  We introduce the study of designing allocation mechanisms for fairly
allocating indivisible goods in settings with interdependent valuation
functions. In our setting, there is a set of goods that needs to be allocated
to a set of agents (without disposal). Each agent is given a private signal,
and his valuation function depends on the signals of all agents. Without the
use of payments, there are strong impossibility results for designing
strategyproof allocation mechanisms even in settings without interdependent
values. Therefore, we turn to design mechanisms that always admit equilibria
that are fair with respect to their true signals, despite their potentially
distorted perception. To do so, we first extend the definitions of pure Nash
equilibrium and well-studied fairness notions in literature to the
interdependent setting. We devise simple allocation mechanisms that always
admit a fair equilibrium with respect to the true signals. We complement this
result by showing that, even for very simple cases with binary additive
interdependent valuation functions, no allocation mechanism that always admits
an equilibrium, can guarantee that all equilibria are fair with respect to the
true signals.
