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

Lipschitz Stability Estimate and Uniqueness in the Retrospective Analysis for The Mean Field Games System via Two Carleman Estimates