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We study in detail the role of short-cuts in promoting the emergence ofcooperation in a network of agents playing the Prisoner's Dilemma Game (PDG).We introduce a model whose topology interpolates between the one-dimensionaleuclidean lattice (a ring) and the complete graph by changing the value of oneparameter (the probability p to add a link between two nodes not alreadyconnected in the euclidean configuration). We show that there is a region ofvalues of p in which cooperation is largely enhanced, whilst for smaller valuesof p only a few cooperators are present in the final state, and for p\rightarrow 1- cooperation is totally suppressed. We present analyticalarguments that provide a very plausible interpretation of the simulationresults, thus unveiling the mechanism by which short-cuts contribute to promote(or suppress) cooperation.

Random Topologies and the emergence of cooperation: the role of short-cuts