Research on Dynamic Incentive Mechanism for Co-Creation of Value in Innovation-Oriented Platform Ecosystem Considering Supervision

Abstract

With the advent of the digital age, platform ecosystems have emerged as a crucial organizational form. Focusing on innovation-oriented platforms where collaborative innovation is paramount, this study developed a two-stage principal–agent model to examine how a platform enterprise’s value preference parameter governs collaborative outcomes. Our framework demonstrates that this parameter systematically regulates the endogenous portfolio of incentives and supervision, determining governance effectiveness and value co-creation outcomes in platform ecosystems. Further analysis revealed that as the platform enterprise deepens its understanding of an embedded enterprise’s capabilities, its governance mode spontaneously transitions from supervision-intensive to incentive-intensive, establishing a self-reinforcing cycle of value creation. These findings provide a principled basis for designing dynamic governance mechanisms and advance the platform governance literature by establishing the central role of the platform enterprise’s value preference parameter in coordinating endogenous governance instruments.

1. Introduction

Digital platforms have profoundly transformed value creation across industries, shifting traditional value chains into dynamic value co-creation ecosystems driven by multi-stakeholder collaboration [1,2]. As ecosystem orchestrators, the platform enterprise must not only facilitate transactions but also govern interactions and align incentives among diverse participants [3]. However, a critical yet often overlooked dimension in the literature is the fundamental heterogeneity among platforms. Following the seminal typology by Gawer [4] and Mcintyre & Srinivasan [5], we distinguish between transaction-oriented platforms (focused on the efficient exchange of goods and services) and innovation-oriented platforms (orchestrating collaborative innovation among participants). This study is squarely situated within the context of innovation-oriented platforms (e.g., digital R&D sandboxes, advanced manufacturing ecosystems), where the governance of long-term, uncertain, and non-contractible innovation processes present distinct and critically underexplored challenges.

Collaboration within these innovation-oriented ecosystems is inherently fraught with information asymmetry and strategic misalignment [6]. Participating enterprises may engage in opportunistic behaviors, such as concealing proprietary information or diverting resources to private projects, especially when the platform enterprise lacks visibility into their true efforts and capabilities [7]. Thus, platform enterprises require sophisticated governance mechanisms that not only encourage deep collaboration but also mitigate agency risks over the long-term.

Existing research has extensively explored two primary governance tools: incentive design and supervision. On the one hand, studies have introduced mechanisms like revenue-sharing, cost-sharing, and dynamic bonuses to align stakeholder interests [8,9]. On the other hand, supervisory governance, including algorithmic monitoring and third-party audits, has gained attention for its role in enhancing enforcement credibility and reducing opportunism [10,11]. Notably, a growing consensus suggests that incentive and supervision mechanisms are complementary and can achieve superior outcomes when designed in an integrated manner [12,13,14].

Nevertheless, significant limitations persist. First, the literature remains dominated by static or single-period models, which fail to capture the intertemporal dependencies and learning processes inherent in long-term innovation partnerships [15]. Second, supervision is frequently modeled as an exogenous, fixed variable, overlooking its nature as a continuous strategic lever that the platform enterprise can and does dynamically optimize in practice [16]. Most critically, existing governance models are often presented as one-size-fits-all, thereby lacking specificity to the unique context of innovation-oriented platforms, where the tension between controlling opportunism and fostering creative autonomy is most acute.

In response to these limitations, this study developed a two-stage principal–agent model that incorporates dynamic incentive contracts, endogenous supervision intensity, and the platform enterprise’s value preferences into a unified analytical framework. Our model was specifically designed to unravel the cross-stage governance dynamics in innovation-oriented platforms and allowed us to examine how the platform enterprise can systematically optimize their governance systems over time, offering strategic insights for fostering sustainable value co-creation.

The remainder of this paper is organized as follows. Section 2 reviews the relevant literature. Section 3 details the model assumptions, formulation, and solution process. Section 4 presents the analysis of the model equilibrium. Section 5 explores the findings through numerical analysis. Finally, Section 6 concludes with a discussion of the implications and limitations.

2. Literature Review

Research on value co-creation in platform ecosystems has advanced considerably, particularly around two interrelated governance mechanisms: incentive alignment and supervisory design. While each stream has contributed important insights, the literature remains fragmented and often under-theorized in the dynamic, multi-stage contexts that characterize innovation-oriented platforms. This section synthesizes key contributions and highlights the need for an integrated, temporal model of platform governance.

2.1. Incentive Structures for Value Co-Creation

A substantial body of research emphasizes the importance of aligning stakeholder incentives to foster cooperative behavior in multi-agent platform ecosystems. Foundational studies have explored various contractual mechanisms, including cost-sharing, revenue-sharing, and performance-based bonuses, which are designed to mitigate free-riding, promote equitable value distribution, and sustain long-term engagement [1,17]. These frameworks are rooted in principal–agent theory and Stackelberg leadership models, typically positioning the platform enterprise as the unilateral designer of incentive structures [18].

Recent research has expanded this paradigm by highlighting data transparency and information-sharing incentives, particularly in the context of industrial Internet and digital manufacturing. Studies indicate that mechanisms such as information subsidies and value-added services can enhance collaboration by reducing strategic data withholding [19]. Furthermore, scholars have begun exploring dynamic incentive contracts that adapt to partner behavior or environmental fluctuations, offering preliminary insights into the evolving nature of collaborative relationships [15,20].

However, the applicability and emphasis of these mechanisms vary significantly across platform types. A key distinction lies between transaction-oriented and innovation-oriented platforms [4]. In transaction-oriented platforms (e.g., e-commerce, ride-hailing), the governance problem centers on ensuring contract compliance and service quality, making monetary incentives like revenue-sharing highly relevant [21]. In contrast, innovation-oriented platforms (e.g., R&D collaboration platforms, advanced manufacturing ecosystems) face the more complex challenge of incentivizing long-term, often non-contractible innovative efforts. Here, formal incentive contracts must be carefully designed to balance the need for measurable performance indicators with the preservation of creative autonomy [22]. This review and our subsequent model primarily address the incentive structures pertinent to innovation-oriented platforms, where the tension between contractual governance and innovation management is most salient.

Notwithstanding these advancements, the literature exhibits two persistent limitations. First, most models remain confined to static or single-period frameworks, failing to capture the intertemporal dependencies and feedback loops inherent in long-term platform partnerships. Second, studies often treat incentive effectiveness as context-independent, thereby overlooking the systematic influence of platform-specific endogenous factors on incentive design. A pivotal yet under-examined factor of this kind is the platform enterprise’s value preference, which quantifies its strategic trade-off between private gains and ecosystem-wide value creation.

2.2. Supervisory Governance Under Information Asymmetry

In parallel with incentive design, a growing body of literature acknowledges the importance of supervision in curbing opportunism under information asymmetry. This is particularly relevant for innovation-oriented platforms, where the intangible nature of innovative work heightens information opacity. Given the platform enterprise’s limited visibility into partner operations, effective supervision is essential to ensure compliance and uphold contractual credibility. Scholars have explored various forms of supervisory mechanisms, such as public supervision, algorithmic monitoring, and third-party audits, each of which offers distinct advantages in terms of scalability, objectivity, and cost-effectiveness [11,23,24].

