For current and future cellular networks, small cell structure with licensed and unlicensed bandwidth, caching content provisioning, and device-to-device (D2D) communications is seen as a necessary architecture. Recently, a series of control methods have been developed to address a myriad of challenges in next-generation small cell networks. In this study, we focus on the design of novel D2D-enabled small cell network control scheme by allowing caching and unlicensed D2D communications. Motivated by game theory and learning algorithm, the proposed scheme adaptively selects caching contents and splits the available bandwidth for licensed and unlicensed communications. Under dynamically changing network environments, we capture the dynamics of the network system and design a new dynamic Stackelberg game model. Based on a hierarchical and feedback based control manner, small base stations and users can be leaders or followers dynamically while improving 5G network performance. Simulations and performance analysis verify the efficiency of the proposed scheme, showing that our approach can outperform existing schemes by about 5%~15% in terms of bandwidth utilization, cache hit ratio, and system throughput.