Limit Hamilton]Jacobi]Isaacs Equations for Singularly Perturbed Zero-Sum Differential Games

A singularly perturbed zero-sum differential game with full information is considered. Upper and lower value functions of this game are shown to have limits as the singular perturbations parameter tends to zero. These limits are established to coincide with viscosity solutions of some Hamilton]Jacobi type equations. A special case and two examples are considered to illustrate the general results.