Abstract: I will discuss a mean field game model on the synchronization of coupled oscillators, initially proposed by Yin, Mehta, Meyn, and Shanbhag, and recently examined by Carmona, Cormier, and Soner. This model aims to study phase transitions in non-cooperative dynamic games involving a large number of agents. I will present a recent result obtained on this model in collaboration with Marco Cirant (University of Padova). Our work focuses on characterizing synchronized equilibria and their local dynamic stability. This seminar is part of the activities of the Excellence Department Project CUP B83C23001390001 and it is funded by the European Union – Next Generation EU.