  In the recently introduced topological distance games, strategic agents need
to be assigned to a subset of vertices of a topology. In the assignment, the
utility of an agent depends on both the agent's inherent utilities for other
agents and its distance from them on the topology. We study the computational
complexity of finding individually rational outcomes; this notion is widely
assumed to be the very minimal stability requirement and requires that the
utility of every agent in a solution is non-negative. We perform a
comprehensive study of the problem's complexity, and we prove that even in very
basic cases, deciding whether an individually rational solution exists is
intractable. To reach at least some tractability, one needs to combine multiple
restrictions of the input instance, including the number of agents and the
topology and the influence of distant agents on the utility.