Importantly, supervision is no longer regarded as a standalone enforcement tool but as a dynamic complement to incentive structures within a governance framework. Empirical and theoretical studies consistently demonstrate that integrating performance-based incentives with credible supervision significantly reduces moral hazard and enhances cooperative revenue [14,25,26]. This incentive-supervision complementarity is crucial in complex, innovation-oriented platforms like industrial Internet platforms, where compliance and trust must be enforced across diverse partners [27].

However, a fundamental limitation persists: most models treat supervision as an exogenous parameter rather than as a continuous strategic variable subject to dynamic optimization. Consequently, existing theories fail to capture the core managerial practice wherein the platform enterprise continuously adjusts supervision intensity based on behavioral signals, historical compliance, and risk forecasts. Although a few studies have begun to model supervision as an endogenous decision variable [16], most examine supervisory mechanisms in isolation, lacking a unified framework for the synergistic design and dynamic coordination of incentives and supervision.

2.3. Synthesis and Implications for Research

Synthesizing the discussions in Section 2.1 and Section 2.2, it becomes evident that while substantial progress has been made in understanding incentive and supervisory mechanisms independently, the literature exhibits consistent limitations that hinder a holistic understanding of governance in innovation-oriented platform ecosystems.

These shortcomings primarily revolve around the interrelated challenges of temporal rigidity, modeling oversimplification, and lack of platform specificity. Existing research predominantly relies on static or single-period models, which fail to adequately capture the iterative and adaptive nature of real-world innovation partnerships. Such models overlook the learning processes and feedback mechanisms essential for sustaining long-term collaborative innovation.

Moreover, the prevailing conceptualization of supervision as an exogenous variable constitutes a substantial oversimplification. This perspective neglects the practical dynamic calibration of governance tools [28] and fails to account for the complex interrelationships among a platform enterprise’s value preferences, its trade-off between self-interest and collective value, and its concurrent selection of incentive and supervision mechanisms [29]. Most critically, existing governance models often lack specificity to different platform types, particularly innovation-oriented platforms where the tension between controlling opportunism and fostering creative autonomy is most acute. Taken together, these limitations highlight the necessity of an integrated, dynamic theoretical framework that accounts for the specificities of innovation-oriented platforms.

In response, this study developed a two-stage principal–agent model as both a parsimonious and powerful analytical framework. This structure enables the precise examination of fundamental intertemporal trade-offs, including the platform’s optimization between short-term monitoring expenditures and long-term collaborative benefits, alongside the embedded enterprise’s strategic effort allocation between immediate and deferred compensation. The model incorporates dynamic incentive contracts, endogenous supervision intensity, and platform value preferences into a unified analytical framework specifically tailored to the innovation-oriented platform context. This model is designed to capture the co-evolution of governance strategies and partner behaviors over time, allowing for an examination of how the platform enterprise can systematically optimize their governance systems across stages of collaboration in innovation-oriented ecosystems. The analytical insights generated through this tractable modeling approach establish valuable theoretical benchmarks and create a solid foundation for subsequent research employing more extended temporal frameworks.

3. Model Assumptions, Formulation and Solution

3.1. Model Assumptions

This study employed a principal–agent model within the context of value co-creation in platform ecosystems to describe the strategic collaboration between the platform and embedded enterprises. To capture the essential dynamics of this governance relationship, we adopted a two-stage architecture. While a necessary simplification, this structure effectively models the platform’s capacity to leverage historical collaboration data, thereby informing and adapting its subsequent governance mechanisms to systematically influence partner behavior over time. The following basic assumptions are proposed for this cross-stage dynamic incentive model:

Assumption 1: In the cross-stage dynamic incentive mechanism model, the entire platform innovation collaboration process spans two stages. The effort exerted by the embedded enterprise (acting as the agent) in each stage is denoted as $e_t=(e_{t1},e_{t2})\in E_1\times E_2$, focusing primarily on business innovation and opportunistic behavior, where $e_{t1}$ represents productive effort, $e_{t2}$ represents opportunistic effort, and $t=1, 2$ represents the two stages. The productive effort $e_{t1}$ represents the embedded enterprise’s investment in innovation activities such as product development and service improvement, while opportunistic effort $e_{t2}$ captures resources diverted to self-serving activities like data manipulation or quality shirking. Following the approach in references [30,31,32], the productive effort of the embedded enterprise creates total potential innovation revenue, expressed as $y_{t1}=r_1{e}_{t1}+f\left(m\right)+\theta +{\epsilon }_t$. It is critical to distinguish that $y_{t1}$ represents the gross revenue created before any opportunistic diversion; it is not directly observable or contractible by the platform enterprise due to information asymmetry. In this expression, $r_1$ is the marginal revenue coefficient of productive effort (simplified to 1 for computational convenience). $f\left(m\right)$ represents the exogenous impact on the embedded enterprise’s performance revenue due to supervision by the platform enterprise, expressed as $f\left(m\right)=\gamma m_t$, where $m_t$ denotes the intensity of supervision and $\gamma$ is the externality revenue coefficient of supervision. This supervision externality coefficient $\gamma$ quantifies how platform monitoring generates positive spillover effects by enhancing user trust and collaboration quality. This signaling effect is empirically observed in platform ecosystems where certified supervision serves as a reliability signal to end-users, thereby increasing their engagement and willingness to collaborate. In practice, the embedded enterprise often informs users of being under constant supervision by the platform enterprise, thus gaining user trust and increasing performance revenue. $\theta$ represents the operational capability of the embedded enterprise (time-independent) and is an exogenous independent random variable. ${\epsilon }_t$ represents an exogenous random shock to the platform’s operating environment, such as unexpected market volatility, which introduces noise into the observation of the innovation revenue $y_{t1}$. The opportunistic effort brings observable opportunistic revenue to the embedded enterprise itself, denoted as $y_{t2}=r_2{e}_{t2}+{\epsilon }_t^{\prime }$, where $r_2$ is the marginal revenue coefficient of the embedded enterprise’s opportunistic effort (simplified to 1 for calculation convenience). ${\epsilon }_t^{\prime }$ captures exogenous random shocks that affect the efficacy or risk of opportunistic behavior, for instance, stemming from transient regulatory loopholes, thereby causing variability in the observed opportunistic revenue $y_{t2}$. Furthermore, assume that $\theta$ and ${\epsilon }_t$ are independently normally distributed with the same variance, and they follow $\theta ~\left(\eta ,{\sigma }^2\right),{\epsilon }_t~\left(0,{\sigma }^2\right),$ ${\epsilon }_t^{\prime }~\left(0,{\sigma }^2\right)$, with $\mathit{Cov}\left({\epsilon }_1,{\epsilon }_2\right)=0$ and $\mathit{Cov}\left({\epsilon }_1^{\prime },{\epsilon }_2^{\prime }\right)=0$. The temporal independence of these shocks is a standard modeling technique that ensures that any perceived persistence in performance is rationally attributed by the platform to the updating of its belief about the embedded enterprise’s capability $\theta$, which is the core engine of the dynamic incentives in this two-stage framework.

