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