The role of memory in transition from direct to indirect reciprocity.

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.