  We show that the value function in a stochastic differential game does not
change if we keep the same space $(\Omega,\mathcal{F})$ but introduce
probability measures by means of Girsanov's transformation {\em depending} on
the policies of the players. We also show that the value function does not
change if we allow the driving Wiener processes to depend on the policies of
the players. Finally, we show that the value function does not change if we
perform a random time change with the rate depending on the policies of the
players.
