  This paper studies robust time-inconsistent (TIC) linear-quadratic stochastic
control problems, formulated by stochastic differential games. By a spike
variation approach, we derive sufficient conditions for achieving the Nash
equilibrium, which corresponds to a time-consistent (TC) robust policy, under
mild technical assumptions. To illustrate our framework, we consider two
scenarios of robust mean-variance analysis, namely with state- and
control-dependent ambiguity aversion. We find numerically that with time
inconsistency haunting the dynamic optimal controls, the ambiguity aversion
enhances the effective risk aversion faster than the linear, implying that the
ambiguity in the TIC cases is more impactful than that under the TC
counterparts, e.g., expected utility maximization problems.
