Colloque / Séminaire

Mean field games are concerned with the limit of large-population stochastic differential games where the agents interact through their empirical distribution. In the classical setting, the number of players is large but fixed throughout the game. However, in various applications, such as population dynamics or economic growth, the number of players can vary across time which may lead to different Nash equilibria. For this reason, we introduce a branching mechanism in the population of agents and obtain a new formulation of mean field games. As a first step, we  study a simple linear-quadratic model using a PDE approach to emphasize the main differences with the classical setting. Then we prove existence of a solution in a general setting by a probabilistic approach, based upon the relaxed formulation of stochastic control problems. Joint work with Zhenjie Ren and Xiaolu Tan.