Assumption 2: The opportunistic behavior of the embedded enterprise diverts a portion of the platform’s total innovation revenue. However, as the principal, the platform enterprise cannot directly observe either the total innovation revenue or the portion appropriated by the embedded enterprise’s opportunistic actions. It can only observe the revenue after the opportunistic behavior occurs (i.e., the innovation revenue adjusted for opportunistic behavior), which is denoted as $y_t=y_{t1}-y_{t2}$. Furthermore, assume that the platform enterprise compensates the embedded enterprise based on this observed revenue with a linear contract $S_t=a_t+{\beta }_t{y}_t$, for $t=1, 2$, where $a_t$ is the fixed revenue of the embedded enterprise, and ${\beta }_t\in \left[\mathrm{0,1}\right]$ is the performance-sharing coefficient for the innovation revenue. This linear contract structure reflects real-world platform compensation structures where fixed components ($a_t$) ensure partner participation while performance-based elements (${\beta }_t$) align incentives. This formulation captures the essential trade-off in platform–partner relationships: providing income stability while maintaining performance incentives, mirroring contractual arrangements observed in platform ecosystems from app stores to industrial platforms. This type of information asymmetry and incentive structure is widely observed in principal–agent relationships, particularly in platform ecosystems where the agent (embedded enterprise) possesses superior information about its own actions and revenue [33,34]. In practice, the platform enterprise typically formulates contracts based on performance revenue reflected in the annual reports and operational business reports provided by the embedded enterprise. However, such information is often selectively disclosed or filtered by the embedded enterprise, which aligns with the concepts of moral hazard and adverse selection as discussed in agency theory. This makes it difficult for the platform enterprise to detect opportunistic behavior or accurately ascertain the true innovation performance. The rationality of this assumption, grounded in information asymmetry, has been widely supported and discussed in empirical research related to platform governance and ecosystem collaboration [5].

Assumption 3: To mitigate the opportunistic behavior of the embedded enterprise, the platform enterprise implements supervision over its conduct. Correspondingly, the supervision cost incurred by the platform enterprise is expressed as $C_m=k{m}_t$, for $t=1, 2$, where $k$ represents the unit cost coefficient of supervision intensity. The linear form of the cost function is adopted for analytical tractability, following the modeling approach in references [25,35]. Importantly, this formalization receives empirical support from studies on digital platforms, which indicate that investments in monitoring technologies such as API surveillance, data auditing, and algorithmic oversight tend to demonstrate approximately linear cost scalability within certain operational ranges [36]. These findings enhance the practical plausibility of the proposed cost structure.

Assumption 4: The embedded enterprise incurs effort costs when engaging in both productive and opportunistic behaviors across the two stages. The productive effort cost is $c_{t1}=b_1{e}_{t1}^2/2$, for $t=1, 2$, where $b_1$ is the cost coefficient of productive effort. For analytical convenience, we normalize $b_1$ to 1, i.e., $c_{t1}=e_{t1}^2/2$, for $t=1, 2$. This quadratic functional form reflects the increasing marginal disutility of effort documented in empirical studies of innovation work [37]. In the context of Internet platform ecosystems, the embedded enterprise indeed incurs significant effort costs beyond fixed investments, such as employee overtime compensation and operational expenses for platform information management, further justifying the convex cost structure. The opportunistic effort cost is ${ c}_{t2}=b_2{e}_{t2}^2/2+m_t{e}_{t2}$, for $t=1, 2,$ where $b_2$ is the cost coefficient of opportunistic effort. Similarly, we normalize $b_2$ to 1 for simplicity, i.e., $c_{t2}=e_{t2}^2/2+m_t{e}_{t2}$, for $t=1, 2.$ This formulation captures how platform supervision amplifies the marginal cost of opportunistic effort, thus acting as a deterrent. Such a cost-modifying effect of monitoring is widely adopted in principal–agent models to align incentives and mitigate moral hazard [18], and is consistent with behavioral evidence showing that enhanced detection probability significantly deters opportunism.

Assumption 5: The platform enterprise is risk-neutral, whereas the embedded enterprise is risk-averse. This risk attitude setting aligns with the standard framework of principal–agent theory [33]. Risk aversion implies that the embedded enterprise seeks to maximize the utility derived from returns rather than simply maximizing expected returns. Its coefficient of absolute risk aversion is $\rho >0$, resulting in a concave utility function.

Assumption 6: As the principal, the platform enterprise serves as the organizer and manager of the platform ecosystem. This role definition stems from research on platform governance [38], emphasizing that the platform enterprise must internalize cross-side network effects and interdependencies among stakeholders. In its decision-making process, it must consider not only its own interests but also the value creation for other stakeholders within the platform, thereby promoting overall value co-creation in the ecosystem and thus maintaining the health and sustainable development of the ecosystem.

In our framework, the dynamic incentive mechanism is operationalized through the coordinated adjustment of two key governance parameters: the value preference parameter (${\lambda }_t$), which determines the platform enterprise’s distribution strategy between self-interest and ecosystem value, and the supervision intensity ($m_t$), which monitors and constrains opportunistic behavior. This parameterized approach enables the platform enterprise to dynamically align incentives across collaboration stages.

3.2. The Game-Theoretic Framework

The strategic problem of platform ecosystem governance is formalized through a two-stage dynamic principal–agent model, the basic rules of which are detailed in this section. The game involves two rational players: the platform enterprise (principal) and an embedded enterprise (agent). The platform enterprise, as the mechanism designer, holds the first-mover advantage by committing to incentive contracts before the embedded enterprise chooses its actions.

(1) Players and Their Roles

The platform enterprise serves as the ecosystem orchestrator and contract designer. As the principal, it possesses the authority to establish governance rules and determine incentive structures. Its strategic decisions encompass determining fixed payments ($a_1$, $a_2$) and incentive coefficients (${\beta }_1$, ${\beta }_2$) for both stages, as well as setting supervision intensity levels ($m_1$, $m_2$) to monitor opportunistic behavior. These operational decisions are guided by the platform enterprise’s exogenous value preference parameter ($\lambda$), which captures its pre-determined strategic trade-off between self-interest and ecosystem value creation. This parameter, while not a choice variable within the game, fundamentally shapes the platform enterprise’s objective function and its resulting equilibrium strategies.

The embedded enterprise operates as the contracting partner within the ecosystem. As the agent, it possesses private information about its operational capability ($\theta$) from the outset and makes effort allocation decisions based on the platform enterprise’s incentive design. Its strategic choices include choosing its effort combination ($e_{t1}$, $e_{t2}$) between productive and opportunistic effort in each stage, responding to incentive contracts and supervision mechanisms, and leveraging its private information about operational capability.

(2) Information Structure and Timing

The game evolves through two distinct stages under asymmetric information, with the sequence illustrated in Figure 1. Initially, the embedded enterprise’s operational capability $\theta$ remains private information, unknown to the platform enterprise. The sequential game proceeds as follows. In Stage 1, the platform enterprise offers an initial contract ($a_1$, ${\beta }_1$) and announces supervision intensity $m_1$. Subsequently, the embedded enterprise accepts the contract and selects effort allocation $e_1$ = ($e_{11}$, $e_{12}$), leading to the realization of the first-stage innovation revenue adjusted for opportunistic behavior $y_1$, which is observed by both parties. In the inter-stage period, the platform enterprise updates its belief about $\theta$ using Bayesian inference based on the observed $y_1$. Following this belief updating, in Stage 2, the platform enterprise designs a refined contract ($a_2$, ${\beta }_2$) and supervision level $m_2$. The embedded enterprise then chooses its second-stage effort allocation $e_2$ = ($e_{21}$, $e_{22}$), culminating in the realization of the second-stage innovation revenue adjusted for opportunistic behavior $y_2$ and the distribution of final payoffs.

