  In this work, we develop an equilibrium model for price formation of
securities in a market composed of two populations of different types: the
first one consists of cooperative agents, while the other one consists of
non-cooperative agents. The trading of every cooperative member is assumed to
be coordinated by a central planner. In the large population limit, the problem
for the central planner is shown to be a conditional extended mean-field
control. In addition to the convexity assumptions, if the relative size of the
cooperative population is small enough, then we are able to show the existence
of a unique equilibrium for both the finite-agent and the mean-field models.
The strong convergence to the mean-field model is also proved under the same
conditions.
