Cooperative scale-free networks despite the presence of defector hubs

¹  Institute for Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza E-50009 Zaragoza, Spain, EU
²  Departamento de Matemática Aplicada, ESCET, Universidad Rey Juan Carlos E-28933 Móstoles (Madrid), Spain, EU
³  Departamento de Física de la Materia Condensada, Universidad de Zaragoza - E-50009 Zaragoza, Spain, EU
⁴  Departamento de Física Teórica, Universidad de Zaragoza - E-50009 Zaragoza, Spain, EU
⁵  Grupo Interdisciplinar de Sistemas Complejos (GISC), Departamento de Matemáticas, Universidad Carlos III de Madrid - E-28911 Leganés (Madrid), Spain, EU
⁶  Instituto de Ciencias Matemáticas, CSIC-UAM-UC3M-UCM - E-28006 Madrid, Spain, EU

Corresponding author: gardenes@gmail.com

Received: 21 July 2009
Accepted: 13 October 2009

Abstract

Recent results have shown that heterogeneous populations are better suited to support cooperation than homogeneous settings when the Prisoner's Dilemma drives the evolutionary dynamics of the system. The same occurs when the network growth is coevolving together with the evolutionary dynamics, which also gives rise to highly cooperative scale-free networks. In the latter case, however, the organization of cooperation is radically different with respect to the case in which the underlying network is static. In this paper we study the structure of cooperation in static networks grown together with evolutionary dynamics and show that the general belief that hubs can only be occupied by cooperators does not hold. Moreover, these scale-free networks support high levels of cooperation despite having defector hubs. Our results have several important implications for the explanation of cooperative behavior in scale-free networks and highlight the importance that the formation of complex systems have on its function.