  Dynamically exact calculations of a quasi-bound state in the
$\bar{K}\bar{K}N$ three-body system are performed using Faddeev-type AGS
equations. As input two phenomenological and one chirally motivated $\bar{K}N$
potentials are used, which describe the experimental information on the
$\bar{K}N$ system equally well and produce either a one- or two-pole structure
of the $\Lambda(1405)$ resonance. For the $\bar{K}\bar{K}$ interaction
separable potentials are employed that are fitted to phase shifts obtained from
two theoretical models. The first one is a phenomenological $\bar{K}\bar{K}$
potential based on meson exchange, which is derived by SU(3) symmetry arguments
from the J\"ulich $\pi \pi - \bar{K} K$ coupled-channels model. The other
interaction is a variant of the first one, which is adjusted to the $KK$ s-wave
scattering length recently determined in lattice QCD simulations. The position
and width of the $\bar{K}\bar{K}N$ quasi-bound state is evaluated in two ways:
(i) by a direct pole search in the complex energy plane and (ii) using an
"inverse determinant" method, where one needs to calculate the determinant of
the AGS system of equations only for real energies. A quasi-bound state is
found with binding energy $B_{\bar{K}\bar{K}N} = 12 - 26$ MeV and width
$\Gamma_{\bar{K}\bar{K}N} = 61 - 102$ MeV, which could correspond to the
experimentally observed $\Xi(1950)$ state.
