  In communication networks, cooperative strategies are coding schemes where
network nodes work together to improve network performance metrics such as the
total rate delivered across the network. This work studies encoder cooperation
in the setting of a discrete multiple access channel (MAC) with two encoders
and a single decoder. A network node, here called the cooperation facilitator
(CF), that is connected to both encoders via rate-limited links, enables the
cooperation strategy. Previous work by the authors presents two classes of
MACs: (i) one class where the average-error sum-capacity has an infinite
derivative in the limit where CF output link capacities approach zero, and (ii)
a second class of MACs where the maximal-error sum-capacity is not continuous
at the point where the output link capacities of the CF equal zero. This work
contrasts the power of the CF in the maximal- and average-error cases, showing
that a constant number of bits communicated over the CF output link can yield a
positive gain in the maximal-error sum-capacity, while a far greater number of
bits, even numbers that grow sublinearly in the blocklength, can never yield a
non-negligible gain in the average-error sum-capacity.
