The topological issues of cooperation

AbstractIn the last years the Prisoner Dilemma (PD) has become a paradigm forthe study ofthe emergence of cooperationin spatially structured populations.Such structure is usually assumed to be given by a graph. In general, thesuccess of cooperative strategies is associated with the possibility of formingglobular clusters, which in turn depends on a feature of the network that ismeasured by its clustering coefficient. In this work we test the dependenceof the success of cooperation with the clustering coefficient of the network,for several different families of networks. We have found that this depen-dence is far from trivial. Additionally, for both stochastic and deterministicdynamics we have also found that there is a strong dependence on the ini-tial composition of the population. This hints at the existence of severaldifferent mechanisms that could promote or hinder cluster expansion. Wehave studied in detail some of these mechanisms by concentrating on com-pletely ordered networks (large clustering coefficient) or completely randomnetworks (vanishing clustering coefficient).Keywords:PACS: