical user utility, leading to a unique symmetric equilibrium without cross-category innovation. The equilibrium price is $p_A=p_B={\displaystyle \frac{t-\mu }{2}}$, the market share is  $n_A=n_B={\displaystyle \frac{1}{2}}$, profit is  ${\pi }_A={\pi }_B={\displaystyle \frac{t-\mu +2\gamma }{4}}$, the remaining consumer is $CS={\displaystyle \frac{{(t-\mu )}^2}{12t}}+\gamma$.

Lemma 1 indicates that in the benchmark competitive landscape of digital platform ecosystems, duopoly platforms exhibit a symmetric equilibrium structure. The equilibrium outcome depends solely on the utility difference retained between platforms. The level of homogenization among digital platform ecosystems is relatively high; any implementation of a differentiation strategy by one party will impact the competitive landscape. The equilibrium price and market share are determined by the interaction between service differentiation parameter t and network effects intensity $\mu$. The equilibrium price is that the profit of the platform increases with the increase of service difference t, strengthens the monopoly power of the platform by matching costs, and decreases with the enhancement of the network effects $\mu$. By promoting the multi-homing users, the network effect plays the role of weakening the monopoly and can help the platform to expand the user scale. Consumer surplus increases with the expansion of service differentiation and decreases with the enhancement of network effects. These findings corroborate the discoveries of Armstrong’s research on bilateral market theory [49]. The equilibrium indicates that in platform competition under baseline conditions, service heterogeneity is the key influencing factor, while network effects drive market competition towards efficiency through the expansion of user scale.

4.2. Category Emergence Equilibria and Strategies

Category emergence stage shows how network effects drive category breakthroughs, transitioning the ecosystem from homogeneity to initial differentiation. Platform A leverages data network effects to launch cross-category innovation, introducing novel digital technology services that expand the market. There are two points of user utility indifference, and the state and choice of all parties are the same as the equilibrium state of the benchmark. Substituting Formulas (8) and (9), its equilibrium characteristics are obtained as follows:

Lemma 2.

When  $2\gamma <t-{\mu }_m<2t$, if platform services are not complementary, the ownership of user segments is partial, the platform undertakes category emergence innovation while no other platform emulates, the balanced price remains unchanged, and the market share is  ${\overline{n}}_A={\displaystyle \frac{1}{2}}+{\displaystyle \frac{\delta }{2t}}$,  ${\overline{n}}_B={\displaystyle \frac{1}{2}}-{\displaystyle \frac{\delta }{2t}}$, profit is  ${\overline{\pi }}_A={\displaystyle \frac{(t-{\mu }_m+2\gamma )}{4}}+\gamma \delta$,  ${\overline{\pi }}_B={\displaystyle \frac{(t-{\mu }_m+2\gamma )}{4}}$, consumer surplus is  $\overline{CS}={\displaystyle \frac{{(t-{\mu }_m)}^2}{12t}}+\gamma +{\displaystyle \frac{{\delta }^2}{8t}}$.

Lemma 2 indicates that user ownership and cross-category innovation of digital platform A are intertwined. Category emergency represents the subversion and innovation of the organizational category, changing the classification hierarchy and creating new and valuable categories in the market. In the early stages, new categories often lacking clear definitions are marked by significant uncertainty among early entrants regarding their meaning, boundaries, and even existence, with stakeholders’ understanding remaining unstable and no specific category gaining a large following. After platform A enhances its digital technology services through technological innovation, generating a market expansion effect—achieved by integrating societal development trends and audience cognition into its cross-category innovations, which thus resonate with the growing audience preference for innovative and non-traditional products amid social advancement and gain broader recognition. By using more efficient practices, new categories replace the existing organizational categories, bringing value to consumers or the society. Therefore, the settlement income belongs to platform A, which becomes its brand-new profit growth point. The settlement commission does not affect the price and market share, but the root cause is that such digital innovation can add new competitive advantages and, thus, improve social benefits. For example, user behavior data analysis helps to gain insight into the market and user needs and recommend algorithms to optimize products and services. Data network effects ${\mu }_m$ facilitate this expansion by enhancing service value through user data mining and lowering users’ cognitive barriers to new categories while also reducing the cost of users’ cross-category cognition and assisting complementary enterprises in making scientific decisions. Compared with the equilibrium situation described in Lemma 1, only platform A shows profit growth. Thus, under the new model framework, because of innovation benefits not involved in competition, platform B lacks similar resources endowment. Innovation strategy is difficult to adjust the price, market share, and profits to maintain the original equilibrium, but it will affect the long-term competition. The category emergence breaks through the traditional price war trap, prompting the whole platform market to achieve Pareto improvement.

The category emergence implemented by digital platform ecosystems breaks through existing classification systems through technological innovation, expanding market share without reducing prices and validating that digital technology promotes positive network effects. Category emergence platforms can capture all newly added market shares with their technological advantages, becoming leaders. Platforms that do not engage in category emergence are constrained by innovation barriers and will gradually fall into a disadvantageous position over time. Non-competitive benefits provide continuous innovation incentives for leading platforms, which can simultaneously increase consumer surplus and social welfare, achieving Pareto improvement optimization. This conclusion can be formulated as the following proposition.

Proposition 1.

Category emergence platform can capture the entire newly created market share through their technological advantages leveraging data network effects, thus emerging as market leaders. In contrast, other platforms face innovation barriers and gradually slip into a disadvantaged position over time. Furthermore, non-rivalrous benefits sustain incentives for continuous innovation among leading platforms, which increases both consumer surplus and social welfare, achieving Pareto improvements.

4.3. Category Creation Equilibria and Strategies

Platform B implements the category creation strategy in response to the category emergence for platform A, leveraging integrated network effects ${\mu }_b$ to reducing the cost of multi-homing c. In this scenario, there are also two points of user utility indifference, which are substituted into Equations (15) and (16), and their equilibrium characteristics are as follows:

Lemma 3.

When  $2\gamma +c<t-{\mu }_b<2\gamma +3c$, the equilibrium price and market share of platform B are  ${\widehat{p}}_B={\displaystyle \frac{t-{\mu }_b-c}{2}}$,  ${\widehat{n}}_B={\displaystyle \frac{1}{2}}+{\displaystyle \frac{c}{2t}}$, When  $c<{\displaystyle \frac{t-{\mu }_b+2\gamma }{2}}$, platform B has a larger market share than platform A. Profit and consumer surplus are,  ${\widehat{\pi }}_B=({\displaystyle \frac{t-{\mu }_b-c}{2}}+\gamma )({\displaystyle \frac{1}{2}}+{\displaystyle \frac{c}{2t}})$,  $\widehat{CS}={\displaystyle \frac{{(t-{\mu }_b-c)}^2}{12t}}+\gamma +{\displaystyle \frac{c(t-{\mu }_b)}{4t}}$.

Lemma 3 demonstrates that under the condition of innovation competition in category creation, ${\widehat{p}}_A>{\widehat{p}}_B$, ${\widehat{n}}_A<{\widehat{n}}_B$, ${\widehat{\pi }}_A<{\widehat{\pi }}_B$. Notably, when multi-homing users engage with platforms, the leading platform’s category emergence strategy forces lagging platforms to align user expectations with characteristics—extracting value from stable industrial category frameworks rather than creating entirely new categories. The novelty lies not in creating new categories but in redefining the boundaries between existing category elements or entities, enabling precise market positioning to avoid value penalties from rigid classical imperatives during category evolution. Platform A’s first-mover advantage necessitates that Platform B possess inherent operational advantages, just as cost efficiency in digital manufacturing processes, to achieve equivalent utility. Based on the above calculations and analysis, when the category creator provides users with a price subsidy of no less than the total utility of users increases, allowing platform B to gain competitive momentum, market share expands and enhances profitability. This leads to the following conclusion: When $c>\delta$, platform B has a larger market share than platform A, realizing the advantage of category creation, verifying the attractiveness of late innovation to multi-homing users, avoiding the value loss caused by classification rules, combining with price subsidy strategy to realize the reversal of advantages in market share and profit level, and breaking the dominant pattern of leading platforms.

Proposition 2.

When category creation platform implements with advantages in both data network effects and existing network effects, it can surpass category emergence platform in market share and gain advantages through late-mover innovation. When combined with a price subsidy strategy, category creation platform can break the dominant position of the leading platform.

Under the study’s hypothesis, innovative services work with the original service to provide value to users, with category creation intensity measurable by the adoption rate of upgraded services. By Lemma 3, ${\widehat{n}}_A={\displaystyle \frac{1}{2}}-{\displaystyle \frac{c}{2t}}$, ${\widehat{n}}_B={\displaystyle \frac{1}{2}}+{\displaystyle \frac{c}{2t}}$, so ${\displaystyle \frac{d{\widehat{n}}_A}{dt}}=-{\displaystyle \frac{1}{2t^2}}<0$, ${\displaystyle \frac{d{\widehat{n}}_B}{dt}}={\displaystyle \frac{1}{2t^2}}>0$; as the difference of the original service level increases, the possibility of successful category creation increases. When $t=\pm {\mu }_b$, in the cross-vertical category scenario, vertical category scenarios—such as precision machining versus bulk manufacturing, which exhibit higher category embeddability in industrial taxonomies—will witness that deeper vertical specialization can enhance user familiarity. This research echoes the vertical and horizontal network effects [56]. As a result, it can reduce the barriers to the adoption of relevant products or services and is conducive to Platform B’s innovation. When $t={\mu }_b$, category creation has the greatest chance of success, with leading platforms exiting the market altogether. When $t=-{\mu }_b$, category creation is the most likely to fail, category creation completely fails, and the latecomer platform completely exits the market. When $-{\mu }_b<t<{\mu }_b$, for the horizontal category scenarios like cross-sector supply chain integration where differentiation is marginal, the level category represents the category in the system in multiple aggregation level in a meaningful way of combination and the category of inclusive, while the category combination entity is still recognizable and coherent. Horizontal extension strategies enable platform coexistence; users will choose between two platforms, with competition from both sides sharing across category innovation brought by the increased market share.

To illustrate the differences between vertical and horizontal extension strategies more concretely, consider the following cases: In digital platform ecosystems governed by network effects, where platforms like Siemens MindSphere aggregate thousands of manufacturing enterprises, cross-platform competition hinges on critical user scale thresholds. Once the enterprise user base surpasses this threshold, a category creator’s baseline service level directly amplifies the success probability of extended innovations. For instance, when a precision machining platform enhances its baseline service by integrating real-time tool wear monitoring (a core vertical service), the subsequent launch of AI-driven quality control modules (an extended innovative service) benefits from pre-established user familiarity with its industrial process taxonomy, reducing adoption friction and accelerating market penetration. Conversely, in horizontally integrated ecosystems, such as Schneider Electric’s cross-sector collaboration with retail logistics providers, where differentiation between platforms may lie in marginal data analytics capabilities, horizontal extension strategies prioritize interoperability over exclusivity. Platforms might use open API frameworks to share real-time data across systems. Such strategies prevent excessive concentration, ensuring cross-category innovation benefits—like reduced lead times through synchronized planning—are distributed across the ecosystem, aligning with principles of collaborative capacity optimization. The above analysis is summarized and the following conclusions are obtained.

Proposition 3.

When innovative services within the same category have significant differential advantages, adopting an innovation strategy across vertical domains can maximize the success possibility of category creation; otherwise, when differential advantages are not prominent, choosing a horizontal extension strategy is more prudent.

Comparing Lemma 3 with Lemma 2, both platforms have increased in price, market share, and profit. The category creates a policy feasible domain of $t-{\mu }_b\mathsf{ϵ}(2\gamma +c, 2\gamma +3c)$, greater than the category of the emergence of competition $(2\gamma , 2t)$; the market can accommodate more transactions and user participation, and the market activity and scale have been increased. The reason is that platform B conducts category creation competition through subsidy strategy, so that its price declines to stimulate demand and attract more users. Subtract the consumer surplus of the two cases to obtain $\widehat{CS}\left(x\right)-\overline{CS}\left(x\right)={\displaystyle \frac{c\left(t-\mu \right)}{4t}}-{\displaystyle \frac{{\delta }^2}{8t}}$. When $t>0$ and $c>0$, the conditions for establishment are $t>\mu +{\displaystyle \frac{{\delta }^2}{2c}}$; consumer surplus will not be reduced. When the social welfare of the two cases is reduced, we obtain $\widehat{W}-\overline{W}={\displaystyle \frac{-ct+c\mu -c^2-3{\delta }^2}{12t}}-\gamma \delta$; the calculation is obtained only when the utility satisfies the one $t<{\displaystyle \frac{c\mu -c^2-3{\delta }^2}{c+12\gamma \delta }}$, and social welfare will only be improved. When $2\gamma +c<t-\mu <2\gamma +3c$, $u\widehat{W}-u\widehat{CS}=4t-\mu -\gamma >0$, at this point, consumer surplus will be reduced before social welfare.

Analysis of the computational model reveals that in scenarios with multi-homing users, the competitive landscape between platforms undergoes structural changes. First, the category creation strategy enables platform B to attract users through integrated network effects and cost subsidies, expanding industry-wide market capacity. Second, as platform dominance intensifies, market concentration gradually emerges, leading to social welfare degradation, with associated welfare losses ultimately transferred to users. While cross-category innovation strategies in platforms enhance enterprise revenue, their impact on users remains contingent on market structure dynamics. From the perspective of consumer surplus and social welfare, although multi-homing weakens direct platform competition, excessive concentration of platform monopoly power negatively affects both metrics, with welfare losses further borne by users. While platform cross-category competition boosts revenue, its user impact is ambivalent: When platform market share becomes overly concentrated and dominant positions solidify, users actively seek new competitive configurations to improve their utility, thereby catalyzing further evolution of the competitive landscape in ecosystems.

Proposition 4.

Category creation strategies empower lagging platforms to initiate category competition, achieving market share growth and profit expansion while expanding industry-wide market capacity. However, once platform monopoly power surpasses a critical threshold, user surplus and social welfare transition from increasing to decreasing trends, with users absorbing the resulting losses.

4.4. Differentiation Equilibria and Strategies

Digital platform ecosystems deliver exclusive value ε to users through a wider range of complementary products, thereby promoting user single-homing. In this case, there is no difference in user utility, and substitution (21) forms a differentiated competitive balance:

Lemma 4.

When  $\epsilon \le t-{\mu }_i$, on the basis of implementing category emergence innovation and category creation innovation, the two platforms choose to formulate differentiated strategies, and some users choose single-homing to form differentiated competition. The equilibrium price and market share are:  $p_A^{*}=p_B^{*}=t-{\mu }_i-\epsilon$,  $n_A^{*}=n_B^{*}={\displaystyle \frac{1}{2}}$. The calculation yields a profit of  ${\pi }_i^{*}={\displaystyle \frac{p_i^{*}+\gamma }{2}}$. Consumer surplus is  ${CS}^{*}={\displaystyle \frac{{(t-{\mu }_i-\epsilon )}^2}{8t}}+\gamma$.

Summarizing the above analysis, digital platform ecosystems must balance categorical imperative and differentiation in ecosystems. Once an organization gains an initial competitive edge in a specific category, it must promptly establish market differentiation; otherwise, latecomers may replicate the advantage through category creation within short timeframes. Achieving category emergence—such as developing a novel production standard or modular assembly system—is rarely feasible in the short term. Instead, user single-homing fosters differentiated market positioning through exclusive integration with a specific platform, enabling the platform to secure a dedicated market share.

