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

The paper addresses how scientific and technological-based SMEs can design effective incentive mechanisms to engage external scientific research innovation teams in open innovation. Traditional incentives often emphasize monetary rewards, but teams are also motivated by non-monetary recognition and reputation. The authors argue that fairness preferences within research teams and information asymmetry between SMEs (principal) and teams (agent) critically shape behavior. The study builds a principal-agent-based reputation incentive model, incorporating fairness preference, to analyze how parameters such as innovation ability, effort costs, risk aversion, income distribution, and environmental uncertainty affect optimal reputation incentives and effort levels under complete versus incomplete information. The goal is to improve open innovation outcomes for resource-constrained SMEs by aligning incentives with team motivations and context.

The literature on open innovation, since Chesbrough’s conceptualization, categorizes modes by knowledge flows (inbound vs. outbound), breadth and depth of openness, and forms of collaboration (knowledge sales, technology procurement, collaborative R&D, outsourcing). Motivations include accessing knowledge, reducing risk, shortening cycles, expanding markets, and improving performance; external drivers include consumer demand and competition; uncertainties in technology and market can promote openness. Benefits include learning, knowledge transfer, capability enhancement, and faster, higher-quality development; drawbacks include reduced control, increased transaction costs, knowledge spillover risks, and potential negative effects from imbalance in openness depth/breadth/novelty. For SMEs, open innovation can provide reach, revenues, market entry, credibility, and complementary knowledge, but poses challenges such as IP protection, negotiating asymmetries with larger partners, and learning to interact with powerful organizations; SMEs exhibit heterogeneity by technology intensity. Reputation incentives are recognized as effective, with early work on implicit incentives and repeated games (Fama; Kreps, Milgrom, Roberts; KMRW) extended to various settings including labor markets, relationship contracts, crowdsourcing, and collective reputation. However, gaps remain regarding reputation incentive mechanisms in SME open innovation that account for agents’ fairness preferences. This study addresses that gap by modeling SME–research team interactions with fairness preferences.

Setting: An inbound open innovation context where a scientific and technological-based SME (principal, risk-neutral) contracts a university or research institute team (agent, risk-averse) to conduct R&D. The SME combines explicit monetary incentives (fixed funds, income share) with implicit reputation incentives to raise the team’s effort. Model framework: Principal–agent model incorporating fairness preference (Fehr–Schmidt). Key assumptions and parameters include: effort e; innovation output A = ηe + α where α is a normally distributed external environment variable with variance; effort cost M = λe² with λ the effort cost coefficient; agent risk aversion with coefficient p and risk cost z; reputation incentive coefficient ρ (0≤ρ≤1); income distribution proportion β (0<β<1); fairness preference coefficient K (0≤K≤1); fixed project fund a from SME. The agent’s profit π_A and SME’s profit π_E are defined via linear contracts S = a + (β + ρ)A and the output process; utility includes disutility from unfair outcomes proportional to K times the profit gap with the principal. Constraints: Individual rationality (IR) and incentive compatibility (IC) conditions are derived for the agent. Two informational regimes are considered:

• Complete information: the SME observes e. The SME maximizes expected profit subject to agent’s IR. Closed-form expressions are derived for the optimal reputation incentive coefficient and for the agent’s optimal effort level, and comparative statics are obtained analytically (e.g., ∂ρ/∂K>0; e increases with η and decreases with λ) under this regime.
• Incomplete information: the SME cannot observe e; the agent chooses e to maximize own expected utility, leading to an IC condition e = f(η,β,ρ,K,λ,variance). The SME optimizes expected profit subject to both IR and IC. Expressions for optimal ρ and e are derived; comparative statics with respect to η, λ, risk aversion, income share β, and environmental variance are analyzed using derivatives. The effect of K on ρ is ambiguous analytically, assessed via simulation. Numerical simulations: MATLAB simulations examine how parameters influence ρ and e, using baseline values informed by Chinese SME open innovation practice and literature: β=0.1, η=6, λ=2, variance parameter=1, risk aversion p=0.4, and K varying in [0,1]. Graphs report how fairness preference and other parameters affect ρ and e under complete and incomplete information. Illustrative values shown include p≈0.8783 vs 0.8716 at specific K for ρ under different regimes, and e ranging approximately from 2.85 to 3.1 as K varies in complete vs incomplete information.

• Under complete information, the fairness preference coefficient K of research teams is positively related to the optimal reputation incentive coefficient ρ, while K does not affect the optimal effort level e. Effort increases with innovation ability η and decreases with effort cost λ.
• Under incomplete information, K has no significant effect on ρ but is negatively related to e; higher fairness concern leads to lower effort when effort is unobservable.
• Regardless of fairness preference, ρ increases with e and with η, and decreases with λ, risk aversion, environmental variance, and the income distribution share β.
• Effort level e increases with innovation ability η and decreases with effort cost λ, risk aversion, and environmental variance under incomplete information.
• Simulations corroborate theory: as K increases, ρ rises under complete information but is essentially flat under incomplete information; e is higher under complete than incomplete information at the same K; ρ rises with e and η, and falls with λ and risk aversion; e rises with η and falls with λ, risk aversion, and variance. Example simulated values show ρ≈0.878 under complete vs ≈0.872 under incomplete information at a given K, and e around 2.85–3.10 across K values.

The study shows that incorporating fairness preferences into the design of reputation incentives meaningfully alters optimal contracts depending on information regimes. When effort is observable, SMEs can and should adjust reputation incentives upward for teams with stronger fairness concerns to sustain motivation and alignment, while effort is determined by technological capability and costs. When effort is unobservable, fairness preferences become a source of moral hazard that depresses effort, and SMEs cannot effectively tailor reputation incentives to K; instead, they should manage other levers such as recognizing high-ability teams and controlling effort costs and uncertainty. The demonstrated positive linkage between team ability and both reputation incentives and effort underlines the value of selecting capable partners and publicly recognizing their performance. Negative effects of cost, risk aversion, and environmental volatility suggest SMEs should mitigate uncertainty and structure contracts to share risk appropriately. Overall, findings address the central question of how to structure reputation incentives for external research teams in SME open innovation to enhance performance while accounting for behavioral preferences and information asymmetry.

The paper develops a principal–agent reputation incentive model for SME open innovation that incorporates research teams’ fairness preferences and analyzes complete versus incomplete information settings. It derives optimal incentives and effort and provides comparative statics, then validates insights via MATLAB simulations. Main contributions include: (1) demonstrating that under complete information, fairness preference raises optimal reputation incentives while not affecting effort; (2) under incomplete information, fairness preference has little impact on incentives but reduces effort; (3) establishing that innovation ability increases reputation incentives and effort, whereas effort cost, risk aversion, environmental variance, and a higher team income share reduce reputation incentives, and the former three also reduce effort. Managerial implications: SMEs should design reputation mechanisms that recognize fairness concerns and create transparent, equitable environments; combine explicit contracts (fixed funding, revenue sharing) with implicit reputation rewards and use phased assessments to manage long-term relationships; collaborate with public agencies to build reliable reputation systems and reward reputable teams. Future research should incorporate bounded rationality and other behavioral factors and extend the model to multi-stage cooperation settings.

The model assumes fully rational agents and a single-stage formal cooperation, omitting potential irrational behaviors and dynamic, multi-stage interactions. Effort observability is considered only in the two extremes of complete versus incomplete information. Empirical validation beyond simulations is not provided, and some parameter notations and variance modeling are simplified. Future work should incorporate behavioral biases, learning and reputation dynamics over multiple periods, and empirical or experimental tests.