Dynamical Organization of Cooperation in Complex Topologies

Details Dynamical Organization of Cooperation in Complex Topologies Dynamical Organization of Cooperation in Complex Topologies

2006-12-12

arxiv.org/abs/physics/0612108v3

Physical Review Letters 98, 108103 (2007)

Physics

Physics and Society

4 pages and 4 figures. Final version as published in Physical Review Letters

Scientific paper

10.1103/PhysRevLett.98.108103

In this Letter, we study how cooperation is organized in complex topologies by analyzing the evolutionary (replicator) dynamics of the Prisoner's Dilemma, a two-players game with two available strategies, defection and cooperation, whose payoff matrix favors defection. We show that, asymptotically, the population is partitioned into three subsets: individuals that always cooperate ({\em pure cooperators}), always defect ({\em pure defectors}) and those that intermittently change their strategy. In fact the size of the latter set is the biggest for a wide range of the "stimulus to defect" parameter. While in homogeneous random graphs pure cooperators are grouped into several clusters, in heterogeneous scale-free (SF) networks they always form a single cluster containing the most connected individuals (hubs). Our results give further insights into why cooperation in SF networks is favored.

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