Responsible innovation is an important engine for balancing economic and social benefits and achieving sustainable development. It emphasizes that a wide range of stakeholders should be included in the innovation decision-making process to reduce the potential harm of emerging technologies. Multi-agent cooperation is a key element for responsible innovation. However, it is not clear how multi-agent can cooperate more effectively to promote responsible innovation. Based on the differential game theory, this paper discusses the responsible innovation behavior of enterprises, government, and the public under three cooperation mechanisms: enterprise-dominated, government traction, and deep collaboration, while simultaneously considering the influence of changes in technology and economy levels and social ethical satisfaction. The results show that the optimal strategy of responsible innovation is negatively correlated with cost coefficient and recession coefficient, and positively correlated with the sensitivity coefficient of science and technology economy and support coefficient. Moreover, the optimal strategies, optimal benefits, technology and economy levels and social ethical satisfaction of the three game parties are the highest under the deep collaboration mechanism. There is a threshold for the optimal strategy of the public, and when the threshold is exceeded, the strategy under the enterprise-dominated mechanism is more optimal. Furthermore, the three cooperation mechanisms have different promoting effects on responsible innovation. The enterprise-dominated mechanism can only slowly promote the responsible practice under the low level of responsible innovation, while the deep collaboration mechanism with the close integration of members can still significantly promote the cooperation among subjects and accelerate the process of responsible innovation on the basis of a high level of responsible innovation.