Abstract: The deep integration of digital and real economies (digital-real deep integration) provides new momentum for cross-regional joint technological research through digital technology's penetration, transformation, and empowerment of real economies. Based on the panel data of 284 Chinese cities from 2005 to 2023, this paper examines the impact and mechanism of the deep integration of digital and real economies on inter-city cooperative innovation. The research finds that the deep integration of digital and real economies can significantly promote inter-city cooperative innovation. The mechanisms include enhancing the willingness for cooperative innovation, reducing the spatial similarity of patent technologies, and improving the economic resilience of cities. The heterogeneity analysis results show that, in terms of patent types, the deep integration of digital and real economies promotes collaborative innovation in invention patents, utility model patents, and design patents. In terms of regional differences, this promoting effect only exists in non-central cities and cities with lower AI levels, and has no significant effect on central cities and cities with higher AI levels. Further, the quantile results confirm that the promoting effect of the deep integration of digital and real economies on inter-city cooperative innovation has a diminishing marginal effect. Therefore, relying on the deep integration of digital and real economies, we should proactively deploy new infrastructure, establish a dynamic demand matching mechanism for innovation among cities, and implement differentiated and precise empowerment strategies. This will help break down various barriers that hinder the free flow of factors and promote cooperative innovation to a higher level, greater depth, and broader scope.

Key words: digital-real deep integration, inter-city collaborative innovation, collaborative innovation willingness, patent technology similarity, urban economic resilience