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A Coefficient Inverse Problem (CIP) of the determination of a coefficient ofthe Mean Field Games System (MFGS) of the second order is considered. The inputdata are generated by a single measurement event. Lateral Cauchy data, i.e.Dirichlet and Neumann boundary data are given for solutions of both equationsforming the MFGS. In addition, solutions of both these equations are given at afixed moment of time. H\"older stability estimates are obtained for bothcomplete and incomplete lateral Cauchy data. These estimates imply uniquenessof our CIP. The apparatus of Carleman estimates is the main mathematical toolof this paper.

A Coefficient Inverse Problem for the Mean Field Games System