  The paper deals with a class of time-inconsistent control problems for
McKean-Vlasov dynamics. By solving a backward time-inconsistent
Hamilton-Jacobi-Bellman (HJB for short) equation coupled with a forward
distribution-dependent stochastic differential equation, we investigate the
existence and uniqueness of a closed-loop equilibrium for such
time-inconsistent distribution-dependent control problem. Moreover, a special
case of semi-linear McKean-Vlasov dynamics with a quadratic-type cost
functional is considered due to its special structure.
