Evolution Dynamics Model of Private Enterprises under Simultaneous and Sequential Innovation Decisions

The innovation of private enterprises plays a crucial role. This study focuses on the impacts of market information asymmetry, the technology spillover effect, and the order of innovation research and development (R&D) decisions on the evolution of private enterprises' innovation. This study constructs a dynamic model to analyze how the innovation decision-making order of private enterprises influences their profits and intertemporal innovation decision making. First, we derive the equilibrium point under sequential decisions and the stability of the system at the equilibrium point. Second, we investigate the impact of sequential and simultaneous innovation decisions on the evolution of the dynamic system and its economic implications. Finally, we study the evolutionary dynamics of the attractor with the rate of innovation adjustment and point to the existence of multiple equilibria. The results suggest that the speed of the innovation R&D cost change should be moderate, and the asynchronous updating of the innovation R&D strategy can prevent the system evolution from turning into chaos. These conclusions guide innovation policies.