Mean field game of mutual holding

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.