In this book chapter, we study a problem of distributed content caching in an ultra-dense edge caching network (UDCN), in which a large number of small base stations (SBSs) prefetch popular files to cope with the ever-growing user demand in 5G and beyond. In a UDCN, even a small misprediction of user demand may render a large amount of prefetched data obsolete. Furtherproacmore, the interference variance is high due to the short inter-SBS distances, making it difficult to quantify data downloading rates. Lastly, since the caching decision of each SBS interacts with those of all other SBSs, the problem complexity of exponentially increases with the number of SBSs, which is unfit for UDCNs. To resolve such challenging issues while reflecting time-varying and location-dependent user demand, we leverage mean-field game (MFG) theory through which each SBS interacts only with a single virtual SBS whose state is drawn from the state distribution of the entire SBS population, i.e., mean-field (MF) distribution. This MF approximation asymptotically guarantees achieving the epsilon Nash equilibrium as the number of SBSs approaches infinity. To describe such an MFG-theoretic caching framework, this chapter aims to provide a brief review of MFG, and demonstrate its effectiveness for UDCNs.

26 pages, 9 figures; This chapter is written for the forthcoming book, Edge Caching for Mobile Networks (IET), edited by W. Chen and H. V. Poor. arXiv admin note: substantial text overlap with arXiv:1801.07367