Inverse problems for mean field games

Abstract The theory of mean field games (MFGs) studies the limiting behaviors large systems where agents interact with each other in a certain symmetric way. running and terminal costs are critical for to decide strategies. However, practice they often partially known or totally unknown agents, while total cost is at end game. To address this challenging issue, we propose study several inverse problems MFGs. When Lagrangian kinetic energy, first establish unique identifiability results, showing that one can recover either from knowledge cost. If limited time-independent class, further prove simultaneously both costs. Finally, extend results setup general Lagrangians.