  We investigate a class of zero-sum linear-quadratic stochastic differential
games on a finite time horizon governed by multiscale state equations. The
multiscale nature of the problem can be leveraged to reformulate the associated
generalised Riccati equation as a deterministic singular perturbation problem.
In doing so, we show that, for small enough $\epsilon$, the existence of
solution to the associated generalised Riccati equation is guaranteed by the
existence of a solution to a decoupled pair of differential and algebraic
Riccati equations with a reduced order of dimensionality. Furthermore, we are
able to formulate a pair of asymptotic estimates to the value function of the
game problem by constructing an approximate feedback strategy and observing the
limiting value function.
