  We study the problem of strong coordination in a three-terminal line network,
in which agents use common randomness and communicate over a line network to
ensure that their actions follow a prescribed behavior, modeled by a target
joint distribution of actions. We provide inner and outer bounds to the
coordination capacity region, and show that these bounds are partially optimal.
We leverage this characterization to develop insight into the interplay between
communication and coordination. Specifically, we show that common randomness
helps to achieve optimal communication rates between agents, and that matching
the network topology to the behavior structure may reduce inter-agent
communication rates.
