  The paper is concerned with the feedback approach to the deterministic mean
field type differential games. Previously, it was shown that suboptimal
strategies in the mean field type differential game can constructed based on
functions of time and probability satisfying the stability condition. This
property realizes the dynamic programming principle for the constant control of
one player. We present the infinitesimal form of this condition involving
analogs of the directional derivatives. In particular, we obtain the
characterization of the value function of the deterministic mean field type
differential game in the terms of directional derivatives and the set of
directions feasible by virtue of the dynamics of the game.