(3) Strategic Interdependence and Dynamic Incentives

The timing described above gives rise to a self-enforcing mechanism based on strategic interdependence: the platform enterprise’s challenge in assessing the embedded enterprise’s operational capability $\theta$ in the first stage compels it to rely on the observed revenue y₁ to form beliefs and design second-stage governance, while the embedded enterprise, anticipating this, can strategically use its first-stage effort ($e_{t1}$, $e_{t2}$) as a credible signal to shape these beliefs and secure more favorable future terms. Consequently, its first-stage actions directly impact its second-stage profitability, ensuring cross-stage accountability. The platform enterprise’s value preference parameter $\lambda$ critically moderates this dynamic by determining how the updated beliefs translate into second-stage contract parameters ($a_2$, ${\beta }_2$) and supervision $m_2$, thereby regulating the effective incentive intensity. Ultimately, this game-theoretic structure captures the essential dynamics of platform governance, where information asymmetry and strategic learning necessitate evolving incentive designs. The exogenous nature of $\lambda$ enables comparative static analysis, revealing how equilibrium outcomes vary across fundamentally different platform governance philosophies.

It can be seen that the mechanism through which cross-stage dynamic incentives take effect lies in the difficulty faced by the platform enterprise in accurately assessing the embedded enterprise’s operational capability during the first stage. This leads the platform enterprise to use the observed first-stage innovation revenue to form expectations about the embedded enterprise’s operational capability and subsequently determine the contract payment parameters and supervision intensity for the second stage. The embedded enterprise, on the other hand, can influence these expectations by increasing its effort level in the first stage, thereby improving its future external profit opportunities. Therefore, the effort level invested by the embedded enterprise in the first stage not only determines the profit for that period but also impacts potential revenue in the second stage, which compels the embedded enterprise to take responsibility for its actions.

3.3. Model Formulation

Based on the model description and game logic above, the actual revenue of the embedded enterprise in each of the two stages can be derived as follows:

$$w_1=a_1+{\beta }_1{y}_1+y_{12}$$

(1)

$$w_2=a_2+{\beta }_2{y}_2+y_{22}$$

(2)

Therefore, the cross-stage certainty equivalent revenue for the embedded enterprise is:

$${CE}_A=E\left(w_1\right)+E\left(w_2\right)-{\displaystyle \frac{e_{11}^2}{2}}-{\displaystyle \frac{e_{12}^2}{2}}-m_1{e}_{12}-{\displaystyle \frac{e_{21}^2}{2}}-{\displaystyle \frac{e_{22}^2}{2}}-m_2{e}_{22}-{\displaystyle \frac{\rho \mathit{Var}\left(w_1+w_2\right)}{2}}$$

(3)

The cross-stage risk cost is $\rho \mathit{Var}\left(w_1+w_2\right)/2$.

Furthermore, the cross-stage decision behavior of the platform enterprise can be derived as follows:

$$\underset{a_t,{\beta }_t,m_t}{Max}{\lambda }_1\left[E\left(y_{11}\right)-E\left(w_1\right)-k{m}_1\right]+\left(1-{\lambda }_1\right)E\left(y_{11}\right)+{\lambda }_2\left[E\left(y_{21}\right)-E\left(w_2\right)-k{m}_2\right]+\left(1-{\lambda }_2\right)E\left(y_{21}\right)$$

(4)

s.t.

$${CE}_A\ge {\overline{u}}_1+{\overline{u}}_2$$

(5)

$${CE}_{A2}\ge {\overline{u}}_2$$

(6)

$$e_{1=}(e_{11}, e_{12})\in \arg max{CE}_A$$

(7)

$$e_{2=}(e_{21}, e_{22})\in \arg max{CE}_{A2}$$

(8)

The second-stage certainty equivalent revenue of the platform enterprise and the embedded enterprise are, respectively:

$${CE}_{p2}=E\left(y_2\mid y_1\right)-E\left(w_2\mid y_1\right)+E\left(y_{22}\right)-k{m}_2$$

(9)

$${CE}_{A2}=E\left(w_2\mid y_1\right)-e_{21}^2/2-e_{22}^2/2-m_2{e}_{22}-\rho \mathit{Var}\left(w_2\mid y_1\right)/2$$

(10)

Here, ${\lambda }_1, {\lambda }_2\in (0,1)$ are the value preference parameters of the platform enterprise, quantifying the extent to which it prioritizes its own interests versus the collective interests of the platform ecosystem. For calculation convenience, we set ${\lambda }_1={\lambda }_2=\lambda$. When $\lambda <1/2$, the platform enterprise is more focused on the overall value creation of the platform; when $\lambda >1/2$, it is more inclined towards its own interests. Within the incentive mechanism model, variations in the value preference parameter reflect the platform’s strategic emphasis on value co-creation collaboration. Analyzing this parameter enables the platform enterprise to optimize its decisions concerning the design of value co-creation incentives. Additionally, ${\overline{u}}_1$ and ${\overline{u}}_2$ represent the reservation utilities of the embedded enterprise in the first and second stages, respectively.

3.4. Model Solution

First, solve for the balanced strategy embedded in the enterprise. In the second stage, the performance revenue of the embedded enterprise has no impact on its subsequent revenue. Therefore, for the contract provided, the embedded enterprise will choose an appropriate $e_2$ to maximize current returns. From condition (8), the optimal effort level for the second stage of the embedded enterprise is obtained as follows:

$$e_2=\left({\beta }_2,1-{\beta }_2-m_2\right)$$

(11)

Next, solve for the optimal contract parameters ${\alpha }_2^{*}$ and ${\beta }_2^{*}$ provided by the platform enterprise in the second stage, i.e.,

$$\underset{a_2,{\beta }_2,m_2}{Max}\lambda \left[E\left(y_{21}\mid y_1\right)-E\left(w_2\mid y_1\right)-k{m}_2\right]+(1-\lambda )E\left(y_{21}\mid y_1\right)$$

(12)

$$\mathrm{s}.\mathrm{t}. E\left(w_2\mid y_1\right)-e_{21}^2/2-e_{22}^2/2-m_2{e}_{22}-\rho \mathit{Var}\left(w_2\mid y_1\right)/2⩾{\overline{u}}_2$$

(13)

The above optimization problem can be further transformed into:

$$\underset{a_2,{\beta }_2,m_2}{Max}E\left(y_{21}\mid y_1\right)-\lambda [e_{21}^2/2+e_{22}^2/2+m_2{e}_{22}]-\lambda \rho \mathit{Var}\left(w_2\mid y_1\right)/2-\lambda {\overline{u}}_2-\lambda k{m}_2$$

(14)

At the same time, under the assumption of rational expectations, the expectation of the event is updated according to Bayesian statistics theory as:

$$E\left(\theta \mid y_1\right)=2\eta /3+\left(y_1-\gamma m_1-e_{11}^{\prime }+e_{12}^{\prime }\right)/3$$

(15)

where $e_{11}^{\prime }$ and $e_{12}^{\prime }$ represent the platform enterprise’s estimates of the embedded enterprise’s productive and opportunistic effort in the first stage. Under the assumption of rational expectations, $e_{11}^{\prime }$ and $e_{12}^{\prime }$ are equal to the optimal effort levels $e_{11}^{*}$ and $e_{12}^{*}$ chosen by the embedded enterprise in the first stage.

