Annalisa Cesaroni - Università di Padova The talk will be devoted to the analysis of some first order variational Mean Field Game with density constraints and aggregating interactions. Under suitable symmetry assumptions, I will discuss the existence of periodic equilibria and the behaviour of these equilibria as the period goes to infinity. Finally, I present some results on the discrete counterpart of the problem, which involves the optimal evolution of a finite number of particles that are subject to constraints on reciprocal distances. The results I will present are obtained in collaboration with M. Cirant (Padova).