1. Introduction
Industrial generic technologies (IGTs) constitute foundational and supportive shared technological systems that transcend industrial and organizational boundaries [
1]. Serving as critical linkages between fundamental scientific research and commercial applications, they facilitate structural upgrades in traditional industries and support the emergence of new industrial sectors. The development of IGTs involves two interdependent phases: front-end sourcing (technology identification and research grounded in basic science) and downstream diffusion (commercial-oriented adoption and marketization) [
2]. As pre-competitive “quasi-public goods” characterized by infrastructural supportiveness, inter-industrial relevance, and innovation fertility, IGTs encounter dual uncertainties, such as technological risk in sourcing and market risk in diffusion [
3]. These challenges are compounded by substantial R&D investments, high technical complexity, extended development cycles, and knowledge externalities that render market mechanisms insufficient, leading to systematic underinvestment by individual organizations [
4]. In response, cross-organizational collaboration, where manufacturers act as the primary participants alongside universities and research institutes, has gained prominence in both academic discourse and global practice [
5]. Within contemporary innovation ecosystems, universities demonstrate comparative advantages in IGT sourcing due to their specialized basic research capabilities, while manufacturers lead IGT diffusion as value-realizing entities. The resulting co-creation paradigm enables synergistic resource complementarity and enhances innovation efficiency through the deep integration of universities’ theoretical and frontier research capacities with manufacturers’ operational proficiency and market-driven insights [
6]. This alignment has proven instrumental in advancing innovation-driven industrial development and strengthening sectoral competitiveness, as exemplified by successful applications across various national contexts [
7]. For instance, in the renewable energy sector, Germany’s Fraunhofer Society has collaborated with industrial partners such as Siemens to translate fundamental research from academia into applied solutions, including high-efficiency wind turbine designs and grid stability technologies, significantly enhancing the global competitiveness of its wind power industry. Similarly, in the field of advanced materials, the Ulsan National Institute of Science and Technology (UNIST) and LG Chem established a joint research center in South Korea, co-developing high-energy-density cathode materials for lithium-ion batteries, which accelerated the commercialization of next-generation power batteries and solidified the country’s leading position in battery manufacturing.
Coccia characterized IGTs as foundational technological enablers with cross-sectoral applicability, playing a pivotal role in supporting sustained innovation in proprietary technologies [
8]. Owing to their inherently good public characteristics, IGTs frequently experience chronic under-provision when relying solely on individual enterprises, resulting in systemic innovation failures. Consequently, global policymakers and academics have increasingly prioritized IGT advancement. Valipour et al. demonstrated that the collaborative innovation significantly reduced R&D costs and risks while accelerating the resource integration in the European semiconductor industry [
9]. Building on this, Liao et al. asserted that complementary R&D strategies and organizational learning management enhanced productivity in telecommunications IGTs, thereby improving capital returns [
10]. Lawniczuk et al. further identified multi-agent platform architectures as institutional mechanisms for addressing under-provision in photonic integrated circuits, with notable applications in the Photon Delta consortium in the Netherlands [
11]. Scholarly consensus underscores that cross-organizational cooperation mitigates knowledge fragmentation by leveraging heterogeneous capabilities. Therefore, fostering collaborative commitment is essential for IGT success [
2]. A well-structured contractual framework for benefit distribution serves as a key determinant for building and sustaining innovation partnerships, enabling mutual benefits through deepened collaboration [
12]. As illustrated by Liu et al., collaborative efficiency functions as the core mechanism for IGT development, with empirical evidence from Chinese high-speed rail and electric vehicle battery alliances showing a 30% reduction in time-to-market through effective benefit-sharing mechanisms [
13]. Efficient R&D pathway selection requires precise identification of governing factors and their underlying operational logics. This necessitates formal modeling of participant behavior and incentive structures [
14]. Mahdiraji et al. developed a reference-dependent incentive mechanism using non-cooperative payoffs as benchmarks to optimize stakeholder allocation in university-industry partnerships [
15]. Long-Yue et al. constructed a government-led bilateral incentive framework that reconciled enterprise and research institution interests under conditions of information asymmetry [
16]. Silvestri et al. applied evolutionary game theory to quantify the cost–benefit impacts on strategic stability, validating the effectiveness of dual incentive–sanction mechanisms in resolving value co-creation dilemmas [
17].
