  Linear-quadratic optimal control problems are considered for mean-field
stochastic differential equations with deterministic coefficients.
Time-inconsistency feature of the problems is carefully investigated. Both
open-loop and closed-loop equilibrium solutions are presented for such kind of
problems. Open-loop solutions are presented by means of variational method with
decoupling of forward-backward stochastic differential equations, which lead to
a Riccati equation system lack of symmetry. Closed-loop solutions are presented
by means of multi-person differential games, the limit of which leads to a
Riccati equation system with a symmetric structure.
