In this paper we study a singularly perturbed zero-sum dynamic game with full information. We introduce the upper ( lower) value function of the dynamic game, in which the minimizer (maximizer) can be guaranteed if at the beginning of each interval his move ( the choice of decision) precedes the move of the maximizer ( minimizer). We show that when the singular perturbations parameter tends to zero, the upper ( lower) value function of the dynamic game has a limit which coincides with a viscosity solution of a Hamilton-Jacobi-Isaacs-type equation. Two examples are given to demonstrate the potential of the proposed technique.