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The mean field games theory has broad application in social sciences. Thetopic of inverse problems is new in this theory. Coefficient Inverse Problems(CIPs) for a generalized mean field games system of the second order areconsidered. Dirichlet and Neumann boundary data either at a part of theboundary or on the whole boundary are given. In addition, initial and terminalconditions are given. H\"older stability estimates are proven in the case ofpartial boundary data, and Lipschitz stability estimates are proven in the caseof complete boundary data. These estimates imply uniqueness of correspondingCIPs. The proofs are based on two new Carleman estimates. A new feature ofthese estimates is that the Carleman Weight Function is independent on time.This leads to the mutual cancellation of parasitic integrals over {t=0} and{t=T}, which occur in the integrations of pointwise Carleman estimates.

Coefficient Inverse Problems for a Generalized Mean Field Games System With the Final Overdetermination