We apply the framework of imperfect empirical coordination to a two-node setup where the action X of the first node is not observed directly but via L agents who observe independently impaired measurements hat X of the action. These L agents, using a rate-limited communication that is available to all of them, help the second node to generate the action Y in order to establish the desiredcoordinated behaviour. When L < ∞, we prove that it suffices RiIleft (hat X hat Y) for at least one agent whereas for L -→ ∞, we show that it suffices RiI(hat X hat Y mid X right) for all agents where hat Y is a random variable such that X - hat X - hat Y and pX, hat Y left( x,y) - p X,Y left(x,y) TV (is the pre-specified fidelity).
QC 20211221