Isaacs' Equations for Value-Functions of Differential Games

The authors study value functions of a differential game with payoff which depends on the state at a given end time. They consider differential games with feedback strategies and with nonanticipating strategies. They prove that value-functions are solutions to some Hamilton-Jacobi-Isaacs equations in the viscosity and contingent sense. For these two notions of strategies, with some regularity assumptions, The authors prove that value-functions are the unique solution of Isaacs' equations.