Mean Field Games of Controls with Dirichlet \& Neumann Boundary Conditions

Abstract: In a mean field game of controls, a large population of identical players seek to minimize a cost that depends on the joint distribution of the states of the players and their controls. We consider the classes of mean field games of controls in which the value function and the distribution of player states satisfy either Dirichlet or Neumann boundary conditions. We prove that such systems are well-posed either with sufficient smallness conditions or in the case of monotone couplings.