  In this paper, the edge caching problem in ultra-dense fog radio access
networks (F-RAN) is investigated. Taking into account time-variant user
requests and ultra-dense deployment of fog access points (F-APs), we propose a
dynamic distributed edge caching scheme to jointly minimize the request service
delay and fronthaul traffic load. Considering the interactive relationship
among F-APs, we model the caching optimization problem as a stochastic
differential game (SDG) which captures the temporal dynamics of F-AP states and
incorporates user requests status. The SDG is further approximated as a mean
field game (MFG) by exploiting the ultra-dense property of F-RAN. In the MFG,
each F-AP can optimize its caching policy independently through iteratively
solving the corresponding partial differential equations without any
information exchange with other F-APs. The simulation results show that the
proposed edge caching scheme outperforms the baseline schemes under both static
and time-variant user requests.