To implement differentiation strategies effectively, platforms must meet specific operational conditions as defined in Lemma 4: complementary manufacturing modules or service configurations enhance the utility of single-homing users. The value delivered by these complementary offerings—influenced by the platform’s base pricing and coordination costs—must exceed user acquisition thresholds, ensuring profits do not decline with reduced price subsidies and achieving a balance of value-driven competitive potential. This implies that during price competition, platforms can retain users by lowering service fees or rebating coordination costs, offsetting the “switching costs” associated with adopting complementary modules. Under such constraints, differentiation via complementary manufacturing solutions and service enhancements allows platforms to fend off competitors’ category creation threats. Under this framework, consumer surplus surpasses benchmark competition levels, forming a synergistic pattern of increasing user value and platform revenue—aligned with the adaptive manufacturing configurations and demand balancing analyzed in ecosystem research.

Proposition 5.

Platforms adopting a differentiation strategy via complementary product value can enhance single-homing utility, effectively counter category creation threats to achieve competitive parity. This leads to consumer surplus exceeding benchmark competitive levels, forming a synergistic improvement of user value and platform revenue.

5. Numerical Analysis

To validate the model of cross-category innovation strategies in digital platform ecosystems based on network effects, numerical analyses of market equilibrium outcomes under different strategies are conducted. The numerical analysis is implemented using Matlab, with parameter settings considering both literature benchmarks. In the benchmark competition model, parameters are set as follows: service differentiation parameter t = 0.5, network effects intensity μ = 0.2, and settlement commission rate γ = 0.2. The impacts of these strategies on platform market share, price, profit, consumer surplus, and social welfare are analyzed.

Assuming platform A implements a category emergence strategy with a market expansion effect δ = 0.2, parameter variations reveal distinct market share dynamics. As shown in Figure 2, platform A’s market share increases monotonically with the service differentiation parameter t, while platform B’s share decreases correspondingly, reflecting the competitive advantage from technological innovation. However, both platforms’ market shares decline with stronger network effects μ, attributed to enhanced user multi-homing that weakens monopolistic power and intensifies competition. The market expansion effect δ exerts a significant positive impact on Platform A’s market share (Figure 3), confirming that category emergence can expand market share without price reductions by leveraging technical innovation to surpass existing classification systems, aligning with theoretical predictions of competitive advantage acquisition.

Setting platform B to implement a category creation strategy with multi-homing cost reduction factors c = 0.3 and c = 0.5, Figure 4 illustrates a linear increase in platform B’s market share as c rises, accompanied by a corresponding decline in Alibaba’s share. This demonstrates that reducing multi-homing costs effectively attracts multi-homing users, enhancing platform B’s competitiveness. When $c>\delta$, the reversal of market dominance is validated: at c = 0.5, $n_B$ = 0.75 significantly exceeds $n_A$ = 0.25, showcasing the feasibility of late-mover platforms and achieving market share reversal through cognitive boundary reconstruction and cost-subsidy strategies. However, both platforms’ market shares decline with stronger network effects μ, attributed to enhanced user multi-homing that weakens monopolistic power and intensifies competition.

With the exclusive value of complementary products $\epsilon \in [0, 0.2]$, symmetric equilibrium analysis in Figure 5 shows that increasing ε strengthens Alibaba’s single-homing attractiveness, counteracting competitive pressures from Platform B’s category creation when c = 0.1. The synergistic effect of higher multi-homing cost reduction c = 0.2 and complementary product value further amplifies this trend, where $n_A$ rises with ε, forming a range from category creation stage to differentiation response dynamic. This pattern confirms that differentiation strategies can rebalance market shares through utility enhancement, leading to either symmetric or asymmetric equilibria contingent on c and ε and validating the strategy’s role in resisting competitive threats. This dual strategy framework, rooted in industrial ecology principles, ensures that platform evolution balances innovation momentum with operational stability, aligning with the core objectives of digital platform ecosystems: efficiency, adaptability, and value co-creation.

