To address the impact of base station caching strategies on network performance within edge intelligence network (EIN), this study proposes an edge caching optimization method based on mean-field-type games (MFTG). Both non-cooperative and cooperative MFTG models are developed. By utilizing the coupled Hamilton-Jacobi-Bellman (HJB) equations and Fokker-Planck-Kolmogorov (FPK) equations, the optimal caching strategies for independent base station optimization and global coordination are derived, respectively. The proposed method is compared with MPC, LRU, and LFU algorithms through simulations under peak traffic and fluctuating request conditions. The experimental results show that, unlike the instability of the non-cooperative model during peak periods, the cooperative MFTG algorithm converges faster and significantly reduces redundant caching and backhaul link load. In large-scale systems and during peak periods, its total cost is notably lower than that of traditional algorithms, effectively improving resource allocation efficiency.