take over the whole network. This shows that, somewhat paradoxically, the presence of other cooperators can sometimes hinder the expansion of a cluster. For example, if a square has 2 defecting neighbors, connected to opposite sides of the square, and in turn connected to at least one cooperator outside of the cluster, the square disappears. Note that a 4-cluster in a random network is harder to destroy because a neighbour of the cluster is a neighbour only to one cooperator of the cluster and thus it needs two other cooperating neighbors to be able to destabilize the cluster. Evidently, 3-clusters are much easier to destabilize, as the partial failure of the estimate shows. Fig. \[figer\]B shows one way a 3-cluster can be destabilized by a close cooperator.

Interestingly, there is also a mechanism by which different clusters can collaborate in each other’s expansion, given that the average distance between nodes is small enough. Consider for instance a couple of stable stars of cooperators in a random network. If they are connected, i.e. if a cooperator of one star is connected to a cooperator in the other, these cooperators would be able to turn their non-cooperating neighbors into cooperators, thus increasing 