6. Concluding and Future Directions

6.1. Conclusions

This study uses the Hotelling model to analyze the competition among digital platform ecosystems and establish a dynamic process of market category structure change. Drawing on the theoretical model, equilibrium analyses, and numerical simulations, it addresses the research questions in the introduction, clarifying how network effects drive the dynamics of cross-category innovation in digital platform ecosystems, the stage-specific roles of distinct network effects, and the implications of game equilibria for market outcomes.

To address how network effects characterize the dynamic development of cross-category innovation in digital platform ecosystems, our analysis identifies a sequential four-stage process shaped by the amplification and reconfiguration of network effects—one governed by strategic game logic, where each stage responds to the prior and sets conditions for subsequent competition. In the benchmark competition stage, duopolistic platforms compete with homogeneous services, relying on service differentiation t and basic network effects μ to attract users. The category emergence stage is driven by data network effects, prompting leading platforms to break category boundaries via technological innovation, generating market expansion. Data network effects act as a launchpad, leveraging data-driven learning to legitimize the new category and expand user bases without price concessions. In the category creation stage, the latecomer platform responds by redefining boundaries, using integrated network effects to reduce users’ multi-homing costs. Even the follower overtakes the leader as lower cognitive barriers and subsidies attract multi-homing users. Integrated effects function as a bridge, integrating user bases and complementary services to challenge the leader’s status. The differentiation strategy stage sees that category emergence platforms deploy exclusive complementary products, enhancing single-homing utility via comprehensive network effects and exclusive value. This restores symmetric equilibrium but with higher user stickiness, as exclusive benefits reduce multi-homing and align preferences with platform-specific ecosystems; network effects act as a lock-in mechanism, sustaining differentiation through enhanced interactions and action feedback loops. Overall, network effects are not static but coevolve with strategic choices: data network effects drive breakthroughs, integrated network effects enable catch-up, and comprehensive network effects stabilize differentiation. This sequence mirrors an innovation “life cycle,” where each stage addresses prior limitations, propelled by the need to amplify or counteract network effects.

To address the specific roles of different network effects across the stages of category emergence, creation, and differentiation strategies, our findings highlight distinct, stage-aligned functions of data network effects ${\mu }_m$, integrated network effects ${\mu }_m+{\mu }_c$, and comprehensive network effects μ, each tied to the strategic demands of cross-category innovation. Data network effects drive category emergence by breaking cognitive and technological barriers. Integrated network effects combine data and efficiency effects; they coordinate complementary services and lower multi-homing costs, making the follower’s redefined offerings feel familiar yet improved. Comprehensive network effects sustain differentiation through exclusivity. By amplifying the value of complementary products, they boost single-homing utility. To address the implications of game equilibria for market outcomes, we find distinct impacts across stages, with trade-offs between these dimensions: Category Emergence Equilibria drive the leader’s profit growth via market expansion and expand user scale by attracting untapped users. Social welfare rises as the new category creates value without displacing existing users—a Pareto improvement. Category Creation Equilibria see the follower’s profit and market share grow with reduced multi-homing costs, but excessive concentration can occur. Beyond a threshold, social welfare declines as dominance weakens competition: user surplus initially rises with lower costs but later falls as monopoly power inflates implicit prices. This extends Rochet and Tirole (2003)’s [8] platform competition framework, highlighting that network effects can amplify welfare losses under extreme concentration. Differentiation Equilibria restore symmetric balance, stabilizing profits and user scale. Consumer surplus exceeds benchmark levels as exclusive benefits create value without limiting accessibility, while social welfare improves by avoiding price wars and fostering ongoing innovation in complementary products.

