  In non-network settings, encouragement designs have been widely used to
analyze causal effects of a treatment, policy, or intervention on an outcome of
interest when randomizing the treatment was considered impractical or when
compliance to treatment cannot be perfectly enforced. Unfortunately, such
questions related to treatment compliance have received less attention in
network settings and the most well-studied experimental design in networks, the
two-stage randomization design, requires perfect compliance with treatment. The
paper proposes a new experimental design called peer encouragement design to
study network treatment effects when enforcing treatment randomization is not
feasible. The key idea in peer encouragement design is the idea of personalized
encouragement, which allows point-identification of familiar estimands in the
encouragement design literature. The paper also defines new causal estimands,
local average network effects, that can be identified under the new design and
analyzes the effect of non-compliance behavior in randomized experiments on
networks.
