Abstract: A mixed player model in mean field control theory consists of one (or a few) major player and a large number of minor players, and has the remarkable feature of random mean field.

This talk gives a brief overview of this subarea by presenting different optimization frameworks depending on how the players act non-cooperatively or non-cooperatively and the order to optimize. A linear quadratic mean field team problem will be completely solved via a person-by-person optimality technique in team decision theory and a set of forward-backward stochastic differential equations.