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

Abstract

We study in detail the role of short-cuts in promoting the emergence of cooperation in a network of agents playing the Prisoner’s Dilemma game (PDG). We introduce a model whose topology interpolates between the onedimensional Euclidean lattice (a ring) and the complete graph by changing the value of one parameter (the probability p of adding a link between two nodes not already connected in the Euclidean configuration). We show that there is a region of values of p in which cooperation is greatly enhanced, whilst for smaller values of p only a few cooperators are present in the final state, and for p → 1− cooperation is totally suppressed. We present analytical arguments that provide a very plausible interpretation of the simulation results, thus unveiling the mechanism by which short-cuts contribute to promoting (or suppressing) cooperation.