  We propose a novel model for refugee housing respecting the preferences of
accepting community and refugees themselves. In particular, we are given a
topology representing the local community, a set of inhabitants occupying some
vertices of the topology, and a set of refugees that should be housed on the
empty vertices of graph. Both the inhabitants and the refugees have preferences
over the structure of their neighbourhood.
  We are specifically interested in the problem of finding housings such that
the preferences of every individual are met; using game-theoretical words, we
are looking for housings that are stable with respect to some well-defined
notion of stability. We investigate conditions under which the existence of
equilibria is guaranteed and study the computational complexity of finding such
a stable outcome. As the problem is NP-hard even in very simple settings, we
employ the parameterised complexity framework to give a finer-grained view on
the problem's complexity with respect to natural parameters and structural
restrictions of the given topology.