Existing research on cross-organizational benefit allocation for IGTs primarily follows three analytical orientations: (1) mechanism design approaches that investigate revenue-sharing and cost-bearing structures (e.g., enterprise–university cost-sharing frameworks); (2) factor impact analyses that quantify exogenous influences (e.g., information asymmetry, power imbalance, and capability heterogeneity) on allocation outcomes; and (3) game-theoretic formalizations that model cooperative mechanisms and profit distribution rules. In fact, in the collaborative R&D of IGTs, manufacturers and universities tend to form different decision-making models depending on factors such as the decision environment, sequence, and objectives [
18]. These differences in decision-making models further lead to variations in profit distribution mechanisms and agent behaviors-for instance, a manufacturer-led decentralized decision-making model aimed at maximizing individual benefits, or a centralized decision-making model where both parties make simultaneous decisions to maximize system-wide benefits. Therefore, research on revenue distribution between manufacturers and universities must account for the influence of decision-making models on behavioral strategies. Thus, it is essential to move beyond the traditional framework of bilateral static game theory and incorporate the diversity of decision-making models and their dynamic interactions into the analytical perspective. Existing studies are largely confined to static allocation mechanisms under single-decision scenarios, failing to adequately reflect the strategic complexities arising from real-world differences in decision sequence, power structure, and collaboration objectives. There is also a notable lack of dynamic characterization of adaptive agent behaviors and the evolutionary processes of system equilibrium.
This study aims to develop a game-theoretic model that incorporates both decentralized and centralized decision-making modes, analyzing how manufacturers and universities adjust profit distribution strategies according to the selected decision-making mode during collaborative R&D of IGTs. It further investigates the dynamic evolutionary pathways and stable equilibrium of interactive strategies between the two parties. To present the research theme with greater clarity and precision, the structure of this paper is organized into six sections (
Figure 1).
Section 1 serves as the Introduction, outlining the research background, contextualizing the study through a literature review, and clarifying the research framework and significance.
Section 2, Theoretical Model Assumptions, elaborates on the hypotheses underlying the game-theoretic model, laying the groundwork for the model development in
Section 3.
Section 3, Game Model Construction and Solution Under Different Decision-Making Mechanisms, builds upon the assumptions established in
Section 2 to develop benefit allocation game models between manufacturers and universities under both decentralized and centralized decision-making structures, followed by the derivation of equilibrium solutions.
Section 4, Comparative Analysis of Different Decision-Making Mechanisms, examines the outcomes obtained in
Section 3, comparing the decision-making behaviors of both parties and their influencing factors across different mechanisms, leading to key findings.
Section 5, Numerical Analysis, employs MATLAB R2024a-based simulations to further validate and illustrate the conclusions drawn in
Section 4.
Section 6, Conclusion, summarizes the main findings, discusses theoretical and practical implications, acknowledges limitations, and suggests directions for future research. In this study, to better illustrate the behavioral patterns of manufacturers and universities under different decision-making mechanisms and their influencing factors during the revenue distribution process, we specifically examine how cost coefficients, revenue-sharing ratios, and contribution weights affect both parties’ effort levels, the level of guaranteed benefits, and the total revenue of collaborative projects. This analysis serves to achieve the research objectives and validate the effectiveness of the study.
By revealing the inherent coordination mechanism between collaboration efficiency and distribution fairness under multiple decision-making modes, this research not only enriches the theoretical framework of cross-organizational collaboration and overcomes the static limitations of traditional revenue distribution studies but also offers practical insights for innovation agents to optimize collaboration strategies and enhance synergistic efficiency in diverse decision-making environments. These contributions hold theoretical and practical value for promoting sustainable R&D and systematic coordination of IGTs.
