  Policy-makers are often faced with the task of distributing a limited supply
of resources. To support decision-making in these settings, statisticians are
confronted with two challenges: estimands are defined by allocation strategies
that are functions of features of all individuals in a cluster; and relatedly
the observed data are neither independent nor identically distributed when
individuals compete for resources. Existing statistical approaches are
inadequate because they ignore at least one of these core features. As a
solution, we develop theory for a general policy class of dynamic regimes for
clustered data, covering existing results in classical and interference
settings as special cases. We cover policy-relevant estimands and articulate
realistic conditions compatible with resource-limited observed data. We derive
identification and inference results for settings with a finite number of
individuals in a cluster, where the observed dataset is viewed as a single draw
from a super-population of clusters. We also consider asymptotic estimands when
the number of individuals in a cluster is allowed to grow; under explicit
conditions, we recover previous results, thereby clarifying when the use of
existing methods is permitted. Our general results lay the foundation for
future research on dynamic regimes for clustered data, including the
longitudinal cluster setting.
