Value function of differential games without Isaacs conditions. An approach with nonanticipative mixed strategies

摘要

In the present paper we investigate the problem of the existence of a valuefor differential games without Isaacs condition. For this we introduce asuitable concept of mixed strategies along a partition of the time interval,which are associated with classical nonanticipative strategies (with delay).Imposing on the underlying controls for both players a conditional independenceproperty, we obtain the existence of the value in mixed strategies as the limitof the lower as well as of the upper value functions along a sequence ofpartitions which mesh tends to zero. Moreover, we characterize this value inmixed strategies as the unique viscosity solution of the correspondingHamilton-Jacobi-Isaacs equation.