  We formulate a stochastic differential game in continuous time that
represents the unique viscosity solution to a terminal value problem for a
parabolic partial differential equation involving the normalized
$p(x,t)$-Laplace operator. Our game is formulated in a way that covers the full
range $1<p(x,t)<\infty$. Furthermore, we prove the uniqueness of viscosity
solutions to our equation in the whole space under suitable assumptions.
