  The work at hand presents a finite-blocklength analysis of the multiple
access channel (MAC) sum-rate under the cooperation facilitator (CF) model. The
CF model, in which independent encoders coordinate through an intermediary
node, is known to show significant rate benefits, even when the rate of
cooperation is limited. We continue this line of study for cooperation rates
which are sub-linear in the blocklength $n$. Roughly speaking, our results show
that if the facilitator transmits $\log{K}$ bits, there is a sum-rate benefit
of order $\sqrt{\log{K}/n}$. This result extends across a wide range of $K$:
even a single bit of cooperation is shown to provide a sum-rate benefit of
order $1/\sqrt{n}$.
