We consider an integral form of the Isaacs equations associated to differential games with L_∞ criterion, for the characterization of their value functions. We prove that upper and lower values are, the lowest super-solution and the greatest element of a special set of sub-solutions, of the dynamic programming equation. This is an alternative to the viscosity solutions approach. For finite horizon approximation, we propose an approximation scheme in terms of an infinitesimal operator defined over the set of Lipschitz continuous functions. The images of this operator can be characterized classically in terms of viscosity solutions.

We illustrate these results on a example, which values functions can be determined analytically.