2. Theoretical Model Assumptions
The R&D of IGTs can be divided into two major phases. In the first phase, universities provide foundational technical support, based on which manufacturers conduct further R&D to commercialize the technology, enabling market distribution and revenue generation. During this stage, knowledge flows internally within the manufacturer–university collaboration entity without generating knowledge spillover effects. The second phase begins upon successful collaboration, resulting in joint patents that may produce knowledge spillovers. This study focuses on the revenue distribution mechanism in the first phase, where the outcome of cooperation is uncertain (either success or failure).
Manufacturers engage in cross-organizational collaborations with universities to advance novel technology development and optimize production processes. Within this framework, universities contribute their theoretical research capabilities to develop IGTs, whereas manufacturers apply market-oriented capacities to improve product quality and production efficiency through technology deployment [
19]. To incentivize the generation of high-quality innovation outputs, performance-contingent contracts are established between manufacturers and universities, incorporating upfront funding commitments and variable profit-sharing mechanisms. In such conditions, manufacturers, as the technology demand side and resource investors, act as the incentive principal in the collaboration. Their core objective is to motivate universities to deliver high-quality technological outcomes, thereby enhancing production efficiency and product quality, strengthening market competitiveness, and achieving greater economic benefits [
20]. As the incentive agents, universities leverage their research capabilities and knowledge resources, with primary goals centered on securing R&D funding, elevating academic influence, and facilitating the commercialization of research outcomes. Due to significant differences in resource endowment, objective functions, and risk tolerance, the bargaining positions of the two parties exhibit asymmetry: manufacturers typically possess greater market information and control over financial resources, granting them a dominant role and stronger negotiating power in the collaboration [
21]. Although universities excel in technical expertise, they are relatively disadvantaged in terms of industrialization experience and financial scale, often relying heavily on corporate resource support. These disparities in position and objectives further lead to strategic gaming behaviors in the design of revenue distribution mechanisms [
22]. Throughout the collaboration process, the two parties engage in dynamic bargaining around key parameters such as the level of R&D investment, quality standards of outcomes, and profit-sharing ratios. Ultimately, through negotiation or institutional design, they reach an incentive-compatible equilibrium, thereby ensuring the stability and efficiency of cross-organizational collaboration [
12].
During the collaborative process, effective communication mechanisms and feedback loops facilitate rapid iteration of technological outcomes, thereby enhancing the practical application of research findings [
23]. The following assumptions were made:
Assumption 1. The total output function of collaborative efforts between manufacturers and universities is characterized by a Cobb–Douglas production function dependent on the respective effort levels of both parties [24,25], that is, Equation (1). where and denote the effort levels of the manufacturer and university, respectively; () is the contribution weight of the manufacturer; is the contribution weight of the university; q () represents the collaborative synergy coefficient, determined by technology maturity and strategic importance; and captures the stochastic influence of exogenous factors on output [26]. The Cobb–Douglas function is chosen as the aggregate production function because the efforts of the manufacturer and university satisfy the following characteristics: This indicates that during collaborative efforts, no output is generated if either party fails to contribute, whereas a high level of effort by one party enhances the output as the other party’s effort increases. This aligns with the intrinsic nature of synergy in collaboration. The parameters and represent the contribution weights of the effort levels of the manufacturer and university, respectively, to the total output. These parameters reflect the sensitivity of the total output to the efforts of each party and indicate their relative importance in the collaborative process. A higher value of denotes greater sensitivity of the total output to the effort of the manufacturer, while a higher value of implies greater sensitivity to the effort of the university. The values of and are determined by the inherent attributes of the manufacturer and university involved.
Assumption 2. The effort cost functions for the manufacturer and university are expressed as follows:
where denote their respective effort cost coefficients. As both parties increase their effort inputs within the IGT R&D collaboration, their corresponding effort costs follow a monotonically increasing trend [27], satisfying the conditions .
