Comment: A preliminary version appeared in AAMAS '23We propose a novel model for refugee housing respecting the preferences of the 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 the graph. Both the inhabitants and the refugees have preferences over the structure of their neighborhood. We are specifically interested in the problem of finding housing such that the preferences of every individual are met
using game-theoretical words, we are looking for housing that is 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 parameterized complexity framework to give a finer-grained view of the problem's complexity with respect to natural parameters and structural restrictions of the given topology.