Furthermore from Equation (15), we obtain:

$$\mathit{Var}\left(w_2\mid y_1\right)=8{\beta }_2^2{\sigma }^2/3+8(1-2{\beta }_2){\sigma }^2/9$$

(16)

Substituting Equations (15) and (16) into Equation (14), and then differentiating with respect to ${\beta }_2$ and $m_2$, we obtain:

$${\beta }_2^{*}=\left(9+9\lambda +8\lambda \rho {\sigma }^2\right)/\left(6\lambda \left(3+4\rho {\sigma }^2\right)\right)$$

(17)

$$m_2^{*}=\lambda k-\gamma /\lambda$$

(18)

Substituting Equations (17) and (18) back into Equation (11), we obtain the optimal effort level of the embedded enterprise in the second stage and the optimal fixed revenue, i.e.,

$$e_2^{*}=\left({\displaystyle \frac{9+9\lambda +8\lambda \rho {\sigma }^2}{6\lambda \left(3+4\rho {\sigma }^2\right)}},{\displaystyle \frac{9\lambda +16\lambda \rho {\sigma }^2-9}{6\lambda \left(3+4\rho {\sigma }^2\right)}}-k+{\displaystyle \frac{\gamma }{\lambda }}\right)$$

(19)

$$a_2^{*}={\overline{u}}_2-{\beta }_2{e}_{21}^{*}-{\displaystyle \frac{2{\beta }_2\eta }{3}}-{\displaystyle \frac{{\beta }_2\left(y_1-\gamma m_1-e_{11}^{\prime }+e_{12}^{\prime }\right)}{3}}-\left(1-{\beta }_2\right)e_{22}^{*}-\gamma m_2{\beta }_2+{\displaystyle \frac{\left(e_{21}^{*2}+e_{22}^{*2}\right)}{2}}+m_2{e}_{22}^{*}+{\displaystyle \frac{4{\beta }_2^2\rho {\sigma }^2}{3}}+{\displaystyle \frac{4\left(1-2{\beta }_2\right)\rho {\sigma }^2}{9}}$$

(20)

According to the game sequence of cross-stage dynamic incentives, we continue to solve the subgame perfect Nash equilibrium of the embedded enterprise in the first stage. From condition (7), the optimal effort level of the embedded enterprise in the first stage is:

$$e_1=\left({\beta }_1,1-{\beta }_1-m_1\right)$$

(21)

Finally, solve for the optimal contract parameters provided by the platform enterprise in the first stage. For the optimization problem, i.e.,

$$\underset{a_1,{\beta }_1,m_1}{Max}\lambda \left[E\left(y_{11}\right)-E\left(w_1\right)-k{m}_1\right]+(1-\lambda )E\left(y_{11}\right)+\lambda \left[E\left(y_{21}\right)-E\left(w_2\right)-k{m}_2\right]+(1-\lambda )E\left(y_{21}\right)$$

(22)

$$\mathrm{s}.\mathrm{t}. E\left(w_1\right)-{\displaystyle \frac{e_{11}^2}{2}}-{\displaystyle \frac{e_{12}^2}{2}}-e_{12}{m}_1+E\left(w_2\right)-{\displaystyle \frac{e_{21}^2}{2}}-{\displaystyle \frac{e_{22}^2}{2}}-e_{22}{m}_2-{\displaystyle \frac{\rho \mathit{Var}\left(w_1+w_2\right)}{2}}⩾{\overline{u}}_1+{\overline{u}}_2$$

(23)

Note that $\mathit{Var}\left(w_1+w_2\right)=3{{\beta }_1}^2{\sigma }^2+2{\sigma }^2-\left(1-{\beta }_2\right)\left(2{\beta }_1+8{\beta }_2/3\right){\sigma }^2$. By substituting Equations (17) to (21) into the above model, the solution is obtained as follows:

$${\beta }_1^{*}={\displaystyle \frac{18+18\lambda +15\rho {\sigma }^2+33\lambda \rho {\sigma }^2+16\lambda {\rho }^2{\sigma }^4}{6\lambda (2+3\rho {\sigma }^2)(3+4\rho {\sigma }^2)}}$$

(24)

$$m_1^{*}=\lambda k-\gamma /\lambda$$

(25)

$$a_1^{*}={\overline{u}}_1-{\beta }_1\left(e_{11}^{*}+\eta +\gamma m_1\right)-\left(1-{\beta }_1\right)e_{12}^{*}+\left(e_{11}^{*2}+e_{12}^{*2}\right)/2+m_1{e}_{12}^{*}+3{{\beta }_1}^2\rho {\sigma }^2/2-\left(1-{\beta }_2\right){\beta }_1\rho {\sigma }^2-{\beta }_2\rho {\sigma }^2/3$$

(26)

$$e_1^{*}=\left({\displaystyle \frac{18+18\lambda +15\rho {\sigma }^2+33\lambda \rho {\sigma }^2+16\lambda {\rho }^2{\sigma }^4}{6\lambda (2+3\rho {\sigma }^2)(3+4\rho {\sigma }^2)}},{\displaystyle \frac{-18+18\lambda -15\rho {\sigma }^2+69\lambda \rho {\sigma }^2+56\lambda {\rho }^2{\sigma }^4}{6\lambda (2+3\rho {\sigma }^2)(3+4\rho {\sigma }^2)}}-k+{\displaystyle \frac{\gamma }{\lambda }}\right)$$

(27)

4. Model Equilibrium Analysis

In this section, based on the optimal solution of the cross-stage model obtained in Section 3 and holding other exogenous parameters fixed, we analyze the impact of the platform enterprise’s value preference parameter on profit differentials and their evolution across different stages. Furthermore, we examine the differences in the embedded enterprise’s effort levels and revenue within each stage, as well as the consequent effects on the platform enterprise’s cross-stage endogenously determined optimal supervision intensity, contract incentive design, and its own revenue. The equilibrium results are as follows:

4.1. Analysis of the Impact on the Platform’s Innovation Revenue Levels

Proposition 1.

(1) The effect of the value preference parameter  $\lambda$ on the total potential innovation revenue depends on the externality revenue coefficient  $\gamma$  in both stages: specifically, in the first stage, the innovation revenue decreases with λ if  $\gamma \in \left(0, {\left({\displaystyle \frac{5\rho {\sigma }^2+6}{2\left(3+4\rho {\sigma }^2\right)\left(2+3\rho {\sigma }^2\right)}}\right)}^{1/2}\right)$, and increases otherwise, while in the second stage, the innovation decreases with λ if  $\gamma \in \left(0, {\left(3/2\left(3+4\rho {\sigma }^2\right)\right)}^{1/2}\right)$, and increases otherwise. (2) Both the total potential innovation revenue and the innovation revenue adjusted for opportunistic behavior in the second stage exceed those in the first stage, but these inter-stage differences diminish as  $\lambda$  increases.

Proof of Proposition 1.

See Appendix A.1. □

Proposition 1 demonstrates that the platform enterprise’s value preference parameter exerts a conditional effect on the platform’s innovation revenue, with the direction of this effect determined by the externality revenue coefficient of supervision. When the externality revenue coefficient falls below specific thresholds, innovation revenue decreases with increasing value preference in both collaboration stages. Conversely, when the externality revenue coefficient exceeds these thresholds, innovation revenue increases with value preference.

The analysis further revealed consistent inter-stage patterns in revenue performance. Both the platform’s innovation revenue and the innovation revenue adjusted for opportunistic behavior were higher in the second stage than in the first stage across all parameter configurations. However, these inter-stage differences diminished as the value preference parameter increased, indicating that the platform enterprise’s orientation attenuates the performance advantages gained through continued collaboration.

