This paper delves into the evolutionary dynamics of dynamic games among governments, traditional automotive enterprises, and scientific research institutions during the new energy transition process by establishing a stochastic evolutionary game model. The research focuses on exploring the conditions for the formation of system stability and the key factors influencing strategic choices. MATLAB R2021a software is employed to simulate the game process, visually demonstrating the dynamic changes in the behaviors of each participant. The results indicate that research and development (R&D) costs are a crucial consideration for scientific research institutions when deciding whether to collaborate with traditional automotive enterprises. Traditional automotive enterprises exhibit significantly higher sensitivity to government incentives for cooperation than to potential penalties for non-cooperation. Furthermore, an increase in government support costs notably dampens its enthusiasm for promoting the development of the new energy transition. Reducing government support costs and R&D costs for scientific research institutions, as well as enhancing rewards for cooperative behavior and penalties for non-cooperative behavior, can effectively facilitate the formation of evolutionarily stable strategies among governments, traditional automotive enterprises, and scientific research institutions.