  Direct reciprocity is a powerful mechanism for evolution of cooperation based
on repeated interactions between the same individuals. But high levels of
cooperation evolve only if the benefit-to-cost ratio exceeds a certain
threshold that depends on memory length. For the best-explored case of
one-round memory, that threshold is two. Here we report that intermediate
mutation rates lead to high levels of cooperation, even if the benefit-to-cost
ratio is only marginally above one, and even if individuals only use a minimum
of past information. This surprising observation is caused by two effects.
First, mutation generates diversity which undermines the evolutionary stability
of defectors. Second, mutation leads to diverse communities of cooperators that
are more resilient than homogeneous ones. This finding is relevant because many
real world opportunities for cooperation have small benefit-to-cost ratios,
which are between one and two, and we describe how direct reciprocity can
attain cooperation in such settings. Our result can be interpreted as showing
that diversity, rather than uniformity, promotes evolution of cooperation.
