Remote Empirical Coordination

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 X̑ 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 desired coordinated behaviour. When L <; ∞, we prove that it suffices R
_i
≥ I (X̑; Y̑) for at least one agent whereas for L -→ ∞, we show that it suffices R
_i
≥ I ( X̑; Y̑|X) for all agents where Y̑ is a random variable such that X - X̑ - Y̑ and || p
_X,
Y̑
(x, y) - p
_X,
Y
(x, y) ||
_TV
≤ Δ (Δ is the pre-specified fidelity).