  The purpose of this paper is to study 2-person zero-sum stochastic
differential games, in which one player is a major one and the other player is
a group of $N$ minor agents which are collectively playing, statistically
identical and have the same cost-functional. The game is studied in a weak
formulation; this means in particular, we can study it as a game of the type
"feedback control against feedback control". The payoff/cost functional is
defined through a controlled backward stochastic differential equation, for
which driving coefficient is assumed to satisfy strict concavity-convexity with
respect to the control parameters. This ensures the existence of saddle point
feedback controls for the game with $N$ minor agents. We study the limit
behavior of these saddle point controls and of the associated Hamiltonian, and
we characterize the limit of the saddle point controls as the unique saddle
point control of the limit mean-field stochastic differential game.
