Empirical coordination in the finite blocklength regime: an achievability result---Extended version

TL;DR

This paper extends finite blocklength analysis to empirical coordination, providing an achievability bound on the rate for agents to coordinate actions under communication constraints.

Contribution

It introduces a finite blocklength achievability result for empirical coordination using Shannon's random coding and the method of types.

Findings

Derived an exact and asymptotic rate bound for empirical coordination.

Extended finite blocklength analysis to the empirical coordination setting.

Abstract

Empirical coordination offers a way to understand how agents can coordinate actions under communication constraints. This paper investigates the finite blocklength regime of this problem, where the encoder and decoder aim to produce a sequence of action pairs that is jointly typical with respect to a target distribution. Adopting Shannon's random coding argument and leveraging the method of types, we analyze the average performance of a random codebook to establish an achievability result. The resulting bound on the optimal rate is presented both in exact form and as an asymptotic expansion, aligning with the prevailing characterizations in the finite blocklength literature. This work extends finite blocklength analysis to the empirical coordination setting, complementing existing results on strong coordination.