  Reciprocity is firmly established as an important mechanism that promotes
cooperation. An efficient information exchange is likewise important,
especially on structured populations, where interactions between players are
limited. Motivated by these two facts, we explore the role of facilitators in
social dilemmas on networks. Facilitators are here mirrors to their neighbors
-- they cooperate with cooperators and defect with defectors -- but they do not
participate in the exchange of strategies. As such, in addition to introducing
direct reciprocity, they also obstruct information exchange. In well-mixed
populations, facilitators favor the replacement and invasion of defection by
cooperation as long as their number exceeds a critical value. In structured
populations, on the other hand, there exists a delicate balance between the
benefits of reciprocity and the deterioration of information exchange.
Extensive Monte Carlo simulations of social dilemmas on various interaction
networks reveal that there exists an optimal interplay between reciprocity and
information exchange, which sets in only when a small number of facilitators
occupies the main hubs of the scale-free network. The drawbacks of missing
cooperative hubs are more than compensated by reciprocity and, at the same
time, the compromised information exchange is routed via the auxiliary hubs
with only marginal losses in effectivity. These results indicate that it is not
always optimal for the main hubs to become ''leaders of the masses'', but
rather to exploit their highly connected state to promote tit-for-tat-like
behavior.