Assumption 3. Building on the optimality of linear incentive schemes in cooperative contexts [28], the manufacturer’s revenue-sharing contract with the university can be modeled as Equation (4).
where s is the fixed payment to the university, G is the total output from the IGT R&D project, and represent the revenue-sharing ratios for the manufacturer and university, respectively. Assumption 4. Within the IGT R&D collaboration framework, the manufacturer acts as a risk-neutral incentive principal. Accordingly, the certainty-equivalent revenue M is expressed as Equation (5).
The university is characterized as a risk-averse preference, with strategic emphasis placed on systematic risk management and project evaluation. Its incurred risk cost is defined as Equation (6).where denotes the absolute risk aversion coefficient, and represents the variance of revenue streams. Accordingly, the university’s certainty-equivalent revenue C is expressed as Equation (7). The aggregate certainty-equivalent revenue P of the ICT R&D ecosystem jointly formed by the manufacturer and university is formally defined as Equation (8). 4. Comparative Analysis of Different Decision-Making Mechanisms
Based on the equilibrium outcomes of the two distinct decision-making modes summarized in
Table 1, an analysis of the behavioral decision-making mechanisms, profit distribution patterns, and their underlying interactions between manufacturer and university in cross-organizational collaborative R&D of IGTs leads to the following conclusions.
Theorem 1. In both decentralized and centralized decision-making mechanisms characterized by bilateral moral hazard, the certainty-equivalent income of the university exhibits a negative correlation with its absolute risk aversion coefficient and the degree of return volatility.
Proof of Theorem 1. From Equation (6), it can be derived that . Under the decentralized decision-making framework, the first-order partial derivatives of with respect to are derived as . Under centralized decision-making mechanisms characterized by bilateral moral hazard, the first-order partial derivatives of with respect to are derived as and . □
For universities, an increase in risk aversion implies that decision-makers tend to avoid potential losses and adopt more conservative strategies, preferring low-risk, low-return approaches, which reduces the overall certainty-equivalent income. Meanwhile, greater income volatility further amplifies this conservatism, leading to a more pronounced decline in certainty-equivalent income.
This finding reveals that in the collaborative R&D of IGTs, it is essential to establish a partnership mechanism between manufacturers and universities centered on risk sharing, guided by profit distribution as a linkage, and oriented toward long-term collaboration. On one hand, manufacturers should bear more financial and trial-and-error risks in the early stages of R&D, while mitigating universities’ initial risk exposure through phased risk transfer mechanisms such as third-party guarantees or insurance. On the other hand, both parties should develop an intertemporal collaboration framework involving iterative R&D, continuous optimization, and trust accumulation to gradually enhance their tolerance to volatility, ultimately achieving optimal synergistic innovation efficacy under controlled risk conditions.
Theorem 2. Regardless of the decision-making mechanism, the cost coefficient of either party is negatively correlated with both agents’ effort levels, their deterministic payoffs, and the project’s total revenue.
Proof of Theorem 2. Let denote the manufacturer’s contribution weight in the R&D consortium, and represent the effort cost coefficients of the manufacturer and university, respectively. Under the decentralized decision-making, the first-order partial derivatives of with respect to satisfy the following: , , , , , , , , , . Similar derivations extend to the centralized decision-making scenario, establishing an inverse relationship between cost coefficients and equilibrium decision parameters in both moral hazard settings. □
Rising costs can directly suppress effort investments: higher costs discourage the manufacturer from increasing R&D inputs, reducing ; resource constraints compel the university to curtail efforts, lowering . Systemic reductions in M, C, and P underscore cost control as a critical success factor. This requires rational resource allocation and cost management by both parties to ensure R&D efficiency and long-term partnership sustainability.
This finding reveals that in the R&D of IGTs, cost control exerts a decisive influence on the effectiveness and efficiency of collaboration between the parties involved. It is essential to establish a cost monitoring and coordinated allocation mechanism to achieve refined cost management, thereby ensuring the sustainability and collaborative efficiency of joint R&D efforts for IGTs. Furthermore, the introduction of government subsidies or third-party venture capital can help mitigate initial cost pressures, enhancing both parties’ tolerance for long-term high-cost R&D activities.
