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

TL;DR

This paper investigates how adding random shortcuts to a network influences the emergence of cooperation among agents playing the Prisoner's Dilemma, revealing an optimal range of shortcut probability that promotes cooperation.

Contribution

It introduces a model interpolating between a lattice and a complete graph, analyzing how shortcut probability affects cooperation, with analytical insights explaining the mechanisms involved.

Findings

Cooperation is enhanced at intermediate shortcut probabilities.

High shortcut probabilities suppress cooperation.

Analytical arguments support the simulation results.

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 one-dimensional euclidean lattice (a ring) and the complete graph by changing the value of one parameter (the probability p to add 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 largely enhanced, whilst for smaller values of p only a few cooperators are present in the final state, and for p \rightarrow 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 promote (or suppress) cooperation.