The core managerial implication centers on the strategic integration of value preferences and supervisory characteristics. The platform enterprise must recognize that the effectiveness of value preference settings is intrinsically linked to the externality potential of their supervision mechanisms. This necessitates treating value preferences and supervisory characteristics as interdependent elements within a unified governance framework rather than as independent control variables.

In practice, this calls for an externality-contingent governance strategy. The platform enterprise operating in low-externality environments must restrain value appropriation to avoid revenue deterioration, while those in high-externality contexts can leverage supervisory spillovers to support more self-interested orientations. The governance approach must maintain this alignment throughout the collaboration lifecycle.

4.2. Analysis of Embedded Enterprise’s Effort Levels

Proposition 2.

(1) Under value co-creation, the embedded enterprise’s optimal productive effort per stage is no less than without collaboration, while its optimal opportunistic effort is no greater. (2) As the value preference parameter  $\lambda$ increases, the difference between optimal productive and optimal opportunistic effort at each stage narrows; specifically, the former falls below the latter in the first stage when  $\lambda \in \left({\displaystyle \frac{3\gamma \left(3+4\rho {\sigma }^2\right)\left(2+3\rho {\sigma }^2\right)-15\rho {\sigma }^2-18}{3k\left(3+4\rho {\sigma }^2\right)\left(2+3\rho {\sigma }^2\right)-18\rho {\sigma }^2-20{\rho }^2{\sigma }^4}}, 1\right)$  ,  and likewise in the second stage when  $\lambda \in \left({\displaystyle \frac{3\gamma \left(3+4\rho {\sigma }^2\right)-9}{3k\left(3+4\rho {\sigma }^2\right)-4\rho {\sigma }^2}}, 1\right)$  . (3) Both optimal productive effort and optimal opportunistic effort in the second stage are higher than those in the first. However, as  $\lambda$  increases, these effort levels in both stages decline, diminishing the inter-stage differences in both types of effort.

Proof of Proposition 2.

See Appendix A.2. □

Proposition 2 demonstrates that the platform enterprise’s value preference parameter directly shapes the embedded enterprise’s effort allocation patterns. Under value co-creation, the embedded enterprise’s optimal productive effort per stage is no less than without collaboration, while its optimal opportunistic effort is no greater. This confirms that value co-creation creates conditions conducive to productive effort allocation.

The analysis revealed three key patterns in effort allocation. First, as the value preference parameter increases, the difference between productive and opportunistic effort narrows at each stage, with productive effort falling below opportunistic effort when the parameter exceeds specific thresholds. Second, both types of effort are higher in the second stage, reflecting the enhanced effectiveness of cross-stage incentives. Third, these inter-stage differences diminish as the value preference parameter increases, indicating that excessive self-interest undermines the advantages of dynamic incentives.

The core managerial implication is that effort allocation can be effectively managed through strategic calibration of the value preference parameter. The platform enterprise must recognize that this parameter directly influences the balance between productive and opportunistic effort. Setting appropriate value preferences is essential for maintaining productive effort superiority and preserving the benefits of cross-stage collaboration.

In practice, this necessitates threshold-aware effort management. The platform enterprise should use the narrowing gap between productive and opportunistic effort as a key monitoring metric. When this gap approaches critical thresholds, immediate intervention through value preference moderation is required to prevent effort allocation from tipping toward opportunism.

4.3. Analysis of Embedded Enterprise’s Revenue Levels

Proposition 3.

The certainty equivalent revenue of the embedded enterprise increases with the platform enterprise’s value preference parameter  $\lambda$ in the first stage when $\lambda \in \left(0,{\displaystyle \frac{18-27\gamma \rho {\sigma }^2+15\rho {\sigma }^2-24\gamma {\rho }^2{\sigma }^4}{\rho {\sigma }^2(33\gamma -69)+{\rho }^2{\sigma }^4(16\gamma -56)+6k\left(3+4\rho {\sigma }^2\right)\left(2+3\rho {\sigma }^2\right)+18(\gamma -1)}}\right)$ , and increases with $\lambda$ in the second stage when $\lambda \in \left(0,{\displaystyle \frac{9\left(\gamma -1\right)+24\gamma {\sigma }^2}{9\left(\gamma -1\right)+8\rho {\sigma }^2\left(\gamma -2+3k\right)+18k}}\right)$.

Proof of Proposition 3.

See Appendix A.3. □

Proposition 3 demonstrates that the embedded enterprise’s certainty equivalent revenue exhibits a non-monotonic relationship with the platform’s value preference parameter. The revenue increases with the value preference only within specific threshold ranges in each stage, beyond which the relationship reverses. This pattern holds consistently across both collaboration stages, though with distinct threshold values.

The analysis revealed stage-dependent characteristics in the revenue response. The optimal ranges for value preference differed between the first and second stages, indicating that the embedded enterprise’s revenue exhibits varying sensitivity to governance parameters as collaboration progresses. This dynamic nature underscores the importance of stage-specific governance calibration.

The core managerial implication is that the platform enterprise must recognize the bounded effectiveness of value preference settings. Maintaining the value preference within the identified optimal ranges is essential for enhancing the embedded enterprise’s revenue performance. Exceeding these ranges will inevitably lead to diminished partner revenue, thereby jeopardizing collaboration sustainability.

In practice, this demands stage-specific revenue optimization. The platform enterprise must recognize that the revenue-enhancing range for value preference differs across stages. They should adopt more conservative value preferences in early stages to build partner revenue, then carefully recalibrate within the mathematically defined optimal ranges for later stages to the embedded enterprise’s revenue growth.

4.4. Analysis of the Platform Enterprise’s Governance Decisions and Revenue Levels

Proposition 4.

(1) The optimal supervision intensity increases with the platform enterprise’s value preference parameter λ in both collaboration stages. (2) The optimal performance-sharing coefficient in the second stage consistently exceeds that in the first stage. As the value preference parameter $\lambda$ increases, the performance-sharing coefficients in both stages decrease, with a more pronounced decline observed in the second stage. (3) The platform enterprise’s certainty equivalent revenue increases with its value preference parameter $\lambda$ in the first stage when $\lambda \in (0,{\displaystyle \frac{15\rho {\sigma }^2+18}{18+69\rho {\sigma }^2+56{\rho }^2{\sigma }^4}})$ , and increases with $\lambda$ in the second stage when $\in (0,{\displaystyle \frac{9}{9+16\rho {\sigma }^2}})$.

Proof of Proposition 4.

See Appendix A.4. □

Proposition 4 demonstrated three key patterns in the platform enterprise’s optimal governance decisions and revenue outcomes. First, the optimal supervision intensity increased with the value preference parameter in both stages. Second, while the performance-sharing coefficient was consistently higher in the second stage, both stages exhibited decreasing coefficients as the value preference grew, with a more pronounced reduction in the second stage. Third, the platform’s certainty equivalent revenue increased with the value preference parameter only within specific ranges, beyond which the relationship reversed.

The analysis revealed systematic interconnections between governance parameters and revenue performance. The platform’s strategic orientation, reflected in its value preference, simultaneously shapes its supervision intensity decisions and incentive structure design. This integrated governance approach generates complex effects on revenue outcomes, with the platform’s revenue exhibiting non-monotonic responses to changes in value preference across collaboration stages.

The core managerial implication emphasizes the need for balanced parameter calibration. The platform enterprise must recognize that optimizing supervision intensity and performance-sharing coefficients requires careful consideration of their value preference settings. Maintaining the value preference within revenue-enhancing ranges while appropriately adjusting other governance parameters is essential for achieving sustainable revenue growth throughout the collaboration lifecycle.