6.2. Managerial Implications

The dynamic interplay between network effects and cross-category innovation in this study offers profound managerial insights for digital platform ecosystems, policymakers, and stakeholders navigating competitive reconfiguration.

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Strategic Alignment with Network Effects’ Stage-Specificity

Platform managers must recognize that cross-category innovation is not a one-size-fits-all endeavor, but a staged process requiring deliberate alignment with the dominant network effects at each phase. In the category emergence stage, platforms should prioritize investments in data network effects to solidify their first-mover advantage. This entails allocating resources to data-driven capabilities—such as advanced analytics and AI-enabled learning systems—that enhance the perceived value of new categories, lower user cognitive barriers, and amplify the market expansion effect. However, complacency must be avoided: early investments in differentiation capabilities are critical to fending off subsequent challenges from followers. For the category creation stage, platforms should leverage integrated network effects, which combine data and efficiency effects, to redefine existing category boundaries. This requires strategic efforts to reduce multi-homing costs through ecosystem coordination—such as standardizing interfaces for complementary services and aligning new offerings with user familiarity. Success here hinges on balancing cost reduction with competitive dynamism: excessive focus on cost-cutting may lead to market concentration, eroding social welfare and triggering regulatory scrutiny. In the differentiation stage, managers should view differentiation not as a static strategy but as a dynamic mechanism to balance exclusivity with ecosystem vitality, ensuring that network effects continue to drive value co-creation across the user base.

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Orchestrating User Dynamics and Pricing Strategies

Network effects amplify the complexity of user affiliation and pricing, demanding a nuanced approach that transcends traditional price competition. When network effects are strong, multi-homing behavior intensifies, making tiered pricing strategies—distinguishing between basic services and value-added innovations—critical for expanding the user base while preserving margins. For tech-preferring users, exclusive services tied to data network effects can justify premium pricing, reinforcing the platform’s unique value proposition. Leaders must guard against the “innovation advantage trap”, where unchecked market power erodes user surplus. Similarly, followers employing category creation strategies should avoid over-reliance on subsidies to reduce multi-homing costs; instead, they should link cost reductions to tangible improvements in service quality, ensuring long-term user retention. By designing technical compatibility for non-core services, platforms preserve the benefits of network effects while preventing excessive lock-in, fostering a dynamic ecosystem where innovation thrives. Policymakers play a critical role in safeguarding this balance. They should monitor market concentration during category creation, intervening to ensure network effects amplify rather than restrict competition. Establishing clear standards for data usage, lowering entry barriers for small and medium-sized innovators, and enforcing anti-monopoly measures targeted at excessive network effect lock-in can foster an ecosystem where cross-category innovation benefits both platforms and society.

In summary, successful cross-category innovation in digital platform ecosystems requires managers to treat network effects as dynamic, stage-specific levers rather than static attributes. By aligning strategy with the dominant network effects of each phase, orchestrating user dynamics thoughtfully, translating technical capabilities into ecosystem value, and managing competitive risks proactively, platforms can reconfigure markets while optimizing both commercial success and social welfare.

6.3. Limitations and Future Directions

Theoretically, this study simplifies key factors such as market demand uncertainty and dynamic firm development. It assumes homogeneous user behavior, neglecting buyer–seller heterogeneity and complex cross-side network effect interactions. Focusing on duopolies, it underanalyzes multi-platform competition, dynamic technological iteration, and cross-platform migration costs, limiting generalizability.

Future research could: expand theoretical models by incorporating heterogeneous users, building a “seller–buyer” bilateral dynamic game framework to explore cross-side network effects, and integrating dynamic variables like technology iteration speed. Optimize methods via empirical tests across industries, relaxing assumptions to include real-world factors; and explore cross-domain integration, analyzing dynamic evolution of cross-category competition and strategy interactions in multi-platform scenarios, enhancing conclusion applicability through multi-case comparisons. These efforts will deepen understanding of cross-category innovation and support sustainable platform development.