  We investigate a two-player zero-sum differential game with asymmetric
information on the payoff and without Isaacs condition. The dynamics is an
ordinary differential equation parametrised by two controls chosen by the
players. Each player has a private information on the payoff of the game, while
his opponent knows only the probability distribution on the information of the
other player. We show that a suitable definition of random strategies allows to
prove the existence of a value in mixed strategies. Moreover, the value
function can be characterised in term of the unique viscosity solution in some
dual sense of a Hamilton-Jacobi-Isaacs equation. Here we do not suppose the
Isaacs condition which is usually assumed in differential games.