In practice, this requires balanced parameter coordination. The platform enterprise must manage the inherent trade-off where increasing value preference boosts supervision intensity but reduces performance-sharing coefficients. Particular attention should be paid to maintaining adequate profit-sharing in the second stage, where excessive reduction undermines the cross-stage advantages identified in the model.

5. Numerical Analysis

This section employs numerical simulations to achieve two primary objectives: to visually verify the core relationships revealed by the theoretical propositions in Section 4, and to translate the abstract equilibrium solutions into intuitive managerial insights. To this end, we established a benchmark scenario with a set of representative parameters and employed comparative static analysis. This approach systematically demonstrates how key exogenous governance variables ($\lambda$, $\mathsf{\gamma }$) influence the model’s equilibrium outcomes (such as innovation revenue and its dynamic evolution across stages), thereby providing a quantitative reference for implementing the governance strategies proposed in Section 4.

Parameter values were determined with reference to the methodological approach established in reference [39], with appropriate adjustments to accommodate the specific context of our research framework. A critical modeling assumption requires emphasis: the platform enterprise exhibits risk neutrality, whereas the embedded enterprise is characterized by risk aversion. This fundamental difference in risk preference plays a pivotal role in our model architecture.

To ensure analytical tractability while maintaining economic interpretability, we adopted the following parameter initial values as the benchmark scenario: the absolute risk aversion coefficient of the embedded enterprise was set at $\rho =0.8$; the exogenous random variable $\theta$ followed a normal distribution with mean $\eta =1$ and variance ${\sigma }^2=2$; the externality revenue coefficient of platform supervision $\gamma$ was specified as 0.1, which quantitatively reflects the marginal effect of supervisory intensity on value generation; the unit cost coefficient of supervision intensity $k$ was set to 2.0, representing plausible cost constraints in monitoring activities. These parameter configurations satisfy all regularity conditions of the model while ensuring numerical stability in subsequent computational experiments. Based on this benchmark parameter set, we will subsequently employ comparative static analysis by fixing other parameter values and examining the impact of changes in individual parameters on equilibrium revenue, thereby providing substantial support for validating the research propositions.

5.1. Impact of the Value Preference Parameter on the Platform’s Innovation Revenue Levels

Figure 2 respectively illustrates the trends in the platform’s total potential innovation revenue ($E{y}_{11}$ and $E{y}_{21}$) and the innovation revenue adjusted for opportunistic behavior ($E{y}_1^{\prime }$ and $E{y}_2^{\prime }$) under low ($\gamma =0.1$) and high ($\gamma =0.8$) externality revenue coefficients of supervision, as the value preference parameter $\lambda$ varied from 0.2 to 0.9 in increments of 0.1.

From Figure 2, it can be observed that across both stages of the dynamic game, when the externality revenue coefficient of supervision was low, both the total potential innovation revenue and the opportunistically adjusted innovative revenue of the platform decreased as the value preference parameter increased. Conversely, when this coefficient was high, both revenue measures increased with a rising value preference parameter. Furthermore, for both revenue measures, the revenue level in the second stage was consistently higher than that in the first stage; however, the gap between stages narrowed gradually as the value preference parameter increased. These numerical results align precisely with the theoretical predictions outlined in Proposition 1.

This empirical validation underscores a key managerial insight: the platform enterprise can leverage cross-stage dynamic incentives to enhance overall innovation revenue, yet the benefit of pursuing self-interest (a high $\lambda$) is critically dependent on the externality revenue coefficient of its supervisory framework. The numerical analysis demonstrates that under low externality conditions, the platform enterprise’s self-interested orientation is counterproductive, while under high externality conditions, it can be sustainable. Furthermore, the advantage of second-stage collaboration is consistently eroded by excessive self-interest, thus highlighting the practical importance of maintaining balanced value preferences to sustain the benefits of dynamic incentives.

These numerical findings quantitatively corroborate the managerial implication of Proposition 1: that the platform enterprise’s strategic value preference must be calibrated in direct consideration of the externality characteristics of its supervisory framework.

5.2. Impact of the Value Preference Parameter on the Embedded Enterprise’s Effort Levels

Figure 3 respectively illustrates the trends in the embedded enterprise’s optimal productive effort ($e_{11}$ and $e_{21}$) and optimal opportunistic effort ($e_{12}$ and $e_{22}$) across both stages under the value preference parameter $\lambda$ varying within the interval [0.2, 0.9] with increments of 0.1.

From Figure 3, it can be observed that as the value preference parameter increased, the embedded enterprise’s optimal productive effort continuously decreased across both stages, while its optimal opportunistic effort exhibited a sustained increase. Furthermore, both types of optimal effort in the second stage consistently exceeded those in the first stage; however, these inter-stage differences narrowed gradually as the value preference parameter increased. These numerical results align precisely with the theoretical predictions outlined in Proposition 2.

This empirical validation underscores that the platform enterprise’s value preference parameter directly governs the evolution of effort allocation patterns across stages. While cross-stage dynamic incentives stimulate higher effort levels in subsequent stages, the platform enterprise’s excessively self-interested behavior erodes productive effort superiority and diminishes the inter-stage incentive advantage. The findings highlight the importance of maintaining the value preference parameter below critical thresholds to preserve effective effort allocation and sustain collaborative benefits.

These simulation results vividly demonstrate how strategic calibration of the value preference parameter serves as an effective mechanism for managing the embedded enterprise’s effort allocation, as elaborated in Proposition 2.

5.3. Impact of the Value Preference Parameter on Embedded Enterprise’s Revenue Levels

Figure 4 illustrates the trend of the embedded enterprise’s certainty equivalent revenue across both collaboration stages as the value preference parameter $\lambda$ varied within the interval [0.2, 0.9] with increments of 0.1.

As shown in Figure 4, the embedded enterprise’s certainty equivalent revenue exhibited a non-monotonic relationship with the platform enterprise’s value preference parameter. The revenue increased with the parameter only within stage-specific ranges before declining, with revenue-maximizing values of $\lambda$ approximately 0.35 in the first stage and 0.28 in the second stage. These numerical results align precisely with the theoretical predictions in Proposition 3.

This empirical validation confirms that the platform enterprise’s strategic value preference must be maintained within the identified threshold ranges. The second-stage collaboration demonstrated higher sensitivity to the platform enterprise’s self-interested behavior, as reflected in its lower optimal threshold. Exceeding these critical values (particularly when $\lambda >0.28$ in the second stage) directly diminished the embedded enterprise’s revenue level, thereby jeopardizing the partnership’s economic foundation.

These findings quantitatively substantiate the core managerial implication of Proposition 3: the platform enterprise should adopt diagnostic and stage-appropriate calibration methods to maintain the value preference parameter within revenue-enhancing ranges, thereby securing the embedded enterprise’s cooperative commitment and promoting sustainable value co-creation.

5.4. Impact of the Value Preference Parameter on the Platform Enterprise’s Governance Decisions and Revenue Levels

Figure 5 systematically demonstrates the platform enterprise’s governance decisions and revenue outcomes as the value preference parameter $\lambda$ varied within the interval [0.2, 0.9] with increments of 0.1. Figure 5a presents the optimal supervision intensity and performance-sharing coefficients across both stages, while Figure 5b shows the platform enterprise’s certainty equivalent revenue in both collaboration stages.

