A Lagrangian Approach for Aggregative Mean Field Games of Controls with Mixed and Final Constraints

The objective of this paper is to analyze the existence of equilibria for a of deterministic mean field games of controls. The interaction between is due to both a congestion term and a price function which depends on distributions of the optimal strategies. Moreover, final state and mixed-control constraints are considered, the dynamics being nonlinear and with respect to the control. The existence of equilibria is obtained by's theorem, applied to a fixed point formulation of the problem., uniqueness results are shown under monotonicity assumptions.