Reputation incentive model of open innovation of scientific and technological-based SMEs considering fairness preference

The increasing prevalence of open innovation models, particularly among scientific and technological-based small and medium enterprises (SMEs), necessitates effective incentive mechanisms to encourage external research team participation. Traditional models often overlook the internal characteristics and external environmental factors influencing scientific research teams. This study addresses this gap by incorporating fairness preference into a reputation incentive model. Open innovation, characterized by the integration of internal and external resources and knowledge, has become crucial for SMEs to compete effectively in a rapidly evolving marketplace. While open innovation offers many advantages, like reduced R&D costs and enhanced innovation capabilities, it also presents challenges. One critical challenge is designing effective incentive mechanisms to motivate external scientific research teams to collaborate successfully. Simply providing financial incentives may not be sufficient, as researchers also seek recognition and reputational benefits. This research focuses on developing a reputation incentive model that considers the fairness preferences of scientific research teams to enhance their participation and improve the overall success of open innovation in SMEs.

The literature review examines existing research on open innovation, focusing on its types (inward, outward, market-based, collaborative, etc.), motivations (knowledge acquisition, risk reduction, cost savings), and effects (enhanced innovation performance, potential risks). The review also delves into the concept of reputation incentives, highlighting their role as long-term motivators that cater to non-monetary needs, promoting collaborative relationships between SMEs and external research teams. While significant work exists on open innovation and reputation incentives individually, there's a gap in research exploring the integration of fairness preference within reputation incentive mechanisms, particularly in the context of SME open innovation. Existing research on reputation often uses the principal-agent model, focusing on implicit versus explicit incentives and repeated games, examining the impact of reputation on various economic and management contexts. This paper intends to bridge this gap by integrating fairness theory into the principal-agent model to analyze the open innovation reputation incentive mechanism within SMEs, considering the fairness preferences of the scientific research innovation team.

This research employs a principal-agent theory framework to model the open innovation system involving an SME (principal) and a scientific research innovation team (agent). The model incorporates fairness preference, considering the relative profit gap between the SME and the team, using a fairness preference model similar to that of Fehr and Schmidt (1999). The model analyzes the influence of parameters such as fairness preference coefficient (K), reputation incentive coefficient (ρ), innovation ability (η), effort cost (λ), risk aversion (p), income distribution coefficient (β), and external environment variance (δ) on the reputation incentive and effort level of the research team. The analysis differentiates between scenarios with complete information (SME observes the effort level) and incomplete information (SME cannot observe the effort level). Mathematical equations are derived to represent the profit function of the research team, considering fairness preference, and the objective function of the SME. Optimization techniques are used to derive the optimal reputation incentive coefficient and effort level under both complete and incomplete information scenarios. Finally, numerical simulations using MATLAB software are conducted to verify the model's findings and explore the impact of the parameters on the reputation incentive and effort level under different scenarios. The simulation uses parameter values informed by research on open innovation practices and funding mechanisms in Chinese SMEs, providing contextually relevant insights.

The study's key findings are presented as conclusions, derived from both analytical solutions and numerical simulations: 1. **Complete Information:** Fairness preference positively correlates with reputation incentive but not with effort level. This suggests that under complete information, SMEs need to offer higher reputation incentives to address fairness concerns, but effort levels are primarily driven by innovation capability and effort cost. 2. **Incomplete Information:** Fairness preference has no significant effect on reputation incentive but negatively correlates with effort level. With incomplete information, the lack of observable effort leads to opportunistic behavior, reducing effort level as fairness preference increases. 3. **Both Information Scenarios:** Innovation ability positively correlates with both reputation incentive and effort level, while effort cost, risk aversion, income distribution coefficient, and external environment variance negatively correlate with reputation incentive. This highlights the critical role of innovation capacity and its impact on incentives and effort. 4. **Both Information Scenarios:** Effort cost, risk aversion, and external environment variance negatively affect effort levels. This reflects the expected impact of higher costs, risk aversion, and environmental uncertainties on the research team's willingness to exert effort. The numerical simulations using MATLAB further validated these conclusions by illustrating the relationships between various parameters and the reputation incentive and effort levels under complete and incomplete information scenarios. The graphs clearly demonstrate the positive and negative relationships identified in the analytical results, confirming the robustness of the model and its findings.

The findings highlight the significance of incorporating fairness preference into reputation incentive models, especially under conditions of information asymmetry. The results suggest that while fairness concerns can significantly influence the required level of reputation incentives, they may not always directly affect the effort level of the research team, particularly under conditions of complete information. The contrasting effects of fairness preference under complete and incomplete information highlight the importance of transparency and information sharing in promoting effective open innovation. The study contributes to a better understanding of incentive mechanisms in open innovation, offering practical implications for SMEs aiming to foster successful collaborations with external research teams. The significant influence of factors like innovation capability and risk aversion further underscores the need for a holistic approach to incentivizing open innovation partnerships.

This study develops a reputation incentive model for open innovation in SMEs that incorporates fairness preference and considers information asymmetry. The model's findings offer valuable insights into designing effective incentive mechanisms to encourage collaboration with external research teams. Future research could extend this model by incorporating dynamic factors, multi-stage cooperation, and the effects of irrational behavior. Examining the model's application in different cultural contexts and industrial settings would also be valuable.

The study assumes rational behavior of both SMEs and research teams, neglecting potential irrational decision-making. It also focuses on single-stage formal cooperation, excluding the complexities of multi-stage interactions. Future studies should address these limitations for a more comprehensive understanding of open innovation incentives.