  We introduce a mean field model for optimal holding of a representative agent
of her peers as a natural expected scaling limit from the corresponding
$N-$agent model. The induced mean field dynamics appear naturally in a form
which is not covered by standard McKean-Vlasov stochastic differential
equations. We study the corresponding mean field game of mutual holding in the
absence of common noise. Our main result provides existence of an explicit
equilibrium of this mean field game, defined by a bang-bang control consisting
in holding those competitors with positive drift coefficient of their dynamic
value. Our analysis requires to prove an existence result for our new class of
mean field SDE with the additional feature that the diffusion coefficient is
irregular.
