New energy vehicles (NEV) have become a major trajectory changer for the global auto industry and an important catalyst for global sustainable economic growth. The implementation of carbon cap and dual credit regulations has altered the competitive environment and strategy of conventional vehicles (CV) and NEV, and has attracted extensive scholarly attention. However, the collaborative governance of the two regulations is relatively limited. This paper constructs two stylized production models based on Cournot game to examine the impacts of different combinations of two regulations, including no regulatory intervention (NC, ND), consideration of dual credit regulation without carbon cap regulation (NC, D), consideration of carbon cap regulation without dual credit regulation (C, ND), and consideration of both regulations (C, D), on vehicle production decisions, and determine the optimal regulatory scheme and intervention intensity under varying conditions. The Lagrange functions and Karush-Kuhn-Tucker (KKT) optimization conditions are employed to solve for the optimal CV and NEV production decisions. The results show that carbon cap regulation not only reduces carbon emissions but also expands the NEV market size. Different regulatory combinations are applicable in different contexts, while collaborative efforts between carbon cap and dual credit regulation can enhance social, economic, and environmental potential within the auto industry under specific conditions. These findings provide important theoretical guidance for expanding NEV market and improving government intervention mechanism.