A continuous time tug-of-war game for parabolic p(x, t)-Laplace-type equations

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) < infinity. Furthermore, we prove the uniqueness of viscosity solutions to our equation in the whole space under suitable assumptions.