  We deal with Monge-Amp\`ere type equations modeled upon general anisotropic
norms $H$ in $\mathbb R^n$. An overdetermined problem for convex solutions to
these equations is analyzed. The relevant solutions are subject to both a
homogeneous Dirichlet condition and a second boundary condition, designed on
$H$, on the gradient image of the domain. The Wulff shape symmetry associated
with $H$ of the solutions is established.
