  It has been suggested that direct reciprocity operates well within small
groups of people where it would be hard to get away with cheating one another
but no research has been done yet to show how exactly the mechanism of direct
reciprocity fails to operate as the group size increases. Unlike previous
models that have neglected the role of memory, our model takes into account the
memory capacity of the agents as well as the cost of having such memory. We
have shown that the optimal memory capacity for handling the exploiters grows
with the group size in a similar way as the relative size of the neocortex
grows with the group size of the primates as it was found by Robin Dunbar. The
time required for reaching the relative fitness of the defectors increases
rapidly with the group size which points to the conclusion that there is an
upper group size limit over which the mechanism of direct reciprocity is
insufficient to maintain the cooperation.
