  The paper investigates the long-time behavior of zero-sum linear-quadratic
stochastic differential games, aiming to demonstrate that, under appropriate
conditions, both the saddle strategy and the optimal state process exhibit the
exponential turnpike property. Namely, for the majority of the time horizon,
the distributions of the saddle strategy and the optimal state process closely
stay near certain (time-invariant) distributions $\nu_1^*$, $\nu_2^*$ and
$\mu^*$, respectively. Additionally, as a byproduct, we solve the infinite
horizon version of the differential game and derive closed-loop representations
for its open-loop saddle strategy, which has not been proved in the literature.
