Remote Empirical Coordination
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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 X̂ 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(X̂;Ŷ) for at least one agent whereas for L⟶∞, we show that it suffices R_i≥ I(X̂;Ŷ|X) for all agents where Ŷ is a random variable such that X-X̂-Ŷ and p_X,Ŷ(x,y)-p_X,Y(x,y)_TV≤Δ ( Δ is the pre-specified fidelity).
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