  In network cooperation strategies, nodes work together with the aim of
increasing transmission rates or reliability. This paper demonstrates that
enabling cooperation between the transmitters of a two-user multiple access
channel, via a cooperation facilitator that has access to both messages, always
results in a network whose maximal- and average-error sum-capacities are the
same---even when those capacities differ in the absence of cooperation and the
information shared with the encoders is negligible. From this result, it
follows that if a multiple access channel with no transmitter cooperation has
different maximal- and average-error sum-capacities, then the maximal-error
sum-capacity of the network consisting of this channel and a cooperation
facilitator is not continuous with respect to the output edge capacities of the
facilitator. This shows that there exist networks where sharing even a
negligible number of bits per channel use with the encoders yields a
non-negligible benefit.
