  A system of two coupled nonlinear parabolic partial differential equations
with two opposite directions of time is considered. In fact, this is the
so-called "Mean Field Games System" (MFGS), which is derived in the mean field
games (MFG) theory. This theory has numerous applications in social sciences.
The topic of Coefficient Inverse Problems (CIPs) in the MFG theory is in its
infant age, both in theory and computations. A numerical method for this CIP is
developed. Convergence analysis ensures the global convergence of this method.
Numerical experiments are presented.
