Empirical Coordination Subject to a Fidelity Criterion

We study the problem of empirical coordination subject to a fidelity criterion for a general set-up. We prove a result which indicates a strong connection between our frame-work and the framework of empirical coordination developed in [1]. It turns out that when we design codes that achieve empirical coordination according to a given distribution and subject to the fidelity criterion, it is sufficient to consider codes that produce actions of the same joint type for a class of types which is close enough to our desired distribution is some sense.