  This paper studies experimental designs for estimation and inference on
policies with spillover effects. Units are organized into a finite number of
large clusters and interact in unknown ways within each cluster. First, we
introduce a single-wave experiment that, by varying the randomization across
cluster pairs, estimates the marginal effect of a change in treatment
probabilities, taking spillover effects into account. Using the marginal
effect, we propose a test for policy optimality. Second, we design a
multiple-wave experiment to estimate welfare-maximizing treatment rules. We
provide strong theoretical guarantees and an implementation in a large-scale
field experiment.
