Optimal control and zero-sum stochastic differential game problems of   mean-field type
  We establish existence of nearly-optimal controls, conditions for existence of an optimal control and a saddle-point for respectively a control problem and zero-sum differential game associated with payoff functionals of mean-field type, under dynamics driven by weak solutions of stochastic differential equations of mean-field type. 
Boualem Djehiche and Said Hamad\`ene
math.PR math.OC