Optimizing collaborative innovation models in megaprojects with capital and knowledge inputs: a Stackelberg game approach

Abstract

This study investigates collaborative technological innovation models between the owner and the supplier in megaprojects. It aims to optimize heterogeneous resource inputs, namely capital and knowledge and balance expected returns against systemic risks during dynamic technology accumulation under stochastic disturbances to advance core technology development. This study develops a continuous-time stochastic differential game framework. By solving the Hamilton-Jacobi-Bellman (HJB) equations and endogenizing the supplier's unobservable effort, this study compares three innovation models: the independent innovation model, the capital sharing model and the collaborative research and development (R&D) model. The marginal revenue ratio acts as the primary driver of cooperation. Analysis reveals a “proportional rigidity” phenomenon where optimal investment allocation proportions remain unaffected by external stochastic shocks, determined solely by the internal benefit structure. Moreover, high supplier absorptive capacity and knowledge spillover risks induce a “defensive substitution mechanism,” which leads the owner to reduce capital sharing and increase direct technical intervention. Although collaborative R&D increases systemic variance, it achieves Pareto optimality and maximizes technology output. By integrating capital and knowledge within a dynamic framework of risk and return trade-offs, this study extends the existing literature on single-resource inputs. Furthermore, the research provides structural explanations for moral hazard and collaborative breakdown, thereby offering governance strategies and performance-based incentive mechanisms for complex engineering consortia. Methodologically, by embedding knowledge spillovers, absorptive capacity and endogenous effort into a stochastic differential game, this study defines the robustness boundaries and risk-return trade-offs across different collaborative models.