Mean field games with branching

Mean field games are concerned with the limit of large-population stochastic differential where agents interact through their empirical distribution. In classical setting, number players is large but fixed throughout game. However, in various applications, such as population dynamics or economic growth, can vary across time and this may lead to different Nash equilibria. order account for evolution, we introduce a branching mechanism obtain variant original mean game problem. As first step, study simple model using PDE approach illustrate main differences setting. We prove existence solution show that it provides an approximate Nash-equilibrium games. also present numerical example linear–quadratic model. Then problem general setting by probabilistic approach. It based upon relaxed formulation control problems which allows us result.