Theorem 3. The optimal revenue-sharing ratio must be strictly interior (), as both agents contribute non-trivially to IGT outputs ( and ). This ratio is exclusively determined by relative contribution weights.
Proof of Theorem 3. Under decentralized decision-making, the optimal sharing ratio can satisfy . Given , it directly follows that . Differentiation yields , establishing a positive relationship between and . Symmetrical logic applies to the university’s share. For the centralized bilateral moral hazard scenario, ; thus, . As , the manufacturer’s revenue share increases strictly with its output contribution weight . Symmetrically, a university’s revenue share increases monotonically with its contribution weight. □
As the partner’s output contribution weight increases, its equilibrium revenue share increases strictly. Specifically, when the manufacturer’s contribution weight increases, it secures a higher revenue share to incentivize its marginal inputs. Conversely, an increase in the university’s contribution weight increases its share while reducing the manufacturer’s allocation.
This finding reveals that the core principle of profit distribution in collaboration between the manufacturer and university is the determination of benefit shares by contribution weights. Essentially, it establishes an incentive-compatible mechanism linked to marginal contributions, aligning individual objectives with collective goals. From a game-theoretic perspective, this design constructs a non-zero-sum game: when one party increases its benefit share by enhancing its contribution weight, it does not merely deprive the other party’s vested interests but achieves Pareto improvement by expanding the overall benefits. Such a dynamic adjustment mechanism effectively mitigates free-riding behavior while incentivizing both parties to sustain high-quality resource investments.
Theorem 4. Under bilateral moral hazard with decentralized or centralized decision-making, the fixed payment s exhibits rigorous neutrality towards the university’s effort decisions.
Proof of Theorem 4. Under decentralized decision-making and bilateral moral hazard settings with centralized decision-making mechanisms, . Thus, fixed payment s induces a linear transformation in the university’s payoff C, characterized by a constant marginal effect. Regardless of the numerical variations in s, the university’s payoff changes in a constant proportion. □
This finding reveals the limited incentive effect and structural role of fixed payments in collaborative contexts. From a mechanistic perspective, fixed compensation essentially functions as a risk buffer, safeguarding universities’ basic returns on initial R&D investments. However, due to its linear nature, it fails to provide marginal incentivizing effects. Consequently, universities’ decision-making logic tends to rely more heavily on variable reward mechanisms-such as output-based profit sharing or intellectual property rights—which more accurately reflect the actual value of their effort levels and thereby stimulate greater innovation engagement.
Theorem 5. Under decentralized decision-making, the effort levels of both manufacturers and universities progressively increase in response to their respective return-sharing allocations. In contrast, under centralized decision-making with bilateral moral hazard, the manufacturer’s effort level initially rises but subsequently declines as the profit-sharing ratio increases, while the university’s effort level consistently decreases as the manufacturer’s revenue share expands.
Proof of Theorem 5. Based on Theorem 3, the optimal revenue-sharing allocation satisfies . Under decentralized mechanisms, the partial derivative of the manufacturer’s effort level with respect to is given by . Under the same mechanism, the derivative of the university’s effort level with respect to is . Under a bilateral moral hazard regime with centralized coordination, the derivative of the manufacturer’s effort level with respect to is , whereas the derivative of with respect to is . □
Under decentralized governance, increasing profit potential prompts both agents to intensify resource investments and efforts to maximize overall returns. However, under centralized governance with bilateral moral hazard, rising profits stimulate the manufacturer to enhance effort input only up to a certain threshold, beyond which diminishing incentives may discourage further investment. Meanwhile, a university’s effort level continues to grow in tandem with increasing profit-sharing ratios.
