%0 Journal Article
%T Value Function of Differential Games without Isaacs Conditions. An Approach with Non-Anticipative Mixed Strategies
%A Rainer Buckdahn
%A Juan Li
%A Marc Quincampoix
%J Mathematics
%D 2012
%I arXiv
%X In the present paper we investigate the problem of the existence of a value for differential games without Isaacs condition. For this we introduce a suitable 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 independence property, we obtain the existence of the value in mixed strategies as the limit of the lower as well as of the upper value functions along a sequence of partitions which mesh tends to zero. Moreover, we characterize this value in mixed strategies as the unique viscosity solution of the corresponding Hamilton-Jacobi-Isaacs equation.
%U http://arxiv.org/abs/1202.1443v1