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We consider solutions satisfying the zero Neumann boundary condition and alinearized mean field game equation in $\Omega \times (0,T)$ whose principalcoefficients depend on the time and spatial variables with general Hamiltonian,where $\Omega$ is a bounded domain in $\Bbb R^d$ and $(0,T)$ is the timeinterval. We first prove the Lipschitz stability in $\Omega \times(\varepsilon, T-\varepsilon)$ with given $\varepsilon>0$ for the determinationof the solutions by Dirichlet data on arbitrarily chosen subboundary of$\partial\Omega$. Next we prove the Lipschitz stability for an inverse problemof determining spatially varying factors of source terms and a coefficient byextra boundary data and spatial data at intermediate time.

Lipschitz stability for determination of states and inverse source problem for the mean field game equations