This finding reveals the differences in incentive compatibility under different decision-making mechanisms and their impact on collaborative dynamics. Under a decentralized decision-making structure, both parties benefit directly from marginal revenue sharing, creating a bidirectional incentive mechanism that fosters a positive feedback loop between effort investment and revenue growth. In contrast, under a centralized decision-making framework, where manufacturers hold dominant authority and universities assume a subordinate role, the profit distribution mechanism may lead to an asymmetry between power and responsibility, resulting in incentive distortions [
31]. The reduction in effort by manufacturers beyond a certain revenue threshold reflects a rational choice based on balancing short-term gains and long-term costs; when marginal revenue falls below the marginal cost of effort, manufacturers may proactively reduce their input to optimize their own utility, even as total revenue continues to rise. Meanwhile, universities, as technology providers, demonstrate a stable positive response in their effort levels, as their behavior is more dependent on sustained expectations of profit-sharing.
Theorem 6. The comparative analysis of IGT cooperation profits across three decision-making mechanisms revealed that the decentralized mechanisms yielded the highest returns, followed by centralized coordination under bilateral moral hazard, with centralized governance under no moral hazard generating the least profits. Furthermore, the profit-sharing ratio under decentralized mechanisms consistently outperformed that under centralized coordination involving bilateral moral hazard.
Proof of Theorem 6. When comparing R&D cooperation profits between decentralized mechanisms and centralized mechanisms with bilateral moral hazard, the ratio of profits is . Here, the risk-neutral benchmark term is less than 1, and the risk-averse adjustment term is ; thus, . Further comparison of cooperation profits under centralized decision-making revealed that , implying . Therefore, the overall ranking of industrial generic technology cooperation profits across decision-making modes follows . Moreover, by comparing the profit-sharing ratios under decentralized mechanisms and centralized governance with bilateral moral hazard, the following inequality is established: ; thus, . □
Under decentralized decision-making, both actors independently determine their strategies based on their respective advantages and situational awareness, enabling them to fully realize their potential for profit maximization. Within centralized coordination under bilateral moral hazard, despite the presence of information asymmetry and opportunism, cooperative synergy can still be partially achieved through institutional mechanisms. Conversely, under no-moral-hazard scenarios, although transparent decision-making and idealized cooperation are present, the lack of adaptability and limited market responsiveness constrain profit realization, rendering this mechanism inferior to the former two in terms of total returns.
This finding reveals the applicability boundaries and efficiency differentials of distinct decision-making mechanisms in bilateral collaboration. Decentralized mechanisms facilitate Pareto improvements by incentivizing bilateral autonomy, yet their effectiveness relies on information symmetry and goal alignment between the parties. Centralized mechanisms, while capable of mitigating moral hazard through enforced coordination, may stifle innovative dynamism due to structural rigidity. In contrast, the idealized scenario devoid of moral hazard, though theoretically optimal, often fails to achieve practical efficacy due to its detachment from real-world constraints.
5. Numerical Analysis
To more intuitively observe the research conclusions and verify the aforementioned propositions, in this section, MATLAB is employed for numerical case analysis. MATLAB’s efficient numerical computation capabilities and integrated visualization tools facilitate intuitive analysis of data trends and verification of results, thereby providing a clearer visual representation of the conclusions in
Section 4.
To ensure consistency with the established assumptions and validate the logical coherence of inter-variable relationships, the key decision parameters were set as follows: the synergistic cooperation output coefficient , the university’s absolute risk aversion , and its revenue fluctuation risk . Fixed remuneration was assumed to have no influence on university decision-making behavior; thus, . The simulation investigated the influence of cost coefficients, profit-sharing ratios, and contribution weights on bilateral decision-making behaviors, effort intensities, and total revenue of the IGT R&D system.
- (1)
Influence of Cost Coefficients on Decision Parameters and Outcomes
Under all decision-making mechanisms, the cost coefficients exhibited a negative correlation with bilateral effort intensities, certainty-equivalent incomes, and overall project revenues. Taking decentralized coordination as a representative case, the influence of cost coefficients on decision variables and outcome indicators is analyzed, as illustrated in
Figure 2 and
Figure 3. In
Figure 2 and
Figure 3,
denotes the cost coefficient of the manufacturer, while
represents the cost coefficient of the university.
