Moran process stochastic evolutionary game model for cooperative innovation strategies in green technology

The innovation paradigm of enterprises in the digital economy era has shifted from closed to cooperative innovation between enterprises and external subjects. Cooperative innovation has increasingly become a crucial strategy for enterprises to improve their technology. This study examines enterprise green technology innovation cooperation through a stochastic evolution game perspective and introduces the digitalization level, green finance, and technological knowledge complementarity. Based on the principle of Moran's process of birth and death, we construct a game model of enterprise green technology cooperative innovation to describe the decision-making interaction mechanism among the main subjects. We calculate fixation and exit times for enterprise green technology innovation cooperation behavior under the weak choice. We discovered that when the synergy benefit is more pronounced than a specific multiplier cost, it helps fix cooperative strategies. As synergy benefit increases, fixation and exit times shorten and prolong, respectively. Compared to low green finance, the probability of the fixation of a separate innovation strategy under high green finance is reduced, fixation time is prolonged continuously, and the exit time of the cooperative strategy is prolonged. Furthermore, through numerical simulation, the digitalization level, green finance, and technological knowledge complementarity synergize the impact of cooperative innovation strategies, strengthening the sustainability stability of green technology cooperative innovation. This conclusion is further corroborated by an empirical test using data from listed companies in 2007–2022. It also provides new ideas for theoretical research on cooperative innovation, offers lessons on how to build innovation consortia, and shapes the implementation of innovation clusters.