  The paper is concerned with the dependence of the solution of the
deterministic mean field game on the initial distribution of players. The main
object of study is the mapping which assigns to the initial time and the
initial distribution of players the set of expected rewards of the
representative player corresponding to solutions of mean field game. This
mapping can be regarded as a value multifunction. We obtain the sufficient
condition for a multifunction to be a value multifunction. It states that if a
multifunction is viable with respect to the dynamics generated by the original
mean field game, then it is a value multifunction. Furthermore, the
infinitesimal variant of this condition is derived.
