  We extend the construction of equilibria for linear-quadratic and
mean-variance portfolio problems available in the literature to a large class
of mean-field time-inconsistent stochastic control problems in continuous time.
Our approach relies on a time discretization of the control problem via
n-person games, which are characterized via the maximum principle using
Backward Stochastic Differential Equations (BSDEs). The existence of equilibria
is proved by applying weak convergence arguments to the solutions of n-person
games. A numerical implementation is provided by approximating n-person games
using finite Markov chains.
