  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.