Analysis of Figure 5a revealed systematic responses of governance decisions to strategic orientation. The supervision intensity increased monotonically with $\lambda$ while maintaining identical values across both stages, which resulted from the simplified treatment of the platform enterprise’s value preference parameter in the model (${\lambda }_1={\lambda }_2=\lambda$). Meanwhile, the performance-sharing coefficients decreased monotonically with $\lambda$, with the second-stage coefficient consistently exceeding the first-stage one. This complementary pattern of “strengthening supervision while weakening incentives” reveals the platform enterprise’s coordinated application and inherent trade-off logic among different governance tools in its governance design.

Figure 5b demonstrates distinct phase characteristics in revenue generation. The platform enterprise’s certainty equivalent revenue exhibited a non-monotonic relationship with λ, showing enhancement within stage-specific ranges followed by performance deterioration beyond critical thresholds. Although the second stage maintained higher revenue levels, it exhibited greater vulnerability to excessive self-interested behavior.

These numerical findings provide comprehensive validation for Proposition 4, confirming that the value preference parameter coordinates governance mechanisms through systematic decision patterns and determines revenue performance via stage-dependent pathways. The results elucidate the complete causal relationship from strategic orientation to performance outcomes in the platform enterprise’s governance.

6. Conclusions and Discussions

6.1. Research Conclusions

This study developed a cross-stage dynamic incentive model to examine governance mechanisms within innovation-oriented platform ecosystems. By establishing a perfect Bayesian equilibrium, we demonstrated how the platform enterprise’s value preference systematically governs decision-making processes, embedded enterprise behaviors, and value co-creation outcomes. Four principal findings emerged from our theoretical analysis.

First, the platform enterprise’s value preference parameter fundamentally determines governance effectiveness. This parameter directly governs the optimal incentive intensity and supervision level in equilibrium. Platform enterprises prioritizing ecosystem value creation achieve superior outcomes through higher profit-sharing rates combined with moderate supervision intensity. This governance configuration effectively stimulates the embedded enterprise’s productive contributions while constraining its opportunistic behaviors.

Second, cross-stage dynamic incentives generate substantial performance improvements through adaptive governance mechanisms. Second-stage outcomes consistently surpass first-stage performance across innovation revenue, productive effort levels, and optimal profit-sharing rates. These improvements stem from the platform enterprise’s capacity to refine embedded enterprise capability assessments using first-stage collaboration data. However, these performance advantages diminish as the platform enterprise’s self-interest orientation intensifies, revealing a crucial trade-off between short-term value appropriation and long-term value creation.

Third, economic returns for both parties exhibit a non-monotonic relationship with the platform enterprise’s value preference. Our theoretical framework identifies optimal parameter ranges that simultaneously maximize economic returns for both platform enterprises and embedded enterprises. Beyond these ranges, increasing self-interest orientation reduces the certainty equivalent revenue for all participants. This finding challenges the conventional zero-sum perspective, demonstrating that precise calibration of value preferences can enhance both value creation and appropriation simultaneously.

Finally, supervision and incentives function as complementary governance instruments through endogenous coordination. The platform enterprise jointly determines supervision intensity and profit-sharing rates as endogenous complementary variables. Effective supervision creates necessary conditions for implementing strong incentives, while appropriate profit-sharing reduces requirements for excessive monitoring. This complementary relationship remains bounded by information asymmetry constraints, where neither instrument alone achieves optimal governance effectiveness. The platform enterprise’s value preference ultimately determines how these instruments combine in endogenous decision-making processes.

6.2. Managerial Implications

Our equilibrium results yielded four essential implications for platform enterprise governance practice.

First, the platform enterprise should establish a clear value preference as the strategic foundation for its governance system. The platform’s prioritization between ecosystem value creation and self-interest appropriation guides all subsequent endogenous governance decisions. This strategic orientation determines the optimal calibration direction for governance instruments.

Second, the platform enterprise should coordinate incentive intensity and supervision levels as an integrated endogenous governance portfolio. Decisions regarding profit-sharing rates and supervision intensity require simultaneous optimization based on the strategic orientation. Theoretical analysis confirms these instruments complement each other functionally.

Third, a platform enterprise needs institutionalized learning mechanisms for dynamic governance optimization. Utilizing collaboration data to update the assessment of the embedded enterprise enables targeted adjustments to the endogenous governance portfolio across stages. This adaptive approach unlocks performance advantages in extended collaborations.

Finally, managers of the platform enterprise must understand how value preference settings affect governance effectiveness. Pursuing excessive self-interest beyond optimal ranges generates distorted incentive-supervision allocations. This damages the motivation of the embedded enterprise and ultimately undermines the platform’s own performance. Proper calibration is essential for maintaining sustainable ecosystem development.

6.3. Limitations and Future Research Directions

This study contains several limitations that suggest valuable research opportunities. We identified four main directions for future inquiry based on these limitations.

First, the model incorporates several simplifying technical assumptions to ensure analytical tractability, which nevertheless delineate boundaries for its application and suggest directions for refinement. Two key simplifications are the equality constraint on value preference parameters across stages and the representation of the embedded enterprise’s operational capability as an exogenous, time-invariant random variable with a unitary marginal contribution. Future research could relax these assumptions by allowing for dynamically adjusted value preferences, introducing calibrated productivity coefficients for core parameters, and investigating how critical thresholds for value preference parameters vary under different externality conditions and collaboration stages. This approach would enhance the model’s descriptive richness and improve its applicability to specific empirical contexts while preserving the core insights into cross-stage dynamic incentives.

Second, this study primarily examined the independent effects of governance parameters, leaving the interaction mechanisms among supervision intensity, value preference parameters, and performance-sharing coefficients underdeveloped. Future research could establish more sophisticated theoretical frameworks to investigate the synergistic effects and substitution relationships among these core governance instruments under different externality conditions, with particular attention to their dynamic interactions in multi-stage environments. This would offer more systematic guidance for designing governance portfolios for the platform enterprise.

Third, while the two-stage framework captures essential dynamic incentive features, it cannot fully represent the continuously evolving partnerships between the platform enterprise and embedded enterprises. Multi-stage or infinite-horizon frameworks would better examine how governance mechanisms co-evolve with trust and reputation over extended periods, revealing the adaptive adjustment patterns of governance modes in intertemporal collaborations and providing theoretical support for sustaining long-term partnerships.

Fourth, although the focus on bilateral relationships provides analytical precision, it neglects the influences of other ecosystem participants. Incorporating multi-sided market perspectives would enhance our understanding of how user feedback and network effects moderate the platform enterprise’s governance effectiveness. Future research should investigate how multi-agent interactions shape governance efficiency, including the roles of consumer behavior and complementor strategies. Such investigation would improve the model’s explanatory power for real-world ecosystems.

Fifth, while the choice of linear contracts and specific functional forms is theoretically justified, it may not fully capture the complexity of real-world governance. Examining nonlinear contracts, heterogeneous cost structures, and behavioral factors would improve the practical relevance of theoretical models for the platform enterprise’s governance. Building on this, introducing behavioral economic elements such as bounded rationality and social preferences could provide more actionable insights for the platform enterprise’s practical governance decisions.

Notwithstanding these limitations, this study provides a systematic theoretical foundation for understanding value preference interactions with incentive design and supervision mechanisms in platform ecosystems. The endogenous dynamic governance framework offers valuable insights for both the platform enterprise’s governance research and management practice.