  In a cooperative coding scheme, network nodes work together to achieve higher
transmission rates. To obtain a better understanding of cooperation, we
consider a model in which two transmitters send rate-limited descriptions of
their messages to a "cooperation facilitator", a node that sends back
rate-limited descriptions of the pair to each transmitter. This model includes
the conferencing encoders model and a prior model from the current authors as
special cases. We show that except for a special class of multiple access
channels, the gain in sum-capacity resulting from cooperation under this model
is quite large. Adding a cooperation facilitator to any such channel results in
a network that does not satisfy the edge removal property. An important special
case is the Gaussian multiple access channel, for which we explicitly
characterize the sum-rate cooperation gain.
