  We consider solutions satisfying the Neumann zero boundary condition and a
linearized mean field game system in $\Omega \times (0,T)$, where $\Omega$ is a
bounded domain in $\mathbb{R}^d$ and $(0,T)$ is the time interval. We prove two
kinds of stability results in determining the solutions. The first is H\"older
stability in time interval $(\epsilon, T)$ with arbitrarily fixed $\epsilon>0$
by data of solutions in $\Omega \times \{T\}$. The second is the Lipschitz
stability in $\Omega \times (\epsilon, T-\epsilon)$ by data of solutions in
arbitrarily given subdomain of $\Omega$ over $(0,T)$.
