Unique determination of cost functions in a multipopulation mean field game model

This paper studies an inverse problem for a multipopulation mean field game (MFG) system where the objective is to reconstruct the running and terminal cost functions of the system that couples the dynamics of different populations. We derive uniqueness results for the inverse problem with different types of available data. In particular, we show that it is possible to uniquely reconstruct some simplified forms of the cost functions from data measured only on a single population component under mild additional assumptions on the coupling mechanism. The proofs are based on the standard multilinearization technique that allows us to reduce the inverse problems into simplified forms.