An increase in the cost coefficient for either the manufacturer or the university signifies elevated cost burdens incurred during collaborative technological R&D. Excessive cost intensities lead to reduced effort inputs, thereby suppressing the certainty-equivalent income of both actors. Consequently, project revenue levels determined by bilateral cooperative efforts and technological depth are diminished. As effort intensities decline, manufacturers may face reduced product quality and diminished technological innovation capacity, whereas universities may experience weakened abilities in knowledge production and application, lowering their effective earnings. Thus, the elevated cost coefficients reflect lower project return rates and impair the overall feasibility and attractiveness of R&D engagement, ultimately constraining the total revenue performance of industrial generic technology innovation initiatives.
- (2)
Impact of Profit-Sharing Shares on Effort Levels
Under various decision-making mechanisms and different cost coefficient settings between manufacturing firms and universities, the influence of profit-sharing ratios on bilateral effort intensities is illustrated in
Figure 4,
Figure 5 and
Figure 6.
Under decentralized decision-making, the effort levels of both manufacturers and universities progressively increased as their respective profit-sharing ratios increased, with both parties autonomously making decisions and implementing strategies to enhance their own efforts. As the profit-sharing ratio increased, manufacturing enterprises were incentivized by the expectation of greater revenue, leading to intensified R&D investment, improved production efficiency, and expanded market deployment. Simultaneously, universities received stronger incentives from industry partners, thereby elevating their own effort input. However, under bilateral moral hazard scenarios within centralized frameworks, the manufacturer’s effort level exhibited nonlinear dynamics. Initially, a rising profit-sharing share rate encouraged higher revenue expectations, motivating manufacturers to intensify their participation in technological R&D and collaborative implementation, thereby increasing effort levels. Conversely, as the profit-sharing ratio continued to rise beyond a critical point, manufacturers experienced a “diminishing marginal effect”, where the perceived return on incremental effort diminished. This perception led to a reduced input intensity, resulting in a decline in the effort level once the profit-sharing threshold was exceeded. Specifically, regardless of the decision-making mode, when , the manufacturer captures all revenue distribution, while the university only receives a fixed payment. In this scenario, the university’s effort level drops to zero, indicating that the revenue-sharing mechanism decisively influences its effort incentives, whereas fixed payments fail to provide any motivational effect.
- (3)
Impact of Contribution Weight on Decision Parameters
Assuming that the manufacturer’s cost coefficient is
and the university’s cost coefficient is
, the influence of contribution weight on decision parameters is depicted in
Figure 7,
Figure 8,
Figure 9,
Figure 10,
Figure 11 and
Figure 12.
Under various decision-making mechanisms, both effort levels and profit-sharing shares of manufacturers and universities tended to increase with increasing contribution weights. However, the revenue trajectory of manufacturing enterprises demonstrated an initial decline, followed by recovery and growth as their contribution share θ increased. In the early phase of technological R&D, manufacturers typically faced elevated costs or risks that contributed to temporary revenue suppression. As the contribution weight continued to increase, manufacturers’ associated effort and investment began to yield tangible returns, thereby enhancing revenue outcomes. Simultaneously, owing to high upfront costs and delayed payoff cycles, the total revenue of the industrial generic technology system may initially be constrained. Nonetheless, with strengthened cooperative relationships and refined partnership models, the total revenue of both participants gradually rebounded and steadily improved.
Under the centralized decision-making mechanism with bilateral moral hazard, the university’s revenue initially declined and subsequently increased as the manufacturer’s contribution weight increased. In the early stages of cooperation, substantial investment by manufacturers reduced the university’s share in the output distribution. As the manufacturer transitioned its R&D inputs into tangible innovation outcomes, the university’s revenue began to increase owing to the commercialization of research outputs and knowledge spillovers. The profit-sharing mechanism exhibited a dynamic equilibrium, in which the revenue distribution was directly linked to the relative output contributions of each party. An effective profit allocation structure not only fostered continuous productivity improvement but also strengthened the long-term cooperative engagement between manufacturing enterprises and universities [
4]. This ensured that both parties could obtain equitable and sustainable returns in the context of industrial generic technology R&D.