Evolution of cooperation through the heterogeneity of random networks

Abstract

We use the standardized variance (vst) of the degree distribution of a random network as an analytic measure of its heterogeneity. We show that vst accurately predicts, quantitatively, the success of cooperators in an evolutionary prisoner's dilemma. Moreover, we show how the generating functional expression for vst suggests an intrinsic interpretation for the heterogeneity of the network that helps explain local mechanisms through which cooperators thrive in heterogeneous populations. Finally, we give a simple relationship between vst, the cooperation level, and the epidemic threshold of a random network that reveals an appealing connection between epidemic disease models and the evolutionary prisoner's dilemma. © 2009 The American Physical Society.