Deterministic limit of mean field games

The mean field games is the modern and most developed part of control theory. It aims to study many decision maker system by consideration the limit case when the number of decision makers tends to infinity. Mean field game theory consider the case of weak players in the assumption that the behaviour of each player depends on her state, her control and the distribution of all players. From the mathematical point of view the mean field game theory reduces to the study of the system consisting of Hamilton-Jacobi PDE and kinetic equation. Now the case of stochastic mean field games is primary studied. This includes the stochastic system of general form considered in VN Kolokoltsov, Jiajie Li, Wei Yang. Mean Field Games and Nonlinear Markov Processes. ArXiv:1112.3744. Deterministic case isn't so well-studied. This is due to the generalized solution are indispensable in the deterministic case. In the paper YuV. Averboukh. A minimax approach to mean field games. Mat. Sb., 206:7 (2015), 3–32 the notion of minimax solution for deterministic MFG were proposed and the existence theorem was established. The talk is concerned with the convergence problem the solution of stochastic MFG to the minimax solution of deterministic MFG when the dynamics of stochastic system converges to the dynamics of deterministic system.