In recent years, the rapid development of 5G networks has reinforced the importance of mobile edge computing in ensuring low latency and high bandwidth for content delivery in traffic-intensive applications. In particular, a large part of traffic load on the Internet is due to the repeated access to popular content, placing significant loads on cloud servers. Mobile edge caching mitigates this issue by storing frequently accessed data at edge devices, such as base stations and specialized edge nodes. Thus, this paper proposes a cooperative distributed caching architecture with tailored small base stations (SBSs) as edge nodes optimized through a game-theoretic model that achieves Nash equilibrium. The experiments exhibit that our proposal can reduce the latency of redundant data transmission, mitigate data traffic on the backbone, and alleviate the workload on cloud servers.