  A retrospective analysis process for the mean field games system (MFGS) is
considered. For the first time, Carleman estimates are applied to the analysis
of the MFGS. Two new Carleman estimates are derived. They allow to obtain the
Lipschitz stability estimate with respect to the possible error in the input
initial and terminal data for a retrospective problem for MFGS. This stability
estimate, in turn implies uniqueness theorem for the problem under the
consideration. The idea of using Carleman estimates to obtain stability and
uniqueness results came from the field of Ill-Posed and Inverse Problems.
