  We investigate a stochastic differential game in which a major player has a
private information (the knowledge of a random variable), which she discloses
through her control to a population of small players playing in a Nash Mean
Field Game equilibrium. The major player's cost depends on the distribution of
the population, while the cost of the population depends on the random variable
known by the major player. We show that the game has a relaxed solution and
that the optimal control of the major player is approximatively optimal in
games with a large but finite number of small players.
