  Social, biological and economic networks grow and decline with occasional
fragmentation and re-formation, often explained in terms of external
perturbations. We show that these phenomena can be a direct consequence of
simple imitation and internal conflicts between 'cooperators' and 'defectors'.
We employ a game-theoretic model of dynamic network formation where successful
individuals are more likely to be imitated by newcomers who adopt their
strategies and copy their social network. We find that, despite using the same
mechanism, cooperators promote well-connected highly prosperous networks and
defectors cause the network to fragment and lose its prosperity; defectors are
unable to maintain the highly connected networks they invade. Once the network
is fragmented it can be reconstructed by a new invasion of cooperators, leading
to the cycle of formation and fragmentation seen, for example, in bacterial
communities and socio-economic networks. In this endless struggle between
cooperators and defectors we observe that cooperation leads to prosperity, but
prosperity is associated with instability. Cooperation is prosperous when the
network has frequent formation and fragmentation.
